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Determination of radionuclide concentratins of U and Th in unprocessed soil samples

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Determination of radionuclide concentratins of U and Th in unprocessed soil samples
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Lazo, Edward Nicholas
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Edward Nicholas Lazo
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English

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Subjects / Keywords:
Attenuation coefficients ( jstor )
Average linear density ( jstor )
Coordinate systems ( jstor )
Gamma rays ( jstor )
Geometry ( jstor )
Photons ( jstor )
Radionuclides ( jstor )
Soil samples ( jstor )
Soils ( jstor )
Solar X rays ( jstor )

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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DETERMINATION OF RADIONUCLIDE CONCENTRATIONS
OF U AND Th IN UNPROCESSED SOIL SAMPLES


















By
EDWARD NICHOLAS LAZO















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1988


"~~z'lF `~
















So as it turned out, just as I suspected from the start, this dissertation was a lot of

work. It took a lot of time, pulling me around its ins and outs for over five years. It took

lots of long days and lots of weeks without weekends. It took me from the valley of the

shadow of death, so to speak, to the heights of exhilaration and joy. It was among the most

important things in my life, and certainly was the primary thing for which I strove for all

that time. And throughout that time I had a fairly vague but very warm feeling as to why

I was doing this, and that feeling kept me going during this work.

So putting that vague feeling into words, this dissertation is dedicated to my parents, Dr.

Robert Martin Lazo and Rosemarie Lazo, who taught me by their example that learning is a

large part of what life is all about. And that the other biggest part of life is the satisfaction

that comes with trusting yourself enough to follow through on your dreams.

During this time I met the woman who is now my wife, I acquired two nephews, one

sister-in-law, and one brother-in-law, rounding out a very eventful time for the Lazo clan.

This dissertation is also dedicated to my family; my wife, my two brothers, my sister, their

families, and my two cats Max and Milli, who helped me all along the way. It is especially

dedicated to my wife, Corinne Ann Coughanowr, who has supported me, encouraged me,

helped me, put up with me, and continued to love me through the worst of times. To you

all, I love you.















ACKNOWLEDGEMENTS


This publication is based on work performed in the Laboratory Graduate Participation

Program under contract #DE-AC05760R00033 between the U.S. Department of Energy

and Oak Ridge Associated Universities.

In that the production of this dissertation has been a very difficult process which I

could not have finished without the help of numerous others, I would like to acknowledge

those who have given me so much invaluable assistance.

I would like to thank Corinne Ann Coughanowr, my wife, who provided me with excel-

lent advice, guidance, and support throughout the project.

I would like to thank Dr. Genevieve S. Roessler, committee chair, University of Florida,

who provided technical and procedural guidance.

I would like to thank Dr. David Hintenlang, committee member, University of Florida,

who provided guidance which helped assure a quality final product.

I would like to thank Dr. Edward E. Carroll, committee member, University of Florida,

who taught me enough instrumental expertise to properly perform experiments.

I would like to thank Dr. Emmett Bolch, committee member, University of Florida,

who provided support in soil sample analysis.

1 would like to thank Dr. A. G. Hornsby, committee member, University of Florida,

who provided support for work in soil moisture content determination.

I would like to thank Dr. II. Van Rinsvelt, committee member, University of Florida,

who provided support in EDXRF analysis.









I would like to thank Dr. Barry Berven, committee member, Oak Ridge National

Laboratory (ORNL), who provided me with technical guidance and the managerial backing

necessary to ensure the purchase of the equipment necessary for this work.


I would like to thank Dr. Guven Yalcintas, committee member, ORNL, who provided

me with technical assistance throughout the work at ORNL.


I would like to thank Dr. Joel Davis, University of Tennessee at Chattanooga, who

provided invaluable assistance, guidance and technical expertise in every aspect of the work

performed at ORNL. Without Dr. Davis' help and friendship this dissertation would have

required much more time and would not have been half as fun as it was.


I would like to thank Dr. Keith Eckerman, ORNL, who provided expert assistance in

development of the mathematical model, which is the core of this dissertation, and in just

about any other areas where I needed help. Again, without the assistance and friendship

of Dr. Eckerman this work would have been very much more tedious.


I would like to thank Dr. Jeff Ryman, ORNL, who provided assistance in the develop-

ment of the transport mathematics used in the mathematical model.


I would like to thank Dr. George Keogh, ORNL, who provided assistance in developing

the analytical mathematics used in the computer model.


I would like to thank Debbie Roberts, ORNL, who performed several invaluable exper-

iments for me after I had left ORNL, and who performed the soil assay against which I am

gaging my technique.


I would like to thank Dr. Rowena Chester, ORNL, who provided managerial backing

for the project and its purchases.









I would like to thank Dr. Mark Mercier, Nuclear Data Incorporated, who helped

introduce me to peak shaping and provided invaluable assistance in the development of the

peak shaping programs used in this work.

I would like to thank John Hubble, National Bureau of Standards, who as the "God of

all Cross Sections" provided me with the latest cross- sectional data and plenty of friendly

encouragement and expert advice.

I would like to thank Dr. Raymond Gunnink, Lawrence Livermore National Laboratory,

who provided me with the peak shaping program GRPANL and helped me to understand

the theory behind the program.

I would like to thank Dr. Wayne Ruhter, Lawrence Livermore National Laboratory,

who nursed me through the intricacies of GRPANL and analyzed several of my peaks to

verify my program.

I would like to thank Isabell Harrity of Brookhaven National Laboratory who provided

invaluable assistance, all the way up to the last minute, in getting this document prepared

using TEX.

I would like to thank Dr. Eric Myers who also provided last minute advice as to how

to get TgXto do its thing.

Finally, I would like to thank Oak Ridge Associated Universities who provided me with

a Laboratory Graduate Research Fellowship so that I could work at Oak Ridge National

Laboratory for two years and complete this project.





















TABLE OF CONTENTS


ACKNOWLEDGMENTS ..........


LIST OF TABLES .............


LIST OF FIGURES ............


ABSTRACT .. .. . .. .... ..


CHAPTERS


I INTRODUCTION ............


Soil Sample Assay for Radionuclide Content


Standards Method for Gamma Spectroscopic


Radionuclides of Interest . . . . .


Process Sensitivity ............


Statement of Problem ..........


X-Ray Fluorescent Analysis . . . .


Assay Technique .............


Literature Search . . . . . .


II MATERIALS AND METHODS .....


Peak Shaping ..............

A Fitting Peak .. .........

A Fitting Background ........


Page


. ili


Sxi


xiv


. xv


...........


...........


...........


. . . . . .





...........





Assay of Soil Samples


...........


. . . . . .


...........





...........


...........





...........

...........

...........










Soil Moisture Content and Attenuation Coefficients . . .
Soil Attenuation Coefficient . . . . . . . .
Soil Moisture Content . . . . . . . . .

System M odel .. .. .. .. .. .. .. .. .. . ..
Introduction . . . . . . . . . . . .
Technique Description ..................
Mathematical Model ...................
Compton Scatter Gamma Production of Fluorescent X Rays
Compton scatter gamnna model . . . . . .
Mathematical model ..................
Electron Density . .. .. .. .. .. .. .. .. ..
Natural Production of Fluorescent X Rays . . . .


S32
S33
. 37


. . . 37
. . . 37
. . . 38
. . . 41
. . . . 51
. . . . 51
. . . 52
. . . 60
. . . . 61


Isotopic Identification . . . . . . . . . . . . .

Error Analysis . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . .
Least Squares Peak Fitting .......................
Covariance Matrix and Functional Error . . . . . . . .
Error Propagation .. .. .. . .. .. .. . .. . .. . .
Linear Function Fitting .. .... ........ ...... ...

Experimental Procedure . . . . . . . . . . . . .
Sample Counting . . . . . . . . . . . . . .
Data Analysis . . . . . . . . . . . . . . .

II RESULTS AND CONCLUSIONS . . . . . . . . . .


Experimental Results .......
Assay Results ..........
Peak Fitting Results .......

Conclusions . . . . . .


. . . . . . . . . . . 88
. . . . . . . . . . . 88
. . . . . . . . . . 112


Recommended Future Work .......................


. 63


S 65
S .65
S .66
S 69
S 71
S 72


S74
S74
. 86

S88









APPENDICES

A EQUIPMENT AND SETUP ........................ 124

System Hardware ............. ... .......... 124
The ND-9900 MCA ......... .. .... ........ 124
The ADC ................... .............. 125
The IIPGe Detector ........................... 125
XRF Excitation Source and Transmission Sources . . . . . . 125
The XRF Excitation Source Holder and Detector Shield . . . .. 126

System Calibration ................ ......... 127

Mass Attenuation Coefficients . . . . . . . .. .. . 134

Pulse Pileup . . . . . . . . . . . . . . . . 142

Compton to Total Scatter Ratio in Soil . . . . . . . . . 142

B UNSUCCESSFUL ANALYSIS TECHNIQUES . . . . . . . 146

Sample Inhomogeneity Analysis . . . . . . . . .. . 146

Reasons for Inhomogeneity Analysis Failure . . . . . . . . 149

Soil Moisture Content Analysis . . . . . . . . . . . 158

Reason for Soil Moisture Content Analysis Failure . . . . . .. 161

C COMPUTER PROGRAMS ....................... 163

Peak Shaping Programs .......................... 163
POLYBK.BAS ............................ 164
BKG.BAS . . . . . . . . . . . . . . . . 172
PEAKFIT.BAS ............................ 175

Geometry Factor Programs ......................... 184
DIST.FOR .. . . . . . . . . . . . ... 185
IMAGE.FOR .................... ........ 190
COMPTON.FOR .................. ......... 196
ASSAY.FOR .. .. . .. .. .. .. .. . .. .. .. .. .. 205









. . . . . . . . . . . . . . 211


REV6.FOR . . . . . .. . . . . . . . . 212
COMDTA.FOR ............................ 215
XRFDTA.FOR ............................ 218
GEOM5A.FOR .............................. 221
GEOM 5C.FOR ........... .............. ... 223
GEOM 5E.FOR ............................ 225
GEOM5G.FOR ............................. 227
GEOM SI.FOR ........................ ..... 229
GEOM5K.FOR .............................. 231
GOEM5M.FOR ............................ 233
GEOM50.FOR ............................ 235

Sample Description Programs . . . . . . . .. . . 237
SAMPLE2.FOR ............................ 238
SAMPLE3.FOR ............................ 240
SAMPLE4.FOR ............................ 242
SAMPLEU1.FOR ........................... 244
SAMPLEU1A.FOR ........................... 246
SAMPLETH1.FOR ........................... 248
SAMPLETH1A.FOR .... ..................... 250
SAMPLENJAU.FOR .......................... 252
SAMPLENJATH.FOR . . ................... ...... 254
SAMPLENJBU.FOR .......................... 256
SAMPLENJBTI.FOR .......................... 258
SAMPLEUSA.FOR ........................... 260
SAMPLEUSB.FOR ........................... 262
SAMPLEUSC.FOR ........................... 264
SAMPLEUSD.FOR ........................... 266
S2XRF.FOR .. .. .. .. .. .. .. .. . .. . .. .. 268
S3XRF.FOR ... .. .. .. .. .. .. .. .. .. . .. .. 272
S4XRF.FOR. . . . . . . . . . . . . . . . 276
U1XRF.FOR . . . . . . . . . . . . . . . . .. 280
U1AXRF.FOR ............................ ..... 284
TH1XRF.FOR ..................... ....... 288
TIIH AXRF.FOR ............................ 292
NJAUXRF.FOR ............................ .... 296
NJATHXRF.FOR ........................... 300
NJBUXRF.FOR ................... ......... 304
NJBTHXRF.FOR ........................... 308


Date File Programs











USAXRF.FOR

USBXRF.FOR

USCXRF.FOR

USDXRF.FOR


S312

S 316

S 320

324


LIST OF REFERENCES .......................... .... 328


BIOGRAPHICAL SKETCII ......................... 330


............................

............................

............................

............................


















LIST OF TABLES


Table


1. Uranium 238 Decay Chain ..............

2. Thorium 232 Decay Chain ..............

3. Summary of DOE Residual Contamination Guidelines

4. U and Th K-Shell Absorption and Emission . . .

5. Co-57 and Eu-155 Emission Energies and Yields . .

6. Co-57 and Eu-155 Physical Characteristics . . .

7. Typical Soil Linear Attenuation Coefficients . . .

8. Isotopic Concentrations: ppm vs. pCi/gm . . . .


9. Soil Assay Results for U and Th Contaminated Soil .


10. Assay Sensitivity to the Number of Fitting Points Used

11. Measured vs. Fitted Detector Response for U1 . .


Measured vs.

Measured vs.

Measured vs.

Measured vs.

Measured vs.

Measured vs.


Measured vs.

Measured vs.


Fitted Detector Response for Ula . .

Fitted Detector Response for NJA-U .

Fitted Detector Response for NJB-U .

Fitted Detector Response for USC . .

Fitted Detector Response for USD . .

Fitted Detector Response for Sample 2

Fitted Detector Response for Sample 3

Fitted Detector Response for Sample 4


Page

. . . . . . 7






.......... . 32
. . . . . . 11




. . . . . . 32

. . . . . 32


. . . . . . 36

. . . . . . 63

. . . . . . 93


....... .. 94

. . . . . . 95

. . . . . . 96

. . . . . . 97

. . . . . . 98

. . . . . . 99

. . . . . . 100

. . . . . . 101

. . . . . . 102

. . . . . . 103


20. Measured vs. Fitted Detector Response for Thl


. . . . . . 104









21. Measured vs. Fitted Detector Res

22. Measured vs. Fitted Detector Res

23. Measured vs. Fitted Detector Res

24. Measured vs. Fitted Detector Res

25. Measured vs. Fitted Detector Res

26. Sample Physical Characteristics

27. Measured Sample Linear Attenuat

28. Comparison of KaI Peak Areas as

29. Peak Fit Results for Sample U1

30. Peak Fit Results for Sample Ula

31. Peak Fit Results for Sample NJA-

32. Peak Fit Results for Sample NJB-

33. Peak Fit Results for Sample USC

34. Peak Fit Results for Sample USD

35. Peak Fit Results for Sample 2

36. Peak Fit Results for Sample 3

37. Peak Fit Results for Sample 4

38. Peak Fit Results for Sample Thl

39. Peak Fit Results for Sample Thla

40. Peak Fit Results for Sample NJA-

41. Peak Fit Results for Sample NJB-

42. Peak Fit Results for Sample USA

43. Peak Fit Results for Sample USB

A-1. Shield Material X-Ray Emission


ponse for Th-la . . . . . . 105

ponse for NJA-Th . . . . . .. 106

ponse for NJB-Th . . . . . .. 107

ponse for USA . . . . . . . 108

ponse for USB . . . . . . .. 109

. . . . . . . . . . . 110

ion Characteristics . . . . . . 111

Determined by PEAKFIT and GRPANL 112

. . . . . . . . . . . 113

. . . . . . . . . . 113

U . . . . . . . . . . 114

U . . . . . . . . . . 114

. . . . . . . . . . 115

. . . . . . . . . . 115

. . . . . . . . . . . 116

. . . . . . . . . . . 117

. . . . . . . . . . . 118

. . . . . . . . . . 119

. . . . . . . . . . 119

Th . . . . . . . . . 120

Th . . . . . . . . . 120

. . . . . . . . . . 121

. . . . . . . . . . 121

Energies . . . . . . . . 127


A-2. NBS Source, SRM 4275-B-7, Emission Rates


. . . . . . 129









A-3. NBS Source, SRM 4275-B-7, Physical Characteristics . . . . . 129

A-4. System Calibration Parameters . . . . . . . . . . 133

A-5. Water Attenuation Coefficients, p (E)f2,, Actual and Calculated Values . 140

A-6. Water Attenuation Coefficients, p (E)oo
Calculated Values vs. Target Distance from the Detector . . . . 141

A-7. Representative Soil Elemental Concentrations . . . . . . . 144

A-8. Compton to Total Scatter Coefficients for Soil at 150 keV and 100 keV . 144

A-9. Average Compton to Total Scatter Ratio for Soil . . . . . . 145

B-1. Relative Sample Separation vs. Solution Matrix Condition . . . ... 151

B-2. Target-Detector Distance vs. Measured Peak Area . . . . . .. 154















LIST OF FIGURES


Figure Page

1. Typical Gamma Ray Spectral Peak and Background . . . . .... . 16

2. Lorentzian X Ray as Seen Through the Gaussian Response of a Detector . 22

3. Typical Th K,~ X-Ray Spectral Peak . . . . . . . .... ... .25

4. Polynomial and Step Function X-Ray Peak Background . . . .... ... 29

5. Source Target Detector Physical Geometry . . . . . .. ... .39

6. Source Target Detector Spatial Geometry . . . . . ... . . 49

7. Compton Scatter Spatial Geometry . . . . . . . . . . 53

8. Exploded View of Target Holder Assembly . . . . . . .... ... .76

9. Target in Place above Detector ..................... .78

10. Target in Place above Detector Showing Laser Alignment System . . .80

11. ND-9900 Multichannel Analyzer, ADC, Amplifier, and Detector Power Supply . 82

12. Typical XRF K,1 Peak on MCA ................... ... 84

B-1. Relative Sample Separation vs. Solution Matrix Condition . . . . 152

B-2. Target-Detector Distance vs. Measured Peak Area . . . . . .. 155














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

DETERMINATION OF RADIONUCLIDE CONCENTRATIONS
OF U AND Th IN UNPROCESSED SOIL SAMPLES

By
Edward Nicholas Lazo

December, 1988

Chairman: Genevieve S. Roessler
Major Department: Nuclear Engineering Sciences

Work with systems used to assay soil samples for U-238 and Th-232 indicated that the

need existed to more directly measure the concentrations of these radionuclides. An x-ray

fluorescent analysis system was developed here to directly measure the concentrations of

these radionuclides in bulk (125 gm), unprocessed (not dried and not ground to uniform

particle size), soil samples. This technique improves on gamma spectroscopic analysis be-

cause progeny equilibrium is not required, improves on neutron activation analysis because

bulk samples are assayed, and improves on both methods because standard soil samples are

not needed for system calibration.

The assay system developed equates a measured K1a x-ray peak area to a calculated

"Geometry Factor" (GF) times the unknown soil sample radionuclide concentration. From

this equation the radionuclide concentration is determined. Spectral data are generated

by irradiating the soil sample with Co-57 gammas to induce fluorescent x rays which are

measured using an intrinsic Ge detector. The Co-57 sources, the sample, and the detector

are oriented to optimize the production of fluorescent x rays. Transmission gamma rays

are then used to determine the sample linear attenuation coefficient at the Ka, energy of

interest.









Peak areas are determined by shaping spectral data to a Voigt Profile using an algorithm

from the peak shaping program GRPANL. The steeply sloping nature of the Compton

backscatter hump on which the IKa x-ray peaks rest necessitated the development of a

unique polynomial/erfc background function which is subtracted prior to peak shaping. The

GF of a sample is the calculated number of K x rays which would be counted in the full

energy spectral peak if the contamination concentration in the sample were one picoCurie

per gram. This calculated GF includes considerations of the sample linear attenuation

coefficient, fluorescence induced by unscattered source gammas, fluorescence induced by

singly scattered Compton gammas which account for approximately 15% of all production,

and natural fluorescence production.

Experimentally, thirteen test samples were analyzed using this method, gamma spectro-

scopic analysis, and neutron activation analysis. Results compared very well with gamma

spectroscopic analysis. Neutron activation analysis of small portions of each sample did not

match well with the results of either of the other methods due to sample inhomogeneities.















CHAPTER I

INTRODUCTION



In returning to school to pursue a Ph.D. in health physics, I knew that I would have to

complete an original research project and I knew that I wanted my research to be practical in

nature. I wanted to pick some existing process or procedure and inject it with "SCIENCE"

to facilitate its operation and improve its accuracy and precision. I stumbled upon such a

process in need of science during a summer working experience in 1983. After obtaining

a fellowship to go to Oak Ridge National Laboratory to develop an improved process, I

discovered that such a process would have a much more general application than I had

originally thought.



Soil Sample Assay for Radionuclide Content


The summer position that sparked this dissertation involved health physics work for

the Formerly Utilized Sites Remedial Action Program, known as FUSRAP. Begun in 1974,

FUSRAP is a Department of Energy (DOE) project to clean up 26 contaminated sites

within the United States. Twenty-two of the sites were formerly used during the Manhattan

Engineer's District (MED) project in World War II. The other four sites are civilian and

were added by Congress in 1976.

Sites range from a contaminated floor drain at Lawrence Berkeley Laboratory to a

contaminated Th ore processing plant and several surrounding residential properties in

northern New Jersey, containing approximately 100,000 cubic yards of contaminated soil.









In general, all sites are contaminated with varying levels of U, Th, their progeny, or some

mixture thereof. Sites typically include at least one building and the surrounding lands.

Clean up typically includes scrubbing and/or vacuuming of contaminated building surfaces

to remove contamination, destruction of facilities too contaminated or too uneconomical

to clean up, and digging up of contaminated soils. All contaminated wastes are deposited

in a controlled and monitored temporary storage area to await their ultimate disposition.

Wastes are generally low level and thus their ultimate disposition will be in the low level

waste repository of the state or compact area from which the wastes came.

One portion of this process that is of scientific interest and could stand some improve-

ment is the assay of soils to determine whether or not they are contaminated. During

the course of site decontamination, many soil samples are taken. Preliminary soil samples

are taken to determine the approximate extent and concentration of radionuclides present.

Periodic soil samples are taken during soil excavation to determine whether preliminary

estimates were correct and to locate previously unidentified radionuclide deposits. Final

soil samples are taken to confirm that all contaminated soil has been removed. With so

many samples being collected, quick and accurate assay becomes important.

All soil samples are assayed twice: once when they arrive at the lab as wet, inhomo-

geneous soil, and once after they have been processed. The standards comparison method

for ganina spectroscopic analysis is used to assay the soil samples. This method will be

discussed in detail later. Soil sample processing involves drying the soil in an oven, grinding

the soil into a powder that will fit through a standard 200 mesh per square inch sieve, and

stirring the powdered soil into a relatively homogeneous mixture. Soil sample processing

adds approximately 2 days to sample analysis time. Samples are analyzed twice because,

while the first analysis is fast enough to meet stingy construction schedules, it is not ac-

curate enough to meet quality control guidelines. When a "fudge factor" is applied, the









fudge factor being the average ratio of sample analysis results for processed vs. unprocessed

samples, the results of the analysis of unprocessed soil samples are accurate enough to use

and to guide further work. Even with the fudge factor, analysis of unprocessed soil samples

is not sufficiently accurate to prove, for example, that an area is free of contamination and

needs no further work. The second analysis, of the processed soil, is accurate but takes too

long to meet construction schedules.

The process in need of development, then, was an assay technique that was accurate but

could be performed on unprocessed soil samples. This would eliminate the time-consuming

step of sample drying and grinding.

Upon selecting this topic, I received a Laboratory Graduate Participation Fellowship

from Oak Ridge Associated Universities (ORAU) to pursue the research at Oak Ridge Na-

tional Laboratory (ORNL). The Radiological Survey Activities section (RASA), currently

called the Measurement Applications and Development (MAD) section, of the Health and

Safety Research Division (HASRD) sponsored this work because it has been in the business

of performing radiological assessment surveys of various contaminated government sites

around the country. At the MAD lab at ORNL soil samples are processed in the same

method as used by the FUSRAP analysis lab, and the standards comparison method of

gamma spectroscopic analysis is used to determine radionuclide concentrations. As with

the FUSRAP project, soil sample processing is a time-consuming endeavor.

Further research indicated that the processing of soil samples prior to analysis was

standard procedure at most soil assay labs. Thus a procedure that eliminated the processing

step would be universally useful.

My research also indicated that there was a second drawback to standard gamma spec-

troscopic techniques. A description of the standards comparison method of gamma spec-

troscopic analysis will help provide a better understanding of this problem.









Standards Method for Gamma Spectroscopic Assay of Soil Samples



The standards method for ganmma spectroscopic assay of soil or any other sort of ra-

dioactive sample is a simple process. A sample of unknown radionuclide content is placed

in a fixed geometry, relative to a detector, and a spectrum is collected for a fixed length

of time. A sample containing a known amount of radionuclide is then placed in the same

geometry as that used to count the unknown sample, and a second spectrum is collected.

By comparing these two spectra, the identity and amount of radionuclide in the unknown

sample can be determined.

Qualitatively, the presence of a radionuclide in a sample is determined by the presence

of spectral peaks at energies characteristic of that radionuclide. For example, Co-57 emits

gannma rays at 136 keV and 122 keV in a known ratio. If spectral peaks of these energies

and of proper relative intensity are present in a spectrum, then Co-57 is probably present

in the unknown sample.

Quantitatively, the concentration of a radionuclide in a sample is determined by com-

paring the area of a spectral peak generated by an unknown sample to the area of a spectral

peak generated by a sample of known concentration. For example, a sample known to con-

tain 100 pCi of Co-57 is counted in a standard geometry relative to a detector. After one

hour of counting this known sample, the area beneath the 136 keV peak is 10,600 counts

and the area beneath the 122 keV peak is 85,500 counts. Next, an unknown sample is

counted, in the same geometry in which the known sample was counted, and after one

hour of counting the areas beneath the 136 keV and 122 keV peaks are 21,200 counts and

171,000 counts, respectively. The unknown sample resulted in peak areas twice those of the

known sample and thus the unknown contains 200 pCi of Co-57. Further details of gamma

spectroscopy can be found in Knoll.1









The drawback to this technique is that it relies upon the known sample, referred to as

the standard, being physically similar to each unknown sample counted. This is because the

density, moisture content, consistency, and elemental makeup of a sample will determine

that sample's radiation attenuation properties. A homogeneous sample of given properties

containing 100 pCi of a radionuclide will attenuate a given fraction of the gammas emitted by

that radionuclide. A second homogeneous sample, of different properties but also containing

100 pCi of the same radionuclide, will attenuate a different fraction of the gammas emitted

by that radionuclide. Therefore two homogeneous samples containing the same amount of

a radionuclide can yield spectra with characteristic gamma energy peaks of different areas.

This makes it very important that the standards chosen match the unknowns as closely as

possible.

Unfortunately, the standards used for analysis are often significantly different in atten-

uation properties from the unknown samples. Dry, ground, and homogeneous standards are

obviously different from unprocessed, wet, inhomogeneous unknown samples. And although

standards can be fairly similar to processed unknown samples, mineral content differences

do result in differences in attenuation properties. Thus the process to be developed should

take the attenuation properties of each unknown sample into account in order to properly

determine radionuclide content.



Radionuclides of Interest


Two elements that are of particular interest to both FUSRAP and MAD are U and

Th. These are common contaminants at sites around the country. Many of the MED sites

of FUSRAP became contaminated while receiving, processing, or shipping U to be used

in the fabrication of the first atomic bomb. The Grand Junction, Colorado, site that the

MAD program is surveying is contaminated with mill tailings from U mining operations.









Two of the civilian FUSRAP sites were chemical plants involved in processing Th from ore.

Although less prevalent, Th is also found in mill tailings and, thus, is of interest to the

MAD program.

The main reason to develop an assay technique specifically designed to detect U and

Th is that U-238 and Th-232, the most common radioisotopes of U and Th respectively,

emit only low energy and low yield gamma rays. In order to perform gamma spectroscopic

analysis of these radioisotopes, gamma rays emitted by progeny must be used, equilibrium

of the parent with the progeny must be assumed, and concentrations must be inferred from

the presence of the progeny. Table 1 lists the U-238 decay chain and the radiations emitted

by each member. Table 2 shows equivalent information for the Th-232 decay chain.

Unfortunately, U and Th require long periods to reach equilibrium, and equilibrium

may not have been reached in the soil samples to be analyzed. Also, each decay product

has its own rate of dissolution in ground water. Thus as contamination waits in the soil to

be sampled, varying amounts of U, Th, and their progeny dissolve and diffuse. This also

confuses the equilibrium situation. Since equilibrium can not always be correctly assumed,

the assay technique to be developed must also directly measure U and Th and should not

rely on measurements of progeny.



Process Sensitivity


Since the process to be developed is to be practical in nature, some guidelines as to

sensitivity and accuracy should be followed. Since process application is soil assay for

contaminated sites undergoing decontamination, it is sensible to use guidelines established

by DOE for releasing sites for unrestricted public use.









TABLE 12
U-238 Decay Chain
S Major Radiation Energies
MeV) and Intensities
Radionuclide IIalf-Life Alpha Beta Gamma


4.15 (25%)
4.20 (75%)


Th-234

Pa-234
(Branches)

Pa-234
(.13%)


U-234
(99.8%)

Th-230


Ra-226


Rn-222

Po-218
(Branches)

Pb-214
(99.98%)


At-218
(.02%)

Bi-214
(Branches)


U-238


4.59E9 a


24.1 d

1.17 min


6.75 h




2.47E5 a


8.0E4 a



1.602E3 a


3.823 d

3.05 min


26.8 min




2.0 s



19.7 min


0.103 (21%)

2.29 (98%)
1.75 (12%)

0.53 (66%)
1.13 (13%)
















0.33 (0.019%)



0.65 (50%)
0.71 (40%)
0.98 (6%)





1.0 (23%)
1.51(40%)
3.26(91%)


4.72 (28%)
4.77 (72%)

4.62 (24%)
4.68 (76%)

4.60 (6%)
4.78 (95%)

5.49 (100%)

6.00 (100%)







6.65 (6%)
6.70 (94%)

5.45 (.012%)
5.51 (.008%)


0.063 (3.5%)+

0.765 (0.30%)
1.001 (0.60%)+

0.100 (50%)
0.70 (24%)
0.90 (70%)

0.053 (0.2%)


0.068 (0.6%)
0.142 (0.07%)

0.186 (4%)


0.510 (0.07%)





0.295 (19%)
0.352 (36%)






0.609(47%)
1.120 (17%)
1.764 (17%)








TABLE 1 (continued)
Major Radiation Energies
(MeV) and Intensities
Radionuclide Half-Life Alpha Beta Ganuna
Po-214 164.0 us 7.69 (100%) 0.799 (0.014%)
(99.98%)

TI-210 1.3 min 1.3 (25%) 0.296 (80%)
(.02%) 1.9 (56%) 0.795 (100%)
2.3 (19%) 1.31 (21%)

Pb-210 21.0 a 3.72 (2E-6%) 0.016(85%) 0.047 (4%)
0.061(15%)

Bi-210 5.10 d 4.65 (7E-5%) 1.161 (100%)
(Branches) 4.69 (5E-5%)

Po-210 138.4 d 5.305 (100%) 0.803(0.0011%)
(100%)

TI-206 4.19 min 1.571 (100%)
(.00013%)

Pb-206 Stable
NOTES + Indicates those gamma rays that are commonly used to identify U-238. Equilibrium
must be assumed.









TABLE 22
Th-323 Decay Chain
S Major Radiation Energies
(MeV) and Intensities
Radionuclide Half-Life Alpha Beta Gamma


3.95 (24%)
4.01 (76%)


Ra-228

Ac-228




Th-228



Ra-224



Rn-220

Po-216

Pb-212



Bi-212
(Branches)



Po-212
(64%)

TI-208
(36%)


6.7 a

6.13 h




1.91 a



3.64 d



55.0 s

.15 s

10.65 h



60.6 min




304.0 ns



3.10 min





Stable


0.055 (100%)

1.18 (35%)
1.75 (12%)
2.09 (12%)














0.346 (81%)
0.586 (14%)

1.55 (5%)
2.26 (55%)






1.28 (25%)
1.52 (21%)
1.80 (50%)


NOTES: + Indicates those gamma rays that are commonly used to identify Th-232. Equilibrium
must be assumed.


Th-323


5.34 (28%)
5.43 (71%)

5.45 (6%)
5.68 (94%)

6.29 (100%)

6.78 (100%)





6.05 (25%)
6.09 (10%)



8.78 (100%)


Pb-210


1.41E10 a


0.34 (15%)+
0.908 (25%)+
0.96 (20%)+

0.084 (1.6%)
0.214 (0.3%)

0.241 (3.7%)



0.55 (0.07%)




0.239 (47%)
0.300 (3.3%)

0.040 (2%)
0.727 (7%)+
1.620 (1.8%)





0.511 (23%)
0.583 (86%)+
0.860 (12%)
2.614 (100%)+









The decontamination criteria established by DOE are based on the "Homestead Farmer"

scenario. This scenario assumes that a farmer will homestead on contaminated lands, will

grow all his/her own food on the land, will raise and graze his/her own livestock on the

land, will drink water from wells on the land, and eat fish from a stream running through

the land. Limiting radionuclide concentrations were calculated such that the homestead

farmer would not build up radionuclide body burdens greater than those suggested by the

National Council on Radiation Protection and Measurements (NCRP). Table 3 lists relevant

guidelines. Soil radionuclide content limitations are in units of pCi/gm of dry soil.



Statement of Problem


The objective of this research is to develop a fast and economical technique for lab-

oratory assay of U and Th in an inhomogeneous sample consisting of moist, chunky soil

compressed into a plastic, cylindrical jar. The product of this assay should be the isotopic

concentrations of U-238, U-235, Th-232, and Th-230 in pCi per gram of dry soil averaged

over the entire sample. To accomplish this assay the technique must determine the dry

soil weight, must be sensitive to U and Th isotopic concentrations from approximately 100

pCi/gm to 2000 pCi/gm, and must account for the effects of sample inhomogeneity.

Current teclmiques for the non-destructive assay of U in soil samples include neutron

activation analysis and gamma spectroscopy. Gamma spectroscopy and its limitations have

been discussed previously. Neutron activation depends upon the availability of a large

neutron source. Since it is advantageous to develop a process that is as simple, portable,

and as inexpensive as possible, neutron activation can be ruled out. The technique chosen for

this application is x-ray fluorescent analysis (XRF). Details of the technique are described

in the following sections.









TABLE 3 (a, b, c) 3
Summary of DOE Residual Contamination Guidelines
Soil Guidelines (Maximum limits for Unrestricted Use)
Radionuclide Soil Concentration (pCi/g) above Background
Ra-226 5 pCi/g averaged over the first 15 cm of
Ra-228 soil below the surface.
Th-232 15 pCi/g when averaged over any 15 cm
Th-230 thick soil layer below the surface layer.

Other -Soil guidelines will be calculated on a
radionuclides site specific basis using the DOE manual
developed for this use.

a: These guidelines take into account ingrowth of Ra-226 from Th-230, and
Ra-228 from Th-232 and assume secular equilibrium. If either Th-230 and
Ra-226, or Th-232 and Ra-228 are both present, not in secular equilibrium,
the guidelines apply to the higher concentration. If other mixtures of ra-
dionuclides occur, the concentrations of individual radionuclides shall be
reduced so that the dose for the mixtures will not exceed the basic dose
limit.
b: These guidelines represent unrestricted-use residual concentrations above
background, averaged across any 15 cm thick layer to any depth and over
any contiguous 100m2 surface area.
c: If the average concentration in any surface or below surface area less than
or equal to 25m2 exceeds the authorized limit or guideline by a factor of
V/-lO/A where A is the area of the elevated region in square meters, limits
for "HOT SPOTS" shall be applicable. These hot spot limits depend on the
extent of the elevated local concentrations and are given in the supplement.
In addition, every reasonable effort shall be made to remove any source of
radionuclide that exceeds 30 times the appropriate soil limit irrespective of
the average concentration in the soil.




X-Ray Fluorescent Analysis (XRF)


Atoms can be ionized, i.e., have one or more electrons removed, via several processes. In

the case of x-ray fluorescence, gamma or x rays incident on an atom undergo photoelectric

reactions resulting in the ionization of the atom. The ionized atom then de-excites via the

emission of x rays. An upper shell electron falls into the hole vacated by the ionized electron

and x rays, equal in energy to the difference in shell energies, are emitted. Since elements

have characteristic atomic energy levels, the emitted x rays are characteristic of the element









and can be used to identify the element. The intensity of the emitted x rays is proportional

to the concentration of the element in the x-ray emitting material. This technique can thus

be said to directly determine U and Th concentrations in soil samples. For a more detailed

description of x-ray fluorescent spectrometry see Woldseth.4





Assay Technique


In overview, the assay process is simple. Each sample is irradiated to induce fluorescence

and the emitted fluorescent x rays are detected by a hyper-pure intrinsic Ge planar detector.

The areas under the Ka& x-ray peaks from U and Th are determined by a spectral analysis

system. The Ka peak was chosen because the K-shell lines are highest in energy, thus

minimizing attenuation effects, and the Kai line is the most predominant K-shell line. The

areas of these peaks are used to determine U and Th concentrations. This determination

involves two steps; the determination of sample moisture content and attenuation properties,

and the handling of sample inhomogeneity. The isotopic fractions are determined by looking

at the relative intensities of gamma rays from U and Th daughters. The details of these

processes are discussed in subsequent sections.

This research is divided into two broad sections; development of a mathematical model

of the assay system, and experimental verification of that model. The model is divided into

three sections. The first section involves the development of a peak shaping program to

accurately determine the areas of the Kai x-ray peaks of U and Th. The second section

involves the determination of the sample moisture content and attenuation properties. This

is done by measuring how gamma rays are transmitted through the sample. The third

section uses the peak areas, determined in section one, and the soil moisture content and

attenuation coefficients, determined in section two, to mathematically model the sample so









that an accurate assay can be performed. In the third section the final result of the analysis,

the radionuclide concentrations of U and Th in the soil sample, is calculated.



Literature Search


In order to learn more about existing techniques of gamma spectroscopic analysis, x-

ray fluorescent analysis, peak shaping tecluiques, soil moisture determination, and assay of

inhomogeneous samples, a computer literature search was performed. The central research

library at ORNL performed the search, looking through Chemical Abstracts, Physical Ab-

stracts, and the DOE Energy Data Base. Many references which discussed these topics

were located, however no references were found which discussed data analysis techniques

similar to that presented in this work were located.















CHAPTER II

METHODS AND MATERIALS



This chapter describes the theoretical basis for the U and Th assay technique. The

theory is divided into three sections: peak shaping, soil moisture content and attenuation

properties, and system modeling. Following this theory are descriptions of the error analysis

and the experimental procedure used in this work.



Peak Shaping


In order to determine the physical properties physical measurements must be made. In

the case of this soil sample assay technique, the induced fluorescent x rays emitted by the

target are the physical quality measured. The measurement takes the form of an energy

spectrum. The number of x rays emitted by the sample is proportional to the concentration

of U and/or Th in the sample. The areas of the Kai x-ray peaks are the number of x

rays that hit the detector and are counted in the full energy peak. These areas, then, are

proportional to the concentrations of U and/or Th in the soil sample. The details of the

proportionality are discussed in subsequent sections. This section describes the method

used to determine peak areas.

The fitting of spectral data to mathematical functions is known as peak shaping or

peak fitting. As stated above, the motivation for fitting peaks is to accurately determine

the peak area which is proportional, in this case, to the concentration of U and/or Th in a

soil sample. The "art" of peak fitting has been steadily perfected over the years, particularly









with the advent of high resolution semiconductor detectors. A good overview of current

theory and of the variety of functions available to fit peaks and backgrounds is provided by

Prussin.5 As an introduction to the theory of peak shaping he states that:

As is well known, the shape of a photopeak from monoenergetic photons
in spectra taken with semiconductor detectors is closely approximated by
a Gaussian with more or less severe tailing below the centroid. The peak
is joined smoothly to a lower-energy continuum of small curvature until it
meets the relatively sharp Compton edge. This continuum, which is pro-
duced mainly by the loss of some of the energy of photoelectrons from the
sensitive volume of the detector, leads to the appearance of a step-like dis-
tribution upon which the main intensity is superimposed. Under conditions
of low input rate, short counting times with stable electronics and negligi-
ble background at higher energies, the high-energy edge is indeed found to
be nearly Gaussian. The low energy edge begins to deviate from Gaussian
form at fractions of the peak maximum in the range of .5 to .01 depending
upon the detector type, its quality and its history. While Gaussian shape
results from statistical spread due to fluctuations in electron-hole pairs
produced in the stopping process and random noise from the amplifying
electronics, the low energy tailing represents pulse-height degradation from
a number of phenomena including charge trapping and recombination, en-
ergy loss of primary and secondary electrons in the insensitive volume of
the detector or by bremsstrahlung.


Figure 1 shows a typical spectral gamma peak and its component parts; the Gaussian

peak and step function background. Typically, peak fitting programs will fit the background

to some function, subtract the background from beneath the peak, and fit the remaining

data to some peak function. The following sections will discuss the peak and background

fitting functions used in this work.


A Fitting Peak


Peak shaping and peak area determination are commonly done by gamma spectroscopy

systems in an efficient manner. Such systems usually contain long computer programs to

locate all spectral peaks, to determine and subtract the baselines from beneath those peaks,

and to determine peak areas by summing of channel counts or by least squares fitting to a


Gaussian shape.
























FIGURE 1
Typical Gamma Ray Spectral Peak and Background








1000000


100000


V)
--
a 10000
0
0


1000=


* Spectral Data


Gaussian Fit

ERFC Background


0**


100--
1200


1250


1300


Channel Number


I


1350


I I









The x-ray fluorescent analysis system described in this paper uses its own peak shaping

program for the following reasons. First, since only the Ka& peaks from U and Th will

be used, only two peaks at known energies, need to be determined. It is not necessary

to search the entire spectrum to shape each peak and to calculate the area of all possible

peaks since only the Kai peaks are of interest. This eliminates much of the computational

software necessary for large spectral analysis programs, thus decreasing processing time.

Since most processing programs are quite fast, this is not the most important reason to

have a separate peak shaping program. The second and more important reason is that

most spectral analysis programs perform Gaussian peak shaping, which is inappropriate for

x rays. This results in inaccurate area determination.

The spectral response of a detector system can be mathematically described as a con-

volution of the detector system's inherent response function and the energy distribution of

the "monoenergetic" incident radiation (Knoll1 pp 732-739).


N(H)= R( ,E) x S(E)dE


where


N (H) = the differential pulse height spectrum,

R (H, E) = the differential probability that a pulse of
amplitude II originates from a photon of
energy within dE of E,

S (E) = the photon energy distribution.


Detector system response functions are typically Gaussian (Knoll1 pp 434-440). Mo-

noenergetic gamma rays emitted by the de-excitation of a nucleus in an excited state are

actually not monoenergetic but are distributed in energy about a central value. This distri-

bution is described by the function S(E). The width of this energy distribution is inversely









proportional to the mean lifetime of the excited nuclear state (Evans6 pp 397-403). This is

directly attributable to the Heisenberg uncertainty principle such that (Evans6 pp 397-403)

r (eV) =.66E 15 (eV s) /tm (8)

where

r = energy distribution width (eV),

.66E 15 (eV s) = Plank's Constant/27r,

t, = mean lifetime of excited state.

NOTE: half life (t/z2) = t,/ln(2)

Therefore, for a gamma ray to have an energy distribution width greater than 1 eV,

its mean life would have to be less than 1E-15 s. Since most gamma rays are emitted

from radionuclides with half lives much longer than that, the width of ganuna ray energy

distributions is zero for practical purposes. Since the width of the energy distribution for

gamma rays is so small, S(E) is effectively a delta function. The convolution of a delta

function energy distribution and a Gaussian distribution detector response results in a

Gaussian shape spectral peak for gamma rays (Knoll1 pp 434-440).

X rays, however, are generated by electrons falling from upper to lower orbitals, as

described in a previous section. These transitions take place very rapidly, and therefore the

emitted x rays have fairly large widths which increase with increasing energy.7,8 Experimen-

tal measurements have shown K, x rays to have widths of from 1 eV for Ca to 103 eV for

U.9 X-ray energy distributions must therefore be described by a Lorentzian distribution10

and an x-ray spectral peak must therefore be described by the convolution of a Gaussian

detector response function and a Lorentzian x-ray energy distribution.11 Mathematically,

this convolution is written as

C(E) = G (E') xL (E E') dE',
J -0








where


G (E') = Gaussian distribution function,

= Aexp (-.5 ((E' E.) /)2)

E' = convolution dummy variable,

E. = peak centroid,

a = Gaussian peak standard deviation,

A = Gaussian peak height constant, and

L (E E') = Lorentzian distribution function,

= A'/ ((E E' E)2 + .25r) ,

E = energy,

E' = convolution dummy variable,

Eo = peak centroid,

r = Lorentzian peak full peak width at half
the maximum peak height,

A = Lorentzian peak height constant.


The resulting convolution, C (E), can be solved numerically in the following manner.12


C (E) = A" (exp (-X2) x (C1 + C2 x X2 + C3 x (1 2X2)))

+A" x C4 x P (X),

where


X" = (1/2)((E E.)/,)2,

C1 = 1 (i/v) (F/a),

C2 = (1/2v7) (r/lV2),









C3 = (1/8)(r/a) ,

C4 = (2/7rV)(/o),

B(X) = (-exp (-X)) (f (X)),


S() ((exp(-n/4)) ) x (1- cosh(nX)) and
n=l
A" = new peak height constant.


This is a numerical equation in four unknowns; E., r, o, and A". This equation

lends itself to weighted least squares fitting to the spectral data. The result of this fitting

will be values for the above four unknowns and their associated errors. Figure 2 shows

the Lorentzian distribution of the incident x rays, the Gaussian response function of the

detector system, and the resulting convoluted distribution that is the spectral x-ray peak.

It should be remembered that the objective of this exercise is to determine number of x

rays that hit the detector. As will be explained further in the section describing data analysis

and the section describing detector system calibration, the measured number of x rays will

be compared to the calculated number of x rays to determine concentrations of U and Th

in the soil. By properly calibrating the detector system, the area under the convoluted peak

will be proportional to the number of x rays that hit the detector. Determination of the

area of the convoluted peak is thus the desired end result of this peak analysis. Therefore it

should be noted that the Lorentzian x-ray distribution and the Gaussian detector response

function, shown in Figure 2, are for reference only and will not actually be seen in the

spectrum or have their areas calculated.

With the peak parameters determined, the peak area can be determined. Since the

convolution function is rather complex, the peak area is determined by numerical integra-

tion. The peak shaping program defines the spectral peak as having a beginning channel

and an ending channel and performs the integration between these limits. Only a small

























FIGURE 2
Lorentzian X Ray as Seen Through
the Gaussian Response of a Detector







10000000 --


1000000



100000-
0


10000



1000--
920


Gaussian
----- Lorentzian

Convolution


940
940


960 980
Channel Number


1000
1000


1020








portion of the peak area lies beyond those limits and is accounted for by use of an equation

from Wilkinson.12 Wilkinson's equation determines the fractional area beyond a specified

distance from a peak centroid. It should be noted that the numerical integration is per-

formed on the fitted peak function and not on the actual spectral data. Figure 3 shows a

typical x-ray spectrum in the vicinity of the Ka x-ray peak of Th.

Thus once the spectral data is fit to the proper peak shape and the four fitting parame-

ters are known, the peak area can be determined. Since least squares fitting techniques also

lend themselves to convenient error analysis, the errors associated with the above fitting

parameters can be found and propagated to determine the error in the peak area.


A Fitting Background

As was previously mentioned, before a proper peak shape can be determined, the back-

ground must be subtracted from the peak. In the case under consideration in this work both

the U and Th Ka~ peaks lie on top of a large, steeply sloping background (see Figure 3).

This background is the sum of the Compton continuum step function background, described

by Prussin5 and others13, 14, and gammas from the excitation source that backscatter in

the target and hit the detector.

The step function portion of the background is described in several well known peak

fitting programs as a complementary error function, erfc.13, 15, 16 While details of the

functions used vary slightly from program to program, most use an equation of the form


SB (X) = A X erfc (( Y) /r) ,


where


SB (X) = step background value at channel X,

A = amplitude,

























FIGURE 3
Typical Th K1a Spectral Peak
























1500


0 500 1000
Channel Number









X = peak centroid, and

a = detector response function width for
peak centered at X.


The numeric approximation to this function used in this work in HYPERMET16 and

in GRPANL15 is


SB(X,) = BL + (BH BL)x Y (X) / Y(X) ,
j=1 j=l

where


SB (Xi) = step background value at channel Xi,

BL = average background value on the low energy
side of the peak,

BH = average background value on the high energy
side of the peak,
i
Y (Xi) = the sum of the gross channel counts from the
first peak channel to channel Xi, and
N
Y (Xi) = the sum of the gross channel counts from the
first peak channel to the last peak channel.


The above algorithm assumes that the background to either side of the peak is relatively

flat. This will not necessarily be the case for all spectra and is certainly not the case for

this work.

GRPANL,15 in addition to using the above step function, allows the use of two different

background slopes, one for each side of the peak. The average slope of the background under

the peak is then the average of the background slopes from either side of the peak. The

change in background attributable to this slope is then equal to the vertical change of a

line, having the average background slope, over a horizontal change equal to the number









of channels in the peak. The actual vertical change in the background is equal to the

difference between the number of counts in the last low energy side background channel

and the number of counts in the first high energy side background channel. Then the

vertical background change due to the step function is equal to the actual vertical change

minus the vertical change due to the slope. The use of this rationale results in a step

function background whose slope at either side of the peak fits smoothly with the actual

background slopes.

Unfortunately, the background slope of the spectrum under consideration in this work

does not change uniformly from the low energy side of the peak to the high energy side.

Rather, the slope on the low energy side is very steep, changes very quickly, and then

approaches the slope on the high energy side. The average background slope, as described

above, will therefore be too steep and the vertical change attributable to the slope will exceed

the actual vertical change. Under these circumstances, GRPANL will fit the background to

a smoothly changing slope without a step change.

While this might seem contrary to theory, Baba et al.14 state, for large peaks in a

multiple group or even for smaller single peaks, that the peak areas and centroids are

determined with sufficient accuracy by using a properly fit straight line, curved, or step

function background. As mentioned earlier, peak fitting is as much an art as a defined

science.

Bearing all of the above in mind, the approach used in this work was to use both the

step function and the sloping background. The background is easily fit to a third or fourth

order polynomial. In this work then, the vertical change in background beneath the peak is

attributed half to the polynomial and half to the step function. The resulting background is

shown in Figure 4. Source listings of POLYBK.FIT and BKG, the codes used to accomplish

the background determination and subtraction, are supplied in Appendix C.

























FIGURE 4
Polynomial and Step Function X-Ray Peak Background







1000000


S_ \ D~c .grouLl.iU.
0 100000-
0







10000 -
920 940 960 980 1000 1020
Channel Number









Ill that the steeply sloping nature of this background is somewhat unusual in spec-

troscopy, some explanation as to its origin is warranted. The excitation source, Co-57,

which emits gammas at 122 keV and 136 keV, was chosen because of the proximity of its

gamma energies to the K-shell absorption energy. At these energies, U and Th have high

cross sections for photoelectric reactions with K-shell electrons. Table 4 shows the absorp-

tion and emission energies for U and Th. Table 5 shows the emission energies and yields

for Co-57. Table 5 also lists emission energies and gamma yields for Eu-155. The latter

radionuclide is used for transmission measurements which are explained in a subsequent

section. Table 6 shows relevant source physical properties.

Unfortunately, when 122 keV ganunas Compton scatter at approximately 180 degrees,

the resulting gamma is 83 keV. This is called a backscatter gamma. The backscatter gamma

from an incident 136 keV gamma is 89 keV. These backscatter gammas are at inconvenient

energies because they form the majority of the background beneath the U and Th Ka, x

ray, thus somewhat obscuring the peaks. And the shape of the background depends upon

the geometry of the scattering soil sample. That is, the size and relative position of the

source, soil sample, and detector determine what scatter angles, and thus what energies,

will be seen as backscatter gammas. Thus the shape of the background does not lend itself

to simple theoretical treatment and a third or fourth order polynomial fit, as mentioned

earlier, is necessary. The peak areas calculated by this technique are used in subsequent

analyses to determine the soil sample concentrations of U and Th.









TABLE 4
U and Th K-Shell Absorption and Emissionl7
K-Shell K.i Ka2
Element Absorption Emission Emission
U 115.591 keV 98.434 keV 94.654 keV
Th 109.63 keV 93.350 keV 89.957 keV

TABLE 5
Co-57 and Eu-155 Emission Energies and Yields18
Backscatter
Element Emission Energy Gamma Yield Energy
Co 57 122.063 keV .8559 82.6 keV
136.476 keV .1061 89.0 keV
Eu 155 105.308 keV .207 74.6 keV
86.545 keV .309 64.6 keV
*: The gamma yields for Eu 155 are not known to the same precision as
those of Co-57. Europium-155 sources, therefore, are described by gamma
emission rates, Activity (Ci) x Yield (gammas/s). The listed yields are for
estimation purposes only.


TABLE 6
Co-57 and Eu-155 Physical


Characteristics


Soil Moisture Content and Attenuation Coefficients


In order to properly analyze spectral data, the soil attenuation coefficient as a function

of energy must be known. The details of their use are described in a subsequent section.

Since the goal of this assay is to determine the soil U and Th concentrations in units of pCi

per gm of dry soil, the water weight fraction is needed to determine the soil dry weight.

Fortunately, both of these parameters are easily measured.


Co-57 Eu-155
Activity 5 mCi 15% 2 mCi 15%
(1 October 1985) (1 April 1986)
Half Life 271.7 d 1741 d









Soil Attenuation Coefficient


It is well known that as monoenergetic gamma rays pass through any medium, the

fraction of uncollided gammas, as a function of thickness of the medium, is given by


Transmission Fraction = exp (-p (E) po),


where


p (E) = mass attenuation coefficient at the
energy E, (cm/gm2),

Po = density of the attenuating medium,
(gm/cc), and

x = thickness of the attenuating medium (cm).


For a monoenergetic point source, with emission rate Ao, the number of gammas which

strike and are detected by a detector of area AD located at distance r from the source is


AA (E) x AD x 7 (E) x CT
A (E)42 (1)


where


Ao (E) = source gamma emission rate at energy E
(Gammas/s),

AD = detector surface area (cm2),

q (E) = detector intrinsic energy efficiency at
energy E, gammass counted in the full energy.
peak per ganuna hitting the detector),

CT = pulse pileup corrected live time (s),

r = distance from source to detector (cm).








Thus for a monoenergetic gamma passing through an attenuating medium, the number of

gammuas counted in the full energy peak can be described by the product of the above two

attenuations:

(E A (E) x AD x {!(E) x CT
A (E)= xexp(- i(E)pox),


where A (E) = full energy peak area at energy E.

Next, once the above measurement is made and A (E) is determined, the attenuating

object can be removed from between the source and detector and the measurement of

A (E) repeated. This time, however, the new measurement, A' (E), is described by Eq. 1

alone since no attenuating object is between the source and the detector. The ratio of

A (E) /A' (E) is then proportional to the objects transmission fraction at energy E:

A(E) A, CT
x x exp (-p (E) pz),
A' (E) A(E') CT' -

where all terms are as defined previously.

The terms that differ from one measurement to the next are A, (E) and CT. The source

emission rate, A, (E), changes from measurement to measurement because of source decay.

If the measurements are made sequentially, this change is small, but it is always finite. The

count live time also varies from measurement to measurement due to pulse pileup. Pulse

pileup corrections are discussed in detail in a subsequent section. Since A. (E) and CT vary

from measurement to measurement, they remain to be accounted for in the above ratio. All

other terms divide out.

Since all the terms in the above equation are measured except the transmission fraction

term, the transmission fraction can be calculated. If the thickness of the attenuating object

is known, then the attenuation coefficient can be determined.


TF(E)= exp (-p (E)poP),









where


TF (E) = transmission fraction for gammas at
energy E, gammass transmitted through
the object uncollided per gamma incident
on the object), and


other terms are as previously defined.

Therefore



t (E) x p = (-1/x) x In(TF(E)),

where

pt(E)x po = object linear attenuation coefficient, (cm-).

In the case where the attenuating object is a cylindrical jar of soil, this equation results

in the soil's linear attenuation coefficient at energy E. This information is used in the

next phase of this assay process, dealing with data analysis, to eventually determine U and

Th concentrations. As will be described in the next section, the soil's linear attenuation

coefficient is necessary at four energies; 136 keV and 122 keV, which are the energies of the

Co-57 gamma rays used to induce x-ray fluorescence in U and Th, 98 keV, the energy of

the K,, x ray from U, and 93 keV, the energy of the Ka1 x ray from Th.

It should be noted here that the "soil" in the jar is actually a mixture of dry soil and

water. For the purposes of simplicity the term "soil" will be used to refer to this soil water

mixture.

Since Co-57 is used to induce x-ray fluorescence, the same source can be used to measure

transmission gamma rays and thus determine the soil's linear attenuation coefficients the

energies of the Co-57 ganmmas. Unfortunately, no clean and calibrated source of U or Th x

rays is available. In this case, clean refers to a source that emits x rays only at the energy





of interest. Additional x rays or garm as will complicate the transmission spectra, add

background, and generally complicate the results such that true peak areas at the energies

of interest are hard to determine.

Fortunately, over a small energy range attenuation coefficients can be described as a

simple function of energy (personal conversation with John Hubble):


In (p (E)) = A + B x hi (E) + C x (In (E))2,

or

p (E) = exp (A + B x In(E) C x (In(E))2),

where A, B, and C are constants.

Therefore, the gamma rays from Eu-155, at 105 keV and 86 keV, are also used and the

soil's linear attenuation coefficients at these energies are measured. The four data points,

two from Co-57 gammas and two from Eu-155 gammas, are then fit to the above equation,

using a least squares fit technique, and the linear attenuation coefficients at the U and

Th Ka, x-ray energies can be calculated from the resulting curve fit. Table 7 shows typical

soil linear attenuation coefficients.


TABLE 7

Typical Soil Linear Attenuation Coefficients

Measured Curve Fit
Energy (keV) p (E) (1/cm) p (E) (1/cm)



136.476 0.20505 0.20517
122.063 0.21505 0.21479
105.308 0.23114 0.23132
98.428 0.24056
93.334 0.24866
86.545 0.26159 0.26155









Soil Moisture Content


The above analysis of soil linear attenuation coefficients assumes that the "soil" in the

jar consists of everything in the jar, water and soil. As will be seen, this is the appropriate

linear attenuation coefficient to be determined here. The moisture fraction of this soil

is also needed for the data analysis for final U and Th concentration determination. As

such, after the transmission and XRF measurements have been made, each sample jar is

placed in a microwave oven and dried in the jar. Jar weights before and after drying are

used to determine soil moisture weight fraction. Soil sample densities, before drying, were

determined by dividing the known wet soil weight by the know bottle volume.

Initially, soil moisture content was to be determined via use of the same transmission

gamma rays described in the last section. Unfortunately, the set of four simultaneous

equations that were to be used resulted in a non-unique solution set instead of one unique

answer. Although this approach could not be used, the details of this approach and the

reasons for its failure are included in Appendix B.



System Model



Introduction


In general, XRF determination of elemental concentrations is done by comparing the

area of a peak from an unknown sample to the area of a peak from a sample of known ele-

mental concentration, called a standard. The concentration of that element in the unknown

sample is simply the ratio of unknown sample peak area to standard peak area times the

elemental concentration in the standard.

This technique assumes that the measurement geometry and attenuation properties of

the unknown sample are identical to those of the known standard. Practically speaking,








this means that both the standard and unknown must be as close to physically identical as

possible and must be measured using the same detector and in the same position. To achieve

this for soil samples, standards and unknowns usually are dried soil that has been crushed

into powder form, thoroughly mixed into a homogeneous mass, and put into containers.

These containers can then be exposed to an x-ray excitation source and the fluorescent x

rays can be counted. Experiments of this type are easily reproducible.

Unfortunately, standards and unknowns do not always match. The attenuation prop-

erties of a soil sample vary with elemental concentrations and soil makeup. Clays, for

example, have different attenuation properties than black dirt. Comparison of unknowns

to standards of different attenuation properties may lead to erroneous results. This may

be compensated for by using very thin samples such that attenuation is not a factor. With

large samples, however, attenuation variations will cause problems.

To eliminate this problem and to eliminate the need to dry and crush soil samples,

and thus significantly decrease sample processing time, the technique described in this

paper is an absolute technique. That is, this technique does not compare unknown samples

to known standards to determine elemental concentrations. This technique can be used

on unprocessed samples which may be inhomogeneous. The teclmique also provides a

quantitative measure, in the form of a X2 value of statistical significance, of whether the

sample is too inhomogeneous to be analyzed without prior processing.



Technique Description


Figure 5 shows the source-target-detector geometry used for this XRF analysis tech-

nique. In this configuration, the target is exposed to excitation gammas from the source and

emits fluorescent x rays which are seen at the detector. The detector is shielded from direct

exposure to the sources by the Pb and W source holder. The spectrum seen by the detector

























FIGURE 5
Source Target Detector Physical Geometry










TARGET


POINT
SOURCE


POINT
SOURCE


DETECTOR









is composed of gammna rays from the source which have backscattered in the target and hit

the detector, and of fluorescent x rays from the U and/or Th in the soil. The number of

fluorescent x rays counted by the detector is proportional to the U or Th concentration in

the target. In overview, the assay technique is quite simple.

The target can be thought of as many small point sources. The fluorescent x rays

produced at each point source contribute separately to the the full energy photopeak of

Ka, x rays seen by the detector. A mathematical model of each point source is used to

calculate the x-ray contribution from each point source. These calculated individual point

source contributions can be summed to yield a calculated total detector response. The

calculated response is then compared to the actual measured response, in a least squares

sense, to determine the contamination concentration in the target sample.


Mathematical Model

All of the equations in this section stem from well known first principles. To begin

with, it is well known that the excitation gamma ray flux (FL) that reaches a point in the

target can be described by



ER(E)
FL(E) = 4ER x exp(-/p(E)poR2), (2)




where




FL (E) = excitation gamma flux at a point in the
target, (gammas/cm2s),

ER (E) = source emission rate at energy E,
(gammas/s),








RI = distance from the source to the point, (cm),

pI (E) po = sample mass attenuation coefficient at
energy E, p (E) (gm/cm') times sample
density, Po (gm/cm3), and

R2 = that portion of the total distance that
lies within the attenuating sample, (cm).


The photoelectric reaction rate (RX) at the point, due to the above excitation gamma

flux, can be described by



RX (E)= FL(E)x PE (E) x x AD, (3)

where


RX (E) = photoelectric reaction rate at the point,
(reactions/s) / (pCi/gm of dry soil),

FL (E) = excitation gamma flux at a point in the
target, (gammas/cm2s) ,

PE (E) = photoelectric cross section for U or Th at
energy E, (cm2/atom),

V = volume of the point source, (cm3),

AD = atom density of U or Th,
(atoms/cm3of soil) / (pCi/gm of dry soil),

= .037 (dis/s) / (pCi) x x p,,

and:



.037 = the number of disintegrations per second
per pCi of activity,








A = disintegration constant for U or Th,
(s-1),

Note : the units of .037 A are
(atoms/pCi), and

p, = soil bulk density,
(gm of dry soil)/ (cm3 of soil).


The fluorescent yield (FY) at the point, due to the above photoelectric reaction rate,

can be described by


FY (E',E) = RX (E) x KS (E) x KY (E'),


where


FY (E', E) =


the flux of fluorescent x rays of energyE' at
the point, that are caused by excitation gammas
of energy E,
((Ka, x rays) /s) / (pCi/gm of dry soil),


RX (E) = photoelectric reaction rate at the point,
(reactions/s) / (pCi/gm of dry soil),



KS (E) = fraction of photoelectric reactions that result
in K shell vacancies,
(K shell vacancies) / (photoelectric reaction),
= (Rk- 1)/Rk



Rk = K shell Jump Ratio, and

KY (E') = fraction of K shell x rays that are K&I
x rays, (K~1 x rays) / (K shell x ray).








The flux at the detector (FD), of the Ka~ x rays that hit the detector, due to the above

x-ray fluorescent yield, can be described by



FDE' FY (E',E)x DA
FD (E) = DA x exp(-p (E')por2),
4irr?

where


FD (E') = the flux of fluorescent x rays of energy E' that
hit the detector,
((Ka1 x rays) /s) / (pCi/gm of dry soil),

FY (E', E) = the flux of fluorescent x rays of energy E' at
the point, that are caused by excitation gammas
of energy E,
((Kai T rays) /s) / (pCi/gm of dry soil),

DA = detector area, (cm2) ,

rl = distance from the point to the detector, (cm),

p (E') x p = sample mass attenuation coefficient at energy
E', (gm/cm2), times sample density, (gm/cm3),
and,

r2 = that portion of the total distance that
lies within the attenuating sample, (cm).


It should be noted that this equation does not include any terms to account for small

angle scatter, and correspondingly small energy change, x rays which are mathematically

removed from the x ray beam but would actually still hit the detector and be counted in

the full energy peak. Looking at the geometry of the situation, the largest scatter angle

which would leave an x ray still traveling toward the detector is ten degrees. Integrating

the Klein-Nishina differential scattering cross section (Evans6 pp 677-689) over 27r, for do,

and over ten degrees, for dO, the ratio of this to the total scattering cross section is .029.








Considering that ten degrees is the upper bound for scatters which will still hit the detector,

this 3% error can be ignored.

As evidence of this, if small angle scatter were a significant contributor to the total peak

area, peaks would be broadened on the low energy side of their centroids and would not be

well described by the peak fitting equations shown earlier. Data in Chapter III shows that

the measured peaks are fit very well by the previously described peak fitting equations. As

such it is concluded that small angle scatter of x rays is not a significant problem and need

not be accounted for here.

Finally, the fluorescent signal (FS), the number of K,1 x rays that are counted in the

full energy peak at energy E', due to the above flux at the detector, can be described by



FS (E') = FD (E') x DE (E') x CT,

where


FS (E') = the number of counts in the full energy peak at
energy E', ie. peak area,
(Kai rays) / (pCi/gm of dry soil),

FD (E') = the flux of fluorescent x rays of energy E' that
hit the detector,
((K.a z rays) /s) / (pCi/gm of dry soil),

DE (E') = the detector intrinsic energy efficiency at
energy E',
(x rays counted) / (x ray hitting the detector),
and,

CT = total counting time, (s), corrected for pulse
pileup as described in a subsequent section.


This equation can also be written in the following more useful form











DR, (E') = GF (E'),

where


DR, (E') = detector response at energy E' to point
node i,
(counts/s) / (pCi/gm of dry soil),

GF, (E') = FD (E') x DE (E') x CT,

= geometry factor at energy E' for point
node i,
(counts/s) / (pCi/gm of dry soil).


The above equations are a mathematical description of the fluorescent x ray flux,

counted by a detector, due to a single point target irradiated by a point excitation source.

Looking at equation 3 more closely, the term AD, atom density of U or Th at the point

node, is in units of (atoms/cm3 of soil)/(pCi/gm of soil). The geometry factor, GFT, is

thus normalized to a contamination concentration at the point node of 1 pCi/gm. And the

detector response to a point node contaminated to any concentration, C pCi/gm, is a linear

function of the geometry factor.

Since both DR, (E') and GFC (E') are "per pCi/gm of dry soil", the detector response

to a point node contaminated to a concentration of "C" pCi/gm, would be



DR, (E') = C x GF (E'),
where

DR, (E') = FS (E')
= detector response at energy E' to point
node i,
(counts/s) / (C pCi/gm of dry soil),









C = contamination concentration at point
node i, pCi/gm of dry soil,

GFj (E') = FD (E')x DE (E') x CT,
= geometry factor at energy E' for point
node i,
(counts/s) / (pCi/gm of dry soil).


If a large target of uniformly distributed contamination, with a concentration of C

pCi/gm, were broken into nodes small enough to approximate point nodes then the fluo-

rescent x rays from each point node could be calculated by the above equations assuming

that the source target detector geometry was sufficiently well described. The total signal

from the large target and seen at the detector would then be the sum of the signals from

each of the target point nodes. The detector response could then be modeled as the sum of

all the point node geometry factors.



DR = C x GFI,

where


DR = the photopeak area as measured by a
detector, (counts/s),

C = the uniformly distributed concentration
of contamination in the target,
(pCi/gm of dry soil), and

GFi = the calculated geometry factor for
point node i,
(counts/s) / (pCi/gm of dry soil).









These equations thus make up a mathematical model of a physical situation. The

model can be experimentally verified by calculating all the nodal Geometry Factors, GFj,

for a particular geometry and then making an actual measurement of the signal, DR, from

a target in that geometry. The sum of the geometry factors, referred to hereafter as the

"target geometry factor", times the contamination concentration in the source should equate

to the signal seen at the detector. This model can then be used to assay unknown target

samples. The unknown contamination concentration of a sample is given by



DR
C=
SGFi'

where all terms are as previously defined.

This equation is thus the basis for target sample assay. Figure 6 shows the spatial

relationships of the source, target, and detector that were used to experimentally verify the

mathematical model.

To further verify the model and to provide a better assay of the target, each target is

measured in more than one geometry. This is accomplished easily by varying the target to

detector distance between measurements. A graph of detector response vs target geometry

factor is closely approximated by a straight line



DR(P) =C x GF(P),

where


DR (P) = fluorescent signal seen at the detector
from a target at position P,
(counts/s),

C = contamination concentration in the
target, pCi/gm,


























FIGURE 6
Source Target Detector Spatial Geometry









Target Cylinder
Center


Y Z


Detector Point Source
Center
@ Origin -





Point Source









GF (P) = target geometry factor, or, the sum of
all point node geometry factors for a
target located at position P,
(counts/s) / (pCi/gm).


Using the contamination concentration, C, as the fit parameter, the data collected from

measurements made at several different geometries is then least squares fit to the above

equation. This yields a value for C, the contamination concentration in the target sample,

which is the desired result of the assay.


Compton Scatter Gamma Production of Fluorescent X Rays

The fluorescent x-ray production described by the previous equations is due to unscat-

tered source gammas undergoing photoelectric interactions in the target. Since the target is

thick, gammas will also Compton scatter. If the scatter angle is small enough, the scattered

gamma will still be of sufficient energy to undergo a photoelectric interaction in the sam-

ple and produce more fluorescent x rays. As will be discussed in the experimental results

section, approximately 15% of the fluorescent x rays produced are due to singly Compton

scattered gammas. It is therefore important to calculate this production term and include

it in the model.


Compton scatter gamma model

Qualitatively, Compton scatter gamma production of fluorescent x rays is due to ex-

citation source gammas which undergo a single Compton scatter interaction at point A

in a target, change direction and energy, and then undergo a photoelectric interaction at

point B in a target. Quantitatively, this is slightly more complicated to describe. Consider

two target points, A and B, as shown in Figure 7. Using equations similar to those used

previously, the flux at scatter point A is calculated, the scatter flux and gamma energy of









gammas which are scattered toward point B are calculated, the photoelectric reaction rate

and fluorescent x-ray production at point B are calculated, and the number of fluorescent

x rays which are counted by the detector is calculated. In a fashion similar to that used

previously, the microscopic calculations for each point in a large target are summed into

the macroscopic total fluorescent x-ray production due to Compton scatter gammas.



Mathematical model

Looking at Figure 7, the excitation gamma flux at point A is given, again, by Eq. 2



ER (E)
FLI (E) = ER-(E x exp (-MP(E)poR2),

where




FL1 (E) = excitation gamma flux at a point in the
target, (gammas/cm2s) ,

ER(E) = source emission rate at energy E,
(gammas/s),

R, = distance from the source to the point, (cm),

p (E) po = sample mass attenuation coefficient at
energy E, p (E) (gm/cm2), times sample
density, Po (gm/cm3),

R2 = that portion of the total distance that
lies within the attenuating sample, (cm), and

E = energy of the incident gamma.


The flux that arrives at point B is dependent upon the flux that arrives at point A,

and on the differential Compton scatter cross section for scatter through an angle 0. The


























FIGURE 7
Compton Scatter Spatial Geometry







R sin


in 0 6d


X AXIS


d4
INCIDENT









Klein-Nishina differential scatter cross section, in units of (cm2/electron) / (dl), is given

by (Evans6 pp 677-689)



doa = rx X do x [- -],


where


do = differential cross section,
(cm2/electron) ,

ro = classical electron radius, (cm),

d2 = sin (0) dOdo


and


0 = gamma ray scatter angle with respect
to the original direction of motion,

S= rotational angel about the original
direction of motion,

[. ] = terms from equation, see reference 6 (pp 677 689).


Using these two equations, the reaction rate for gammas scattering at A into the solid

angle dil about 0, in other words towards B, is given by



RX = FL1 (E) x do x EDens x Vol,

where


RX = scatter reaction rate, (scatters/s),

FLi (E) = flux of excitation gammas at point A,
(gammas/cm2s) ,









dr = Klein Nishina differential scatter cross
section, (cm2/electron) ,

= r, x dfx x [...]

EDens = electron density at point A, (electrons/cm3) ,

Vol = volume of point A, (cm3).


The energy of the scattered gamma is given by (Evans6 pp 677-689)



,! mo c2
1 cos(0) + (/a)'

where


E' = energy of the scattered gamma, (keV),

0 = scatter angle,

mo c2 = electron rest mass,
= 511keV,

E
m0 c2

E = energy of the incident gamma, (keV).


The flux at point B due to Compton scatter at point A is then described by



RX
FL2 (E') = si( exp (-P Po X),
X2 sin (0) d~do

where


FL2 (E') = flux at point B due to Compton scatter
at point A, (gammas/cm2s),

E' = energy of scattered gamma, (keV),

RX = scatter reaction rate, (scatters/s),









exp (-p Po X) = attenuation factor for
gammas passing through soil,


and


pt = soil attenuation coefficient
at energy E',

p = soil density, (gm/cm3),

X = distance from point A to
point B, (cm),

X2 sin (0) dOdO = surface area through which
garmnas, scattered at point
A into d2 about 0,
pass upon reaching point B.


But since the reaction rate, RX, contains the term do which contains the term sin(0)

dO do, this will cancel out of the numerator and denominator leaving



FL1 (E) x r2 x [* ] x EDens x Vol
FL2 (E') = X exp (-p X),


where all terms are as previously defined.

Knowing the flux at point B and the energy of the incident gammas, allows the calcu-

lation, using the equations described in the previous section, of the photoelectric reaction

rate at point B due to scatter in point A, the fluorescent x-ray production rate at point B

due to scatter in point A, the x- ray attenuation from point B to the detector due to scatter

in point A, and the number of fluorescent x-rays from point B due to scatter in point A

counted by the detector. To determine the entire production of fluorescent x rays at point

B, scatter from every other point node in the target that results in gammas reaching point

B must be calculated. A summation of all these contributions yields a Compton Geometry








Factor for point B, analogous to the Geometry Factor calculated in the previous section for

unscattered gammas. The result of these equations is a summation equation completely

analogous to that derived in the previous section



CDR, (E') = C x CGFi (E'),

where


CDRi (E') = detector response at energy E'
to Compton scatter production at point
node i,
(counts/s) / (CpCi/gm of dry soil),

C = contamination concentration at point
node i, (pCi/gm of dry soil),

CGF, (E') = Compton geometry factor at energy E'
for point node i,
(counts/s) / (pCi/gm of dry soil).

As before, the contribution from each point node of a large target could be summed to

yield the total calculated detector response due to Compton scatter gamma production. The

Compton scatter production portion of the detector response cannot, however, be measured.

Actually the measured detector response is the sum of fluorescent x-ray production due to

unscattered excitation gammas and Compton scattered excitation gammas, and these two

contributions cannot be physically separated. The solution is to alter the model such that

the measured detector response is modeled as being the sum of the unscattered gamma

Geometry Factors and the Compton scattered Geometry Factors


DR. (E') = C x (GFi (E') + CGF, (E')),


where all terms are as previously defined.








Then, for a large target of uniform contamination concentration C pCi/gm of dry soil,

the detector response is modeled as



DR = C x (GF, (E') + CGF, (E')),

where


DR = the photopeak area as measured by a
detector, (counts/s),

C = the uniformly distributed concentration
of contamination in the target,
(pCi/gm dry soil),

GFi = the calculated geometry factor for
point node i,
(counts/s) / (pCi/gm of dry soil),

CGF, = the calculated Compton geometry factor
for point node i,

(counts/s) / (pCi/gm of dry soil).


This set of equations then constitutes a mathematical model of the fluorescent x-ray

production due to unscattered gammas and Compton scatter gammas. As stated before,

the desired result of the assay, the value of C, could theoretically be calculated using only

one measurement made in one geometry. In this work, multiple measurements are used to

achieve a more statistically significant answer. As discussed earlier, this model is verified

by actual measurements of targets in several known geometries. As will be discussed in the

results section, the model is in very good agreement with actual measurements.









Electron density

The electron density used above is a parameter which will vary from sample to sample

due to changes in density, elemental makeup, and water content. Electron density must

therefore be calculated for each sample. This is accomplished in a simple fashion using the

transmission measurement described earlier.

The total linear attenuation coefficient is made up of an absorption coefficient, a pair

production coefficient, a Compton scatter coefficient, and a coherent scatter coefficient.

A conversation with John Hubble of the National Bureau of Standards and a follow-up

computer study indicated that for various soils, the ratio of Compton scatter coefficient

to total linear attenuation coefficient is approximately constant for a given energy gamma.

Appendix A details the computer study done to verify this and to arrive at an appropriate

average Compton to total ratio. Knowing this ratio, the measured total linear attenuation

coefficient can be used to calculate the electron density as follows



cale = CTR x Iea"'

where



aelc = calculated Compton linear attenuation
coefficient as ratioed from the total
linear attenuation coefficient, (cm-'),

pnea = measured total linear attenuation
coefficient, (cm-), measured as
described in a previous section,

CTR = ratio of Compton linear attenuation
coefficient to total linear attenuation
coefficient,









but




Fi"le = EDens x a K-N


where


EDens = soil electron density, (electrons/cm2),

,-N" = Klein Nishina Compton scatter cross
section, (cnm2/electron).


therefore



eale
Cate
EDens- = -
o-K-N


where all terms are as previously defined.



Natural Production of Fluorescent X Rays


Since progeny of both U-238 and Th-232 emit U and Th x rays (see tables 1 and 2) the

natural x-ray production rate was also calculated. As will be seen in the results section,

this term contributed less than 1% to the total fluorescent x-ray production.

The decay chains of U-238 and Th-232 are very similar. In both cases, the parent alpha

decays to the first progeny, the first progeny beta decays to the second progeny, and the

second progeny beta decays to the parent element with an atomic weight four less than that

of the parent. As the second progeny decays, the beta is emitted leaving the meta-stable

decayed atom looking very much like a parent atom with one extra electron. During the

complicated events that follow beta decay, the decayed atom emits x rays that are of energy

characteristic of the parent atom.









In the case of U, U-238 alpha decays to Th-234, which beta decays to Pa-234, which

beta decays to U-234. As the Pa-234 decays to U-234, U x rays are emitted. ICRP report

#3819 gives the emission rate of these x rays as 0.00232 Ka,/decay.

In the case of Th, Th-232 alpha decays to Ra-228, which beta decays to Ac-228, which

beta decays to Th-228. As the Ac-228 decays to Th-228, Th x rays are emitted. ICRP

report #3819 gives the emission rate of these x rays as 0.0428 K,1/decay.

Since natural decay production of x rays contributes so little to the total production,

the assumptions that Th-232 is in equilibrium with Ac-228, and that U-238 is in equilibrium

with Pa-234 will introduce little error. As such, one pCi of Th-232 will be in equilibrium

with one pCi of Ac-228, and one pCi of U-238 will be in equilibrium with one pCi of Pa-234.

The production rate of U and Th x rays can now be calculated.

For thorium




K,,yield= (0.0428 Ka x (0.037 decay/s
Sdecay) pCi Th 232 '
= 0.001584 K s
pCi Th 232

For uranium




Klyield = 0.00232 Kdeci 0 .037 decay/s
decay) pCi U 238 /
= 0.00008584 K, i/
pCi U 238

These terms are in the correct units to be added directly into the previously described

mathematical model at the point where fluorescent x-ray production in each point node is

calculated. With this small correction added, the mathematical model is complete.









Isotopic Identification




As mentioned earlier, the two isotopes which are of principle interest for this assay

technique are U-238 and Th-232. In fact, these are the only two isotopes of U and Th

which can be seen at small concentrations using XRF. This is because XRF is dependent

upon the number of atoms present. In the cases of other U or Th isotopes, tremendously

high numbers of curies would have to be present before there would be enough atoms of

these isotopes to be seen by XRF. This is due to the very long half lives of U-238 and Th-232

with respect to their other isotopes, since the number of curies is equal to the number of

atoms times the decay constant. Table 8 illustrates this point.


The sensitivity of the experimental setup tested in this work is approximately 50 pCi/gm

of Th-232, which corresponds to 500 ppm. The system sensitivity then, in terms of number

of atoms required, is approximately 500 ppm. The table clearly shows that huge quantities,

in terms of pCi/gm, of all the isotopes except U-238 and Th-232 would be required to reach

concentrations 500 ppm. Since these huge concentrations are rarely seen, and since one of

the objectives of this assay system is to achieve a low sensitivity in terms of pCi/gm, it can

be concluded that this XRF assay technique cannot be used for U and Th isotopes other

than 238 and 232 respectively.
TABLE 8
Isotopic Concentrations: PPM vs. pCi/gm
Concentration Concentration
Isotope (ppm) (pCi/gm)
U-238 500 168.1
U-235 500 1.081E3
U-234 500 3.125E6
Th-232 500 54.65
Th-234 500 1.158E13
Th-230 500 1.009E7
Th-228 500 4.098E11









It is also reasonable to conclude that all U and Th seen by XRF is U-238 and Th-

232 respectively. Based on the above table, such large quantities of other isotopes would

be required before these isotopes could be seen by XRF, the radiation levels of the sources

would be too large for analysis using sensitive Ge detectors. It is also extremely unlikely that

such large quantities of other isotopes would be found. Even if U-238 were in equilibrium

with Th-234, U-234, and Th-230, or if Th-232 were in equilibrium with Th-228, while the

curie contents of the sample would be high in these other isotopes, the ppm concentrations

of these other isotopes would be much to low to register using XRF. It would thus be safe

to assume that all of the signal seen at the detector was from U-238 or Th-232.

Prior knowledge of the nature of the process which lead to the contamination might

point toward high concentrations of other isotopes. For example, excavation near a plant

which previously processed Th-230 to remove Ra-226 would be expected to show high Th-

230 levels and natural Th-232 levels. Again though, unless the Th-230 levels were extremely

high, XRF would not be of any use.

Unfortunately then, this XRF technique is not useful in determining the concentrations

of isotopes other than U-238 and Th-232. If it were known that the contamination in

question was primarily U-238 and/or Th-232, progeny equilibrium with U-238 and Th-232

could be assumed thus establishing an upper limit of other isotopic concentrations. This

would not, however, constitute an adequate assay unless the upper limit were below some

lower bound of regulatory concern.

However, the analysis technique used, that is measuring the attenuation properties of

the sample at the energies of the gamma rays of interest, and the calculation of geometry

factors, could be applied to gamma spectroscopic techniques or to neutron activation anal-

ysis techniques to improve their accuracy. This work is, however, beyond the scope of this

project.









The value of this technique is that it measures U-238 and Th-232 directly and without

relying on equilibrium with progeny. Neutron activation and its associated neutron source

was previously required to achieve this independence.



Error Analysis



Introduction


A soil contamination assay must be accompanied by an estimate of the error associated

with the measured contamination concentration. The assay system presented in this work

is based on fitting measured data to mathematical models using the least squares technique.

Least squares analyses lend themselves well to propagation of error from one curve fit to

the next, as well as to calculation of the chi-squared test statistic as a measure of goodness

of fit.

This work begins with measured spectral data and the error associated with each data

point. This data is fit to a mathematical model of an x-ray peak as viewed through a Ge

detector, and the peak parameters are determined. These parameters are used to determine

the area of the peak and the error associated with the peak area. This operation is repeated

for several different target configurations yielding several peak areas and their associated

errors. These areas are then fit to a mathematical model which predicts the detector

response as a function of target geometry and contamination concentration. The only

fitting parameter of this model is the contamination concentration in the target, which

is calculated by least squares fitting the previously calculated peak areas to the modeled

function. The error in the fitting parameter is extracted from the least squares fitting

process and the desired result, determination of the soil contamination concentration and

its associated error, is achieved.









Least Squares Peak Fitting

The least squares fitting technique is fairly simple and is described in numerous books

and articles. The mathematics used in this work was taken from Forsythe et al.20 This

technique was used in this work to properly determine the spectral peak areas and their

associated errors.

Least squares fitting is an iterative technique based on minimizing the square of the

difference between a measured value and a value calculated based on a mathematical model.

The minimization is performed by properly choosing the parameters of the mathematical

model. The model may be linear in these parameters or non-linear. Each successive iteration

refines the fitting parameters such that the sum of the squares is minimized. To begin, the

mathematical model is chosen. An initial guess as to the fitting parameters is also required.



F (XY : P1, P2, P3,..., Pn), = Yi,

where

Xi = independent variable,

Pn = fit parameters of the mathematical model,

1i = dependent variable.

Note: the "1" indicates that the fitting parameters are the current guess. The previous guess,

or for the first iteration, the initial guess, will be used to determine the new, or current,

guess.


Using current guess as to the fitting parameters, the sum of the squares of the difference

between the measured values and the calculated values is calculated.


S = (F (X), -- y)2








where


S = sum of squares,

F (X), = ,

= calculated dependent variable based
on current fittingparameters,

yi = measured dependent variables.


To mininiize this equation


dS dS dS dS
dPI dP2 dP3 dPn

This creates a set of "n" independent equations each looking

like this


dS dF (X)
dP1 = 2 x (F (X)i yi x dP1 -0,

where

F (Y,), = F(X,: PL1,P21, P31,...,Pn).

This equation is mathematically correct, however only the initial guess parameters are

known at this point. Fortunately F (X,), can be approximated by a Taylor expansion,

truncated after the first order terms, knowing 1. the values of F (Xi)o which are based on

the previous best guess of the fitting parameters, and 2. the function partial derivatives at

each X,

dF (X,)o
F(X,)l = F (X1)o + (P11 Plo) x

dF(X,)o dF(X,)o
+ (P2, P2o) x d + (P31 P3o) x dP
dP2 dP3
dF (Xi)o
+ ... (Pni Pno) x d
dPn









where all terms are previously defined.


Substituting this into the least squares minimization equation yields



dS dF(X-)o dF (X,)o x (F(X) y,)= ,
dP1i dp1 x ["] + dP xF() -=0


where


[* ] = DP1 x d ) + DP2
dP1


dF (X,)o dF (X )o dF (X,).
x + DP3 x o+ + + DPn x
dP2 dP3 dPn '


DPn = Pnl Pno.


This can be rewritten as



dF(X,)"o dF (X,)
dF x [**) ] = Z (XP x (y, F(X,)o).



As previously stated, similar equations are generated for each differential equation


dS
dPI


dS dS
=-0, 0 ..." = 0.
dP2 dPn


This system of equations lends itself to the matrix form




DFt (n, m) x DF (m, n) x A (n, 1) = DFt (n, m) x DY (m, 1),


where


DF(m,n) =


/ dF(X,)
dP1
dPI

dPF(X)o
SdP1


dF(XI)o
dP2
dF(X2 )
dP2

dF(X )o
dP2


dF(X1)o
dP3
dF(X2)0
dP3

dF(XPm)
dP3


. dPn
S. dPn


dF(X), P
dPn


DFt (n, m) = the transpose of DF (m, n),


n = the number of parameters in the fitting function,


m = the number of data points used in the fit,








/ (Pl, P10o) \
(P21 P2o)
A(n,1)= (P31 P30)

\(Pn Pno)
/(y, F(X,)o)
(y2 F (X2)0)
DY(m, 1)= (Y- F (X)o)

\(ym F (X-)0)
This matrix equation is solved by Gaussian elimination to yield the values of the A (n, 1)

matrix. These values are used to update the parameter guesses from the initial guesses of

Plo, P20, ..., Pno, to P11, P21, ..., Pni, since Pil = Pio + A (i, 1). New values of F (X,)

are calculated based on these new parameters, these new parameters become the "initial

guesses" for the next iteration, and the matrix solution is repeated. This iteration process

is continued until the sum of squares is "minimized" based on some predetermined cutoff

criteria. The result of the minimization is the calculation of the "best" fitting parameters

for the mathematical model.


Covariance Matrix and Functional Error

As a by-product of this method, the variances and covariances of the fitting parameters

are calculated. The inverse of the matrix product, DFE x DF, is defined as the covariance

matrix 20



(DF' (n, m) x DF (m, n))-1 = Covar (n, n).

The diagonal values of this matrix, Covar(i,i), are the variances of the model fitting

parameters.











Covar (1,1) = 02 (P),

Covar (2, 2) = o2 (P2),

Covar (3,3) = '2 (P3),




Covar (n, n) = 2 (Pn).

The covariance matrix is diagonally symmetrical, with the off diagonal elements being

the covariances of the various parameters, for example

Covar (1, 2) = -2 (P1, P2).

These values are used to calculate the errors associated with fitting parameters at

various stages of determining the final solution, the soil contaminant concentration and its

associated error. But in addition to knowing the errors associated with fitting parameters,

the errors associated with functions of those fitting parameters are necessary. For this

work, only linear functions of fitting parameters are used. The error associated with a

linear function of fitting parameters is given by the following equation20



if: F(X : P1,P2,P3,...,Pn),

where : PI, P2, P3, ..., Pn and their associated errors
are known,

then for: Q (X : P1, P2, P3,..., Pn),
n nL
'2 (Q (X,)) = Pi2 x (Pi)+ Pi x Pj x Covar (Pi, Pj). (4)
i=l ,i=-1
This equation and the covariance matrix as determined via the least squares process

described here are all that is needed to properly propagate error through the peak fitting

portion of this work.









Error Propagation


The various stages of the assay analysis have all been thoroughly described. This section

will describe how error is propagated through these calculations.

To begin with, a spectral peak is collected. The error associated with each spectral

data point is







The first manipulation performed on this data is the calculation of the background

beneath the x-ray peak being analyzed. This calculation is performed in two steps. First, a

polynomial background (POLYBK) is calculated using data points to the right and left of

the peak. These points are least squares fit to a fourth order polynomial yielding the best fit

and a covariance matrix. Using the covariance matrix and Eq. 4, the error associated with

each calculated data point is determined, Var(POLYBKi). Second, the "complimentary

error function (erfc)" background (ERFBK) is determined. This is a numerical process, the

error associated with each of these points is estimated to be



0.2 (ERFBKS) = ERFBKj.


The two backgrounds, polynomial and erfc, are assumed to each contribute equally to

the complete background, thus the complete background is equal to




POLYBK, + ERFBKj
BKi =
2

and,

o 2 (BKi) = C2 (POLYBKI) + o2 (ERFBKi).









The next step in the analysis is to subtract the background from the spectral data

(SPEC) to yield an estimated peak. The variance associated with each of the peak points

is then




0.2 (PKi) = 02 (SPECi) + .2 (BKi).


The peak is then least squares fit to a Voigt peak shape, yielding the covariance matrix

for this process. Equation 4 is then used to calculate the error associated with the numeri-

cally calculated peak area. These steps are repeated for several geometric configurations of

the soil sample target yielding several peak areas and their associated errors.



Linear Function Fitting


Once the peak areas and their associated errors have been determined, the last step

of the assay is to determine the concentration of contamination in the sample jar and its

associated error. As described earlier, the measured detector response is a linear function

of calculated GFs, the slope of this line being the concentration of contamination in the

sample jar. The measured detector response data, the error associated with this data, and

calculated GFs need only to be fit to a linear function to determine the desired assay result.

Easier still, the fitted line must pass through the origin since if the calculated GF for a

sample were zero, the measured detector response would also have to be zero. This sort of

statistical data fitting is common to most introductory statistic books. The treatment used

here is from handouts prepared for a statistics class at Cornell University 21

For any linear function of X,




Y = x F (X),
a=1









where


aa = the ath of m fitting parameters,

F. (X) = the a'h of m linear functions of X,


then the values of the fitting parameters a, are given

by,



Em E= I" F.F (XY)a
ai = )H (a, i),
a. 0"-2

where




H-1 (i, i) = the covariance matrix,

ab = the standard deviation of
detector response b,
and,

-1i,j)= E= F, (X,) Fj(X)
a .

For a simple function such as DR = C x GF, where C is the unknown fitting parameter

al, = DR, X = GF, and Fi (X) = X = GF, these equations are extremely easy to solve

and yield the desired result of this analysis, the value of C. The error in the value of C is

also quite simple.



a' = H-1 (ii).

This then yields the desired result of this analysis, the soil contamination concentration,

C, and its associated error.









Experimental Procedure



Sample Counting


Once the experimental apparatus is constructed and properly calibrated, as described

in Appendix A, the processing of samples is straight forward and requires only eight steps.


1. Samples are placed in 100 ml plastic jars and weighed. The soil may be wet and not

completely uniformly mixed. The sample jars are of radius 2.32 cm with an active

height of 6.50 cm.

2. The sample is weighed, wet or dry in the jar, and the average jar weight, 20.7 0.1

gm, is subtracted to obtain the sample weight.

3. The sample jar is placed in a known geometry above a Ge detector, described in detail

in Appendix A, such that the center of the sample is directly in line with the center of

the detector. In this work, the jar center is 11.6 0.1 cm from the detector window,

and the detector window to detector distance is 0.5 cm.

4. A Co-57 source is placed directly in line with the center of the detector such that the

sample jar is between the source and the detector. The source to detector window

distance is 89.4 0.2 cm. The transmitted fraction of 136 keV and 122 keV gammas

from Co-57 is then measured. Count duration is dependent upon source strength. In

this work, count times of one hour are used. Shorter times could be used by placing

the source closer to the detector such that the detector system dead time remained

below 20% or so, and the total counts under the peaks in question were statistically

significant. In this work, peak areas are on the order of 100,000 counts.

5. The Co-57 source is replaced with an Eu-155 source and step three is repeated, mea-

suring the transmitted fraction of 105 keV and 86 keV gammas from Eu-155. The









transmission fractions are then used to calculate the sample linear attenuation coeffi-

cients as described in a previous section.

6. The next step is sample XRF analysis. The sample is placed such that the center of the

sample is again directly above the center of the detector. The source holder and sample

holder assemblies are shown in exploded view in Figure 8. Figure 9 shows the sample in

its holder positioned above the detector and above the source holder shield. Using the

center of the detector as the origin of an X-Y-Z coordinate system, the sample center

is located at coordinate (10.5 0.1 cm, 0.0 cm, 0.0 cm). Figure 10 shows the sample

in position and the laser alignment beam used to ensure that it is properly centered.

The source holder, described in detail in Appendix A, holds two sources located in the

X-Z plane formed by the long axis of the sample bottle and the detector center. The

sources are located at coordinates (4.42 0.01 cm, 0.0 cm, 4.42 0.01 cm) and (4.42

0.01 cm, 0.0 cm, -4.42 1 0.01 cm).

Once the sample is properly positioned, the sources are placed in their holders and the

sample is irradiated for one hour. In this work, fluorescent x-ray peaks ranged in area

from 20,000 counts to 1,500,000 counts depending upon the U or Th concentration in

the samples. Figure 11 shows the multichannel analyzer system used to collect spectral

information. Figure 12 shows a typical spectrum on the MCA.

7. For the next seven counts, the sample is next raised 0.3 0.01 cm and step six is

repeated. The yields a total of eight counts with the sample center being at 10.5, 10.8,

11.1, 11.4, 11.7, 12.0, 12.3, and 12.6 cm from the detector. The detector and XRF

excitation sources remain in fixed positions for all eight counts.

8. Finally the sample is dried, if necessary, in an oven or a microwave and weighed again.

The dry soil weight and soil moisture fraction are thus determined.

























FIGURE 8
Exploded View of Target Holder Assembly








































l I I


C~1 :~ :a
"~
'?1


? .. l


i l

























FIGURE 9
Target in Place Above Detector





79
































f
l i



i JW

























FIGURE 10
Target in Place Above Detector
Showing Laser Alignment System






























































































































































































































































































































I
























FIGURE 11
ND-9900 Multichannel Analyzer, ADC,
Amplifier, and Detector Power Supply






































Ai a

























FIGURE 12
Typical XRF Ka Peak on MCA




Full Text
181
5340 NEXT C
5380 NEXT R1
5390 PRINT
5460 NEXT R
6000 SU = 0
6010 M2 = M 1
6020 DA(M) = (AM(M,MD) / (AM(M,M))
6040 FOR R = 1 TO M2
6060 RP = M R
6070 M3 = M RP
6080 FOR C = 1 TO M3
6100 SP = Ml C
6120 SU = SU + AM(RP,SP) DA(SP)
6140 NEXT C
6160 DA(RP) = (AM(RP.Ml) SU) / (AM(RP,RP))
6180 SU = 0
6200 NEXT R
6203 FOR I = 1 TO M
6204 FOR J = 1 TO M + 1
6205 AM(I,J) = 0
6206 NEXT J
6207 NEXT I
6220 RETURN
6490 REM
6492 REM This subroutine creats the matrices necessary to solve the
6494 REM the equation described in the previous subroutine. This
6496 REM subroutine calls the previous subroutine
6498 REM
6500 W = N
6510 FOR I = 1 TO M
6520 FOR J = 1 TO N
6530 Q2(I,J) = TA(I,J)
6540 NEXT J
6550 NEXT I
6560 FOR I = 1 TO N
6570 FOR J = 1 TO N
6580 Q1(I,J) = W(I,J)
6590 NEXT J
6600 NEXT I
6610 GOSUB 4500
6620 FOR I = 1 TO M
6630 FOR J = 1 TO N
6640 TA(I,J) = q3(I,J)
6650 NEXT J
6660 NEXT I
7000 W = M
7010 FOR I = 1 TO M
7020 FOR J = 1 TO N


TABLE 35
Peak Fit Results for Sample 2
Sample Contamination Concentration: 93.6 pCi/gm Th232
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
264562 1.1%
56.9
2
240029 1.0%
37.7
3
212015 1.0%
31.8
4
199047 0.6%
13.2
5
166260 0.6%
11.1
6
148666 0.9%
35.1
7
127251 1.0%
24.4
8
115378 0.6%
5.9


100
TABLE 16
Measured vs. Fitted Detector Response for
USD
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 138.9 pCi/gm E/238
Reduced X2 Value for Fitted Data : 0.264
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.421
58.4
54.9
2
0.371
51.5
51.9
3
0.327
45.5
45.6
4
0.290
40.3
43.4
5
0.258
35.8
37.9
6
0.230
31.9
29.5
7
0.206
28.5
25.7
8
0.184
25.6
21.8


CHAPTER I
INTRODUCTION
In returning to school to pursue a Ph.D. in health physics, I knew that I would have to
complete an original research project and I knew that I wanted my research to be practical in
nature. I wanted to pick some existing process or procedure and inject it with SCIENCE
to facilitate its operation and improve its accuracy and precision. I stumbled upon such a
process in need of science during a summer working experience in 1983. After obtaining
a fellowship to go to Oak Ridge National Laboratory to develop an improved process, I
discovered that such a process would have a much more general application than I had
originally thought.
Soil Sample Assay for Radionuclide Content
The summer position that sparked this dissertation involved health physics work for
the Formerly Utilized Sites Remedial Action Program, known as FUSRAP. Begun in 1974,
FUSRAP is a Department of Energy (DOE) project to clean up 26 contaminated sites
within the United States. Twenty-two of the sites were formerly used during the Manhattan
Engineers District (MED) project in World War II. The other four sites are civilian and
were added by Congress in 1976.
Sites range from a contaminated floor drain at Lawrence Berkeley Laboratory to a
contaminated Th ore processing plant and several surrounding residential properties in
northern New Jersey, containing approximately 100,000 cubic yards of contaminated soil.
1


189
C
c *
C SUBROUTINE DISTANCE *
C *
c ******************************
c
SUBROUTINE DISTANCE(XI,Y1,Z1,X2,Y2,Z2,R1,R2,K1)
COMMON XT, YT, TR
Di = X2 XI
D2 = Y2 Y1
D3 = Z2 Z1
R1 = SQRT (D1*D1 + D2*D2 + D3*D3)
U = D1 / R1
V = D2 / R1
W = D3 / R1
X1XT = XI XT
Y1YT = Y1 YT
A = U*U + V*V
B = 2 U X1XT + 2 V Y1YT
C = X1XT X1XT + Y1YT Y1YT TR TR
R3 = ( B + SQRT (B*B 4 A C)) / (2 A)
IF (R3 .LT. O.O) GOTO 100
IF (R3 .LT. Rl) GOTO 500
100
R3 = ( B SQRT (B*B -
IF (R3 .LT. 0.0) GOTO 200
IF (R3 .LT. Rl) GOTO 500
4 A C))
/ (2 A)
200
WRITE(6,250)
250
FORMAT(/,IX,The Distance
K1 = 10
GOTO 1000
Calculation
is Screwed up!)
500
R2 = Rl R3
K1 = 1
1000
RETURN
END


149
from which any other needed points could be calculated. The system of 15 to 30 equations
could be developed with from four to ten measurements.
By solving this system of equations one can estimate the unknown concentrations in
each zone. By multiplying the concentration in each zone by its corresponding zone volume,
the number of pCi in each zone is found. Then, by summing the number of pCi in all zones
and dividing by the total mass of dry soil in the sample, the average concentration of U or
Th in the soil is found, pCi/gm of dry soil which is the desired final result of the analysis.
It should be noted at this point that this technique is similar to imaging techniques
used in early computer assisted tomography (CAT) or positron emission tomography (PET)
scanning. But both CAT and PET perform much more detailed scans of the object being
imaged, using pencil beams to view small tracks through the object being imaged. Then
many of these tracks are summed and processed to reconstruct an image of the original
object This work, instead, looks at radiation emanations from the whole object all at
once and develops a set of equations by looking at the whole object from several discrete
views. While this system of equations has no unique solution, all solutions will yield the
same value for the average concentrations of radionuclide in the object. And since the
average value is all that is needed, more complex imaging techniques are not necessary.
Thus while the radionuclide concentrations determined for each zone will probably not be
correct, tlieir average will be correct.
Reasons for Inhomogeneity Analysis Failure
Unfortunately, this analysis technique does not work. The system of eight equations
that must be solved to determine the contamination concentration in a soil target is very
close to singular and thus cannot be solved explicitly. The reason that the system is nearly
singular is that the equations are not fully independent. As will explained, the equations


251
C
C Data is now written into file SAMPLETH1.DAT
C
OPEN(1,FILE=*SAHPLETH1A.DAT,STATUS= *NEW *)
WRITE(1,(A3)) ELEMENT
WRITE(1,*) WF
WRITEd.O SD
WRITE(if*) A1
WRITE(1,*) 51
WRITE(1,*) Cl
WRITE(1,*) US1
WRITE(1,*) US2
WRITE(1,*) US3
CLOSE(1,STATUS=KEEP *)
END


21
C3= (1/8) (r/<7)2,
C4 (2/ttv^) (r/ B(X)= (-exp (-X2)) £(/(*)),
\ ^ ((exp(-n2/4))/n2)
Zl / W = Z Ti X (1 cosh (nX)) and
n=l
A" = new peak height constant.
This is a numerical equation in four unknowns; E, T, cr, and A". This equation
lends itself to weighted least squares fitting to the spectral data. The result of this fitting
will be values for the above four unknowns and their associated errors. Figure 2 shows
the Lorentzian distribution of the incident x rays, the Gaussian response function of the
detector system, and the resulting convoluted distribution that is the spectral x-ray peak.
It should be remembered that the objective of this exercise is to determine number of x
rays that hit the detector. As will be explained further in the section describing data analysis
and the section describing detector system calibration, the measured number of x rays will
be compared to the calculated number of x rays to determine concentrations of U and Th
in the soil. By properly calibrating the detector system, the area under the convoluted peak
will be proportional to the number of x rays that hit the detector. Determination of the
area of the convoluted peak is thus the desired end result of this peak analysis. Therefore it
should be noted that the Lorentzian x-ray distribution and the Gaussian detector response
function, shown in Figure 2, are for reference only and will not actually be seen in the
spectrum or have their areas calculated.
With the peak parameters determined, the peak area can be determined. Since the
convolution function is rather complex, the peak area is determined by numerical integra
tion. The peak shaping program defines the spectral peak as having a beginning channel
and an ending channel and performs the integration between these limits. Oidy a small


I would like to thank Dr. Mark Mercier, Nuclear Data Incorporated, who helped
introduce me to peak shaping and provided invaluable assistance in the development of the
peak shaping programs used in this work.
I would like to thank John Hubble, National Bureau of Standards, who as the God of
all Cross Sections provided me with the latest cross- sectional data and plenty of friendly
encouragement and expert advice.
I would like to thank Dr. Raymond Gunnink, Lawrence Livermore National Laboratory,
who provided me with the peak shaping program GRPANL and helped me to understand
the theory behind the program.
I would like to thank Dr. Wayne Ruhter, Lawrence Livermore National Laboratory,
who nursed me through the intricacies of GRPANL and analyzed several of my peaks to
verify my program.
I would like to thank Isabell Harrity of Brookhaven National Laboratory who provided
invaluable assistance, all the way up to the last minute, in getting this document prepared
using T^X.
I would like to thank Dr. Eric Myers who also provided last minute advice as to how
to get Tj7¡Xto do its thing.
Finally, I would like to thank Oak Ridge Associated Universities who provided me with
a Laboratory Graduate Research Fellowship so that I could work at Oak Ridge National
Laboratory for two years and complete this project.
v




67
where
5 = sum of squares,
m) i yu
calculated dependent variable based
on current fittingparameters,
yi = measured dependent variables.
To minimize this equation
dS dS dS _dS
dPl ~ dP2 ~ dPZ dpn "
This creates a set of n independent equations each looking
like this
dS
dPl
= £2x(m)i -1ft) x
dF(X)
dPl
where
F (X<)i ~ F : -P2x, P3l5..., Pni) .
This equation is mathematically correct, however only the initial guess parameters are
known at this point. Fortunately F (X{)1 can be approximated by a Taylor expansion,
truncated after the first order terms, knowing 1. the values of F(Xf)0 which are based on
the previous best guess of the fitting parameters, and 2. the function partial derivatives at
each Xi
n*i\
F {Xi)0 (-^It P\o) X
dF{Xt)0
dPl
+ (F2i P2q) X
dF(Xt) 0
dP2
+ (P3i P3o) X
dF(Xt) Q
dP3
+ + (Pni Pn0) X
dF(Xt) Q
dPn


209
C
C i*****************************
c *
C SUBROUTINE EXPLICIT *
C *
C i*****************************
c
C This subroutine determins the explicit solution
C to the linear regression:
C
C DR(I) = Zero + Slope X(I)
C
C The errors associated with the fitting parameters
C Zero and Slope are also calculated.
C
SUBROUTINE EXPLICITCX,Y,SIG,NP,F,SLOPE,ZERO,DS,DZ,CHISq)
REAL H(2,2), C0V(2,2), X(8), Y(8), SIG(8), F(8)
M = 2
H(l,l) = 0.0
C0V(1,1) = 0.0
DO 5 I = 1,NP
S H(1,1) = H(l,l) + (X(I) / SIG(I))**2
C0V(1,1) = 1.0 / H(l,l)
DO 7 I = 1,NP
7 SLOPE = SLOPE + C0V(1,1) Y(I) X(I) / (SIG(I)**2)
DS = SQRT(C0V(1,1))
ZERO = 0.0
DZ = 0.0
DO 9 I = 1,NP
F(I) = SLOPE X(I)
9 CHISq = CHISq + ((Y(I) F(I))**2) / (F(I) (NP 2))
RETURN
DO 10 I = i,NP
10 H(1,1) = H(1,1) + (1.0 / (SIG(I)**2))
H(l,2) = 0.0
DO 20 I = 1,NP
20 H(l,2) = H(l,2) + (X(I) / (SIG(I)**2))
H(2,1) = H(l,2)
H(2,2) = 0.0
DO 30 I = 1,NP
30 H(2,2) = H(2,2) + ((X(I)**2) / (SIG(I)**2))
C0V(1,1) = 1.0
C0V(1,2) = 0.0
C0V(2,1) = 0.0
C0V(2,2) = 1.0
DO 200 I = 1,M
T1 = H(I,I)
DO 50 J = 1,H


123
2. The sensitivity of the assay system should be determined and optimized by varying the
detector system design.
3. Recommendations as to a detector system design, which would turn the system into a
black box counting system requiring very little operator work and no operator sample
alignment, should be developed.
4. The coupling of this data processing technique to conventional gamma spectroscopic
and neutron activation analysis techniques should be explored.
5. Rotating the target sample during counting should be experimentally explored to de
termine whether this will expand the application of this assay technique to extremely
inhomogeneous samples.
6. Samples of varying inhomogeneity should be assayed to determine how sensitive the
system is to sample inhomogeneity and the accuracy of the assay of inhomogeneous
samples.


90
of the spike in the sample, were seen as being fairly large and difficult to accurately char
acterize. As such the laboratory assays, which are more accurate than the assays based on
sample preparation data, were used as the sample contamination concentrations. Samples
2, 3, and 4 were blended from other samples of known concentrations. Again, because the
uncertainties in the blended weights, as well as in the original sample contamination con
centrations, the contamination concentrations of these samples were also determined using
analysis by other laboratories as opposed to using sample preparation data.
Six samples were collected from various locations and analyzed au naturel. These
wet, inhomogeneous samples are representative of typical samples collected during soil char
acterization activities.
NJA: Inhomogeneous, wet sample of highly contaminated material brought
collected at a FUSRAP site at Lodi, New Jersey.
NJB: Second inhomogeneous, wet sample collected at the same site as NJA.
USA: Inhomogeneous, wet sample collected at the Y-12 weapons production
plant, Oak Ridge, Tennessee, from an area known to be contaminated
with Th.
USB: Second inhomogeneous, wet sample collected at the same site as USA.
USC: Inhomogeneous, wet sample collected at the Y-12 weapons production
plant, Oak Ridge, Tennessee, from an area known to be contaminated
with U.
USD: Second inhomogeneous, wet sample collected at the same site as USC.
It should be noted here that this assay technique requires a relatively small aliquot of
contaminated soil; approximately 120 gm. The two assay techniques used to verify this
assay require approximately 250 gm of soil. As such, tandem samples were required so that
they could be blended together to form samples large enough for analysis by the other two


DATA FROM
XRF5JJSA. CNF; 1
D4(5)
=
14.0
M5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
9.0
HN(5)
=
21.0
RH(5)
=
1.0
RH(5)
=
12.0
RS(5)
=
B9.74
PH(5)
=
252671.0
ER(5)
=
1573.0
DATA FROM
XRF6_USA.CNF;i
D4(6)
=
14.0
H5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
10.0
MN(6)
=
52.0
RH(6)
=
1.0
RM(6)
=
11.0
RS(6)
=
44.54
PH(6)
=
212386.0
ER(6)
=
983.0
DATA FROM
XRF7JUSA.CNF;1
D4C7)
=
14.0
H5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
14.0
MN(7)
=
2.0
RH(7)
=
1.0
RH(7)
=
10.0
RS(7)
=
54.16
PH(7)
=
184506.0
ER(7)
=
1017.0


69
A (n, 1)
/ {PU ~ Plo) \
(P2t P20)
(P3j P30)
DY (m, 1) =
{(Put Pn0)
/ (yl-F(x1)0) \
(j/2-P(X2)0)
(j/3-P(X3)0)
\(j/m-P(Xm)0)/
This matrix equation is solved by Gaussian elimination to yield the values of the A (n, 1)
matrix. These values are used to update the parameter guesses from the initial guesses of
Pl0, P20, ..Pn0, to Pli, P2i, ..Pni, since Pi = Pi0 + A (i, 1). New values of F (X<)
are calculated based on these new parameters, these new parameters become the initial
guesses for the next iteration, and the matrix solution is repeated. This iteration process
is continued until the sum of squares is minimized based on some predetermined cutoff
criteria. The result of the minimization is the calculation of the best fitting parameters
for the mathematical model.
Covariance Matrix and Functional Error
As a by-product of this method, the variances and covariances of the fitting parameters
are calculated. The inverse of the matrix product, DF1 x DF, is defined as the covariance
matrix 20.
(DF1 (n, m) x DF (m, n)) 1 = Covar (n, n).
The diagonal values of this matrix, Covar(i,i), are the variances of the model fitting
parameters.


142
detector. The results of this experiment also confirm that the contribution of incoherently
scattered photons is small.
Pulse Pileup
Pulse pileup is a well known phenomenon that occurs in counting systems. Each de
tected photon results in a voltage pulse that travels from the detector, through the pre
amplifier, through the amplifier, through the ADC, and into the MCA. Each devise requires
a finite amount of time to process each pulse. If a second photon strikes the detector and
generates a second voltage pulse before the first pulse has had time to be completely pro
cessed, the pulses can pile up. This usually occurs in the amplifier and the ADC.^4>25
Pileup in the ADC is usually handled by circuitry that only allows a new pulse to enter the
ADC once it is free of the last pulse. This is known as live time correction. Pulse pileup in
the amplifier, however, is better accounted for by calculation of a correction factor.^.
The ND-9900 is equipped with a program to properly account for amplifier pulse pileup.
The correction factor used is described by R. M. Lindstrom and R. F. Fleming.This
correction factor was applied to all data used for system calibration.
Compton to Total Scatter Ratio in Soil
As mentioned in Chapter II, it is necessary to know the approximate ratio of the
compton scatter coefficient to the total linear attenuation coefficient for soil. This ratio is
used in calculating the production of fluorescent x rays due to compton scattered gammas
from the excitation sources. It was first determined that this ratio in soil is relatively
independent of soil trace constituents. It was then determined, using the computer code
XSECT, what the ratio actually is for soil at various gamma energies.


313
DATA FROM
XRF2JUSA.CNF;1
D4(2)
=
13.0
M5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
9.0
MN(2)
=
21.0
RH(2)
=
1.0
RM(2)
=
16.0
RS(2)
=
16.45
PH(2)
=
351203.0
ER(2)
=
1525.0
DATA FROM
XRF3JJSA. CNF; 1
D4(3)
=
13.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
10.0
MN(3)
=
47.0
RH(3)
=
1.0
RM(3)
=
14.0
RS(3)
=
45.83
PH(3)
=
315751.0
ER(3)
=
1473.0
DATA FROM
XRF4_USA.CNF;1
D4(4)
=
13.0
M5(4)
=
7.0
YB(4)
=
87.0
HR(4)
=
15.0
MN(4)
=
35.0
RH(4)
=
1.0
RM(4)
=
13.0
RS(4)
=
30.71
PH(4)
=
275494.0
ER(4)
=
1688.0


139
exp (-n{E) p R)olj = (A7)
FL{E)
ER(E)xADxr,[E)xcT x exp (-// (E) pR) x exp (-mu(E)pR)AiT x exp {-p(E)pR)Be,
where all terms are as previously described.
Using Equation A-7 the fraction of photons which are transmitted through the plastic
jar unchanged was calculated using both mass attenuation coefficient data sets. The av
erages of the twenty values for each data set were used as the jars attenuation factors for
each data set.
Next, the jar was filled with water and the twenty counts of one hour each were repeated.
Since another attenuating material, water, was been placed in the beam, another term was
added to Equation A-7. Equation A-7 can then be used to determine the attenuation factor
for water.
exp {-(i{E) p R)Hj0 = {AS)
FL (E)
E*{s)*ADgi{E)*CT x exp(-p(E)pR),, x exp{-mu(E)pR)Mr x exp{-p{E)pR)obj x exp(-p(E) pR)Bt
where all terms are as previously described.
Remembering that the object of this experiment was to measure the mass attenuation
coefficient of water, the value of the right side of Equation A-8, K(E), was calculated for
each data set for each of the twenty counts. Equation A-8 was then be rearranged to solve
for p (E)Hi0.
p{E)h,o =
h(g(g))
(po R)h,0
(A9)


280
C ****************************
c *
C U1XRF.FOR *
C *
C FILE PROGRAM *
C *
C ****************************
c
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
f PKFIL = '[LAZO.DISS.Ul]U1XRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE Ul IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE Ul IS 186 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
DATA FROM
XRF1JU1.CNF;1
D4(l)
=
2.0
M5(l)
=
6.0
Y5C1)
=
87.0
HR(1)
=
8.0
MN(1)
=
47.0
RH(1)
=
1.0
RM(1)
=
22.0
RS(1)
=
42.64
PH(1)
=
127598.0
ER(1)
=
774.0


DATA FROM
XRF5 JIJB.CNF;1
D4(5)
8.0
M5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
12.0
MN(5)
=
15.0
RH(5)
=
1.0
RM(5)
=
11.0
RS(5)
=
24.29
PHC5)
=
1910431.0
ER(B)
=
2887.0
DATA FROM
XRF6 JIJB.CNF;1
D4(6)
=
8.0
M5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
14.0
MN(6)
=
42.0
RH(6)
=
1.0
RM(6)
=
10.0
RS(6)
=
36.35
PH(6)
=
1692538.0
ER(6)
=
1708.0
DATA FROM
XRF7 JIJB.CNF;1
D4(7)
=
8.0
M5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
16.0
MN(7)
=
22.0
RH(7)
=
1.0
RM(7)
=
9.0
RS(7)
=
59.44
PH(7)
=
1507566.0
ER(7)
=
3183.0


Date File Programs
REV6.FOR .
COMDTA.FOR
XRFDTA.FOR
GEOM5A.FOR
GEOM5C.FOR
GEOM5E.FOR
GEOM5G.FOR
GEOM5I.FOR .
GEOM5K.FOR
GOEM5M.FOR
GE0M50.F0R
211
212
215
218
221
223
225
227
229
231
233
235
Sample Description Programs
SAMPLE2.FOR
SAMPLE3.FOR
SAMPLE4.FOR
SAMPLEU1.FOR . .
SAMPLEU1A.FOR . .
SAMPLET1I1.FOR . .
SAMPLETH1A.FOR .
SAMPLENJAU.FOR .
SAMPLENJATH.FOR .
SAMPLENJBU.FOR .
SAMPLENJBTH.FOR .
SAMPLEUSA.FOR . .
SAMPLEUSB.FOR . .
SAMPLEUSC.FOR . .
SAMPLEUSD.FOR . .
S2XRF.FOR
S3XRF.FOR
S4XRF.FOR
U1XRF.FOR
U1AXRF.FOR
TH1XRF.FOR
Till AXRF.FOR
NJAUXRF.FOR
NJATHXRF.FOR . .
NJBUXRF.FOR
NJBTHXRF.FOR . .
237
238
240
242
244
246
248
250
252
254
256
258
260
262
264
266
268
272
276
280
284
288
292
296
300
304
308
IX


TABLE 36
Peak Fit Results for Sample 3
Sample Contamination Concentration: 221.7 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
541821 0.4%
14.1
2
479982 0.1%
1.7
3
428292 0.2%
2.3
4
375253 0.3%
7.3
5
344559 0.3%
5.1
6
301884 0.4%
10.0
7
261608 0.4%
9.8
8
233651 0.5%
5.6


234
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5M.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITEd*) X(I),Y(I),Z(I)
WRITEd,*) XT, YT, ZT
WRITEd,*) TH, TR
WRITEd,*) RT, CT, VT
CLOSE(1,STATUS='KEEP)
END


So as it turned out, just as I suspected from the start, this dissertation was a lot of
work. It took a lot of time, pulling me around its ins and outs for over five years. It took
lots of long days and lots of weeks without weekends. It took me from the valley of the
shadow of death, so to speak, to the heights of exhilaration and joy. It was among the most
important things in my life, and certainly was the primary thing for which I strove for all
that time. And throughout that time I had a fairly vague but very warm feeling as to why
I was doing this, and that feeling kept me going during this work.
So putting that vague feeling into words, this dissertation is dedicated to my parents, Dr.
Robert Martin Lazo and Rosemarie Lazo, who taught me by their example that learning is a
large part of what life is all about. And that the other biggest part of life is the satisfaction
that comes with trusting yourself enough to follow through on your dreams.
During this time I met the woman who is now my wife, I acquired two nephews, one
sister-in-law, and one brother-in-law, rounding out a very eventful time for the Lazo clan.
This dissertation is also dedicated to my family; my wife, my two brothers, my sister, their
families, and my two cats Max and Milli, who helped me all along the way. It is especially
dedicated to my wife, Corinne Ann Coughanowr, who has supported me, encouraged me,
helped me, put up with me, and continued to love me through the worst of times. To you
all, I love you.


LIST OF FIGURES
Figure Page
1. Typical Gamma Ray Spectral Peak and Background 16
2. Lorentzian X Ray as Seen Through the Gaussian Response of a Detector . .22
3. Typical Th Kai X-Ray Spectral Peak 25
4. Polynomial and Step Function X-Ray Peak Background 29
5. Source Target Detector Physical Geometry 39
6. Source Target Detector Spatial Geometry 49
7. Compton Scatter Spatial Geometry 53
8. Exploded View of Target Holder Assembly 76
9. Target in Place above Detector 78
10. Target in Place above Detector Showing Laser Alignment System 80
11. ND-9900 Multichannel Analyzer, ADC, Amplifier, and Detector Power Supply . 82
12. Typical XRF Kai Peak on MCA 84
B-l. Relative Sample Separation vs. Solution Matrix Condition 152
B-2. Target-Detector Distance vs. Measured Peak Area 155
xiv


248
C
c *********************
c *
C SAMPLETH1.FOR *
C *
Q *********************
c
CHARACTER *3 ELEMENT
C
C This program creatB a data file of input
C data pertaining to Sample #TH1, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH>
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.8977
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.13064
Bl = 0.65512
Cl =-0.48956
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.27465
US2 = 0.29197
US3 = 0.33854


224
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5C.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW')
WRITEd,*) NS
DO 100 I = 1,NS
100 WRITEd,*) X(I),Y(I),Z(I)
WRITEd,*) XT, YT, ZT
WRITEd*) TH, TR
WRITEd,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
END


FIGURE 11
ND-9900 Multichannel Analyzer, ADC,
Amplifier, and Detector Power Supply


2
In general, all sites are contaminated with varying levels of U, Th, their progeny, or some
mixture thereof. Sites typically include at least one building and the surrounding lands.
Clean up typically includes scrubbing and/or vacuuming of contaminated building surfaces
to remove contamination, destruction of facilities too contaminated or too uneconomical
to clean up, and digging up of contaminated soils. All contaminated wastes are deposited
in a controlled and monitored temporary storage area to await their ultimate disposition.
Wastes are generally low level and thus their ultimate disposition will be in the low level
waste repository of the state or compact area from which the wastes came.
One portion of this process that is of scientific interest and could stand some improve
ment is the assay of soils to determine whether or not they are contaminated. During
the course of site decontamination, many soil samples are taken. Preliminary soil samples
are taken to determine the approximate extent and concentration of radionuclides present.
Periodic soil samples are taken during soil excavation to determine whether preliminary
estimates were correct and to locate previously unidentified radionuclide deposits. Final
soil samples are taken to confirm that all contaminated soil has been removed. With so
many samples being collected, quick and accurate assay becomes important.
All soil samples are assayed twice: once when they arrive at the lab as wret, inhomo
geneous soil, and once after they have been processed. The standards comparison method
for gannna spectroscopic analysis is used to assay the soil samples. This method will be
discussed in detail later. Soil sample processing involves drying the soil in an oven, grinding
the soil into a powder that will fit through a standard 200 mesh per square inch sieve, and
stirring the powdered soil into a relatively homogeneous mixture. Soil sample processing
adds approximately 2 days to sample analysis time. Samples are analyzed twice because,
while the first analysis is fast enough to meet stingy construction schedules, it is not ac
curate enough to meet quality control guidelines. When a fudge factor is applied, the


APPENDIX B
UNSUCCESSFUL ANALYSIS TECHNIQUES
During tliis work, it became evident that two portions of the data analysis technique,
which originally looked very promising, would not work. The failed techniques were aban
doned in favor of other ideas which did work, however there is value in describing the failed
techniques and why they failed. The most important of the two techniques was that which
allowed the analysis of samples which were very inhomogeneous. The other failed analy
sis technique was that which allowed soil moisture analysis by use of transmission gamma
rays. Further investigation showed that both techniques failed for the same reason. This
appendix will discuss both analysis techniques and the reason that they failed.
Sample Inhomogeneity Analysis
The sample geometry used for the assay technique which proved to be successful is
described in Chapter II. The inhomogeneity analysis which is described here uses this same
geometry and the same mathematical description of the system.
If the soil sample is divided mathematically into small point sources then FS(E) is
equal to the contribution of a point source, with an elemental concentration of 1 pCi/gm of
dry soil, to the full energy peak. The equation which delines FS(E) is listed in Chapter II.
The full energy peak area is then equal to the sum of the contributions from all the point
sources. FS(E) can be thought of as a Geometry Factor which, when multiplied by the
146


73
where
aa the ath of m fitting parameters,
Fa (X) = the ath of m linear functions of X,
then the values of the fitting parameters a are given
by,
a,
Em \pp
a~ 1 2-^/b-
YFa(Xb)
H 1 (a, i),
where
H 1 (i, i) = the covariance matrix,
cr6 = the standard deviation of
detector response b,
and,
lr, {i j) = F¡(X)
& *
For a simple function such as DR = C X GF, where C is the unknown fitting parameter
at, Y = DR, X = GF, and Fx (X) = X GF, these equations are extremely easy to solve
and yield the desired result of this analysis, the value of C. The error in the value of C is
also quite simple.
= n 1 (*, i)
This then yields the desired result of this analysis, the soil contamination concentration,
G, and its associated error.


TABLE 11
Measured vs. Fitted Detector Response for
U1
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 152.3 pCi/gm U238
Reduced X2 Value for Fitted Data : 0.183
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.529
80.5
82.4
2
0.466
70.9
75.1
3
0.411
62.7
60.9
4
0.365
55.5
59.1
5
0.324
49.4
49.5
6
0.289
44.0
40.3
7
0.258
39.3
37.8
8
0.232
35.3
32.8


31
In that the steeply sloping nature of this background is somewhat unusual in spec
troscopy, some explanation as to its origin is warranted. The excitation source, Co-57,
which emits gammas at 122 keV and 136 keV, was chosen because of the proximity of its
gamma energies to the K-shell absorption energy. At these energies, U and Th have liigh
cross sections for photoelectric reactions with K-shell electrons. Table 4 shows the absorp
tion and emission energies for U and Th. Table 5 shows the emission energies and yields
for Co-57. Table 5 also lists emission energies and gamma yields for Eu-155. The latter
radionuclide is used for transmission measurements which are explained in a subsequent
section. Table 6 shows relevant source physical properties.
Unfortunately, when 122 keV ganunas Compton scatter at approximately 180 degrees,
the resulting gamma is 83 keV. This is called a backscatter gamma. The backscatter gamma
from an incident 136 keV gamma is 89 keV. These backscatter gammas are at inconvenient
energies because they form the majority of the background beneath the U and Th Kai x
ray, thus somewhat obscuring the peaks. And the shape of the background depends upon
the geometry of the scattering soil sample. That is, the size and relative position of the
source, soil sample, and detector determine what scatter angles, and thus what energies,
will be seen as backscatter gammas. Thus the shape of the background does not lend itself
to simple theoretical treatment and a third or fourth order polynomial fit, as mentioned
earlier, is necessary. The peak areas calculated by tins technique are used in subsequent
analyses to determine the soil sample concentrations of U and Th.


263
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(i,FILE='SAHPLEUSB.DAT',STATUS=NEW)
WRITE(1,'(A3)) ELEMENT
WRITE(1,*) WF
WRITEd,*) SD
WRITE(1,*) A1
WRITEd,*) B1
WRITE(1,*) Cl
WRITEd,*) US1
WRITEd,*) US2
WRITEd,*) US3
CL0SE(1,STATUS='KEEP *)
END


219
C
C Jump Ratio (Rk) used to calculate the fractional K-shell
C vaceincies per photoelectric interaction.
C KS = (Rk 1)/Rk, was calculated from U cross sections
C sent to me by Hubble. The fractional K x ray yield, KY,
C is from, 11 The Table of Radioactive Isotopes, by
C E. Browne and R. B. Firestone, 1986, LLNL.
C
DATA KS(1),KY(1) /.7640, .4510/
C
C The elemental concentration per pCi/gm, EC,
C (Atoms U/gm Soil)/(pCi U/gm Soil), was calculated
C using a U-238 half life of 4.468E9 y from, The
C Table of Radioactive Isotopes, by E. Browne and
C R. B. Firestone.
DATA EC(1) /7.5265E15/
C
C The following data is for Thorium
C
C K-alpha-1 X-Ray energy (MeV) for Th
C from Data Tables, by Kocher
C
DATA E(2) /.093334/
C
C Air mass attenuation coefficients, sq cm/gm,
C from, Photon Mass Attenuation and Energy
C Attenuation Coefficients from 1 keV to 20 MeV,
C by Hubble.
C
DATA UA(2) /.1581/
C
C Be transmission fractions as measured using a
C Be window similar to that actually used with
C the detector.
C
DATA UB(2) /.1330/
C
C Intrinsic detector efficiency as calculated by
C NBS.EFF and EFFICIENCY.
C
DATA ETA(2) /.86088/
C
C Transmission fraction for an average jar
C calculated using TRANSMISSION and REV.6 data.
C
DATA JA(2) /.96860/


166
605 FOR J = 1 TO N
610 Q2(I,J) = TA(I,J)
615 NEXT J
620 NEXT I
625 GOSUB 4500
630 FOR I = 1 TO H
635 FOR J = 1 TO N
640 TA(I,J) = Q3(I,J)
645 NEXT J
650 NEXT I
740 W = M
750 FOR I = 1 TO M
760 FOR J = 1 TO N
770 Q1(J,I) = A(J,I)
780 q2(I,J) = TA(I,J)
790 NEXT J
800 NEXT I
810 GOSUB 4500
820 FOR I = 1 TO H
830 FOR J = 1 TO H
840 AA(I,J) = q3(I,J)
845 HLD(I.J) = q3(I,J)
850 NEXT J
860 NEXT I
900 S(0) = 1E+17
910 CHISq = 0
1000 PRINT
1005 PRINT ITTERATION ;W1
1010 PRINT
1015 FOR J = 1 TO M
1020 PRINT V(";J;) = ;V(J)
1023 PRINT
1030 NEXT J
1032 PRINT
1035 FOR I = 1 TO N
1040 PRINT X(;I; ) = ;X(I)+XT(1) 'Y(* ;Ij ) = }Y(I)*5000
1045 FOR J = 1 TO H
1050 F(I) = V(J) (CX(I)) ** (J 1)) + F(I)
1055 NEXT J
1060 PRINT ,,X(;I;) = ";X(I)+XT(1),F(,,;I;) = ,;F(I)*5000
1065 PRINT
1150 DY(I) = Y(I) F(I)
1155 CHISq = CHISq + (CDY(I)) ** 2) / (F(I) (N H))
1160 S(W1) = S(W1) + (DY(I)) ** 2
1170 NEXT I
1180 IF ABS (S(W1) S(W1 1)) < (S(W1) .0000001) THEN GOTO 2000
1185 IF ( S(W1-1) < S(H1) ) THEN GOTO 1900
1190 FOR I = 1 TO H


21. Measured vs. Fitted Detector Response for Th-la 105
22. Measured vs. Fitted Detector Response for NJA-Th 106
23. Measured vs. Fitted Detector Response for NJB-Th 107
24. Measured vs. Fitted Detector Response for USA 108
25. Measured vs. Fitted Detector Response for USB 109
26. Sample Physical Characteristics 110
27. Measured Sample Linear Attenuation Characteristics Ill
28. Comparison of Kai Peak Areas as Determined by PEAKFIT and GRPANL 112
29. Peak Fit Results for Sample U1 113
30. Peak Fit Results for Sample Ula 113
31. Peak Fit Results for Sample NJA-U 114
32. Peak Fit Results for Sample NJB-U 114
33. Peak Fit Results for Sample USC 115
34. Peak Fit Results for Sample USD 115
35. Peak Fit Results for Sample 2 116
36. Peak Fit Results for Sample 3 117
37. Peak Fit Results for Sample 4 118
38. Peak Fit Results for Sample Till 119
39. Peak Fit Results for Sample Thla 119
40. Peak Fit Results for Sample NJA-Th 120
41. Peak Fit Results for Sample NJB-Th 120
42. Peak Fit Results for Sample USA 121
43. Peak Fit Results for Sample USB 121
A-l. Shield Material X-Ray Emission Energies 127
A-2. NBS Source, SRM 4275-B-7, Emission Rates 129
xii


72
The next step in the analysis is to subtract the background from the spectral data
(SPEC) to yield an estimated peak. The variance associated with each of the peak points
is then
o-2 (PKi) = The peak is then least squares fit to a Voigt peak shape, yielding the covariance matrix
for this process. Equation 4 is then used to calculate the error associated with the numeri
cally calculated peak area. These steps are repeated for several geometric configurations of
the soil sample target yielding several peak areas and their associated errors.
Linear Function Fitting
Once the peak areas and their associated errors have been determined, the last step
of the assay is to determine the concentration of contamination in the sample jar and its
associated error. As described earlier, the measured detector response is a linear function
of calculated GFs, the slope of this line being the concentration of contamination in the
sample jar. The measured detector response data, the error associated with this data, and
calculated GFs need only to be fit to a linear function to determine the desired assay result.
Easier still, the fitted line must pass through the origin since if the calculated GF for a
sample were zero, the measured detector response would also have to be zero. This sort of
statistical data fitting is common to most introductory statistic books. The treatment used
here is from handouts prepared for a statistics class at Cornell University ^1.
For any linear function of X,
Y = x Fa(X),




232
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, & VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5K.DAT
C
OPEN(1,FILE=GEOM,STATUS=5 NEW)
WRITE(i,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
WRITEd.O XT, YT, ZT
WRITECl,*) TH, TR
WRITEd,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
END


4
Standards Method for Gamma Spectroscopic Assay of Soil Samples
The standards method for gamma spectroscopic assay of soil or any other sort of ra
dioactive sample is a simple process. A sample of unknown radionuclide content is placed
in a fixed geometry, relative to a detector, and a spectrum is collected for a fixed length
of time. A sample containing a known amount of radionuclide is then placed in the same
geometry as that used to count the unknown sample, and a second spectrum is collected.
By comparing these two spectra, the identity and amount of radionuclide in the unknown
sample can be determined.
Qualitatively, the presence of a radionuclide in a sample is determined by the presence
of spectral peaks at energies characteristic of that radionuclide. For example, Co-57 emits
gamma rays at 136 keV and 122 keV in a known ratio. If spectral peaks of these energies
and of proper relative intensity are present in a spectrum, then Co-57 is probably present
in the unknown sample.
Quantitatively, the concentration of a radionuclide in a sample is determined by com
paring the area of a spectral peak generated by an unknown sample to the area of a spectral
peak generated by a sample of known concentration. For example, a sample known to con
tain 100 pCi of Co-57 is counted in a standard geometry relative to a detector. After one
hour of counting this known sample, the area beneath the 136 keV peak is 10,600 counts
and the area beneath the 122 keV peak is 85,500 counts. Next, an unknown sample is
counted, in the same geometry in which the known sample was counted, and after one
hour of counting the areas beneath the 136 keV and 122 keV peaks are 21,200 counts and
171,000 counts, respectively. The unknown sample resulted in peak areas twice those of the
known sample and thus the unknown contains 200 pCi of Co-57. Further details of gamma
spectroscopy can be fomid in Knoll.^


147
elemental concentration of U or Th at the point source, equals the contribution of the point
source to the full energy peak.
The first step to properly assaying an inhomogeneous sample is to mathematically
divide the sample into point sources. This involves knowing the spatial relationships among
the excitation source, the target sample, and the detector. Figure 3 shows this geometry.
Then, together with the sample mass attenuation coefficients and water content FS(E) can
be calculated for each point source. Once FS(E) is known for all points, the full energy
peak area of an unknown sample is a function of those known geometry factors and the
unknown point concentrations.
Suppose that an unknown target sample is divided into N point sources. Then by mak
ing one spectral measurement, the full energy peak area is equal to the sum of the N known
geometry factors, FS(E), times their respective N unknown elemental concentrations. If
the target cylinder were rotated by 360/N degrees and the mathematical integrity of the
N points was maintained, a second spectral measurement could be taken. New geometry
factors could be calculated for each point source, now rotated slightly from its original po
sition. The area of the full energy peak for the new spectrum would be the sum of the
new geometry factors multiplied by their respective unknown concentrations. Note that
since the point sources have maintained their spatial identity, the unknown elemental
concentrations are the same as before. Then by taking N measurements, each after rotating
the target cylinder 3G0/N degrees, a system of N equations and N unknowns would be de
veloped and could be solved. The total elemental content of U or Th in the target cylinder
would be the sum of the N unknown concentrations times their respective point volumes.
Mathematically, a 500 ml cylinder, 10 cm tall and 4 cm in radius, must be divided into
approximately 2000 point sources before it can be adequately modeled using point source
mathematics. This was determined by use of a computer model, using the fluorescence


296
C ****************************
c *
C NJAUXRF.FOR *
C *
C FILE PROGRAM *
C *
c ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.NJA]NJAUXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE NJA-U IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY SA, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE NJA-U IS 171 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRFl_NJA.CNF;i
D4(l)
=
30.0
M5(i)
=
6.0
Y5(l)
=
87.0
HR(1)
=
17.0
MN(1)
=
37.0
RHCl)
=
1.0
RM(1)
=
14.0
RS(1)
=
48.70
PH(1)
=
70722.0
ER(1)
=
645.0


Matrix Condition
0
100


319
C
C DATA FROM XRF8_USB.CNF;1
C
C
C
C
D4(8) = 17.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 9.0
MN(8) = 53.0
RH(8) = 1.0
RM(8) = 10.0
RS(8) = 29.18
PH(8) = 153290.0
ER(8) = 1208.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS*NEW)
WRITE(1,5) NF
5 F0RHAT(1I2)
WRITE(l.lO) LH, LM, LS
10 F0RHAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RHATC1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 FORMAT(2F15.5)
100 CONTINUE
END


TABLE 20
Measured vs. Fitted Detector Response for
Till
Fitting Equation : DR = GF x CC
Where : DR Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 143.5 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.465
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.839
264.0
262.2
2
1.620
232.6
239.6
3
1.432
205.5
213.6
4
1.269
182.1
188.6
5
1.128
161.9
156.2
6
1.005
144.2
143.6
7
0.898
128.9
120.0
8
0.805
115.5
103.8


12
and can be used to identify the element. The intensity of the emitted x rays is proportional
to the concentration of the element in the x-ray emitting material. This technique can thus
be said to directly determine U and Th concentrations in soil samples. For a more detailed
description of x-ray fluorescent spectrometry see Woldseth.^
Assay Technique
In overview, the assay process is simple. Each sample is irradiated to induce fluorescence
and the emitted fluorescent x rays are detected by a hyper-pure intrinsic Ge planar detector.
The areas under the Kai x-ray peaks from U and Th are determined by a spectral analysis
system. The Kal peak was chosen because the K-shell lines are highest in energy, thus
minimizing attenuation effects, and the Kal line is the most predominant K-shell line. The
areas of these peaks are used to determine U and Th concentrations. This determination
involves two steps; the determination of sample moisture content and attenuation properties,
and the handling of sample inhomogeneity. The isotopic fractions are determined by looking
at the relative intensities of gamma rays from U and Th daughters. The details of these
processes are discussed in subsequent sections.
This research is divided into two broad sections; development of a mathematical model
of the assay system, and experimental verification of that model. The model is divided into
three sections. The first section involves the development of a peak shaping program to
accurately deterndne the areas of the Kal x-ray peaks of U and Th. The second section
involves the determination of the sample moisture content and attenuation properties. This
is done by measuring how gamma rays are transmitted through the sample. The third
section uses the peak areas, determined in section one, and the soil moisture content and
attenuation coefficients, determined in section two, to mathematically model the sample so


242
C
C i*###*###***#**#******
c *
C SAMPLE4.F0R *
C *
C *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample #4, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH'
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.3112
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.11124
Bl = 1.11667
Cl =-0.96296
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.25104
US2 = 0.28282
US3 = 0.35714


APPENDIX A
EQUIPMENT AND SETUP
System Hardware
In order to verify the theory described in the previous three sections, equipment for
the assay system was purchased or designed and fabricated. All equipment used for this
assay system was purchased specifically for this research. This includes a computer based
multichannel analyzer (MCA), an analog to digital converter (ADC), a spectroscopy grade
amplifier, a planar Ge detector, a spectroscopy grade detector power supply, a combination
source holder and detector shield, a Co-57 source for x-ray excitation and for transmission
measurements, and an Eu-155 source for transmission measurements.
The ND-9900 MCA
The brain of the system is a Nuclear Data model ND-9900 computer based multichannel
analyzer (MCA). Fundamentally, this unit receives, saves, and manipulates spectral infor
mation. The beauty of the ND-9900 is that spectral collection is run independently of other
operations. This allows full use of the systems Micro-VAX computer for analysis of an old
spectrum while a new spectrum is being collected. The Micro-VAX is a very powerful and
fast computer allowing the use of complicated spectral analysis programs.
124


APPENDICES
A EQUIPMENT AND SETUP 124
System Hardware 124
The ND-9900 MCA 124
The ADC 125
The HPGe Detector 125
XRF Excitation Source and Transmission Sources 125
The XRF Excitation Source Holder and Detector Shield 126
System Calibration 127
Mass Attenuation Coefficients 134
Pulse Pileup 142
Compton to Total Scatter Ratio in Soil 142
B UNSUCCESSFUL ANALYSIS TECHNIQUES 146
Sample Inhomogeneity Analysis 146
Reasons for Inhomogeneity Analysis Failure 149
Soil Moisture Content Analysis 158
Reason for Soil Moisture Content Analysis Failure 161
C COMPUTER PROGRAMS 163
Peak Shaping Programs 163
POLYBK.BAS 164
BKG.BAS 172
PEAKFIT.BAS 175
Geometry Factor Programs 184
DIST.FOR 185
IMAGE.FOR 190
COMPTON.FOR 196
ASSAY.FOR 205
via


2100
2200
2225
2250
9000
203
WRITE(1,*) TOTAL
CL0SE(1,STATUS=*KEEP)
WRITE(6,2100)
FORHAT(/fIX,Geometry Factors Calculated)
WRITE(6,2200) TOTAL
FORHAT(/,IX,The sum of all Geometry Factors is .1E16.10)
WRITE(6,2225) GFCT
F0RMAT(/,1X,The sum of Compton Geometry Factors is ,1E16.10)
WRITE(6,2250) GFNT
F0RMAT(/,IX,The sum of Natural Geometry Factors is .1E16.10)
END


162
together. The equations are therefore not wholly independent and the system of equations
to be solved is close to singular.
In order to remedy this situation, gammas of more widely spaced energies could be
chosen. Unfortunately, the equation which approximates linear attenuation coefficients as a
function of energy is applicable only over a limited energy range. Beyond that range there
is no single function which adequately describes linear attenuation coefficients as a function
of energy. Because of this, the above described soil moisture content analysis technique was
abandoned in favor of simply weighing each sample before and after it was put into a drying
oven or microwave.


169
2477 NEXT I
2480 CLOSE #1
2482 PRINT
2483 PRINT
2490 LPRINT Peak data stored in file ;PEAK$
2500 GOTO 9000
4500 FOR I = 1 TO H
4502 FOR J = 1 TO H
4503 q3(I,J) = 0
4504 NEXT J
4505 NEXT I
4510 FOR K = 1 TO H
4520 FOR I = 1 TO W
4540 FOR J = 1 TO N
4560 Q3(K,I) = Q3(K,I) + q2(K,J) qi(J,I)
4580 NEXT J
4600 NEXT I
4620 NEXT K
4640 RETURN
5000 FOR I = 1 TO H
5020 FOR J = 1 TO M
5040 AM(I,J) = AA(I,J)
5060 NEXT J
5080 NEXT I
5090 HI = M + 1
5100 FOR I = 1 TO H
5120 AM(I,H1) DT(I,1)
5140 NEXT I
5160 SH = 0
5180 FOR R = 2 TO M
5200 R2 = R 1
5220 FOR R1 = R TO H
5240 SH = AH(R1,R2) / AH(R2,R2)
5260 AH(R1,R2) = 0
5300 FOR Cl = R TO HI
5320 AH(R1,C1) = AH(R1,C1) AH(R2,C1) SH
5340 NEXT Cl
5380 NEXT R1
5460 NEXT R
6000 SU = 0
6010 H2 = H 1
6020 DA(H) = (AH(H.Hl)) / (AH(H,H))
6040 FOR R = 1 TO H2
6060 RP = H R
6070 H3 = H RP
6080 FOR Cl = 1 TO H3
6100 SP = HI Cl
6120 SU = SU + AH(RP.SP) DA(SP)


138
and
p(E) removal mass attenuation coefficient
for stainless steel (SS), for air, for an
object in the beam, or for Be, at
energy E, {cm2¡gm),
Pq density of stainless steal, orair, or an object in the beam, or Be,
(gm/cm3),
R = thickness of stainless steal, or air,
or an object in the beam, or Be,
(cm).
To verify that it is proper to use the removal mass attenuation coefficient, and not the
total mass attenuation coefficient, the mass attenuation coefficient of water was measured
at four energies and compared to literature values. In order to ensure consistency, two data
sets were used in calculations. The first set consisted of total mass attenuation coefficients.
The second set consisted of removal mass attenuation coefficients. Again to ensure consis
tency, the system was calibrated, including detector intrinsic energy efficiencies and source
strengths, using both data sets. Both calibration calculations were performed on the same
set of spectral data, but each calculation used a different mass attenuation coefficient set.
The above calculations constituted calibrating the system twice, once for each mass
attenuation coefficient data set. This completed, a plastic soil jar was placed, empty, be
tween the source and the detector and twenty counts of one hour each were collected. In
Equation A-6, the plastic jar becomes the attenuating object. The attenuation of this jar
was determined by rearranging Equation A-6.


132
In order to determine the detector intrinsic energy efficiency at 136 keV, Equation A-l
was rearranged slightly.
V ^ ER (E) x AD xCT x ATN (E)
FL (E) x 4irRl
(A2)
where all terms are as previously defined.
Since this equation is valid for any energy at which FL(E) is measured, the ratio of
i](E 1) to r/(E2) is
J7(£x) FL{E1) ,,ER{E2) w ATN{E2)
tj (E2) ~ FL(E2) X ER (Er) X ATN (Ei)"
(A3)
Therefore, given Ex = 136keV and E2 = 122feeF, the above equation can be solved
for 7/(13GkeV). The spectra that were used to determine the Co-hl source emission rates
contained peaks at 122 keV and 136 keV. These spectra were therefore used to determine
tj (13GkeV).
The calibration process thus determined precise source strengths of the Isotope Products
sources, as well as the detector intrinsic energy efficiency at 86 keV, 105 keV, 122 keV, 123
keV, and 136 keV. The resulting data is presented in Table A-4.
It should be noted that in order to precisely calculate the above efficiencies and source
strengths, a precise knowledge of the system geometry was needed. The distances from
source to detector were measured to within 1 mm, and the source was centered over the
detector using a plum-bob and a laser. The mass attenuation coefficients used were also
precisely known, the choice of which bares some discussion.


J**********^*****************
* *
* TH1XRF.F0R *
* *
* FILE PROGRAM *
* *
****************************
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = >[LAZO.DISS.TH1DTH1XRF.DAT'
THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE TH1 IN
BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
GEOMETRY 50. SAMPLE #3 IS 130 PCI/GM TH-232 AND
WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
AND THE COUNT LIVE TIME, LH, LM, t LS. THEN FOR
EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
ERROR, ER(I).
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM XRF1_TH1.CNF;1
D4(l) = 15.0
M5(l) = 6.0
Y5(l) = 87.0
HR(1) = 9.0
MN(1) = 44.0
RH(1) = 1.0
RM(1) = 21.0
RSCl) = 40.53
PH(1) = 396916.0
ER(1) = 1708.0


38
this means that both the standard and unknown must be as close to physically identical as
possible and must be measured using the same detector and in the same position. To achieve
this for soil samples, standards and unknowns usually are dried soil that has been crushed
into powder form, thoroughly mixed into a homogeneous mass, and put into containers.
These containers can then be exposed to an x-ray excitation source and the fluorescent x
rays can be counted. Experiments of this type are easily reproducible.
Unfortunately, standards and unknowns do not always match. The attenuation prop
erties of a soil sample vary with elemental concentrations and soil makeup. Clays, for
example, have different attenuation properties than black dirt. Comparison of unknowns
to standards of different attenuation properties may lead to erroneous results. This may
be compensated for by using very thin samples such that attenuation is not a factor. With
large samples, however, attenuation variations will cause problems.
To eliminate this problem and to eliminate the need to dry and crush soil samples,
and thus significantly decrease sample processing time, the technique described in this
paper is an absolute technique. That is, this technique does not compare unknown samples
to known standards to determine elemental concentrations. This technique can be used
on unprocessed samples which may be inhomogeneous. The teclmique also provides a
quantitative measure, in the form of a X2 value of statistical significance, of whether the
sample is too inhomogeneous to be analyzed without prior processing.
Technique Description
Figure 5 shows the source-target-detector geometry used for this XRF analysis tech
nique. In this configuration, the target is exposed to excitation gammas from the source and
emits fluorescent x rays which are seen at the detector. The detector is shielded from direct
exposure to the sources by the Pb and W source holder. The spectrum seen by the detector


321
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MN(2) =
RH(2) =
RM(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MH(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2JUCB.CNF;1
21.0
7.0
87.0
9.0
28.0
1.0
17.0
44.46
64825.0
575.0
XRF3JJCB. CNF; 1
21.0
7.0
87.0
10.0
59.0
1.0
16.0
5.22
61715.0
613.0
XRF4JJCB. CNF; 1
21.0
7.0
87.0
12.0
43.0
1.0
14.0
58.13
58935.0
398.0


268
C
****************************
c *
c *
c *
c *
c *
c *
****************************
FILE PROGRAM
S2XRF.F0R
*
C
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = '[LAZO.DISS.S23S2XRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE #2 IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE #2 IS 87 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND PEAK AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1.S2B2.CNF; 1
C
D4(l) = 27.0
M5(l) = 5.0
Y5(l) = 87.0
HR(1) = 14.0
MN(i) = 33.0
RH(i) = 1.0
RM(1) = 22.0
RS(1) = 25.46
PH(1) = 264561.0
ER(1) = 2926.0


DATA FROM
XRF2 JS3B1. CNF; 1
D4(2)
26.0
H5(2)
=
5.0
Y5(2)
=
87.0
HR(2)
=
18.0
MN(2)
s
44.0
RH(2)
=
1.0
RM(2)
=
17.0
RS(2)
=
39.50
PH(2)
=
479982.0
ER(2)
=
718.0
DATA FROM
XRF3 J33B1.CNF;1
D4(3)
=
26.0
M5(3)
=
5.0
Y5(3)
=
87.0
HR(3)
=
20.0
MH(3)
=
12.0
RH(3)
=
1.0
RM(3)
=
16.0
RS(3)
=
7.27
PH(3)
=
428292.0
ER(3)
968.0
DATA FROM
XRF4J53B1. CNF; 1
D4(4)
=
26.0
M5(4)
=
5.0
YS(4)
=
87.0
HR(4)
a
21.0
MN(4)
=
31.0
RH(4)
=
1.0
RM(4)
=
14.0
RS(4)
=
49.72
PH(4)
=
375253.0
ER(4)
=
999.0


243
C
C Data is now written into file SAMPLE4.DAT
C
OPEN(1,FILE=SAMPLE4.DAT,STATUS=NEW)
WRITE(lf(A3)) ELEMENT
WRITE(1,*) WF
WRITEd,*) SD
WRITECi,*) Ai
WRITE(1,*) B1
WRITEd,*) Ci
WRITE(1,*) USi
WRITEd,*) US2
WRITE(1,*) US3
CLOSE(1,STATUS='KEEP)
END


47
C contamination concentration at point
node i, pCi/gm of dry soil,
GFi (E1) = FD (E1) x DE (E') x CT,
= geometry factor at energy E' for point
node i,
(counts/s) / (pCi/gm of dry soil).
If a large target of uniformly distributed contamination, with a concentration of C
pCi/gm, were broken into nodes small enough to approximate point nodes then the fluo
rescent x rays from each point node could be calculated by the above equations asstiming
that the source target detector geometry was sufficiently well described. The total signal
from the large target and seen at the detector would then be the sum of the signals from
each of the target point nodes. The detector response could then be modeled as the sum of
all the point node geometry factors.
DR = C x Y, QFi,
where
DR = the photopeak area as measured by a
detector, (counts/s),
C = the uniformly distributed concentration
of contamination in the target,
(pCi/gm of dry soil), and
GFi = the calculated geometry factor for
point node i,
{counts/s) / {pCi/gm of dry soil).


TABLE 31
Peak Fit Results for Sample NJA-U
Sample Contamination Concentration: 196.9 pCi/gm U23B
Counting Geometry
Peak Area
(Count Channels)
Reduced
X2
1
70722 0.9%
6.4
2
67460 0.9%
8.0
3
65292 0.7%
3.3
4
58533 0.9%
4.8
5
51170 0.8%
4.4
6
44378 1.1%
6.0
7
39759 0.6%
2.4
8
34988 1.2%
10.3
TABLE 32
Peak Fit Results for Sample NJB-U
Sample Contamination Concentration: 142.0 pCi/gm U238
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
53408 1.0%
7.5
2
52018 0.9%
6.9
3
45726 0.7%
3.9
4
42182 1.0%
5.2
5
38196 1.0%
6.2
6
34393 1.4%
7.3
7
31299 0.9%
2.2
8
25097 1.3%
4.1


6
Two of the civilian FUSRAP sites were chemical plants involved in processing Th from ore.
Although less prevalent, Th is also found in mill tailings and, thus, is of interest to the
MAD program.
The main reason to develop an assay technique specifically designed to detect U and
Th is that U-238 and Th-232, the most common radioisotopes of U and Th respectively,
emit only low energy and low yield gamma rays. In order to perform gamma spectroscopic
analysis of these radioisotopes, gamma rays emitted by progeny must be used, equilibrium
of the parent with the progeny must be assumed, and concentrations must be inferred from
the presence of the progeny. Table 1 lists the 7-238 decay chain and the radiations emitted
by each member. Table 2 shows equivalent information for the Th-232 decay chain.
Unfortunately, U and Th require long periods to reach equilibrium, and equilibrium
may not have been reached in the soil samples to be analyzed. Also, each decay product
has its own rate of dissolution in ground water. Thus as contamination waits in the soil to
be sampled, varying amounts of U, Th, and their progeny dissolve and diffuse. This also
confuses the equilibrium situation. Since equilibrium can not always be correctly assumed,
the assay technique to be developed must also directly measure U and Th and should not
rely on measurements of progeny.
Process Sensitivity
Since the process to be developed is to be practical in nature, some guidelines as to
sensitivity and accuracy should be followed. Since process application is soil assay for
contaminated sites undergoing decontamination, it is sensible to use guidelines established
by DOE for releasing sites for unrestricted public use.


FIGURE 6
Source Target Detector Spatial Geometry


212
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
* *
* REV6.F0R *
* *
* ATTENUATION COEFFICIENT *
* DATA VERSION 6 *
* *
******************************
CHARACTER *10 DATFIL
DIMENSION MTH(12),E(4),FA(4),UA(4),UB(4),ED(4)
DIMENSION A0(3),E0(2),YI(2)
REAL JA(4)
DATFIL = REV6.DAT
DATA SOURCE REV.6 IS THE FINAL SYSTEM CALIBRATION.
FOR AIR, THE TOTAL MASS ATTENUATION COEFFICIENT IS
USED. FOR BE, THE REMOVAL MASS ATTENUATION COEFFICIENT
IS USED. FOR STEAL AND FOR JARS, MEASURED TRANSMISSION
FRACTIONS ARE USED.
NUMBER OF DAYS PER MONTH DATA FOR CURIE CALCULATIONS
DATA MTH(l), MTH(2), MTH(3), MTH(4) / 31, 28, 31, 30 /
DATA MTH(5), MTH(6), MTH(7), MTH(8) / 31, 30, 31, 31 /
DATA MTH(9), MTH(IO), MTH(ll), MTH(12) / 30, 31, 30, 31 /
GAMMA ENERGIES, KEV, FROM, RADIOACTIVE DECAY
DATA TABLES, BY KOCHER
DATA E(1),E(2),E(3),E(4) / .136476, .122063, .105308, .086545 /
THE FOLLOWING TRANSMISSION FRACTIONS WERE MEASURED. FOR
THE CO-57 SOURCES, THE WINDOW IS INTEGRAL WITH THE SOURCE
CAPSUL, IS MADE OF 304L STAINLESS, AND IS APPROXIMATELY
.0254 CM THICK. FOR THE EU-15S SOURCE, THE WINDOW IS
WELDED IN PLACE, IS MADE OF 302 STAINLESS, AND IS
APPROXIMATELY .005 CM THICK. TRANSMISSION SPECTRA ARE
LOCATED IN FILES SSC03.DATA AND SSEU.DATA.
DATA FA(1),FA(2),FA(3),FA(4) / .94598, .93925, .98771, .98146 /
AIR MASS ATTENUATION COEFFICIENTS, SQ CM/GM, FROM
PHOTON MASS ATTENUATION AND ENERGY ATTENUATION
COEFFICIENTS FROM 1 KEV TO 20 MEV, BY HUBBLE.
DATA UA(1),UA(2),UA(3),UA(4) / .1406, .1459, .1521, .1623 /


FIGURE 7
Compton Scatter Spatial Geometry


TABLE A-7
Representative Soil Elemental Compositions
Elemental Weight Fraction
Element
SI
S2
S3
S4
S5
S6
II
0.02798
-
0.03
0.011
0.005
0.005
Si
0.09414
0.4674
0.29
0.334
0.350
0.400
A1
0.03750
-
0.04
0.099
0.064
0.055
K
0.01060
-
0.01
0.035
0.007
0.020
Ca
0.00965
-
0.01
0.008
0.005
0.011
Fe
0.01652
-
0.02
0.058
0.018
0.017
0
0.06361
0.5326
0.60
0.455
0.551
0.492
Total
1.00000
1.0000
1.00
1.000
1.000
1.000
SI: Average soil composition from Ryman et al.^,
S2: Composition of Sand, Si02,
S3: Soil composition at Hiroshima Bomb Dome,^
S4: Soil composition at Hirosliima Castle,
S5: Soil composition at Nagasaki Hypocenter Monument,
S6: Soil composition at Nagasaki University.^
TABLE A-8
Compton to Total Scatter Coefficient For Soils
at 150keV and 100 keV
Case #
CTR @ 150 keV
CTR @ 100 keV
SI
0.90996
0.78854
S2
0.93484
0.84490
S3
0.92822
0.83065
S4
0.94019
0.85854
S5
0.94076
0.86029
S6
0.93902
0.85526


TABLE 15
Measured vs. Fitted Detector Response for
use
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 135.2 pCi/gm t/238
Reduced X2 Value for Fitted Data : 0.274
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.391
53.0
45.2
2
0.345
46.6
45.2
3
0.305
41.2
42.3
4
0.270
36.5
40.0
5
0.240
32.5
33.9
6
0.214
28.9
28.8
7
0.191
25.9
26.9
8
0.172
23.2
23.0


FIGURE 8
Exploded View of Target Holder Assembly


of interest. Additional x rays or gammas will complicate the transmission spectra, add
background, and generally complicate the results such that true peak areas at the energies
of interest are hard to determine.
Fortunately, over a small energy range attenuation coefficients can be described as a
simple function of energy (personal conversation with John Hubble):
In (n{E)) = A + B x hi{E) + C x (In (E))2,
or
ft (E) = exp (a + Bx In (E) + C x (In (E))2) ,
where A, B, and C are constants.
Therefore, the gamma rays from Eu-155, at 105 keV and 86 keV, are also used and the
soils linear attenuation coefficients at these energies are measured. The four data points,
two from Co-57 gammas and two from Eu-155 gammas, are then fit to the above equation,
using a least squares fit technique, and the linear attenuation coefficients at the U and
Th KaX x-ray energies can be calculated from the resulting curve fit. Table 7 shows typical
soil linear attenuation coefficients.
TABLE 7
Typical Soil'
Anear Attenuation Coefficients
Measured
Curve Fit
Energy (keV)
H{E) (1/cm)
V(E) (1/cm)
136.476
0.20505
0.20517
122.063
0.21505
0.21479
105.308
0.23114
0.23132
98.428
-
0.24056
93.334
-
0.24866
86.545
0.26159
0.26155


83


8
TABLE 1 (continued)
; 1
| Ma)or Radiation Energies |
1 0
VIeV) and Intensities |
Radionuclide
Half-Life
Alpha
Beta
Gamma
Po-214
164.0 us
7.69 (100%)
-
0.799 (0.014%)
(99.98%)
77-210
1.3 min
-
1.3 (25%)
0.296 (80%)
(.02%)
1.9 (56%)
0.795 (100%)
2.3 (19%)
1.31 (21%)
P6-210
21.0 a
3.72 (2E-6%)
0.016(85%)
0.047 (4%)
0.061(15%)
P-210
5.10 d
4.65 (7E-5%)
1.161 (100%)
-
(Branches)
4.69 (5E-5%)
Po- 210
138.4 d
5.305 (100%)
-
0.803(0.0011%)
(100%)
-
77-206
4.19 min
-
1.571 (100%)
-
(.00013%)
P6-206
Stable
NOTES + Indicates those gamma rays that are commonly used to identify U-238. Equilibrium
must be assumed.


312
C ****************************
c *
C USAXRF.FOR *
C *
C FILE PROGRAM *
C *
c ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = '[LAZO.DISS.USA]USAXRF.DAT'
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE USA IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY BA, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE USA IS 165 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRF1_USA.CNF;1
D4(l)
=
9.0
M5(l)
=
7.0
Y5(l)
=
87.0
HR(1)
=
14.0
MN(1)
=
8.0
RH(1)
=
1.0
RM(1)
=
17.0
RS(1)
=
56.43
PH(1)
=
386406.0
ER(1)
=
1848.0


1175
1176
1177
1178
1179
1180
1181
1182
1183
1185
1186
1187
1188
1190
1192
1194
1196
1198
1200
1205
1207
1210
1215
1219
1221
1223
1225
1230
1235
1240
1245
1247
1248
1249
1251
1252
1253
1254
1255
1256
1257
1259
1260
1265
1270
1272
1282
1284
GOTO 970
S = SI
FOR I = 1 TO H
VAR(I) = OLDVAR(I)
NEXT I
SIG = VAR(l)
XB = VAR(2)
A = VAR(3)
CHisq = ocHisq
AREA = 0
FOR I = 1 TO 27
X(I) = INT (XB) 13 + (I 1)
FOR J = 1 TO NP
IF X(I) = PK(1,J) THEN GOTO 1198
NEXT J
Y(I) = 0
GOTO 1200
Y(I) = PK(2,J)
GOSUB 2000
FIT(I) = F6
IF F6 < 0 THEN FIT(I) = 0
PRINT X(I),Y(I),FIT(I)
AREA = AREA + FIT(I)
NEXT I
GOSUB 8000
GOSUB 1500
REM
LPRINT This is a WHOLEPK.BAS run'
LPRINT
LPRINT The Peak Data was obtained from disk file ;FILE$
LPRINT
LPRINT Convergence in ;W1; itterations. S = ;S
LPRINT
LPRINT Reduced Chi Squared Value = ;CHISq
LPRINT
LPRINT Peak Area = ; AREA; +- ;DAREA; Count-Channels
LPRINT with ;(FR 100);*/, of the area
LPRINT beyond XB +- 13 channels
LPRINT
LPRINT Fitted Parameters
LPRINT
LPRINT GA = ;GA
FOR I = 1 TO M
LPRINT VA$(I); = ;VAR(I)
NEXT I
LPRINT
LPRINT Peak Fit Results
LPRINT


LIST OF TABLES
Table Page
1. Uranium 238 Decay Chain 7
2. Thorium 232 Decay Chain 9
3. Summary of DOE Residual Contamination Guidelines 11
4. U and Th K-Shell Absorption and Emission 32
5. Co-57 and Eu-155 Emission Energies and Yields 32
6. Co-57 and Eu-155 Physical Characteristics .32
7. Typical Soil Linear Attenuation Coefficients 36
8. Isotopic Concentrations: ppm vs. pCi/gm 63
9. Soil Assay Results for U and Th Contaminated Soil 93
10. Assay Sensitivity to the Number of Fitting Points Used 94
11. Measured vs. Fitted Detector Response for U1 95
12. Measured vs. Fitted Detector Response for Ula 96
13. Measured vs. Fitted Detector Response for NJA-U 97
14. Measured vs. Fitted Detector Response for NJB-U 98
15. Measured vs. Fitted Detector Response for USC 99
16. Measured vs. Fitted Detector Response for USD 100
17. Measured vs. Fitted Detector Response for Sample 2 101
18. Measured vs. Fitted Detector Response for Sample 3 102
19. Measured vs. Fitted Detector Response for Sample 4 103
20. Measured vs. Fitted Detector Response for Till 104
xi


279
C
C DATA FROM XRF8_S3B1.CNF;1
C
C
C
C
D4(8) = 26.0
M5(8) = 5.0
Y5(8) = 87.0
HR(8) = 15.0
MN(8) = 33.0
RH(8) = 1.0
RM(8) = 10.0
RS(8) = 50.94
PH(8) = 636039.0
ER(8) = 2614.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
5 F0RMAT(1I2)
WRITE(1,10) LH, LH, LS
10 F0RMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), H5(I), Y5(I)
25 FORMAT(IF10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


237
Sample Description Programs
These programs were written to create data files which provide data concerning each
individual sample. These programs are written in FORTRAN-77 and were run on a VAX
Cluster main-frame computer. SAMPLE2.FOR through SAMPLEUSD.FOR provide spe
cific information about the physical characteristics of each sample. S2XRF.F0R through
USDXRF.FOR provide specific information about the counting data for each individual
sample.


254
C
C *********************
c *
C SAMPLENJATH.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample NJA-TH, a non-homogenous
C Th and U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Height Fraction, HF
C
HF = 0.91408
C
C Sample Density, SD
C
SD = 0.97771
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.05487
Bl = 1.35142
Cl =-1.47242
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.25367
US2 = 0.30389
US3 = 0.38495


da = Klein Nishina differential scatter cross
section, (cm2 / electron) ,
= rl X d X [ ]
EDens = electron density at point A, (electrons/cm3) ,
Vol = volume of point A, (cm3) .
The energy of the scattered gaimna is given by (Evans pp 677-689)
1 cos (0) + (1 /a)
where
E' = energy of the scattered gamma, (keV),
0 scatter angle,
m0 c2 = electron rest mass,
= 511 keV,
E
~ 2
m0 c2
E energy of the incident gamma, (keV).
The flux at point B due to Compton scatter at point A is then described by
where
FL2 (E') =
RX
X2 sin (0) d0d X exp (-[i po X),
FL2 (E1) = flux at point B due to Compton scatter
at point A, (gammas/cm2s) ,
E' energy of scattered gamma, (keV),
RX scatter reaction rate, (scatters/s),


13
that an accurate assay can be performed. In the third section the final result of the analysis,
the radionuclide concentrations of U and Th in the soil sample, is calculated.
Literature Search
In order to learn more about existing techniques of gamma spectroscopic analysis, x-
ray fluorescent analysis, peak shaping techniques, soil moisture determination, and assay of
inhomogeneous samples, a computer literature search was performed. The central research
library at ORNL performed the search, looking through Chemical Abstracts, Physical Ab
stracts, and the DOE Energy Data Base. Many references which discussed these topics
were located, however no references were found which discussed data analysis techniques
similar to that presented in this work were located.


28
of channels in the peak. The actual vertical change in the background is equal to the
difference between the number of counts in the last low energy side background channel
and the number of counts in the first high energy side background channel. Then the
vertical background change due to the step function is equal to the actual vertical change
minus the vertical change due to the slope. The use of this rationale results in a step
function background whose slope at either side of the peak fits smoothly with the actual
background slopes.
Unfortunately, the background slope of the spectrum under consideration in this work
does not change uniformly from the low energy side of the peak to the high energy side.
Rather, the slope on the low energy side is very steep, changes very quickly, and then
approaches the slope on the high energy side. The average background slope, as described
above, will therefore be too steep and the vertical change attributable to the slope will exceed
the actual vertical change. Under these circumstances, GRPANL will fit the background to
a smoothly changing slope without a step change.
Wliile this might seem contrary to theory, Baba et al.^ state, for large peaks in a
multiple! group or even for smaller single peaks, that the peak areas and centroids are
determined with sufficient accuracy by using a properly fit straight line, curved, or step
function background. As mentioned earlier, peak fitting is as much an art as a defined
science.
Bearing all of the above in mind, the approach used in this work was to use both the
step function and the sloping background. The background is easily fit to a third or fourth
order polynomial. In this work then, the vertical change in background beneath the peak is
attributed half to the polynomial and half to the step function. The resulting background is
shown in Figure 4. Source listings of POLYBK.FT and BKG, the codes used to accomplish
the background determination and subtraction, are supplied in Appendix C.


TABLE 38
Peak Fit Results for Sample Thl
Sample Contamination Concentration: 143.5 pCi/gm Th232
Counting Geometry
Peak Area
(C omit Channels)
Reduced
X2
1
396916 0.4%
8.6
2
367607 0.4%
10.3
3
333507 0.5%
11.6
4
298668 0.5%
14.0
5
251311 0.9%
42.4
6
232490 0.5%
8.5
7
196953 0.7%
20.4
8
171638 0.8%
20.6
TABLE 39
Peak Fit Results for Sample Thla
Sample Contamination Concentration: 144.2 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
390175 0.5%
21.3
2
359972 0.7%
37.4
3
331580 0.5%
15.2
4
298234 0.5%
10.8
5
259990 0.5%
11.5
6
221465 0.4%
4.8
7
199930 0.6%
14.9
8
178059 0.7%
13.7


259
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(1,FILE=SAMPLENJBTH.DAT,STATUS^'NEW)
WRITE(1,'(A3)') ELEMENT
WRITECl,*) WF
WRITE(1,*) SD
WRITE(1,*) A1
WRITECl,*) B1
WRITECl,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSEC1,STATUS=KEEP')
END


61
but
ficcale = EDens X tr?~N
where
EDens = soil electron density, (electrons / cm2),
crf~N = Klein Nislvina Compton scatter cross
section, (cm2/electron).
therefore
EDens
calc
c
aK-N
where all terms are as previously defined.
Natural Production of Fluorescent X Rays
Since progeny of both 17-238 and Th-232 emit U and Th x rays (see tables 1 and 2) the
natural x-ray production rate was also calculated. As will be seen in the results section,
this term contributed less than 1% to the total fluorescent x-ray production.
The decay chains of 17-238 and Th-232 are very similar. In both cases, the parent alpha
decays to the first progeny, the first progeny beta decays to the second progeny, and the
second progeny beta decays to the parent element with an atomic weight four less than that
of the parent. As the second progeny decays, the beta is emitted leaving the meta-stable
decayed atom looking very much like a parent atom with one extra electron. During the
complicated events that follow beta decay, the decayed atom emits x rays that are of energy
characteristic of the parent atom.


58
Factor for point B, analogous to the Geometry Factor calculated in the previous section for
unscattered gammas. The result of these equations is a summation equation completely
analogous to that derived in the previous section
CDRi (E') = C x CGFi {E'),
where
CDRi {E') detector response at energy E'
to Compton scatter production at point
node i,
{counts/s) / (CpCi/gm of dry soil),
C contamination concentration at point
node i, (pCi/gm of dry soil),
CGFi {E') = Compton geometry factor at energy E'
for point node i,
{counts/s) / {pCi/gm of dry soil).
As before, the contribution from each point node of a large target could be summed to
yield the total calculated detector response due to Compton scatter gamma production. The
Compton scatter production portion of the detector response cannot, however, be measured.
Actually the measured detector response is the sum of fluorescent x-ray production due to
unscattered excitation gammas and Compton scattered excitation gammas, and these two
contributions cannot be physically separated. The solution is to alter the model such that
the measured detector response is modeled as being the sum of the unscattered gamma
Geometry Factors and the Compton scattered Geometry Factors
DRi {E!) = C x {GFi {E!) + CGFi {E')),
where all terms are as previously defined.


TABLE 42
Peak Fit Results for Sample USA
Sample Contamination Concentration: 181.4 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
386406 0.5%
15.1
2
351203 0.4%
9.8
3
315752 0.5%
6.7
4
275494 0.6%
21.8
5
252671 0.6%
18.0
6
212386 0.5%
6.1
7
184506 0.6%
10.5
8
164036 0.6%
9.3
TABLE 43
Peak Fit Results for Sample USB
Sample Contamination Concentration: 159.6 pCi/gm Th232
Counting Geometry
Peak Area
(C ount- Channels)
Reduced
X2
1
352365 0.4%
12.0
2
310193 0.7%
21.3
3
274348 0.5%
12.0
4
253452 0.3%
2.9
5
216978 0.5%
7.2
6
185294 0.6%
13.0
7
157422 0.6%
10.3
8
153290 0.8%
18.5


137
source is made of stainless steel and has a .0254 cm stainless steel window. Between the
source and the detector is a large body of air. And finally, a .0254 cm Be window covers the
Ge crystal detector. Any additional objects put between the source and the detector also
attenuate photons. Thus the number of photons that reach the detector and are counted
in the full energy peak can be described by
FL (E) =
ER(E) AD tj(E) CT
4 tR\
ATN (E),
(A6)
where
FL (E) = the gamma flux measured by the detector, ie., the
full energy peak area at energy E, (gammas),
ER(E) = the emission rate of the source at energy E,
(gammas/s),
AD = the detector area, (cm2) ,
Tj(E) = the detector intrinsic energy efficiency at
energy E,
(gammas counted per gamma hitting the detector)
CT = count time, (s),
Ri = the distance from the source to the
detector, (cm),
ATN (E) = gamma attenuation, at energy E, due to the
stainless steel source capsule, the air
between the source and the detector, any other
object put between the source and the detector,
and the Be window of the detector,
= exp(~p(£) p0 R) x exp (~p{E) p0 R)Air
x exp {-fi(E) p0 R)obj x exp (/x (E) p0 R)Be,


164
2REM **********************************
3 REM *
4 REM POLYBK.BAS *
5 REM with Error Analysis *
6 REM *
7 REM **********************************
8 REM
10 DIM X(50),Y(50),A(50,9),TA(9,50),F(50),DY(50),V(9),DF(2),DS(9)
20 DIM XT(50),YT(50),S(50),K1(5),K2(5),V0LD(5),SL(5),HLD(9,9),H(50,5)
30 DIM Ql(50,50),Q2(9,50),Q3(9,50),AA(9,9),DT(9,1),AM(9,10),DA(9)
40 DIM C0V(9,9), SIG(50), C0EF(9)
50 W1 = 1
55 PI = 3.141592653#
90 PRINT How many of the Right Background points should be
92 PRINT used for the background polynomial fit?
94 INPUT RF
96 PRINT
100 PRINT Input the Order of the Polynomial to be fit
105 INPUT 01
110 M = 01 + 1
116 PRINT
119 PRINT Input the name of the Spectrum data file
120 INPUT BK$
122 OPEN I*, #1, BK$
126 INPUT #1, DP
130 INPUT #1, LB
134 INPUT #1, RB
140 FOR I = 1 TO DP
150 INPUT #1, XT(I)
157 NEXT I
158 FOR I = 1 TO DP
165 INPUT #1, YT(I)
170 NEXT I
175 CLOSE #1
180 FOR I = 1 TO LB
185 X(I) = XT(I) XT(1)
190 Y(I) = YT(I) / 5000
195 NEXT I
198 J = DP RB + 1
200 FOR I = (LB + 1) TO (LB + RF)
205 X(I) = XT(J) XT(1)
210 Y(I) = YT(J) / 5000
215 J = J + 1
220 NEXT I
225 PRINT Background Data Points"
230 PRINT
235 PRINT X(I)", Y(I)"
237 PRINT


11
TABLE 3 (a, b, c) 3
Summary of DOE Residual Contamination Guidelines
Soil Guidelines (Maximum limits for Unrestricted Use)
Radionuclide
Soil Concentration (pCi/g) above Background
Ra- 226
- 5 pCi/g averaged over the first 15 cm of
Ra- 228
soil below the surface.
T/i-232
- 15 pCi/g when averaged over any 15 cm
Th- 230
thick soil layer below the surface layer.
Other
-Soil guidelines will be calculated on a
radionuclides
site specific basis using the DOE manual
developed for this use.
a: These guidelines take into account ingrowth of Ra-226 from Th-230, and
Ra-228 from Th-232 and assume secular equilibrium. If either Th-230 and
JRa-226, or T/i-232 and Ra-228 are both present, not in secular equilibrium,
the guidelines apply to the higher concentration. If other mixtures of ra
dionuclides occur, the concentrations of individual radionuclides shall be
reduced so that the dose for the mixtures will not exceed the basic dose
limit.
b: These guidelines represent unrestricted-use residual concentrations above
background, averaged across any 15 cm thick layer to any depth and over
any contiguous 100m2 surface area.
c: If the average concentration in any surface or below surface area less than
or equal to 25m2 exceeds the authorized limit or guideline by a factor of
\/l0 0/A where A is the area of the elevated region in square meters, limits
for HOT SPOTS shall be applicable. These hot spot limits depend on the
extent of the elevated local concentrations and are given in the supplement.
In addition, every reasonable effort shall be made to remove any source of
radionuclide that exceeds 30 times the appropriate soil limit irrespective of
the average concentration in the soil.
X-Ray Fluorescent Analysis (XRF)
Atoms can be ionized, i.e., have one or more electrons removed, via several processes. In
the case of x-ray fluorescence, gamma or x rays incident on an atom undergo photoelectric
reactions resulting in the ionization of the atom. The ionized atom then de-excites via the
emission of x rays. An upper shell electron falls into the hole vacated by the ionized electron
and x rays, equal in energy to the difference in shell energies, are emitted. Since elements
have characteristic atomic energy levels, the emitted x rays are characteristic of the element


229
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5I.F0R *
* *
I****************************
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5I.DAT
This program creats file GE0M5I.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Zi
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 11.7
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32


TABLE 18
Measured vs. Fitted Detector Response for
Sample 3
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC Fitted Contamination Concentration
Calculated CC : 221.7 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.242
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.462
324.1
333.9
2
1.287
285.4
290.0
3
1.137
252.1
255.0
4
1.008
223.4
220.6
5
0.895
198.5
194.9
6
0.798
176.9
174.4
7
0.713
158.1
150.0
8
0.639
141.7
133.2


252
C
C *********************
C *
C SAMPLENJAU.FOR *
C *
C *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample NJA-U, a non-homogenous
C Th and U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Height Fraction, WF
C
WF = 0.91408
C
C Sample Density, SD
C
SD = 0.97771
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.05487
Bl = 1.35142
Cl =-1.47242
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.25367
US2 = 0.30389
US3 = 0.35591


266
C
C ***#!*****************
c *
C SAMPLEUSD.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample USD, a non-homogenous
C U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Height Fraction, WF
C
HF = 0.78909
C
C Sample Density, SD
C
SD = 1.6687
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.25039
Bl = 0.61177
Cl =-0.33336
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.24413
US2 = 0.25768
US3 = 0.28921


264
C
C *********************
c *
C SAMPLEUSC.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample USC, a non-homogenous
C U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Weight Fraction, WF
C
WF = 0.76647
C
C Sample Density, SD
C
SD = 1.6058
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.24604
Bl = 0.59428
Cl =-0.37477
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.24741
US2 = 0.26040
US3 = 0.29039


317
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MW(2) =
RH(2) =
RH(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MN(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2JJSB. CNF; 1
15.0
7.0
87.0
10.0
5.0
1.0
15.0
50.74
310193.0
2039.0
XRF3JUSB.CNF;1
15.0
7.0
87.0
11.0
28.0
1.0
14.0
45.12
274348.0
1409.0
XRF4JJSB. CNF; 1
15.0
7.0
87.0
13.0
6.0
1.0
13.0
55.72
253452.0
738.0


292
C ****************************
c *
C TH1AXRF.F0R *
C *
C FILE PROGRAM *
C *
C ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),YS(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = '[LAZ0.DISS.TH1A3TH1AXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE TH1A IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE TH1A IS 130 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRFIJTHIA.CNF;1
D4(l)
=
18.0
M5(l)
=
6.0
Y5(l)
=
87.0
HR(1)
=
11.0
MN(i)
=
38.0
RH(1)
=
1.0
RM(1)
=
21.0
RS(1)
=
47.00
PH(1)
=
390175.0
ER(1)
=
2084.0


1
REM
2
REM
*
*
3
REM
*
BKG.BAS *
4
REM
*
*
5
REM
*
with Polynomial *
6
REM
*
and Step Function *
7
REM
*
Background Subtraction *
8
REM
*
*
9
REM
******************************
10 REM
15 DIM X(99),Y(99),SIG(99),VAR(99)
20 DIM PK(99),BK(99),PF(99)
30 DIM PBK(99),SBK(99),SL(99)
55 PI = 3.141592653#
100 PRIHT Input the name of the Spectrum data file
105 INPUT BK$
110 OPEN I ,#1,BK$
120 INPUT #1, DP
130 INPUT #1, LB
140 INPUT #1, RB
145 FOR I = 1 TO DP
155 INPUT #1, X(I)
160 NEXT I
165 FOR I = 1 TO DP
175 INPUT #1, Y(I)
180 NEXT I
185 CLOSE #1
190 FOR I = 1 TO DP
195 PRINT X(;I;) = ;X(I), Y(;I;) = ;Y(I)
200 NEXT I
500 PRINT Input the name of the Polynomial fit data file
505 INPUT POLY$
510 PRINT
515 OPEN I',,#1,P0LY$
525 INPUT #1, N
530 FOR I = 1 TO N
540 INPUT #1, K
550 INPUT #1, K
553 INPUT #1, SIG(I)
555 NEXT I
565 INPUT #1, PO
570 FOR I = 1 TO PO
580 INPUT #1, PF(I)
585 NEXT I
590 CLOSE #1
1000 L = 0
1005 Y1 = 0
1010 Y2 = 0


DATA FROM
XRF5J33B1. CNF; 1
D4(5)
=
26.0
H5(B)
=
B.O
YB(5)
=
87.0
HR(B)
=
10.0
MN(6)
=
23.0
RH(5)
=
1.0
RH(5)
=
12.0
RS(B)
=
SB. 03
PH(B)
=
899790.0
ER(5)
2317.0
DATA FROM
XRF6J33B1. CNF;1
D4(6)
=
26.0
MB(6)
=
6.0
YB(6)
=
87.0
HR(6)
=
12.0
MN(6)
=
13.0
RH(6)
=
1.0
RM(6)
=
12.0
RS(6)
=
7.9B
PH(6)
=
798214.0
ER(6)
=
2662.0
DATA FROM
XRF7_S3B1.CNF; 1
D4(7)
=
26.0
M5(7)
=
B.O
YB(7)
=
87.0
HR(7)
=
14.0
MN(7)
=
19.0
RH(7)
=
1.0
RM(7)
=
11.0
RS(7)
=
26.93
PH(7)
=
710364.0
ER(7)
=
1878.0


283
C
C DATA FROM XRF8_U1.CNF;1
C
C
C
C
D4(8) = 2.0
M5(8) = 6.0
Y5(8) = 87.0
HR(8) = 22.0
MN(8) = 56.0
RH(8) = 1.0
RM(8) = 12.0
RS(8) = 21.82
PH(8) = 56134.0
ER(8) = 450.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS='NEW')
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RMATC1F1O.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 FORMAT(2F15.5)
100 CONTINUE
END


308
C ****************************
c *
C NJBTHXRF.FOR *
C *
C FILE PROGRAM *
C *
C ****************************
C
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.NJB]NJBTHXRF.DAT*
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE NJB-TH IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE NJA-TH IS 2590 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1JTJB.CNF; 1
C
D4(l) = 7.0
M5(l) = 7.0
Y5(l) = 87.0
HR(1) = 11.0
MN(1) = 10.0
RH(1) = 1.0
RM(1) = 15.0
RS(1) = 32.81
PH(1) = 2896677.0
ER(1) = 3378.0


255
C
C Data is non written into file SAMPLE4.DAT
C
OPEN(i,FILE=SAMPLENJATH.DAT,STATUS='NEW)
WRITE(1,(A3)') ELEMENT
WRITECl,*) WF
WRITECl,*) SD
WRITECl,*) A1
WRITECl,*) B1
WRITECl,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSEC1,STATUS=KEEP)
END


Soil Moisture Content and Attenuation Coefficients 32
Soil Attenuation Coefficient 33
Soil Moisture Content 37
System Model 37
Introduction 37
Technique Description 38
Mathematical Model 41
Compton Scatter Gamma Production of Fluorescent X Rays 51
Compton scatter gamma model 51
Mathematical model 52
Electron Density 60
Natural Production of Fluorescent X Rays 61
Isotopic Identification 63
Error Analysis 65
Introduction 65
Least Squares Peak Fitting 66
Covariance Matrix and Functional Error 69
Error Propagation 71
Linear Function Fitting 72
Experimental Procedure 74
Sample Counting 74
Data Analysis 86
III RESULTS AND CONCLUSIONS 88
Experimental Results 88
Assay Results 88
Peak Fitting Results 112
Conclusions 122
Recommended Future Work 122
Vll


195
C0(1) = C0(2)
C0(2) = HOLD
DO 950 I = 1,VT
DO 950 J = 1,RT CT / 2
950 GF(I,J) = 0.0
WRITE(6,955) 19
955 FORMAT(/,IX,GF data completed for Geometry #,11)
WRITE(3,*) GFT0TALCI9)
1000 CONTINUE
CLOSE(3,STATUS=KEEP)
C
C THIS SECTION PRINTS OUT ALL THE USER SUPPLIED
C SETUP INFORMATION FOR EACH IMAGE RUN.
C
CTO = BOTTLE
WRITE(6,1010) SMPLE,CTO,WF,SD,EL
1010 F0RMAT(/,1X,THIS IS AN IMAGE RUN,//,
1 THE FOLLOWING DATA IS THE USER SUPPLIED IMAGE INPUT,//,
2 THIS DATA IS FOR ,A10, / ,A6,//,
3 SAMPLE DRY SOIL WEIGHT FRACTION (WF): .F8.6,//,
4 SAMPLE DENSITY (SD): ,F8.6, gm/cc,//,
5 THIS SAMPLE IS CONTAMINATED WITH ,A2,//,
6 SOIL LINEAR ATTENUATION COEFFICIENTS (1 / cm),/,
7 ENERGY (MeV),US (1/cm))
DO 960 I = 1,3
960 WRITE(6,*) E(I),US(I)
DO 963 I = 1,8
963 WRITE(6,965) I.GFTOTAL(I)
965 FORMAT(/,IX,GF total for Geometry #,I1, is .F12.8)
WRITE(6,970) GFFILE
970 FORMAT(/,IX,GEOMETRY FACTORS STORED IN FILE ,A30)
9000 END


223
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5C.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5C.DAT
This program creats file GE0M5C.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 10.8
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32


70
Covar (1,1) = cr2 (Pi),
Covar (2,2) = cr2 (P2) ,
Covar (3,3) = Covar (n, n) = cr2 (Pn).
The covariance matrix is diagonally symmetrical, with the off diagonal elements being
the covariances of the various parameters, for example
Covar (1, 2) = cr2 (PI, P2).
These values are used to calculate the errors associated with fitting parameters at
various stages of determining the final solution, the soil contaminant concentration and its
associated error. But in addition to knowing the errors associated with fitting parameters,
the errors associated with functions of those fitting parameters are necessary. For this
work, only linear functions of fitting parameters are used. The error associated with a
linear function of fitting parameters is given by the following equation^
if: F(X : Pl,P2,P3,...,Pn),
where : P1,P2,P3, ...,Pn and their associated errors
are known,
then for : Q (X : PI, P2, P3,..., Pn),
n n
<72(Q(Xi)) == Pi2 X =1 *,=1
This equation and the covariance matrix as determined via the least squares process
described here are all that is needed to properly propagate error through the peak fitting
portion of this work.


UF Libraries:Digital Dissertation Project
Internet Distribution Consent Agreement
In reference to the following dissertation:
AUTHOR: Lazo, Edward
TITLE: Determination of radionuclide concentratins of U and Th in unprocessed
soil samples / (record number: 1130251)
PUBLICATION DATE: 1988
I, /K ,/ as copyright holder for the aforementioned
dissertation, hereby grant specific and limited archive and distribution rights to the Board of Trustees
of the University of Florida and its agents. I authorize the University of Florida to digitize and
distribute the dissertation described above for nonprofit, educational purposes via the Internet or
successive technologies.
This is a non-exclusive grant of permissions for specific off-line and on-line uses for an indefinite
term. Off-line uses shall be limited to those specifically allowed by "Fair Use" as prescribed by the
terms of United States copyright legislation (cf, Title 17, U.S. Code) as well as to the maintenance
and preservation of a digital archive copy. Digitization allows the University of Florida to generate
image- and text-based versions as appropriate and to provide and enhance access using search
software.
This grant of permissions prohibits use of the digitized versions for commercial use or profit.
Signature of Copyright Holder
Printed or Tvned Name of Convrisht Holder/Licensee
Personal information blurred
// i** f
Date of Signature
Please print, sign arid return to:
Cathleen Martyniak
UF Dissertation Project
PreservationDepartittent
University of Florida Libraries
P.O. Box 117007
Gainesville, FL 32611-7007
2 of 2
10-Jun-08 15:23


299
C
C DATA FROM XRF8_NJA.CNF;i
C
D4(8) = 7.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 9.0
HN(8) = 49.0
RH(8) = 1.0
RM(8) = 9.0
RS(8) = 4.26
PH(8) = 34988.0
ER(8) = 430.0
C
C STORE DATA ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS=NEW')
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 F0RMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,2B) D4(I), M5(I), Y5(I)
25 F0RMATC1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


93
TABLE 9
Soil Assay Results for U and Th Contaminated Soil
17-238
(pCi/gm)
Sample
XRF(l)
ORNL(2)
U1
152.3 0.4
-
Ula
164.6 0.3
-
Ul/Ula avg.
158.6 0.5
184.5 10.5
N.TA
196.9 0.6
-
NJB
142.0 0.5
-
NJA/NJB avg.
168.5 0.8
171.0 db 17.0
use
135.2 0.4
-
USD
138.9 0.4
-
USC/USD avg.
137.1 0.6
133.4 10.4
Th-232
(pCi/gm)
Sample
XRF(l)
ORNL(2)
Sample 2
93.6 0.3
87.5 1.8
Sample 3
221.7 0.2
228 4.0
Sample 4
683.0 0.6
688 17.0
Till
143.5 0.3
-
THla
144.2 0.3
-
TlIl/TIIla avg.
143.8 0.4
119.5 3.9
NJA
2436.7 0.9
_
NJB
2267.0 1.0
-
NJA/NJB avg.
2348.9 1.3
2590.0 72.0
USA
181.4 0.3
-
USB
159.6 0.3
-
USA/USB avg.
170.7 0.4
165.2 4.0
1. Analysis performed by the technique developed in this dissertation. Reported
errors are lcr and were calculated as described in chapter II.
2. Analysis performed by gamma spectroscopy on dry and homogeneous samples
at Oak Ridge National Laboratory.


323
C
C DATA FROM XRF8JJSC.CNF;1
C
D4(8) = 22.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 10.0
HN(8) = 29.0
RH(8) = 1.0
RM(8) =10.0
RS(8) = 36.56
PH(8) = 35238.0
ER(8) = 307.0
C
C STORE DATA ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS='NEW)
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 FORMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


89
Till: Homogeneous sample made from clean soil spiked with Th02 to a con
centration of approximately 125 pCi/gm. The spike used was pure
Th 232.
THla: A second homogeneous sample made from the same spike as TH1. Again,
the approximate concentration of the sample was 125 pCi/gm.
Ul: Homogeneous sample made from clean soil spiked with U3Oa to a con
centration of approximately 170 pCi/gm. The spike used was natural
U30B.
Ula: A second sample made from the same spike as Ul. Again, the concen
tration of the sample was approximately 170 pCi/gm.
Sample 2: Homogeneous sample made from the mixture of several samples
collected at FUSRAP sites in Northern New Jersey. The sample
concentration was designed to be approximately 80 pCi/gm.
Sample 3: Homogeneous sample made from the mixture of several samples
collected at FUSRAP sites in Northern New Jersey. The sample
concentration was designed to be approximately 225 pCi/gm.
Sample 4: Homogeneous sample made from the mixture of several samples
collected at FUSRAP sites in Northern New Jersey. The sample
concentration was designed to be approximately 650 pCi/gm.
It should be noted here that the actual concentrations of Th or U in samples Ul, Ula,
TH1, and THla were determined by two assays from two separate laboratories. The uncer
tainties of source preparation, such as accurate weighing of the spike material, transference
of all the spike material from the weighing foil to the soil, and the complete homogenization


131
by rearranging the equation. As with the NBS source, twenty measurements of the Eu-
155 source were made to insure statistical significance. Average values for ER(E) were
determined and used in subsequent calculations.
To determine the precise activities of the Co-57 sources using the same method as
above, the detector intrinsic energy efficiency at 122 keV was needed. The efficiency data
from the NBS source was fit to a curve and the detector intrinsic energy efficiency at 122
keV was determined from the curve. Keeping in mind that the area of the spectrum that
is of interest extends only from 86 keV to 136 keV, only three efficiencies were used to fit
a quadratic curve. The efficiencies at 86 keV, 105 keV, and 123 keV were chosen because
they are all within the energy range of interest.
The data point at 176 keV was too far from the area of interest to be used. The shape
of the efficiency curve is a function of the detector and the associated electronics. While the
shape of this curve can be approximated as quadratic over a limited energy range, extending
that range beyond necessary limits is questionable. The fitted curve was thus only able to
provide information as to the efficiency at 122 keV.
Using Equation A-l then, the emission rates of the three Isotope Products Co-57 sources
were determined in the same manner as the Eu-155 emission rates were determined. Only
the 122 keV peak was used. For Co-57 the relative yields of the 122 keV and 136 keV
gammas are well known and are listed in Table 5. The emission rate of the 122 keV gamma
(gammas/s) is equal to source activity (dis/s) times gamma yield (122 keV gammas/dis).
The measured 122 keV emission rate was thus used to determine the source activity in
disintegrations per second, and in Curies. This activity also applies to the 136 keV gamma.
As with the NBS source and the Eu-155 source, twenty measurements of each Co-57 source
were made to insure statistical accuracy. Average values of source strength (Ci) for each
Co-57 source were determined and used in all subsequent calculations.


307
C
C DATA FROM XRF8JTJABCNF; 1
C
C
C
C
D4(8) = 9.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 11.0
MN(8) = 27.0
RH(8) = 1.0
RM(8) = 9.0
RS(8) = 24.32
PH(8) = 25097.0
ER(8) = 327.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS='NEW)
WRITE(1,5) NF
5 F0RMAT(1I2)
WRITEC1.10) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


134
Mass Attenuation Coefficients
Photons traveling from a source to a detector, through any material, will reach the
detector if they are aimed properly and if they do not undergo an interaction which changes
their direction or energy. For a source that emits photons isotropically, those photons which
are emitted into the solid angle subtended by the detector are properly aimed. Thus if the
source emits S gammas/s, then the number of gammas per second that are emitted into the
proper solid angel is
Sd =
S x AD
4wR2
(A4)
where
Sd = the number of photons/s that enter the
solid angle subtended by the detector,
AD = detector area, (cm2),
R the distance from the source to the
detector (cm).
But not all the photons that are properly aimed will reach the detector. Photons can
undergo several types of interactions with atoms of the medium between the source and
the detector. Photons can be completely absorbed. Photons can undergo photoelectric
interactions, yielding an electron-positron pair. Photons can undergo compton scatter,
yielding a scattered electron and a gamma of new energy and new direction. Or photons
can undergo coherent scatter, yielding a gamma of unchanged energy but traveling in a
slightly altered direction.
But not all of these interactions will necessarily remove a photon from the beam. Here
removal means that a photon which entered the solid angle subtended by the detector is


141
Table A-5 lists only one set of calculated values because the calculated value of // (E)If_¡0
did not vary with data set. This means two things. First, that the removal attenuation
coefficient fits the data better than the total attenuation coefficient. This is evident since
both data sets yielded the same coefficients. Second, that coherent scatter in the source
stainless steal window, in the air between the source and the detector, and in the detector
Be window, is an insignificant contributor to the situation. This is evident, again, because
whether or not the coherent scatter attenuation coefficient was included, the calculation
yielded the same answer.
A second experiment, which supports the same conclusions, was also conducted. The
mass attenuation coefficient of water was measured with the jar center located 12.1 cm,
16.6 cm, and 21.0 cm from the detector. Twenty counts were performed at each location.
The average values h(E)Hi0 are listed in Table A-6.
TABLE A-6
n(E)h2oi Calculated Values
vs. Target Distance from the Detector +
Distance
pi (136AreV)Ha0
fi (122keV)Hj0
(cm)
(cm2/gm)
(cm2/gm)
12.6
0.1509 0.0004
0.1551 dh 0.0001
16.6
0.1512 0.0003
0.1553 0.0001
21.0
0.1512 0.0003
0.1554 0.0001
+: The reported standard deviations are calculated using repetition statistics only.
Although the average of the twenty measurements at 12.6 cm is within the error bounds
of the average values of the measurements at the other two distances, there is a statistical
difference between the first and the second two averages. This is due to low angle incoherent
scattering. When the target is close to the detector, the angle at which photons can inco
herently scatter and still ldt the detector is larger than when the target is farther from the


7
TABLE l2
U-238 Decay Chain
Radionuclide
Half-Life
I Me
1
Alpha
ijor Radiation Ene
MeV) and Intensii
Beta
rgies |
ies |
Gamma
U- 238
4.59E9 a
4.15 (25%)
4.20 (75%)
"
"
T/i-234
24.1 d
0.103 (21%)
0.063 (3.5%)+
Pa-234
(Branches)
1.17 min
-
2.29 (98%)
1.75 (12%)
0.765 (0.30%)
1.001 (0.60%)+
Pa-234
(.13%)
6.75 h

0.53 (66%)
1.13 (13%)
0.100 (50%)
0.70 (24%)
0.90 (70%)
P-234
(99.8%)
2.47E5 a
4.72 (28%)
4.77 (72%)
-
0.053 (0.2%)
T/i-230
8.0E4 a
4.62 (24%)
4.68 (76%)
-
0.068 (0.6%)
0.142 (0.07%)
Pa-226
1.602E3 a
4.60 (6%)
4.78 (95%)
-
0.186 (4%)
Rn-222
3.823 d
5.49 (100%)
-
0.510 (0.07%)
Po-218
(Branches)
3.05 min
6.00 (100%)
0.33 (0.019%)
-
P6-214
(99.98%)
26.8 min

0.65 (50%)
0.71 (40%)
0.98 (6%)
0.295 (19%)
0.352 (36%)
Af-218
(.02%)
2.0 s
6.65 (6%)
6.70 (94%)
-
-
Pz-214
19.7 min
5.45 (.012%)
1.0 (23%)
0.609(47%)
(Branches)
5.51 (.008%)
1.51(40%)
3.26(91%)
1.120 (17%)
1.764 (17%)


G8
where all terms are previously defined.
Substituting this into the least squares minimization equation yields
dS _vdF(,Y<)0 ^dF(Xt)Q
dPl ^ dPl 1 J ^ dPl
x(P(X,.)o-y,) = 0,
where
[ ] = DPI X
dF{Xt)0
dPl
+ DP2 x
dF(Xt) Q
dP2
+ PP3 x
dP3
+ h DPn x
dPn
DPn = Pn\ Pn0.
This can be rewritten as
^ dP 1 1 J ^ dPl
X^-PTOo).
As previously stated, similar equations are generated for each differential equation
dS dS
dPl ~rfP2 dPn ~ '
This system of equations lends itself to the matrix form
DF4 (n, m) X DF (m, n) x
A(n,l)
= PP (n,
m) X PT (m
/ dF{Xi )n
dP(Xt)n
dF(Xt)n
dF(X,)
dP 1
dP 2
dPZ
' dPn
dF{X,)
dF{X,)0
dF(X,)
dF(X3)
DF (m,
n) =
dP 1
dP 2
dP 3
dPn
dP(jir)0
dF(Xm)
*F(Xm)0
' dP 1 dP 2 dP 3 dPn
DFl (n, rn) = the transpose of DF (m, n),
n = the number of parameters in the fitting function,
m = the number of data points used in the fit,


225
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5E.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5E.DAT
This program creats file GE0M5E.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 11.1
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32


CLOSE(i,STATUS=KEEP)
OPEN(1,FILE=CGFFILE,STATUS=OLD)
DO 200 P = 1,NP
READ(1,*) CGFT(P)
GFTOT(P) = GFT(P) + CGFT(P)
WRITE(6,147) P,CGFT(P)
147 FORMAT(/,IX,Compton GF Total for Position #,I1,
1 ,1X, is .F10.5)
200 CONTINUE
CLOSE(1,STATUS=KEEP)
C
C THIS PROGRAM FITS DETECTOR RESPONSE DATA TO AN
C LINIAR FUNCTION. THE X-AXIS REPRESENTS THE
C CALCULATED SAMPLE GEOMETRY FACTOR, GF, WHILE THE
C Y-AXIX REPRESENTS THE MEASURED DETECTOR RESPONSE.
C
W1 = 1
OPEN(1,FILE=PKFIL,STATUS=OLD)
READCl,237) NP
237 F0RMAT(1I2)
READ(1,240) LH, LM, LS
240 F0RMATC3F1O.5)
TI = 1.0
DO 300 I = 1,NP
READ(1,245) D4, M5, Y5
245 FORMAT(1F10.5, 112, 1F10.5)
READ(1,250) HR, MN
250 FORMAT(2F10.5)
READ(1,255) RH, RM, RS
255 FORMAT(3F10.5)
READ(1,260) DR(I),ER(I)
260 F0RMAT(2F15.5)
CH = RH + RM / 60.0 + RS / 3600.0
CALL DECAY(HR, MN, CH, D4, M5, Y5, NF,MK)
LT = LH 3600.0 + LM 60.0 + LS
RT = RH 3600.0 + RM 60.0 + RS
CR = DR(I) / LT
NCR = EXP ( LOG (CR) .583863 (LT RT) / LT)
NLT = LT CR / NCR
X(I) = GFTOT(I)
Y(I) = DR(I) / (NLT NF)
NER(I) = ER(I) / (NLT NF)
WRITE(6,*) I, X(I), Y(I), NER(I)
TI = TI + 1.0
300 CONTINUE
CLOSE(1,STATUS=KEEP)
M = 1
N = NP
CALL EXPLICIT(X,Y,NER,NP,F,Ai,ZERO,DAI,DZERO,CHI)


233
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
****************************
* *
* GE0M5M.F0R *
* *
***************************lf:
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GEOMSM.DAT
This program creats file GEOMSM.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(i) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft S)
XT = 12.3
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.SO
TR = 2.32


TABLE A-4
System Calibration Parameters
Detector Intrinsic Energy Efficiency:
Energy (keV)
Efficiency
136.476
0.6934
123.073
0.7609
122.063
0.7656
105.308
0.8302
98.428
0.8493
93.334
0.8609
86.545
0.8736
Source Strengths:
- Co57
1 October, 1986
Source #
Activity (mCi)
1
2.022
2
2.207
3
2.388
- Eu165
Gamma Energy (keV)
Emission Rate (Gamma/s)
105.308
1.8250xl07
86.545
2.5484a:107


122
Conclusions
1. An XRF assay technique for 7-238 and Th-232 in bulk unprocessed soil samples has
been developed.
2. The assay technique developed here provides results which are comparable in accuracy
and precision to those provided by gamma spectroscopy.
3. The assay technique developed here works well on dry homogeneous samples as well as
on actual collected samples which have not been processed.
4. The assay technique developed here does not work well on samples which are very
inhomogeneous. Samples wliich are very inhomogeneous will result in data points which
do not yield good least squares fits to straight lines. The user is free to choose the level
of significance, by using the X2 value of the straight line fit, at which he/she will
reject the calculated value of U and Th concentrations. Samples which are rejected for
being too inhomogeneous to be analyzed by this technique should be dried, ground,
homogenized, and re-analyzed.
5. The assay technique developed here requires no fudge factor to accurately determine
contamination concentrations in samples which are not processed.
6. It has been determined that approximately 15% of the fluorescent x-ray production
is due to singly scattered Compton gammas. Compton production has therefore been
included in this XRF analysis of bulk samples.
Recommended Future Work
Dased on this work there are several research areas worthy of follow-up.
1. The computer programs used for data processing should be optimized to shorten their
run times.


272
c *
C S3XRF.F0R *
C *
C FILE PROGRAM *
C *
£ $$$$$$$ $$$$$*$ $££££$$ 3f:it:3(c*stJ|c)|[
c
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, MB(20)
PKFIL = [LAZO.DISS.S3]S3XRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE #3 IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY SO. SAMPLE #3 IS 228 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRF1.S3B1.CNF;1
D4(l)
=
26.0
M5(l)
=
5.0
Y5(l)
=
87.0
HR(i)
=
16.0
MN (1)
=
54.0
RH(1)
=
1.0
RM(i)
=
19.0
RS(1)
=
41.51
PH(1)
=
541821.0
ER(1)
=
2133.0


27
X = peak centroid, and
a = detector response function width for
peak centered at X.
The numeric approximation to this function used in this work in HYPERMET^ and
in GRPANL15 is
where
SB{ X,)
BL + (BH BL) x
j=1 i=1
5
SB (X{) = step background value at channel X,
BL = average background value on the low energy
side of the peak,
BH = average background value on the high energy
side of the peak,
y Y (Xi) = the sum of the gross channel counts from the
1 first peak channel to channel X, and
N
y Y (Xi) = the sum of the gross channel counts from the
3 first peak channel to the last peak channel.
The above algorithm assumes that the background to either side of the peak is relatively
flat. This will not necessarily be the case for all spectra and is certainly not the case for
this work.
GRPANL, in addition to using the above step function, allows the use of two different
background slopes, one for each side of the peak. The average slope of the background under
the peak is then the average of the background slopes from either side of the peak. The
change in background attributable to this slope is then equal to the vertical change of a
line, having the average background slope, over a horizontal change equal to the number


I would like to thank Dr. Barry Berven, committee member, Oak Ridge National
Laboratory (ORNL), who provided me with technical guidance and the managerial backing
necessary to ensure the purchase of the equipment necessary for this work.
I would like to thank Dr. Guven Yalcintas, committee member, ORNL, who provided
me with technical assistance throughout the work at ORNL.
I would like to thank Dr. Joel Davis, University of Tennessee at Chattanooga, who
provided invaluable assistance, guidance and technical expertise in every aspect of the work
performed at ORNL. Without Dr. Davis help and friendship this dissertation would have
required much more time and would not have been half as fun as it was.
I would like to thank Dr. Keith Eckerman, ORNL, who provided expert assistance in
development of the mathematical model, which is the core of this dissertation, and in just
about any other areas where I needed help. Again, without the assistance and friendship
of Dr. Eckerman this work would have been very much more tedious.
I would like to thank Dr. Jeff Ryman, ORNL, who provided assistance in the develop
ment of the transport mathematics used in the mathematical model.
I would like to thank Dr. George Keogh, ORNL, who provided assistance in developing
the analytical mathematics used in the computer model.
I would like to thank Debbie Roberts, ORNL, who performed several invaluable exper
iments for me after I had left ORNL, and who performed the soil assay against which I am
gaging my technique.
I wrould like to thank Dr. Rowena Chester, ORNL, who provided managerial backing
for the project and its purchases.
IV


291
C
C DATA FROM XRF8_TH1.CNF;1
C
C
C
C
D4(8) = 16.0
M5(8) = 6.0
Y6(8) = 87.0
HR(8) = 12.0
MN(8) =58.0
RH(8) = 1.0
RM(8) = 12.0
RS(8) = 17.70
PH(8) = 171638.0
ER(8) = 1446.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITEC1.5) NF
5 F0RMAT(1I2)
WRITE(l.lO) LH, LH, LS
10 FORHAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), H5(I), Y5(I)
25 FORHATdFlO.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 F0RMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 F0RMATC3F1O.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


143
To determine this ratio, John Hubble of the National Bureau of Standards was con
tacted. From this conversation it was determined that trace elements in soils do not con
tribute significantly to the ratio of compton scatter cross section to total linear attenuation
coefficient. This was then tested using the computer code XSECT at Oak Ridge National
Laboratory. XSECT is a data base type program which calculates cross sectional data for
a mixture of elements given the elements of the mixture and their weight fractions.
Several compositions of soil were used. Ryman et al. ^ sampled the compositions of 19
soil samples to determine a representative average composition. This average composition
was used to investigate gamma ray doses at air- ground interfaces, thus it is very applicable
to this work. The composition used is listed in table A-7. Four other soil compositions, from
Kerr et al. which were determined for areas near the Hiroshima and Nagasaki bomb sites
for neutron dose studies, were also used and are listed in table A-7. Finally, the composition
of sand, Si02, was used. Table A-8 lists the compton to total ratios at 150 keV and 100
keV for each of these soil compositions. These ratios were determined from data calculated
using XSECT. Finally, table A-9 lists the average ratio values at 150 keV and 100 keV,
and the linearly interpolated values at 136.476 keV and 122.063 keV. These are the values
which were used in the program COMPTON.FOR to determine the rate of fluorescent x-ray
production by compton scatter gamma.
As can be seen from these tables, the compton to total scatter ratio for soils is relatively
constant for various different soil compositions. This consistency justifies the use of this
ratio in the calculations of Chapter II.


Geometry Factor Programs
These programs were written to perform the main body of the soil assay calculations.
All four programs are written in FORTRAN-77, were run on a VAX Cluster main-frame
computer, and are described in Chapter II. D1ST.FOR is a preliminary program which
creates data files for use by subsequent programs. The data files consist of the distances
from each source to each of the 3840 points of the target, and files of the distances from
each of the 3840 target points to each of the 24 nodes of the detector. These distances
include the total distance as well as the distance from the point to the boundary of the
soil target. IMAGE.FOR uses the distances stored by DIST.FOR to calculate Geometry
Factors (GFs) for each of the 3840 points of the target. The sum of the GFs is then stored.
COMPTON.FOR calculates, in addition to the distances described above, the distances
from each target point to each other target point. These are used to determine the Compton
Geometry Factors (CGFs) for each of the 3840 target points. The sum of the CGFs is then
stored. Finally ASSAY.FOR uses the stored GFs and CGFs, as well as detector response
data, and fits this data to a straight line. The slope of the line, which is the only fitting
parameter, is the soil contamination concentration and is the desired result of the assay.


57
exp (fi po X) = attenuation factor for
gammas passing through soil,
and
p soil attenuation coefficient
at energy E',
p = soil density, (gm/cm3),
X = distance from point A to
point B, (cm),
X2sin(0) d0d(j> = surface area through which
gammas, scattered at point
A into dfi about fi,
pass upon reaching point B.
But since the reaction rate, RX, contains the term da which contains the term sin (#)
dO d, this will cancel out of the numerator and denominator leaving
, FLi (E) X r* x [ ] x EDens x Vol
FL2 {E') = 5L_J x exp (-p p X),
where all terms are as previously defined.
Knowing the flux at point B and the energy of the incident gammas, allows the calcu
lation, using the equations described in the previous section, of the photoelectric reaction
rate at point B due to scatter in point A, the fluorescent x-ray production rate at point B
due to scatter in point A, the x- ray attenuation from point B to the detector due to scatter
in point A, and the number of fluorescent x-rays from point B due to scatter in point A
counted by the detector. To determine the entire production of fluorescent x rays at point
B, scatter from every other point node in the target that results in gammas reaching point
B must be calculated. A summation of all these contributions yields a Compton Geometry


1015 NS = LB + 1
1020 NE = DP RB
1025 BK(NS 1) = Y(NS 1)
1030 DT = Y(NE + 1) Y(NS 1)
1035 FOR I = NS TO NE
1040 Y1 = Y(I) + Y1
1045 NEXT I
1050 FOR I = (NS 1) TO NE
1055 XN = X(I) X(l)
1060 FOR J = 2 TO PO
1065 SL(I) = (J 1) PF(J) (XN ** (J 2)) + SL(I)
1070 NEXT J
1075 SL(I) = SL(I) 5000
1080 IF I = (NS 1) THEN GOTO 1120
1085 Y2 = Y2 + Y(I)
1090 SBK(I) = .5 (Y(NS 1) + DT (Y2 / Yl))
1095 PBK(I) = .5 (BK(I 1) + .5 (SL(I 1) + SL(I)))
1100 BK(I) = SBK(I) + PBK(I)
1105 PK(I) = Y(I) BK(I)
1115 VAR(I) = Y(I) + SBK(I) + .5 ((SIG(I)) ** 2)
1120 NEXT I
2005 LPRINT This is a BKG.BAS run"
2010 LPRINT
2015 LPRINT Gross Counts data from file ;BK$
2020 LPRINT
2025 LPRINT Polynomial fit data from file ;POLY$
2030 LPRINT Polynomial of order ;(PO 1)
2035 LPRINT
2040 FOR I = 1 TO PO
2045 LPRINT V(;I;) = ;PF(I)
2050 NEXT I
2100 LPRINT
2105 LPRINT Channel, Counts", Peak, Bkg,,,Sig
2110 LPRINT
2115 FOR I = NS TO NE
2120 LPRINT X(I),Y(I),PK(I),BK(I),SQR(VAR(I))
2125 LPRINT
2130 NEXT I
2300 FOR I = NS TO NE
2310 PRINT X(I),PK(I),SQR(VAR(I))
2315 PRINT
2320 NEXT I
2370 PRINT In what file is the Peak data to be stored?
2375 INPUT PEAK!
2380 PRINT
2400 PRINT In what file is the Background data to be stored?
2405 INPUT BK$
2412 PRINT


241
C
C Data is now written into file SAMPLE2.DAT
C
OPEN(1,FILE=SAMPLE3.DAT,STATUS=NEW)
WRITE(1,(A3)) ELEMENT
WRITECl,*) WF
HRITECl,*) SD
WRITE(1,*) A1
WRITECi,*) B1
WRITE(1,*) Cl
WRITEd,*) US1
WRITE(1,*) US2
WRITEd,*) US3
CLO SE(1,STATUS=KEEP)
END


35
where
TF (E) = transmission fraction for gammas at
energy E, (gammas transmitted through
the object uncollided per gamma incident
on the object), and
Therefore
other terms are as previously defined.
tt(E)xp. = (-l/x)xln(TF(£!)),
where
n(E)xp0 object linear attenuation coefficient, (cm-1).
In the case where the attenuating object is a cylindrical jar of soil, this equation results
in the soils linear attenuation coefficient at energy E. This information is used in the
next phase of this assay process, dealing with data analysis, to eventually determine U and
Th concentrations. As will be described in the next section, the soils linear attenuation
coefficient is necessary at four energies; 136 keV and 122 keV, which are the energies of the
Co-57 gamma rays used to induce x-ray fluorescence in U and Th, 98 keV, the energy of
the Kal x ray from U, and 93 keV, the energy of the Kai x ray from Th.
It should be noted here that the soil in the jar is actually a mixture of dry soil and
water. For the purposes of simplicity the term soil will be used to refer to this soil water
mixture.
Since Co-57 is used to induce x-ray fluorescence, the same source can be used to measure
transmission gamma rays and thus determine the soils linear attenuation coefficients the
energies of the Co-57 gammas. Unfortunately, no clean and calibrated source of U or Th x
rays is available. In this case, clean refers to a source that emits x rays only at the energy


Measured Peak Area
(CountChannels)
15G


****************************
* *
* COMPTON.FOR *
* *
****************************
COMMON XTC,YTC,ZTC,TR
INTEGER RT, CT, VT, RD, CD
CHARACTER *1 RAM, A
CHARACTER *2 ELEMENT
CHARACTER *35 XRF, COMDTA
CHARACTER *35 DATFIL, GFFILE
CHARACTER *35 TGFILE, GEOM
DIMENSION XT(3840),YT(3840),ZT(3840),XD(24),YD(24),ZD(24)
DIMENSION XS(2),YS(2),ZS(2)
DIMENSION R1T(2,3840),R2T(2,3840),R1DC24,3840),R2D(24,3840)
DIMENSION U(2,3840),V(2,3840),W(2,3840)
DIMENSION V0L(3840),AD(24),EDENSITY(2)
DIMENSION Q(10),ED(3),UB(3),US(3),UA(3),TF(2),A0(2),YI(2)
DIMENSION E(2),CTRATI0(2),ALPHA(2),SCAT(2),DSCAT(2,2)
DIMENSION FL1(2,2),FL2(2,2),C0TH(2),ES(2,2),PE(2,2),USS(2,2)
DIMENSION RX(3840),GF(3840)
REAL JA(3),M0C2,KS,KY,KA1NAT
PI = 3.14159
M0C2 = .511
RO = 2.81784E-13
RAM = 'RAM'
TGFILE = TGFILE'
GFFILE = GFFILE
DATFIL = DATFIL
GEOM = GEOM
READ GEOMETRY DATA FROM FILE GEOM
OPEN(1,FILE=GEOM,STATUS=OLD)
NUMBER OF SOURCES USED
READ(1,*) NS
SOURCE COORDINATES
DO 80 I = 1,NS
READCl,*) XS(I), YS(I), ZS(I)
TARGET CENTER CpORDINATES


DATA FROM
XRF2JUi.CNF;1
D4(2)
=
2.0
H5(2)
=
6.0
Y5(2)
=
87.0
HR(2)
=
11.0
MN(2)
=
63.0
RH(2)
=
1.0
RM(2)
=
20.0
RS(2)
=
59.48
PH(2)
=
118246.0
ER(2)
=
694.0
DATA FROM
XRF3_U1.CNF;1
D4(3)
=
2.0
M5(3)
=
6.0
Y5(3)
=
87.0
HR(3)
=
13.0
MN(3)
=
29.0
RH(3)
=
1.0
RM(3)
=
18.0
RS(3)
=
42.19
PH (3)
=
98117.0
ER(3)
=
767.0
DATA FROM
XRF4JUI.CNF;1
D4(4)
=
2.0
M5(4)
=
6.0
Y5(4)
=
87.0
HR(4)
=
16.0
MN(4)
=
8.0
RH(4)
=
1.0
RM(4)
=
17.0
RS(4)
=
17.48
PH(4)
=
96466.0
ER(4)
=
763.0


FIGURE 10
Target in Place Above Detector
Showing Laser Alignment System


10
The decontamination criteria established by DOE are based on the Homestead Farmer
scenario. This scenario assumes that a farmer will homestead on contaminated lands, will
grow all his/her own food on the land, will raise and graze his/her own livestock on the
land, will drink water from wells on the land, and eat fish from a stream running through
the land. Limiting radionuclide concentrations were calculated such that the homestead
farmer would not build up radionuclide body burdens greater than those suggested by the
National Council on Radiation Protection and Measurements (NCRP). Table 3 lists relevant
guidelines. Soil radionuclide content limitations are in units of pCi/gm of dry soil.
Statement of Problem
The objective of this research is to develop a fast and economical technique for lab
oratory assay of U and Th in an inhomogeneous sample consisting of moist, chunky soil
compressed into a plastic, cylindrical jar. The product of this assay should be the isotopic
concentrations of 7-238, {7-235, Th-232, and Th-230 in pCi per gram of dry soil averaged
over the entire sample. To accomplish tins assay the technique must determine the dry
soil weight, must be sensitive to U and Th isotopic concentrations from approximately 100
pCi/gm to 2000 pCi/gm, and must account for the effects of sample inhomogeneity.
Current teclmiques for the non-destructive assay of U in soil samples include neutron
activation analysis and gamma spectroscopy. Gamma spectroscopy and its limitations have
been discussed previously. Neutron activation depends upon the availability of a large
neutron source. Since it is advantageous to develop a process that is as simple, portable,
and as inexpensive as possible, neutron activation can be ruled out. The technique chosen for
this application is x-ray fluorescent analysis (XRF). Details of the technique are described
in the following sections.


329
14. Baba, H., Baba, S., Suzuki, T., Effect of Baseline Shape on the Unfolding of
Peaks in the Ge(Li) Gamma-Ray Spectrum Analysis, Nuclear Instruments and
Methods, 145 (1977), 517 523.
15. Gunnink, R., Ruhter, W. P., GRPANL: A Program for Fitting Complex
Peak Groupings for Gamma and X-ray Energies and Intensities, UCRL-52917,
Lawrence Livermore Laboratory, Livermore, CA, January, 1980.
16. Phillips, G. W., Marlow, K. W., Automatic Analysis of Gamma-Ray Spectra
from Germanium Detectors, Nuclear Instruments and Methods, 137 (1976),
525 536.
17. Browne, E., Firestone, R. B., Table of Radioactive Isotopes, John Wiley &
Sons, New York, NY (1986).
18. Koclier, D. C., Radioactive Decay Data Tables, Technical Information Cen
ter Office of Scientific & Technical Information, United States Department of
Energy, DOE/TIC-11026, Oak Ridge, TN (1981).
19. ICRP Report No. 38, Radiological Transformations, Energy and Intensity of
Emissions, Pergamon Press, Oxford, England (1983).
20. Forsythe, G. E., Malcolm, M. A., Moler, C., Computer Methods for Mathemat
ical Computations, Prentice-Hall, Englewood Cliffs, New Jersey (1972).
21. J. Orear, Notes on Statistics for Physicists, Revised, Laboratory for Nuclear
Studies, Cornell University, Ithaca, NY (1982).
22. Chan, Heaug-Ping, Doi, Kunio, Physical Characteristics of Scattered Radiation
in Diagnostic Radiology: Monte Carlo Simulation Studies, Medical Physics, Vol
12, Mar/Apr (1985).
23. Hubble, J. II., Photon Mass Attenuation and Energy Absorption Coefficients
for 1 keV to 20 MeV, Int. J. Appl. Radiat. Isot., 33 (1982), 1269 1290.
24. Lindstrom, R. M., Fleming, R. F., Accuracy in Activation Analysis: Count
Rate Effects, Proceedings, Fourth International Conference on Nuclear Meth
ods in Environmental and Energy Research, University of Missouri, Columbia,
CONF-800433 (1980), 25 35.
25. Olson, D. G., Counting Losses in Gamma Ray Spectrometry Not Eliminated by
Dead Time Correction Circuitry, Health Physics, 51, No. 3 (1986), 380 381.
26. Ryman, J. C., Faw, R. E., Slmltis, K., Air-Ground Interface Effects on Gamma-
Ray Submersion Dose, Health Physics, Pergamon Press, New York, New York,
Vol. 41, No. 5 (1981), 759 768.
27. Kerr, G. D., Pace, J. V., Scott, W. H., Tissue Kerma vs. Distance from
Initial Nuclear Radiation from Atomic Devices Detonated over Hiroshima and
Nagasaki, ORNL/TM 8727, Oak Ridge National Laboratory (1979).
28. Brooks, R. A., Di Cliiro, G., Principles of Computer Assisted Tomography and
Radioisotopic Imaging, Phys. Med. Biol., 21, No. 5 (1976), 689 732.


FIGURE 4
Polynomial and Step Function X-Ray Peak Background


74
Experimental Procedure
Sample Counting
Once the experimental apparatus is constructed and properly calibrated, as described
in Appendix A, the processing of samples is straight forward and requires only eight steps.
1. Samples are placed in 100 ml plastic jars and weighed. The soil may be wet and not
completely uniformly mixed. The sample jars are of radius 2.32 cm with an active
height of 6.50 cm.
2. The sample is weighed, wet or dry in the jar, and the average jar weight, 20.7 0.1
gm, is subtracted to obtain the sample weight.
3. The sample jar is placed in a known geometry above a Ge detector, described in detail
in Appendix A, such that the center of the sample is directly in line with the center of
the detector. In this work, the jar center is 11.6 0.1 cm from the detector window,
and the detector window to detector distance is 0.5 cm.
4. A Co-57 source is placed directly in line with the center of the detector such that the
sample jar is between the source and the detector. The source to detector window
distance is 89.4 0.2 cm. The transmitted fraction of 136 keV and 122 keV gammas
from Co-57 is then measured. Count duration is dependent upon source strength. In
this work, count times of one hour are used. Shorter times could be used by placing
the source closer to the detector such that the detector system dead time remained
below 20% or so, and the total counts under the peaks in question were statistically
significant. In this work, peak areas are on the order of 100,000 counts.
5. The Co-57 source is replaced with an Eu-155 source and step three is repeated, mea
suring the transmitted fraction of 105 keV and 86 keV gammas from Eu-155. The


182
7030
qi(j,i) = A(J,I)
7040
q2(I,J) = TA(I,J)
7050
NEXT J
7060
NEXT I
7070
GOSUB 4500
7080
FOR I = 1 TO M
7090
FOR J = 1 TO M
7100
AA(I,J) = q3(I,J)
7105
HLD(I,J) = q3(I,J)
7110
NEXT J
7120
NEXT I
7130
W = 1
7140
FOR I = 1 TO N
7150
qi(i.i) = dy(i)
7160
FOR 11 = 2 TO M
7170
qi(i,n) = 0
7180
NEXT 11
7190
NEXT I
7200
GOSUB 4500
7210
FOR I = 1 TO M
7220
DT(I,1) = q3(i,i)
7230
NEXT I
7240
GOSUB 5000
7250
FOR I = 1 TO H
7255
OLDVAR(I) = VAR(I)
7260
VAR(I) = VAR(I) + DA(I)
7265
DA(I) = 0
7270
NEXT I
7280
RETURN
8000
REM
8002
REM Subroutine to calculate Error in
Peak Area
8004
REM
8006
REM The first part of the subroutine
inverts AA(M,
8008
REM yield the covariance matrix, COV(M,M)
8009
REM
8010
FOR I = 1 TO M
8015
COVCI.I) = 1
8020
NEXT I
8025
FOR I = 1 TO M
8030
T1 = HLD(I,I)
8035
FOR J = 1 TO M
8040
HLD(I.J) = HLD(I.J) / Tl
8045
COV(I.J) = COV(I,J) / Tl
8050
NEXT J
8055
FOR J = 1 TO M
8060
IF J = I THEN GOTO 8090
8065
T2 = HLD(J.I)
8070
FOR K = 1 TO M


305
DATA FROM
XRF2_NJB.CNF; 1
D4(2)

7.0
M5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
14.0
HN(2)
=
10.0
RH(2)
=
1.0
RM(2)
=
14.0
RS(2)
=
31.67
PH(2)
=
52018.0
ER(2)
=
453.0
DATA FROM
XRF3_NJB.CNF;1
D4(3)
=
7.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
16.0
HN(3)
=
8.0
RH(3)
=
1.0
RM(3)
=
13.0
RS(3)
=
3.41
PH(3)
=
45726.0
ER(3)
=
315.0
DATA FROM
XRF4 JJJB. CNF; 1
D4(4)
8.0
M5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
10.0
MN(4)
=
18.0
RH(4)
=
1.0
RM(4)
=
12.0
RS(4)
=
12.69
PH(4)
=
42182.0
ER(4)
=
435.0


DO 850 I = 1,RD CD
850 WRITEC2,*) AD(I)
SLICE = SLICE + 1
DO 900 I = 1,RT CT / 2
900 PTS(I,3) = PTS(I,3) + TH / VT
IF(PTS(1,3) .GT. ZT) GOTO 1000
GOTO 275
1000 CLOSECl.STATUS^KEEP)
CLOSE(2,STATUS^*KEEP')
9000 END


FIGURE 5
Source Target Detector Physical Geometry


277
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MW(2) =
RH(2) =
RH(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MN(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2J53B1.CNF;1
25.0
5.0
87.0
19.0
23.0
1.0
16.0
30.31
1287314.0
2590.0
XRF3_S3B1.CHF;1
25.0
5.0
87.0
20.0
42.0
1.0
15.0
3.62
1148003.0
1957.0
XRF4J33B1. CNF; 1
25.0
5.0
87.0
22.0
3.0
1.0
13.0
53.55
1014348.0
2344.0


DO 95 I = 1,4
95 READ(1,*) UB(I)
UB(3) = 0.0
UB(4) =0.0
DO 100 I = 1,4
100 READ(1,*) ED(I)
ED(3) = 0. 0
ED(4) = 0.0
DO 105 I = 1,3
105 READ(1,*) AO(I)
DO 110 I = 1,2
110 READ(1,*) EO(I)
DO 115 I = 1,2
115 READd,*) YI(I)
READ(1,*) FHOLD
DO 120 I = 1,4
READ(1,*) JACI)
120 JA(I) = SQRTCJA(I))
JA(3) = 0.0
JA(4) =0.0
CLOSE(1,STATUS=*KEEP)
C
C SOURCE-TARGET DISTANCE (STD5A TO 50) FILES AND
C TARGET-DETECTOR DISTANCE (TDD5A TO 50) FILES
C
150
160
175
SPFILE(l) = [LAZO.DISS.DATA]STD5A.DAT
SPFILE(2) = [LAZO.DISS.DATA]STD5C.DAT
SPFILE(3) = [LAZO.DISS.DATA]STD5E.DAT
SPFILE(4) = [LAZO.DISS.DATA]STD5G.DAT
SPFILE(5) = [LAZO.DISS.DATA]STD5I.DAT
SPFILE(6) = [LAZO.DISS.DATA]STD5K.DAT
SPFILEC7) = [LAZO.DISS.DATA]STDSM.DAT
SPFILE(8) = [LAZO.DISS.DATA]STD50.DAT
PDFILE(l) = [LAZO.DISS.DATA]TDD5A.DAT
PDFILEC2) = [LAZO.DISS.DATA]TDD5C.DAT
PDFILE(3) = [LAZO.DISS.DATA]TDD5E.DAT
PDFILEC4) = [LAZO.DISS.DATA]TDD5G.DAT
PDFILE(5) = [LAZO.DISS.DATA]TDD5I.DAT'
PDFILE(6) = [LAZO.DISS.DATA]TDD5K.DAT
PDFILE(7) = [LAZO.DISS.DATA]TDD5H.DAT
PDFILEC8) = [LAZO.DISS.DATA]TDD50.DAT
WRITE(6,150) XRFFIL
FORHATC/,IX,'READING XRF DATA FROM FILE ,A30)
OPEN(1,FILE=XRFFIL,STATUS=OLD)
IF (EL .EQ. U>) GOTO 175
DO 160 I = 1,10
READd,*) QHOLD
DO 180 I = 1,10


55
Klein-Nisliina differential scatter cross section, in units of {cm2 / electron) / (dfl), is given
by (Evans pp 677-689)
do = r2 X dfl X [],
where
do differential cross section,
{cm2 / electron),
r0 = classical electron radius, (cm),
dil = sin {6) dOd(j)
and
0 = gamma ray scatter angle with respect
to the original direction of motion,
= rotational angel about the original
direction of motion,
[...] = terms from equation, see reference 6 (pp 677 689).
Using these two equations, the reaction rate for gammas scattering at A into the solid
angle d about fi, in other words towards B, is given by
RX = FLX {E) x do x EDens x Vol,
where
RX = scatter reaction rate, {scatters/s),
FLy {E) = flux of excitation gammas at point A,
{gammas/cm2s) ,


8075
8080
8085
8090
8095
8100
8110
8120
8130
8140
8200
8210
8220
8230
8240
8250
8253
8255
8260
8270
8280
8284
8290
8300
8305
8310
8320
8325
8330
8340
8350
8360
8370
8380
8390
8395
8400
8410
8420
8500
8510
8520
8525
8530
8540
8550
8560
8570
9000
183
HLD(J.K) = HLD(J,K) (HLD(I,K) T2)
COV(J.K) = C0V(J,K) (C0V(I,K) T2)
NEXT K
NEXT J
NEXT I
FOR I = 1 TO M
FOR J = 1 TO M
COV(I.J) = COV(I,J) S/(N M)
NEXT J
NEXT I
FOR II = 1 TO M STEP 2
DF(2) = 0
FOR J = 1 TO M
DS(J) = 0
NEXT J
DS(Ii) = VAR(Il) .001
PRINT
PRINT AREA *, NAREA *'
SIG = VAR(l) + DS(1)
XB = VAR(2)
A = VAR(3) + DS(3)
NAREA = 0
FOR I = 1 TO 27
GOSUB 2000
IF F6 < 0 THEN F6 = 0
NAREA = NAREA + F6
NEXT I
PRINT AREA,NAREA
DF(1) = (NAREA AREA)/DS(I1)
TE = DF(1) DF(2)
IF ABS(TE) <= ABS(.001 DF(1)) GOTO 8390
DS(I1) = DS(I1) .5
DF(2) = DF(1)
GOTO 8260
DA(I1) = DF(1)
PRINT DA(jll; ) = jDACll)
NEXT II
T1 = 0
T2 = 0
FOR I = 1 TO H
T1 = T1 + ((DA(I)) ** 2) COV(I.I)
FOR J = 1 TO H
IF J = I THEN GOTO 8540
T2 = T2 + DA(I) DA(J) COV(I,J)
NEXT J
NEXT I
DAREA = SqRCTl + T2)
RETURN
END


FIGURE B-l
Relative Sample Separation vs. Solution Matrix Condition


208
C
C **************************
c *
C SUBROUTINE DECAY *
C *
C **************************
c
C THIS SUBROUTINE DETERMINES CO-57 SOURCE ACTIVITY
C DECAYED FROM 1 OCTOBER, 1986, TO HALF WAY THROUGH
C THE XRF COUNT UNDER CONSIDERATION. AS OF
C 1 OCTOBER, 1986, ALL THREE CO-57 SOURCES WERE
C ROUGHLY 2 MCI.
C
SUBROUTINE DECAY(HR,MN,CH,D4,M5,Y5,NF,MK)
REAL MN, NF, MTH(12), LA
IF(MK .EQ. 1) GOTO 25
MTH(l) = 31.0
MTH(2) =28.0
MTH(3) =31.0
MTH(4) =30.0
MTH(5) = 31.0
MTH(6) =30.0
MTH(7) = 31.0
MTH(8) = 31.0
MTH(9) = 30.0
MTH(IO) = 31.0
MTH(ll) = 30.0
MTH(12) = 31.0
25 MK = 1
HC057 = 271.7
H6 = HR + MN / 60.0 + CH / 2.0
IF(H6 .GT. 24.0) GOTO 50
D5 = D4 1.0 + H6 / 24.0
GOTO 55
50 D5 = D4 + (H6 24.0) / 24.0
55 Ti = 91.5
IF(M5 .EQ. 1) GOTO 80
DO 75 J = 1,(M5 1)
75 Tl = Tl + MTH(J)
80 T = Tl + D5
LA = LOG (2.0) / HC057
NF = EXP ( LA T)
RETURN
END


158
Soil Moist ure Content Analysis
Originally, transmission gamina rays were to be used to determine the moisture content
of each sample. The following is a description of this failed technique.
For a moist soil sample, the sample weight can be thought of as partially due to water
and partially due to everything else. In this case, everything else is the soil, the minerals
in the soil, the air in the soil, etc. In essence, everything else is an unknown composition
of stuff. This stuff will, from now on, be called soil.
Thus, the mass of the sample, M, equals the mass of water, M, plus the mass of soil,
M,. If the volume of the sample is V, then the density of the sample, p0, is
M
Po y,
Mw + M,
~ V
_ M,
~ V + V
= Pv, + P.-
where
pw water bulk density in the sample
(gm of water/cm3 of sample),
p, soil bulk density in the sample
(gm of soil/cm3 of sample).
The value of this equation is that, since the total sample mass and volume can be
measured, the density of the soil can be expressed in terms of the measured total density
and the unknown water density
P. ~ P Pv,-


TABLE 25
Measured vs. Fitted Detector Response for
USB
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 159.6 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.426
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.461
233.3
241.4
2
1.287
205.4
209.0
3
1.137
181.5
182.9
4
1.008
160.8
167.7
5
0.895
142.9
141.6
6
0.798
127.4
120.2
7
0.713
113.8
101.3
8
0.639
102.0
98.5


TABLE 17
Measured vs. Fitted Detector Response for
Sample 2
Fitting Equation : DR GF X CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC Fitted Contamination Concentration
Calculated CC : 93.5 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.274
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.732
162.1
167.8
2
1.526
142.8
148.8
3
1.348
126.1
129.1
4
1.194
111.8
119.5
5
1.061
99.3
98.5
6
0.946
88.5
87.4
7
0.845
79.1
74.1
8
0.757
70.9
66.7


276
C *********>>********>1!*********
c *
C S4XRF.F0R *
C *
C FILE PROGRAM *
C *
C ****************************
c
CHARACTER *25 PKFIL
DIMENSION D4(20),YS(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.S4]S4XRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE #4 IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE #4 IS 689 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRF1_S3B1.CNF;1
D4(i)
=
25.0
M5(l)
=
5.0
Y5(l)
=
87.0
HR(1)
=
17.0
MN(1)
=
24.0
RH(1)
=
1.0
RM(1)
=
18.0
RS(1)
=
27.82
PH(i)
=
1453181.0
ER(1)
=
2711.0


327
C
C DATA FROM XRF8_USD.CNF;1
C
D4(8) = 28.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) =10.0
MN(8) = 45.0
RH(8) = 1.0
RH(8) = 10.0
RS(8) = 47.35
PH(8) = 32926.0
ER(8) = 534.0
C
C STORE DATA ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 FORMAT(1F10.5, 112, 1F10.5)
HRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
HRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


TABLE 12
Measured vs. Fitted Detector Response for
Ula
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC Fitted Contamination Concentration
Calculated CC : 164.6 pCi/gm U238
Reduced X2 Value for Fitted Data : 0.047
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.557
91.7
92.1
2
0.491
80.7
78.4
3
0.433
71.3
69.0
4
0.384
63.2
61.7
5
0.342
56.2
57.5
6
0.304
50.1
51.4
7
0.272
44.9
46.0
8
0.244
40.1
40.4


TABLE 22
Measured vs. Fitted Detector Response for
NJA-Th
Fitting Equation : DR = GF X CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 2436.7 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.993
Positiou
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.819
1996.7
1967.7
2
0.722
1758.5
1718.0
3
0.638
1553.5
1617.4
4
0.565
1376.4
1404.0
5
0.502
1223.0
1224.7
6
0.447
1089.5
1075.3
7
0.400
973.5
963.7
8
0.358
872.1
845.1


DATA FROM
XRF5_U1.CNF;1
D4(5)
=
2.0
M5(E)
=
6.0
Y5(5)
=
87.0
HR(5)
=
16.0
MN(5)
=
49.0
RH(5)
=
1.0
RM(5)
=
1B.0
RS(5)
=
35.92
PH(5)
=
82104.0
ER(5)
=
387.0
DATA FROM
XRF6_U1.CNF;1
D4(6)
=
2.0
M5(6)
=
6.0
Y5(6)
=
87.0
HR(6)
=
18.0
MN(6)
=
12.0
RH(6)
=
1.0
RM(6)
sr
14.0
RS(6)
=
4.84
PH(6)
=
67923.0
ER(6)
=
1109.0
DATA FROM
XRF7JU1.CNF;!
D4(7)
=
2.0
M5(7)
=
6.0
Y5(7)
=
87.0
HR(7)
=
19.0
MN(7)
=
28.0
RH(7)
=
1.0
RM(7)
=
13.0
RS(7)
=
30.73
PH(7)
s
63979.0
ERC7)
=
407.0


294
C
C DATA FROM
C
D4(5) =
M5(5) =
Y5(5) =
HR(5) =
MN(5) =
RH(5) =
RM(5) =
RS(5) =
PH(5) =
ER(5) =
C
C DATA FROM
C
D4(6) =
M5(6) =
Y5(6) =
HR(6) =
MN(6) =
RH(6) =
RM(6) =
RS(6) =
PH(6) =
ER(6) =
C
C DATA FROM
C
D4(7) =
M5(7) =
Y5(7) =
HR(7) =
MN(7) =
RH(7) =
RM(7) =
RS(7) =
PH(7) =
ER(7) =
XRF5_TH1A.CHF;1
17.0
6.0
87.0
13.0
29.0
1.0
15.0
21.60
259990.0
1398.0
XRF6JTH1A.CNF;1
16.0
6.0
87.0
17.0
18.0
1.0
13.0
47.19
221465.0
831.0
XRF7JTH1A.CNF; 1
16.0
6.0
87.0
15.0
39.0
1.0
13.0
24.31
199931.0
1160.0


USAXRF.FOR 312
USBXRF.FOR 316
USCXRF.FOR 320
USDXRF.FOR 324
LIST OF REFERENCES 328
BIOGRAPHICAL SKETCH 330


TABLE 33
Peak Fit Results for Sample USC
Sample Contamination Concentration: 135.2 pCi/gm U238
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
65157 1.0%
13.4
2
64825 0.9%
5.1
3
61715 1.0%
7.5
4
58934 0.7%
3.7
5
50625 1.0%
4.1
6
43545 0.5%
1.5
7
41045 1.2%
5.6
8
35238 0.9%
2.8
TABLE 34
Peak Fit Results for Sample USD
Sample Contamination Concentration: 138.9 pCi/gm U238
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
77305 1.0%
14.1
2
74508 0.6%
3.3
3
66612 0.7%
3.2
4
63801 0.5%
1.9
5
56354 0.8%
3.7
6
44377 1.1%
8.1
7
38989 1.0%
6.8
8
32926 1.6%
8.8


228
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, t VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5G.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
WRITEd,*) XT, YT, ZT
WRITEd, *) TH, TR
WRITEd,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
END


66
Least Squares Peak Fitting
The least squares fitting technique is fairly simple and is described in numerous books
and articles. The mathematics used in this work was taken from Forsythe et al.^O This
technique was used in this work to properly determine the spectral peak areas and their
associated errors.
Least squares fitting is an iterative technique based on minimizing the square of the
difference between a measured value and a value calculated based on a mathematical model.
The minimization is performed by properly choosing the parameters of the mathematical
model. The model may be linear in these parameters or non-linear. Each successive iteration
refines the fitting parameters such that the sum of the squares is minimized. To begin, the
mathematical model is chosen. An initial guess as to the fitting parameters is also required.
F(Xi:Pl,P2,P3,...,Pn)l=Yi,
where
Xi = independent variable,
Pn = fit parameters of the mathematical model,
Yi = dependent variable.
Note: the 1 indicates that the fitting parameters are the current guess. The previous guess,
or for the first iteration, the initial guess, will be used to determine the new, or current,
guess.
Using current guess as to the fitting parameters, the sum of the squares of the difference
between the measured values and the calculated values is calculated.
S = £(*(*<),-Si)2 >


Peak areas are determined by shaping spectral data to a Voigt Profile using an algorithm
from the peak shaping program GRPANL. The steeply sloping nature of the Compton
backscatter hump on which the Kal x-ray peaks rest necessitated the development of a
unique polynomial/erfc background function which is subtracted prior to peak shaping. The
GF of a sample is the calculated number of Kal x rays which would be counted in the full
energy spectral peak if the contamination concentration in the sample were one picoCurie
per gram. This calculated GF includes considerations of the sample linear attenuation
coefficient, fluorescence induced by unscattered source gammas, fluorescence induced by
singly scattered Compton gammas which account for approximately 15% of all production,
and natural fluorescence production.
Experimentally, thirteen test samples were analyzed using this method, gamma spectro
scopic analysis, and neutron activation analysis. Results compared very well with gamma
spectroscopic analysis. Neutron activation analysis of small portions of each sample did not
match well with the results of either of the other methods due to sample inhomogeneities.
xvi


257
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(1,FILE=SAMPLERJBU.DAT,STATUS=NEW)
WRITE(1,'(A3)') ELEMENT
WRITECl,*) WF
WRITECl,*) SD
WRITECl,*) Ai
WRITECl,*) B1
WRITECl,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSEC1,STATUS=KEEP)
END


316
C ******** ***!(! ********** *****
c *
C USBXRF.FOR *
C *
C FILE PROGRAM *
C *
c ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.USB]USBXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE USB IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE USA IS 165 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1_USB.CNF;1
C
D4(l) = 14.0
M5(l) = 7.0
Y5(l) = 87.0
HR(1) = 16.0
MN(1) = 50.0
RH(1) = 1.0
RM(i) = 17.0
RS(i) = 43.05
PH(1) = 352365.0
ER(1) = 1565.0


213
C
C BE HASS ATTENUATION COEFFICIENTS, SQ CH/GH, FROM
C PHOTON HASS ATTENUATION AND ENERGY ABSORPTION
C COEFFICIENTS FROH 1 KEV TO 20 HEV, BY HUBBLE
C
DATA UB(1),UB(2),UB(3),UB(4) / .1217, .1253, .1296, .1352 /
C
C INTRINSIC DETECTOR EFFICIENCIES FOR THE ABOVE ENERGIES
C AS CALCULATED BY NBS.EFF AND EFFICIENCY.
C
DATA ED(1),ED(2),ED(3),ED(4) / .69336, .76561, .83025, .87363 /
C
C CO-57 SOURCE STRENGTHS, IN mCi AS OF 1 OCT, 1986,
C FOR SOURCES #1, #2, AND #3 RESPECTIVELY. SOURCE
C WERE CALCULATED BY NBS.EFF AND EFFICIENCY FROH
C THIS ATTENUATION COEFFICIENT DATA.
C
DATA A0(1),A0(2),A0(3) / 2.02203, 2.20737, 2.38809 /
C
C EU-155 EHISSION RATES, IN GAHHAS/SEC AS OF 1 APRIL,
C 1986, FOR ENERGIES 105.308 KEV AND 86.545 KEV
C RESPECTIVELY. EHISSION RATES WERE CALCULATED BY
C NBS.EFF AND EFFICIENCY FROH THIS ATTENUATION
C COEFFICIENT DATA.
C
DATA E0(1),E0(2) / 1.82496E7, 2.54845E7 /
C
C GAHHA YIELDS FOR CO-57 AT ENERGIES 136.476 KEV
C AND 122.063 KEV, RESPECTIVIELY, TAKEN FROH
C NCRP REPORT #58, APPENDIX A.3.
C
DATA YI(1),YI(2) / .1061, .8559 /
C
C DETECTOR AREA, SQ CH, TAKEN FROH VENDOR DOCUHENTS
C
DATA AD / 10.1788 /
C
C AVERAGE BOTTLE TRANSHISSION FRACTIONS FOR THE ABOVE ENERGIES
C CALCULATED BY TRANSHISSION USING REV.6 DATA.
C
DATA JA(1),JA(2),JA(3),JA(4) / .97190, .97110, .96970, .96792 /


293
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MN(2) =
RH(2) =
RM(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
H5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RH(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MIi(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2JTH1A.CNF;1
18.0
6.0
87.0
9.0
19.0
1.0
19.0
41.40
359972.0
2600.0
XRF3JTH1A.CNF;1
17.0
6.0
87.0
16.0
50.0
1.0
18.0
9.68
331580.0
1750.0
XRF4JTH1A.CNF;1
17.0
6.0
87.0
15.0
27.0
1.0
16.0
42.01
298234.0
1383.0


FIGURE B-2
Target Detector Distance vs. Measured Peale Area


TABLE 13
Measured vs. Fitted Detector Response for
NJA-U
Fitting Equation : DR GF X CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC Fitted Contamination Concentration
Calculated CC : 196.9 pCi/gm U238
Reduced X2 Value for Fitted Data : 0.129
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.255
50.3
45.4
2
0.225
44.3
42.8
3
0.199
39.1
41.2
4
0.176
34.7
36.6
5
0.157
30.8
31.8
6
0.140
27.5
27.4
7
0.125
24.6
24.4
8
0.112
22.0
21.6


75
transmission fractions are then used to calculate the sample linear attenuation coeffi
cients as described in a previous section.
6. The next step is sample XRF analysis. The sample is placed such that the center of the
sample is again directly above the center of the detector. The source holder and sample
holder assemblies are shown in exploded view in Figure 8. Figure 9 shows the sample in
its holder positioned above the detector and above the source holder shield. Using the
center of the detector as the origin of an X-Y-Z coordinate system, the sample center
is located at coordinate (10.5 0.1 cm, 0.0 cm, 0.0 cm). Figure 10 shows the sample
in position and the laser alignment beam used to ensure that it is properly centered.
The source holder, described in detail in Appendix A, holds two sources located in the
X-Z plane formed by the long axis of the sample bottle and the detector center. The
sources are located at coordinates (4.42 0.01 cm, 0.0 cm, 4.42 0.01 cm) and (4.42
0.01 cm, 0.0 cm, -4.42 0.01 cm).
Once the sample is properly positioned, the sources are placed in their holders and the
sample is irradiated for one hour. In this work, fluorescent x-ray peaks ranged in area
from 20,000 counts to 1,500,000 counts depending upon the U or Th concentration in
the samples. Figure 11 shows the multichannel analyzer system used to collect spectral
information. Figure 12 shows a typical spectrum on the MCA.
7. For the next seven counts, the sample is next raised 0.3 0.01 cm and step six is
repeated. The yields a total of eight counts with the sample center being at 10.5, 10.8,
11.1, 11.4, 11.7, 12.0, 12.3, and 12.6 cm from the detector. The detector and XRF
excitation sources remain in fixed positions for all eight counts.
8. Finally the sample is dried, if necessary, in an oven or a microwave and weighed again.
The dry soil weight and soil moisture fraction are thus determined.


253
C
C Data is now written into file SAMPLENJAU.DAT
C
OPEN(1,FILE=SAMPLENJAU. D AT \STATUS=NEW)
WRITE(1,(A3)) ELEMENT
WRITEd,*) WF
WRITEd, *) SD
WRITEd,*) A1
WRITEd,*) B1
WRITEd,*) Cl
WRITEd*) US1
WRITE(1,*) US2
WRITEd,*) US3
CLOSE(1,STATUS='KEEP)
END


332
research at; Oak Ridge National Laboratory (ORNL). He worked at ORNL for two years,
three months of which was spent working for Bechtel at Three Mile Island. During his time
at ORNL, he completed the experimental portion of his dissertation work. Upon completion
of his experiments, he took a position as a health physicist with the Safety and Environmen
tal Protection (S&EP) Division at Brookhaven National Laboratory (BNL). This choice of
jobs was driven by the fact that Corinne was at BNL finishing her Ph.D. research experi
ments. Over the course of a year at BNL the development of the mathematical model used
in Edwards dissertation research was completed.
Edward is currently at BNL with S&EP and, with his wife, has two lovely cats. He is
a member of the local and national Health Physics Societies as well as the local American
Nuclear Society. Edward has an older brother, Robert Linden, who is currently in Medical
School at the University of Virginia and has a wife, Theresa, and two sons Nicholas and
James; a younger sister, Lisamarie, who works for a nuclear consulting firm in Knoxville,
Tennessee, and is married to Steven Jarriel; and a younger brother, Thomas Christopher,
who works for NASA in Houston, Texas, and has a wife, Margerie.


TARGET
POINT
SOURCE
SHIELD
DETECTOR
POINT
SOURCE
SHIELD


FIGURE 12
Typical XRF Kal Peak on MCA


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
LIST OF TABLES xi
LIST OF FIGURES xiv
ABSTRACT xv
CHAPTERS
I INTRODUCTION 1
Soil Sample Assay for Radionuclide Content 1
Standards Method for Gamma Spectroscopic Assay of Soil Samples 4
Radionuclides of Interest 5
Process Sensitivity 6
Statement of Problem 10
X-Ray Fluorescent Analysis 11
Assay Technique 12
Literature Search 13
II MATERIALS AND METHODS 14
Peak Shaping 14
A Fitting Peak 15
A Fitting Background 24
vi


306
DATA FROM
XRF6_NJB.CNF;1
D4(5)
=
8.0
H5(B)
=
7.0
Y5(5)
=
87.0
HR(5)
=
12.0
MN(5)
=
15.0
RH(5)
=
1.0
RH(5)
=
11.0
RS(5)
=
24.29
PH(5)
=
38196.0
ER(5)
=
378.0
DATA FROM
XRF6JJJB. CNF; 1
D4(6)
=
8.0
H5(6)
=
7.0
Y5(6)
=
87.0
HRC6)
=
14.0
MN(6)
=
42.0
RH(6)
=
1.0
RH(6)
=
10.0
RS(6)
=
36.35
PH(6)
=
34393.0
ER(6)
=
495.0
DATA FROM
XRF7_NJB.CNF;1
D4(7)
=
8.0
M5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
16.0
MN(7)
=
22.0
RH(7)
=
1.0
RMC7)
=
9.0
RS(7)
=
59.44
PH(7)
=
31229.0
ER(7)
=
295.0


226
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5E.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW *)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITECl,*) X(I),Y(I),Z(I)
WRITECl,*) XT, YT, ZT
WRITECl,*) TH, TR
WRITECl,*) RT, CT, VT
CLOSE C1,STATUS=*KEEP)
END


TABLE 24
Measured vs. Fitted Detector Response for
USA
Fitting Equation : DR -- GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 181.4 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.386
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.423
258.2
261.8
2
1.253
227.4
236.4
3
1.107
200.9
209.5
4
0.981
178.0
180.6
5
0.872
158.2
165.2
6
0.777
141.0
137.2
7
0.694
126.0
118.2
8
0.622
112.9
104.6


250
C
c *********************
c *
C SAMPLETH1A.FOR *
C *
C *********************
C
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample #TH1A, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.8217
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.16196
Bl = 0.64704
Cl =-0.42909
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.26534
US2 = 0.28262
US3 = 0.32782


260
C
c *********************
c *
C SAMPLEUSA.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample USA, a non-homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Weight Fraction, WF
C
WF = 0.9221
C
C Sample Density, SD
C
SD = 1.4589
C
C Hubble Fit Parameters, Al, Bl, t Cl
C
A1 = 1.27985
Bl = 0.73205
Cl =-0.50038
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.23116
US2 = 0.24787
US3 = 0.29318


2101
2105
2106
2107
2110
2115
2120
2125
2180
2185
2190
2195
2250
2262
2254
2260
2262
2265
2270
2275
2277
2280
2285
2290
2292
2294
2296
2300
2305
2310
2315
2320
2325
2335
2400
2405
2410
2413
2415
2425
2427
2435
2445
2447
2450
2460
2465
2475
168
LPRINT
LPRINT Fit parameters for polynomial of order *;01
LPRINT Y(I) = A + B X(I) + C X(I)**2 + .
LPRINT
FOR J = 1 TO M
LPRINT V( ; J; ) = ;V(J)
LPRINT
NEXT J
LPRINT Background Fit Results
LPRINT
LPRINT 'X(I) ,*Y(I) ,BKCD ,*SIG(I)
LPRINT
FOR I = 1 TO N
F(I) = 0
NEXT I
FOR I = 1 TO DP
X(I) = XT(I) XT(1)
FOR J = 1 TO H
F(I) = V(J) ((X(D) ** (J 1)) + F(I)
NEXT J
F(I) = F(I) 5000
LPRINT XT(I),YT(I),F(I),SIG(I)
NEXT I
LPRINT
LPRINT Background Slope at ;XT(LB + 1); = ;SL(1)
LPRINT
LPRINT Background Slope at ;XT(DP RB); = ;SL(2)
PRINT Background Fit Results
PRINT
PRINT 'XT(I) ,BR(I) ,*SIG(I)*
PRINT
FOR I = 1 TO DP
PRINT XT(I),F(I),SIG(I)
NEXT I
PRINT
PRINT In what file are the Polynomial fit data to be stored?
INPUT PEAK$
IF PEAK$ = NO THEN GOTO 9000
OPEN 0, #1,PEAK$
PRINT #1, DP RB + RF
FOR I = 1 TO (DP RB + RF)
PRINT #1, XT(I)
PRINT #1, F(I)
PRINT #1, SIG(I)
NEXT I
PRINT II, R
FOR I ~ 1 TO H
PRINT #1, V(I)


975
PRINT Itteration # ";W1
977
PRINT
980
FOR I = 1 TO M
985
PRINT VA$(I); = '>;VAR(I)
987
PRINT
990
NEXT I
995
FOR I = 1 TO N
1000
SIG = VAR(l)
1005
XB = VAR(2)
1008
A = VAR(3)
1010
PRINT X;I; = ' ;X(I), Y;I;
= ;Y(I)
1015
GOSUB 2000
1020
F(I) = F6
1025
PRINT X;I; = ;X(I), F* ;I;
= ';F(I)
1030
PRINT
1035
FOR 11 = 1 TO H
1040
DF(2) = 0
1045
FOR 12 = 1 TO M
1050
DS(I2) = 0
1055
NEXT 12
1060
DS(I1) = VAR(Il) .001
1065
SIG = VAR(l) + DS(1)
1070
XB = VAR(2) + DS(2)
1080
A = VAR(3) + DS(3)
1085
GOSUB 2000
1090
DF(1) = (F6 F(I)) / DS(I1)
1095
TE = DF(1) DF(2)
1100
IF ABS (TE) < = ABS (.001 DF(1))
GOTO 1120
1105
DS(I1) = DS(I1) .5
1110
DF(2) = DF(1)
1115
GOTO 1065
1120
A(I,I1) = DF(1)
1125
TA(I1,I) = DF(1)
1130
NEXT 11
1135
DY(I) = Y(I) F(I)
1140
S = S + (DY(I)) ** 2
1143
CHISQ = CHISq + ((DY(I)) ** 2) / (F(I)
* (N M))
1145
NEXT I
1150
IF S > SI THEN GOTO 1176
1151
IF ABS (S SI) < (S / 1000) THEN GOTO 1180
1152
SI = S
1153
ochisq = cHisq
1155
GOSUB 6500
1160
PRINT
1165
PRINT S = ;S
1166
PRINT
1167
PRINT CHISq = CHISq
1170
W1 = W1 + 1


37
Soil Moisture Content
The above analysis of soil linear attenuation coefficients assumes that the soil in the
jar consists of everything in the jar, water and soil. As will be seen, this is the appropriate
linear attenuation coefficient to be determined here. The moisture fraction of this soil
is also needed for the data analysis for final U and Th concentration determination. As
such, after the transmission and XRF measurements have been made, each sample jar is
placed in a microwave oven and dried in the jar. Jar weights before and after drying are
used to determine soil moisture weight fraction. Soil sample densities, before drying, were
determined by dividing the known wet soil weight by the know bottle volume.
Initially, soil moisture content was to be determined via use of the same transmission
gamma rays described in the last section. Unfortunately, the set of four simultaneous
equations that were to be used resulted in a non-unique solution set instead of one unique
answer. Although this approach could not be used, the details of this approach and the
reasons for its failure are included in Appendix B.
System Model
Introduction
In general, XRF determination of elemental concentrations is done by comparing the
area of a peak from an unknown sample to the area of a peak from a sample of known ele
mental concentration, called a standard. The concentration of that element in the unknown
sample is simply the ratio of unknown sample peak area to standard peak area times the
elemental concentration in the standard.
This technique assumes that the measurement geometry and attenuation properties of
the unknown sample are identical to those of the known standard. Practically speaking,


204
C
C
C
C
c
c
c
10
20
30
50
75
80
*****************************
* *
* SUBROUTINE DISTANCE *
* *
*****************************
SUBROUTINE DISTANCE (Xl,Yl,ZltX2,Y2tZ2,U,V,W,Rl,R2,K)
COMMON XTC,YTC.ZTC.TR
DI = X2 XI
D2 = Y2 Y1
D3 = Z2 Z1
R1 = SQRT(D1*D1 + D2*D2 + D3*D3)
U = D1 / R1
V = D2 / Ri
W = D3 / R1
IF (K .EQ. 1) GOTO 75
X1XT = XI XTC
Y1YT = Y1 YTC
A = U*U + V*V
B = 2 U X1XT + 2 V Y1YT
C = X1XT*X1XT + Y1YT*Y1YT TR*TR
R3 = ( B + SQRT(B*B 4 A C)) / (2 A)
IF (R3 .LT. 0.) GOTO 10
IF (R3 .LT. Rl) GOTO 50
R3 = ( B SQRT(B*B 4 A C)) / (2 A)
IF (R3 .LT. 0.) GOTO 20
IF (R3 .LT. Rl) GOTO 50
WRITE(6,30)
FORMAT(/.IX,DISTANCE CALCULATION IS SCREWED UP!)
K = 10
GOTO 80
R2 = Rl R3
K = 0
RETURN
END


160
^ ^ ^ 111 (E^) ^ ^ P'B) (- 1)
where
a: = the thickness of the soil sample (cm),
A (E) = the measured full energy peak area at
energy E, (counts),
K (E) a grouping of constants as follows,
_ A0 (E) X Area x tj (E) X CT
4 7T r2
and
Aa (E) = source gamma emission rate at energy E,
(Gammas / s),
Area = detector surface area (cm2),
i] (E) detector intrinsic energy efficiency at
energy E, (NoUnits),
CT = total counting time (s),
r = distance from source to detector (cm).
Tlie left hand side of the equation is made up of measured or known quantities. Thus
we have one equation with two unknowns, p, (E) and pw.
Fortunately, p, (E) can be described, over a small energy range, by the following func
tion


309
DATA FROM
XRF2_NJB.CNF;1
D4(2)
=
7.0
H5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
14.0
MH(2)
=
10.0
RH(2)
=
1.0
RH(2)
=
14.0
RS(2)
=
31.67
PH(2)
=
2689680.0
ER(2)
=
2332.0
DATA FROM
XRF3JIJB. CNF; 1
D4(3)
=
7.0
H5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
16.0
MN(3)
=
8.0
RH(3)
=
1.0
RH(3)
=
13.0
RS(3)
=
3.41
PH(3)
=
2364069.0
ER(3)
=
2875.0
DATA FROM
XRF4.NJB. CNF; 1
D4(4)
=
8.0
M5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
10.0
MN(4)
=
18.0
RH(4)
=
1.0
RH(4)
=
12.0
RS(4)
=
12.69
PH(4)
=
2133681.0
ER(4)
=
3002.0


112
Peak Fitting Results
In order to verify that the peak fitting routine used in this work was indeed functioning
properly, Jfal peaks from three spectra were analyzed by PEAKFIT, the technique used
in this work, and by GRPANL. The results of this comparison are shown in Table 28.
TABLE 28
Comparison of Kai Peak Areas
as Deter minee
by PEAKFIT and G1
UPANL
PEAKFIT Area
GRPANL Area
Sample
Geometry
(Count- Channels)
( Count- Channels)
Sample 2
1
264561 1.1%
260041 0.9%
Sample 3
1
541821 0.4%
565890 0.4%
Sample 4
1
1453181 0.2%
1535171 0.2%
As can be seen from the table, the PEAKFIT results are in very good agreement
with the GRPANL results. The difference between the two peak shaping programs, which
results in the small peak area differences above, is in the way they handle background
shaping. The background shaping in PEAKFIT, described in detail in Chapter II, was
developed specifically for use in this application and more accurately accounts for the shape
of the steeply negative sloping curve on which the peak sits. GRPANL assumes a linear
background if the slope of the background is negative
Complete results of the peak fitting for each sample are listed in Tables 29 through 43.


20
where
G (E') = Gaussian distribution function,
= A exp (-.5 {{E' E0) /a)2) ,
E' = convolution dummy variable,
E = peak centToid,
<7 = Gaussian peak standard deviation,
A Gaussian peak height constant, and
L(E E') = Lorentzian distribution function,
= A'/ ((£ E' E0f + .25r2) ,
E = energy,
E' convolution dummy variable,
E0 = peak centroid,
T = Lorentzian peak full peak width at half
the maximum peak height,
A = Lorentzian peak height constant.
The resulting convolution, C (E), can be solved numerically in the following manner.
C (E) = A" (exp (-X2) x (Cl 4- C2 x X2 + C3 X (1 2X2)))
+ A" x C4 X/3(X),
where
X2 = (112){{E-E0)I*)\
C\ = \- (I/v^tt) (r/cr),
C2 = (1/2V5r) (r/

127
TABLE A-l
Shield Material X Ray
Emission and Absorption Energies +
Emission and Absorption Energies (keV)
Element
K*i
Ka 2
Kp i
A>2
Absorption
Pb
74.957
72.794
84.922
87.343
88.001
W
59.310
57.973
67.233
69.090
69.508
Cd
23.172
22.982
26.093
26.641
26.712
Cu
8.047
8.027
8.904
8.976
8.980
-f: X-ray emission and absorption energies were taken from Kocher.^
System Calibration
In that all the equipment used for this research arrived new, the system required calibra
tion. Calibration of the system refers to setting the amplifier gain, determining the spectral
energy calibration, determining the detector intrinsic energy efficiency, and determining
accurate source strengths.
The amplifier gain must be properly set. This is done by exposing the detector to
gamma ray sources emitting gammas in the energy range of interest. Here, Co-57 and
Eu-155, which emit gammas of energies described in Table 5, and Am-241, which emits at
about 59 keV, were used. The amplifier gain is then changed until the spectrum covers a
significant portion of the 4096 channel screen. A spectrum of the above gamma sources is
then collected at the calibrated gain set ting. The result is a spectrum consisting of peaks
which correspond to known gamma energies. The ND-9900 is equipped with a calibration
program which looks at this spectrum and asks what energies to assign to each peak. The
program then shapes each peak, to determine the peak centroid, and assigns the designated
energy to the channel number of peak centroid. Once tliis has been done for all peaks, the


186
C
C TARGET CENTER COORDINATES
C
READ(1,*) XT,YT,ZT
C
C TARGET HEIGHT, TH, AND RADIOUS, TR
C
READ(1,*) TH.TR
READ(1,*) RT.CT.VT
CLOSE(1,STATUS=KEEP>)
WRITE(6,75)
75 F0RMAT(/,1X,In what file should the Source-Target,/,
1 IX,distances be stored?)
READ(5,80) SPD
80 FORHAT(AIO)
WRITE(6,85)
85 F0RMAT(/,1X,In what file should the Target-Detector,/,
1 IX,distances be stored?)
READ(5,90) PDD
90 FORMAT(AIO)
C
C DETERMINE DETECTOR NODE POINTS
C
RD = 8
CD = 3
II = 1
DO 100 I = 1,CD
DO 100 J = 1,RD
T = (2 PI / RD) (J .5)
DTRCI1.3) = (DR / CD) (I .5) SIN (T)
DTR(I1,2) = (DR / CD) (I .5) COS (T)
DTR(Il.l) = 0
AD(I1)=PI*((I*DR/CD)**2-((I-1)*DR/CD)**2)/RD
100 II = II + 1
WRITE(6,210)
210 FORMAT(/,IX,Completed Detector Node Points)
C
C DETERMINE TARGET NODE POINTS
C
II = 1
DO 250 I = 1,CT
DO 250 J = 1,RT / 2
T = (2 PI / RT) (J .5)
PTS(Il.l) = (TR / CT) (I .5) COS (T) + XT
PTS(I1,2) = (TR / CT) (I .5) SIN (T) + YT
PTS(I1,3) = ( TH / 2.0) + (TH / (2.0 VT)) + ZT
VOLT(Il) = PI*(TH/VT)*((I*TR/CT)**2 ((I 1)*TR/CT)**2)/RT
II = II + 1
250


303
C
C DATA FROM XRF8JIJA.CNF; 1
C
C
C
C
D4(8) = 7.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 9.0
MN(8) = 49.0
RH(8) = 1.0
RM(8) = 9.0
RS(8) = 4.26
PH(8) = 1367233.0
ER(8) = 2223.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 FORMAT(1F10.5, 112, 1F10.6)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


262
C
C *********************
c *
C SAMPLEUSB.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program create a data file of input
C data pertaining to Sample USB, a non-homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH'
C
C Soil Height Fraction, HF
C
HF = 0.94997
C
C Sample Density, SD
C
SD = 1.4152
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.33008
Bl = 0.73746
Cl =-0.50040
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.21953
US2 = 0.23533
US3 = 0.27892


81


324
C ****************************
c *
C USDXRF.FOR *
C *
C FILE PROGRAM *
C *
Q 3|E3fC9|e>|Ej|C3|C9|C3fe3fe3tC3|e3|e^i3|E3tC3te3|e9|e3|e3|C3fC|e)|E3fE3tG9tC3te3te
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN{20), LH, LM, LS
INTEGER NF, MS(20)
PKFIL = [LAZO.DISS.USD]USDXRF.DAT'
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE USB IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE USA IS 130 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRF 1JJSD. CNF ;1
D4(l)
t=
22.0
M5(l)
=
7.0
Y5(l)
=
87.0
HR(1)
=
13.0
MN(1)
=
30.0
RH(1)
=
1.0
RM(1)
=
19.0
RS(1)
=
27.55
PH(1)
=
77305.0
ER(1)
=
743.0


285
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MN(2) =
RH(2) =
RH(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
HN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
H5(4) =
Y5(4) =
HR(4) =
HN(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2_U1A.CNF;1
3.0
6.0
87.0
12.0
28.0
1.0
20.0
22.14
123835.0
815.0
XRF3_U1A.CNF;1
3.0
6.0
87.0
13.0
51.0
1.0
18.0
22.25
111116.0
538.0
XRF4JJ1A.CHF; 1
3.0
6.0
87.0
15.0
21.0
1.0
17.0
0.37
100696.0
634.0


DATA FROM
XRF5J52B2. CNF; 1
D4(B)
=
27.0
M5(5)
=
B.O
Y5(B)
=
87.0
HR(5)
=
21.0
MN(6)
=
0.0
RH(5)
=
1.0
RH(5)
=
16.0
RS(B)
=
23.91
PH(B)
=
166260.0
ER(B)
=
1076.0
DATA FROM
XRF6J32B2. CNF; 1
D4(6)
=
28.0
MB(6)
=
B.O
Y6C6)
=
87.0
HR(6)
=
9.0
MN(6)
=
2.0
RH(6)
=
1.0
RM(6)
=
14.0
RS(6)
=
22.64
PH(6)
=
148666.0
ER(6)
=
1407.0
DATA FROM
XRF7 J52B2.CHF;1
D4(7)
=
28.0
MB(7)
=
B.O
YB(7)
=
87.0
HR(7)
=
10.0
MN(7)
=
18.0
RH(7)
=
1.0
RM(7)
=
13.0
RS(7)
=
26.42
PHC7)
=
127261.0
ER(7)
=
1422.0


6140 NEXT Cl
6160 DA(RP) = (AM(RP,M1) SU) / (AM(RP,RP))
6180 SU = 0
6200 NEXT R
6203 FOR I = 1 TO M
6204 FOR J = 1 TO M + 1
6205 AM(I,J) = 0
6206 NEXT J
6207 NEXT I
6220 RETURN
8000 REM
8002 REM Subroutine to calculate Error in Peak Area
8004 REM
8006 REM The first part of the subroutine inverts AA(M,M) to
8008 REM yield the covariance matrix, C0V(M,M)
8009 REM
8010 FOR I = 1 TO M
8015 C0V(I,I) = 1
8020 NEXT I
8025 FOR I = 1 TO M
8030 T1 = HLD(I,I)
8035 FOR J = 1 TO M
8040 HLD(I.J) = HLD(I.J) / T1
8045 COV(I.J) = COV(I.J) / Ti
8050 NEXT J
8055 FOR J = 1 TO M
8060 IF J = I THEN GOTO 8090
8065 T2 = HLD(J.I)
8070 FOR K = 1 TO M
8075 HLD(J,K) = HLD(J.K) (HLD(I,K) T2)
8080 COV(J.K) = COV(J.K) (COV(I.K) T2)
8085 NEXT K
8090 NEXT J
8095 NEXT I
8100 FOR I = 1 TO M
8110 FOR J = 1 TO M
8120 COV(I,J) = COV(I.J) S(W1)/(N M)
8130 NEXT J
8140 NEXT I
8150 PRINT X(I),',Y(I)',SIG(I)
8155 PRINT
8160 FOR K = 1 TO (DP RB + RF)
8200 FOR I = 1 TO M
8210 DA(I) = (XT(K) XT(1)) ** (I 1)
8220 NEXT I
8400 Tl = 0
8410 T2 = 0
8500 FOR I = 1 TO M


301
DATA FROM
XRF2 JIJA.CNF;1
D4(2)
=
1.0
M5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
10.0
MN(2)
=
36.0
RH(2)
=
1.0
RH(2)
=
13.0
RS(2)
=
23.13
PH(2)
=
2709169.0
ER(2)
2614.0
DATA FROM
XRF3 JIJA.CNF;1
D4(3)
=
1.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
14.0
MN(3)
=
59.0
RH(3)
=
1.0
RH(3)
=
12.0
RS(3)
=
48.61
PH(3)
=
2560958.0
ER(3)
=
2554.0
DATA FROM
XRF4 JIJA. CNF ;1
D4(4)
=
1.0
M5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
16.0
MN(4)
=
17.0
RH(4)
=
1.0
RH(4)
=
11.0
RS(4)
=
45.29
PH(4)
=
2245527.0
ER(4)
=
1712.0


128
program determines a quadratic fit to this energy vs. channel number data, completing the
energy calibration.
The detector intrinsic energy efficiency refers to the efficiency term introduced in Equa
tion 4 and used in many subsequent equations. The intrinsic energy efficiency of a detector
is the fraction of monoenergetic photons hitting the detector that are counted in the full
energy peak. That is, if 100 photons of energy 122 keV hit the detector surface, the detector
is 83% efficient at 122 keV if the area of the 122 keV peak is 83 counts. This efficiency term
is required by many of the equations in the section describing soil moisture determination
and sample inhomogeneity. The actual calibration technique will be described later.
The Isotope Products sources described in Table 5 and Table 6 also require calibration
in that the errors in listed source activities were much too large for use in precise work.
In this case, the Isotope Products sources were compared to a source of precisely known
activity to determine their true activities.
Proper technique for calibration of a source or a system requires the use of a precisely
calibrated source. The most common supplier of precision sources is the National Bureau of
Standards (NBS) in Gaithersburg, Maryland. A mixed radionuclide NBS point source was
borrowed from EG&G Ortec to perform system calibration. Standard Reference Material
(SRM) 4275-B-7 is a mixed 56-125/Te-125m, Ett-154, and Eu-155 point source having
precisely defined emission rates. Table A-2 summarizes emission rates for the energies of
interest. Table A-3 lists pertinent physical qualities of the radionuclides of interest.


71
Error Propagation
The various stages of the assay analysis have all been thoroughly described. This section
will describe how error is propagated through these calculations.
To begin with, a spectral peak is collected. The error associated with each spectral
data point is
a2(Yi) = Y¡.
The first manipulation performed on this data is the calculation of the background
beneath the x-ray peak being analyzed. This calculation is performed in two steps. First, a
polynomial background (POLYBK) is calculated using data points to the right and left of
the peak. These points are least squares fit to a fourth order polynomial yielding the best fit
and a covariance matrix. Using the covariance matrix and Eq. 4, the error associated with
each calculated data point is determined, Var(POLYBKi). Second, the complimentary
error function (erfc) background (ERFBK) is determined. This is a numerical process, the
error associated with each of these points is estimated to be
a2 (ERFBKi) = ERFBKi.
The two backgrounds, polynomial and erfc, are assumed to each contribute equally to
the complete background, thus the complete backgromid is equal to
_ r. POLYBKi + ERFBKi
BKs
2
and,
o-2 {BKi) =

48
These equations thus make up a mathematical model of a physical situation. The
model can he experimentally verified by calculating all the nodal Geometry Factors, GF{,
for a particular geometry and then making an actual measurement of the signal, DR, from
a target in that geometry. The sum of the geometry factors, referred to hereafter as the
target geometry factor, times the contamination concentration in the source should equate
to the signal seen at the detector. This model can then be used to assay unknown target
samples. The unknown contamination concentration of a sample is given by
r DR
ZGFi1
where all terms are as previously defined.
This equation is thus the basis for target sample assay. Figure 6 shows the spatial
relationships of the source, target, and detector that were used to experimentally verify the
mathematical model.
To further verify the model and to provide a better assay of the target, each target is
measured in more than one geometry. This is accomplished easily by varying the target to
detector distance between measurements. A graph of detector response vs target geometry
factor is closely approximated by a straight line
DR(P) = Cx GF(P),
where
DR (P) fluorescent signal seen at the detector
from a target at position P,
(counts/s),
C contamination concentration in the
target, pCi/gm,


DATA FROM
XRF2JJSD.CNF;1
D4(2)
=
22.0
H5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
15.0
HH(2)
=
34.0
RH(2)
=
1.0
RM(2)
17.0
RS(2)
=
17.89
PH(2)
=
74508.0
ER(2)
=
467.0
DATA FROM
XRF3JJSD. CNF; 1
D4(3)
=
23.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
9.0
MN(3)
=
27.0
RH(3)
=
1.0
RM(3)
=
15.0
RS(3)
=
19.36
PH(3)
=
66612.0
ER(3)
=
482.0
DATA FROM
XRF4JJSD.CUF;1
D4(4)
=
23.0
H5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
13.0
MN(4)
=
40.0
RH(4)
=
1.0
RM(4)
=
14.0
RS(4)
=
47.99
PH(4)
=
63801.0
ER(4)
=
341.0


DATA FROM
XRF5JJSD. CNF; 1
D4(5)

24.0
M5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
12.0
MN(S)
=
48.0
RH(5)
=
1.0
RM(5)
=
13.0
RS(5)
=
8.51
PH(5)
=
56354.0
ER(5)
=
428.0
DATA FROM
XRF6JJSD.CNF;1
D4(6)
=
24.0
H5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
15.0
MN(6)
=
0.0
RH(6)
=
1.0
RH(6)
=
12.0
RS(6)
=
1.30
PH(6)
=
44377.0
ER(6)
=
510.0
DATA FROM
XRF7JUSD.CNF; 1
D4(7)
-
24.0
H5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
16.0
MH(7)
=
20.0
RH(7)
=
1.0
RH(7)
=
11.0
RS(7)
=
18.62
PH(7)
=
38989.0
ER(7)
=
373.0


297
DATA FROM
XRF2 JIJA.CNF;1
D4(2)
=
1.0
M5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
10.0
MN(2)
=
36.0
RH(2)
=
1.0
RM(2)
=
13.0
RS(2)
=
23.13
PH(2)
=
67460.0
ER(2)

586.0
DATA FROM
XRF3JJJA. CNF; 1
D4(3)
=
1.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
14.0
MN(3)
=
59.0
RH(3)
=
1.0
RM(3)
=
12.0
RS(3)
=
48.61
PH(3)
=
65292.0
ER(3)
=
452.0
DATA FROM
XRF4 JIJA. CNF ;1
D4(4)
=
1.0
M5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
16.0
MN(4)
=
17.0
RH(4)
=
1.0
RM(4)
=
11.0
RS(4)
=
45.29
PH(4)
=
58533.0
ER(4)
=
503.0


135
prevented from reaching the detector with its energy unchanged. Photons which coherently
scatter at small angles will still reach the detector.
Then, the logical question is; What mass attenuation coefficients are we looking for?
Mass attenuation coefficients are used in the calculations to calibrate the system, in trans
mission measurements to determine soil attenuation properties, and in inhomogeneity cal
culations. Based on the following discussion, the removal mass attenuation coefficient is the
correct coefficient to use in all calculations.
Ah = fit fie,
(A5)
where
fiT = removal mass attenuation coefficient,
(cm? /gm),
// = coherent scatter mass attenuation coefficient,
(cm? /gm),
Ht = total mass attenuation coefficient,
(cm? I gm),
= Ah* + Ah* + AV + Pppi
fii, incoherent (compton) scatter mass
attenuation coefficient, (cm?/gm),
HPe = photoelectric mass attenuation
coefficient, (cm2/gm),
Hpv pair production mass attenuation
coefficient, (cm?/gm).
The theoretical justification for using the removal, rather that the total, mass atten
uation coefficient is as follows. Generally attenuation measurements are made using a


331
In 1974 Edward entered the University of Virginia as a First Year student. Until en
countering organic chemistry that year, he had planned to study chemical engineering. The
organic experience, however, suggested that nuclear engineering would be a better choice.
During his four years at Virginia he again proved to be an above average student, partici
pated in student government and the local American Nuclear Society, and lived modestly in
apartments with affectionate names such as the Bungalow, the Cave, and the Farm.
He graduated with distinction in 1978 with a Bachelor of Science in Nuclear Engineering.
He moved directly into the Virginia graduate program in nuclear engineering, during which
time he spent a summer and a semester co oping with Bechtel Power Corporation, at the
Gaithersburg, Maryland, office. After graduating in December of 1979 with a Master of
Engineering degree, he went to work for Bechtel as a site liaison engineer stationed at the
then recently damaged unit 2 reactor at Three Mile Island (TMI).
He enjoyed his time at TMI very much and built a reputation for knowing how to get
things done properly. Over the 3.5 years that he worked at TMI his duties included site
specific review of home office documents, development of a data acquisition plan for the
removal items from the containment building, development and performance of decontam
ination experiments for the containment building, and development of work packages for
the Reactor Building Gross Decontamination Experiment.
In July, 1983, he left Bechtel to return to school to pursue his Pli.D. in health physics
at the University of Florida (UF). It was during this time that he met Corinne Ann
Coughanowr, who was working on her Ph.D. in chemical engineering at UF, and who he
would marry on 5 July, 1986. After four semesters of classes and one summer working
for Bechtel as a health physicist on the Formerly Utilized Sites Remedial Action Program
(FUSRAP), he completed his preliminary exams and was awarded a Laboratory Graduate
Participation Fellowship by Oak Ridge Associated Universities to perform his dissertation


238
C
C lH********************
c *
C SAMPLE2.F0R *
C *
Q #
c
CHARACTER *3 ELEMENT
C
C This program craats a data file of input
C data pertaining to Sample #2, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.6608
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.24476
Bl = 0.75112
Cl =-0.63255
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.24400
US2 = 0.25061
US3 = 0.30424


645 CLOSE #1
650 PRINT XRF Peak, with background subtracted,
553 PRINT from data file ;FILE$
555 PRINT
560 PRINT Channel", Count s, Sigma
565 PRINT
570 FOR I = 1 TO NP
575 PRINT PK(1,1),PK(2,I),SQR(PK(3,I))
580 PRINT
585 NEXT I
600 FOR I = 5 TO NP
605 II = I + i
607 12 = I + 2
609 SI = (PK(2,Ii) PK(2,I)) / (PK(l.Il) PK(1,I))
610 S2 = (PK(2,I2) PK(2,I1)) / (PK(1,I2) PK(1,I1))
611 HOLD = II
612 IF SI > 0 AND S2 < 0 GOTO 630
615 NEXT I
620 PRINT NO MAXIMUM FOUND IN LINE 620
625 GOTO 9000
630 IF PK(1,I1) < XB 1.005 GOTO 650
635 HOLD = I
650 VAR(l) = SIG
655 VAR(2) = XB
660 VAR(3) = PK(2,H0LD)
700 FOR J = (HOLD 6) TO HOLD
705 IF PK(2,J) < 0 THEN GOTO 715
710 IF PK(2,J) > .2 PK(2,H0LD) GOTO 730
715 NEXT J
720 PRINT No Low Energy Start Point Found at Line 720
725 GOTO 9000
730 START = J
900 PRINT
905 PRINT POINTS FOR VOIGT PEAK CALCULATION
910 FOR J = 1 TO NP
915 13 = START + (J 1)
920 X(J) = PK(1,I3)
925 Y(J) = PK(2,I3)
930 H(J,J) = 1
935 IF 13 < HOLD GOTO 950
940 IF Y(J) < .2 PK(2,H0LD) GOTO 960
950 PRINT X(J),Y(J),W(J,J)
955 NEXT J
960 N = J 1
965 M = 3
967 SI = 1E+15
970 S = 0
973 CHISQ = 0


9
TABLE 22
Th-323 Decay Chain
1
Radionuclide
Half-Life
| Ma
1 (
Alpha
jor Radiation Ein
VIeV) and Intensi
Beta
;rgies |
;ies |
Gamma
Th-323
1.41E10 a
3.95 (24%)
4.01 (76%)
-
Ra- 228
6.7 a
-
0.055 (100%)
-
Ac-228
6.13 h
-
1.18 (35%)
1.75 (12%)
2.09 (12%)
0.34 (15%)+
0.908 (25%)+
0.96 (20%)+
Th- 228
1.91 a
5.34 (28%)
5.43 (71%)
-
0.084 (1.6%)
0.214 (0.3%)
Pa-224
3.64 d
5.45 (6%)
5.68 (94%)
-
0.241 (3.7%)
Rn-220
55.0 s
6.29 (100%)
-
0.55 (0.07%)
Po- 216
.15 s
6.78 (100%)
-
-
Pb-2L2
10.65 h
-
0.346 (81%)
0.586 (14%)
0.239 (47%)
0.300 (3.3%)
Bi-212
(Branches)
60.6 min
6.05 (25%)
6.09 (10%)
1.55 (5%)
2.26 (55%)
0.040 (2%)
0.727 (7%)+
1.620 (1.8%)
Po-212
(64%)
304.0 ns
8.78 (100%)
-
-
77-208
(36%)
P6-210
3.10 min
Stable
1.28 (25%)
1.52 (21%)
1.80 (50%)
0.511 (23%)
0.583 (86%)+
0.860 (12%)
2.614 (100%)+
NOTES: + Indicates those gamma rays that are commonly used to identify Th-232. Equilibrium
must be assumed.


46
DRi (E') = GFi (E'),
where
DR{ (E') = detector response at energy E to point
node i,
{counts/s) / {pCi/gm of dry soil),
GFi {E') = FD {E') x DE {E') x CT,
geometry factor at energy E' for point
node i,
(counts/s) / (pCi/gm of dry soil).
The above equations are a mathematical description of the fluorescent x ray flux,
counted by a detector, due to a single point target irradiated by a point excitation source.
Looking at equation 3 more closely, the term AD, atom density of U or Th at the point
node, is in units of (atoms/cm3 of soil)/(pCi/gm of soil). The geometry factor, GF{, is
thus normalized to a contamination concentration at the point node of 1 pCi/gm. And the
detector response to a point node contaminated to any concentration, C pCi/gm, is a linear
function of the geometry factor.
Since both DR¡ (E1) and GF¡ {E') are per pCi/gm of dry soil, the detector response
to a point node contaminated to a concentration of C pCi/gm, would be
DRi {E') = C x GFi {E'),
where
DRi (E') = FS (E')
= detector response at energy E' to point
node i,
{counts/s) / {C pCi/gm of dry soil),


239
C
C Data is now written into file SAMPLE2.DAT
C
OPENCl,FILE=SAMPLE2.DAT,STATUS=NEW)
WRITE(1,*(A3)) ELEMENT
WRITE(1,*) WF
WRITEd,*) SD
WRITECl,*) A1
WRITECl,*) Bi
WRITEd,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSE Cl,STATUS=KEEP)
END


315
C
C DATA FROM XRF8JJSA.CNF; 1
D4(8)
=
14.0
M5(8)
=
7.0
75(8)
=
87.0
HR(8)
=
15.0
MN(8)
=
19.0
RH(8)
=
1.0
RM(8)
=
10.0
RS(8)
=
20.85
PH(8)
=
164036.0
ER(8)
=
1041.0
STORE DATA
ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS= *NEW)
WRITE(1,5) NF
5 FORHATC1I2)
WRITE(l.lO) LH, LM, LS
10 FORHAT(3F10.5)
DO 100 I = 1,NF
WRITE(i,25) D4(I), H5(I), Y5(I)
25 FORMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
HRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


113
TABLE 29
Peak Fit Results for Sample U1
Sample Contamination Concentration: 152.3 pCi/gm U238
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
127599 0.6%
6.1
2
118246 0.6%
5.7
3
98117 0.8%
4.1
4
96465 0.8%
4.6
5
82104 0.5%
2.5
6
67923 1.6%
2.9
7
63979 0.6%
2.6
8
56134 0.8%
6.3
TABLE 30
Peak Fit Results for Sample Ula
Sample Contamination Concentration: 164.6 pCi/gm U238
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
141648 0.4%
3.5
2
123835 0.7%
6.0
3
111115 0.5%
3.5
4
100697 0.6%
6.1
5
94625 0.8%
7.9
6
85532 0.4%
4.2
7
77306 0.5%
2.7
8
68731 0.8%
6.9


91
techniques. This is why all the samples analyzed, except Sample 2, Sample 3, and Sample 4
were paired. Since these samples were made by blending samples together, they were large
enough to provide adequate samples for the other two analysis techniques that were used.
Table 9 lists the assay results of the three techniques for U and Th contaminated soil.
Table 10 lists the results of a sensitivity study described below. Tables 11 to 25 list the
measured and fit detector responses for each sample. Table 26 lists various physical qualities
of the above samples. Table 27 lists sample attenuation qualities.
In order to further verify the statistical validity of these results, a short sensitivity
study was performed. As described in Chapter II the assay technique described here fits
peak area data, collected from a sample counted in several geometries, to a straight line
passing through the origin. The slope of this line is the concentration of radionuclide in the
sample, which is the desired result of the assay. In this work, this line was fit using eight
points. To test the sensitivity of the resulting slope to the number of fitting points used
the program ASSAY.FOR was used to reprocess the data from Sample 3. In this case data
from positions 1, 3, 5, and 7 were used for one run, and data from positions 2, 4, 6, and 8
were used for a second run. The results of these runs as well as the result of the original
Sample 3 run using eight points are listed in Table 10 and show that the assay results using
four fitting points are similar to the assay results using eight fitting points.
It should be noted that the errors presented in Tables 9 and 10 were calculated using
the techniques described in the error section of Chapter II. Put simply, each point on the
line represents a peak area which is calculated by least squares fitting measured data to a
theoretical peak shape function. Each calculated area thus has an associated error. Since
the peak areas are large, as is shown in Tables 29 through 43, the errors associated with
each data point are small. The peak area data points are then least squares fit to a straight
line, the slope of which is the concentration of U or Th in the target soil sample. The error


ACKNOWLEDGEMENTS
This publication is based on work performed in the Laboratory Graduate Participation
Program under contract #DE-AC05760R00033 between the U.S. Department of Energy
and Oak Ridge Associated Universities.
In that the production of this dissertation has been a very difficult process which I
could not have finished without the help of numerous others, I would like to acknowledge
those who have given me so much invaluable assistance.
I would like to thank Corinne Ann Coughanowr, my wife, who provided me with excel
lent advice, guidance, and support throughout the project.
I would like to thank Dr. Genevieve S. Roessler, committee chair, University of Florida,
who provided technical and procedural guidance.
I would like to thank Dr. David Hintenlang, committee member, University of Florida,
who provided guidance which helped assure a quality final product.
I would like to thank Dr. Edward E. Carroll, committee member, University of Florida,
who taught me enough instrumental expertise to properly perform experiments.
I would like to thank Dr. Emmett Bolch, committee member, University of Florida,
who provided support in soil sample analysis.
1 would like to thank Dr. A. G. Hornsby, committee member, University of Florida,
who provided support for work in soil moisture content determination.
I would like to thank Dr. II. Van Rinsvelt, committee member, University of Florida,
who provided support in EDXRF analysis.
in


120
TABLE 40
Peak Fit Results for Sample NJA-Th
Sample Contamination Concentration: 2436.7 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
3062432 0.1%
2.0
2
2709169 0.1%
4.5
3
2560958 0.1%
4.6
4
2245527 0.1%
2.2
5
2002194 0.1%
4.8
6
1742420 0.2%
7.2
7
1568213 0.2%
9.7
8
1367233 0.2%
2.2
TABLE 41
Peak Fit Results for Sample NJB-Th
Sample Contamination Concentration: 2267.0 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
2896677 0.1%
4.0
2
2689680 db 0.1%
3.5
3
2364069 0.1%
5.6
4
2133681 0.1%
7.4
5
1910431 0.1%
9.7
6
1692538 0.1%
2.9
7
1507566 0.2%
12.3
8
1336647 0.2%
9.0


247
C
C Data is now written into file SAMPLE2.DAT
C
OPEN(1,FILE=SAMPLEU1A.DAT,STATUS=NEW *)
WRITE(1,(A3)') ELEMENT
WRITE(lf*) WF
WRITECl,*) SD
WRITECl,*) A1
WRITEC1,*) 61
WRITE(1,*) Cl
WRITEd,*) US1
WRITE(1,*) US2
WRITE(1,*) US3
CLOSE(1,STATUS=KEEP)
END


41
is composed of gamma rays from the source which have backscattered in the target and hit
the detector, and of fluorescent x rays from the U and/or Th in the soil. The number of
fluorescent x rays counted by the detector is proportional to the U or Th concentration in
the target. In overview, the assay technique is quite simple.
The target can be thought of as many small point sources. The fluorescent x rays
produced at each point source contribute separately to the the full energy pliotopeak of
Kai x rays seen by the detector. A mathematical model of each point source is used to
calculate the x-ray contribution from each point source. These calculated individual point
source contributions can be summed to yield a calculated total detector response. The
calculated response is then compared to the actual measured response, in a least squares
sense, to determine the contamination concentration in the target sample.
Mathematical Model
All of the equations in this section stem from well known first principles. To begin
with, it is well known that the excitation gamma ray flux (FL) that reaches a point in the
target can be described by
FL(E)=SMx<¡x¡,(-II(E)p0Il,), (2)
where
FL (E) = excitation gamma flux at a point in the
target, (gammas/cm2s) ,
ER(E) = source emission rate at energy E,
(gammas/s),


136
columnated beam. With a columnated beam small scatter angles will remove photons from
the beam. But the application of the attenuation coefficients measured here is a broad
beam situation. So for every gamma that coherently scatters out of the beam, another will
coherently scatter into the beam.
Consider the situation of a Co-57 source shining gamma rays isotropically on a cylin
drical soil sample. Remember that the soil sample is thought of as approximately 2000
individual volumes, each small enough to be described using point source mathematics (see
assay section). Considering a single point, the Co-57 source emits gammas isotropically,
some of which are aimed at the point in question. Of those gammas aimed at the point,
some will coherently scatter out of the beam that will reach the point. Some gammas that
are almost aimed at the source will coherently scatter into the beam that will reach the
point. Only those gammas that incoherently scatter, have photoelectric reactions, or un
dergo pair production reactions will be removed from the beam. Note that very small angle
incoherently scattered gammas should act the same way as coherently scattered gammas,
ie. some should scatter out of the beam while others scatter into the beam. This is only
a small fraction of the incoherent scatters and makes little statistical difference, unlike co
herent scatters which are all at very small angles.Thus the removal mass attenuation
coefficient properly describes the situation. The same argument can be made for the mass
attenuation coefficient which describes the transport of the fluorescent x rays from a point
in the soil to the detector.
To properly measure this coefficient, then, a broad beam should be used. This is
the technique that is described earlier in the system calibration section. The following
experimental evidence confirms the choice of the removal mass attenuation coefficient.
Looking at the calibration geometry in Figure 14, photons leaving the source encounter
several attenuating materials on their way to the detector. The capsule that holds the


A-3. NBS Source, SRM 4275-B-7, Physical Characteristics 129
A-4. System Calibration Parameters 133
A-5. Water Attenuation Coefficients, n(E)H70, Actual and Calculated Values . 140
A-6. Water Attenuation Coefficients, ft {E)Hi0,
Calculated Values vs. Target Distance from the Detector 141
A-7. Representative Soil Elemental Concentrations 144
A-8. Compton to Total Scatter Coefficients for Soil at 150 keV and 100 keV . 144
A-9. Average Compton to Total Scatter Ratio for Soil 145
B-l. Relative Sample Separation vs. Solution Matrix Condition 151
B-2. Target-Detector Distance vs. Measured Peak Area 154
xiii


TABLE 19
Measured vs. Fitted Detector Response for
Sample 4
Fitting Equation : DR = GF X CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 683.0 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.416
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.258
859.2
882.6
2
1.108
756.6
767.3
3
0.979
668.4
674.8
4
0.867
592.3
589.6
5
0.770
526.4
518.8
6
0.686
468.8
456.7
7
0.613
418.9
403.8
8
0.550
375.3
359.5


44
The flux at the detector (FD), of the Kai x rays that hit the detector, due to the above
x-ray fluorescent yield, can be described by
where
FD (E') =
FY{E',E) x DA
A-xr2
X exp(-p(E')p0r2),
FD (E1) = the flux of fluorescent x rays of energy E' that
hit the detector,
({Kai x rays) /s) / (pCi/gm of dry soil),
FY (E1, E) = the flux of fluorescent x rays of energy E' at
the point, that are caused by excitation gammas
of energy E,
((Aq1 x rays) /s) / (pCi/gm of dry soil),
DA = detector area, (cm2) ,
rt = distance from the point to the detector, (cm),
p(E') X p = sample mass attenuation coefficient at energy
E', (gm/cm2), times sample density, (gm/cm3) ,
and,
r2 = that portion of the total distance that
lies within the attenuating sample, (cm).
It should be noted that this equation does not include any terms to account for small
angle scatter, and correspondingly small energy change, x rays which are mathematically
removed from the x ray beam but would actually still hit the detector and be counted in
the full energy peak. Looking at the geometry of the situation, the largest scatter angle
which would leave an x ray still traveling toward the detector is ten degrees. Integrating
the Klein-Nishina differential scattering cross section (Evans pp 677-689) over 2tt, for d,
and over ten degrees, for d0, the ratio of this to the total scattering cross section is .029.


295
C
C DATA FROM XRF8_TH1A.CNF;1
D4(8)
=
16.0
M5(8)
=
6.0
75(8)
=
87.0
HR(8)
=
14.0
MN(8)
=
19.0
RH(8)
=
1.0
RM(8)
=
12.0
RS(8)
=
18.12
PH(8)
=
178059.0
ER(8)
=
1317.0
STORE DATA
ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS=NEW')
WRITE(1,5) NF
5 F0RMAT(1I2)
WRITE(l.lO) LH, LM, LS
10 F0RHATC3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), HN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 FORMAT(2F15.5)
100 CONTINUE
END


TABLE 37
Peak Fit Results for Sample 4
Sample Contamination Concentration: 683.0 pCi/gm Th232
Counting Geometry
Peak Area
(C ount- Channels )
Reduced
X2
1
1453181 0.2%
9.7
2
1287314 0.2%
10.1
3
1148003 0.2%
7.7
4
1014348 0.2%
12.6
5
899790 0.3%
12.0
6
789214 0.3%
21.4
7
710364 0.3%
11.1
8
636039 0.4%
23.5


227
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
***********+****************
* *
* GE0M5G.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5G.DAT
This program creats file GE0M5G.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-67 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(i) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 6)
XT = 11.4
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32


249
C
C Data is now written into file SAMPLETH1.DAT
C
OPEN(i,FILE=SAMPLETH1.DAT',STATUS=NEW)
WRITE(1,'(A3)) ELEMENT
WRITECl,*) WF
WRITE(1,*) SD
HRITEd,*) A1
WRITE(1,*) B1
WRITE(1,*) Cl
WRITE(1,*) US1
WRITE(1,*) US2
WRITE(1,*) US3
CL0SE(1,STATUS='KEEP)
END


2415
2425
2427
2435
2445
2447
2450
2455
2500
2510
2515
2525
2535
2540
2545
2600
2610
2615
2625
9000
174
OPEN 0,#1,PEAK$
PRINT #1, NE NS + 1
FOR I = NS TO NE
PRINT #1, X(I)
PRINT #1, PK(I)
PRINT #1, VAR(I)
NEXT I
CLOSE #1
OPEN O ,#1,BK$
PRINT #1, NE NS + 1
FOR I = NS TO NE
PRINT #1, X(I)
PRINT #1, BK(I)
NEXT I
CLOSE #1
LPRINT
LPRINT Peak data saved in file ;PEAK$
LPRINT
LPRINT Background data saved in file ;BK$
END


19
proportional to the mean lifetime of the excited nuclear state (Evans pp 397-403). This is
directly attributable to the Heisenberg uncertainty principle such that (Evans pp 397-403)
T {eV) = .66E 15 (eV s) /tm (a)
where
r = energy distribution width (eV),
.66E 15(eFs) = Plank's Constant/27T,
tm = mean lifetime of excited state.
NOTE: half life (tl/2) = fm/ln(2)
Therefore, for a gamma ray to have an energy distribution width greater than 1 eV,
its mean life would have to be less than IE-15 s. Since most gamma rays are emitted
from radionuclides with half lives much longer than that, the width of gamma ray energy
distributions is zero for practical purposes. Since the width of the energy distribution for
gamma rays is so small, S(E) is effectively a delta function. The convolution of a delta
function energy distribution and a Gaussian distribution detector response results in a
Gaussian shape spectral peak for gamma rays (Knoll* pp 434-440).
X rays, however, are generated by electrons falling from upper to lower orbitals, as
described in a previous section. These transitions take place very rapidly, and therefore the
emitted x rays have fairly large widths which increase with increasing energy.^ Experimen
tal measurements have shown Kai x rays to have widths of from 1 eV for Ca to 103 eV for
E7. X-ray energy distributions must therefore be described by a Lorentzian distribution*
and an x-ray spectral peak must therefore he described by the convolution of a Gaussian
detector response function and a Lorentzian x-ray energy distribution.** Mathematically,
this convolution is written as
/OQ
G{E')x L{E E')dE',


217
C
C Data files filled with correct values
C
WRITE(6,*) JA(1),JA(2)
DTFILE = COHDTA.DAT
OPEN(1,FILE=DTFILE,STATUS=NEW)
WRITE(1,*) E(l), E(2),
1 CTRATIOCl), CTRATI0(2),
2 TF(1), TF(2), UA(1), UA(2),
3 A0(1), A0(2), YI(1), YI(2),
4 JA(1), JA(2)
DO 150 I = 1,2
150 WRITE(1,*) EKAB(I), PE1(I), PE2(I), EC(I)
CLOSE(1,STATUS='KEEP)
END


193
READ(1,*) V(I)
180 WRITE(6,*) V(I)
CLOSE(1,STATUS=KEEP)
E(3) = V(l)
UA(3) = V(2)
UB(3) = V(3)
ED(3) = V(4)
JA(3) = SQRT(V(5))
PE(1) = V(6)
PE(2) = V(7)
KS = V(8)
KY = V(9)
EC = V(10)
500 DO 1000 19 = 1,8
C
C READ SOURCE TO POINT DISTANCES AND VOLUMES FROM DISK
C
DO 950 N1 = 1,2
OPEN(1,FILE=SPFILE(19),STATUS=OLD)
READCl.O XS(1),YS(1),ZS(1),XS(2),YS(2),ZS(2)
READ(1,*) XT,YT,ZT,TR,TH,RT,CT,VT
READ(1,*) XD,YD,ZD,DR,RD,CD,NS
IF(N1 .Eq. 2) GOTO 550
13 = 1
14 = VT/2
15 = 1
GOTO 575
550 13 = VT
14 = 1 + (VT / 2)
15 = -1
575 DO 900 12 = 13,14,15
C
C READ SOURCE TO TARGET DISTANCES FROM DISK
C
DO 675 J = 1,RT CT / 2
675 READd.O SP(J, 1) ,SP(J,2) ,SP(J,3) ,SP(J,4) ,VOL(J)
C
C READ TARGET TO DETECTOR DISTANCES FROM DISK
C
OPEN(2,FILE=PDFILE(19),STATUS=OLD)
DO 700 J = i,RT CT / 2
DO 700 K = 1,RD CD
700 READ(2,*) P1(J,K),P2(J,K)
DO 710 J = 1,RD CD
710 READ(2,*) AD(J)
C
C DETERMINE GEOMETRY FACTORS
C


Counts


157
Area = 3.6E7 X Exp (A X Distance).
Using this equation we arrive at a detector response of 32872 counts for the target at
17.5 cm (thats position #1 + 7 cm). For the target at 24.5 cm (position #1 + 14 cm),
the predicted detector response is 1989 counts. For the target at 31.5 cm the predicted
detector response is just 120 counts. Thus to maintain proper relative target separation of
7 cm and to approximate a sample as having only four zones, the peak area of the fourth
count would be statistically very small. Based on experience with the experimental detector
system used for this work, a peak this small would not be detectable. The validity of the
peak from the third position is also questionable from a detectability standpoint. As such,
having eight measurements is not possible. In performing an analysis on a sample which is
very inhomogeneous, more than two zones are necessary, yet based on this analysis more
than two zones is not practically possible.
The types of things that could be done to make the system work are larger and/or
more detectors, and longer count times. The use of larger and/or more detectors makes
the system far less portable and the computer analysis far more complicated. Both of these
push the system out of the field analysis arena. And while longer count times would
make peak areas larger, there would still exist a large difference between measured peak
areas from position to position, and this would have a destabilizing effect on the matrix
(large round ofF errors). As such, this analysis technique for inhomogeneous samples is
theoretically possible, but is actually an idea whose time has not yet come.


287
C
C
c
DATA FROM XRF8JJ1A.CNF;1
C
C
C
D4(8)
M5(8)
Y5(8)
HR(8)
MN(8)
RH(8)
RM(8)
RS(8)
PH(8)
ER(8)
3.0
6.0
87.0
22.0
29.0
1.0
12.0
43.31
68731.0
530.0
10
25
50
75
90
100
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
F0RMAT1I2)
HRITE(l.lO) LH, LM, LS
F0RHATC3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
FORMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
F0RMAT2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
F0RMATC3F10.5)
WRITE(1,90) PH(I),ER(I)
FORMAT(2F15.5)
CONTINUE
END


286
C
C DATA FROM
C
D4(5) =
M5(5) =
Y5(5) =
HR(5) =
MN(5) =
RH(5) =
RM(5) =
RS(5) =
PH(5) =
ER(5) =
C
C DATA FROM
C
D4(6) =
H5(6) =
Y5(6) =
HR(6) =
HN(6) =
RH(6) =
RH(6) =
RS(6) =
PH(6) =
ER(6) =
C
C DATA FROM
C
D4(7) =
H5(7) =
Y5(7) =
HR(7) =
HN(7) =
RH(7) =
RMC7) =
RS(7) =
PH(7) =
ER(7) =
XRF5_U1A.CNF;1
3.0
6.0
87.0
16.0
67.0
1.0
16.0
9.13
94625.0
728.0
XRF6JJ1A.CNF; 1
3.0
6.0
87.0
19.0
26.0
1.0
14.0
54.18
85532.0
367.0
XRF7JU1A.CNF;1
3.0
6.0
87.0
20.0
49.0
1.0
13.0
54.04
77306.0
425.0


50
100
150
200
250
300
210
H(I,J) = H(I,J) / T1
C0V(I,J) = C0V(I,J) / T1
DO 150 J = 1,M
IF(J .EQ. I) GOTO 150
T2 = H(J,I)
DO 100 K = 1,H
H(J,K) = H(J,K) (H(I,K) T2)
COV(J.K) = COV(J.K) (COVCI.K) T2)
CONTINUE
CONTINUE
WRITE(6,0 H(l,l), H(1,2), H(2,l), H(2,2)
WRITE(6,0 C0V(1,1), C0V(1,2), C0V(2,1), C0V(2,2)
DO 250 I = 1,NP
PI = PI + C0V(1,1) Y(I) /
P2 = P2 + C0V(2,1) Y(I) *
P3 = P3 + C0V(1,2) Y(I) /
P4 = P4 + C0V(2,2) Y(I) *
ZERO = PI + P2
SLOPE = P3 + P4
DZ = SqRT(COV(l,l))
DS = SQRT(C0V(2,2))
DO 300 I = 1,NP
F(I) = ZERO + SLOPE 1(1)
CHISQ = CHISq + ((Y(I) F(I))**2)
RETURN
END
(SIG(I)**2)
1(1) / (SIG(I)**2)
(SIG(I)**2)
X(I) / (SIG(I)**2)
/ (F(I) (NP 2))


WRITE(6,1100)
1100 F0RMAT(/,1X,'XRF Reaction Rates due to Compton Scatter
1 /,IX,calculated. Calculating Detector Respons
2 /,lX,due to Compton Scatter XRF.)
1105 XRF = $2$DUA14:[LAZO.DISS.DATA]XRFDTA.DAT
WRITE(6,1110) XRF
1110 F0RHAT(/,IX,'Reading XRF data from file ,1A31)
OPEN(1,FILE=XRF,STATUS=OLD')
IF (ELEMENT .Eq. U') GOTO 1150
DO 1125 I = 1,10
1125 READ(1,*) QHOLD
1150 DO 1155 I = 1,10
1155 READ(1,*) q(I)
CLOSE(1,STATUS='KEEP')
UA(3) = q(2)
UB(3) = q(3)
ED(3) = q(4)
JA(3) = SqRT(q(5))
KS = q(8)
KY = q(9)
c
C Read in Target-Detector Distances and Calculate
C Detector Responses for each target point.
C
GFNT = 0.0
GFCT = 0.0
BE = EXP(-UB(3) 1.842 .0254)
DO 1400 I = 1,RTCTVT
DO 1350 J = 1,24
R1DJI = R1D(J,I)
R2DJI = R2D(J,I)
SOIL = EXP(-US(3) R2DJI)
AIR = EXP(-UA(3) .001205 (R1DJI R2DJI))
1350 AA = AA + SOIL JA(3) AIR BE AD(J)
1 / (4 PI R1DJI R1DJI)
GFCOMPTON = RX(I) AA KS KY ED(3)
GFNAT = KA1NAT VOL(I) SD WF AA ED(3)
GF(I) = GFCOMPTON + GFNAT
AA = 0.0
GFNT = GFNT + GFNAT
GFCT = GFCT + GFCOMPTON
1400 CONTINUE
WRITE(6,2350)
2350 F0RMAT(/,1X,'In what file should the data be saved,/,
1 IX,(Filename.Ext))
WRITE(6,*) GFFILE
2375 OPEN(1,FILE=GFFILE,STATUS=NEW)
TOTAL = GFNT + GFCT


140
where
fi {E)u_¡0 = the measured mass attenuation
coefficient at energy E, for water,
{cm2/gm),
In {K (E)) = the natural log of the right hand side
of Equation A 8, (nounits)
Po = the density of water
= 1 gm/crn3
R = the effective diameter of the plastic
water jar, (cm).
In Equation A-9, R is represents the average distance that each photon traveled through
the water. Since the jar is curved and since the path from the source to the detector is
actually a three dimensional solid angle, the average path length for a photon in the water
must be calculated numerically. This done, the mass attenuation coefficients for water were
calculated. The results of these calculations are shown in Table A-5.
TABLE A-5
Water Attenuation Coefficients
fi{E)Hj0, Actual and Calculated Values -f
Energy (keV)
Actual
ft (e)ITi0
Total
{cm2/gm)
Actual
A* (E)ir2o
Removal
{cm2/gm)
Calculated
A4 {E)H3o
{cm2 ¡gm)
136.476
0.1559
0.1526
0.1512 0.0003
122.063
0.1617
0.1576
0.1554 0.0001
105.308
0.1685
0.1634
0.1610 0.0002
86.545
0.1793
0.1719
0.1696 0.0004
+: Actual values from Hubble ^3.


I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Arthur Hornsby
Professor of Soil Science
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy
HenrFVan Rinsvelt
Professor of Nuclear Engineering Sciences
1 certify that 1 have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
G uvgn'Yalcintas
Director, Office of Technology Applications
Martin Marietta Energy Systems
This dissertation was submitted to the Graduate Faculty of the College of Engineering
and the Graduate School and was accepted as partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
December, 1988
iUlj-C. 6.
41* j
Dean, College of Engineering
Dean, Graduate School


126
The XRF Excitation Source Holder and Detector Shield
The Co-57 source, used to induce x-ray fluorescence in a soil target, is held in a lead
shield very close to the detector. The source holder positions the source in a known and
reproducible geometry and shields the detector from gamma rays directly from the source.
Direct shine of Co-57 gammas onto the detector would increase the spectral background.
By minimizing the number of background photons that hit the detector, counting dead time
is minimized leading to shorter count times. The shorter the count time the more samples
can be analyzed per day. Figures 5 and 9 show the shield in position over the detector.
The shield is layered to optimize its shielding ability. Figure 8 shows a photograph of the
sliield pieces.
Since Co-57 emits gamma rays of energy high enough to induce x-ray fluorescence in
any element, all shield material will emit fluorescent x rays. Each layer of shield should
therefore effectively sliield any gammas or x rays that reach it while emitting x rays that
can be shielded effectively by the next shield layer. The source holder / detector shield was
therefore designed with the first layer Pb, followed by W, then Cd, then Cu.
Lead has the highest attenuation coefficients of any of the shield materials used. Its
primary function is to shield the detector from direct gamma rays from the Co-57 source.
While the Pb stops most of these gamma rays, it also emits fluorescent x rays induced by
the gamma rays. The next layer of the shield, W, shields the detector from any gamma
rays penetrating the Pb shield and from any Pb x rays. The W, however, emits fluorescent
x rays also. The next layer, Cd, shields the detector from and gamma rays that penetrated
the previous two shields, from Pb x rays, and from W x rays. The final layer, Cu, shields
the detector from any photons reaching that level. Table A-l lists the x-ray absorption and
emission energies of the shield materials. No other major equipment is used in this research.


180
2400 F6=(EXP(-(CHI**2)))*(C1+C2*(CHI**2)+C3*(1"2*(CHI**2)))
2420 F6 = (F6 + C4 BX) A
2640 RETURN
4490 REM
4492 REM Subroutine to perform the matrix multiplication:
4494 REM Q3(M,W) = Q2(M,N) Q1(N,W)
4496 REM
4500 PRINT GO SUB 4500
4501 FOR I = 1 TO M
4502 FOR J = 1 TO M
4503 Q3(I,J) = 0
4504 NEXT J
4505 NEXT I
4510 FOR K = 1 TO M
4520 FOR I = 1 TO W
4540 FOR J = 1 TO N
4560 Q3(K,I) = Q3(K,I) + Q2(K,J) Q1(J,I)
4580 NEXT 3
4600 NEXT I
4620 NEXT K
4640 RETURN
4980 REM
4982 REM
4984 REM
4986 REM
4990 REM
4992 REM
4994 REM
4996 REM
4997 REM
4998 REM
5000 FOR I = 1 TO M
5020 FOR J = 1 TO M
5040 AM(I,J) = (I,J)
5060 NEXT J
5080 NEXT I
5090 Ml = M + 1
5100 FOR I = 1 TO M
5120 AM(I.Ml) = DTCl.l)
5140 NEXT I
5160 SM = 0
5180 FOR R = 2 TO M
5200 R2 = R 1
5220 FOR R1 = R TO M
5240 SM = AM(R1,R2) / AM(R2,R2)
5260 AM(R1,R2) = 0
5300 FOR C = R TO Ml
5320 AM(R1,C) = AM(R1,C) AM(R2,C) SM
Subroutine to solve the matrix equation:
TA(M,N)*W(N,N)*A(N,M)*DT(M,1) = TA(M,N)*W(N,N)*DY(N,1)
where: TA(M,N) W(N,N) A(N,M) = AA(M,M)
DT(M,1) = Variable Matrix
DY(M,1) = Solution Matrix
This subroutine solves the above equation by Gaussian
Elimination


43
A = disintegration constant for U or Th,
(s'1),
Note : the units of .037 A are
(atoms/pCi), and
p, = soil bulk density,
(gm of dry soil) / (cm3 of soil).
The fluorescent yield (FY) at the point, due to the above photoelectric reaction rate,
can be described by
FY (E', E) = RX (E) x KS (E) x KY (E1),
where
FY (jE, E) = the flux of fluorescent x rays of energyE' at
the point, that are caused by excitation gammas
of energy E,
((Kai x rays) /s) / (pCi/gm of dry soil),
RX (E) = photoelectric reaction rate at the point,
(reactions/s) / (pCi/gm of dry soil),
KS (E) = fraction of photoelectric reactions that result
in K shell vacancies,
(K shell vacancies) / (photoelectric reaction),
= (Rk 1 )/Rk
Rk = K shell Jump Ratio, and
KY (E1) = fraction of K shell x rays that are Kai
x rays, (Kal x rays) / (K shell x ray).


267
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(i,FILE= *SAMPLEUSD.DAT,STATUS=NEW)
WRITE(1,(A3)) ELEMENT
WRITEd,*) HF
WRITEd,*) SD
WRITEd,*) Ai
WRITEd,*) B1
WRITEd,*) Cl
WRITEd,*) US1
WRITEd,*) US2
WRITEd,*) US3
CLOSE(1,STATUS=KEEP)
END


320
C ****** iii*********************
c *
C USCXRF.FOR *
C *
C FILE PROGRAM *
C *
C ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = CLAZ0.DISS.USC3USCXRF.DAT'
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE USB IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE USA IS 130 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1016 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1JJSC.CNF; 1
C
D4(i) = 17.0
M5(l) = 7.0
Y5(l) = 87.0
HR(1) = 17.0
MN(1) = 3.0
RH(i) = 1.0
RM(1) = 18.0
RS(1) = 15.57
PH(l) = 65157.0
ER(1) = 666.0


DETERMINATION OF R ADIONUCLIDE CONCENTRATIONS
OF U AND Th IN UNPROCESSED SOIL SAMPLES
By
EDWARD NICHOLAS LAZO
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988


201
1 + W(I1,I) WP1P2
Q9 = O
DO 560 II = 1 ,NS
DO 560 J1 = 1,2
ES(Il.Jl) = H0C2 / (1 COTH(Il) + (1 / ALPHA(Jl)))
IF (ES(Il.Jl) .LT. EKAB) GOTO 555
IF (COTH(Il) .EQ. 1.0) GOTO 555
PE(I1,J1) = PEI ((.15 ES(Il.Jl)) / (.15 EKAB))
1 (PEI PE2)
GOTO 560
555 Q9 = Q9 + 1.
PE(I1,J1) = 0.
560 CONTINUE
IF (q9 .Eq. 4.) GOTO 900
C
C Calculate the Soil Differential Scatter XSect (1/cm)
C
DO 650 II = 1,NS
DO 650 J1 = 1,2
IF (PE(I1,Jl) .NE. 0.) GOTO 600
DSCAT(Il.Jl) = 0.
GOTO 650
600 PI = (1 / (1 + ALPHA(Jl) (1 C0TH(I1))))**2
P2 = (1 + C0TH(I1)**2) / 2
P3 = (ALPHA(J1)**2 (1 C0TH(I1))**2)
P4 = (1 + C0TH(I1)**2) (1 + ALPHA(Jl) (1 -COTH(Ii)))
DSCT = RO*RO PI P2 (1.0 + P3 / P4)
DSCAT(Il.Jl) = DSCT EDENS
650 CONTINUE
C
C Calculate the Soil Attenuation Coefficients for Scatter Gammas
C
DO 700 II = 1,NS
DO 700 Jl = 1,2
700 USS(Il.Jl) = EXP(-(A1 + B1 L0G(ES(I1,Jl)*10)
1 + Cl (L0G(ES(I1,Jl)*10))**2))
C
C Calculate the Photoelectric Reaction Rate at Target Point
C
DO 800 II = 1,NS
DO 800 Jl = 1,2
SOIL = EXP(-USS(I1,Jl) R1P2P1)
FL2(I1,Jl) = FLKI1.J1) DSCAT(I1,Jl) VOL(I)
1 SOIL / R1P2P1**2
800 RX(J) = FL2(I1,Jl) PE(I1,J1) EC WF SD VOL(J)
1 + RX(J)
900 CONTINUE
1000 CONTINUE


FIGURE 2
Lorentzian X Ray as Seen Through
the Gaussian Response of a Detector


Detector
Center
@ Origin
Point Source
Point Source
Target Cylinder
Center
cn
o


130
AD = the detector area, (cm2) ,
t](E) = the detector intrinsic energy efficiency at
energy E, (gammas counted per gamma hitting the detector)
CT count time, (s),
Ri = the distance from the source to the detector, (cm),
ATN (E) = gamma attenuation, at energy E, due to the air
between the source and the detector, and the Be
window of the detector,
= exp(-jt(jE) pR)Air Xexp (-p(E) p R)Bt
and
p(E) mass attenuation coefficient for air
or for Be at energy E, (cm2/gm),
p density of air or Be, (gm/cm3) ,
R = the thickness of the air or Be layer
through which the gammas pass, (cm).
By counting the NBS source,positioned at a known distance directly above the detector,
FL(E) can be measured. The only unknown in Equation A-l is i](E), which can then be
calculated at the five energies listed in Table A-2. This includes 86 keV and 105 keV,
the emission energies of Eu-155. In order to insure statistical significance, twelve separate
measurements of the NBS source were made at twelve different distances from the detector.
Average values for i](E) were determined and used in subsequent calculations.
Once the detector intrinsic energy efficiency had been determined for the two Eu-155
energies, the Isotope Products sources could be calibrated.
Again using Equation A-l, the Isotope Products Eu-155 source was counted. Now the
unknown in Equation A-l was the source emission rate, ER(E), which could be determined


200
400 CONTINUE
435 WRITE(6,440)
440 FORMAT/,IX,Target and Detector Node Point,/,
1 Coordinates Calculated)
C
C Calculate Soil Electron Density
C
DO 450 J1 = 1,2
ALPHA(Jl) = E(J1) / M0C2
TERM = (1 + 2 ALPHA(Jl))
PI = (1 + ALPHA(Jl)) / ALPHA(J1)**2
P2 = (TERM + 1) / TERM
P3 = (1 / ALPHA(Jl)) LOG(TERM)
P4 = (1 / (2 ALPHA(Jl))) LOG(TERM)
P5 = (1 + 3 ALPHA(Jl)) / (TERM**2)
SCAT(Jl) = 2 PI R0**2 (PI (P2 P3) + P4 P5)
450 EDENSITY(Jl) = US(J1) CTRATIO(Jl) / SCAT(Jl)
EDENS = (EDENSITY(l) + EDENSITY(2)) / 2
C
C Calculate Source Flux at the Scatter Point
C
RTCTVT = RT CT VT
DO 1000 I = 1,RTCTVT
DO 500 II = 1,NS
DO 500 Jl = 1,2
R1TI1I = R1T(I1,I)
R2TI1I = R2T(I1,I)
AIR = EXP(-UA(J1) .001205 (R1TI1I R2TI1I))
SOIL = EXP(-US(Ji) R2TI1I)
SA = TF(J1) AIR SOIL JA(J1)
500 FLl(Il.Jl) = A0(I1) YI(J1) 3.7E+07 SA
1 / (4 PI R1TI1I R1TI1I)
C
C Determine XRF contribution of scatter in point I
C to every point J, ( J O I).
C
DO 900 J = 1,RTCTVT
IF (J .Eq. I) GOTO 900
C
C Determine Scatter Photon Angle, Energy, and PE Cross Section
C
K7 = 1
CALL DISTANCE (XT(I),YT(I),ZT(I),XT(J),YT(J),ZT(J),
1 UP1P2,VP1P2,WP1P2,
2 R1P2P1,HLD1,K7)
IF (K7 .Eq. 10) GOTO 9000
DO 550 II = 1,NS
550 COTH(Il) = U(I1,I) UP1P2 + V(Ii,I) VP1P2


79


86
Data Analysis
Once all the spectral information is collected, the data is processed, using the computer
codes described earlier, to determine soil 7-238 and/or Th-232 concentrations. This process
requires 7 steps. All computer programs referenced here are listed in Appendix C.
1. POLYBK.BAS is run for each spectrum to determine the coefficients of the fourth order
polynomial used to fit the background shape.
2. BKG.BAS is run for each spectrum and, using the coefficients determined by POLYBK.BAS,
calculates a background which is a combination of a fourth order polynomial and a com
plementary error function. The background is then subtracted from the spectrum to
yield the peak data.
3. PEAKF1T.BAS is run for each spectrum and, using the peak data calculated by
BKG.BAS, fits the peak data to a Voigt peak shape and determines the peak area
based on the calculated fitting parameters. Once all eight spectra have been shaped
and had their areas determined, the peak area data is used to calculate soil contami
nation concentrations.
4. DIST.FOR is run once for each of the eight geometries used and stores source-target-
detector geometry information. The information stored includes, for each geometry,
distances from each source to each point in the target, the portion of that distance
which lies within the target (where soil attenuation coefficients are used), and the
distance from each point to each of the 24 mathematical nodes of the detector. This
data is compiled only once and is then used for the analysis of all samples.
5. 1MAGE.FOR is run once for each of the eight geometries and must be run for each soil
sample. This program uses the distances calculated by DIST.FOR and the attenuation
coefficients calculated by SOILTRANS.BAS to determine the sample GFs for each


246
C
C *********************
c *
C SAMPLEU1A.F0R *
C *
Q *********************
c
CHARACTER *3 ELEMENT
C
C This program create a data file of input
C data pertaining to Sample U1A, a homogenous
C II sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U>
C
C Soil Height Fraction, HF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.8348
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.16053
Bl = 0.67181
Cl =-0.43485
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.26460
US2 = 0.27996
US3 = 0.31671


TABLE A-9
Average Compton to Tota
Scatter Ratio for Soil
Energy (keV)
CTR Avg.
150
0.93212
136.476
0.90712
122.063
0.88048
100
0.83970


289
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MH(2) =
RH(2) =
RM(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MN(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2_TH1.CNF;1
15.0
6.0
87.0
11.0
17.0
1.0
20.0
17.86
367607.0
1486.0
XRF3JTH1.CNF;1
15.0
6.0
87.0
13.0
27.0
1.0
18.0
26.36
333507.0
1647.0
XRF4-TH1.CHF; 1
15.0
6.0
87.0
15.0
4.0
1.0
16.0
58.22
298668.0
1629.0


APPENDIX C
COMPUTER PROGRAMS
Peak Shaping Programs
Three programs were written to properly determine the area of x-ray peaks. All three
of these programs are written in IBM BASIC, were run on an IBM personal computer,
and are described in Chapter II. POLYBK.BAS determines the shape of the 4th order
polynomial background beneath the x-ray peak. BKG.BAS uses the polynomial fit deter
mined by POLYBK.BAS and completes the background calculation by attributing half of
the background to the polynomial and half to a numerically calculated compensated error
function (erfc). This background is then subtracted from the spectrum and the remaining
peak is stored. PEAKFIT.BAS then performs a least-squares fit on the stored peak data to
determine the Voigt Peak parameters and uses these parameters to numerically calculate
the peak area.
163


245
C
C Data is now written into file SAMPLE2.DAT
C
OPEN(i,FILE=SAHPLEU1.DAT,STATUS=NEW)
WRITECl.CA3)) ELEMENT
WRITECl,*) WF
WRITECl,*) SD
WRITECI,*) A1
WRITECl,*) B1
WRITECl,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSECl,STATUS=KEEP')
END


258
C
C *********************
C *
C SAMPLESJBTH.FOE *
C *
C i*********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample NJB-TH, a non-homogenous
C Th and U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH'
C
C Soil Weight Fraction, WF
C
WF = 0.87653
C
C Sample Density, SD
C
SD = 1.06198
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.07694
Bl = 1.19446
Cl =-1.36489
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.25818
US2 = 0.30521
US3 = 0.37231


311
C
C DATA FROM XRF8JJJABCNF; 1
C
C
C
C
D4(8) = 9.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 11.0
MN(8) = 27.0
RH(8) = 1.0
RH(8) = 9.0
RS(8) = 24.32
PH(8) = 1336647.0
ER(8) = 2666.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
5 F0RHATC1I2)
WRITE(l.lO) LH, LH, LS
10 FORHAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RHAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORHAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORHAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RHATC2F15.5)
100 CONTINUE
END


52
gammas which are scattered toward point B are calculated, the photoelectric reaction rate
and fluorescent x-ray production at point B are calculated, and the number of fluorescent
x rays which are counted by the detector is calculated. In a fashion similar to that used
previously, the microscopic calculations for each point in a large target are summed into
the macroscopic total fluorescent x-ray production due to Compton scatter gammas.
Mathematical model
Looking at Figure 7, the excitation gamma flux at point A is given, again, by Eq. 2
FLl {E) = x
where
FIn (E) = excitation gamma flux at a point in the
target, (gammas/cm2s) ,
ER(E) = source emission rate at energy E,
(gammas/s),
Ri = distance from the source to the point, (cm),
fi(E)p0 = sample mass attenuation coefficient at
energy E, p(E) (gm/cm2), times sample
density, p0 (gm/cm3),
R2 = that portion of the total distance that
lies within the attenuating sample, (cm), and
E = energy of the incident gamma.
The flux that arrives at point B is dependent upon the flux that arrives at point A,
and on the differential Compton scatter cross section for scatter through an angle 0. The


197
READ(1,*) XTC, YTC, ZTC
C
C TARGET HEIGHT, TH, RADIOUS, TR,
C AND NUMBER OF TARGET DIVISIONS, RT, CT, AND VT
C
READ(1,*) TH, TR
READd,*) RT, CT, VT
CLOSE(l,STATUS=KEEP)
C
C Detector Center Coordinates
C
XDC = 0.0
YDC = 0.0
ZDC = 0.0
C
C Detector Radious, DR, and Number of Divisions, RD, CD
C
DR = 1.8
RD = 8
CD = 3
WRITE(6,100)
100 F0RMAT(/,IX,Enter the name of the Soil Data File)
WRITE(6,(1A35)) DATFIL
125 OPEN (1,FILE=DATFIL,STATUS3OLD)
WRITE(6,150)
150 F0RMAT(/,1X,Is the Sample Contaminated with U or Th?)
READ(1,(A3)) ELEMENT
WRITE(6,(A3)) ELEMENT
WRITE(6,160)
160 FORMAT(/,IX,What weight fraction of the sample is Soil?)
READ(1,*) WF
WRITE(6,*) WF
WRITE(6,170)
170 F0RMAT(/,1X,What is the Soil Density (gm/cc) ?)
READ(1,*) SD
WRITE(6,*) SD
WRITE(6,180)
180 F0RMAT(/,1X,What are the Hubble Fit parameters for the Soil
1 Liniar Attenuation Coefficient d/cm) fit?,/,
2 IX,Note: Energy units for this fit are 1/10 MeV,,/,
4 IX,(Ex: 136keV=1.36),/,
5 lX,Us(l/cm) = Exp(-(A1 + B1 LOG(E) + Cl (L0G(E))**2)),/,
6 IX,Input Al, Bl, Cl)
READ(1,*) Al
WRITEC6,*) Al
READ(1,*) Bl
WRITE(6,*) Bl
READ(1,*) Cl


62
In the case of U, 17-238 alpha decays to Th-234, which beta decays to Pa-234, which
beta decays to 17-234. As the Pa-234 decays to 17-234, U x rays are emitted. ICRP report
# 38^ gives the emission rate of these x rays as 0.00232 Aq1/decay.
In the case of 7'h, Th-232 alpha decays to Ra-228, which beta decays to Ac-228, which
beta decays to Th-228. As the Ac-228 decays to Th-228, Th x rays are emitted. ICRP
report #38^ gives the emission rate of these x rays as 0.0428 R'1/decay.
Since natural decay production of x rays contributes so little to the total production,
the assumptions that Th-232 is in equilibrium with Ac-228, and that 17-238 is in equilibrium
with Pa-234 will introduce little error. As such, one pCi of Th-232 will be in equilibrium
with one pCi of Ac-228, and one pCi of 17-238 will be in equilibrium with one pCi of Pa-234.
The production rate of U and Th x rays can now be calculated.
For thorium
Kalyield
= ^0.0428
= 0.001584
Ka i \
decayJ
Ka\/ s
pCi Th- 232'
^0.037
decay/s
pCi Th 232
For uranium
Kaiyield
= ("
00232 Ail-) xf0.037 *C!'/s
decayJ \
decay/s ^
pCi U 238)
= 0.00008584
Kgy/S
pCi U 238
These terms are in the correct units to be added directly into the previously described
mathematical model at the point where fluorescent x-ray production in each point node is
calculated. With this small correction added, the mathematical model is complete.


DATA FROM
XRF5_TH1.CNF;1
D4(5)
=
15.0
M5(5)
=
6.0
Y5(5)
=
87.0
HR(5)
=
16.0
HN(5)
=
31.0
RH(5)
=
1.0
RM(5)
=
15.0
RS(5)
=
20.36
PH(5)
=
251310.0
ER(5)
=
2221.0
DATA FROM
XRF6JTH1.CNF;1
D4(6)
=
16.0
M5(6)
=
6.0
Y5(6)
=
87.0
HR(6)
=
9.0
MN(6)
=
28.0
RH(6)
=
1.0
RM(6)
=
14.0
RS(6)
=
30.19
PH(6)
=
232490.0
ER(6)
=
1121.0
DATA FROM
XRF7_THl.CNF;i
D4(7)
=
16.0
M5(7)
=
6.0
Y5(7)
=
87.0
HR(7)
=
10.0
MN(7)
=
54.0
RH(7)
=
1.0
RM(7)
=
13.0
RS(7)
=
3.79
PH(7)
=
196953.0
ER(7)
=
1430.0


194
DO 900 II = 1,RT CT / 2
DO 750 1 = 1,NS
A2 = 2 Al 1
A3 = 2 A1
SOIL = EXP ( US(1) SP(I1,A3))
AIR = EXP( UA(1) .001205 (SP(I1,A2) SP(I1,A3)))
SA FA(1) AIR JA(1) SOIL
IT(A2) = SA AO(CO(A1)) (3.7E+07) YI(1)
/ ((SP(I1,A2) SP(I1,A2)) 4 PI)
SOIL = EXP ( US(2) SP(I1,A3))
AIR = EXP( UA(2) .001205 (SP(I1,A2) SP(I1,A3)))
SA = FA(2) AIR JA(2) SOIL
IT(A3) = SA A0(C0(A1)) (3.7E+07) YI(2)
/ ((SP(I1,A2) SP(I1,A2)) 4 PI)
DO 775 L = 1,2
DO 775 LI = 1,NS
L2 = (2 LI) 1 + (L 1)
RX(L) = IT(L2) PE(L) EC WF SD + RX(L)
FY = (RX(1) + RX(2)) KS KY
RX(1) = 0.0
RX(2) = 0.0
DO 800 K = 1,RD CD
SOIL = EXP( US(3) P2(I1,K))
BE = EXP( UB(3) 1.842 .0254)
AIR = EXP( UA(3) .001205 (P1(I1,K) P2(I1,K)))
AA = SOIL JA(3) AIR BE
/ (4 PI (P1(I1,K) Pl(Il.K)))
GF(I2,I1) = FY AA VOL(Il) AD(K) ED(3)
+ GF(I2,I1)
CONTINUE
CLOSEC1,STATUS='KEEP')
CL0SE(2,STATUS='KEEP')
IF(I9 .GT. 1) GOTO 915
IF(N1 .EQ. 2) GOTO 915
HRITE(6,910) GFFILE
910 FORHATC/,IX,'Ready to store GF data in file ,A30)
0PEN(3,FILE=GFFILE,STATUS='NEW)
915 IF(N1 .Eq. 2) GOTO 920
16 = 1
17 = VT/2
GOTO 925
920 16 = 1 + (VT/2)
17 = VT
925 DO 930 I = 16,17
DO 930 J = 1,RT CT / 2
930 GFT0TALCI9) = GFT0TAL(I9) + GF(I,J)
WRITEC6,*) I9.GFT0TALCI9)
HOLD = C0(1)
1
750
1
775
1
800
1
900


261
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(1,FILE='SAMPLEUSA.DAT,STATUS=*NEW*)
WRITE(i,(A3)) ELEMENT
WRITE(i,*) WF
WRITE(1,*) SD
WRITECl,*) A1
WRITEd,*) B1
WRITECl,*) Ci
WRITE(1,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSE C1,STATUS=KEEP)
END




I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Genevieve S. Roessler, Chair
Associate Professor of Nuclear Engineering Sciences
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
TS
Barry B erven
Section Head,
Environmental Measurements and Applications Section
Health and Safety Research Division
Oak Ridge National Laboratory
I certify that 1 have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Emmett W. Bolch
Professor of Nuclear Engineering Sciences
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosppliy.
Edward Carroll
Professor of Nuclear Engineering Sciences
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
David Hintenlang
Assistant Professor of Nuclear Engineering Sciences


125
The ADC
The MCA is fed by ail ND-582 analog to digital converter (ADC) which is, in turn, fed
by an EG&G Ortec 571 spectroscopy amplifier. The amp receives voltage pulses from the
detectors pre-amp, boosts their voltage, and sends them to the ADC. The ADC converts
each voltage pulse to a digital signal, corresponding to the energy of the x ray that created
the pulse, that the MCA can store properly in the spectrum.
The lIPGe Detector
The detector is an EG&G Ortec High Purity Ge (HPGe) Low-Energy Photon Spec
trometer. The Ge crystal has an active diameter of 36 mm (1018mm2) and a sensitive
depth of 15 mm. The detector has an intrinsic energy efficiency of approximately 83% at
100 keV. That is, out of every 100 x rays, of energy 100 keV, that hit the detector surface,
83 will deposit their full energy in the detector. This will yield a spectral peak of area 83.
The method by which this efficiency is determined will be described later.
The XRF Excitation Source and Transmission Sources
Two different radionuclide gamma ray sources are used in this research: Co-57 and
jEJu-155. The Co-57 source serves as a source of x-ray excitation gamma rays, and as a
source of transmission gamma rays. The Eu-155 source serves as a source of transmission
gamma rays. These sources emit four gamma rays that are important. These gamma ray
energies are listed in Table 5. The sources were purchased from Isotope Products, emit at
energies listed in Table 5, and have the physical characteristics described in Table 6. Three
Co-57 sources and one Eu-155 source were purchased.


240
C
C *********************
c *
C SAHPLE3.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample #3, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Height Fraction, HF
C
HF = 1.0
C
C Sample Density, SD
C
SD = 1.3706
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.29107
Bl = 0.88278
Cl =-0.60210
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.22009
US2 = 0.23913
US3 = 0.29308


236
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M50.DAT
C
OPEN(1,FILE=GEOH,STATUS=NEW')
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
WRITE(1,*) XT, YT, ZT
WRITEd,*) TH, TR
HRITEd,*) RT, CT, VT
CLO SE(1,STATUS=KEEP)
END


TABLE 10
Assay Sensitivity to the Number of Fitting Points Used
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Positions
Used
Calculated CC
pCi/gm Th232
Reduced X2
1 to 8
221.7 0.2
0.242
1, 3, 5, 7
221.0 0.3
0.401
2, 4, 6, 8
222.1 0.3
0.343


221
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5A.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5A.DAT
This program creats file GE0M5A.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 10.5
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32


148
equations just developed, and dividing the cylinder into successively larger numbers of
points. The fluorescent signal at the detector for a 2000 point model was less that .1%
different from the fluorescent signal for a 1500 point model. The model size was thus
chosen as 2000 points.
A model of 2000 points will yield a system of 2000 equations in 2000 unknowns, and
this is well beyond the limit of that which can be solved precisely by a computer. The
computer time and the round off error for such a task are both unacceptably large.
To formulate a problem that is manageable, the point sources can be grouped into
homogeneous zones such that a sample is made up of only 15 to 30 zones. Since the zones
are assumed to be homogeneous, the contribution of each zone to the area of the full energy
peak at energy E will be the sum of the point source geometry factors from the points in
the zone times the unknown zone concentration. A system of from 15 to 30 equations in
15 to 30 unknowns can be solved precisely by a computer. Practically speaking, when soil
is dug out of the ground and placed into a 500 nd jar, a few homogeneous zones are more
likely to exist than many discrete point sources.
However, practically speaking, 15 to 30 measurements of perhaps an hour each is very
time consuming. To alleviate this problem, one can make use of the fact that cylinders are
symmetrical with respect to rotation. That is, as the cylinder is rotated and counted at
discrete intervals, the function of full energy peak area, AREA(0), versus rotational angle
will be periodic with period 2n. For a homogeneous sample, a graph of AREA(0) vs. 9
would be a straight line, constant at one value. For sample containing a single point source,
the graph would be a sine function. Practically, most samples of soil dug up and put into
a jar will be somewhere in between but probably closer to homogeneous. Thus a slowly
varying curve is expected. Such a curve could be fit given eight points or so within one
period. Thus eight measurements could be made and from these points a curve could be fit


235
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M50.FOR *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M50.DAT
This program create file GE0M50.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 12.6
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32


59
Then, for a large target of uniform contamination concentration C pCi/gm of dry soil,
the detector response is modeled as
DR = C {GFi (E') + CGFi (E1)),
where
DR = the photopeak area as measured by a
detector, (counts/s),
C the uniformly distributed concentration
of contamination in the target,
(pCi/gm dry soil),
GFi = the calculated geometry factor for
point node i,
(counts/s) / (pCi/gm, of dry soil),
CGFi = the calculated Compton geometry factor
for point node i,
(counts/s) / (pCi/gm of dry soil).
This set of equations then constitutes a mathematical model of the fluorescent x-ray
production due to unscattered gammas and Compton scatter gammas. As stated before,
the desired result of the assay, the value of C, could theoretically be calculated using only
one measurement made in one geometry. In this work, multiple measurements are used to
achieve a more statistically significant answer. As discussed earlier, this model is verified
by actual measurements of targets in several known geometries. As will be discussed in the
results section, the model is in very good agreement with actual measurements.


Ill
TABLE 27
Measured Sample Linear Attenuation Characteristics
Sample
H (136fceF)
(cm-1)
fi(l22keV)
(cm-1)
n(98keV)
(cm-1)
p(93fceF)
(cm-1)
Sample 2
0.24400
0.25061
0.29150
0.30424
Sample 3
0.22009
0.23913
0.27889
0.29308
Sample 4
0.25104
0.28282
0.33511
0.35714
U1
0.26889
0.28471
0.32173
0.33400
Ula
0.26460
0.27996
0.31671
0.32886
TH1
0.27465
0.29197
0.32623
0.33854
THla
0.26534
0.28262
0.31613
0.32782
NJA
0.25367
0.30389
0.35591
0.38495
NJB
0.25818
0.30521
0.34727
0.37231
USA
0.23116
0.24787
0.28136
0.29318
USB
0.21953
0.23533
0.26760
0.27892
use
0.24741
0.26040
0.29039
0.30022
USD
0.24413
0.25768
0.28921
0.29921


304
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
****************************
* *
* NJBUXRF.FOR *
* *
* FILE PROGRAM *
* *
****************************
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, MB(20)
PKFIL = '[LAZO.DISS.NJB]NJBUXRF.DAT'
THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE NJB-TH IN
BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
IN GEOMETRY BA, AND A THROUGH I + 1 THROUGH 14, IN
GEOMETRY 60. SAMPLE NJA-U IS 2B90 PCI/GM TH-232 AND
WAS IRRADIATED BY C0-B7 SOURCES #3 AND #2.
LINE 101B CONSISTS OF THE NUMBER OF DATA POINTS, NF,
AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
EACH SPECTRA, COUNTING DATE, D4, MB, Y6, AND TIME,
HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
ERROR, ER(I).
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM XRF1JIJB.CNF; 1
D4(l) = 7.0
MS(1) = 7.0
YS(1) = 87.0
HR(1) = 11.0
MN(1) = 10.0
RH(1) = 1.0
RM(1) = 1B.0
RS(1) = 32.81
PH(1) = 63408.0
ER(1) = B19.0


LIST OF REFERENCES
1. Knoll, G. F., Radiation Detection and Measurement, John Wiley & Sons, New
York (1979).
2. Bureau of Radiological Health, U.S. Department of Health, Education, and
Welfare, Radiological Health Handbook, U.S. Government Printing Office,
Washington, D.C. (1970).
3. DOE Memorandum, U.S. Department of Energy Guidelines for Residual Ra
dioactive Material at Formerly Utilized Sites Remedial Action Program and
Remote Surplus Facilities Management Program Sites, Revision 2, Oak Ridge
Area Office, Oak Ridge, TN, March, 1987.
4. Woldseth, R., All You Ever Wanted to Know about X- Ray Energy Spectrom
etry, Kevex Corporation, Burlingame, CA (1973).
5. Prussin, S. G., Prospects for Near State-of-the-Art Analysis of Complex Semi
conductor Spectra in the Small Laboratory, Nuclear Instruments and Methods,
193 (1982), 121 128.
6. Evans, R. D., The Atomic Nucleus, McGraw-Hill Book Co., New York, 14th
printing (1972).
7. Scofield, J. II., Radiative Deca,y Rates of Vacancies in the K and L Shells,
Physical Review, 179 (1969), 9.
8. Gunnink, R., Niday, J. B., Siemens, P. D., UCRL-51577, Lawrence Livermore
Laboratory, Livermore, CA, April, 1974.
9. Salem, S. I., Lee, P. C., Experimental Widths of K and L X-Ray Lines, Atomic
Data and Nuclear Data Tables, 18 (1976), 233 214.
10. Wiesskopf, V., Wagner, E., Berechnug der naturlichen Linienbreite auf Grund
der Diracschen Lichttheorie, Z. Pliysik, 63 (1930), 54.
11. Gunnink, R., An Algorithm for Fitting Lorentzian-Broadened, K-Series X-Ray
Peaks of Heavy Elements, Nuclear Instruments and Methods, 143 (1977), 145
- 149.
12. Wilkinson, D. II., Breit-Wigners Viewed Through Gaussians, Nuclear Instru
ments and Methods, 95 (1971), 259 264.
13. Sasamoto, N., Koyama, K., Tanaka, S., An Analysis Method of Gamma-Ray
Pulse Height Distributions Obtained with a Ge(Li) Detector, Nuclear Instru
ments and Methods, 125 (1975), 507 523.
328


24
portion of the peak area lies beyond those limits and is accounted for by use of an equation
from Wilkinson. Wilkinsons equation determines the fractional area beyond a specified
distance from a peak centroid. It should be noted that the numerical integration is per
formed on the fitted peak function and not on the actual spectral data. Figure 3 shows a
typical x-ray spectrum in the vicinity of the Kai x-ray peak of Th.
Thus once the spectral data is fit to the proper peak shape and the four fitting parame
ters are known, the peak area can be determined. Since least squares fitting techniques also
lend themselves to convenient error analysis, the errors associated with the above fitting
parameters can be found and propagated to determine the error in the peak area.
A Fitting Background
As was previously mentioned, before a proper peak shape can be determined, the back
ground must be subtracted from the peak. In the case under consideration in this work both
the U and Th Kai peaks lie on top of a large, steeply sloping background (see Figure 3).
This background is the sum of the Compton continuum step function background, described
by Prussin and others* 1^, and gammas from the excitation source that backscatter in
the target and hit the detector.
The step function portion of the background is described in several well known peak
fitting programs as a complementary error function, erfc.*> 1 While details of the
functions used vary slightly from program to program, most use an equation of the form
SB (X) -Ax erfc ((x x) /a) ,
where
SB (X) = step background value at channel X,
A amplitude,


Counts


1195 VOLD(I) = V(I)
1200 NEXT I
1210 ocHisq = CHisq
1340 FOR I = 1 TO N
1350 qi(I.l) = DY(I)
1360 NEXT I
1370 GOSUB 4500
1380 FOR I = 1 TO H
1390 DT(I,1) = q3(I,l)
1400 NEXT I
1410 GOSUB 5000
1430 FOR I = 1 TO H
1440 V(I) = V(I) + DA(I)
1450 NEXT I
1455 PRINT
1460 FOR I = 1 TO HI
1465 PRINT S(;I;) = ;S(I) 2.5E+07
1470 NEXT I
1475 PRINT
1485 FOR I = 1 TO N
1490 F(I) = 0
1495 NEXT I
1505 HI = HI + 1
1510 GOTO 910
1900 FOR I = 1 TO H
1905 V(I) = VOLD(I)
1910 NEXT I
1920 S(Hi) = S(H1 1)
1930 CHISq = OCHISq
2000 GOSUB 8000
2003 LPRINT This is a POLYBK.BAS run"
2005 LPRINT for ;LB + RF; background points
2010 LPRINT
2015 LPRINT Gross Counts data from file ;BK$
2020 LPRINT
2050 X(l) = XT(LB + 1) XT(1)
2055 X(2) = XT(DP RB) XT(1)
2060 FOR I = 1 TO 2
2065 FOR J = 2 TO M
2070 SL(I) = SL(I) + (J 1) V(J) ((X(D) ** (J
2075 NEXT J
2077 SL(I) = SL(I) 5000
2080 NEXT I
2085 LPRINT Convergence in ;H1; iterations
2087 LPRINT
2090 LPRINT S = ;S(H1) 2.5E+07
2093 LPRINT
2095 LPRINT CHISq = ;CHISq 5000


63
Isotopic Identification
As mentioned earlier, the two isotopes which are of principle interest for this assay
technique are 7-238 and Th-232. In fact, these are the only two isotopes of U and Th
which can be seen at small concentrations using XRF. This is because XRF is dependent
upon the number of atoms present. In the cases of other U or Th isotopes, tremendously
high numbers of curies would have to be present before there would be enough atoms of
these isotopes to be seen by XRF. This is due to the very long half lives of E/-238 and Th-232
with respect to their other isotopes, since the number of curies is equal to the number of
atoms times the decay constant. Table 8 illustrates this point.
The sensitivity of the experimental setup tested in this work is approximately 50 pCi/gm
of T/i-232, which corresponds to 500 ppm. The system sensitivity then, in terms of number
of atoms required, is approximately 500 ppm. The table clearly shows that huge quantities,
in terms of pCi/gm, of all the isotopes except 7-238 and Th-232 would be required to reach
concentrations 500 ppm. Since these huge concentrations are rarely seen, and since one of
the objectives of this assay system is to achieve a low sensitivity in terms of pCi/gm, it can
be concluded that this XRF assay technique cannot be used for U and Th isotopes other
than 238 and 232 respectively.
TABLE 8
Isotopic Concentrations: PFM vs. pCi/gm
Isotope
Concentration
(ppm)
Concentration
(pCi/gm)
17-238
500
168.1
U-235
500
1.081E3
U- 234
500
3.125E6
Th-232
500
54.65
Th- 234
500
1.158E13
Th- 230
500
1.009E7
Th-228
500
4.098E11


230
C
C TARGET RADIAL, CIRCUMFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5I.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
WRITE(1,*) XT, YT, ZT
WRITEd,*) TH, TR
WRITE(1,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
END


CHAPTER III
RESULTS AND CONCLUSIONS
This research is broken into two broad sections, the first being the development of a
mathematical model of the soil assay technique, which has three sections as mentioned
earlier, and the second being an experimental verification of the technique. Chapter II
described the model and the experimental setup used to test the model. This chapter
describes the results of the experimentation and the conclusions which can be drawn from
those results.
Experimental Results
Assay Results
Thirteen samples were assayed using the previously described experimental and data
processing techniques. Four of the samples were artificial, clean soil spiked with either U or
Th oxides. Three samples were collected in Northern New Jersey during the summer of 1984
and analyzed such that their contamination concentrations were known. And six samples
were unknowns collected from other sites in 1986. The samples are described briefly here.
Seven homogeneous samples were prepared, either by spiking clean soil with pure U or
Th, or by mixing together of quantities of soil of known contamination concentrations. All
these samples were analyzed in dry, homogeneous states.
88


34
Thus for a monoenergetic gamma passing through an attenuating medium, the number of
gammas counted in the full energy peak can be described by the product of the above two
attenuations:
A(E) x AD x tj(E) x CT
A (E) = ^ 47rr2 xexp (~n(E)Pox),
where A(E) = full energy peak area at energy E.
Next, once the above measurement is made and A (E) is determined, the attenuating
object can be removed from between the source and detector and the measurement of
A(J5) repeated. This time, however, the new measurement, A' (£7), is described by Eq. 1
alone since no attenuating object is between the source and the detector. The ratio of
A (E) /A' (E) is then proportional to the objects transmission fraction at energy E:
A(E) A0 CT .
*W) = AAm x c¥ x p(-c(*)*').
where all terms are as defined previously.
The terms that differ from one measurement to the next are Aa (E) and CT. The source
emission rate, Aa (E), changes from measurement to measurement because of source decay.
If the measurements are made sequentially, this change is small, but it is always finite. The
count live time also varies from measurement to measurement due to pulse pileup. Pulse
pileup corrections are discussed in detail in a subsequent section. Since A0 (E) and CT vary
from measurement to measurement, they remain to be accounted for in the above ratio. All
other terms divide out.
Since all the terms in the above equation are measured except the transmission fraction
term, the transmission fraction can be calculated. If the thickness of the attenuating object
is known, then the attenuation coefficient can be determined.
TF(E) = exp (fi (E)px),


244
C
£ $$$£$$$$$$$$$$$$$$$$$
C *
C SAMPLEU1.F0R *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample Ul, a homogenous
C U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.7587
C
C Hubble Fit Parameters, Al, 61, ft Cl
C
Al = 1.14474
B1 = 0.66790
Cl =-0.42794
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.26889
US2 = 0.28471
US3 = 0.32173


DETERMINATION OF R ADIONUCLIDE CONCENTRATIONS
OF U AND Th IN UNPROCESSED SOIL SAMPLES
By
EDWARD NICHOLAS LAZO
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988

So as it turned out, just as I suspected from the start, this dissertation was a lot of
work. It took a lot of time, pulling me around its ins and outs for over five years. It took
lots of long days and lots of weeks without weekends. It took me from the valley of the
shadow of death, so to speak, to the heights of exhilaration and joy. It was among the most
important things in my life, and certainly was the primary thing for which I strove for all
that time. And throughout that time I had a fairly vague but very warm feeling as to why
I was doing this, and that feeling kept me going during this work.
So putting that vague feeling into words, this dissertation is dedicated to my parents, Dr.
Robert Martin Lazo and Rosemarie Lazo, who taught me by their example that learning is a
large part of what life is all about. And that the other biggest part of life is the satisfaction
that comes with trusting yourself enough to follow through on your dreams.
During this time I met the woman who is now my wife, I acquired two nephews, one
sister-in-law, and one brother-in-law, rounding out a very eventful time for the Lazo clan.
This dissertation is also dedicated to my family; my wife, my two brothers, my sister, their
families, and my two cats Max and Milli, who helped me all along the way. It is especially
dedicated to my wife, Corinne Ann Coughanowr, who has supported me, encouraged me,
helped me, put up with me, and continued to love me through the worst of times. To you
all, I love you.

ACKNOWLEDGEMENTS
This publication is based on work performed in the Laboratory Graduate Participation
Program under contract #DE-AC05760R00033 between the U.S. Department of Energy
and Oak Ridge Associated Universities.
In that the production of this dissertation has been a very difficult process which I
could not have finished without the help of numerous others, I would like to acknowledge
those who have given me so much invaluable assistance.
I would like to thank Corinne Ann Coughanowr, my wife, who provided me with excel
lent advice, guidance, and support throughout the project.
I would like to thank Dr. Genevieve S. Roessler, committee chair, University of Florida,
who provided technical and procedural guidance.
I would like to thank Dr. David Hintenlang, committee member, University of Florida,
who provided guidance which helped assure a quality final product.
I would like to thank Dr. Edward E. Carroll, committee member, University of Florida,
who taught me enough instrumental expertise to properly perform experiments.
I would like to thank Dr. Emmett Bolch, committee member, University of Florida,
who provided support in soil sample analysis.
1 would like to thank Dr. A. G. Hornsby, committee member, University of Florida,
who provided support for work in soil moisture content determination.
I would like to thank Dr. II. Van Rinsvelt, committee member, University of Florida,
who provided support in EDXRF analysis.
in

I would like to thank Dr. Barry Berven, committee member, Oak Ridge National
Laboratory (ORNL), who provided me with technical guidance and the managerial backing
necessary to ensure the purchase of the equipment necessary for this work.
I would like to thank Dr. Guven Yalcintas, committee member, ORNL, who provided
me with technical assistance throughout the work at ORNL.
I would like to thank Dr. Joel Davis, University of Tennessee at Chattanooga, who
provided invaluable assistance, guidance and technical expertise in every aspect of the work
performed at ORNL. Without Dr. Davis help and friendship this dissertation would have
required much more time and would not have been half as fun as it was.
I would like to thank Dr. Keith Eckerman, ORNL, who provided expert assistance in
development of the mathematical model, which is the core of this dissertation, and in just
about any other areas where I needed help. Again, without the assistance and friendship
of Dr. Eckerman this work would have been very much more tedious.
I would like to thank Dr. Jeff Ryman, ORNL, who provided assistance in the develop
ment of the transport mathematics used in the mathematical model.
I would like to thank Dr. George Keogh, ORNL, who provided assistance in developing
the analytical mathematics used in the computer model.
I would like to thank Debbie Roberts, ORNL, who performed several invaluable exper
iments for me after I had left ORNL, and who performed the soil assay against which I am
gaging my technique.
I wrould like to thank Dr. Rowena Chester, ORNL, who provided managerial backing
for the project and its purchases.
IV

I would like to thank Dr. Mark Mercier, Nuclear Data Incorporated, who helped
introduce me to peak shaping and provided invaluable assistance in the development of the
peak shaping programs used in this work.
I would like to thank John Hubble, National Bureau of Standards, who as the God of
all Cross Sections provided me with the latest cross- sectional data and plenty of friendly
encouragement and expert advice.
I would like to thank Dr. Raymond Gunnink, Lawrence Livermore National Laboratory,
who provided me with the peak shaping program GRPANL and helped me to understand
the theory behind the program.
I would like to thank Dr. Wayne Ruhter, Lawrence Livermore National Laboratory,
who nursed me through the intricacies of GRPANL and analyzed several of my peaks to
verify my program.
I would like to thank Isabell Harrity of Brookhaven National Laboratory who provided
invaluable assistance, all the way up to the last minute, in getting this document prepared
using T^X.
I would like to thank Dr. Eric Myers who also provided last minute advice as to how
to get Tj7¡Xto do its thing.
Finally, I would like to thank Oak Ridge Associated Universities who provided me with
a Laboratory Graduate Research Fellowship so that I could work at Oak Ridge National
Laboratory for two years and complete this project.
v

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
LIST OF TABLES xi
LIST OF FIGURES xiv
ABSTRACT xv
CHAPTERS
I INTRODUCTION 1
Soil Sample Assay for Radionuclide Content 1
Standards Method for Gamma Spectroscopic Assay of Soil Samples 4
Radionuclides of Interest 5
Process Sensitivity 6
Statement of Problem 10
X-Ray Fluorescent Analysis 11
Assay Technique 12
Literature Search 13
II MATERIALS AND METHODS 14
Peak Shaping 14
A Fitting Peak 15
A Fitting Background 24
vi

Soil Moisture Content and Attenuation Coefficients 32
Soil Attenuation Coefficient 33
Soil Moisture Content 37
System Model 37
Introduction 37
Technique Description 38
Mathematical Model 41
Compton Scatter Gamma Production of Fluorescent X Rays 51
Compton scatter gamma model 51
Mathematical model 52
Electron Density 60
Natural Production of Fluorescent X Rays 61
Isotopic Identification 63
Error Analysis 65
Introduction 65
Least Squares Peak Fitting 66
Covariance Matrix and Functional Error 69
Error Propagation 71
Linear Function Fitting 72
Experimental Procedure 74
Sample Counting 74
Data Analysis 86
III RESULTS AND CONCLUSIONS 88
Experimental Results 88
Assay Results 88
Peak Fitting Results 112
Conclusions 122
Recommended Future Work 122
Vll

APPENDICES
A EQUIPMENT AND SETUP 124
System Hardware 124
The ND-9900 MCA 124
The ADC 125
The HPGe Detector 125
XRF Excitation Source and Transmission Sources 125
The XRF Excitation Source Holder and Detector Shield 126
System Calibration 127
Mass Attenuation Coefficients 134
Pulse Pileup 142
Compton to Total Scatter Ratio in Soil 142
B UNSUCCESSFUL ANALYSIS TECHNIQUES 146
Sample Inhomogeneity Analysis 146
Reasons for Inhomogeneity Analysis Failure 149
Soil Moisture Content Analysis 158
Reason for Soil Moisture Content Analysis Failure 161
C COMPUTER PROGRAMS 163
Peak Shaping Programs 163
POLYBK.BAS 164
BKG.BAS 172
PEAKFIT.BAS 175
Geometry Factor Programs 184
DIST.FOR 185
IMAGE.FOR 190
COMPTON.FOR 196
ASSAY.FOR 205
via

Date File Programs
REV6.FOR .
COMDTA.FOR
XRFDTA.FOR
GEOM5A.FOR
GEOM5C.FOR
GEOM5E.FOR
GEOM5G.FOR
GEOM5I.FOR .
GEOM5K.FOR
GOEM5M.FOR
GE0M50.F0R
211
212
215
218
221
223
225
227
229
231
233
235
Sample Description Programs
SAMPLE2.FOR
SAMPLE3.FOR
SAMPLE4.FOR
SAMPLEU1.FOR . .
SAMPLEU1A.FOR . .
SAMPLET1I1.FOR . .
SAMPLETH1A.FOR .
SAMPLENJAU.FOR .
SAMPLENJATH.FOR .
SAMPLENJBU.FOR .
SAMPLENJBTH.FOR .
SAMPLEUSA.FOR . .
SAMPLEUSB.FOR . .
SAMPLEUSC.FOR . .
SAMPLEUSD.FOR . .
S2XRF.FOR
S3XRF.FOR
S4XRF.FOR
U1XRF.FOR
U1AXRF.FOR
TH1XRF.FOR
Till AXRF.FOR
NJAUXRF.FOR
NJATHXRF.FOR . .
NJBUXRF.FOR
NJBTHXRF.FOR . .
237
238
240
242
244
246
248
250
252
254
256
258
260
262
264
266
268
272
276
280
284
288
292
296
300
304
308
IX

USAXRF.FOR 312
USBXRF.FOR 316
USCXRF.FOR 320
USDXRF.FOR 324
LIST OF REFERENCES 328
BIOGRAPHICAL SKETCH 330

LIST OF TABLES
Table Page
1. Uranium 238 Decay Chain 7
2. Thorium 232 Decay Chain 9
3. Summary of DOE Residual Contamination Guidelines 11
4. U and Th K-Shell Absorption and Emission 32
5. Co-57 and Eu-155 Emission Energies and Yields 32
6. Co-57 and Eu-155 Physical Characteristics .32
7. Typical Soil Linear Attenuation Coefficients 36
8. Isotopic Concentrations: ppm vs. pCi/gm 63
9. Soil Assay Results for U and Th Contaminated Soil 93
10. Assay Sensitivity to the Number of Fitting Points Used 94
11. Measured vs. Fitted Detector Response for U1 95
12. Measured vs. Fitted Detector Response for Ula 96
13. Measured vs. Fitted Detector Response for NJA-U 97
14. Measured vs. Fitted Detector Response for NJB-U 98
15. Measured vs. Fitted Detector Response for USC 99
16. Measured vs. Fitted Detector Response for USD 100
17. Measured vs. Fitted Detector Response for Sample 2 101
18. Measured vs. Fitted Detector Response for Sample 3 102
19. Measured vs. Fitted Detector Response for Sample 4 103
20. Measured vs. Fitted Detector Response for Till 104
xi

21. Measured vs. Fitted Detector Response for Th-la 105
22. Measured vs. Fitted Detector Response for NJA-Th 106
23. Measured vs. Fitted Detector Response for NJB-Th 107
24. Measured vs. Fitted Detector Response for USA 108
25. Measured vs. Fitted Detector Response for USB 109
26. Sample Physical Characteristics 110
27. Measured Sample Linear Attenuation Characteristics Ill
28. Comparison of Kai Peak Areas as Determined by PEAKFIT and GRPANL 112
29. Peak Fit Results for Sample U1 113
30. Peak Fit Results for Sample Ula 113
31. Peak Fit Results for Sample NJA-U 114
32. Peak Fit Results for Sample NJB-U 114
33. Peak Fit Results for Sample USC 115
34. Peak Fit Results for Sample USD 115
35. Peak Fit Results for Sample 2 116
36. Peak Fit Results for Sample 3 117
37. Peak Fit Results for Sample 4 118
38. Peak Fit Results for Sample Till 119
39. Peak Fit Results for Sample Thla 119
40. Peak Fit Results for Sample NJA-Th 120
41. Peak Fit Results for Sample NJB-Th 120
42. Peak Fit Results for Sample USA 121
43. Peak Fit Results for Sample USB 121
A-l. Shield Material X-Ray Emission Energies 127
A-2. NBS Source, SRM 4275-B-7, Emission Rates 129
xii

A-3. NBS Source, SRM 4275-B-7, Physical Characteristics 129
A-4. System Calibration Parameters 133
A-5. Water Attenuation Coefficients, n(E)H70, Actual and Calculated Values . 140
A-6. Water Attenuation Coefficients, ft {E)Hi0,
Calculated Values vs. Target Distance from the Detector 141
A-7. Representative Soil Elemental Concentrations 144
A-8. Compton to Total Scatter Coefficients for Soil at 150 keV and 100 keV . 144
A-9. Average Compton to Total Scatter Ratio for Soil 145
B-l. Relative Sample Separation vs. Solution Matrix Condition 151
B-2. Target-Detector Distance vs. Measured Peak Area 154
xiii

LIST OF FIGURES
Figure Page
1. Typical Gamma Ray Spectral Peak and Background 16
2. Lorentzian X Ray as Seen Through the Gaussian Response of a Detector . .22
3. Typical Th Kai X-Ray Spectral Peak 25
4. Polynomial and Step Function X-Ray Peak Background 29
5. Source Target Detector Physical Geometry 39
6. Source Target Detector Spatial Geometry 49
7. Compton Scatter Spatial Geometry 53
8. Exploded View of Target Holder Assembly 76
9. Target in Place above Detector 78
10. Target in Place above Detector Showing Laser Alignment System 80
11. ND-9900 Multichannel Analyzer, ADC, Amplifier, and Detector Power Supply . 82
12. Typical XRF Kai Peak on MCA 84
B-l. Relative Sample Separation vs. Solution Matrix Condition 152
B-2. Target-Detector Distance vs. Measured Peak Area 155
xiv

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DETERMINATION OF RADIONUCLIDE CONCENTRATIONS
OF U AND Th IN UNPROCESSED SOIL SAMPLES
By
Edward Nicholas Lazo
December, 1988
Chairman: Genevieve S. Roessler
Major Department: Nuclear Engineering Sciences
Work with systems used to assay soil samples for U-238 and Th-232 indicated that the
need existed to more directly measure the concentrations of these radionuclides. An x-ray
fluorescent analysis system was developed here to directly measure the concentrations of
these radionuclides in bulk (125 gm), unprocessed (not dried and not ground to uniform
particle size), soil samples. Tliis technique improves on gamma spectroscopic analysis be
cause progeny equilibrium is not required, improves on neutron activation analysis because
bulk samples are assayed, and improves on both methods because standard soil samples are
not needed for system calibration.
The assay system developed equates a measured KaX x-ray peak area to a calculated
Geometry Factor (GF) times the unknown soil sample radionuclide concentration. From
this equation the radionuclide concentration is determined. Spectral data are generated
by irradiating the soil sample with Co-57 gammas to induce fluorescent x rays which are
measured using an intrinsic Ge detector. The Co-57 sources, the sample, and the detector
are oriented to optimize the production of fluorescent x rays. Transmission gamma rays
are then used to determine the sample linear attenuation coefficient at the KaX energy of
interest.
xv

Peak areas are determined by shaping spectral data to a Voigt Profile using an algorithm
from the peak shaping program GRPANL. The steeply sloping nature of the Compton
backscatter hump on which the Kal x-ray peaks rest necessitated the development of a
unique polynomial/erfc background function which is subtracted prior to peak shaping. The
GF of a sample is the calculated number of Kal x rays which would be counted in the full
energy spectral peak if the contamination concentration in the sample were one picoCurie
per gram. This calculated GF includes considerations of the sample linear attenuation
coefficient, fluorescence induced by unscattered source gammas, fluorescence induced by
singly scattered Compton gammas which account for approximately 15% of all production,
and natural fluorescence production.
Experimentally, thirteen test samples were analyzed using this method, gamma spectro
scopic analysis, and neutron activation analysis. Results compared very well with gamma
spectroscopic analysis. Neutron activation analysis of small portions of each sample did not
match well with the results of either of the other methods due to sample inhomogeneities.
xvi

CHAPTER I
INTRODUCTION
In returning to school to pursue a Ph.D. in health physics, I knew that I would have to
complete an original research project and I knew that I wanted my research to be practical in
nature. I wanted to pick some existing process or procedure and inject it with SCIENCE
to facilitate its operation and improve its accuracy and precision. I stumbled upon such a
process in need of science during a summer working experience in 1983. After obtaining
a fellowship to go to Oak Ridge National Laboratory to develop an improved process, I
discovered that such a process would have a much more general application than I had
originally thought.
Soil Sample Assay for Radionuclide Content
The summer position that sparked this dissertation involved health physics work for
the Formerly Utilized Sites Remedial Action Program, known as FUSRAP. Begun in 1974,
FUSRAP is a Department of Energy (DOE) project to clean up 26 contaminated sites
within the United States. Twenty-two of the sites were formerly used during the Manhattan
Engineers District (MED) project in World War II. The other four sites are civilian and
were added by Congress in 1976.
Sites range from a contaminated floor drain at Lawrence Berkeley Laboratory to a
contaminated Th ore processing plant and several surrounding residential properties in
northern New Jersey, containing approximately 100,000 cubic yards of contaminated soil.
1

2
In general, all sites are contaminated with varying levels of U, Th, their progeny, or some
mixture thereof. Sites typically include at least one building and the surrounding lands.
Clean up typically includes scrubbing and/or vacuuming of contaminated building surfaces
to remove contamination, destruction of facilities too contaminated or too uneconomical
to clean up, and digging up of contaminated soils. All contaminated wastes are deposited
in a controlled and monitored temporary storage area to await their ultimate disposition.
Wastes are generally low level and thus their ultimate disposition will be in the low level
waste repository of the state or compact area from which the wastes came.
One portion of this process that is of scientific interest and could stand some improve
ment is the assay of soils to determine whether or not they are contaminated. During
the course of site decontamination, many soil samples are taken. Preliminary soil samples
are taken to determine the approximate extent and concentration of radionuclides present.
Periodic soil samples are taken during soil excavation to determine whether preliminary
estimates were correct and to locate previously unidentified radionuclide deposits. Final
soil samples are taken to confirm that all contaminated soil has been removed. With so
many samples being collected, quick and accurate assay becomes important.
All soil samples are assayed twice: once when they arrive at the lab as wret, inhomo
geneous soil, and once after they have been processed. The standards comparison method
for gannna spectroscopic analysis is used to assay the soil samples. This method will be
discussed in detail later. Soil sample processing involves drying the soil in an oven, grinding
the soil into a powder that will fit through a standard 200 mesh per square inch sieve, and
stirring the powdered soil into a relatively homogeneous mixture. Soil sample processing
adds approximately 2 days to sample analysis time. Samples are analyzed twice because,
while the first analysis is fast enough to meet stingy construction schedules, it is not ac
curate enough to meet quality control guidelines. When a fudge factor is applied, the

3
fudge factor being the average ratio of sample analysis results for processed vs. unprocessed
samples, the results of the analysis of unprocessed soil samples are accurate enough to use
and to guide further work. Even with the fudge factor, analysis of unprocessed soil samples
is not sufficiently accurate to prove, for example, that an area is free of contamination and
needs no further work. The second analysis, of the processed soil, is accurate but takes too
long to meet construction schedules.
The process in need of development, then, was an assay technique that was accurate but
could be performed on unprocessed soil samples. This would eliminate the time-consuming
step of sample drying and grinding.
Upon selecting this topic, I received a Laboratory Graduate Participation Fellowship
from Oak Ridge Associated Universities (ORAU) to pursue the research at Oak Ridge Na
tional Laboratory (ORNL). The Radiological Survey Activities section (RASA), currently
called the Measurement Applications and Development (MAD) section, of the Health and
Safety Research Division (HASRD) sponsored this work because it has been in the business
of performing radiological assessment surveys of various contaminated government sites
around the country. At the MAD lab at ORNL soil samples are processed in the same
method as used hy the FUSRAP analysis lab, and the standards comparison method of
gamma spectroscopic analysis is used to determine radionuclide concentrations. As with
the FUSRAP project, soil sample processing is a time-consuming endeavor.
Further research indicated that the processing of soil samples prior to analysis was
standard procedure at most soil assay labs. Thus a procedure that eliminated the processing
step would be universally useful.
My research also indicated that there was a second drawback to standard gamma spec
troscopic techniques. A description of the standards comparison method of gamma spec
troscopic analysis will help provide a better understanding of this problem.

4
Standards Method for Gamma Spectroscopic Assay of Soil Samples
The standards method for gamma spectroscopic assay of soil or any other sort of ra
dioactive sample is a simple process. A sample of unknown radionuclide content is placed
in a fixed geometry, relative to a detector, and a spectrum is collected for a fixed length
of time. A sample containing a known amount of radionuclide is then placed in the same
geometry as that used to count the unknown sample, and a second spectrum is collected.
By comparing these two spectra, the identity and amount of radionuclide in the unknown
sample can be determined.
Qualitatively, the presence of a radionuclide in a sample is determined by the presence
of spectral peaks at energies characteristic of that radionuclide. For example, Co-57 emits
gamma rays at 136 keV and 122 keV in a known ratio. If spectral peaks of these energies
and of proper relative intensity are present in a spectrum, then Co-57 is probably present
in the unknown sample.
Quantitatively, the concentration of a radionuclide in a sample is determined by com
paring the area of a spectral peak generated by an unknown sample to the area of a spectral
peak generated by a sample of known concentration. For example, a sample known to con
tain 100 pCi of Co-57 is counted in a standard geometry relative to a detector. After one
hour of counting this known sample, the area beneath the 136 keV peak is 10,600 counts
and the area beneath the 122 keV peak is 85,500 counts. Next, an unknown sample is
counted, in the same geometry in which the known sample was counted, and after one
hour of counting the areas beneath the 136 keV and 122 keV peaks are 21,200 counts and
171,000 counts, respectively. The unknown sample resulted in peak areas twice those of the
known sample and thus the unknown contains 200 pCi of Co-57. Further details of gamma
spectroscopy can be fomid in Knoll.^

5
The drawback to this technique is that it relies upon the known sample, referred to as
the standard, being physically similar to each unknown sample counted. This is because the
density, moisture content, consistency, and elemental makeup of a sample will determine
that samples radiation attenuation properties. A homogeneous sample of given properties
containing 100 pCi of a radionuclide will attenuate a given fraction of the gammas emitted by
that radionuclide. A second homogeneous sample, of different properties but also containing
100 pCi of the same radionuclide, will attenuate a different fraction of the gammas emitted
by that radionuclide. Therefore two homogeneous samples containing the same amount of
a radionuclide can yield spectra with characteristic gamma energy peaks of different areas.
This makes it very important that the standards chosen match the unknowns as closely as
possible.
Unfortunately, the standards used for analysis are often significantly different in atten
uation properties from the unknown samples. Dry, ground, and homogeneous standards are
obviously different from unprocessed, wet, inhomogeneous unknown samples. And although
standards can be fairly similar to processed unknown samples, mineral content differences
do residt in differences in attenuation properties. Thus the process to be developed should
take the attenuation properties of each unknown sample into account in order to properly
determine radionuclide content.
Radionuclides of Interest
Two elements that are of particular interest to both FUSRAP and MAD are U and
Th. These are common contaminants at sites around the country. Many of the MED sites
of FUSRAP became contaminated while receiving, processing, or shipping U to be used
in the fabrication of the first atomic bomb. The Grand Junction, Colorado, site that the
MAD program is surveying is contaminated with mill tailings from U mining operations.

6
Two of the civilian FUSRAP sites were chemical plants involved in processing Th from ore.
Although less prevalent, Th is also found in mill tailings and, thus, is of interest to the
MAD program.
The main reason to develop an assay technique specifically designed to detect U and
Th is that U-238 and Th-232, the most common radioisotopes of U and Th respectively,
emit only low energy and low yield gamma rays. In order to perform gamma spectroscopic
analysis of these radioisotopes, gamma rays emitted by progeny must be used, equilibrium
of the parent with the progeny must be assumed, and concentrations must be inferred from
the presence of the progeny. Table 1 lists the 7-238 decay chain and the radiations emitted
by each member. Table 2 shows equivalent information for the Th-232 decay chain.
Unfortunately, U and Th require long periods to reach equilibrium, and equilibrium
may not have been reached in the soil samples to be analyzed. Also, each decay product
has its own rate of dissolution in ground water. Thus as contamination waits in the soil to
be sampled, varying amounts of U, Th, and their progeny dissolve and diffuse. This also
confuses the equilibrium situation. Since equilibrium can not always be correctly assumed,
the assay technique to be developed must also directly measure U and Th and should not
rely on measurements of progeny.
Process Sensitivity
Since the process to be developed is to be practical in nature, some guidelines as to
sensitivity and accuracy should be followed. Since process application is soil assay for
contaminated sites undergoing decontamination, it is sensible to use guidelines established
by DOE for releasing sites for unrestricted public use.

7
TABLE l2
U-238 Decay Chain
Radionuclide
Half-Life
I Me
1
Alpha
ijor Radiation Ene
MeV) and Intensii
Beta
rgies |
ies |
Gamma
U- 238
4.59E9 a
4.15 (25%)
4.20 (75%)
"
"
T/i-234
24.1 d
0.103 (21%)
0.063 (3.5%)+
Pa-234
(Branches)
1.17 min
-
2.29 (98%)
1.75 (12%)
0.765 (0.30%)
1.001 (0.60%)+
Pa-234
(.13%)
6.75 h

0.53 (66%)
1.13 (13%)
0.100 (50%)
0.70 (24%)
0.90 (70%)
P-234
(99.8%)
2.47E5 a
4.72 (28%)
4.77 (72%)
-
0.053 (0.2%)
T/i-230
8.0E4 a
4.62 (24%)
4.68 (76%)
-
0.068 (0.6%)
0.142 (0.07%)
Pa-226
1.602E3 a
4.60 (6%)
4.78 (95%)
-
0.186 (4%)
Rn-222
3.823 d
5.49 (100%)
-
0.510 (0.07%)
Po-218
(Branches)
3.05 min
6.00 (100%)
0.33 (0.019%)
-
P6-214
(99.98%)
26.8 min

0.65 (50%)
0.71 (40%)
0.98 (6%)
0.295 (19%)
0.352 (36%)
Af-218
(.02%)
2.0 s
6.65 (6%)
6.70 (94%)
-
-
Pz-214
19.7 min
5.45 (.012%)
1.0 (23%)
0.609(47%)
(Branches)
5.51 (.008%)
1.51(40%)
3.26(91%)
1.120 (17%)
1.764 (17%)

8
TABLE 1 (continued)
; 1
| Ma)or Radiation Energies |
1 0
VIeV) and Intensities |
Radionuclide
Half-Life
Alpha
Beta
Gamma
Po-214
164.0 us
7.69 (100%)
-
0.799 (0.014%)
(99.98%)
77-210
1.3 min
-
1.3 (25%)
0.296 (80%)
(.02%)
1.9 (56%)
0.795 (100%)
2.3 (19%)
1.31 (21%)
P6-210
21.0 a
3.72 (2E-6%)
0.016(85%)
0.047 (4%)
0.061(15%)
P-210
5.10 d
4.65 (7E-5%)
1.161 (100%)
-
(Branches)
4.69 (5E-5%)
Po- 210
138.4 d
5.305 (100%)
-
0.803(0.0011%)
(100%)
-
77-206
4.19 min
-
1.571 (100%)
-
(.00013%)
P6-206
Stable
NOTES + Indicates those gamma rays that are commonly used to identify U-238. Equilibrium
must be assumed.

9
TABLE 22
Th-323 Decay Chain
1
Radionuclide
Half-Life
| Ma
1 (
Alpha
jor Radiation Ein
VIeV) and Intensi
Beta
;rgies |
;ies |
Gamma
Th-323
1.41E10 a
3.95 (24%)
4.01 (76%)
-
Ra- 228
6.7 a
-
0.055 (100%)
-
Ac-228
6.13 h
-
1.18 (35%)
1.75 (12%)
2.09 (12%)
0.34 (15%)+
0.908 (25%)+
0.96 (20%)+
Th- 228
1.91 a
5.34 (28%)
5.43 (71%)
-
0.084 (1.6%)
0.214 (0.3%)
Pa-224
3.64 d
5.45 (6%)
5.68 (94%)
-
0.241 (3.7%)
Rn-220
55.0 s
6.29 (100%)
-
0.55 (0.07%)
Po- 216
.15 s
6.78 (100%)
-
-
Pb-2L2
10.65 h
-
0.346 (81%)
0.586 (14%)
0.239 (47%)
0.300 (3.3%)
Bi-212
(Branches)
60.6 min
6.05 (25%)
6.09 (10%)
1.55 (5%)
2.26 (55%)
0.040 (2%)
0.727 (7%)+
1.620 (1.8%)
Po-212
(64%)
304.0 ns
8.78 (100%)
-
-
77-208
(36%)
P6-210
3.10 min
Stable
1.28 (25%)
1.52 (21%)
1.80 (50%)
0.511 (23%)
0.583 (86%)+
0.860 (12%)
2.614 (100%)+
NOTES: + Indicates those gamma rays that are commonly used to identify Th-232. Equilibrium
must be assumed.

10
The decontamination criteria established by DOE are based on the Homestead Farmer
scenario. This scenario assumes that a farmer will homestead on contaminated lands, will
grow all his/her own food on the land, will raise and graze his/her own livestock on the
land, will drink water from wells on the land, and eat fish from a stream running through
the land. Limiting radionuclide concentrations were calculated such that the homestead
farmer would not build up radionuclide body burdens greater than those suggested by the
National Council on Radiation Protection and Measurements (NCRP). Table 3 lists relevant
guidelines. Soil radionuclide content limitations are in units of pCi/gm of dry soil.
Statement of Problem
The objective of this research is to develop a fast and economical technique for lab
oratory assay of U and Th in an inhomogeneous sample consisting of moist, chunky soil
compressed into a plastic, cylindrical jar. The product of this assay should be the isotopic
concentrations of 7-238, {7-235, Th-232, and Th-230 in pCi per gram of dry soil averaged
over the entire sample. To accomplish tins assay the technique must determine the dry
soil weight, must be sensitive to U and Th isotopic concentrations from approximately 100
pCi/gm to 2000 pCi/gm, and must account for the effects of sample inhomogeneity.
Current teclmiques for the non-destructive assay of U in soil samples include neutron
activation analysis and gamma spectroscopy. Gamma spectroscopy and its limitations have
been discussed previously. Neutron activation depends upon the availability of a large
neutron source. Since it is advantageous to develop a process that is as simple, portable,
and as inexpensive as possible, neutron activation can be ruled out. The technique chosen for
this application is x-ray fluorescent analysis (XRF). Details of the technique are described
in the following sections.

11
TABLE 3 (a, b, c) 3
Summary of DOE Residual Contamination Guidelines
Soil Guidelines (Maximum limits for Unrestricted Use)
Radionuclide
Soil Concentration (pCi/g) above Background
Ra- 226
- 5 pCi/g averaged over the first 15 cm of
Ra- 228
soil below the surface.
T/i-232
- 15 pCi/g when averaged over any 15 cm
Th- 230
thick soil layer below the surface layer.
Other
-Soil guidelines will be calculated on a
radionuclides
site specific basis using the DOE manual
developed for this use.
a: These guidelines take into account ingrowth of Ra-226 from Th-230, and
Ra-228 from Th-232 and assume secular equilibrium. If either Th-230 and
JRa-226, or T/i-232 and Ra-228 are both present, not in secular equilibrium,
the guidelines apply to the higher concentration. If other mixtures of ra
dionuclides occur, the concentrations of individual radionuclides shall be
reduced so that the dose for the mixtures will not exceed the basic dose
limit.
b: These guidelines represent unrestricted-use residual concentrations above
background, averaged across any 15 cm thick layer to any depth and over
any contiguous 100m2 surface area.
c: If the average concentration in any surface or below surface area less than
or equal to 25m2 exceeds the authorized limit or guideline by a factor of
\/l0 0/A where A is the area of the elevated region in square meters, limits
for HOT SPOTS shall be applicable. These hot spot limits depend on the
extent of the elevated local concentrations and are given in the supplement.
In addition, every reasonable effort shall be made to remove any source of
radionuclide that exceeds 30 times the appropriate soil limit irrespective of
the average concentration in the soil.
X-Ray Fluorescent Analysis (XRF)
Atoms can be ionized, i.e., have one or more electrons removed, via several processes. In
the case of x-ray fluorescence, gamma or x rays incident on an atom undergo photoelectric
reactions resulting in the ionization of the atom. The ionized atom then de-excites via the
emission of x rays. An upper shell electron falls into the hole vacated by the ionized electron
and x rays, equal in energy to the difference in shell energies, are emitted. Since elements
have characteristic atomic energy levels, the emitted x rays are characteristic of the element

12
and can be used to identify the element. The intensity of the emitted x rays is proportional
to the concentration of the element in the x-ray emitting material. This technique can thus
be said to directly determine U and Th concentrations in soil samples. For a more detailed
description of x-ray fluorescent spectrometry see Woldseth.^
Assay Technique
In overview, the assay process is simple. Each sample is irradiated to induce fluorescence
and the emitted fluorescent x rays are detected by a hyper-pure intrinsic Ge planar detector.
The areas under the Kai x-ray peaks from U and Th are determined by a spectral analysis
system. The Kal peak was chosen because the K-shell lines are highest in energy, thus
minimizing attenuation effects, and the Kal line is the most predominant K-shell line. The
areas of these peaks are used to determine U and Th concentrations. This determination
involves two steps; the determination of sample moisture content and attenuation properties,
and the handling of sample inhomogeneity. The isotopic fractions are determined by looking
at the relative intensities of gamma rays from U and Th daughters. The details of these
processes are discussed in subsequent sections.
This research is divided into two broad sections; development of a mathematical model
of the assay system, and experimental verification of that model. The model is divided into
three sections. The first section involves the development of a peak shaping program to
accurately deterndne the areas of the Kal x-ray peaks of U and Th. The second section
involves the determination of the sample moisture content and attenuation properties. This
is done by measuring how gamma rays are transmitted through the sample. The third
section uses the peak areas, determined in section one, and the soil moisture content and
attenuation coefficients, determined in section two, to mathematically model the sample so

13
that an accurate assay can be performed. In the third section the final result of the analysis,
the radionuclide concentrations of U and Th in the soil sample, is calculated.
Literature Search
In order to learn more about existing techniques of gamma spectroscopic analysis, x-
ray fluorescent analysis, peak shaping techniques, soil moisture determination, and assay of
inhomogeneous samples, a computer literature search was performed. The central research
library at ORNL performed the search, looking through Chemical Abstracts, Physical Ab
stracts, and the DOE Energy Data Base. Many references which discussed these topics
were located, however no references were found which discussed data analysis techniques
similar to that presented in this work were located.

CHAPTER II
METHODS AND MATERIALS
This chapter describes the theoretical basis for the U and Th assay technique. The
theory is divided into three sections: peak shaping, soil moisture content and attenuation
properties, and system modeling. Following this theory are descriptions of the error analysis
and the experimental procedure used in this work.
Peak Shaping
In order to determine the physical properties physical measurements must be made. In
the case of this soil sample assay technique, the induced fluorescent x rays emitted by the
target are the physical quality measured. The measurement takes the form of an energy
spectrum. The number of x rays emitted by the sample is proportional to the concentration
of U and/or Th in the sample. The areas of the Kal x-ray peaks are the number of x
rays that hit the detector and are counted in the full energy peak. These areas, then, are
proportional to the concentrations of U and/or Th in the soil sample. The details of the
proportionality are discussed in subsequent sections. This section describes the method
used to determine peak areas.
The fitting of spectral data to mathematical functions is known as peak shaping or
peak fitting. As stated above, the motivation for fitting peaks is to accurately determine
the peak area which is proportional, in this case, to the concentration of U and/or Th in a
soil sample. The art of peak fitting has been steadily perfected over the years, particularly
14

15
with the advent of high resolution semiconductor detectors. A good overview of current
theory and of the variety of functions available to fit peaks and backgrounds is provided by
Prussin.^ As an introduction to the theory of peak shaping he states that:
As is well known, the shape of a photopeak from monoenergetic photons
in spectra taken with semiconductor detectors is closely approximated by
a Gaussian with more or less severe tailing below the centroid. The peak
is joined smoothly to a lower-energy continuum of small curvature until it
meets the relatively sharp Compton edge. This continuum, which is pro
duced mainly by the loss of some of the energy of photoelectrons from the
sensitive volume of the detector, leads to the appearance of a step-like dis
tribution upon which the main intensity is superimposed. Under conditions
of low input rate, short counting times with stable electronics and negligi
ble background at higher energies, the high-energy edge is indeed found to
be nearly Gaussian. The low energy edge begins to deviate from Gaussian
form at fractions of the peak maximum in the range of .5 to .01 depending
upon the detector type, its quality and its history. While Gaussian shape
results from statistical spread due to fluctuations in electron-hole pairs
produced in the stopping process and random noise from the amplifying
electronics, the low energy tailing represents pulse-lieight degradation from
a number of phenomena including charge trapping and recombination, en
ergy loss of primary and secondary electrons in the insensitive volume of
the detector or by bremsstralilung.
Figure 1 shows a typical spectral gamma peak and its component parts; the Gaussian
peak and step function background. Typically, peak fitting programs will fit the background
to some function, subtract the background from beneath the peak, and fit the remaining
data to some peak function. The following sections will discuss the peak and background
fitting functions used in this work.
A Fitting Peak
Peak shaping and peak area determination are commonly done by gamma spectroscopy
systems in an efficient manner. Such systems usually contain long computer programs to
locate all spectral peaks, to determine and subtract the baselines from beneath those peaks,
and to determine peak areas by summing of channel counts or by least squares fitting to a
Gaussian shape.

FIGURE 1
Typical Gamma Ray Spectral Peak and Background

Counts

18
The x-ray fluorescent analysis system described in this paper uses its own peak shaping
program for the following reasons. First, since only the Kai peaks from U and Th will
be used, only two peaks at known energies, need to be determined. It is not necessary
to search the entire spectrum to shape each peak and to calculate the area of all possible
peaks since only the Kai peaks are of interest. This eliminates much of the computational
software necessary for large spectral analysis programs, thus decreasing processing time.
Since most processing programs are quite fast, this is not the most important reason to
have a separate peak shaping program. The second and more important reason is that
most spectral analysis programs perform Gaussian peak shaping, which is inappropriate for
x rays. This results in inaccurate area determination.
The spectral response of a detector system can be mathematically described as a con
volution of the detector systems inherent response function and the energy distribution of
the monoenergetic incident radiation (Knoll^ pp 732-739).
N{H) = f R{H,E)xS{E)dE
J OO
where
N (H) = the differential pulse height spectrum,
R(H,E) = the differential probability that a pulse of
amplitude II originates from a photon of
energy within dE of E,
5 (E) = the photon energy distribution.
Detector system response functions are typically Gaussian (Knoll^ pp 434-440). Mo
noenergetic gamma rays emitted by the de-excitation of a nucleus in an excited state are
actually not monoenergetic but are distributed in energy about a central value. This distri
bution is described by the function S(E). The width of this energy distribution is inversely

19
proportional to the mean lifetime of the excited nuclear state (Evans pp 397-403). This is
directly attributable to the Heisenberg uncertainty principle such that (Evans pp 397-403)
T {eV) = .66E 15 (eV s) /tm (a)
where
r = energy distribution width (eV),
.66E 15(eFs) = Plank's Constant/27T,
tm = mean lifetime of excited state.
NOTE: half life (tl/2) = fm/ln(2)
Therefore, for a gamma ray to have an energy distribution width greater than 1 eV,
its mean life would have to be less than IE-15 s. Since most gamma rays are emitted
from radionuclides with half lives much longer than that, the width of gamma ray energy
distributions is zero for practical purposes. Since the width of the energy distribution for
gamma rays is so small, S(E) is effectively a delta function. The convolution of a delta
function energy distribution and a Gaussian distribution detector response results in a
Gaussian shape spectral peak for gamma rays (Knoll* pp 434-440).
X rays, however, are generated by electrons falling from upper to lower orbitals, as
described in a previous section. These transitions take place very rapidly, and therefore the
emitted x rays have fairly large widths which increase with increasing energy.^ Experimen
tal measurements have shown Kai x rays to have widths of from 1 eV for Ca to 103 eV for
E7. X-ray energy distributions must therefore be described by a Lorentzian distribution*
and an x-ray spectral peak must therefore he described by the convolution of a Gaussian
detector response function and a Lorentzian x-ray energy distribution.** Mathematically,
this convolution is written as
/OQ
G{E')x L{E E')dE',

20
where
G (E') = Gaussian distribution function,
= A exp (-.5 {{E' E0) /a)2) ,
E' = convolution dummy variable,
E = peak centToid,
<7 = Gaussian peak standard deviation,
A Gaussian peak height constant, and
L(E E') = Lorentzian distribution function,
= A'/ ((£ E' E0f + .25r2) ,
E = energy,
E' convolution dummy variable,
E0 = peak centroid,
T = Lorentzian peak full peak width at half
the maximum peak height,
A = Lorentzian peak height constant.
The resulting convolution, C (E), can be solved numerically in the following manner.
C (E) = A" (exp (-X2) x (Cl 4- C2 x X2 + C3 X (1 2X2)))
+ A" x C4 X/3(X),
where
X2 = (112){{E-E0)I*)\
C\ = \- (I/v^tt) (r/cr),
C2 = (1/2V5r) (r/
21
C3= (1/8) (r/<7)2,
C4 (2/ttv^) (r/ B(X)= (-exp (-X2)) £(/(*)),
\ ^ ((exp(-n2/4))/n2)
Zl / W = Z Ti X (1 cosh (nX)) and
n=l
A" = new peak height constant.
This is a numerical equation in four unknowns; E, T, cr, and A". This equation
lends itself to weighted least squares fitting to the spectral data. The result of this fitting
will be values for the above four unknowns and their associated errors. Figure 2 shows
the Lorentzian distribution of the incident x rays, the Gaussian response function of the
detector system, and the resulting convoluted distribution that is the spectral x-ray peak.
It should be remembered that the objective of this exercise is to determine number of x
rays that hit the detector. As will be explained further in the section describing data analysis
and the section describing detector system calibration, the measured number of x rays will
be compared to the calculated number of x rays to determine concentrations of U and Th
in the soil. By properly calibrating the detector system, the area under the convoluted peak
will be proportional to the number of x rays that hit the detector. Determination of the
area of the convoluted peak is thus the desired end result of this peak analysis. Therefore it
should be noted that the Lorentzian x-ray distribution and the Gaussian detector response
function, shown in Figure 2, are for reference only and will not actually be seen in the
spectrum or have their areas calculated.
With the peak parameters determined, the peak area can be determined. Since the
convolution function is rather complex, the peak area is determined by numerical integra
tion. The peak shaping program defines the spectral peak as having a beginning channel
and an ending channel and performs the integration between these limits. Oidy a small

FIGURE 2
Lorentzian X Ray as Seen Through
the Gaussian Response of a Detector

Counts

24
portion of the peak area lies beyond those limits and is accounted for by use of an equation
from Wilkinson. Wilkinsons equation determines the fractional area beyond a specified
distance from a peak centroid. It should be noted that the numerical integration is per
formed on the fitted peak function and not on the actual spectral data. Figure 3 shows a
typical x-ray spectrum in the vicinity of the Kai x-ray peak of Th.
Thus once the spectral data is fit to the proper peak shape and the four fitting parame
ters are known, the peak area can be determined. Since least squares fitting techniques also
lend themselves to convenient error analysis, the errors associated with the above fitting
parameters can be found and propagated to determine the error in the peak area.
A Fitting Background
As was previously mentioned, before a proper peak shape can be determined, the back
ground must be subtracted from the peak. In the case under consideration in this work both
the U and Th Kai peaks lie on top of a large, steeply sloping background (see Figure 3).
This background is the sum of the Compton continuum step function background, described
by Prussin and others* 1^, and gammas from the excitation source that backscatter in
the target and hit the detector.
The step function portion of the background is described in several well known peak
fitting programs as a complementary error function, erfc.*> 1 While details of the
functions used vary slightly from program to program, most use an equation of the form
SB (X) -Ax erfc ((x x) /a) ,
where
SB (X) = step background value at channel X,
A amplitude,

FIGURE 3
Typical Th KaX Spectral Peak

Counts

27
X = peak centroid, and
a = detector response function width for
peak centered at X.
The numeric approximation to this function used in this work in HYPERMET^ and
in GRPANL15 is
where
SB{ X,)
BL + (BH BL) x
j=1 i=1
5
SB (X{) = step background value at channel X,
BL = average background value on the low energy
side of the peak,
BH = average background value on the high energy
side of the peak,
y Y (Xi) = the sum of the gross channel counts from the
1 first peak channel to channel X, and
N
y Y (Xi) = the sum of the gross channel counts from the
3 first peak channel to the last peak channel.
The above algorithm assumes that the background to either side of the peak is relatively
flat. This will not necessarily be the case for all spectra and is certainly not the case for
this work.
GRPANL, in addition to using the above step function, allows the use of two different
background slopes, one for each side of the peak. The average slope of the background under
the peak is then the average of the background slopes from either side of the peak. The
change in background attributable to this slope is then equal to the vertical change of a
line, having the average background slope, over a horizontal change equal to the number

28
of channels in the peak. The actual vertical change in the background is equal to the
difference between the number of counts in the last low energy side background channel
and the number of counts in the first high energy side background channel. Then the
vertical background change due to the step function is equal to the actual vertical change
minus the vertical change due to the slope. The use of this rationale results in a step
function background whose slope at either side of the peak fits smoothly with the actual
background slopes.
Unfortunately, the background slope of the spectrum under consideration in this work
does not change uniformly from the low energy side of the peak to the high energy side.
Rather, the slope on the low energy side is very steep, changes very quickly, and then
approaches the slope on the high energy side. The average background slope, as described
above, will therefore be too steep and the vertical change attributable to the slope will exceed
the actual vertical change. Under these circumstances, GRPANL will fit the background to
a smoothly changing slope without a step change.
Wliile this might seem contrary to theory, Baba et al.^ state, for large peaks in a
multiple! group or even for smaller single peaks, that the peak areas and centroids are
determined with sufficient accuracy by using a properly fit straight line, curved, or step
function background. As mentioned earlier, peak fitting is as much an art as a defined
science.
Bearing all of the above in mind, the approach used in this work was to use both the
step function and the sloping background. The background is easily fit to a third or fourth
order polynomial. In this work then, the vertical change in background beneath the peak is
attributed half to the polynomial and half to the step function. The resulting background is
shown in Figure 4. Source listings of POLYBK.FT and BKG, the codes used to accomplish
the background determination and subtraction, are supplied in Appendix C.

FIGURE 4
Polynomial and Step Function X-Ray Peak Background

Counts

31
In that the steeply sloping nature of this background is somewhat unusual in spec
troscopy, some explanation as to its origin is warranted. The excitation source, Co-57,
which emits gammas at 122 keV and 136 keV, was chosen because of the proximity of its
gamma energies to the K-shell absorption energy. At these energies, U and Th have liigh
cross sections for photoelectric reactions with K-shell electrons. Table 4 shows the absorp
tion and emission energies for U and Th. Table 5 shows the emission energies and yields
for Co-57. Table 5 also lists emission energies and gamma yields for Eu-155. The latter
radionuclide is used for transmission measurements which are explained in a subsequent
section. Table 6 shows relevant source physical properties.
Unfortunately, when 122 keV ganunas Compton scatter at approximately 180 degrees,
the resulting gamma is 83 keV. This is called a backscatter gamma. The backscatter gamma
from an incident 136 keV gamma is 89 keV. These backscatter gammas are at inconvenient
energies because they form the majority of the background beneath the U and Th Kai x
ray, thus somewhat obscuring the peaks. And the shape of the background depends upon
the geometry of the scattering soil sample. That is, the size and relative position of the
source, soil sample, and detector determine what scatter angles, and thus what energies,
will be seen as backscatter gammas. Thus the shape of the background does not lend itself
to simple theoretical treatment and a third or fourth order polynomial fit, as mentioned
earlier, is necessary. The peak areas calculated by tins technique are used in subsequent
analyses to determine the soil sample concentrations of U and Th.

32
TABLE 4
U anc
Th K-Sliell Absorption and Emi
17
3 sionJ'
Element
K-Sliell
Absorption
Ka i
Emission
Ka2
Emission
U
115.591 keV
98.434 keV
94.654 keV
Th
109.63 keV
93.350 keV
89.957 keV
TABLE 5
Co-57 and Eu-155 Emission Energies and Yields
Element
Emission Energy
Gamma Yield
Backscatter
Energy
Co 57
122.063 keV
.8559
82.6 keY
136.476 keV
.1061
89.0 keV
Eu 155
105.308 keV
.207 *
74.6 keV
86.545 keV
.309 *
64.6 keV
*: The gamma yields for Eu 155 are not known to the same precision as
those of Co57. Europium-155 sources, therefore, are described by gamma
emission rates, Activity (Ci) X Yield (gammas/s). The listed yields are for
estimation purposes only.
TABLE 6
Co- 57 and Eu-155 Physical C
aracteristics
Co-57
Eu-155
Activity
5 mCi 15%
2 mCi 15%
(1 October 1985)
(1 April 1986)
Half Life
271.7 d
1741 d
Soil Moisture Content and Attenuation Coefficients
In order to properly analyze spectral data, the soil attenuation coefficient as a function
of energy must be known. The details of their use are described in a subsequent section.
Since the goal of this assay is to determine the soil U and Th concentrations in units of pCi
per gm of dry soil, the water weight fraction is needed to determine the soil dry weight.
Fortunately, both of these parameters are easily measured.

33
Soil Attenuation Coefficient
It is well known that as monoenergetic gamma rays pass through any medium, the
fraction of uncollided gammas, as a function of thickness of the medium, is given by
Transmission Fraction = exp (p (E) px),
where
p (E) = mass attenuation coefficient at the
energy E, (cm/gm2) ,
p0 = density of the attenuating medium,
(gm/cc), and
x = thickness of the attenuating medium (cm).
For a monoenergetic point source, with emission rate A, the number of gammas which
strike and are detected by a detector of area AD located at distance r from the source is
A(E) =
A0 (E) xADx t;(E) x CT
47rr2
(1)
where
Aa (E) = source gamma emission rate at energy E
(Gammas/s),
AD = detector surface area (cm2) ,
t](E) = detector intrinsic energy efficiency at
energy E, (gammas counted in the full energy.
peak per gamma hitting the detector),
CT = pulse pileup corrected live time (s),
r = distance from source to detector (cm).

34
Thus for a monoenergetic gamma passing through an attenuating medium, the number of
gammas counted in the full energy peak can be described by the product of the above two
attenuations:
A(E) x AD x tj(E) x CT
A (E) = ^ 47rr2 xexp (~n(E)Pox),
where A(E) = full energy peak area at energy E.
Next, once the above measurement is made and A (E) is determined, the attenuating
object can be removed from between the source and detector and the measurement of
A(J5) repeated. This time, however, the new measurement, A' (£7), is described by Eq. 1
alone since no attenuating object is between the source and the detector. The ratio of
A (E) /A' (E) is then proportional to the objects transmission fraction at energy E:
A(E) A0 CT .
*W) = AAm x c¥ x p(-c(*)*').
where all terms are as defined previously.
The terms that differ from one measurement to the next are Aa (E) and CT. The source
emission rate, Aa (E), changes from measurement to measurement because of source decay.
If the measurements are made sequentially, this change is small, but it is always finite. The
count live time also varies from measurement to measurement due to pulse pileup. Pulse
pileup corrections are discussed in detail in a subsequent section. Since A0 (E) and CT vary
from measurement to measurement, they remain to be accounted for in the above ratio. All
other terms divide out.
Since all the terms in the above equation are measured except the transmission fraction
term, the transmission fraction can be calculated. If the thickness of the attenuating object
is known, then the attenuation coefficient can be determined.
TF(E) = exp (fi (E)px),

35
where
TF (E) = transmission fraction for gammas at
energy E, (gammas transmitted through
the object uncollided per gamma incident
on the object), and
Therefore
other terms are as previously defined.
tt(E)xp. = (-l/x)xln(TF(£!)),
where
n(E)xp0 object linear attenuation coefficient, (cm-1).
In the case where the attenuating object is a cylindrical jar of soil, this equation results
in the soils linear attenuation coefficient at energy E. This information is used in the
next phase of this assay process, dealing with data analysis, to eventually determine U and
Th concentrations. As will be described in the next section, the soils linear attenuation
coefficient is necessary at four energies; 136 keV and 122 keV, which are the energies of the
Co-57 gamma rays used to induce x-ray fluorescence in U and Th, 98 keV, the energy of
the Kal x ray from U, and 93 keV, the energy of the Kai x ray from Th.
It should be noted here that the soil in the jar is actually a mixture of dry soil and
water. For the purposes of simplicity the term soil will be used to refer to this soil water
mixture.
Since Co-57 is used to induce x-ray fluorescence, the same source can be used to measure
transmission gamma rays and thus determine the soils linear attenuation coefficients the
energies of the Co-57 gammas. Unfortunately, no clean and calibrated source of U or Th x
rays is available. In this case, clean refers to a source that emits x rays only at the energy

of interest. Additional x rays or gammas will complicate the transmission spectra, add
background, and generally complicate the results such that true peak areas at the energies
of interest are hard to determine.
Fortunately, over a small energy range attenuation coefficients can be described as a
simple function of energy (personal conversation with John Hubble):
In (n{E)) = A + B x hi{E) + C x (In (E))2,
or
ft (E) = exp (a + Bx In (E) + C x (In (E))2) ,
where A, B, and C are constants.
Therefore, the gamma rays from Eu-155, at 105 keV and 86 keV, are also used and the
soils linear attenuation coefficients at these energies are measured. The four data points,
two from Co-57 gammas and two from Eu-155 gammas, are then fit to the above equation,
using a least squares fit technique, and the linear attenuation coefficients at the U and
Th KaX x-ray energies can be calculated from the resulting curve fit. Table 7 shows typical
soil linear attenuation coefficients.
TABLE 7
Typical Soil'
Anear Attenuation Coefficients
Measured
Curve Fit
Energy (keV)
H{E) (1/cm)
V(E) (1/cm)
136.476
0.20505
0.20517
122.063
0.21505
0.21479
105.308
0.23114
0.23132
98.428
-
0.24056
93.334
-
0.24866
86.545
0.26159
0.26155

37
Soil Moisture Content
The above analysis of soil linear attenuation coefficients assumes that the soil in the
jar consists of everything in the jar, water and soil. As will be seen, this is the appropriate
linear attenuation coefficient to be determined here. The moisture fraction of this soil
is also needed for the data analysis for final U and Th concentration determination. As
such, after the transmission and XRF measurements have been made, each sample jar is
placed in a microwave oven and dried in the jar. Jar weights before and after drying are
used to determine soil moisture weight fraction. Soil sample densities, before drying, were
determined by dividing the known wet soil weight by the know bottle volume.
Initially, soil moisture content was to be determined via use of the same transmission
gamma rays described in the last section. Unfortunately, the set of four simultaneous
equations that were to be used resulted in a non-unique solution set instead of one unique
answer. Although this approach could not be used, the details of this approach and the
reasons for its failure are included in Appendix B.
System Model
Introduction
In general, XRF determination of elemental concentrations is done by comparing the
area of a peak from an unknown sample to the area of a peak from a sample of known ele
mental concentration, called a standard. The concentration of that element in the unknown
sample is simply the ratio of unknown sample peak area to standard peak area times the
elemental concentration in the standard.
This technique assumes that the measurement geometry and attenuation properties of
the unknown sample are identical to those of the known standard. Practically speaking,

38
this means that both the standard and unknown must be as close to physically identical as
possible and must be measured using the same detector and in the same position. To achieve
this for soil samples, standards and unknowns usually are dried soil that has been crushed
into powder form, thoroughly mixed into a homogeneous mass, and put into containers.
These containers can then be exposed to an x-ray excitation source and the fluorescent x
rays can be counted. Experiments of this type are easily reproducible.
Unfortunately, standards and unknowns do not always match. The attenuation prop
erties of a soil sample vary with elemental concentrations and soil makeup. Clays, for
example, have different attenuation properties than black dirt. Comparison of unknowns
to standards of different attenuation properties may lead to erroneous results. This may
be compensated for by using very thin samples such that attenuation is not a factor. With
large samples, however, attenuation variations will cause problems.
To eliminate this problem and to eliminate the need to dry and crush soil samples,
and thus significantly decrease sample processing time, the technique described in this
paper is an absolute technique. That is, this technique does not compare unknown samples
to known standards to determine elemental concentrations. This technique can be used
on unprocessed samples which may be inhomogeneous. The teclmique also provides a
quantitative measure, in the form of a X2 value of statistical significance, of whether the
sample is too inhomogeneous to be analyzed without prior processing.
Technique Description
Figure 5 shows the source-target-detector geometry used for this XRF analysis tech
nique. In this configuration, the target is exposed to excitation gammas from the source and
emits fluorescent x rays which are seen at the detector. The detector is shielded from direct
exposure to the sources by the Pb and W source holder. The spectrum seen by the detector

FIGURE 5
Source Target Detector Physical Geometry

TARGET
POINT
SOURCE
SHIELD
DETECTOR
POINT
SOURCE
SHIELD

41
is composed of gamma rays from the source which have backscattered in the target and hit
the detector, and of fluorescent x rays from the U and/or Th in the soil. The number of
fluorescent x rays counted by the detector is proportional to the U or Th concentration in
the target. In overview, the assay technique is quite simple.
The target can be thought of as many small point sources. The fluorescent x rays
produced at each point source contribute separately to the the full energy pliotopeak of
Kai x rays seen by the detector. A mathematical model of each point source is used to
calculate the x-ray contribution from each point source. These calculated individual point
source contributions can be summed to yield a calculated total detector response. The
calculated response is then compared to the actual measured response, in a least squares
sense, to determine the contamination concentration in the target sample.
Mathematical Model
All of the equations in this section stem from well known first principles. To begin
with, it is well known that the excitation gamma ray flux (FL) that reaches a point in the
target can be described by
FL(E)=SMx<¡x¡,(-II(E)p0Il,), (2)
where
FL (E) = excitation gamma flux at a point in the
target, (gammas/cm2s) ,
ER(E) = source emission rate at energy E,
(gammas/s),

42
Ri = distance from the source to the point, (cm),
H (E) p0 = sample mass attenuation coefficient at
energy E, /t (E) (gm/cm2), times sample
density, p0 (gm/cm?) and
iZ2 = that portion of the total distance that
lies within the attenuating sample, (cm).
The photoelectric reaction rate (RX) at the point, due to the above excitation gamma
flux, can be described by
RX (E) = FL (E) x PE (E) xfx AD,
(3)
where
and:
RX (E) = photoelectric reaction rate at the point,
(reactions/a) / (pCi/gm of dry soil),
FL (E) = excitation gamma flux at a point in the
target, (gammas/cm2s) ,
PE (E) photoelectric cross section for U or Th at
energy E, (cm2/atom),
V = volume of the point source, (cm3),
AD = atom density of U or Th,
(atoms/cm3of soil) / (pCi/gm of dry soil),
= .037 (dis/s) / (pCi) X A X /)
.037 = the number of disintegrations per second
per pCi of activity,

43
A = disintegration constant for U or Th,
(s'1),
Note : the units of .037 A are
(atoms/pCi), and
p, = soil bulk density,
(gm of dry soil) / (cm3 of soil).
The fluorescent yield (FY) at the point, due to the above photoelectric reaction rate,
can be described by
FY (E', E) = RX (E) x KS (E) x KY (E1),
where
FY (jE, E) = the flux of fluorescent x rays of energyE' at
the point, that are caused by excitation gammas
of energy E,
((Kai x rays) /s) / (pCi/gm of dry soil),
RX (E) = photoelectric reaction rate at the point,
(reactions/s) / (pCi/gm of dry soil),
KS (E) = fraction of photoelectric reactions that result
in K shell vacancies,
(K shell vacancies) / (photoelectric reaction),
= (Rk 1 )/Rk
Rk = K shell Jump Ratio, and
KY (E1) = fraction of K shell x rays that are Kai
x rays, (Kal x rays) / (K shell x ray).

44
The flux at the detector (FD), of the Kai x rays that hit the detector, due to the above
x-ray fluorescent yield, can be described by
where
FD (E') =
FY{E',E) x DA
A-xr2
X exp(-p(E')p0r2),
FD (E1) = the flux of fluorescent x rays of energy E' that
hit the detector,
({Kai x rays) /s) / (pCi/gm of dry soil),
FY (E1, E) = the flux of fluorescent x rays of energy E' at
the point, that are caused by excitation gammas
of energy E,
((Aq1 x rays) /s) / (pCi/gm of dry soil),
DA = detector area, (cm2) ,
rt = distance from the point to the detector, (cm),
p(E') X p = sample mass attenuation coefficient at energy
E', (gm/cm2), times sample density, (gm/cm3) ,
and,
r2 = that portion of the total distance that
lies within the attenuating sample, (cm).
It should be noted that this equation does not include any terms to account for small
angle scatter, and correspondingly small energy change, x rays which are mathematically
removed from the x ray beam but would actually still hit the detector and be counted in
the full energy peak. Looking at the geometry of the situation, the largest scatter angle
which would leave an x ray still traveling toward the detector is ten degrees. Integrating
the Klein-Nishina differential scattering cross section (Evans pp 677-689) over 2tt, for d,
and over ten degrees, for d0, the ratio of this to the total scattering cross section is .029.

45
Considering that ten degrees is the upper bound for scatters which will still hit the detector,
this 3% error can be ignored.
As evidence of this, if small angle scatter were a significant contributor to the total peak
area, peaks would be broadened on the low energy side of their centroids and would not be
well described by the peak fitting equations shown earlier. Data in Chapter III shows that
the measured peaks are fit very well by the previously described peak fitting equations. As
such it is concluded that small angle scatter of x rays is not a significant problem and need
not be accounted for here.
Finally, the fluorescent signal (FS), the number of Kal x rays that are counted in the
full energy peak at energy E, due to the above flux at the detector, can be described by
FS (E') = FD (E') x DE (£') x CT,
where
FS (E1) = the number of counts in the full energy peak at
energy E', ie. peak area,
(Kai rays) / (pCi/gm of dry soil),
FD (E1) the flux of fluorescent x rays of energy E' that
hit the detector,
((Kai rays) /s) / (pCi/gm, of dry soil),
DE (E') = the detector intrinsic energy efficiency at
energy E',
(x rays counted) / (x ray hitting the detector),
and,
CT = total counting time, (s), corrected for pulse
pileup as described in a subsequent section.
This equation can also be written in the following more useful form

46
DRi (E') = GFi (E'),
where
DR{ (E') = detector response at energy E to point
node i,
{counts/s) / {pCi/gm of dry soil),
GFi {E') = FD {E') x DE {E') x CT,
geometry factor at energy E' for point
node i,
(counts/s) / (pCi/gm of dry soil).
The above equations are a mathematical description of the fluorescent x ray flux,
counted by a detector, due to a single point target irradiated by a point excitation source.
Looking at equation 3 more closely, the term AD, atom density of U or Th at the point
node, is in units of (atoms/cm3 of soil)/(pCi/gm of soil). The geometry factor, GF{, is
thus normalized to a contamination concentration at the point node of 1 pCi/gm. And the
detector response to a point node contaminated to any concentration, C pCi/gm, is a linear
function of the geometry factor.
Since both DR¡ (E1) and GF¡ {E') are per pCi/gm of dry soil, the detector response
to a point node contaminated to a concentration of C pCi/gm, would be
DRi {E') = C x GFi {E'),
where
DRi (E') = FS (E')
= detector response at energy E' to point
node i,
{counts/s) / {C pCi/gm of dry soil),

47
C contamination concentration at point
node i, pCi/gm of dry soil,
GFi (E1) = FD (E1) x DE (E') x CT,
= geometry factor at energy E' for point
node i,
(counts/s) / (pCi/gm of dry soil).
If a large target of uniformly distributed contamination, with a concentration of C
pCi/gm, were broken into nodes small enough to approximate point nodes then the fluo
rescent x rays from each point node could be calculated by the above equations asstiming
that the source target detector geometry was sufficiently well described. The total signal
from the large target and seen at the detector would then be the sum of the signals from
each of the target point nodes. The detector response could then be modeled as the sum of
all the point node geometry factors.
DR = C x Y, QFi,
where
DR = the photopeak area as measured by a
detector, (counts/s),
C = the uniformly distributed concentration
of contamination in the target,
(pCi/gm of dry soil), and
GFi = the calculated geometry factor for
point node i,
{counts/s) / {pCi/gm of dry soil).

48
These equations thus make up a mathematical model of a physical situation. The
model can he experimentally verified by calculating all the nodal Geometry Factors, GF{,
for a particular geometry and then making an actual measurement of the signal, DR, from
a target in that geometry. The sum of the geometry factors, referred to hereafter as the
target geometry factor, times the contamination concentration in the source should equate
to the signal seen at the detector. This model can then be used to assay unknown target
samples. The unknown contamination concentration of a sample is given by
r DR
ZGFi1
where all terms are as previously defined.
This equation is thus the basis for target sample assay. Figure 6 shows the spatial
relationships of the source, target, and detector that were used to experimentally verify the
mathematical model.
To further verify the model and to provide a better assay of the target, each target is
measured in more than one geometry. This is accomplished easily by varying the target to
detector distance between measurements. A graph of detector response vs target geometry
factor is closely approximated by a straight line
DR(P) = Cx GF(P),
where
DR (P) fluorescent signal seen at the detector
from a target at position P,
(counts/s),
C contamination concentration in the
target, pCi/gm,

FIGURE 6
Source Target Detector Spatial Geometry

Detector
Center
@ Origin
Point Source
Point Source
Target Cylinder
Center
cn
o

51
GF(P) = target geometry factor, or, the sum of
all point node geometry factors for a
target located at position P,
(counts/a) / (pCi/gm).
Using the contamination concentration, C, as the fit parameter, the data collected from
measurements made at several different geometries is then least squares fit to the above
equation. This yields a value for C, the contamination concentration in the target sample,
which is the desired result of the assay.
Compton Scatter Gamma Production of Fluorescent X Rays
The fluorescent x-ray production described by the previous equations is due to unscat
tered source gammas undergoing photoelectric interactions in the target. Since the target is
thick, gammas will also Compton scatter. If the scatter angle is small enough, the scattered
gamma will still be of sufficient energy to undergo a photoelectric interaction in the sam
ple and produce more fluorescent x rays. As will be discussed in the experimental results
section, approximately 15% of the fluorescent x rays produced are due to singly Compton
scattered ganunas. It is therefore important to calculate this production term and include
it in the model.
Compton scatter gamma model
Qualitatively, Compton scatter gamma production of fluorescent x rays is due to ex
citation source gammas which undergo a single Compton scatter interaction at point A
in a target, change direction and energy, and then undergo a photoelectric interaction at
point B in a target. Quantitatively, this is slightly more complicated to describe. Consider
two target points, A and B, as shown in Figure 7. Using equations similar to those used
previously, the flux, at scatter point A is calculated, the scatter flux and gamma energy of

52
gammas which are scattered toward point B are calculated, the photoelectric reaction rate
and fluorescent x-ray production at point B are calculated, and the number of fluorescent
x rays which are counted by the detector is calculated. In a fashion similar to that used
previously, the microscopic calculations for each point in a large target are summed into
the macroscopic total fluorescent x-ray production due to Compton scatter gammas.
Mathematical model
Looking at Figure 7, the excitation gamma flux at point A is given, again, by Eq. 2
FLl {E) = x
where
FIn (E) = excitation gamma flux at a point in the
target, (gammas/cm2s) ,
ER(E) = source emission rate at energy E,
(gammas/s),
Ri = distance from the source to the point, (cm),
fi(E)p0 = sample mass attenuation coefficient at
energy E, p(E) (gm/cm2), times sample
density, p0 (gm/cm3),
R2 = that portion of the total distance that
lies within the attenuating sample, (cm), and
E = energy of the incident gamma.
The flux that arrives at point B is dependent upon the flux that arrives at point A,
and on the differential Compton scatter cross section for scatter through an angle 0. The

FIGURE 7
Compton Scatter Spatial Geometry


55
Klein-Nisliina differential scatter cross section, in units of {cm2 / electron) / (dfl), is given
by (Evans pp 677-689)
do = r2 X dfl X [],
where
do differential cross section,
{cm2 / electron),
r0 = classical electron radius, (cm),
dil = sin {6) dOd(j)
and
0 = gamma ray scatter angle with respect
to the original direction of motion,
= rotational angel about the original
direction of motion,
[...] = terms from equation, see reference 6 (pp 677 689).
Using these two equations, the reaction rate for gammas scattering at A into the solid
angle d about fi, in other words towards B, is given by
RX = FLX {E) x do x EDens x Vol,
where
RX = scatter reaction rate, {scatters/s),
FLy {E) = flux of excitation gammas at point A,
{gammas/cm2s) ,

da = Klein Nishina differential scatter cross
section, (cm2 / electron) ,
= rl X d X [ ]
EDens = electron density at point A, (electrons/cm3) ,
Vol = volume of point A, (cm3) .
The energy of the scattered gaimna is given by (Evans pp 677-689)
1 cos (0) + (1 /a)
where
E' = energy of the scattered gamma, (keV),
0 scatter angle,
m0 c2 = electron rest mass,
= 511 keV,
E
~ 2
m0 c2
E energy of the incident gamma, (keV).
The flux at point B due to Compton scatter at point A is then described by
where
FL2 (E') =
RX
X2 sin (0) d0d X exp (-[i po X),
FL2 (E1) = flux at point B due to Compton scatter
at point A, (gammas/cm2s) ,
E' energy of scattered gamma, (keV),
RX scatter reaction rate, (scatters/s),

57
exp (fi po X) = attenuation factor for
gammas passing through soil,
and
p soil attenuation coefficient
at energy E',
p = soil density, (gm/cm3),
X = distance from point A to
point B, (cm),
X2sin(0) d0d(j> = surface area through which
gammas, scattered at point
A into dfi about fi,
pass upon reaching point B.
But since the reaction rate, RX, contains the term da which contains the term sin (#)
dO d, this will cancel out of the numerator and denominator leaving
, FLi (E) X r* x [ ] x EDens x Vol
FL2 {E') = 5L_J x exp (-p p X),
where all terms are as previously defined.
Knowing the flux at point B and the energy of the incident gammas, allows the calcu
lation, using the equations described in the previous section, of the photoelectric reaction
rate at point B due to scatter in point A, the fluorescent x-ray production rate at point B
due to scatter in point A, the x- ray attenuation from point B to the detector due to scatter
in point A, and the number of fluorescent x-rays from point B due to scatter in point A
counted by the detector. To determine the entire production of fluorescent x rays at point
B, scatter from every other point node in the target that results in gammas reaching point
B must be calculated. A summation of all these contributions yields a Compton Geometry

58
Factor for point B, analogous to the Geometry Factor calculated in the previous section for
unscattered gammas. The result of these equations is a summation equation completely
analogous to that derived in the previous section
CDRi (E') = C x CGFi {E'),
where
CDRi {E') detector response at energy E'
to Compton scatter production at point
node i,
{counts/s) / (CpCi/gm of dry soil),
C contamination concentration at point
node i, (pCi/gm of dry soil),
CGFi {E') = Compton geometry factor at energy E'
for point node i,
{counts/s) / {pCi/gm of dry soil).
As before, the contribution from each point node of a large target could be summed to
yield the total calculated detector response due to Compton scatter gamma production. The
Compton scatter production portion of the detector response cannot, however, be measured.
Actually the measured detector response is the sum of fluorescent x-ray production due to
unscattered excitation gammas and Compton scattered excitation gammas, and these two
contributions cannot be physically separated. The solution is to alter the model such that
the measured detector response is modeled as being the sum of the unscattered gamma
Geometry Factors and the Compton scattered Geometry Factors
DRi {E!) = C x {GFi {E!) + CGFi {E')),
where all terms are as previously defined.

59
Then, for a large target of uniform contamination concentration C pCi/gm of dry soil,
the detector response is modeled as
DR = C {GFi (E') + CGFi (E1)),
where
DR = the photopeak area as measured by a
detector, (counts/s),
C the uniformly distributed concentration
of contamination in the target,
(pCi/gm dry soil),
GFi = the calculated geometry factor for
point node i,
(counts/s) / (pCi/gm, of dry soil),
CGFi = the calculated Compton geometry factor
for point node i,
(counts/s) / (pCi/gm of dry soil).
This set of equations then constitutes a mathematical model of the fluorescent x-ray
production due to unscattered gammas and Compton scatter gammas. As stated before,
the desired result of the assay, the value of C, could theoretically be calculated using only
one measurement made in one geometry. In this work, multiple measurements are used to
achieve a more statistically significant answer. As discussed earlier, this model is verified
by actual measurements of targets in several known geometries. As will be discussed in the
results section, the model is in very good agreement with actual measurements.

60
Electron density
The electron density used above is a parameter which will vary from sample to sample
due to changes in density, elemental makeup, and water content. Electron density must
therefore be calculated for each sample. This is accomplished in a simple fashion using the
transmission measurement described earlier.
The total linear attenuation coefficient is made up of an absorption coefficient, a pair
production coefficient, a Compton scatter coefficient, and a coherent scatter coefficient.
A conversation with John Hubble of the National Bureau of Standards and a follow-up
computer study indicated that for various soils, the ratio of Compton scatter coefficient
to total linear attenuation coefficient is approximately constant for a given energy gamma.
Appendix A details the computer study done to verify this and to arrive at an appropriate
average Compton to total ratio. Knowing this ratio, the measured total linear attenuation
coefficient can be used to calculate the electron density as follows
Hccaic = CTR x fira
where
Hccalc = calculated Compton linear attenuation
coefficient as ratioed from the total
linear attenuation coefficient, (cm-1),
^rneo measured total linear attenuation
coefficient, (cm-1), measured as
described in a previous section,
CTR = ratio of Compton linear attenuation
coefficient to total linear attenuation
coefficient,

61
but
ficcale = EDens X tr?~N
where
EDens = soil electron density, (electrons / cm2),
crf~N = Klein Nislvina Compton scatter cross
section, (cm2/electron).
therefore
EDens
calc
c
aK-N
where all terms are as previously defined.
Natural Production of Fluorescent X Rays
Since progeny of both 17-238 and Th-232 emit U and Th x rays (see tables 1 and 2) the
natural x-ray production rate was also calculated. As will be seen in the results section,
this term contributed less than 1% to the total fluorescent x-ray production.
The decay chains of 17-238 and Th-232 are very similar. In both cases, the parent alpha
decays to the first progeny, the first progeny beta decays to the second progeny, and the
second progeny beta decays to the parent element with an atomic weight four less than that
of the parent. As the second progeny decays, the beta is emitted leaving the meta-stable
decayed atom looking very much like a parent atom with one extra electron. During the
complicated events that follow beta decay, the decayed atom emits x rays that are of energy
characteristic of the parent atom.

62
In the case of U, 17-238 alpha decays to Th-234, which beta decays to Pa-234, which
beta decays to 17-234. As the Pa-234 decays to 17-234, U x rays are emitted. ICRP report
# 38^ gives the emission rate of these x rays as 0.00232 Aq1/decay.
In the case of 7'h, Th-232 alpha decays to Ra-228, which beta decays to Ac-228, which
beta decays to Th-228. As the Ac-228 decays to Th-228, Th x rays are emitted. ICRP
report #38^ gives the emission rate of these x rays as 0.0428 R'1/decay.
Since natural decay production of x rays contributes so little to the total production,
the assumptions that Th-232 is in equilibrium with Ac-228, and that 17-238 is in equilibrium
with Pa-234 will introduce little error. As such, one pCi of Th-232 will be in equilibrium
with one pCi of Ac-228, and one pCi of 17-238 will be in equilibrium with one pCi of Pa-234.
The production rate of U and Th x rays can now be calculated.
For thorium
Kalyield
= ^0.0428
= 0.001584
Ka i \
decayJ
Ka\/ s
pCi Th- 232'
^0.037
decay/s
pCi Th 232
For uranium
Kaiyield
= ("
00232 Ail-) xf0.037 *C!'/s
decayJ \
decay/s ^
pCi U 238)
= 0.00008584
Kgy/S
pCi U 238
These terms are in the correct units to be added directly into the previously described
mathematical model at the point where fluorescent x-ray production in each point node is
calculated. With this small correction added, the mathematical model is complete.

63
Isotopic Identification
As mentioned earlier, the two isotopes which are of principle interest for this assay
technique are 7-238 and Th-232. In fact, these are the only two isotopes of U and Th
which can be seen at small concentrations using XRF. This is because XRF is dependent
upon the number of atoms present. In the cases of other U or Th isotopes, tremendously
high numbers of curies would have to be present before there would be enough atoms of
these isotopes to be seen by XRF. This is due to the very long half lives of E/-238 and Th-232
with respect to their other isotopes, since the number of curies is equal to the number of
atoms times the decay constant. Table 8 illustrates this point.
The sensitivity of the experimental setup tested in this work is approximately 50 pCi/gm
of T/i-232, which corresponds to 500 ppm. The system sensitivity then, in terms of number
of atoms required, is approximately 500 ppm. The table clearly shows that huge quantities,
in terms of pCi/gm, of all the isotopes except 7-238 and Th-232 would be required to reach
concentrations 500 ppm. Since these huge concentrations are rarely seen, and since one of
the objectives of this assay system is to achieve a low sensitivity in terms of pCi/gm, it can
be concluded that this XRF assay technique cannot be used for U and Th isotopes other
than 238 and 232 respectively.
TABLE 8
Isotopic Concentrations: PFM vs. pCi/gm
Isotope
Concentration
(ppm)
Concentration
(pCi/gm)
17-238
500
168.1
U-235
500
1.081E3
U- 234
500
3.125E6
Th-232
500
54.65
Th- 234
500
1.158E13
Th- 230
500
1.009E7
Th-228
500
4.098E11

64
It is also reasonable to conclude that all U and Th seen by XRF is C/-238 and Th-
232 respectively. Based on the above table, such large quantities of other isotopes would
be required before these isotopes could be seen by XRF, the radiation levels of the sources
would be too large for analysis using sensitive Ge detectors. It is also extremely unlikely that
such large quantities of other isotopes would be found. Even if U-238 were in equilibrium
with Th-234, 7-234, and Th-230, or if Th-232 were in equilibrium with Th-228, while the
curie contents of the sample would be high in these other isotopes, the ppm concentrations
of these other isotopes would be much to low to register using XRF. It would thus be safe
to assume that all of the signal seen at the detector was from U-238 or Th-232.
Prior knowledge of the nature of the process which lead to the contamination might
point toward high concentrations of other isotopes. For example, excavation near a plant
which previously processed Th-230 to remove Ra-226 would be expected to show high Th-
230 levels and natural Th-232 levels. Again though, unless the T/i-230 levels were extremely
high, XRF would not be of any use.
Unfortunately then, tills XRF technique is not useful in determining the concentrations
of isotopes other than U-238 and Th-232. If it were known that the contamination in
question was primarily U-238 and/or Th-232, progeny equilibrium with U-238 and Th-232
could be assumed thus establishing an upper limit of other isotopic concentrations. This
would not, however, constitute an adequate assay unless the upper limit were below some
lower bound of regulatory concern.
However, the analysis teclmique used, that is measuring the attenuation properties of
the sample at the energies of the gamma rays of interest, and the calculation of geometry
factors, could be applied to gamma spectroscopic techniques or to neutron activation anal
ysis techniques to improve their accuracy. This work is, however, beyond the scope of this
project.

65
The value of this technique is that it measures 7-238 and Th-232 directly and without
relying on equilibrium with progeny. Neutron activation and its associated neutron source
was previously required to achieve this independence.
Error Analysis
Introduction
A soil contamination assay must be accompanied by an estimate of the error associated
with the measured contamination concentration. The assay system presented in this work
is based on fitting measured data to mathematical models using the least squares technique.
Least squares analyses lend themselves well to propagation of error from one curve fit to
the next, as well as to calculation of the chi-squared test statistic as a measure of goodness
of fit.
This work begins with measured spectral data and the error associated with each data
point. This data is fit to a mathematical model of an x-ray peak as viewed through a Ge
detector, and the peak parameters are determined. These parameters are used to determine
the area of the peak and the error associated with the peak area. This operation is repeated
for several different target configurations yielding several peak areas and their associated
errors. These areas are then fit to a mathematical model which predicts the detector
response as a function of target geometry and contamination concentration. The only
fitting parameter of this model is the contamination concentration in the target, which
is calculated by least squares fitting the previously calculated peak areas to the modeled
function. The error in the fitting parameter is extracted from the least squares fitting
process and the desired result, determination of the soil contamination concentration and
its associated error, is achieved.

66
Least Squares Peak Fitting
The least squares fitting technique is fairly simple and is described in numerous books
and articles. The mathematics used in this work was taken from Forsythe et al.^O This
technique was used in this work to properly determine the spectral peak areas and their
associated errors.
Least squares fitting is an iterative technique based on minimizing the square of the
difference between a measured value and a value calculated based on a mathematical model.
The minimization is performed by properly choosing the parameters of the mathematical
model. The model may be linear in these parameters or non-linear. Each successive iteration
refines the fitting parameters such that the sum of the squares is minimized. To begin, the
mathematical model is chosen. An initial guess as to the fitting parameters is also required.
F(Xi:Pl,P2,P3,...,Pn)l=Yi,
where
Xi = independent variable,
Pn = fit parameters of the mathematical model,
Yi = dependent variable.
Note: the 1 indicates that the fitting parameters are the current guess. The previous guess,
or for the first iteration, the initial guess, will be used to determine the new, or current,
guess.
Using current guess as to the fitting parameters, the sum of the squares of the difference
between the measured values and the calculated values is calculated.
S = £(*(*<),-Si)2 >

67
where
5 = sum of squares,
m) i yu
calculated dependent variable based
on current fittingparameters,
yi = measured dependent variables.
To minimize this equation
dS dS dS _dS
dPl ~ dP2 ~ dPZ dpn "
This creates a set of n independent equations each looking
like this
dS
dPl
= £2x(m)i -1ft) x
dF(X)
dPl
where
F (X<)i ~ F : -P2x, P3l5..., Pni) .
This equation is mathematically correct, however only the initial guess parameters are
known at this point. Fortunately F (X{)1 can be approximated by a Taylor expansion,
truncated after the first order terms, knowing 1. the values of F(Xf)0 which are based on
the previous best guess of the fitting parameters, and 2. the function partial derivatives at
each Xi
n*i\
F {Xi)0 (-^It P\o) X
dF{Xt)0
dPl
+ (F2i P2q) X
dF(Xt) 0
dP2
+ (P3i P3o) X
dF(Xt) Q
dP3
+ + (Pni Pn0) X
dF(Xt) Q
dPn

G8
where all terms are previously defined.
Substituting this into the least squares minimization equation yields
dS _vdF(,Y<)0 ^dF(Xt)Q
dPl ^ dPl 1 J ^ dPl
x(P(X,.)o-y,) = 0,
where
[ ] = DPI X
dF{Xt)0
dPl
+ DP2 x
dF(Xt) Q
dP2
+ PP3 x
dP3
+ h DPn x
dPn
DPn = Pn\ Pn0.
This can be rewritten as
^ dP 1 1 J ^ dPl
X^-PTOo).
As previously stated, similar equations are generated for each differential equation
dS dS
dPl ~rfP2 dPn ~ '
This system of equations lends itself to the matrix form
DF4 (n, m) X DF (m, n) x
A(n,l)
= PP (n,
m) X PT (m
/ dF{Xi )n
dP(Xt)n
dF(Xt)n
dF(X,)
dP 1
dP 2
dPZ
' dPn
dF{X,)
dF{X,)0
dF(X,)
dF(X3)
DF (m,
n) =
dP 1
dP 2
dP 3
dPn
dP(jir)0
dF(Xm)
*F(Xm)0
' dP 1 dP 2 dP 3 dPn
DFl (n, rn) = the transpose of DF (m, n),
n = the number of parameters in the fitting function,
m = the number of data points used in the fit,

69
A (n, 1)
/ {PU ~ Plo) \
(P2t P20)
(P3j P30)
DY (m, 1) =
{(Put Pn0)
/ (yl-F(x1)0) \
(j/2-P(X2)0)
(j/3-P(X3)0)
\(j/m-P(Xm)0)/
This matrix equation is solved by Gaussian elimination to yield the values of the A (n, 1)
matrix. These values are used to update the parameter guesses from the initial guesses of
Pl0, P20, ..Pn0, to Pli, P2i, ..Pni, since Pi = Pi0 + A (i, 1). New values of F (X<)
are calculated based on these new parameters, these new parameters become the initial
guesses for the next iteration, and the matrix solution is repeated. This iteration process
is continued until the sum of squares is minimized based on some predetermined cutoff
criteria. The result of the minimization is the calculation of the best fitting parameters
for the mathematical model.
Covariance Matrix and Functional Error
As a by-product of this method, the variances and covariances of the fitting parameters
are calculated. The inverse of the matrix product, DF1 x DF, is defined as the covariance
matrix 20.
(DF1 (n, m) x DF (m, n)) 1 = Covar (n, n).
The diagonal values of this matrix, Covar(i,i), are the variances of the model fitting
parameters.

70
Covar (1,1) = cr2 (Pi),
Covar (2,2) = cr2 (P2) ,
Covar (3,3) = Covar (n, n) = cr2 (Pn).
The covariance matrix is diagonally symmetrical, with the off diagonal elements being
the covariances of the various parameters, for example
Covar (1, 2) = cr2 (PI, P2).
These values are used to calculate the errors associated with fitting parameters at
various stages of determining the final solution, the soil contaminant concentration and its
associated error. But in addition to knowing the errors associated with fitting parameters,
the errors associated with functions of those fitting parameters are necessary. For this
work, only linear functions of fitting parameters are used. The error associated with a
linear function of fitting parameters is given by the following equation^
if: F(X : Pl,P2,P3,...,Pn),
where : P1,P2,P3, ...,Pn and their associated errors
are known,
then for : Q (X : PI, P2, P3,..., Pn),
n n
<72(Q(Xi)) == Pi2 X =1 *,=1
This equation and the covariance matrix as determined via the least squares process
described here are all that is needed to properly propagate error through the peak fitting
portion of this work.

71
Error Propagation
The various stages of the assay analysis have all been thoroughly described. This section
will describe how error is propagated through these calculations.
To begin with, a spectral peak is collected. The error associated with each spectral
data point is
a2(Yi) = Y¡.
The first manipulation performed on this data is the calculation of the background
beneath the x-ray peak being analyzed. This calculation is performed in two steps. First, a
polynomial background (POLYBK) is calculated using data points to the right and left of
the peak. These points are least squares fit to a fourth order polynomial yielding the best fit
and a covariance matrix. Using the covariance matrix and Eq. 4, the error associated with
each calculated data point is determined, Var(POLYBKi). Second, the complimentary
error function (erfc) background (ERFBK) is determined. This is a numerical process, the
error associated with each of these points is estimated to be
a2 (ERFBKi) = ERFBKi.
The two backgrounds, polynomial and erfc, are assumed to each contribute equally to
the complete background, thus the complete backgromid is equal to
_ r. POLYBKi + ERFBKi
BKs
2
and,
o-2 {BKi) =
72
The next step in the analysis is to subtract the background from the spectral data
(SPEC) to yield an estimated peak. The variance associated with each of the peak points
is then
o-2 (PKi) = The peak is then least squares fit to a Voigt peak shape, yielding the covariance matrix
for this process. Equation 4 is then used to calculate the error associated with the numeri
cally calculated peak area. These steps are repeated for several geometric configurations of
the soil sample target yielding several peak areas and their associated errors.
Linear Function Fitting
Once the peak areas and their associated errors have been determined, the last step
of the assay is to determine the concentration of contamination in the sample jar and its
associated error. As described earlier, the measured detector response is a linear function
of calculated GFs, the slope of this line being the concentration of contamination in the
sample jar. The measured detector response data, the error associated with this data, and
calculated GFs need only to be fit to a linear function to determine the desired assay result.
Easier still, the fitted line must pass through the origin since if the calculated GF for a
sample were zero, the measured detector response would also have to be zero. This sort of
statistical data fitting is common to most introductory statistic books. The treatment used
here is from handouts prepared for a statistics class at Cornell University ^1.
For any linear function of X,
Y = x Fa(X),

73
where
aa the ath of m fitting parameters,
Fa (X) = the ath of m linear functions of X,
then the values of the fitting parameters a are given
by,
a,
Em \pp
a~ 1 2-^/b-
YFa(Xb)
H 1 (a, i),
where
H 1 (i, i) = the covariance matrix,
cr6 = the standard deviation of
detector response b,
and,
lr, {i j) = F¡(X)
& *
For a simple function such as DR = C X GF, where C is the unknown fitting parameter
at, Y = DR, X = GF, and Fx (X) = X GF, these equations are extremely easy to solve
and yield the desired result of this analysis, the value of C. The error in the value of C is
also quite simple.
= n 1 (*, i)
This then yields the desired result of this analysis, the soil contamination concentration,
G, and its associated error.

74
Experimental Procedure
Sample Counting
Once the experimental apparatus is constructed and properly calibrated, as described
in Appendix A, the processing of samples is straight forward and requires only eight steps.
1. Samples are placed in 100 ml plastic jars and weighed. The soil may be wet and not
completely uniformly mixed. The sample jars are of radius 2.32 cm with an active
height of 6.50 cm.
2. The sample is weighed, wet or dry in the jar, and the average jar weight, 20.7 0.1
gm, is subtracted to obtain the sample weight.
3. The sample jar is placed in a known geometry above a Ge detector, described in detail
in Appendix A, such that the center of the sample is directly in line with the center of
the detector. In this work, the jar center is 11.6 0.1 cm from the detector window,
and the detector window to detector distance is 0.5 cm.
4. A Co-57 source is placed directly in line with the center of the detector such that the
sample jar is between the source and the detector. The source to detector window
distance is 89.4 0.2 cm. The transmitted fraction of 136 keV and 122 keV gammas
from Co-57 is then measured. Count duration is dependent upon source strength. In
this work, count times of one hour are used. Shorter times could be used by placing
the source closer to the detector such that the detector system dead time remained
below 20% or so, and the total counts under the peaks in question were statistically
significant. In this work, peak areas are on the order of 100,000 counts.
5. The Co-57 source is replaced with an Eu-155 source and step three is repeated, mea
suring the transmitted fraction of 105 keV and 86 keV gammas from Eu-155. The

75
transmission fractions are then used to calculate the sample linear attenuation coeffi
cients as described in a previous section.
6. The next step is sample XRF analysis. The sample is placed such that the center of the
sample is again directly above the center of the detector. The source holder and sample
holder assemblies are shown in exploded view in Figure 8. Figure 9 shows the sample in
its holder positioned above the detector and above the source holder shield. Using the
center of the detector as the origin of an X-Y-Z coordinate system, the sample center
is located at coordinate (10.5 0.1 cm, 0.0 cm, 0.0 cm). Figure 10 shows the sample
in position and the laser alignment beam used to ensure that it is properly centered.
The source holder, described in detail in Appendix A, holds two sources located in the
X-Z plane formed by the long axis of the sample bottle and the detector center. The
sources are located at coordinates (4.42 0.01 cm, 0.0 cm, 4.42 0.01 cm) and (4.42
0.01 cm, 0.0 cm, -4.42 0.01 cm).
Once the sample is properly positioned, the sources are placed in their holders and the
sample is irradiated for one hour. In this work, fluorescent x-ray peaks ranged in area
from 20,000 counts to 1,500,000 counts depending upon the U or Th concentration in
the samples. Figure 11 shows the multichannel analyzer system used to collect spectral
information. Figure 12 shows a typical spectrum on the MCA.
7. For the next seven counts, the sample is next raised 0.3 0.01 cm and step six is
repeated. The yields a total of eight counts with the sample center being at 10.5, 10.8,
11.1, 11.4, 11.7, 12.0, 12.3, and 12.6 cm from the detector. The detector and XRF
excitation sources remain in fixed positions for all eight counts.
8. Finally the sample is dried, if necessary, in an oven or a microwave and weighed again.
The dry soil weight and soil moisture fraction are thus determined.

FIGURE 8
Exploded View of Target Holder Assembly


FIGURE 9
Target in Place Above Detector

79

FIGURE 10
Target in Place Above Detector
Showing Laser Alignment System

81

FIGURE 11
ND-9900 Multichannel Analyzer, ADC,
Amplifier, and Detector Power Supply

83

FIGURE 12
Typical XRF Kal Peak on MCA


86
Data Analysis
Once all the spectral information is collected, the data is processed, using the computer
codes described earlier, to determine soil 7-238 and/or Th-232 concentrations. This process
requires 7 steps. All computer programs referenced here are listed in Appendix C.
1. POLYBK.BAS is run for each spectrum to determine the coefficients of the fourth order
polynomial used to fit the background shape.
2. BKG.BAS is run for each spectrum and, using the coefficients determined by POLYBK.BAS,
calculates a background which is a combination of a fourth order polynomial and a com
plementary error function. The background is then subtracted from the spectrum to
yield the peak data.
3. PEAKF1T.BAS is run for each spectrum and, using the peak data calculated by
BKG.BAS, fits the peak data to a Voigt peak shape and determines the peak area
based on the calculated fitting parameters. Once all eight spectra have been shaped
and had their areas determined, the peak area data is used to calculate soil contami
nation concentrations.
4. DIST.FOR is run once for each of the eight geometries used and stores source-target-
detector geometry information. The information stored includes, for each geometry,
distances from each source to each point in the target, the portion of that distance
which lies within the target (where soil attenuation coefficients are used), and the
distance from each point to each of the 24 mathematical nodes of the detector. This
data is compiled only once and is then used for the analysis of all samples.
5. 1MAGE.FOR is run once for each of the eight geometries and must be run for each soil
sample. This program uses the distances calculated by DIST.FOR and the attenuation
coefficients calculated by SOILTRANS.BAS to determine the sample GFs for each

87
geometry due to unscattered gammas from the XRF activation sources. The total GF
for each geometry is stored for use by subsequent programs.
6. COMPTON.FOR is run once for each of the eight geometries and must he run for each
soil sample. This program uses the distances calculated by DIST.FOR and the atten
uation coefficients calculated by SOILTRANS.BAS to determine the sample Compton
GFs for each geometry due to singly scattered compton gammas from the activation
sources. The total compton GF for each geometry is stored for use by subsequent
programs.
7. ASSAY.FOR is run once for each sample. This is the final processing program and uses
the peak areas calculated by PEAKFIT.BAS and the GFs calculated by IMAGE.FOR
and COMPTON.FOR to determine the soil £7-238 and/or Th-232 concentration^) in
each sample. Errors and the resulting fitted line are reported.

CHAPTER III
RESULTS AND CONCLUSIONS
This research is broken into two broad sections, the first being the development of a
mathematical model of the soil assay technique, which has three sections as mentioned
earlier, and the second being an experimental verification of the technique. Chapter II
described the model and the experimental setup used to test the model. This chapter
describes the results of the experimentation and the conclusions which can be drawn from
those results.
Experimental Results
Assay Results
Thirteen samples were assayed using the previously described experimental and data
processing techniques. Four of the samples were artificial, clean soil spiked with either U or
Th oxides. Three samples were collected in Northern New Jersey during the summer of 1984
and analyzed such that their contamination concentrations were known. And six samples
were unknowns collected from other sites in 1986. The samples are described briefly here.
Seven homogeneous samples were prepared, either by spiking clean soil with pure U or
Th, or by mixing together of quantities of soil of known contamination concentrations. All
these samples were analyzed in dry, homogeneous states.
88

89
Till: Homogeneous sample made from clean soil spiked with Th02 to a con
centration of approximately 125 pCi/gm. The spike used was pure
Th 232.
THla: A second homogeneous sample made from the same spike as TH1. Again,
the approximate concentration of the sample was 125 pCi/gm.
Ul: Homogeneous sample made from clean soil spiked with U3Oa to a con
centration of approximately 170 pCi/gm. The spike used was natural
U30B.
Ula: A second sample made from the same spike as Ul. Again, the concen
tration of the sample was approximately 170 pCi/gm.
Sample 2: Homogeneous sample made from the mixture of several samples
collected at FUSRAP sites in Northern New Jersey. The sample
concentration was designed to be approximately 80 pCi/gm.
Sample 3: Homogeneous sample made from the mixture of several samples
collected at FUSRAP sites in Northern New Jersey. The sample
concentration was designed to be approximately 225 pCi/gm.
Sample 4: Homogeneous sample made from the mixture of several samples
collected at FUSRAP sites in Northern New Jersey. The sample
concentration was designed to be approximately 650 pCi/gm.
It should be noted here that the actual concentrations of Th or U in samples Ul, Ula,
TH1, and THla were determined by two assays from two separate laboratories. The uncer
tainties of source preparation, such as accurate weighing of the spike material, transference
of all the spike material from the weighing foil to the soil, and the complete homogenization

90
of the spike in the sample, were seen as being fairly large and difficult to accurately char
acterize. As such the laboratory assays, which are more accurate than the assays based on
sample preparation data, were used as the sample contamination concentrations. Samples
2, 3, and 4 were blended from other samples of known concentrations. Again, because the
uncertainties in the blended weights, as well as in the original sample contamination con
centrations, the contamination concentrations of these samples were also determined using
analysis by other laboratories as opposed to using sample preparation data.
Six samples were collected from various locations and analyzed au naturel. These
wet, inhomogeneous samples are representative of typical samples collected during soil char
acterization activities.
NJA: Inhomogeneous, wet sample of highly contaminated material brought
collected at a FUSRAP site at Lodi, New Jersey.
NJB: Second inhomogeneous, wet sample collected at the same site as NJA.
USA: Inhomogeneous, wet sample collected at the Y-12 weapons production
plant, Oak Ridge, Tennessee, from an area known to be contaminated
with Th.
USB: Second inhomogeneous, wet sample collected at the same site as USA.
USC: Inhomogeneous, wet sample collected at the Y-12 weapons production
plant, Oak Ridge, Tennessee, from an area known to be contaminated
with U.
USD: Second inhomogeneous, wet sample collected at the same site as USC.
It should be noted here that this assay technique requires a relatively small aliquot of
contaminated soil; approximately 120 gm. The two assay techniques used to verify this
assay require approximately 250 gm of soil. As such, tandem samples were required so that
they could be blended together to form samples large enough for analysis by the other two

91
techniques. This is why all the samples analyzed, except Sample 2, Sample 3, and Sample 4
were paired. Since these samples were made by blending samples together, they were large
enough to provide adequate samples for the other two analysis techniques that were used.
Table 9 lists the assay results of the three techniques for U and Th contaminated soil.
Table 10 lists the results of a sensitivity study described below. Tables 11 to 25 list the
measured and fit detector responses for each sample. Table 26 lists various physical qualities
of the above samples. Table 27 lists sample attenuation qualities.
In order to further verify the statistical validity of these results, a short sensitivity
study was performed. As described in Chapter II the assay technique described here fits
peak area data, collected from a sample counted in several geometries, to a straight line
passing through the origin. The slope of this line is the concentration of radionuclide in the
sample, which is the desired result of the assay. In this work, this line was fit using eight
points. To test the sensitivity of the resulting slope to the number of fitting points used
the program ASSAY.FOR was used to reprocess the data from Sample 3. In this case data
from positions 1, 3, 5, and 7 were used for one run, and data from positions 2, 4, 6, and 8
were used for a second run. The results of these runs as well as the result of the original
Sample 3 run using eight points are listed in Table 10 and show that the assay results using
four fitting points are similar to the assay results using eight fitting points.
It should be noted that the errors presented in Tables 9 and 10 were calculated using
the techniques described in the error section of Chapter II. Put simply, each point on the
line represents a peak area which is calculated by least squares fitting measured data to a
theoretical peak shape function. Each calculated area thus has an associated error. Since
the peak areas are large, as is shown in Tables 29 through 43, the errors associated with
each data point are small. The peak area data points are then least squares fit to a straight
line, the slope of which is the concentration of U or Th in the target soil sample. The error

92
in the slope of this fitted line is easily calculated using linear least squares statistics. As is
shown in Tables 11 to 25 and evidenced by the very low X2 values for the fitted lines, the
data points lie very close to the fitted line and thus small errors in the fitted slope of the
line would be expected. This is seen in the small errors in the resulting answers shown in
Tables 9 and 10.
Table 9 also lists soil U and Th concentrations as calculated by Oak Ridge National
Laboratory using gamma spectroscopic techniques. The errors associated with these con
centrations are larger than those calculated by the technique developed here. This is due
to several factors. Gamma spectroscopy, as described in Chapter I, uses gamma rays from
several progeny of U and Th to determine the contamination concentrations in a given soil
sample. The theoretical relative peak areas of all gammas, assuming equilibrium in the
decay chain, are used in an algorithm to calculate the contamination concentration in the
target soil sample using measured peak areas. The peaks which are used each have associ
ated errors and the error in the calculated contamination concentration is derived from the
proper propagation of those peak errors. In the Table 9 data, the peak areas used for the
ORNL calculated U and Th concentrations were smaller, in general, than the peak areas
used for the XRF calculations. Thus the errors associated with the ORNL gamma peaks
were larger than those associated with the XRF peaks. The algorithm used by the ORNL
gamma spectroscopic analysis system then propagates those peak area errors to determine
the U and Th concentrations. Beginning with errors larger than those of the XRF tech
nique and propagating those errors correctly thus yields resulting errors in contamination
concentrations which are larger for the gamma spectroscopic analysis than for the XRF
analysis.

93
TABLE 9
Soil Assay Results for U and Th Contaminated Soil
17-238
(pCi/gm)
Sample
XRF(l)
ORNL(2)
U1
152.3 0.4
-
Ula
164.6 0.3
-
Ul/Ula avg.
158.6 0.5
184.5 10.5
N.TA
196.9 0.6
-
NJB
142.0 0.5
-
NJA/NJB avg.
168.5 0.8
171.0 db 17.0
use
135.2 0.4
-
USD
138.9 0.4
-
USC/USD avg.
137.1 0.6
133.4 10.4
Th-232
(pCi/gm)
Sample
XRF(l)
ORNL(2)
Sample 2
93.6 0.3
87.5 1.8
Sample 3
221.7 0.2
228 4.0
Sample 4
683.0 0.6
688 17.0
Till
143.5 0.3
-
THla
144.2 0.3
-
TlIl/TIIla avg.
143.8 0.4
119.5 3.9
NJA
2436.7 0.9
_
NJB
2267.0 1.0
-
NJA/NJB avg.
2348.9 1.3
2590.0 72.0
USA
181.4 0.3
-
USB
159.6 0.3
-
USA/USB avg.
170.7 0.4
165.2 4.0
1. Analysis performed by the technique developed in this dissertation. Reported
errors are lcr and were calculated as described in chapter II.
2. Analysis performed by gamma spectroscopy on dry and homogeneous samples
at Oak Ridge National Laboratory.

TABLE 10
Assay Sensitivity to the Number of Fitting Points Used
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Positions
Used
Calculated CC
pCi/gm Th232
Reduced X2
1 to 8
221.7 0.2
0.242
1, 3, 5, 7
221.0 0.3
0.401
2, 4, 6, 8
222.1 0.3
0.343

TABLE 11
Measured vs. Fitted Detector Response for
U1
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 152.3 pCi/gm U238
Reduced X2 Value for Fitted Data : 0.183
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.529
80.5
82.4
2
0.466
70.9
75.1
3
0.411
62.7
60.9
4
0.365
55.5
59.1
5
0.324
49.4
49.5
6
0.289
44.0
40.3
7
0.258
39.3
37.8
8
0.232
35.3
32.8

TABLE 12
Measured vs. Fitted Detector Response for
Ula
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC Fitted Contamination Concentration
Calculated CC : 164.6 pCi/gm U238
Reduced X2 Value for Fitted Data : 0.047
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.557
91.7
92.1
2
0.491
80.7
78.4
3
0.433
71.3
69.0
4
0.384
63.2
61.7
5
0.342
56.2
57.5
6
0.304
50.1
51.4
7
0.272
44.9
46.0
8
0.244
40.1
40.4

TABLE 13
Measured vs. Fitted Detector Response for
NJA-U
Fitting Equation : DR GF X CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC Fitted Contamination Concentration
Calculated CC : 196.9 pCi/gm U238
Reduced X2 Value for Fitted Data : 0.129
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.255
50.3
45.4
2
0.225
44.3
42.8
3
0.199
39.1
41.2
4
0.176
34.7
36.6
5
0.157
30.8
31.8
6
0.140
27.5
27.4
7
0.125
24.6
24.4
8
0.112
22.0
21.6

TABLE 14
Measured vs. Fitted Detector Response for
NJB-U
Fitting Equation :DR = GFxCC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 142.0 pCi/gm U23S
Reduced X2 Value for Fitted Data : 0.071
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.268
38.0
35.2
2
0.236
33.5
33.9
3
0.208
29.6
29.4
4
0.185
26.2
27.0
5
0.164
23.3
24.2
6
0.146
20.8
21.6
7
0.131
18.6
19.5
8
0.117
16.7
15.6

TABLE 15
Measured vs. Fitted Detector Response for
use
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 135.2 pCi/gm t/238
Reduced X2 Value for Fitted Data : 0.274
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.391
53.0
45.2
2
0.345
46.6
45.2
3
0.305
41.2
42.3
4
0.270
36.5
40.0
5
0.240
32.5
33.9
6
0.214
28.9
28.8
7
0.191
25.9
26.9
8
0.172
23.2
23.0

100
TABLE 16
Measured vs. Fitted Detector Response for
USD
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 138.9 pCi/gm E/238
Reduced X2 Value for Fitted Data : 0.264
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.421
58.4
54.9
2
0.371
51.5
51.9
3
0.327
45.5
45.6
4
0.290
40.3
43.4
5
0.258
35.8
37.9
6
0.230
31.9
29.5
7
0.206
28.5
25.7
8
0.184
25.6
21.8

TABLE 17
Measured vs. Fitted Detector Response for
Sample 2
Fitting Equation : DR GF X CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC Fitted Contamination Concentration
Calculated CC : 93.5 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.274
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.732
162.1
167.8
2
1.526
142.8
148.8
3
1.348
126.1
129.1
4
1.194
111.8
119.5
5
1.061
99.3
98.5
6
0.946
88.5
87.4
7
0.845
79.1
74.1
8
0.757
70.9
66.7

TABLE 18
Measured vs. Fitted Detector Response for
Sample 3
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC Fitted Contamination Concentration
Calculated CC : 221.7 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.242
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.462
324.1
333.9
2
1.287
285.4
290.0
3
1.137
252.1
255.0
4
1.008
223.4
220.6
5
0.895
198.5
194.9
6
0.798
176.9
174.4
7
0.713
158.1
150.0
8
0.639
141.7
133.2

TABLE 19
Measured vs. Fitted Detector Response for
Sample 4
Fitting Equation : DR = GF X CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 683.0 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.416
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.258
859.2
882.6
2
1.108
756.6
767.3
3
0.979
668.4
674.8
4
0.867
592.3
589.6
5
0.770
526.4
518.8
6
0.686
468.8
456.7
7
0.613
418.9
403.8
8
0.550
375.3
359.5

TABLE 20
Measured vs. Fitted Detector Response for
Till
Fitting Equation : DR = GF x CC
Where : DR Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 143.5 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.465
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.839
264.0
262.2
2
1.620
232.6
239.6
3
1.432
205.5
213.6
4
1.269
182.1
188.6
5
1.128
161.9
156.2
6
1.005
144.2
143.6
7
0.898
128.9
120.0
8
0.805
115.5
103.8

TABLE 21
Measured vs. Fitted Detector Response for
Thla
Fitting Equation : DR = GF X CC
Where : DR = Measured Detector Response
GF Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 144.1 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.346
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.800
259.5
260.1
2
1.586
228.6
235.0
3
1.401
202.0
212.9
4
1.242
178.9
188.8
5
1.104
159.1
162.4
6
0.983
141.6
135.9
7
0.879
126.7
122.3
8
0.788
113.5
107.7

TABLE 22
Measured vs. Fitted Detector Response for
NJA-Th
Fitting Equation : DR = GF X CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 2436.7 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.993
Positiou
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.819
1996.7
1967.7
2
0.722
1758.5
1718.0
3
0.638
1553.5
1617.4
4
0.565
1376.4
1404.0
5
0.502
1223.0
1224.7
6
0.447
1089.5
1075.3
7
0.400
973.5
963.7
8
0.358
872.1
845.1

TABLE 23
Measured vs. Fitted Detector Response for
NJB-Th
Fitting Equation : DR = GF X CC
Where : DR = Measured Detector Response
GF Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 2267.0 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.462
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.863
1956.3
1907.0
2
0.760
1723.1
1753.9
3
0.672
1522.4
1520.0
4
0.595
1349.0
1363.2
5
0.529
1198.8
1211.4
6
0.471
1068.0
1065.1
7
0.421
954.4
943.2
8
0.377
855.1
833.2

TABLE 24
Measured vs. Fitted Detector Response for
USA
Fitting Equation : DR -- GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 181.4 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.386
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.423
258.2
261.8
2
1.253
227.4
236.4
3
1.107
200.9
209.5
4
0.981
178.0
180.6
5
0.872
158.2
165.2
6
0.777
141.0
137.2
7
0.694
126.0
118.2
8
0.622
112.9
104.6

TABLE 25
Measured vs. Fitted Detector Response for
USB
Fitting Equation : DR = GF x CC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 159.6 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.426
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.461
233.3
241.4
2
1.287
205.4
209.0
3
1.137
181.5
182.9
4
1.008
160.8
167.7
5
0.895
142.9
141.6
6
0.798
127.4
120.2
7
0.713
113.8
101.3
8
0.639
102.0
98.5

TABLE 26
Sample Physical Characteristics
Sample
Weight
(gm)
Density
(gm/ee)
Soil Weight
Fraction
(gm dry/gm wet)
Sample 2
190.0
1.66
1.0
Sample 3
125.4
1.37
1.0
Sample 4
120.0
1.31
1.0
U1
201.2
1.76
1.0
Ula
209.9
1.83
1.0
TH1
229.1
1.90
1.0
THla
208.8
1.82
1.0
NJA
132.5
1.18
0.93
NJB
142.2
1.24
0.89
USA
166.9
1.46
0.92
USB
161.9
1.42
0.95
use
183.7
1.61
0.77
USD
190.6
1.67
0.79

Ill
TABLE 27
Measured Sample Linear Attenuation Characteristics
Sample
H (136fceF)
(cm-1)
fi(l22keV)
(cm-1)
n(98keV)
(cm-1)
p(93fceF)
(cm-1)
Sample 2
0.24400
0.25061
0.29150
0.30424
Sample 3
0.22009
0.23913
0.27889
0.29308
Sample 4
0.25104
0.28282
0.33511
0.35714
U1
0.26889
0.28471
0.32173
0.33400
Ula
0.26460
0.27996
0.31671
0.32886
TH1
0.27465
0.29197
0.32623
0.33854
THla
0.26534
0.28262
0.31613
0.32782
NJA
0.25367
0.30389
0.35591
0.38495
NJB
0.25818
0.30521
0.34727
0.37231
USA
0.23116
0.24787
0.28136
0.29318
USB
0.21953
0.23533
0.26760
0.27892
use
0.24741
0.26040
0.29039
0.30022
USD
0.24413
0.25768
0.28921
0.29921

112
Peak Fitting Results
In order to verify that the peak fitting routine used in this work was indeed functioning
properly, Jfal peaks from three spectra were analyzed by PEAKFIT, the technique used
in this work, and by GRPANL. The results of this comparison are shown in Table 28.
TABLE 28
Comparison of Kai Peak Areas
as Deter minee
by PEAKFIT and G1
UPANL
PEAKFIT Area
GRPANL Area
Sample
Geometry
(Count- Channels)
( Count- Channels)
Sample 2
1
264561 1.1%
260041 0.9%
Sample 3
1
541821 0.4%
565890 0.4%
Sample 4
1
1453181 0.2%
1535171 0.2%
As can be seen from the table, the PEAKFIT results are in very good agreement
with the GRPANL results. The difference between the two peak shaping programs, which
results in the small peak area differences above, is in the way they handle background
shaping. The background shaping in PEAKFIT, described in detail in Chapter II, was
developed specifically for use in this application and more accurately accounts for the shape
of the steeply negative sloping curve on which the peak sits. GRPANL assumes a linear
background if the slope of the background is negative
Complete results of the peak fitting for each sample are listed in Tables 29 through 43.

113
TABLE 29
Peak Fit Results for Sample U1
Sample Contamination Concentration: 152.3 pCi/gm U238
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
127599 0.6%
6.1
2
118246 0.6%
5.7
3
98117 0.8%
4.1
4
96465 0.8%
4.6
5
82104 0.5%
2.5
6
67923 1.6%
2.9
7
63979 0.6%
2.6
8
56134 0.8%
6.3
TABLE 30
Peak Fit Results for Sample Ula
Sample Contamination Concentration: 164.6 pCi/gm U238
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
141648 0.4%
3.5
2
123835 0.7%
6.0
3
111115 0.5%
3.5
4
100697 0.6%
6.1
5
94625 0.8%
7.9
6
85532 0.4%
4.2
7
77306 0.5%
2.7
8
68731 0.8%
6.9

TABLE 31
Peak Fit Results for Sample NJA-U
Sample Contamination Concentration: 196.9 pCi/gm U23B
Counting Geometry
Peak Area
(Count Channels)
Reduced
X2
1
70722 0.9%
6.4
2
67460 0.9%
8.0
3
65292 0.7%
3.3
4
58533 0.9%
4.8
5
51170 0.8%
4.4
6
44378 1.1%
6.0
7
39759 0.6%
2.4
8
34988 1.2%
10.3
TABLE 32
Peak Fit Results for Sample NJB-U
Sample Contamination Concentration: 142.0 pCi/gm U238
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
53408 1.0%
7.5
2
52018 0.9%
6.9
3
45726 0.7%
3.9
4
42182 1.0%
5.2
5
38196 1.0%
6.2
6
34393 1.4%
7.3
7
31299 0.9%
2.2
8
25097 1.3%
4.1

TABLE 33
Peak Fit Results for Sample USC
Sample Contamination Concentration: 135.2 pCi/gm U238
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
65157 1.0%
13.4
2
64825 0.9%
5.1
3
61715 1.0%
7.5
4
58934 0.7%
3.7
5
50625 1.0%
4.1
6
43545 0.5%
1.5
7
41045 1.2%
5.6
8
35238 0.9%
2.8
TABLE 34
Peak Fit Results for Sample USD
Sample Contamination Concentration: 138.9 pCi/gm U238
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
77305 1.0%
14.1
2
74508 0.6%
3.3
3
66612 0.7%
3.2
4
63801 0.5%
1.9
5
56354 0.8%
3.7
6
44377 1.1%
8.1
7
38989 1.0%
6.8
8
32926 1.6%
8.8

TABLE 35
Peak Fit Results for Sample 2
Sample Contamination Concentration: 93.6 pCi/gm Th232
Counting Geometry
Peak Area
(Count-Channels)
Reduced
X2
1
264562 1.1%
56.9
2
240029 1.0%
37.7
3
212015 1.0%
31.8
4
199047 0.6%
13.2
5
166260 0.6%
11.1
6
148666 0.9%
35.1
7
127251 1.0%
24.4
8
115378 0.6%
5.9

TABLE 36
Peak Fit Results for Sample 3
Sample Contamination Concentration: 221.7 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
541821 0.4%
14.1
2
479982 0.1%
1.7
3
428292 0.2%
2.3
4
375253 0.3%
7.3
5
344559 0.3%
5.1
6
301884 0.4%
10.0
7
261608 0.4%
9.8
8
233651 0.5%
5.6

TABLE 37
Peak Fit Results for Sample 4
Sample Contamination Concentration: 683.0 pCi/gm Th232
Counting Geometry
Peak Area
(C ount- Channels )
Reduced
X2
1
1453181 0.2%
9.7
2
1287314 0.2%
10.1
3
1148003 0.2%
7.7
4
1014348 0.2%
12.6
5
899790 0.3%
12.0
6
789214 0.3%
21.4
7
710364 0.3%
11.1
8
636039 0.4%
23.5

TABLE 38
Peak Fit Results for Sample Thl
Sample Contamination Concentration: 143.5 pCi/gm Th232
Counting Geometry
Peak Area
(C omit Channels)
Reduced
X2
1
396916 0.4%
8.6
2
367607 0.4%
10.3
3
333507 0.5%
11.6
4
298668 0.5%
14.0
5
251311 0.9%
42.4
6
232490 0.5%
8.5
7
196953 0.7%
20.4
8
171638 0.8%
20.6
TABLE 39
Peak Fit Results for Sample Thla
Sample Contamination Concentration: 144.2 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
390175 0.5%
21.3
2
359972 0.7%
37.4
3
331580 0.5%
15.2
4
298234 0.5%
10.8
5
259990 0.5%
11.5
6
221465 0.4%
4.8
7
199930 0.6%
14.9
8
178059 0.7%
13.7

120
TABLE 40
Peak Fit Results for Sample NJA-Th
Sample Contamination Concentration: 2436.7 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
3062432 0.1%
2.0
2
2709169 0.1%
4.5
3
2560958 0.1%
4.6
4
2245527 0.1%
2.2
5
2002194 0.1%
4.8
6
1742420 0.2%
7.2
7
1568213 0.2%
9.7
8
1367233 0.2%
2.2
TABLE 41
Peak Fit Results for Sample NJB-Th
Sample Contamination Concentration: 2267.0 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
2896677 0.1%
4.0
2
2689680 db 0.1%
3.5
3
2364069 0.1%
5.6
4
2133681 0.1%
7.4
5
1910431 0.1%
9.7
6
1692538 0.1%
2.9
7
1507566 0.2%
12.3
8
1336647 0.2%
9.0

TABLE 42
Peak Fit Results for Sample USA
Sample Contamination Concentration: 181.4 pCi/gm Th232
Counting Geometry
Peak Area
(Count- Channels)
Reduced
X2
1
386406 0.5%
15.1
2
351203 0.4%
9.8
3
315752 0.5%
6.7
4
275494 0.6%
21.8
5
252671 0.6%
18.0
6
212386 0.5%
6.1
7
184506 0.6%
10.5
8
164036 0.6%
9.3
TABLE 43
Peak Fit Results for Sample USB
Sample Contamination Concentration: 159.6 pCi/gm Th232
Counting Geometry
Peak Area
(C ount- Channels)
Reduced
X2
1
352365 0.4%
12.0
2
310193 0.7%
21.3
3
274348 0.5%
12.0
4
253452 0.3%
2.9
5
216978 0.5%
7.2
6
185294 0.6%
13.0
7
157422 0.6%
10.3
8
153290 0.8%
18.5

122
Conclusions
1. An XRF assay technique for 7-238 and Th-232 in bulk unprocessed soil samples has
been developed.
2. The assay technique developed here provides results which are comparable in accuracy
and precision to those provided by gamma spectroscopy.
3. The assay technique developed here works well on dry homogeneous samples as well as
on actual collected samples which have not been processed.
4. The assay technique developed here does not work well on samples which are very
inhomogeneous. Samples wliich are very inhomogeneous will result in data points which
do not yield good least squares fits to straight lines. The user is free to choose the level
of significance, by using the X2 value of the straight line fit, at which he/she will
reject the calculated value of U and Th concentrations. Samples which are rejected for
being too inhomogeneous to be analyzed by this technique should be dried, ground,
homogenized, and re-analyzed.
5. The assay technique developed here requires no fudge factor to accurately determine
contamination concentrations in samples which are not processed.
6. It has been determined that approximately 15% of the fluorescent x-ray production
is due to singly scattered Compton gammas. Compton production has therefore been
included in this XRF analysis of bulk samples.
Recommended Future Work
Dased on this work there are several research areas worthy of follow-up.
1. The computer programs used for data processing should be optimized to shorten their
run times.

123
2. The sensitivity of the assay system should be determined and optimized by varying the
detector system design.
3. Recommendations as to a detector system design, which would turn the system into a
black box counting system requiring very little operator work and no operator sample
alignment, should be developed.
4. The coupling of this data processing technique to conventional gamma spectroscopic
and neutron activation analysis techniques should be explored.
5. Rotating the target sample during counting should be experimentally explored to de
termine whether this will expand the application of this assay technique to extremely
inhomogeneous samples.
6. Samples of varying inhomogeneity should be assayed to determine how sensitive the
system is to sample inhomogeneity and the accuracy of the assay of inhomogeneous
samples.

APPENDIX A
EQUIPMENT AND SETUP
System Hardware
In order to verify the theory described in the previous three sections, equipment for
the assay system was purchased or designed and fabricated. All equipment used for this
assay system was purchased specifically for this research. This includes a computer based
multichannel analyzer (MCA), an analog to digital converter (ADC), a spectroscopy grade
amplifier, a planar Ge detector, a spectroscopy grade detector power supply, a combination
source holder and detector shield, a Co-57 source for x-ray excitation and for transmission
measurements, and an Eu-155 source for transmission measurements.
The ND-9900 MCA
The brain of the system is a Nuclear Data model ND-9900 computer based multichannel
analyzer (MCA). Fundamentally, this unit receives, saves, and manipulates spectral infor
mation. The beauty of the ND-9900 is that spectral collection is run independently of other
operations. This allows full use of the systems Micro-VAX computer for analysis of an old
spectrum while a new spectrum is being collected. The Micro-VAX is a very powerful and
fast computer allowing the use of complicated spectral analysis programs.
124

125
The ADC
The MCA is fed by ail ND-582 analog to digital converter (ADC) which is, in turn, fed
by an EG&G Ortec 571 spectroscopy amplifier. The amp receives voltage pulses from the
detectors pre-amp, boosts their voltage, and sends them to the ADC. The ADC converts
each voltage pulse to a digital signal, corresponding to the energy of the x ray that created
the pulse, that the MCA can store properly in the spectrum.
The lIPGe Detector
The detector is an EG&G Ortec High Purity Ge (HPGe) Low-Energy Photon Spec
trometer. The Ge crystal has an active diameter of 36 mm (1018mm2) and a sensitive
depth of 15 mm. The detector has an intrinsic energy efficiency of approximately 83% at
100 keV. That is, out of every 100 x rays, of energy 100 keV, that hit the detector surface,
83 will deposit their full energy in the detector. This will yield a spectral peak of area 83.
The method by which this efficiency is determined will be described later.
The XRF Excitation Source and Transmission Sources
Two different radionuclide gamma ray sources are used in this research: Co-57 and
jEJu-155. The Co-57 source serves as a source of x-ray excitation gamma rays, and as a
source of transmission gamma rays. The Eu-155 source serves as a source of transmission
gamma rays. These sources emit four gamma rays that are important. These gamma ray
energies are listed in Table 5. The sources were purchased from Isotope Products, emit at
energies listed in Table 5, and have the physical characteristics described in Table 6. Three
Co-57 sources and one Eu-155 source were purchased.

126
The XRF Excitation Source Holder and Detector Shield
The Co-57 source, used to induce x-ray fluorescence in a soil target, is held in a lead
shield very close to the detector. The source holder positions the source in a known and
reproducible geometry and shields the detector from gamma rays directly from the source.
Direct shine of Co-57 gammas onto the detector would increase the spectral background.
By minimizing the number of background photons that hit the detector, counting dead time
is minimized leading to shorter count times. The shorter the count time the more samples
can be analyzed per day. Figures 5 and 9 show the shield in position over the detector.
The shield is layered to optimize its shielding ability. Figure 8 shows a photograph of the
sliield pieces.
Since Co-57 emits gamma rays of energy high enough to induce x-ray fluorescence in
any element, all shield material will emit fluorescent x rays. Each layer of shield should
therefore effectively sliield any gammas or x rays that reach it while emitting x rays that
can be shielded effectively by the next shield layer. The source holder / detector shield was
therefore designed with the first layer Pb, followed by W, then Cd, then Cu.
Lead has the highest attenuation coefficients of any of the shield materials used. Its
primary function is to shield the detector from direct gamma rays from the Co-57 source.
While the Pb stops most of these gamma rays, it also emits fluorescent x rays induced by
the gamma rays. The next layer of the shield, W, shields the detector from any gamma
rays penetrating the Pb shield and from any Pb x rays. The W, however, emits fluorescent
x rays also. The next layer, Cd, shields the detector from and gamma rays that penetrated
the previous two shields, from Pb x rays, and from W x rays. The final layer, Cu, shields
the detector from any photons reaching that level. Table A-l lists the x-ray absorption and
emission energies of the shield materials. No other major equipment is used in this research.

127
TABLE A-l
Shield Material X Ray
Emission and Absorption Energies +
Emission and Absorption Energies (keV)
Element
K*i
Ka 2
Kp i
A>2
Absorption
Pb
74.957
72.794
84.922
87.343
88.001
W
59.310
57.973
67.233
69.090
69.508
Cd
23.172
22.982
26.093
26.641
26.712
Cu
8.047
8.027
8.904
8.976
8.980
-f: X-ray emission and absorption energies were taken from Kocher.^
System Calibration
In that all the equipment used for this research arrived new, the system required calibra
tion. Calibration of the system refers to setting the amplifier gain, determining the spectral
energy calibration, determining the detector intrinsic energy efficiency, and determining
accurate source strengths.
The amplifier gain must be properly set. This is done by exposing the detector to
gamma ray sources emitting gammas in the energy range of interest. Here, Co-57 and
Eu-155, which emit gammas of energies described in Table 5, and Am-241, which emits at
about 59 keV, were used. The amplifier gain is then changed until the spectrum covers a
significant portion of the 4096 channel screen. A spectrum of the above gamma sources is
then collected at the calibrated gain set ting. The result is a spectrum consisting of peaks
which correspond to known gamma energies. The ND-9900 is equipped with a calibration
program which looks at this spectrum and asks what energies to assign to each peak. The
program then shapes each peak, to determine the peak centroid, and assigns the designated
energy to the channel number of peak centroid. Once tliis has been done for all peaks, the

128
program determines a quadratic fit to this energy vs. channel number data, completing the
energy calibration.
The detector intrinsic energy efficiency refers to the efficiency term introduced in Equa
tion 4 and used in many subsequent equations. The intrinsic energy efficiency of a detector
is the fraction of monoenergetic photons hitting the detector that are counted in the full
energy peak. That is, if 100 photons of energy 122 keV hit the detector surface, the detector
is 83% efficient at 122 keV if the area of the 122 keV peak is 83 counts. This efficiency term
is required by many of the equations in the section describing soil moisture determination
and sample inhomogeneity. The actual calibration technique will be described later.
The Isotope Products sources described in Table 5 and Table 6 also require calibration
in that the errors in listed source activities were much too large for use in precise work.
In this case, the Isotope Products sources were compared to a source of precisely known
activity to determine their true activities.
Proper technique for calibration of a source or a system requires the use of a precisely
calibrated source. The most common supplier of precision sources is the National Bureau of
Standards (NBS) in Gaithersburg, Maryland. A mixed radionuclide NBS point source was
borrowed from EG&G Ortec to perform system calibration. Standard Reference Material
(SRM) 4275-B-7 is a mixed 56-125/Te-125m, Ett-154, and Eu-155 point source having
precisely defined emission rates. Table A-2 summarizes emission rates for the energies of
interest. Table A-3 lists pertinent physical qualities of the radionuclides of interest.

TABLE A-2
NBS Source, SRM 4275-B-7, Emission Rates
129
Radionuclide
Energy
(keV)
Emission Rate
(Gammas/s)+
Uncertainty
(%)
Eu-154/Eu-155
42.8
1.102E4
1.3
Eu-155
86.6
6.320E3
0.8
Eu-155
105.3
4.365E3
1.1
Eu-154
123.1
1.510E4
0.7
56-125
176.4
1.626E3
0.6
+: Emission rates are for 1200 EST, 1 May, 1983
TABLE A-3
NBS Source, SRM 4275-B-7, Physical Characteristics
Radionuclide
Half Life
Decay Constant
56-125
1008.7 1.0 d
6.872E-4 d-1
FJu-154
3127 8
d
2.217E-4 d-1
Eu-155
1741 10
d
3.981E-4 d-1
The first step in efficiency calibration, then, was using the NBS source to determine
detector intrinsic energy efficiencies at the energies listed in Table A-2. The Physical setup
used to count the NBS source is shown in Figure A-l. The equation describing the situation
is
FL(E)=
ER(E) x AD x T) x CT
4xR\
x ATN(E),
(Al)
where
FL (E) = the gamma flux measured by the detector, ie., the
full energy peak area at energy E, (gammas),
ER(E) the emission rate of the source at energy E, (gammas/s),

130
AD = the detector area, (cm2) ,
t](E) = the detector intrinsic energy efficiency at
energy E, (gammas counted per gamma hitting the detector)
CT count time, (s),
Ri = the distance from the source to the detector, (cm),
ATN (E) = gamma attenuation, at energy E, due to the air
between the source and the detector, and the Be
window of the detector,
= exp(-jt(jE) pR)Air Xexp (-p(E) p R)Bt
and
p(E) mass attenuation coefficient for air
or for Be at energy E, (cm2/gm),
p density of air or Be, (gm/cm3) ,
R = the thickness of the air or Be layer
through which the gammas pass, (cm).
By counting the NBS source,positioned at a known distance directly above the detector,
FL(E) can be measured. The only unknown in Equation A-l is i](E), which can then be
calculated at the five energies listed in Table A-2. This includes 86 keV and 105 keV,
the emission energies of Eu-155. In order to insure statistical significance, twelve separate
measurements of the NBS source were made at twelve different distances from the detector.
Average values for i](E) were determined and used in subsequent calculations.
Once the detector intrinsic energy efficiency had been determined for the two Eu-155
energies, the Isotope Products sources could be calibrated.
Again using Equation A-l, the Isotope Products Eu-155 source was counted. Now the
unknown in Equation A-l was the source emission rate, ER(E), which could be determined

131
by rearranging the equation. As with the NBS source, twenty measurements of the Eu-
155 source were made to insure statistical significance. Average values for ER(E) were
determined and used in subsequent calculations.
To determine the precise activities of the Co-57 sources using the same method as
above, the detector intrinsic energy efficiency at 122 keV was needed. The efficiency data
from the NBS source was fit to a curve and the detector intrinsic energy efficiency at 122
keV was determined from the curve. Keeping in mind that the area of the spectrum that
is of interest extends only from 86 keV to 136 keV, only three efficiencies were used to fit
a quadratic curve. The efficiencies at 86 keV, 105 keV, and 123 keV were chosen because
they are all within the energy range of interest.
The data point at 176 keV was too far from the area of interest to be used. The shape
of the efficiency curve is a function of the detector and the associated electronics. While the
shape of this curve can be approximated as quadratic over a limited energy range, extending
that range beyond necessary limits is questionable. The fitted curve was thus only able to
provide information as to the efficiency at 122 keV.
Using Equation A-l then, the emission rates of the three Isotope Products Co-57 sources
were determined in the same manner as the Eu-155 emission rates were determined. Only
the 122 keV peak was used. For Co-57 the relative yields of the 122 keV and 136 keV
gammas are well known and are listed in Table 5. The emission rate of the 122 keV gamma
(gammas/s) is equal to source activity (dis/s) times gamma yield (122 keV gammas/dis).
The measured 122 keV emission rate was thus used to determine the source activity in
disintegrations per second, and in Curies. This activity also applies to the 136 keV gamma.
As with the NBS source and the Eu-155 source, twenty measurements of each Co-57 source
were made to insure statistical accuracy. Average values of source strength (Ci) for each
Co-57 source were determined and used in all subsequent calculations.

132
In order to determine the detector intrinsic energy efficiency at 136 keV, Equation A-l
was rearranged slightly.
V ^ ER (E) x AD xCT x ATN (E)
FL (E) x 4irRl
(A2)
where all terms are as previously defined.
Since this equation is valid for any energy at which FL(E) is measured, the ratio of
i](E 1) to r/(E2) is
J7(£x) FL{E1) ,,ER{E2) w ATN{E2)
tj (E2) ~ FL(E2) X ER (Er) X ATN (Ei)"
(A3)
Therefore, given Ex = 136keV and E2 = 122feeF, the above equation can be solved
for 7/(13GkeV). The spectra that were used to determine the Co-hl source emission rates
contained peaks at 122 keV and 136 keV. These spectra were therefore used to determine
tj (13GkeV).
The calibration process thus determined precise source strengths of the Isotope Products
sources, as well as the detector intrinsic energy efficiency at 86 keV, 105 keV, 122 keV, 123
keV, and 136 keV. The resulting data is presented in Table A-4.
It should be noted that in order to precisely calculate the above efficiencies and source
strengths, a precise knowledge of the system geometry was needed. The distances from
source to detector were measured to within 1 mm, and the source was centered over the
detector using a plum-bob and a laser. The mass attenuation coefficients used were also
precisely known, the choice of which bares some discussion.

TABLE A-4
System Calibration Parameters
Detector Intrinsic Energy Efficiency:
Energy (keV)
Efficiency
136.476
0.6934
123.073
0.7609
122.063
0.7656
105.308
0.8302
98.428
0.8493
93.334
0.8609
86.545
0.8736
Source Strengths:
- Co57
1 October, 1986
Source #
Activity (mCi)
1
2.022
2
2.207
3
2.388
- Eu165
Gamma Energy (keV)
Emission Rate (Gamma/s)
105.308
1.8250xl07
86.545
2.5484a:107

134
Mass Attenuation Coefficients
Photons traveling from a source to a detector, through any material, will reach the
detector if they are aimed properly and if they do not undergo an interaction which changes
their direction or energy. For a source that emits photons isotropically, those photons which
are emitted into the solid angle subtended by the detector are properly aimed. Thus if the
source emits S gammas/s, then the number of gammas per second that are emitted into the
proper solid angel is
Sd =
S x AD
4wR2
(A4)
where
Sd = the number of photons/s that enter the
solid angle subtended by the detector,
AD = detector area, (cm2),
R the distance from the source to the
detector (cm).
But not all the photons that are properly aimed will reach the detector. Photons can
undergo several types of interactions with atoms of the medium between the source and
the detector. Photons can be completely absorbed. Photons can undergo photoelectric
interactions, yielding an electron-positron pair. Photons can undergo compton scatter,
yielding a scattered electron and a gamma of new energy and new direction. Or photons
can undergo coherent scatter, yielding a gamma of unchanged energy but traveling in a
slightly altered direction.
But not all of these interactions will necessarily remove a photon from the beam. Here
removal means that a photon which entered the solid angle subtended by the detector is

135
prevented from reaching the detector with its energy unchanged. Photons which coherently
scatter at small angles will still reach the detector.
Then, the logical question is; What mass attenuation coefficients are we looking for?
Mass attenuation coefficients are used in the calculations to calibrate the system, in trans
mission measurements to determine soil attenuation properties, and in inhomogeneity cal
culations. Based on the following discussion, the removal mass attenuation coefficient is the
correct coefficient to use in all calculations.
Ah = fit fie,
(A5)
where
fiT = removal mass attenuation coefficient,
(cm? /gm),
// = coherent scatter mass attenuation coefficient,
(cm? /gm),
Ht = total mass attenuation coefficient,
(cm? I gm),
= Ah* + Ah* + AV + Pppi
fii, incoherent (compton) scatter mass
attenuation coefficient, (cm?/gm),
HPe = photoelectric mass attenuation
coefficient, (cm2/gm),
Hpv pair production mass attenuation
coefficient, (cm?/gm).
The theoretical justification for using the removal, rather that the total, mass atten
uation coefficient is as follows. Generally attenuation measurements are made using a

136
columnated beam. With a columnated beam small scatter angles will remove photons from
the beam. But the application of the attenuation coefficients measured here is a broad
beam situation. So for every gamma that coherently scatters out of the beam, another will
coherently scatter into the beam.
Consider the situation of a Co-57 source shining gamma rays isotropically on a cylin
drical soil sample. Remember that the soil sample is thought of as approximately 2000
individual volumes, each small enough to be described using point source mathematics (see
assay section). Considering a single point, the Co-57 source emits gammas isotropically,
some of which are aimed at the point in question. Of those gammas aimed at the point,
some will coherently scatter out of the beam that will reach the point. Some gammas that
are almost aimed at the source will coherently scatter into the beam that will reach the
point. Only those gammas that incoherently scatter, have photoelectric reactions, or un
dergo pair production reactions will be removed from the beam. Note that very small angle
incoherently scattered gammas should act the same way as coherently scattered gammas,
ie. some should scatter out of the beam while others scatter into the beam. This is only
a small fraction of the incoherent scatters and makes little statistical difference, unlike co
herent scatters which are all at very small angles.Thus the removal mass attenuation
coefficient properly describes the situation. The same argument can be made for the mass
attenuation coefficient which describes the transport of the fluorescent x rays from a point
in the soil to the detector.
To properly measure this coefficient, then, a broad beam should be used. This is
the technique that is described earlier in the system calibration section. The following
experimental evidence confirms the choice of the removal mass attenuation coefficient.
Looking at the calibration geometry in Figure 14, photons leaving the source encounter
several attenuating materials on their way to the detector. The capsule that holds the

137
source is made of stainless steel and has a .0254 cm stainless steel window. Between the
source and the detector is a large body of air. And finally, a .0254 cm Be window covers the
Ge crystal detector. Any additional objects put between the source and the detector also
attenuate photons. Thus the number of photons that reach the detector and are counted
in the full energy peak can be described by
FL (E) =
ER(E) AD tj(E) CT
4 tR\
ATN (E),
(A6)
where
FL (E) = the gamma flux measured by the detector, ie., the
full energy peak area at energy E, (gammas),
ER(E) = the emission rate of the source at energy E,
(gammas/s),
AD = the detector area, (cm2) ,
Tj(E) = the detector intrinsic energy efficiency at
energy E,
(gammas counted per gamma hitting the detector)
CT = count time, (s),
Ri = the distance from the source to the
detector, (cm),
ATN (E) = gamma attenuation, at energy E, due to the
stainless steel source capsule, the air
between the source and the detector, any other
object put between the source and the detector,
and the Be window of the detector,
= exp(~p(£) p0 R) x exp (~p{E) p0 R)Air
x exp {-fi(E) p0 R)obj x exp (/x (E) p0 R)Be,

138
and
p(E) removal mass attenuation coefficient
for stainless steel (SS), for air, for an
object in the beam, or for Be, at
energy E, {cm2¡gm),
Pq density of stainless steal, orair, or an object in the beam, or Be,
(gm/cm3),
R = thickness of stainless steal, or air,
or an object in the beam, or Be,
(cm).
To verify that it is proper to use the removal mass attenuation coefficient, and not the
total mass attenuation coefficient, the mass attenuation coefficient of water was measured
at four energies and compared to literature values. In order to ensure consistency, two data
sets were used in calculations. The first set consisted of total mass attenuation coefficients.
The second set consisted of removal mass attenuation coefficients. Again to ensure consis
tency, the system was calibrated, including detector intrinsic energy efficiencies and source
strengths, using both data sets. Both calibration calculations were performed on the same
set of spectral data, but each calculation used a different mass attenuation coefficient set.
The above calculations constituted calibrating the system twice, once for each mass
attenuation coefficient data set. This completed, a plastic soil jar was placed, empty, be
tween the source and the detector and twenty counts of one hour each were collected. In
Equation A-6, the plastic jar becomes the attenuating object. The attenuation of this jar
was determined by rearranging Equation A-6.

139
exp (-n{E) p R)olj = (A7)
FL{E)
ER(E)xADxr,[E)xcT x exp (-// (E) pR) x exp (-mu(E)pR)AiT x exp {-p(E)pR)Be,
where all terms are as previously described.
Using Equation A-7 the fraction of photons which are transmitted through the plastic
jar unchanged was calculated using both mass attenuation coefficient data sets. The av
erages of the twenty values for each data set were used as the jars attenuation factors for
each data set.
Next, the jar was filled with water and the twenty counts of one hour each were repeated.
Since another attenuating material, water, was been placed in the beam, another term was
added to Equation A-7. Equation A-7 can then be used to determine the attenuation factor
for water.
exp {-(i{E) p R)Hj0 = {AS)
FL (E)
E*{s)*ADgi{E)*CT x exp(-p(E)pR),, x exp{-mu(E)pR)Mr x exp{-p{E)pR)obj x exp(-p(E) pR)Bt
where all terms are as previously described.
Remembering that the object of this experiment was to measure the mass attenuation
coefficient of water, the value of the right side of Equation A-8, K(E), was calculated for
each data set for each of the twenty counts. Equation A-8 was then be rearranged to solve
for p (E)Hi0.
p{E)h,o =
h(g(g))
(po R)h,0
(A9)

140
where
fi {E)u_¡0 = the measured mass attenuation
coefficient at energy E, for water,
{cm2/gm),
In {K (E)) = the natural log of the right hand side
of Equation A 8, (nounits)
Po = the density of water
= 1 gm/crn3
R = the effective diameter of the plastic
water jar, (cm).
In Equation A-9, R is represents the average distance that each photon traveled through
the water. Since the jar is curved and since the path from the source to the detector is
actually a three dimensional solid angle, the average path length for a photon in the water
must be calculated numerically. This done, the mass attenuation coefficients for water were
calculated. The results of these calculations are shown in Table A-5.
TABLE A-5
Water Attenuation Coefficients
fi{E)Hj0, Actual and Calculated Values -f
Energy (keV)
Actual
ft (e)ITi0
Total
{cm2/gm)
Actual
A* (E)ir2o
Removal
{cm2/gm)
Calculated
A4 {E)H3o
{cm2 ¡gm)
136.476
0.1559
0.1526
0.1512 0.0003
122.063
0.1617
0.1576
0.1554 0.0001
105.308
0.1685
0.1634
0.1610 0.0002
86.545
0.1793
0.1719
0.1696 0.0004
+: Actual values from Hubble ^3.

141
Table A-5 lists only one set of calculated values because the calculated value of // (E)If_¡0
did not vary with data set. This means two things. First, that the removal attenuation
coefficient fits the data better than the total attenuation coefficient. This is evident since
both data sets yielded the same coefficients. Second, that coherent scatter in the source
stainless steal window, in the air between the source and the detector, and in the detector
Be window, is an insignificant contributor to the situation. This is evident, again, because
whether or not the coherent scatter attenuation coefficient was included, the calculation
yielded the same answer.
A second experiment, which supports the same conclusions, was also conducted. The
mass attenuation coefficient of water was measured with the jar center located 12.1 cm,
16.6 cm, and 21.0 cm from the detector. Twenty counts were performed at each location.
The average values h(E)Hi0 are listed in Table A-6.
TABLE A-6
n(E)h2oi Calculated Values
vs. Target Distance from the Detector +
Distance
pi (136AreV)Ha0
fi (122keV)Hj0
(cm)
(cm2/gm)
(cm2/gm)
12.6
0.1509 0.0004
0.1551 dh 0.0001
16.6
0.1512 0.0003
0.1553 0.0001
21.0
0.1512 0.0003
0.1554 0.0001
+: The reported standard deviations are calculated using repetition statistics only.
Although the average of the twenty measurements at 12.6 cm is within the error bounds
of the average values of the measurements at the other two distances, there is a statistical
difference between the first and the second two averages. This is due to low angle incoherent
scattering. When the target is close to the detector, the angle at which photons can inco
herently scatter and still ldt the detector is larger than when the target is farther from the

142
detector. The results of this experiment also confirm that the contribution of incoherently
scattered photons is small.
Pulse Pileup
Pulse pileup is a well known phenomenon that occurs in counting systems. Each de
tected photon results in a voltage pulse that travels from the detector, through the pre
amplifier, through the amplifier, through the ADC, and into the MCA. Each devise requires
a finite amount of time to process each pulse. If a second photon strikes the detector and
generates a second voltage pulse before the first pulse has had time to be completely pro
cessed, the pulses can pile up. This usually occurs in the amplifier and the ADC.^4>25
Pileup in the ADC is usually handled by circuitry that only allows a new pulse to enter the
ADC once it is free of the last pulse. This is known as live time correction. Pulse pileup in
the amplifier, however, is better accounted for by calculation of a correction factor.^.
The ND-9900 is equipped with a program to properly account for amplifier pulse pileup.
The correction factor used is described by R. M. Lindstrom and R. F. Fleming.This
correction factor was applied to all data used for system calibration.
Compton to Total Scatter Ratio in Soil
As mentioned in Chapter II, it is necessary to know the approximate ratio of the
compton scatter coefficient to the total linear attenuation coefficient for soil. This ratio is
used in calculating the production of fluorescent x rays due to compton scattered gammas
from the excitation sources. It was first determined that this ratio in soil is relatively
independent of soil trace constituents. It was then determined, using the computer code
XSECT, what the ratio actually is for soil at various gamma energies.

143
To determine this ratio, John Hubble of the National Bureau of Standards was con
tacted. From this conversation it was determined that trace elements in soils do not con
tribute significantly to the ratio of compton scatter cross section to total linear attenuation
coefficient. This was then tested using the computer code XSECT at Oak Ridge National
Laboratory. XSECT is a data base type program which calculates cross sectional data for
a mixture of elements given the elements of the mixture and their weight fractions.
Several compositions of soil were used. Ryman et al. ^ sampled the compositions of 19
soil samples to determine a representative average composition. This average composition
was used to investigate gamma ray doses at air- ground interfaces, thus it is very applicable
to this work. The composition used is listed in table A-7. Four other soil compositions, from
Kerr et al. which were determined for areas near the Hiroshima and Nagasaki bomb sites
for neutron dose studies, were also used and are listed in table A-7. Finally, the composition
of sand, Si02, was used. Table A-8 lists the compton to total ratios at 150 keV and 100
keV for each of these soil compositions. These ratios were determined from data calculated
using XSECT. Finally, table A-9 lists the average ratio values at 150 keV and 100 keV,
and the linearly interpolated values at 136.476 keV and 122.063 keV. These are the values
which were used in the program COMPTON.FOR to determine the rate of fluorescent x-ray
production by compton scatter gamma.
As can be seen from these tables, the compton to total scatter ratio for soils is relatively
constant for various different soil compositions. This consistency justifies the use of this
ratio in the calculations of Chapter II.

TABLE A-7
Representative Soil Elemental Compositions
Elemental Weight Fraction
Element
SI
S2
S3
S4
S5
S6
II
0.02798
-
0.03
0.011
0.005
0.005
Si
0.09414
0.4674
0.29
0.334
0.350
0.400
A1
0.03750
-
0.04
0.099
0.064
0.055
K
0.01060
-
0.01
0.035
0.007
0.020
Ca
0.00965
-
0.01
0.008
0.005
0.011
Fe
0.01652
-
0.02
0.058
0.018
0.017
0
0.06361
0.5326
0.60
0.455
0.551
0.492
Total
1.00000
1.0000
1.00
1.000
1.000
1.000
SI: Average soil composition from Ryman et al.^,
S2: Composition of Sand, Si02,
S3: Soil composition at Hiroshima Bomb Dome,^
S4: Soil composition at Hirosliima Castle,
S5: Soil composition at Nagasaki Hypocenter Monument,
S6: Soil composition at Nagasaki University.^
TABLE A-8
Compton to Total Scatter Coefficient For Soils
at 150keV and 100 keV
Case #
CTR @ 150 keV
CTR @ 100 keV
SI
0.90996
0.78854
S2
0.93484
0.84490
S3
0.92822
0.83065
S4
0.94019
0.85854
S5
0.94076
0.86029
S6
0.93902
0.85526

TABLE A-9
Average Compton to Tota
Scatter Ratio for Soil
Energy (keV)
CTR Avg.
150
0.93212
136.476
0.90712
122.063
0.88048
100
0.83970

APPENDIX B
UNSUCCESSFUL ANALYSIS TECHNIQUES
During tliis work, it became evident that two portions of the data analysis technique,
which originally looked very promising, would not work. The failed techniques were aban
doned in favor of other ideas which did work, however there is value in describing the failed
techniques and why they failed. The most important of the two techniques was that which
allowed the analysis of samples which were very inhomogeneous. The other failed analy
sis technique was that which allowed soil moisture analysis by use of transmission gamma
rays. Further investigation showed that both techniques failed for the same reason. This
appendix will discuss both analysis techniques and the reason that they failed.
Sample Inhomogeneity Analysis
The sample geometry used for the assay technique which proved to be successful is
described in Chapter II. The inhomogeneity analysis which is described here uses this same
geometry and the same mathematical description of the system.
If the soil sample is divided mathematically into small point sources then FS(E) is
equal to the contribution of a point source, with an elemental concentration of 1 pCi/gm of
dry soil, to the full energy peak. The equation which delines FS(E) is listed in Chapter II.
The full energy peak area is then equal to the sum of the contributions from all the point
sources. FS(E) can be thought of as a Geometry Factor which, when multiplied by the
146

147
elemental concentration of U or Th at the point source, equals the contribution of the point
source to the full energy peak.
The first step to properly assaying an inhomogeneous sample is to mathematically
divide the sample into point sources. This involves knowing the spatial relationships among
the excitation source, the target sample, and the detector. Figure 3 shows this geometry.
Then, together with the sample mass attenuation coefficients and water content FS(E) can
be calculated for each point source. Once FS(E) is known for all points, the full energy
peak area of an unknown sample is a function of those known geometry factors and the
unknown point concentrations.
Suppose that an unknown target sample is divided into N point sources. Then by mak
ing one spectral measurement, the full energy peak area is equal to the sum of the N known
geometry factors, FS(E), times their respective N unknown elemental concentrations. If
the target cylinder were rotated by 360/N degrees and the mathematical integrity of the
N points was maintained, a second spectral measurement could be taken. New geometry
factors could be calculated for each point source, now rotated slightly from its original po
sition. The area of the full energy peak for the new spectrum would be the sum of the
new geometry factors multiplied by their respective unknown concentrations. Note that
since the point sources have maintained their spatial identity, the unknown elemental
concentrations are the same as before. Then by taking N measurements, each after rotating
the target cylinder 3G0/N degrees, a system of N equations and N unknowns would be de
veloped and could be solved. The total elemental content of U or Th in the target cylinder
would be the sum of the N unknown concentrations times their respective point volumes.
Mathematically, a 500 ml cylinder, 10 cm tall and 4 cm in radius, must be divided into
approximately 2000 point sources before it can be adequately modeled using point source
mathematics. This was determined by use of a computer model, using the fluorescence

148
equations just developed, and dividing the cylinder into successively larger numbers of
points. The fluorescent signal at the detector for a 2000 point model was less that .1%
different from the fluorescent signal for a 1500 point model. The model size was thus
chosen as 2000 points.
A model of 2000 points will yield a system of 2000 equations in 2000 unknowns, and
this is well beyond the limit of that which can be solved precisely by a computer. The
computer time and the round off error for such a task are both unacceptably large.
To formulate a problem that is manageable, the point sources can be grouped into
homogeneous zones such that a sample is made up of only 15 to 30 zones. Since the zones
are assumed to be homogeneous, the contribution of each zone to the area of the full energy
peak at energy E will be the sum of the point source geometry factors from the points in
the zone times the unknown zone concentration. A system of from 15 to 30 equations in
15 to 30 unknowns can be solved precisely by a computer. Practically speaking, when soil
is dug out of the ground and placed into a 500 nd jar, a few homogeneous zones are more
likely to exist than many discrete point sources.
However, practically speaking, 15 to 30 measurements of perhaps an hour each is very
time consuming. To alleviate this problem, one can make use of the fact that cylinders are
symmetrical with respect to rotation. That is, as the cylinder is rotated and counted at
discrete intervals, the function of full energy peak area, AREA(0), versus rotational angle
will be periodic with period 2n. For a homogeneous sample, a graph of AREA(0) vs. 9
would be a straight line, constant at one value. For sample containing a single point source,
the graph would be a sine function. Practically, most samples of soil dug up and put into
a jar will be somewhere in between but probably closer to homogeneous. Thus a slowly
varying curve is expected. Such a curve could be fit given eight points or so within one
period. Thus eight measurements could be made and from these points a curve could be fit

149
from which any other needed points could be calculated. The system of 15 to 30 equations
could be developed with from four to ten measurements.
By solving this system of equations one can estimate the unknown concentrations in
each zone. By multiplying the concentration in each zone by its corresponding zone volume,
the number of pCi in each zone is found. Then, by summing the number of pCi in all zones
and dividing by the total mass of dry soil in the sample, the average concentration of U or
Th in the soil is found, pCi/gm of dry soil which is the desired final result of the analysis.
It should be noted at this point that this technique is similar to imaging techniques
used in early computer assisted tomography (CAT) or positron emission tomography (PET)
scanning. But both CAT and PET perform much more detailed scans of the object being
imaged, using pencil beams to view small tracks through the object being imaged. Then
many of these tracks are summed and processed to reconstruct an image of the original
object This work, instead, looks at radiation emanations from the whole object all at
once and develops a set of equations by looking at the whole object from several discrete
views. While this system of equations has no unique solution, all solutions will yield the
same value for the average concentrations of radionuclide in the object. And since the
average value is all that is needed, more complex imaging techniques are not necessary.
Thus while the radionuclide concentrations determined for each zone will probably not be
correct, tlieir average will be correct.
Reasons for Inhomogeneity Analysis Failure
Unfortunately, this analysis technique does not work. The system of eight equations
that must be solved to determine the contamination concentration in a soil target is very
close to singular and thus cannot be solved explicitly. The reason that the system is nearly
singular is that the equations are not fully independent. As will explained, the equations

150
could be made to be independent by varying experimental conditions, but the changes
necessary would cause the measured peaks to drop substantially in size such that accu
rate measurement of peak areas would become impossible. The inhomogeneity analysis
technique, while theoretically possible, is not practically applicable.
To reiterate the theory of the analysis technique briefly, each jar of soil is measured
at eight positions relative to a detector. Each position is 3 mm farther from the detector
than the last. The target is broken into 3840 nodes, each of which acts approximately
as a point source. From the geometry of each position and the measured soil attenuation
properties, a Geometry Factor (GF) for each node is calculated. The sum of each GF times
the contamination concentration at each node is equal to the measured peak area for each
position. New GFs are calculated for each of the eight positions. The 3840 nodes are
grouped into eight zones; the GF of each zone is equal to the sum of the GFs of the nodes
in the zone. Assuming that each zone is contaminated uniformly, this yields a set of eight
equations in eight unknowns. This is the set of equations that is nearly singular. This arises
because the spacing between measurements is oidy 3 mm and the GFs are nearly the same.
This can be seen mathematically by looking at the Condition of the matrix.
G. E. Forsythe et al.^ define the Condition of a matrix as being similar to the inverse
of the matrix determinant. Thus a matrix which is singular, ie. determinant = 0, has a
Condition that is infinite. Practically speaking, the condition of a matrix should not be
much higher than 10 if the matrix is well behaved. Forsythe gives a fortran program for
solving a system of linear equations, using Gaussian elimination, which also determines a
lower bound for the matrixs condition. This is the program which was used to solve the
system of equations that I described above.
To study the effect of relative target separation, from position to position, on matrix
condition, the inliomogeneity analysis program was altered such that it looked at a target

151
with only two zones, not eight as described above. In this analysis then, all that was
necessary was data from the target counted at only two positions. This would show what
effect relative target separation, from position to position, would have on the condition of
the resulting matrix. The measurements used for the analysis and the resulting matrix
conditions are listed in Table B-l. Figure B-l is a graphical representation of this data.
Table B-2 shows the measured peak area verses target-detector separation. Figure B-2
shows shows this data graphically.
TABLE B-l
Relative Sample Separation vs.
Solution Matrix Cone
ition
Positions
Relative Separation
(mm)
Matrix Condition
1 & 2
3
2680
1 & 3
6
1493
1 & 4
9
1112
1 & 5
12
932
1 & 6
15
834
1 & 7
18
778
1 & 8
21
746

FIGURE B-l
Relative Sample Separation vs. Solution Matrix Condition

Matrix Condition
0
100

154
TABLE B-2
Target-Detector Distance vs.
Measured Peak Area
Target-Detector
Distance (cm)
Peak Area
(counts)
10.5
541821
10.8
479982
11.1
428292
11.4
375253
11.7
334559
12.0
301884
12.3
261608
12.6
233651
It can be seen from Table B-l and Figure B-l that as the separation between positions
becomes greater, the resulting matrix equations become more well behaved. This makes
sense intuitively since the relative GFs are also becoming much different as the relative
target separation increases. Then, if a truly well behaved matrix should have a condition
of approximately 10, the curve in Figure 1 can be extrapolated to determine the required
relative target separation. From the crude (and conservative) line drawn on Figure B1 it is
estimated that the matrix condition will be 40 at a target separation of 70 mm.
Moving now to Table B2 and Figure B2, it can be seen that the decline in detector
signal as the target moves away from the detector is very close to exponential. This line
may be fit to the curve,

FIGURE B-2
Target Detector Distance vs. Measured Peale Area

Measured Peak Area
(CountChannels)
15G

157
Area = 3.6E7 X Exp (A X Distance).
Using this equation we arrive at a detector response of 32872 counts for the target at
17.5 cm (thats position #1 + 7 cm). For the target at 24.5 cm (position #1 + 14 cm),
the predicted detector response is 1989 counts. For the target at 31.5 cm the predicted
detector response is just 120 counts. Thus to maintain proper relative target separation of
7 cm and to approximate a sample as having only four zones, the peak area of the fourth
count would be statistically very small. Based on experience with the experimental detector
system used for this work, a peak this small would not be detectable. The validity of the
peak from the third position is also questionable from a detectability standpoint. As such,
having eight measurements is not possible. In performing an analysis on a sample which is
very inhomogeneous, more than two zones are necessary, yet based on this analysis more
than two zones is not practically possible.
The types of things that could be done to make the system work are larger and/or
more detectors, and longer count times. The use of larger and/or more detectors makes
the system far less portable and the computer analysis far more complicated. Both of these
push the system out of the field analysis arena. And while longer count times would
make peak areas larger, there would still exist a large difference between measured peak
areas from position to position, and this would have a destabilizing effect on the matrix
(large round ofF errors). As such, this analysis technique for inhomogeneous samples is
theoretically possible, but is actually an idea whose time has not yet come.

158
Soil Moist ure Content Analysis
Originally, transmission gamina rays were to be used to determine the moisture content
of each sample. The following is a description of this failed technique.
For a moist soil sample, the sample weight can be thought of as partially due to water
and partially due to everything else. In this case, everything else is the soil, the minerals
in the soil, the air in the soil, etc. In essence, everything else is an unknown composition
of stuff. This stuff will, from now on, be called soil.
Thus, the mass of the sample, M, equals the mass of water, M, plus the mass of soil,
M,. If the volume of the sample is V, then the density of the sample, p0, is
M
Po y,
Mw + M,
~ V
_ M,
~ V + V
= Pv, + P.-
where
pw water bulk density in the sample
(gm of water/cm3 of sample),
p, soil bulk density in the sample
(gm of soil/cm3 of sample).
The value of this equation is that, since the total sample mass and volume can be
measured, the density of the soil can be expressed in terms of the measured total density
and the unknown water density
P. ~ P Pv,-

159
The value of this equation will become clear from the ensuing discussion. The Mass
Attenuation Coefficient, /x, mentioned above, is a function of energy. It is also the sum of
the Mass Attenuation coefficients of its composite parts. That is
fl x p = flw x pw + fl, x p
where
fly, = mass attenuation coefficient for water at the
energy of interest {cm2 ¡gm of water) ,
pw water hulk density [gm of water/cm3 of sample),
fi, = mass attenuation coefficient for soil at the
energy of interest {cm2¡gm of soil),
p, = soil bulk density {gm of soil ¡cm3 of sample) .
But
P. = P~ Pvn
therefore
fi X p = fiw X pw + fi, X [p pw).
Since, for the energy of interest, the mass attenuation coefficient for water can be looked
up in a table, and p is a measured quantity, this is an equation in two unknowns; fi, at
the energy of interest (fi, (E)) and p0. This expression for fi X p can now be put into
the Equation 1, which describes the attenuation of gammas by some medium. A source-
attenuator-detector system can be set up and A(E) can be measured. Assuming that source
strength, relevant distances, and attenuator thickness can be accurately measured, again,
we have an equation in two unknowns. By taking the natural log of both sides of that
equation and rearranging tilings slightly, the equation becomes

160
^ ^ ^ 111 (E^) ^ ^ P'B) (- 1)
where
a: = the thickness of the soil sample (cm),
A (E) = the measured full energy peak area at
energy E, (counts),
K (E) a grouping of constants as follows,
_ A0 (E) X Area x tj (E) X CT
4 7T r2
and
Aa (E) = source gamma emission rate at energy E,
(Gammas / s),
Area = detector surface area (cm2),
i] (E) detector intrinsic energy efficiency at
energy E, (NoUnits),
CT = total counting time (s),
r = distance from source to detector (cm).
Tlie left hand side of the equation is made up of measured or known quantities. Thus
we have one equation with two unknowns, p, (E) and pw.
Fortunately, p, (E) can be described, over a small energy range, by the following func
tion

161
In (us (E)) = A + B In (E) + C (In (E))2 ,
or
H, (E) = exp [A + B In (E) + C (In (E))2) ,
where A, B, and C are constants.
If this expression is put into Equation B-l, the result is one equation in four unknowns.
Since, however, the above expression is valid over a small energy range, four measurements
at four different energies (El < E2 < E3 < E4) can be made and that system of equations
can be solved for Row, A, B, and C. As with the peak fitting, this system is solved using a
least squares fitting technique such that the four unknowns are determined. A, B, and C are
then used to determine fi, (E) ,El account for sample inhomogeneity in the determination of U and Th concentrations. The
gamma rays chosen are from Co-57, 122 keV and 136 keV, and from Eu-155, 86 keV and
105 keV. This range encompasses both Kal energies from U and Th (see Table 4) and is
narrow enough such that /(E) can be modeled as a quadratic in In (E). The techniques
developed for processing this information into U and Th concentrations are discussed in the
next section.
Reasons for Soil Moisture Content Analysis Failure
The above described moisture analysis technique relies upon the solution of a set of
four simultaneous equations. As with the inhomogeneity analysis, this set of equations is
very close to singular and thus is not be solved explicitly. In this case, the energies of the
chosen gamma rays are too close together such that the attenuation coefficients are too close

162
together. The equations are therefore not wholly independent and the system of equations
to be solved is close to singular.
In order to remedy this situation, gammas of more widely spaced energies could be
chosen. Unfortunately, the equation which approximates linear attenuation coefficients as a
function of energy is applicable only over a limited energy range. Beyond that range there
is no single function which adequately describes linear attenuation coefficients as a function
of energy. Because of this, the above described soil moisture content analysis technique was
abandoned in favor of simply weighing each sample before and after it was put into a drying
oven or microwave.

APPENDIX C
COMPUTER PROGRAMS
Peak Shaping Programs
Three programs were written to properly determine the area of x-ray peaks. All three
of these programs are written in IBM BASIC, were run on an IBM personal computer,
and are described in Chapter II. POLYBK.BAS determines the shape of the 4th order
polynomial background beneath the x-ray peak. BKG.BAS uses the polynomial fit deter
mined by POLYBK.BAS and completes the background calculation by attributing half of
the background to the polynomial and half to a numerically calculated compensated error
function (erfc). This background is then subtracted from the spectrum and the remaining
peak is stored. PEAKFIT.BAS then performs a least-squares fit on the stored peak data to
determine the Voigt Peak parameters and uses these parameters to numerically calculate
the peak area.
163

164
2REM **********************************
3 REM *
4 REM POLYBK.BAS *
5 REM with Error Analysis *
6 REM *
7 REM **********************************
8 REM
10 DIM X(50),Y(50),A(50,9),TA(9,50),F(50),DY(50),V(9),DF(2),DS(9)
20 DIM XT(50),YT(50),S(50),K1(5),K2(5),V0LD(5),SL(5),HLD(9,9),H(50,5)
30 DIM Ql(50,50),Q2(9,50),Q3(9,50),AA(9,9),DT(9,1),AM(9,10),DA(9)
40 DIM C0V(9,9), SIG(50), C0EF(9)
50 W1 = 1
55 PI = 3.141592653#
90 PRINT How many of the Right Background points should be
92 PRINT used for the background polynomial fit?
94 INPUT RF
96 PRINT
100 PRINT Input the Order of the Polynomial to be fit
105 INPUT 01
110 M = 01 + 1
116 PRINT
119 PRINT Input the name of the Spectrum data file
120 INPUT BK$
122 OPEN I*, #1, BK$
126 INPUT #1, DP
130 INPUT #1, LB
134 INPUT #1, RB
140 FOR I = 1 TO DP
150 INPUT #1, XT(I)
157 NEXT I
158 FOR I = 1 TO DP
165 INPUT #1, YT(I)
170 NEXT I
175 CLOSE #1
180 FOR I = 1 TO LB
185 X(I) = XT(I) XT(1)
190 Y(I) = YT(I) / 5000
195 NEXT I
198 J = DP RB + 1
200 FOR I = (LB + 1) TO (LB + RF)
205 X(I) = XT(J) XT(1)
210 Y(I) = YT(J) / 5000
215 J = J + 1
220 NEXT I
225 PRINT Background Data Points"
230 PRINT
235 PRINT X(I)", Y(I)"
237 PRINT

165
240 N = LB + RF
245 FOR I = 1 TO N
250 PRINT X(I),Y(I)
260 NEXT I
265 PRINT
280 PRINT Points for Initial Parameters Guess
285 PRINT
290 PRINT X(I),Y(D
295 PRINT
300 S3 = INT (N / (M 1))
310 FOR I = 1 TO H
320 J = 1 + (I 1) S3
325 IF J > N THEN J = N
330 K1(I) = X(J)
340 K2(I) = Y(J)
345 PRINT K1(I),K2(I)
350 NEXT I
355 PRINT
360 FOR I = 1 TO H
370 FOR J = 1 TO H
380 AA(I,J) = (Kl(D) ** (J 1)
385 NEXT J
400 DT(I,1) = K2(I)
410 NEXT I
420 GOSUB 5000
430 FOR I = 1 TO M
440 V(I) = DA(I)
450 NEXT I
460 FOR I = 1 TO H
470 FOR J = 1 TO H
480 AA(I,J) = 0
490 NEXT J
500 DT(I,1) = 0
510 NEXT I
520 FOR I = 1 TO N
530 FOR J = 1 TO H
535 A(I,J) = (X(I)) ** (J 1)
540 TA(J,I) = A(I,J)
550 NEXT J
560 NEXT I
565 FOR I = 1 TO N
570 W(I,I) = 1
575 NEXT I
580 W = N
585 FOR I = 1 TO N
590 qi(I,I) = H(I,I)
595 NEXT I
600 FOR I = 1 TO H

166
605 FOR J = 1 TO N
610 Q2(I,J) = TA(I,J)
615 NEXT J
620 NEXT I
625 GOSUB 4500
630 FOR I = 1 TO H
635 FOR J = 1 TO N
640 TA(I,J) = Q3(I,J)
645 NEXT J
650 NEXT I
740 W = M
750 FOR I = 1 TO M
760 FOR J = 1 TO N
770 Q1(J,I) = A(J,I)
780 q2(I,J) = TA(I,J)
790 NEXT J
800 NEXT I
810 GOSUB 4500
820 FOR I = 1 TO H
830 FOR J = 1 TO H
840 AA(I,J) = q3(I,J)
845 HLD(I.J) = q3(I,J)
850 NEXT J
860 NEXT I
900 S(0) = 1E+17
910 CHISq = 0
1000 PRINT
1005 PRINT ITTERATION ;W1
1010 PRINT
1015 FOR J = 1 TO M
1020 PRINT V(";J;) = ;V(J)
1023 PRINT
1030 NEXT J
1032 PRINT
1035 FOR I = 1 TO N
1040 PRINT X(;I; ) = ;X(I)+XT(1) 'Y(* ;Ij ) = }Y(I)*5000
1045 FOR J = 1 TO H
1050 F(I) = V(J) (CX(I)) ** (J 1)) + F(I)
1055 NEXT J
1060 PRINT ,,X(;I;) = ";X(I)+XT(1),F(,,;I;) = ,;F(I)*5000
1065 PRINT
1150 DY(I) = Y(I) F(I)
1155 CHISq = CHISq + (CDY(I)) ** 2) / (F(I) (N H))
1160 S(W1) = S(W1) + (DY(I)) ** 2
1170 NEXT I
1180 IF ABS (S(W1) S(W1 1)) < (S(W1) .0000001) THEN GOTO 2000
1185 IF ( S(W1-1) < S(H1) ) THEN GOTO 1900
1190 FOR I = 1 TO H

1195 VOLD(I) = V(I)
1200 NEXT I
1210 ocHisq = CHisq
1340 FOR I = 1 TO N
1350 qi(I.l) = DY(I)
1360 NEXT I
1370 GOSUB 4500
1380 FOR I = 1 TO H
1390 DT(I,1) = q3(I,l)
1400 NEXT I
1410 GOSUB 5000
1430 FOR I = 1 TO H
1440 V(I) = V(I) + DA(I)
1450 NEXT I
1455 PRINT
1460 FOR I = 1 TO HI
1465 PRINT S(;I;) = ;S(I) 2.5E+07
1470 NEXT I
1475 PRINT
1485 FOR I = 1 TO N
1490 F(I) = 0
1495 NEXT I
1505 HI = HI + 1
1510 GOTO 910
1900 FOR I = 1 TO H
1905 V(I) = VOLD(I)
1910 NEXT I
1920 S(Hi) = S(H1 1)
1930 CHISq = OCHISq
2000 GOSUB 8000
2003 LPRINT This is a POLYBK.BAS run"
2005 LPRINT for ;LB + RF; background points
2010 LPRINT
2015 LPRINT Gross Counts data from file ;BK$
2020 LPRINT
2050 X(l) = XT(LB + 1) XT(1)
2055 X(2) = XT(DP RB) XT(1)
2060 FOR I = 1 TO 2
2065 FOR J = 2 TO M
2070 SL(I) = SL(I) + (J 1) V(J) ((X(D) ** (J
2075 NEXT J
2077 SL(I) = SL(I) 5000
2080 NEXT I
2085 LPRINT Convergence in ;H1; iterations
2087 LPRINT
2090 LPRINT S = ;S(H1) 2.5E+07
2093 LPRINT
2095 LPRINT CHISq = ;CHISq 5000

2101
2105
2106
2107
2110
2115
2120
2125
2180
2185
2190
2195
2250
2262
2254
2260
2262
2265
2270
2275
2277
2280
2285
2290
2292
2294
2296
2300
2305
2310
2315
2320
2325
2335
2400
2405
2410
2413
2415
2425
2427
2435
2445
2447
2450
2460
2465
2475
168
LPRINT
LPRINT Fit parameters for polynomial of order *;01
LPRINT Y(I) = A + B X(I) + C X(I)**2 + .
LPRINT
FOR J = 1 TO M
LPRINT V( ; J; ) = ;V(J)
LPRINT
NEXT J
LPRINT Background Fit Results
LPRINT
LPRINT 'X(I) ,*Y(I) ,BKCD ,*SIG(I)
LPRINT
FOR I = 1 TO N
F(I) = 0
NEXT I
FOR I = 1 TO DP
X(I) = XT(I) XT(1)
FOR J = 1 TO H
F(I) = V(J) ((X(D) ** (J 1)) + F(I)
NEXT J
F(I) = F(I) 5000
LPRINT XT(I),YT(I),F(I),SIG(I)
NEXT I
LPRINT
LPRINT Background Slope at ;XT(LB + 1); = ;SL(1)
LPRINT
LPRINT Background Slope at ;XT(DP RB); = ;SL(2)
PRINT Background Fit Results
PRINT
PRINT 'XT(I) ,BR(I) ,*SIG(I)*
PRINT
FOR I = 1 TO DP
PRINT XT(I),F(I),SIG(I)
NEXT I
PRINT
PRINT In what file are the Polynomial fit data to be stored?
INPUT PEAK$
IF PEAK$ = NO THEN GOTO 9000
OPEN 0, #1,PEAK$
PRINT #1, DP RB + RF
FOR I = 1 TO (DP RB + RF)
PRINT #1, XT(I)
PRINT #1, F(I)
PRINT #1, SIG(I)
NEXT I
PRINT II, R
FOR I ~ 1 TO H
PRINT #1, V(I)

169
2477 NEXT I
2480 CLOSE #1
2482 PRINT
2483 PRINT
2490 LPRINT Peak data stored in file ;PEAK$
2500 GOTO 9000
4500 FOR I = 1 TO H
4502 FOR J = 1 TO H
4503 q3(I,J) = 0
4504 NEXT J
4505 NEXT I
4510 FOR K = 1 TO H
4520 FOR I = 1 TO W
4540 FOR J = 1 TO N
4560 Q3(K,I) = Q3(K,I) + q2(K,J) qi(J,I)
4580 NEXT J
4600 NEXT I
4620 NEXT K
4640 RETURN
5000 FOR I = 1 TO H
5020 FOR J = 1 TO M
5040 AM(I,J) = AA(I,J)
5060 NEXT J
5080 NEXT I
5090 HI = M + 1
5100 FOR I = 1 TO H
5120 AM(I,H1) DT(I,1)
5140 NEXT I
5160 SH = 0
5180 FOR R = 2 TO M
5200 R2 = R 1
5220 FOR R1 = R TO H
5240 SH = AH(R1,R2) / AH(R2,R2)
5260 AH(R1,R2) = 0
5300 FOR Cl = R TO HI
5320 AH(R1,C1) = AH(R1,C1) AH(R2,C1) SH
5340 NEXT Cl
5380 NEXT R1
5460 NEXT R
6000 SU = 0
6010 H2 = H 1
6020 DA(H) = (AH(H.Hl)) / (AH(H,H))
6040 FOR R = 1 TO H2
6060 RP = H R
6070 H3 = H RP
6080 FOR Cl = 1 TO H3
6100 SP = HI Cl
6120 SU = SU + AH(RP.SP) DA(SP)

6140 NEXT Cl
6160 DA(RP) = (AM(RP,M1) SU) / (AM(RP,RP))
6180 SU = 0
6200 NEXT R
6203 FOR I = 1 TO M
6204 FOR J = 1 TO M + 1
6205 AM(I,J) = 0
6206 NEXT J
6207 NEXT I
6220 RETURN
8000 REM
8002 REM Subroutine to calculate Error in Peak Area
8004 REM
8006 REM The first part of the subroutine inverts AA(M,M) to
8008 REM yield the covariance matrix, C0V(M,M)
8009 REM
8010 FOR I = 1 TO M
8015 C0V(I,I) = 1
8020 NEXT I
8025 FOR I = 1 TO M
8030 T1 = HLD(I,I)
8035 FOR J = 1 TO M
8040 HLD(I.J) = HLD(I.J) / T1
8045 COV(I.J) = COV(I.J) / Ti
8050 NEXT J
8055 FOR J = 1 TO M
8060 IF J = I THEN GOTO 8090
8065 T2 = HLD(J.I)
8070 FOR K = 1 TO M
8075 HLD(J,K) = HLD(J.K) (HLD(I,K) T2)
8080 COV(J.K) = COV(J.K) (COV(I.K) T2)
8085 NEXT K
8090 NEXT J
8095 NEXT I
8100 FOR I = 1 TO M
8110 FOR J = 1 TO M
8120 COV(I,J) = COV(I.J) S(W1)/(N M)
8130 NEXT J
8140 NEXT I
8150 PRINT X(I),',Y(I)',SIG(I)
8155 PRINT
8160 FOR K = 1 TO (DP RB + RF)
8200 FOR I = 1 TO M
8210 DA(I) = (XT(K) XT(1)) ** (I 1)
8220 NEXT I
8400 Tl = 0
8410 T2 = 0
8500 FOR I = 1 TO M

8510
8520
8525
8530
8540
8545
8550
8555
8560
8570
8580
8600
8610
8620
9000
171
TI = TI + ((DA(I)) ** 2) C0V(I,I)
FOR J = 1 TO H
IF J = I THEN GOTO 8540
T2 = TI + DA(I) DA(J) COV(I.J)
NEXT J
NEXT I
SIG(K) = (SqR(Tl + T2)) 5000
YFIT = O
FOR I = 1 TO H
YFIT = YFIT + V(I) ((XT(K) XT(1)) ** (I 1))
NEXT I
PRINT XT(K),(YFIT 5000),SIG(K)
NEXT K
RETURN
END

1
REM
2
REM
*
*
3
REM
*
BKG.BAS *
4
REM
*
*
5
REM
*
with Polynomial *
6
REM
*
and Step Function *
7
REM
*
Background Subtraction *
8
REM
*
*
9
REM
******************************
10 REM
15 DIM X(99),Y(99),SIG(99),VAR(99)
20 DIM PK(99),BK(99),PF(99)
30 DIM PBK(99),SBK(99),SL(99)
55 PI = 3.141592653#
100 PRIHT Input the name of the Spectrum data file
105 INPUT BK$
110 OPEN I ,#1,BK$
120 INPUT #1, DP
130 INPUT #1, LB
140 INPUT #1, RB
145 FOR I = 1 TO DP
155 INPUT #1, X(I)
160 NEXT I
165 FOR I = 1 TO DP
175 INPUT #1, Y(I)
180 NEXT I
185 CLOSE #1
190 FOR I = 1 TO DP
195 PRINT X(;I;) = ;X(I), Y(;I;) = ;Y(I)
200 NEXT I
500 PRINT Input the name of the Polynomial fit data file
505 INPUT POLY$
510 PRINT
515 OPEN I',,#1,P0LY$
525 INPUT #1, N
530 FOR I = 1 TO N
540 INPUT #1, K
550 INPUT #1, K
553 INPUT #1, SIG(I)
555 NEXT I
565 INPUT #1, PO
570 FOR I = 1 TO PO
580 INPUT #1, PF(I)
585 NEXT I
590 CLOSE #1
1000 L = 0
1005 Y1 = 0
1010 Y2 = 0

1015 NS = LB + 1
1020 NE = DP RB
1025 BK(NS 1) = Y(NS 1)
1030 DT = Y(NE + 1) Y(NS 1)
1035 FOR I = NS TO NE
1040 Y1 = Y(I) + Y1
1045 NEXT I
1050 FOR I = (NS 1) TO NE
1055 XN = X(I) X(l)
1060 FOR J = 2 TO PO
1065 SL(I) = (J 1) PF(J) (XN ** (J 2)) + SL(I)
1070 NEXT J
1075 SL(I) = SL(I) 5000
1080 IF I = (NS 1) THEN GOTO 1120
1085 Y2 = Y2 + Y(I)
1090 SBK(I) = .5 (Y(NS 1) + DT (Y2 / Yl))
1095 PBK(I) = .5 (BK(I 1) + .5 (SL(I 1) + SL(I)))
1100 BK(I) = SBK(I) + PBK(I)
1105 PK(I) = Y(I) BK(I)
1115 VAR(I) = Y(I) + SBK(I) + .5 ((SIG(I)) ** 2)
1120 NEXT I
2005 LPRINT This is a BKG.BAS run"
2010 LPRINT
2015 LPRINT Gross Counts data from file ;BK$
2020 LPRINT
2025 LPRINT Polynomial fit data from file ;POLY$
2030 LPRINT Polynomial of order ;(PO 1)
2035 LPRINT
2040 FOR I = 1 TO PO
2045 LPRINT V(;I;) = ;PF(I)
2050 NEXT I
2100 LPRINT
2105 LPRINT Channel, Counts", Peak, Bkg,,,Sig
2110 LPRINT
2115 FOR I = NS TO NE
2120 LPRINT X(I),Y(I),PK(I),BK(I),SQR(VAR(I))
2125 LPRINT
2130 NEXT I
2300 FOR I = NS TO NE
2310 PRINT X(I),PK(I),SQR(VAR(I))
2315 PRINT
2320 NEXT I
2370 PRINT In what file is the Peak data to be stored?
2375 INPUT PEAK!
2380 PRINT
2400 PRINT In what file is the Background data to be stored?
2405 INPUT BK$
2412 PRINT

2415
2425
2427
2435
2445
2447
2450
2455
2500
2510
2515
2525
2535
2540
2545
2600
2610
2615
2625
9000
174
OPEN 0,#1,PEAK$
PRINT #1, NE NS + 1
FOR I = NS TO NE
PRINT #1, X(I)
PRINT #1, PK(I)
PRINT #1, VAR(I)
NEXT I
CLOSE #1
OPEN O ,#1,BK$
PRINT #1, NE NS + 1
FOR I = NS TO NE
PRINT #1, X(I)
PRINT #1, BK(I)
NEXT I
CLOSE #1
LPRINT
LPRINT Peak data saved in file ;PEAK$
LPRINT
LPRINT Background data saved in file ;BK$
END

175
2
REM
3
REM
*
*
4
REM
* PEAKFIT.BAS
*
5
REM
* with Error Analysis
*
6
REM
* and entire peak shaping
*
7
REM
*

8
REM
9
REM
15
PI =
3.141592653#
20
W1 =
1
30 DIM (25,15),TA(15,25),Ql(25,15),Q2(15,25),Q3(1S,15)
45 DIM T(25),0LDVAR(4)
40 DIM DT(25,1),DY(25),X(30),Y(30),F(30),SG(2,30),FIT(30),HLD(4,4)
50 DIM AA(15,15),TE(15),LI(2,50),VAR(10),DS(10),PK(3,25),BK(25)
60 DIM CH(2),VA$(3),DF(2),A1(3),B1(3),AM(5,5),DA(5),W(25,25),C0V(4,4)
85 PRINT Is this a II or Th K-alpha-1 x-ray peak?
90 INPUT EL$
95 PRINT
100 PRINT Input the name of the peak data file
105 INPUT FILE$
110 PRINT
150 FWHM = 7
170 IF EL$ = TH THEN GOTO 185
175 GA = .103
177 XB = 993
180 GOTO 190
185 GA = .0947
187 XB = 942
190 Al = 4.63217E-07
195 Bi = 9.986879E-02
200 Cl = .323665
203 EC = A1 ((XB) ** 2) + Bl XB + Cl
205 El = EC (GA / 2)
210 E2 = EC + (GA / 2)
215 CH(1) = ( Bl + SQR (Bl ** 2 4 Al (Cl El))) / (2 Al)
220 CH(2) = ( Bl + SQR (Bl ** 2 4 Al (Cl E2))) / (2 Al)
225 GA = CH(2) CH(1)
230 SIG = FWHM / (2 SQR (2 LOG (2)))
235 VA$(1) = SIG
240 VA$(2) = XB
245 VA$(3) = A
500 OPEN I,#1,FILE$
510 INPUT #1, NP
515 FOR I = 1 TO NP
525 INPUT #1, PK(l.I)
535 INPUT #1, PK(2,I)
537 INPUT #1, PK(3,I)
540 NEXT I

645 CLOSE #1
650 PRINT XRF Peak, with background subtracted,
553 PRINT from data file ;FILE$
555 PRINT
560 PRINT Channel", Count s, Sigma
565 PRINT
570 FOR I = 1 TO NP
575 PRINT PK(1,1),PK(2,I),SQR(PK(3,I))
580 PRINT
585 NEXT I
600 FOR I = 5 TO NP
605 II = I + i
607 12 = I + 2
609 SI = (PK(2,Ii) PK(2,I)) / (PK(l.Il) PK(1,I))
610 S2 = (PK(2,I2) PK(2,I1)) / (PK(1,I2) PK(1,I1))
611 HOLD = II
612 IF SI > 0 AND S2 < 0 GOTO 630
615 NEXT I
620 PRINT NO MAXIMUM FOUND IN LINE 620
625 GOTO 9000
630 IF PK(1,I1) < XB 1.005 GOTO 650
635 HOLD = I
650 VAR(l) = SIG
655 VAR(2) = XB
660 VAR(3) = PK(2,H0LD)
700 FOR J = (HOLD 6) TO HOLD
705 IF PK(2,J) < 0 THEN GOTO 715
710 IF PK(2,J) > .2 PK(2,H0LD) GOTO 730
715 NEXT J
720 PRINT No Low Energy Start Point Found at Line 720
725 GOTO 9000
730 START = J
900 PRINT
905 PRINT POINTS FOR VOIGT PEAK CALCULATION
910 FOR J = 1 TO NP
915 13 = START + (J 1)
920 X(J) = PK(1,I3)
925 Y(J) = PK(2,I3)
930 H(J,J) = 1
935 IF 13 < HOLD GOTO 950
940 IF Y(J) < .2 PK(2,H0LD) GOTO 960
950 PRINT X(J),Y(J),W(J,J)
955 NEXT J
960 N = J 1
965 M = 3
967 SI = 1E+15
970 S = 0
973 CHISQ = 0

975
PRINT Itteration # ";W1
977
PRINT
980
FOR I = 1 TO M
985
PRINT VA$(I); = '>;VAR(I)
987
PRINT
990
NEXT I
995
FOR I = 1 TO N
1000
SIG = VAR(l)
1005
XB = VAR(2)
1008
A = VAR(3)
1010
PRINT X;I; = ' ;X(I), Y;I;
= ;Y(I)
1015
GOSUB 2000
1020
F(I) = F6
1025
PRINT X;I; = ;X(I), F* ;I;
= ';F(I)
1030
PRINT
1035
FOR 11 = 1 TO H
1040
DF(2) = 0
1045
FOR 12 = 1 TO M
1050
DS(I2) = 0
1055
NEXT 12
1060
DS(I1) = VAR(Il) .001
1065
SIG = VAR(l) + DS(1)
1070
XB = VAR(2) + DS(2)
1080
A = VAR(3) + DS(3)
1085
GOSUB 2000
1090
DF(1) = (F6 F(I)) / DS(I1)
1095
TE = DF(1) DF(2)
1100
IF ABS (TE) < = ABS (.001 DF(1))
GOTO 1120
1105
DS(I1) = DS(I1) .5
1110
DF(2) = DF(1)
1115
GOTO 1065
1120
A(I,I1) = DF(1)
1125
TA(I1,I) = DF(1)
1130
NEXT 11
1135
DY(I) = Y(I) F(I)
1140
S = S + (DY(I)) ** 2
1143
CHISQ = CHISq + ((DY(I)) ** 2) / (F(I)
* (N M))
1145
NEXT I
1150
IF S > SI THEN GOTO 1176
1151
IF ABS (S SI) < (S / 1000) THEN GOTO 1180
1152
SI = S
1153
ochisq = cHisq
1155
GOSUB 6500
1160
PRINT
1165
PRINT S = ;S
1166
PRINT
1167
PRINT CHISq = CHISq
1170
W1 = W1 + 1

1175
1176
1177
1178
1179
1180
1181
1182
1183
1185
1186
1187
1188
1190
1192
1194
1196
1198
1200
1205
1207
1210
1215
1219
1221
1223
1225
1230
1235
1240
1245
1247
1248
1249
1251
1252
1253
1254
1255
1256
1257
1259
1260
1265
1270
1272
1282
1284
GOTO 970
S = SI
FOR I = 1 TO H
VAR(I) = OLDVAR(I)
NEXT I
SIG = VAR(l)
XB = VAR(2)
A = VAR(3)
CHisq = ocHisq
AREA = 0
FOR I = 1 TO 27
X(I) = INT (XB) 13 + (I 1)
FOR J = 1 TO NP
IF X(I) = PK(1,J) THEN GOTO 1198
NEXT J
Y(I) = 0
GOTO 1200
Y(I) = PK(2,J)
GOSUB 2000
FIT(I) = F6
IF F6 < 0 THEN FIT(I) = 0
PRINT X(I),Y(I),FIT(I)
AREA = AREA + FIT(I)
NEXT I
GOSUB 8000
GOSUB 1500
REM
LPRINT This is a WHOLEPK.BAS run'
LPRINT
LPRINT The Peak Data was obtained from disk file ;FILE$
LPRINT
LPRINT Convergence in ;W1; itterations. S = ;S
LPRINT
LPRINT Reduced Chi Squared Value = ;CHISq
LPRINT
LPRINT Peak Area = ; AREA; +- ;DAREA; Count-Channels
LPRINT with ;(FR 100);*/, of the area
LPRINT beyond XB +- 13 channels
LPRINT
LPRINT Fitted Parameters
LPRINT
LPRINT GA = ;GA
FOR I = 1 TO M
LPRINT VA$(I); = ;VAR(I)
NEXT I
LPRINT
LPRINT Peak Fit Results
LPRINT

179
1286 LPRINT X(I) ',1 Y(I) ', FIT(I)
1288 LPRINT
1290 FOR I = 1 TO 27
1292 LPRINT X(I),Y(I),FIT(I)
1294 NEXT I
1299 GOTO 9000
1490 REM
1492 REM Subroutine to calculate the fraction of the Viogt Profile
1494 REM area which lies beyond XB +- 13 Channels
1496 REH
1500 Al(l) = .4613135
1505 1(2) = 9.999216E-02
1510 Al(3) = 2.883894E-03
1515 Bl(l) = .1901635
1520 Bl(2) = 1.7844927#
1525 Bl(3) = 5.5253437#
1530 DT = XB X(l)
1535 TH = SIG SQR (2)
1540 FOR I = 1 TO 3
1545 TI = ATN ((2 / GA) (DT + TH SQR (B1(I))))
1550 T2 = ATN ((2 / GA) (DT TH SQR (B1(I))))
1555 FR = FR + (1 / SqR (PI)) A1(I) (PI (TI + T2))
1560 NEXT I
1565 AREA = AREA / (1 FR)
1570 RETURN
1990 REH
1992 REH Subroutine to calculate Voigt Profile data points
1994 REH
2000 AL = 1 / (2 SIG ** 2)
2020 GH = GA / (SIG SqR (2))
2040 Cl = 1 GH / SOR (PI)
2060 C2 = GH / (2 PI)
2080 C3 = .25 GH ** 2
2100 C4 = 2 GH / PI
2120 CHI = (X(I) XB) / (SIG SqR (2))
2140 F4 = 0
2160 F5 = 0
2180 FOR T4 = 1 TO 100
2200 FI = (T4 ** 2) / 4
2220 F2 = (T4 CHI) (T4 ** 2) / 4
2240 F3 = (T4 CHI) + (T4 ** 2) / 4
2260 F9=(EXP(-F1))/(T4**2)-(EXP(F2))/(2*T4**2)-(EXP(-F3))/(2*T4**2)
2270 F4 = F4 + F9
2280 IF ABS (F4 F5) < = .001 ( ABS (F4)) GOTO 2380
2300 F5 = F4
2320 NEXT T4
2340 PRINT DID NOT CONVERGE IN LINE 2340
2360 GOTO 9000
2380 BX = ( EXP ( (CHI ** 2))) F4

180
2400 F6=(EXP(-(CHI**2)))*(C1+C2*(CHI**2)+C3*(1"2*(CHI**2)))
2420 F6 = (F6 + C4 BX) A
2640 RETURN
4490 REM
4492 REM Subroutine to perform the matrix multiplication:
4494 REM Q3(M,W) = Q2(M,N) Q1(N,W)
4496 REM
4500 PRINT GO SUB 4500
4501 FOR I = 1 TO M
4502 FOR J = 1 TO M
4503 Q3(I,J) = 0
4504 NEXT J
4505 NEXT I
4510 FOR K = 1 TO M
4520 FOR I = 1 TO W
4540 FOR J = 1 TO N
4560 Q3(K,I) = Q3(K,I) + Q2(K,J) Q1(J,I)
4580 NEXT 3
4600 NEXT I
4620 NEXT K
4640 RETURN
4980 REM
4982 REM
4984 REM
4986 REM
4990 REM
4992 REM
4994 REM
4996 REM
4997 REM
4998 REM
5000 FOR I = 1 TO M
5020 FOR J = 1 TO M
5040 AM(I,J) = (I,J)
5060 NEXT J
5080 NEXT I
5090 Ml = M + 1
5100 FOR I = 1 TO M
5120 AM(I.Ml) = DTCl.l)
5140 NEXT I
5160 SM = 0
5180 FOR R = 2 TO M
5200 R2 = R 1
5220 FOR R1 = R TO M
5240 SM = AM(R1,R2) / AM(R2,R2)
5260 AM(R1,R2) = 0
5300 FOR C = R TO Ml
5320 AM(R1,C) = AM(R1,C) AM(R2,C) SM
Subroutine to solve the matrix equation:
TA(M,N)*W(N,N)*A(N,M)*DT(M,1) = TA(M,N)*W(N,N)*DY(N,1)
where: TA(M,N) W(N,N) A(N,M) = AA(M,M)
DT(M,1) = Variable Matrix
DY(M,1) = Solution Matrix
This subroutine solves the above equation by Gaussian
Elimination

181
5340 NEXT C
5380 NEXT R1
5390 PRINT
5460 NEXT R
6000 SU = 0
6010 M2 = M 1
6020 DA(M) = (AM(M,MD) / (AM(M,M))
6040 FOR R = 1 TO M2
6060 RP = M R
6070 M3 = M RP
6080 FOR C = 1 TO M3
6100 SP = Ml C
6120 SU = SU + AM(RP,SP) DA(SP)
6140 NEXT C
6160 DA(RP) = (AM(RP.Ml) SU) / (AM(RP,RP))
6180 SU = 0
6200 NEXT R
6203 FOR I = 1 TO M
6204 FOR J = 1 TO M + 1
6205 AM(I,J) = 0
6206 NEXT J
6207 NEXT I
6220 RETURN
6490 REM
6492 REM This subroutine creats the matrices necessary to solve the
6494 REM the equation described in the previous subroutine. This
6496 REM subroutine calls the previous subroutine
6498 REM
6500 W = N
6510 FOR I = 1 TO M
6520 FOR J = 1 TO N
6530 Q2(I,J) = TA(I,J)
6540 NEXT J
6550 NEXT I
6560 FOR I = 1 TO N
6570 FOR J = 1 TO N
6580 Q1(I,J) = W(I,J)
6590 NEXT J
6600 NEXT I
6610 GOSUB 4500
6620 FOR I = 1 TO M
6630 FOR J = 1 TO N
6640 TA(I,J) = q3(I,J)
6650 NEXT J
6660 NEXT I
7000 W = M
7010 FOR I = 1 TO M
7020 FOR J = 1 TO N

182
7030
qi(j,i) = A(J,I)
7040
q2(I,J) = TA(I,J)
7050
NEXT J
7060
NEXT I
7070
GOSUB 4500
7080
FOR I = 1 TO M
7090
FOR J = 1 TO M
7100
AA(I,J) = q3(I,J)
7105
HLD(I,J) = q3(I,J)
7110
NEXT J
7120
NEXT I
7130
W = 1
7140
FOR I = 1 TO N
7150
qi(i.i) = dy(i)
7160
FOR 11 = 2 TO M
7170
qi(i,n) = 0
7180
NEXT 11
7190
NEXT I
7200
GOSUB 4500
7210
FOR I = 1 TO M
7220
DT(I,1) = q3(i,i)
7230
NEXT I
7240
GOSUB 5000
7250
FOR I = 1 TO H
7255
OLDVAR(I) = VAR(I)
7260
VAR(I) = VAR(I) + DA(I)
7265
DA(I) = 0
7270
NEXT I
7280
RETURN
8000
REM
8002
REM Subroutine to calculate Error in
Peak Area
8004
REM
8006
REM The first part of the subroutine
inverts AA(M,
8008
REM yield the covariance matrix, COV(M,M)
8009
REM
8010
FOR I = 1 TO M
8015
COVCI.I) = 1
8020
NEXT I
8025
FOR I = 1 TO M
8030
T1 = HLD(I,I)
8035
FOR J = 1 TO M
8040
HLD(I.J) = HLD(I.J) / Tl
8045
COV(I.J) = COV(I,J) / Tl
8050
NEXT J
8055
FOR J = 1 TO M
8060
IF J = I THEN GOTO 8090
8065
T2 = HLD(J.I)
8070
FOR K = 1 TO M

8075
8080
8085
8090
8095
8100
8110
8120
8130
8140
8200
8210
8220
8230
8240
8250
8253
8255
8260
8270
8280
8284
8290
8300
8305
8310
8320
8325
8330
8340
8350
8360
8370
8380
8390
8395
8400
8410
8420
8500
8510
8520
8525
8530
8540
8550
8560
8570
9000
183
HLD(J.K) = HLD(J,K) (HLD(I,K) T2)
COV(J.K) = C0V(J,K) (C0V(I,K) T2)
NEXT K
NEXT J
NEXT I
FOR I = 1 TO M
FOR J = 1 TO M
COV(I.J) = COV(I,J) S/(N M)
NEXT J
NEXT I
FOR II = 1 TO M STEP 2
DF(2) = 0
FOR J = 1 TO M
DS(J) = 0
NEXT J
DS(Ii) = VAR(Il) .001
PRINT
PRINT AREA *, NAREA *'
SIG = VAR(l) + DS(1)
XB = VAR(2)
A = VAR(3) + DS(3)
NAREA = 0
FOR I = 1 TO 27
GOSUB 2000
IF F6 < 0 THEN F6 = 0
NAREA = NAREA + F6
NEXT I
PRINT AREA,NAREA
DF(1) = (NAREA AREA)/DS(I1)
TE = DF(1) DF(2)
IF ABS(TE) <= ABS(.001 DF(1)) GOTO 8390
DS(I1) = DS(I1) .5
DF(2) = DF(1)
GOTO 8260
DA(I1) = DF(1)
PRINT DA(jll; ) = jDACll)
NEXT II
T1 = 0
T2 = 0
FOR I = 1 TO H
T1 = T1 + ((DA(I)) ** 2) COV(I.I)
FOR J = 1 TO H
IF J = I THEN GOTO 8540
T2 = T2 + DA(I) DA(J) COV(I,J)
NEXT J
NEXT I
DAREA = SqRCTl + T2)
RETURN
END

Geometry Factor Programs
These programs were written to perform the main body of the soil assay calculations.
All four programs are written in FORTRAN-77, were run on a VAX Cluster main-frame
computer, and are described in Chapter II. D1ST.FOR is a preliminary program which
creates data files for use by subsequent programs. The data files consist of the distances
from each source to each of the 3840 points of the target, and files of the distances from
each of the 3840 target points to each of the 24 nodes of the detector. These distances
include the total distance as well as the distance from the point to the boundary of the
soil target. IMAGE.FOR uses the distances stored by DIST.FOR to calculate Geometry
Factors (GFs) for each of the 3840 points of the target. The sum of the GFs is then stored.
COMPTON.FOR calculates, in addition to the distances described above, the distances
from each target point to each other target point. These are used to determine the Compton
Geometry Factors (CGFs) for each of the 3840 target points. The sum of the CGFs is then
stored. Finally ASSAY.FOR uses the stored GFs and CGFs, as well as detector response
data, and fits this data to a straight line. The slope of the line, which is the only fitting
parameter, is the soil contamination concentration and is the desired result of the assay.

185
C
C ****************************
c *
C DIST.FOR *
C *
c ****************************
c
COMMON XT, YT, TR
INTEGER SLICE, RT, CT, VT, RD, CD
CHARACTER *1 Q
CHARACTER *10 GEOM, SPD, PDD
DIMENSION XS(2),YS(2),ZS(2)
DIMENSION DTR(24,3),AD(24),PTS(192,3),V0LT(192)
DIMENSION SP(192,4),PI(192,24),P2(192,24),V(21)
PI = 3.14159
SLICE = 1
Q = Y*
C
C DETECTOR COORDINATES, X, Y, Z, AND RADIOUS (CM)
C
XD = 0.0
YD = 0.0
ZD = 0.0
C
C DETECTOR RADIOUS, DR
C
DR = 1.8
WRITE(6,10)
10 FORMAT(/,IX,Enter the name of the System Geometry File)
READ(5,15) GEOM
15 FORMAT(AIO)
OPEN(1,FILE=GEOM,STATUS=OLD)
C
C NUMBER OF SOURCES USED
C
READ(1,*) NS
C
C SOURCE COORDINATES
C
DO 50 1=1,NS
READ(1,*) XS(I),YS(I),ZS(I)
50

186
C
C TARGET CENTER COORDINATES
C
READ(1,*) XT,YT,ZT
C
C TARGET HEIGHT, TH, AND RADIOUS, TR
C
READ(1,*) TH.TR
READ(1,*) RT.CT.VT
CLOSE(1,STATUS=KEEP>)
WRITE(6,75)
75 F0RMAT(/,1X,In what file should the Source-Target,/,
1 IX,distances be stored?)
READ(5,80) SPD
80 FORHAT(AIO)
WRITE(6,85)
85 F0RMAT(/,1X,In what file should the Target-Detector,/,
1 IX,distances be stored?)
READ(5,90) PDD
90 FORMAT(AIO)
C
C DETERMINE DETECTOR NODE POINTS
C
RD = 8
CD = 3
II = 1
DO 100 I = 1,CD
DO 100 J = 1,RD
T = (2 PI / RD) (J .5)
DTRCI1.3) = (DR / CD) (I .5) SIN (T)
DTR(I1,2) = (DR / CD) (I .5) COS (T)
DTR(Il.l) = 0
AD(I1)=PI*((I*DR/CD)**2-((I-1)*DR/CD)**2)/RD
100 II = II + 1
WRITE(6,210)
210 FORMAT(/,IX,Completed Detector Node Points)
C
C DETERMINE TARGET NODE POINTS
C
II = 1
DO 250 I = 1,CT
DO 250 J = 1,RT / 2
T = (2 PI / RT) (J .5)
PTS(Il.l) = (TR / CT) (I .5) COS (T) + XT
PTS(I1,2) = (TR / CT) (I .5) SIN (T) + YT
PTS(I1,3) = ( TH / 2.0) + (TH / (2.0 VT)) + ZT
VOLT(Il) = PI*(TH/VT)*((I*TR/CT)**2 ((I 1)*TR/CT)**2)/RT
II = II + 1
250

187
C
C
C
WRITE(6,260)
260 F0RMAT(/,IX,Completed Target Node Points)
DETERMINE DISTANCE FROM SOURCE TO POINT
275 DO 350 II = 1,RT CT / 2
DO 300 A1 = 1,NS
A2 = 2 Al i
A3 = 2 A1
PX1 = XS(A1)
PY1 = YS(A1)
PZ1 = ZS(A1)
PX2 = PTS(Ii,l)
PY2 = PTS(I1,2)
PZ2 = PTS(I1,3)
CALL DISTANCE(PX1,PY1,PZ1,PX2,PY2,PZ2,DSTi,DST2,Ki)
IF (Kl .Eq. 10) GOTO 9000
SP(I1,A2) = DSTI
300 SP(I1,A3) = DST2
C
C
C
350
360
400
500
600
650
700
800
DETERMINE DISTANCE FROM POINT TO DETECTOR
DO 350 K = 1,RD CD
PX1 = DTR(K,1)
PY1 = DTR(K,2)
PZ1 = DTR(K,3)
CALL DISTANCE(PXi,PYi,PZ1,PX2,PY2,PZ2,DSTI,DST2,Kl)
IF (Kl .Eq. 10) GOTO 9000
P1(I1,K) = DSTI
P2(I1,K) = DST2
WRITE(6,360) SLICE
FORMAT(/,IX,'Slice #fAl, Completed)
IF (SLICE .HE. 1) GOTO 500
OPEN(1,FILE=SPD,STATUS=NEW)
OPEN(2,FILE=PDD,STATUS=NEW)
WRITE(6,400) SPD
FORMAT(/,IX,Writing Source Target data to file ,A15)
WRITE(1,*) XS(1),YS(1),ZS(1),XS(2),YS(2),ZS(2)
WRITE(1,*) XT,YT,ZT,TR,TH,RT,CT,VT
WRITEd,*) XD,YD,ZD,DR,RD,CD,NS
DO 600 II = 1,RT CT / 2
WRITEd,*) SP(I1,1) ,SP(I1,2) ,SP(I1,3) ,SP(I1,4) ,V0LT(I1)
IF(SLICE .GT. 1) GOTO 700
WRITE(6,650) PDD
FORMAT(/,IX,Writing Target Detector data to file ,A15)
DO 800 I = 1,RT CT / 2
DO 800 J = 1,RD CD
WRITE(2,*) P1(I,J), P2(I,J)

DO 850 I = 1,RD CD
850 WRITEC2,*) AD(I)
SLICE = SLICE + 1
DO 900 I = 1,RT CT / 2
900 PTS(I,3) = PTS(I,3) + TH / VT
IF(PTS(1,3) .GT. ZT) GOTO 1000
GOTO 275
1000 CLOSECl.STATUS^KEEP)
CLOSE(2,STATUS^*KEEP')
9000 END

189
C
c *
C SUBROUTINE DISTANCE *
C *
c ******************************
c
SUBROUTINE DISTANCE(XI,Y1,Z1,X2,Y2,Z2,R1,R2,K1)
COMMON XT, YT, TR
Di = X2 XI
D2 = Y2 Y1
D3 = Z2 Z1
R1 = SQRT (D1*D1 + D2*D2 + D3*D3)
U = D1 / R1
V = D2 / R1
W = D3 / R1
X1XT = XI XT
Y1YT = Y1 YT
A = U*U + V*V
B = 2 U X1XT + 2 V Y1YT
C = X1XT X1XT + Y1YT Y1YT TR TR
R3 = ( B + SQRT (B*B 4 A C)) / (2 A)
IF (R3 .LT. O.O) GOTO 100
IF (R3 .LT. Rl) GOTO 500
100
R3 = ( B SQRT (B*B -
IF (R3 .LT. 0.0) GOTO 200
IF (R3 .LT. Rl) GOTO 500
4 A C))
/ (2 A)
200
WRITE(6,250)
250
FORMAT(/,IX,The Distance
K1 = 10
GOTO 1000
Calculation
is Screwed up!)
500
R2 = Rl R3
K1 = 1
1000
RETURN
END

c
c
c
c
c
c
$**$**$$**£$£******$***$*
* *
* IMAGE.FOR *
* *
Hi#******#******##***#**
INTEGER RT, CT, VT, RD, CD, IV(3), CO(2)
CHARACTER *2 EL
CHARACTER *10 SMPLE, CTO
CHARACTER *30 GFFILE, DTFILE, XRFFIL
CHARACTER *30 SPFILE(8), PDFILE(8)
CHARACTER *30 SFILE
DIMENSION US(3),E(4),FA(4),UA(4),UB(4)
DIMENSION ED(4),YI(2),A0(3),E0(4)
DIMENSION SP(192,4),P1(192,24),P2(192,24)
DIMENSION AD(24),V(21),V0L(192)
DIMENSION PE(2),XS(2),YS(2),ZS(2),RX(2),IT(4)
DIMENSION GF(12,192), GFT0TAL(8)
REAL JA(4), KS, KY
PI = 3.14159
q9 = 0.0
WRITE(6,25)
25 F0RMAT(/,1X,What sample is being counted ?)
READ(5,30) SMPLE
30 FORMAT(AIO)
WRITE(6,40)
40 F0RMAT(/,1X,In what file should the Geometry Factor,/,
1 IX,results be stored? (Ex: Dr:File.Ext))
READ(5,45) GFFILE
45 F0RMAT(A3O)
WRITE(6,50)
50 FORMAT(/,IX,In what file is the Sample data stored?)
READ(5,55) SFILE
55 FORMAT(A30)
OPEN(1,FILE=SFILE,STATUS=OLD)
C
C INPUT THE TARGET CONTAMINATION, U OR TH
C
READ(1,60) EL
60 F0RMAT(A2)
WRITE(6,60) EL
C
C INPUT THE SAMPLE DRY SOIL WEIGHT FRACTION
C
READ(1,*) WF
WRITE(6,*) WF
C
C INPUT THE SAMPLE DENSITY (GM/CC)

191
C
READ(1,*) SD
WRITE(6,*) SD
C
C READ EXTRA DATA STORED IN SAMPLE FILE BUT NOT
C NEEDED BY THIS PROGRAM
C
DO 10 I = 1,3
10 READCl,*) QHLD
C
C INPUT THE SAMPLE LINIAR ATTENUATION COEFFICIENT (1 / CM)
C FOR 136.476 keV
C
READCl,*) US(1)
C
C FOR 122.063 keV
C
READCl,*) US(2)
C
C IF EL = TH, FOR 93.334 keV
C IF EL = U ', FOR 98.428 keV
C
READ(1,*) US(3)
C
C WHICH TWO CO-57 SOURCES WERE USED? (EX:3,2 OR 3,1 ETC.)
C
C0(1) = 3
C0(2) = 2
CLOSE(1,STATUS='KEEP)
DTFILE = [LAZ0.DISS.DATA3REV6.DAT
XRFFIL = '[LAZO.DISS.DATA]XRFDTA.DAT'
WRITEC6.70) DTFILE
70 FORMAT(/,IX,READING ATTENUATION DATA FROM FILE >,A10)
OPEN(1,FILE=DTFILE,STATUS=OLD')
DO 75 I = 1,12
75 READCl,*) IMNTH
DO 80 I = 1,4
80 READCl,*) FHOLD
E(3) = 0.0
E(4) = 0.0
DO 85 I = 1,4
85 READCl,*) FA(I)
FA(3) = 0.0
FA(4) = 0.0
DO 90 I = 1,4
90 READCl,*) UA(I)
UA(3) = 0.0
UA(4) = 0.0

DO 95 I = 1,4
95 READ(1,*) UB(I)
UB(3) = 0.0
UB(4) =0.0
DO 100 I = 1,4
100 READ(1,*) ED(I)
ED(3) = 0. 0
ED(4) = 0.0
DO 105 I = 1,3
105 READ(1,*) AO(I)
DO 110 I = 1,2
110 READ(1,*) EO(I)
DO 115 I = 1,2
115 READd,*) YI(I)
READ(1,*) FHOLD
DO 120 I = 1,4
READ(1,*) JACI)
120 JA(I) = SQRTCJA(I))
JA(3) = 0.0
JA(4) =0.0
CLOSE(1,STATUS=*KEEP)
C
C SOURCE-TARGET DISTANCE (STD5A TO 50) FILES AND
C TARGET-DETECTOR DISTANCE (TDD5A TO 50) FILES
C
150
160
175
SPFILE(l) = [LAZO.DISS.DATA]STD5A.DAT
SPFILE(2) = [LAZO.DISS.DATA]STD5C.DAT
SPFILE(3) = [LAZO.DISS.DATA]STD5E.DAT
SPFILE(4) = [LAZO.DISS.DATA]STD5G.DAT
SPFILE(5) = [LAZO.DISS.DATA]STD5I.DAT
SPFILE(6) = [LAZO.DISS.DATA]STD5K.DAT
SPFILEC7) = [LAZO.DISS.DATA]STDSM.DAT
SPFILE(8) = [LAZO.DISS.DATA]STD50.DAT
PDFILE(l) = [LAZO.DISS.DATA]TDD5A.DAT
PDFILEC2) = [LAZO.DISS.DATA]TDD5C.DAT
PDFILE(3) = [LAZO.DISS.DATA]TDD5E.DAT
PDFILEC4) = [LAZO.DISS.DATA]TDD5G.DAT
PDFILE(5) = [LAZO.DISS.DATA]TDD5I.DAT'
PDFILE(6) = [LAZO.DISS.DATA]TDD5K.DAT
PDFILE(7) = [LAZO.DISS.DATA]TDD5H.DAT
PDFILEC8) = [LAZO.DISS.DATA]TDD50.DAT
WRITE(6,150) XRFFIL
FORHATC/,IX,'READING XRF DATA FROM FILE ,A30)
OPEN(1,FILE=XRFFIL,STATUS=OLD)
IF (EL .EQ. U>) GOTO 175
DO 160 I = 1,10
READd,*) QHOLD
DO 180 I = 1,10

193
READ(1,*) V(I)
180 WRITE(6,*) V(I)
CLOSE(1,STATUS=KEEP)
E(3) = V(l)
UA(3) = V(2)
UB(3) = V(3)
ED(3) = V(4)
JA(3) = SQRT(V(5))
PE(1) = V(6)
PE(2) = V(7)
KS = V(8)
KY = V(9)
EC = V(10)
500 DO 1000 19 = 1,8
C
C READ SOURCE TO POINT DISTANCES AND VOLUMES FROM DISK
C
DO 950 N1 = 1,2
OPEN(1,FILE=SPFILE(19),STATUS=OLD)
READCl.O XS(1),YS(1),ZS(1),XS(2),YS(2),ZS(2)
READ(1,*) XT,YT,ZT,TR,TH,RT,CT,VT
READ(1,*) XD,YD,ZD,DR,RD,CD,NS
IF(N1 .Eq. 2) GOTO 550
13 = 1
14 = VT/2
15 = 1
GOTO 575
550 13 = VT
14 = 1 + (VT / 2)
15 = -1
575 DO 900 12 = 13,14,15
C
C READ SOURCE TO TARGET DISTANCES FROM DISK
C
DO 675 J = 1,RT CT / 2
675 READd.O SP(J, 1) ,SP(J,2) ,SP(J,3) ,SP(J,4) ,VOL(J)
C
C READ TARGET TO DETECTOR DISTANCES FROM DISK
C
OPEN(2,FILE=PDFILE(19),STATUS=OLD)
DO 700 J = i,RT CT / 2
DO 700 K = 1,RD CD
700 READ(2,*) P1(J,K),P2(J,K)
DO 710 J = 1,RD CD
710 READ(2,*) AD(J)
C
C DETERMINE GEOMETRY FACTORS
C

194
DO 900 II = 1,RT CT / 2
DO 750 1 = 1,NS
A2 = 2 Al 1
A3 = 2 A1
SOIL = EXP ( US(1) SP(I1,A3))
AIR = EXP( UA(1) .001205 (SP(I1,A2) SP(I1,A3)))
SA FA(1) AIR JA(1) SOIL
IT(A2) = SA AO(CO(A1)) (3.7E+07) YI(1)
/ ((SP(I1,A2) SP(I1,A2)) 4 PI)
SOIL = EXP ( US(2) SP(I1,A3))
AIR = EXP( UA(2) .001205 (SP(I1,A2) SP(I1,A3)))
SA = FA(2) AIR JA(2) SOIL
IT(A3) = SA A0(C0(A1)) (3.7E+07) YI(2)
/ ((SP(I1,A2) SP(I1,A2)) 4 PI)
DO 775 L = 1,2
DO 775 LI = 1,NS
L2 = (2 LI) 1 + (L 1)
RX(L) = IT(L2) PE(L) EC WF SD + RX(L)
FY = (RX(1) + RX(2)) KS KY
RX(1) = 0.0
RX(2) = 0.0
DO 800 K = 1,RD CD
SOIL = EXP( US(3) P2(I1,K))
BE = EXP( UB(3) 1.842 .0254)
AIR = EXP( UA(3) .001205 (P1(I1,K) P2(I1,K)))
AA = SOIL JA(3) AIR BE
/ (4 PI (P1(I1,K) Pl(Il.K)))
GF(I2,I1) = FY AA VOL(Il) AD(K) ED(3)
+ GF(I2,I1)
CONTINUE
CLOSEC1,STATUS='KEEP')
CL0SE(2,STATUS='KEEP')
IF(I9 .GT. 1) GOTO 915
IF(N1 .EQ. 2) GOTO 915
HRITE(6,910) GFFILE
910 FORHATC/,IX,'Ready to store GF data in file ,A30)
0PEN(3,FILE=GFFILE,STATUS='NEW)
915 IF(N1 .Eq. 2) GOTO 920
16 = 1
17 = VT/2
GOTO 925
920 16 = 1 + (VT/2)
17 = VT
925 DO 930 I = 16,17
DO 930 J = 1,RT CT / 2
930 GFT0TALCI9) = GFT0TAL(I9) + GF(I,J)
WRITEC6,*) I9.GFT0TALCI9)
HOLD = C0(1)
1
750
1
775
1
800
1
900

195
C0(1) = C0(2)
C0(2) = HOLD
DO 950 I = 1,VT
DO 950 J = 1,RT CT / 2
950 GF(I,J) = 0.0
WRITE(6,955) 19
955 FORMAT(/,IX,GF data completed for Geometry #,11)
WRITE(3,*) GFT0TALCI9)
1000 CONTINUE
CLOSE(3,STATUS=KEEP)
C
C THIS SECTION PRINTS OUT ALL THE USER SUPPLIED
C SETUP INFORMATION FOR EACH IMAGE RUN.
C
CTO = BOTTLE
WRITE(6,1010) SMPLE,CTO,WF,SD,EL
1010 F0RMAT(/,1X,THIS IS AN IMAGE RUN,//,
1 THE FOLLOWING DATA IS THE USER SUPPLIED IMAGE INPUT,//,
2 THIS DATA IS FOR ,A10, / ,A6,//,
3 SAMPLE DRY SOIL WEIGHT FRACTION (WF): .F8.6,//,
4 SAMPLE DENSITY (SD): ,F8.6, gm/cc,//,
5 THIS SAMPLE IS CONTAMINATED WITH ,A2,//,
6 SOIL LINEAR ATTENUATION COEFFICIENTS (1 / cm),/,
7 ENERGY (MeV),US (1/cm))
DO 960 I = 1,3
960 WRITE(6,*) E(I),US(I)
DO 963 I = 1,8
963 WRITE(6,965) I.GFTOTAL(I)
965 FORMAT(/,IX,GF total for Geometry #,I1, is .F12.8)
WRITE(6,970) GFFILE
970 FORMAT(/,IX,GEOMETRY FACTORS STORED IN FILE ,A30)
9000 END

****************************
* *
* COMPTON.FOR *
* *
****************************
COMMON XTC,YTC,ZTC,TR
INTEGER RT, CT, VT, RD, CD
CHARACTER *1 RAM, A
CHARACTER *2 ELEMENT
CHARACTER *35 XRF, COMDTA
CHARACTER *35 DATFIL, GFFILE
CHARACTER *35 TGFILE, GEOM
DIMENSION XT(3840),YT(3840),ZT(3840),XD(24),YD(24),ZD(24)
DIMENSION XS(2),YS(2),ZS(2)
DIMENSION R1T(2,3840),R2T(2,3840),R1DC24,3840),R2D(24,3840)
DIMENSION U(2,3840),V(2,3840),W(2,3840)
DIMENSION V0L(3840),AD(24),EDENSITY(2)
DIMENSION Q(10),ED(3),UB(3),US(3),UA(3),TF(2),A0(2),YI(2)
DIMENSION E(2),CTRATI0(2),ALPHA(2),SCAT(2),DSCAT(2,2)
DIMENSION FL1(2,2),FL2(2,2),C0TH(2),ES(2,2),PE(2,2),USS(2,2)
DIMENSION RX(3840),GF(3840)
REAL JA(3),M0C2,KS,KY,KA1NAT
PI = 3.14159
M0C2 = .511
RO = 2.81784E-13
RAM = 'RAM'
TGFILE = TGFILE'
GFFILE = GFFILE
DATFIL = DATFIL
GEOM = GEOM
READ GEOMETRY DATA FROM FILE GEOM
OPEN(1,FILE=GEOM,STATUS=OLD)
NUMBER OF SOURCES USED
READ(1,*) NS
SOURCE COORDINATES
DO 80 I = 1,NS
READCl,*) XS(I), YS(I), ZS(I)
TARGET CENTER CpORDINATES

197
READ(1,*) XTC, YTC, ZTC
C
C TARGET HEIGHT, TH, RADIOUS, TR,
C AND NUMBER OF TARGET DIVISIONS, RT, CT, AND VT
C
READ(1,*) TH, TR
READd,*) RT, CT, VT
CLOSE(l,STATUS=KEEP)
C
C Detector Center Coordinates
C
XDC = 0.0
YDC = 0.0
ZDC = 0.0
C
C Detector Radious, DR, and Number of Divisions, RD, CD
C
DR = 1.8
RD = 8
CD = 3
WRITE(6,100)
100 F0RMAT(/,IX,Enter the name of the Soil Data File)
WRITE(6,(1A35)) DATFIL
125 OPEN (1,FILE=DATFIL,STATUS3OLD)
WRITE(6,150)
150 F0RMAT(/,1X,Is the Sample Contaminated with U or Th?)
READ(1,(A3)) ELEMENT
WRITE(6,(A3)) ELEMENT
WRITE(6,160)
160 FORMAT(/,IX,What weight fraction of the sample is Soil?)
READ(1,*) WF
WRITE(6,*) WF
WRITE(6,170)
170 F0RMAT(/,1X,What is the Soil Density (gm/cc) ?)
READ(1,*) SD
WRITE(6,*) SD
WRITE(6,180)
180 F0RMAT(/,1X,What are the Hubble Fit parameters for the Soil
1 Liniar Attenuation Coefficient d/cm) fit?,/,
2 IX,Note: Energy units for this fit are 1/10 MeV,,/,
4 IX,(Ex: 136keV=1.36),/,
5 lX,Us(l/cm) = Exp(-(A1 + B1 LOG(E) + Cl (L0G(E))**2)),/,
6 IX,Input Al, Bl, Cl)
READ(1,*) Al
WRITEC6,*) Al
READ(1,*) Bl
WRITE(6,*) Bl
READ(1,*) Cl

198
WRITE(6,*) Cl
HRITE(6,190)
190 F0RMAT(/,IX,Input the Soil Liniar Attenuation Coefficients
1 for 136 ft 122 keV,/,
2 IX,136 keV)
READ(1,*) US(1)
WRITE(6,*) US(1)
HRITE(6,195)
195 F0RHAT(/,IX,122 keV)
READ(1,*) US(2)
HRITE(6,*) US(2)
IF (ELEMENT .Eq. TH) GOTO 220
C
C Natural K-alphal emission rate, (Kal/sec)/(pCi U238),
C from ICRP Report #38.
C
KA1NAT = 8.584E-5
WRITE(6,200)
200 F0RMAT(/,IX,98.428 keV)
READ(1,*) US(3)
GOTO 250
C
C Natural K-alphal emission rate, (Kal/sec)/(pCi Th232),
C from ICRP Report #38.
C
220 KA1NAT = .001584
WRITE(6,230)
230 F0RMAT(/,IX,93.334 keV)
READ(1,*) US(3)
250 WRITE(6,*) US(3)
CLOSE(1,STATUS=KEEP)
WRITE(6,260)
260 F0RMAT(/,IX,Compton Data will now be read)
COMDTA = $2$DUA14:[LAZO.DISS.DATA]COMDTA.DAT
OPEN (3,FILE=COMDTA,STATUS='OLD)
C
C Input the energies of Co-57 gammas (MeV), Compton-to-Total
C ratios for Soil, CTRATIO(l), CTRATI0(2), TF and Atten data
C for Steal and Air at 136 ft 122 keV, TF(1),TF(2),UA(1),UA(2),
C Source Strength data, A0(1), A0(2), Gamma Yields, YI(1), YI(2),
C and Jar Transmission Fraction data, JA(1), JA(2).
C
READ(3,*) E(1),E(2)
1
2
3
4
5
CTRATIO(l),CTRATI0(2)
TF(1),TF(2),
UA(1),UA(2),
A0(1),A0(2),
YI(1),YI(2),

199
6 JA(1),JA(2)
qr = ja(i)
JA(1) = SQRT(q7)
q7 = JA(2)
JA(2) = SqRT(q7)
c
C Input data specific to U or Th. PE Cross Sections at 150 keV
C and Ekab, and EC
C
DO 300 I = 1,2
READ(3,*) EKAB, PEI, PE2, EC
300 IF (ELEMENT .Eq. U ) GOTO 310
310 CL0SE(3,STATUS=,KEEP>)
C
C Determine Target and Detector Node Points
C
II = 0
DO 350 I = 1,CD
DO 350 J = 1,RD
II = II + 1
T = (2 PI / RD) (J .5)
XD(I1) = (DR / CD) (I .5) COS(T) + XDC
YD(I1) = (DR / CD) (I .5) SIN(T) + YDC
ZD(I1) = 0.0
350 AD(I1)=PI*((I*DR/CD)**2-((I-1)*DR/CD)**2)/RD
II = 0
DO 400 K = 1,VT
DO 400 I = 1,CT
DO 400 J = 1,RT
II = II + 1
T = (2 PI / RT) (J .5)
XT(I1) = (TR / CT) (I .5) COS (T) + XTC
YT(I1) = (TR / CT) (I .5) SIN (T) + YTC
ZT(I1) = ( TH / 2) + (TH / VT) (K .5) + ZTC
VOL(Il) = PI*(TH/ VT) ((I TR / CT)**2
1 ((I 1) TR / CT)**2) / RT
DO 375 L = 1,2
CALL DISTANCE (XS(L),YS(L),ZS(L),XT(I1),YT(I1),ZT(I1),
1 U(L,I1),V(L,I1),W(L,Ii),
2 R1T(L,I1),R2T(L,I1),K7)
IF (K7 .Eq. 10) GOTO 9000
375 CONTINUE
DO 385 L = 1,24
CALL DISTANCE (XD(L),YD(L),ZD(L),XT(I1),YT(I1),ZT(I1),
1 HLD1.HLD2.HLD3,
2 RID(L,II),R2D(L,I1),K7)
IF (K7 .Eq. 10) GOTO 9000
385 CONTINUE

200
400 CONTINUE
435 WRITE(6,440)
440 FORMAT/,IX,Target and Detector Node Point,/,
1 Coordinates Calculated)
C
C Calculate Soil Electron Density
C
DO 450 J1 = 1,2
ALPHA(Jl) = E(J1) / M0C2
TERM = (1 + 2 ALPHA(Jl))
PI = (1 + ALPHA(Jl)) / ALPHA(J1)**2
P2 = (TERM + 1) / TERM
P3 = (1 / ALPHA(Jl)) LOG(TERM)
P4 = (1 / (2 ALPHA(Jl))) LOG(TERM)
P5 = (1 + 3 ALPHA(Jl)) / (TERM**2)
SCAT(Jl) = 2 PI R0**2 (PI (P2 P3) + P4 P5)
450 EDENSITY(Jl) = US(J1) CTRATIO(Jl) / SCAT(Jl)
EDENS = (EDENSITY(l) + EDENSITY(2)) / 2
C
C Calculate Source Flux at the Scatter Point
C
RTCTVT = RT CT VT
DO 1000 I = 1,RTCTVT
DO 500 II = 1,NS
DO 500 Jl = 1,2
R1TI1I = R1T(I1,I)
R2TI1I = R2T(I1,I)
AIR = EXP(-UA(J1) .001205 (R1TI1I R2TI1I))
SOIL = EXP(-US(Ji) R2TI1I)
SA = TF(J1) AIR SOIL JA(J1)
500 FLl(Il.Jl) = A0(I1) YI(J1) 3.7E+07 SA
1 / (4 PI R1TI1I R1TI1I)
C
C Determine XRF contribution of scatter in point I
C to every point J, ( J O I).
C
DO 900 J = 1,RTCTVT
IF (J .Eq. I) GOTO 900
C
C Determine Scatter Photon Angle, Energy, and PE Cross Section
C
K7 = 1
CALL DISTANCE (XT(I),YT(I),ZT(I),XT(J),YT(J),ZT(J),
1 UP1P2,VP1P2,WP1P2,
2 R1P2P1,HLD1,K7)
IF (K7 .Eq. 10) GOTO 9000
DO 550 II = 1,NS
550 COTH(Il) = U(I1,I) UP1P2 + V(Ii,I) VP1P2

201
1 + W(I1,I) WP1P2
Q9 = O
DO 560 II = 1 ,NS
DO 560 J1 = 1,2
ES(Il.Jl) = H0C2 / (1 COTH(Il) + (1 / ALPHA(Jl)))
IF (ES(Il.Jl) .LT. EKAB) GOTO 555
IF (COTH(Il) .EQ. 1.0) GOTO 555
PE(I1,J1) = PEI ((.15 ES(Il.Jl)) / (.15 EKAB))
1 (PEI PE2)
GOTO 560
555 Q9 = Q9 + 1.
PE(I1,J1) = 0.
560 CONTINUE
IF (q9 .Eq. 4.) GOTO 900
C
C Calculate the Soil Differential Scatter XSect (1/cm)
C
DO 650 II = 1,NS
DO 650 J1 = 1,2
IF (PE(I1,Jl) .NE. 0.) GOTO 600
DSCAT(Il.Jl) = 0.
GOTO 650
600 PI = (1 / (1 + ALPHA(Jl) (1 C0TH(I1))))**2
P2 = (1 + C0TH(I1)**2) / 2
P3 = (ALPHA(J1)**2 (1 C0TH(I1))**2)
P4 = (1 + C0TH(I1)**2) (1 + ALPHA(Jl) (1 -COTH(Ii)))
DSCT = RO*RO PI P2 (1.0 + P3 / P4)
DSCAT(Il.Jl) = DSCT EDENS
650 CONTINUE
C
C Calculate the Soil Attenuation Coefficients for Scatter Gammas
C
DO 700 II = 1,NS
DO 700 Jl = 1,2
700 USS(Il.Jl) = EXP(-(A1 + B1 L0G(ES(I1,Jl)*10)
1 + Cl (L0G(ES(I1,Jl)*10))**2))
C
C Calculate the Photoelectric Reaction Rate at Target Point
C
DO 800 II = 1,NS
DO 800 Jl = 1,2
SOIL = EXP(-USS(I1,Jl) R1P2P1)
FL2(I1,Jl) = FLKI1.J1) DSCAT(I1,Jl) VOL(I)
1 SOIL / R1P2P1**2
800 RX(J) = FL2(I1,Jl) PE(I1,J1) EC WF SD VOL(J)
1 + RX(J)
900 CONTINUE
1000 CONTINUE

WRITE(6,1100)
1100 F0RMAT(/,1X,'XRF Reaction Rates due to Compton Scatter
1 /,IX,calculated. Calculating Detector Respons
2 /,lX,due to Compton Scatter XRF.)
1105 XRF = $2$DUA14:[LAZO.DISS.DATA]XRFDTA.DAT
WRITE(6,1110) XRF
1110 F0RHAT(/,IX,'Reading XRF data from file ,1A31)
OPEN(1,FILE=XRF,STATUS=OLD')
IF (ELEMENT .Eq. U') GOTO 1150
DO 1125 I = 1,10
1125 READ(1,*) QHOLD
1150 DO 1155 I = 1,10
1155 READ(1,*) q(I)
CLOSE(1,STATUS='KEEP')
UA(3) = q(2)
UB(3) = q(3)
ED(3) = q(4)
JA(3) = SqRT(q(5))
KS = q(8)
KY = q(9)
c
C Read in Target-Detector Distances and Calculate
C Detector Responses for each target point.
C
GFNT = 0.0
GFCT = 0.0
BE = EXP(-UB(3) 1.842 .0254)
DO 1400 I = 1,RTCTVT
DO 1350 J = 1,24
R1DJI = R1D(J,I)
R2DJI = R2D(J,I)
SOIL = EXP(-US(3) R2DJI)
AIR = EXP(-UA(3) .001205 (R1DJI R2DJI))
1350 AA = AA + SOIL JA(3) AIR BE AD(J)
1 / (4 PI R1DJI R1DJI)
GFCOMPTON = RX(I) AA KS KY ED(3)
GFNAT = KA1NAT VOL(I) SD WF AA ED(3)
GF(I) = GFCOMPTON + GFNAT
AA = 0.0
GFNT = GFNT + GFNAT
GFCT = GFCT + GFCOMPTON
1400 CONTINUE
WRITE(6,2350)
2350 F0RMAT(/,1X,'In what file should the data be saved,/,
1 IX,(Filename.Ext))
WRITE(6,*) GFFILE
2375 OPEN(1,FILE=GFFILE,STATUS=NEW)
TOTAL = GFNT + GFCT

2100
2200
2225
2250
9000
203
WRITE(1,*) TOTAL
CL0SE(1,STATUS=*KEEP)
WRITE(6,2100)
FORHAT(/fIX,Geometry Factors Calculated)
WRITE(6,2200) TOTAL
FORHAT(/,IX,The sum of all Geometry Factors is .1E16.10)
WRITE(6,2225) GFCT
F0RMAT(/,1X,The sum of Compton Geometry Factors is ,1E16.10)
WRITE(6,2250) GFNT
F0RMAT(/,IX,The sum of Natural Geometry Factors is .1E16.10)
END

204
C
C
C
C
c
c
c
10
20
30
50
75
80
*****************************
* *
* SUBROUTINE DISTANCE *
* *
*****************************
SUBROUTINE DISTANCE (Xl,Yl,ZltX2,Y2tZ2,U,V,W,Rl,R2,K)
COMMON XTC,YTC.ZTC.TR
DI = X2 XI
D2 = Y2 Y1
D3 = Z2 Z1
R1 = SQRT(D1*D1 + D2*D2 + D3*D3)
U = D1 / R1
V = D2 / Ri
W = D3 / R1
IF (K .EQ. 1) GOTO 75
X1XT = XI XTC
Y1YT = Y1 YTC
A = U*U + V*V
B = 2 U X1XT + 2 V Y1YT
C = X1XT*X1XT + Y1YT*Y1YT TR*TR
R3 = ( B + SQRT(B*B 4 A C)) / (2 A)
IF (R3 .LT. 0.) GOTO 10
IF (R3 .LT. Rl) GOTO 50
R3 = ( B SQRT(B*B 4 A C)) / (2 A)
IF (R3 .LT. 0.) GOTO 20
IF (R3 .LT. Rl) GOTO 50
WRITE(6,30)
FORMAT(/.IX,DISTANCE CALCULATION IS SCREWED UP!)
K = 10
GOTO 80
R2 = Rl R3
K = 0
RETURN
END

205
C ************************
c *
C ASSAY.FOR *
C *
c ************************
c
CHARACTER *1 TEST, OS
CHARACTER *30 GEOM, GFFILE, CGFFILE
CHARACTER *30 PKFIL, SAMPLE, DRFIL, OUT
DIMENSION X(32),Y(32),A(32,7),TA(7,32),F(32),DY(32),V(9)
DIMENSION AA(7,7),AM(7,8),H2(7,7),ER(8)
DIMENSION qi(32,7),Q2(7,32),Q3(7,7),DT(7),DA(7)
DIMENSION GF(32,192), GFT(16), DR(32), CHISq(2)
DIMENSION CGFC3840), CGFT(16), GFT0T(16)
REAL MN, LH, LM, LS, LT, NCR, NLT, NF, NER(8)
INTEGER Wl, W, NP
INTEGER RT, CT, VT, q, P
PI = 3.14159
GEOM = '[LAZO.DISS.DATA]GE0M5A.DAT
WRITE(6,20)
20 FORMAT(/,IX,In what file is GF data stored?)
READ(5,25) GFFILE
25 F0RMAT(A25)
WRITE(6,45)
45 FORMAT(/,IX,In what file is the Compton GF data stored?)
READ(5,50) CGFFILE
50 F0RMAT(A25)
WRITE(6,55)
55 F0RMAT(/,1X,In what file is the XRF Peak Data stored?)
READ(5,57) PKFIL
57 F0RMAT(A25)
NP = 8
OPEN(1,FILE=GEOM,STATUS=OLD)
READ(1,*) AHOLD
DO 70 I = 1,AHOLD
70 READ(1,*) AHI, AH2, AH3
READ(1,*) AHI, AH2, AH3
READ(1,*) TH, TR
READ(1,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
100 q = 2
OPEN(1,FILE=GFFILE,STATUS=OLD)
DO 120 P = 1,NP
READd,*) GFT(P)
GFT(P) = GFT(P) 2
WRITE(6,115) P, GFT(P)
115 FORMAT(/,IX,GF Total for Position #,I1, is .F10.5)
120 CONTINUE

CLOSE(i,STATUS=KEEP)
OPEN(1,FILE=CGFFILE,STATUS=OLD)
DO 200 P = 1,NP
READ(1,*) CGFT(P)
GFTOT(P) = GFT(P) + CGFT(P)
WRITE(6,147) P,CGFT(P)
147 FORMAT(/,IX,Compton GF Total for Position #,I1,
1 ,1X, is .F10.5)
200 CONTINUE
CLOSE(1,STATUS=KEEP)
C
C THIS PROGRAM FITS DETECTOR RESPONSE DATA TO AN
C LINIAR FUNCTION. THE X-AXIS REPRESENTS THE
C CALCULATED SAMPLE GEOMETRY FACTOR, GF, WHILE THE
C Y-AXIX REPRESENTS THE MEASURED DETECTOR RESPONSE.
C
W1 = 1
OPEN(1,FILE=PKFIL,STATUS=OLD)
READCl,237) NP
237 F0RMAT(1I2)
READ(1,240) LH, LM, LS
240 F0RMATC3F1O.5)
TI = 1.0
DO 300 I = 1,NP
READ(1,245) D4, M5, Y5
245 FORMAT(1F10.5, 112, 1F10.5)
READ(1,250) HR, MN
250 FORMAT(2F10.5)
READ(1,255) RH, RM, RS
255 FORMAT(3F10.5)
READ(1,260) DR(I),ER(I)
260 F0RMAT(2F15.5)
CH = RH + RM / 60.0 + RS / 3600.0
CALL DECAY(HR, MN, CH, D4, M5, Y5, NF,MK)
LT = LH 3600.0 + LM 60.0 + LS
RT = RH 3600.0 + RM 60.0 + RS
CR = DR(I) / LT
NCR = EXP ( LOG (CR) .583863 (LT RT) / LT)
NLT = LT CR / NCR
X(I) = GFTOT(I)
Y(I) = DR(I) / (NLT NF)
NER(I) = ER(I) / (NLT NF)
WRITE(6,*) I, X(I), Y(I), NER(I)
TI = TI + 1.0
300 CONTINUE
CLOSE(1,STATUS=KEEP)
M = 1
N = NP
CALL EXPLICIT(X,Y,NER,NP,F,Ai,ZERO,DAI,DZERO,CHI)

207
COV = DAI
CHISQ(l) = CHI
600 WRITE(6,605)
605 F0RMAT(/,1X,In what file should results be stored?)
READ(5,(A10)) OUT
OPEN(i,FILE=OUT,STATUS=NEW)
WRITE(1,610)
610 FORMAT(/,IX,This is an ASSAY.FOR run)
WRITEC1,1030) PKFIL
1030 F0RMAT(/,1X,XRF Peak data from file ,A25)
WRITE(1,1040) GFFILE
1040 FORMAT(/,IX,Geometry Factor data form file ,A25)
WRITE(1,1045) CGFFILE
1045 F0RMAT(/,IX,Compton Geometry Factor data from file ,A25)
WRITE(1,1050) GEOH
1050 F0RMAT(/fIX,System Geometry data from file ,A25)
WRITE(1,620)
620 FORMAT(/,IX,Liniar Fit Coefficients,/,
1 IX,Y(I) = A X(I))
WRITE(1,630) Al.COV
630 F0RMAT(/,1X,A = Contamination Concentration (pCi/gm) =
1 ,F10.5, +- .F10.5)
WRITE(1,637) CHISq(l)
637 F0RMAT(/,IX,The Reduced Chi**2 value for the fit = .F10.5)
WRITE(1,640)
640 FORMAT(/,25X,Fit Results,//,
1 IX,Position,Ex,GF Sum,7X,DR Fit,7X,
2 DR Meas,7X, Del ('/,),/)
DO 650 I = 1,NP
DEL = 100.0 (Y(I) F(I)) / Y(I)
650 WRITE(1,660) I,X(I), F(I), Y(I), DEL
660 FORMAT(4X,I1,5X,F10.5,5X,F10.5,3X,F10.5,3X,F10.5)
9000 END

208
C
C **************************
c *
C SUBROUTINE DECAY *
C *
C **************************
c
C THIS SUBROUTINE DETERMINES CO-57 SOURCE ACTIVITY
C DECAYED FROM 1 OCTOBER, 1986, TO HALF WAY THROUGH
C THE XRF COUNT UNDER CONSIDERATION. AS OF
C 1 OCTOBER, 1986, ALL THREE CO-57 SOURCES WERE
C ROUGHLY 2 MCI.
C
SUBROUTINE DECAY(HR,MN,CH,D4,M5,Y5,NF,MK)
REAL MN, NF, MTH(12), LA
IF(MK .EQ. 1) GOTO 25
MTH(l) = 31.0
MTH(2) =28.0
MTH(3) =31.0
MTH(4) =30.0
MTH(5) = 31.0
MTH(6) =30.0
MTH(7) = 31.0
MTH(8) = 31.0
MTH(9) = 30.0
MTH(IO) = 31.0
MTH(ll) = 30.0
MTH(12) = 31.0
25 MK = 1
HC057 = 271.7
H6 = HR + MN / 60.0 + CH / 2.0
IF(H6 .GT. 24.0) GOTO 50
D5 = D4 1.0 + H6 / 24.0
GOTO 55
50 D5 = D4 + (H6 24.0) / 24.0
55 Ti = 91.5
IF(M5 .EQ. 1) GOTO 80
DO 75 J = 1,(M5 1)
75 Tl = Tl + MTH(J)
80 T = Tl + D5
LA = LOG (2.0) / HC057
NF = EXP ( LA T)
RETURN
END

209
C
C i*****************************
c *
C SUBROUTINE EXPLICIT *
C *
C i*****************************
c
C This subroutine determins the explicit solution
C to the linear regression:
C
C DR(I) = Zero + Slope X(I)
C
C The errors associated with the fitting parameters
C Zero and Slope are also calculated.
C
SUBROUTINE EXPLICITCX,Y,SIG,NP,F,SLOPE,ZERO,DS,DZ,CHISq)
REAL H(2,2), C0V(2,2), X(8), Y(8), SIG(8), F(8)
M = 2
H(l,l) = 0.0
C0V(1,1) = 0.0
DO 5 I = 1,NP
S H(1,1) = H(l,l) + (X(I) / SIG(I))**2
C0V(1,1) = 1.0 / H(l,l)
DO 7 I = 1,NP
7 SLOPE = SLOPE + C0V(1,1) Y(I) X(I) / (SIG(I)**2)
DS = SQRT(C0V(1,1))
ZERO = 0.0
DZ = 0.0
DO 9 I = 1,NP
F(I) = SLOPE X(I)
9 CHISq = CHISq + ((Y(I) F(I))**2) / (F(I) (NP 2))
RETURN
DO 10 I = i,NP
10 H(1,1) = H(1,1) + (1.0 / (SIG(I)**2))
H(l,2) = 0.0
DO 20 I = 1,NP
20 H(l,2) = H(l,2) + (X(I) / (SIG(I)**2))
H(2,1) = H(l,2)
H(2,2) = 0.0
DO 30 I = 1,NP
30 H(2,2) = H(2,2) + ((X(I)**2) / (SIG(I)**2))
C0V(1,1) = 1.0
C0V(1,2) = 0.0
C0V(2,1) = 0.0
C0V(2,2) = 1.0
DO 200 I = 1,M
T1 = H(I,I)
DO 50 J = 1,H

50
100
150
200
250
300
210
H(I,J) = H(I,J) / T1
C0V(I,J) = C0V(I,J) / T1
DO 150 J = 1,M
IF(J .EQ. I) GOTO 150
T2 = H(J,I)
DO 100 K = 1,H
H(J,K) = H(J,K) (H(I,K) T2)
COV(J.K) = COV(J.K) (COVCI.K) T2)
CONTINUE
CONTINUE
WRITE(6,0 H(l,l), H(1,2), H(2,l), H(2,2)
WRITE(6,0 C0V(1,1), C0V(1,2), C0V(2,1), C0V(2,2)
DO 250 I = 1,NP
PI = PI + C0V(1,1) Y(I) /
P2 = P2 + C0V(2,1) Y(I) *
P3 = P3 + C0V(1,2) Y(I) /
P4 = P4 + C0V(2,2) Y(I) *
ZERO = PI + P2
SLOPE = P3 + P4
DZ = SqRT(COV(l,l))
DS = SQRT(C0V(2,2))
DO 300 I = 1,NP
F(I) = ZERO + SLOPE 1(1)
CHISQ = CHISq + ((Y(I) F(I))**2)
RETURN
END
(SIG(I)**2)
1(1) / (SIG(I)**2)
(SIG(I)**2)
X(I) / (SIG(I)**2)
/ (F(I) (NP 2))

Dal a File Programs
These programs were written to create data files for the above listed data processing
programs. These programs are written in FORTRAN-77 and were run on a VAX Cluster
main-frame computer. REV6.FOR lists detector system calibration data. COMDTA.FOR
lists data used for the compton x-ray production calculations. XRFDTA.FOR lists data
used for direct gamma ray x-ray production calculations. And finally the GEOM5A.FOR
through GE0M50.F0R list data which describe the geometry of the experimental setup
used to count each soil target.

212
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
* *
* REV6.F0R *
* *
* ATTENUATION COEFFICIENT *
* DATA VERSION 6 *
* *
******************************
CHARACTER *10 DATFIL
DIMENSION MTH(12),E(4),FA(4),UA(4),UB(4),ED(4)
DIMENSION A0(3),E0(2),YI(2)
REAL JA(4)
DATFIL = REV6.DAT
DATA SOURCE REV.6 IS THE FINAL SYSTEM CALIBRATION.
FOR AIR, THE TOTAL MASS ATTENUATION COEFFICIENT IS
USED. FOR BE, THE REMOVAL MASS ATTENUATION COEFFICIENT
IS USED. FOR STEAL AND FOR JARS, MEASURED TRANSMISSION
FRACTIONS ARE USED.
NUMBER OF DAYS PER MONTH DATA FOR CURIE CALCULATIONS
DATA MTH(l), MTH(2), MTH(3), MTH(4) / 31, 28, 31, 30 /
DATA MTH(5), MTH(6), MTH(7), MTH(8) / 31, 30, 31, 31 /
DATA MTH(9), MTH(IO), MTH(ll), MTH(12) / 30, 31, 30, 31 /
GAMMA ENERGIES, KEV, FROM, RADIOACTIVE DECAY
DATA TABLES, BY KOCHER
DATA E(1),E(2),E(3),E(4) / .136476, .122063, .105308, .086545 /
THE FOLLOWING TRANSMISSION FRACTIONS WERE MEASURED. FOR
THE CO-57 SOURCES, THE WINDOW IS INTEGRAL WITH THE SOURCE
CAPSUL, IS MADE OF 304L STAINLESS, AND IS APPROXIMATELY
.0254 CM THICK. FOR THE EU-15S SOURCE, THE WINDOW IS
WELDED IN PLACE, IS MADE OF 302 STAINLESS, AND IS
APPROXIMATELY .005 CM THICK. TRANSMISSION SPECTRA ARE
LOCATED IN FILES SSC03.DATA AND SSEU.DATA.
DATA FA(1),FA(2),FA(3),FA(4) / .94598, .93925, .98771, .98146 /
AIR MASS ATTENUATION COEFFICIENTS, SQ CM/GM, FROM
PHOTON MASS ATTENUATION AND ENERGY ATTENUATION
COEFFICIENTS FROM 1 KEV TO 20 MEV, BY HUBBLE.
DATA UA(1),UA(2),UA(3),UA(4) / .1406, .1459, .1521, .1623 /

213
C
C BE HASS ATTENUATION COEFFICIENTS, SQ CH/GH, FROM
C PHOTON HASS ATTENUATION AND ENERGY ABSORPTION
C COEFFICIENTS FROH 1 KEV TO 20 HEV, BY HUBBLE
C
DATA UB(1),UB(2),UB(3),UB(4) / .1217, .1253, .1296, .1352 /
C
C INTRINSIC DETECTOR EFFICIENCIES FOR THE ABOVE ENERGIES
C AS CALCULATED BY NBS.EFF AND EFFICIENCY.
C
DATA ED(1),ED(2),ED(3),ED(4) / .69336, .76561, .83025, .87363 /
C
C CO-57 SOURCE STRENGTHS, IN mCi AS OF 1 OCT, 1986,
C FOR SOURCES #1, #2, AND #3 RESPECTIVELY. SOURCE
C WERE CALCULATED BY NBS.EFF AND EFFICIENCY FROH
C THIS ATTENUATION COEFFICIENT DATA.
C
DATA A0(1),A0(2),A0(3) / 2.02203, 2.20737, 2.38809 /
C
C EU-155 EHISSION RATES, IN GAHHAS/SEC AS OF 1 APRIL,
C 1986, FOR ENERGIES 105.308 KEV AND 86.545 KEV
C RESPECTIVELY. EHISSION RATES WERE CALCULATED BY
C NBS.EFF AND EFFICIENCY FROH THIS ATTENUATION
C COEFFICIENT DATA.
C
DATA E0(1),E0(2) / 1.82496E7, 2.54845E7 /
C
C GAHHA YIELDS FOR CO-57 AT ENERGIES 136.476 KEV
C AND 122.063 KEV, RESPECTIVIELY, TAKEN FROH
C NCRP REPORT #58, APPENDIX A.3.
C
DATA YI(1),YI(2) / .1061, .8559 /
C
C DETECTOR AREA, SQ CH, TAKEN FROH VENDOR DOCUHENTS
C
DATA AD / 10.1788 /
C
C AVERAGE BOTTLE TRANSHISSION FRACTIONS FOR THE ABOVE ENERGIES
C CALCULATED BY TRANSHISSION USING REV.6 DATA.
C
DATA JA(1),JA(2),JA(3),JA(4) / .97190, .97110, .96970, .96792 /

214
C
C STORE DATA IN FILE REV6.DAT
C
OPEN(1,FILE=DATFIL,STATUS=NEW')
DO 100 I = 1,12
100 WRITE(1,*) MTH(I)
DO 150 I = 1,4
150 WRITECl,*) E(I)
DO 200 I = 1,4
200 WRITECl,*) FA(I)
DO 250 I = 1,4
250 WRITECl,*) UA(I)
DO 300 I = 1,4
300 WRITECl,*) UB(I)
DO 350 I = 1,4
350 WRITECl,*) EDCI)
DO 400 I = 1,3
400 WRITECl,*) AOCl)
DO 450 I = 1,2
450 WRITECl,*) EOCI)
DO 500 I = 1,2
500 WRITECl,*) YICD
WRITECl,*) AD
DO 550 I = 1,4
550 WRITECl,*) JACD
CLOSEC1,STATUS=KEEP >)
END

215
C
c *
C COMDTA.FOR *
C *
c ********************
c
CHARACTER *10 DTFILE
DIMENSION E(2),CTRATI0(2),TF(2),UA(2),
1 A0(2),YI(2),EKAB(2),
2 PE1(2),PE2(2),EC(2)
REAL JA(2)
C
C Co-57 Gamma energies (MeV)
C
DATA E(l),E(2) /.136476, .122063/
C
C Compton Scatter to Total Liniar Attenuation Ratio for Soil
C as averaged for several soil types and calculated by XSECT.
C
DATA CTRATIO(l),CTRATI0(2) /.90712, .88048/
C
C Stainless Steel Co-57 Source end window attenuation fraction
C for the above energies as taken from REV.6 data.
C
DATA TF(1),TF(2) /.94598, .93925/
C
C Air mass attenuation coefficients (sq cm / gm)
C for the above energies as taken from REV.6 data.
C
DATA UA(1),UA(2) /.1406, .1459/
C
C Source Strengths (mCi) for Co-57 sources #3 and #2 as
C of 1 October, 1986, as taken from REV.6 data.
C
DATA A0(1),A0(2) /2.38809, 2.20737/
C
C Co-57 Gamma Yields for the above energies
C as taken from REV.6 data.
C
DATA YI(1),YI(2) /.1061, .8559/
C
C Bottle Transmission Fractions
C for the above energies as taken from REV.6 data.
C
DATA JA(1),JA(2) /.97190, .97110/

216
C
C The following data is for Uranium
C
C PE interpolation energy, K-absorption energy, in MeV
C from data sent to me by Hubble.
C
DATA EKAB(l) /.1156061/
C
C Uranium Photoelectric Cross Section, (sq cm / atom), for
C .150 MeV and E(k-abs) from data sent to me by Hubble.
C
DATA PEi(l),PE2(1) /.9381E-21, 1.819E-21/
C
C Specific Atom Concentration, (Atoms U/gm Soil)/(pCi U/gm Soil),
C caluclated using a Uranium half life of 4.468E9 Y, from The
C Table of Radioactive Isotopes, by E. Browne and R. B. Firestone.
C
DATA EC(1) /7.5265E15/
C
C The following data is for Thorium
C
C PE interpolation energy, K-absorption energy, in MeV
C from data sent to me by Hubble.
C
DATA EKAB(2) /.1096509/
C
C Thorium Photoelectric Cross Section, (sq cm / atom), for
C .150 MeV and E(k-abs) from data sent to me by Hubble.
C
DATA PE1(2),PE2(2) /.8702E-21, 1.939E-21/
C
C Specific Atom Concentration, (Atoms Th/gm Soil)/(pCi Th/gm Soil),
C calculated using Th half life of 1.41E10 y, from The Table
C of Radioactive Isotopes, by E. Browne and R. B. Firestone.
C
DATA EC(2) /2.3752E16/

217
C
C Data files filled with correct values
C
WRITE(6,*) JA(1),JA(2)
DTFILE = COHDTA.DAT
OPEN(1,FILE=DTFILE,STATUS=NEW)
WRITE(1,*) E(l), E(2),
1 CTRATIOCl), CTRATI0(2),
2 TF(1), TF(2), UA(1), UA(2),
3 A0(1), A0(2), YI(1), YI(2),
4 JA(1), JA(2)
DO 150 I = 1,2
150 WRITE(1,*) EKAB(I), PE1(I), PE2(I), EC(I)
CLOSE(1,STATUS='KEEP)
END

218
C
C ********************
c *
C XRFDTA.FOR *
C *
c ********************
c
CHARACTER *10 DTFILE
DIMENSION E(2),UA(2),UB(2),ETA(2),
1 PE(4),EC(2)
REAL JA(2),KS(2),KY(2)
C
C The following data is for U
C
C
C K-alpha-1 X-Ray energy (MeV) for U
C from Data Tables, by Kocher
C
DATA E(l) /.098428/
C
C Air mass attenuation coefficients, sq cm/gm,
C from, Photon Mass Attenuation and Energy
C Attenuation Coefficients from 1 keV to 20 MeV,
C by Hubble.
C
DATA UA(1) /.1550/
C
C Be transmission fractions as measured using a
C Be window similar to that actually used with
C the detector.
C
DATA UB(i) /.1314/
C
C Intrinsic detector efficiency as calculated by
C NBS.EFF and EFFICIENCY.
C
DATA ETA(l) /.84931/
C
C Transmission fraction for an average jar
C calculated using TRANSMISSION and REV.6 data.
C
DATA JA(1) /.96901/
C
C Photoelectric cross sections, in sq cm/atom, from
C U data sent to me by Hubble, for energies .136476 MeV
C and .122063 MeV.
C
DATA PE(1),PE(2) /1.2845E-21, 1.6B36E-21/

219
C
C Jump Ratio (Rk) used to calculate the fractional K-shell
C vaceincies per photoelectric interaction.
C KS = (Rk 1)/Rk, was calculated from U cross sections
C sent to me by Hubble. The fractional K x ray yield, KY,
C is from, 11 The Table of Radioactive Isotopes, by
C E. Browne and R. B. Firestone, 1986, LLNL.
C
DATA KS(1),KY(1) /.7640, .4510/
C
C The elemental concentration per pCi/gm, EC,
C (Atoms U/gm Soil)/(pCi U/gm Soil), was calculated
C using a U-238 half life of 4.468E9 y from, The
C Table of Radioactive Isotopes, by E. Browne and
C R. B. Firestone.
DATA EC(1) /7.5265E15/
C
C The following data is for Thorium
C
C K-alpha-1 X-Ray energy (MeV) for Th
C from Data Tables, by Kocher
C
DATA E(2) /.093334/
C
C Air mass attenuation coefficients, sq cm/gm,
C from, Photon Mass Attenuation and Energy
C Attenuation Coefficients from 1 keV to 20 MeV,
C by Hubble.
C
DATA UA(2) /.1581/
C
C Be transmission fractions as measured using a
C Be window similar to that actually used with
C the detector.
C
DATA UB(2) /.1330/
C
C Intrinsic detector efficiency as calculated by
C NBS.EFF and EFFICIENCY.
C
DATA ETA(2) /.86088/
C
C Transmission fraction for an average jar
C calculated using TRANSMISSION and REV.6 data.
C
DATA JA(2) /.96860/

220
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C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
Photoelectric cross sections, in sq cm/atom, from
U data sent to me by Hubble, for energies .136476 MeV
and .122063 MeV.
DATA PE(3),PE(4) /1.2284E-21, 1.6102E-21/
Jump Ratio (Rk) used to calculate the fractional K-shell
vaceincies per photoelectric interaction.
KS = (Rk 1)/Rk, was calculated from U cross sections
sent to me by Hubble. The fractional K x ray yield, KY,
is from, The Table of Radioactive Isotopes, by
E. Browne and R. B. Firestone, 1986, LLNL.
DATA KS(2),KY(2) /.7693, .4640/
The elemental concentration per pCi/gm, EC,
(Atoms U/gm Soil)/(pCi U/gm Soil), was calculated
using a U-238 half life of 4.468E9 y from, The
Table of Radioactive Isotopes, by E. Browne and
R. B. Firestone.
DATA EC(2) /2.3752E16/
Data files filled with correct values
DTFILE = XRFDTA.DAT
OPEN(1,FILE=DTFILE,STATUS=NEW)
WRITE(1,*) E(i)
WRITE(1,*) UA(1)
WRITEd,*) UB(1)
WRITE(1,*) ETA(l)
WRITEd,*) JA(1)
WRITEd,*) PE(1)
WRITEd,*) PE(2)
WRITEd,*) KS(1)
WRITEd,*) KY(1)
WRITEd,*) EC(1)
WRITEd,*) E(2)
WRITEd,*) UA(2)
WRITEd,*) UB(2)
WRITEd,*) ETA(2)
WRITEd,*) JA(2)
WRITEd,*) PE(3)
WRITEd,*) PE(4)
WRITEd,*) KS(2)
WRITEd,*) KY(2)
WRITEd,*) EC(2)
CLOSE(1,STATUS=KEEP)
END

221
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5A.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5A.DAT
This program creats file GE0M5A.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 10.5
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32

222
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5A.DAT
C
OPEN(1,FILE=GEOM,STATUS='NEW)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
HRITEd,*) XT, YT, ZT
WRITEd,*) TH, TR
HRITEd,*) RT, CT, VT
CLOSE(1,STATUS='KEEP)
END

223
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C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5C.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5C.DAT
This program creats file GE0M5C.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 10.8
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32

224
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5C.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW')
WRITEd,*) NS
DO 100 I = 1,NS
100 WRITEd,*) X(I),Y(I),Z(I)
WRITEd,*) XT, YT, ZT
WRITEd*) TH, TR
WRITEd,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
END

225
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C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5E.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5E.DAT
This program creats file GE0M5E.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 11.1
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32

226
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5E.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW *)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITECl,*) X(I),Y(I),Z(I)
WRITECl,*) XT, YT, ZT
WRITECl,*) TH, TR
WRITECl,*) RT, CT, VT
CLOSE C1,STATUS=*KEEP)
END

227
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
***********+****************
* *
* GE0M5G.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5G.DAT
This program creats file GE0M5G.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-67 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(i) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 6)
XT = 11.4
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32

228
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, t VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5G.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
WRITEd,*) XT, YT, ZT
WRITEd, *) TH, TR
WRITEd,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
END

229
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5I.F0R *
* *
I****************************
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5I.DAT
This program creats file GE0M5I.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Zi
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 11.7
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32

230
C
C TARGET RADIAL, CIRCUMFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5I.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
WRITE(1,*) XT, YT, ZT
WRITEd,*) TH, TR
WRITE(1,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
END

231
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5K.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOH
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5K.DAT
This program creats file GE0M5K.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft S)
XT = 12.0
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32

232
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, & VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5K.DAT
C
OPEN(1,FILE=GEOM,STATUS=5 NEW)
WRITE(i,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
WRITEd.O XT, YT, ZT
WRITECl,*) TH, TR
WRITEd,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
END

233
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
****************************
* *
* GE0M5M.F0R *
* *
***************************lf:
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GEOMSM.DAT
This program creats file GEOMSM.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(i) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft S)
XT = 12.3
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.SO
TR = 2.32

234
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5M.DAT
C
OPEN(1,FILE=GEOM,STATUS=NEW)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITEd*) X(I),Y(I),Z(I)
WRITEd,*) XT, YT, ZT
WRITEd,*) TH, TR
WRITEd,*) RT, CT, VT
CLOSE(1,STATUS='KEEP)
END

235
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M50.FOR *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOM
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M50.DAT
This program create file GE0M50.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft 5)
XT = 12.6
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32

236
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M50.DAT
C
OPEN(1,FILE=GEOH,STATUS=NEW')
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
WRITE(1,*) XT, YT, ZT
WRITEd,*) TH, TR
HRITEd,*) RT, CT, VT
CLO SE(1,STATUS=KEEP)
END

237
Sample Description Programs
These programs were written to create data files which provide data concerning each
individual sample. These programs are written in FORTRAN-77 and were run on a VAX
Cluster main-frame computer. SAMPLE2.FOR through SAMPLEUSD.FOR provide spe
cific information about the physical characteristics of each sample. S2XRF.F0R through
USDXRF.FOR provide specific information about the counting data for each individual
sample.

238
C
C lH********************
c *
C SAMPLE2.F0R *
C *
Q #
c
CHARACTER *3 ELEMENT
C
C This program craats a data file of input
C data pertaining to Sample #2, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.6608
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.24476
Bl = 0.75112
Cl =-0.63255
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.24400
US2 = 0.25061
US3 = 0.30424

239
C
C Data is now written into file SAMPLE2.DAT
C
OPENCl,FILE=SAMPLE2.DAT,STATUS=NEW)
WRITE(1,*(A3)) ELEMENT
WRITE(1,*) WF
WRITEd,*) SD
WRITECl,*) A1
WRITECl,*) Bi
WRITEd,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSE Cl,STATUS=KEEP)
END

240
C
C *********************
c *
C SAHPLE3.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample #3, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Height Fraction, HF
C
HF = 1.0
C
C Sample Density, SD
C
SD = 1.3706
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.29107
Bl = 0.88278
Cl =-0.60210
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.22009
US2 = 0.23913
US3 = 0.29308

241
C
C Data is now written into file SAMPLE2.DAT
C
OPEN(1,FILE=SAMPLE3.DAT,STATUS=NEW)
WRITE(1,(A3)) ELEMENT
WRITECl,*) WF
HRITECl,*) SD
WRITE(1,*) A1
WRITECi,*) B1
WRITE(1,*) Cl
WRITEd,*) US1
WRITE(1,*) US2
WRITEd,*) US3
CLO SE(1,STATUS=KEEP)
END

242
C
C i*###*###***#**#******
c *
C SAMPLE4.F0R *
C *
C *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample #4, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH'
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.3112
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.11124
Bl = 1.11667
Cl =-0.96296
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.25104
US2 = 0.28282
US3 = 0.35714

243
C
C Data is now written into file SAMPLE4.DAT
C
OPEN(1,FILE=SAMPLE4.DAT,STATUS=NEW)
WRITE(lf(A3)) ELEMENT
WRITE(1,*) WF
WRITEd,*) SD
WRITECi,*) Ai
WRITE(1,*) B1
WRITEd,*) Ci
WRITE(1,*) USi
WRITEd,*) US2
WRITE(1,*) US3
CLOSE(1,STATUS='KEEP)
END

244
C
£ $$$£$$$$$$$$$$$$$$$$$
C *
C SAMPLEU1.F0R *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample Ul, a homogenous
C U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.7587
C
C Hubble Fit Parameters, Al, 61, ft Cl
C
Al = 1.14474
B1 = 0.66790
Cl =-0.42794
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.26889
US2 = 0.28471
US3 = 0.32173

245
C
C Data is now written into file SAMPLE2.DAT
C
OPEN(i,FILE=SAHPLEU1.DAT,STATUS=NEW)
WRITECl.CA3)) ELEMENT
WRITECl,*) WF
WRITECl,*) SD
WRITECI,*) A1
WRITECl,*) B1
WRITECl,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSECl,STATUS=KEEP')
END

246
C
C *********************
c *
C SAMPLEU1A.F0R *
C *
Q *********************
c
CHARACTER *3 ELEMENT
C
C This program create a data file of input
C data pertaining to Sample U1A, a homogenous
C II sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U>
C
C Soil Height Fraction, HF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.8348
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.16053
Bl = 0.67181
Cl =-0.43485
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.26460
US2 = 0.27996
US3 = 0.31671

247
C
C Data is now written into file SAMPLE2.DAT
C
OPEN(1,FILE=SAMPLEU1A.DAT,STATUS=NEW *)
WRITE(1,(A3)') ELEMENT
WRITE(lf*) WF
WRITECl,*) SD
WRITECl,*) A1
WRITEC1,*) 61
WRITE(1,*) Cl
WRITEd,*) US1
WRITE(1,*) US2
WRITE(1,*) US3
CLOSE(1,STATUS=KEEP)
END

248
C
c *********************
c *
C SAMPLETH1.FOR *
C *
Q *********************
c
CHARACTER *3 ELEMENT
C
C This program creatB a data file of input
C data pertaining to Sample #TH1, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH>
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.8977
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.13064
Bl = 0.65512
Cl =-0.48956
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.27465
US2 = 0.29197
US3 = 0.33854

249
C
C Data is now written into file SAMPLETH1.DAT
C
OPEN(i,FILE=SAMPLETH1.DAT',STATUS=NEW)
WRITE(1,'(A3)) ELEMENT
WRITECl,*) WF
WRITE(1,*) SD
HRITEd,*) A1
WRITE(1,*) B1
WRITE(1,*) Cl
WRITE(1,*) US1
WRITE(1,*) US2
WRITE(1,*) US3
CL0SE(1,STATUS='KEEP)
END

250
C
c *********************
c *
C SAMPLETH1A.FOR *
C *
C *********************
C
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample #TH1A, a homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Weight Fraction, WF
C
WF = 1.0
C
C Sample Density, SD
C
SD = 1.8217
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.16196
Bl = 0.64704
Cl =-0.42909
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.26534
US2 = 0.28262
US3 = 0.32782

251
C
C Data is now written into file SAMPLETH1.DAT
C
OPEN(1,FILE=*SAHPLETH1A.DAT,STATUS= *NEW *)
WRITE(1,(A3)) ELEMENT
WRITE(1,*) WF
WRITEd.O SD
WRITE(if*) A1
WRITE(1,*) 51
WRITE(1,*) Cl
WRITE(1,*) US1
WRITE(1,*) US2
WRITE(1,*) US3
CLOSE(1,STATUS=KEEP *)
END

252
C
C *********************
C *
C SAMPLENJAU.FOR *
C *
C *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample NJA-U, a non-homogenous
C Th and U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Height Fraction, WF
C
WF = 0.91408
C
C Sample Density, SD
C
SD = 0.97771
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.05487
Bl = 1.35142
Cl =-1.47242
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.25367
US2 = 0.30389
US3 = 0.35591

253
C
C Data is now written into file SAMPLENJAU.DAT
C
OPEN(1,FILE=SAMPLENJAU. D AT \STATUS=NEW)
WRITE(1,(A3)) ELEMENT
WRITEd,*) WF
WRITEd, *) SD
WRITEd,*) A1
WRITEd,*) B1
WRITEd,*) Cl
WRITEd*) US1
WRITE(1,*) US2
WRITEd,*) US3
CLOSE(1,STATUS='KEEP)
END

254
C
C *********************
c *
C SAMPLENJATH.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample NJA-TH, a non-homogenous
C Th and U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Height Fraction, HF
C
HF = 0.91408
C
C Sample Density, SD
C
SD = 0.97771
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.05487
Bl = 1.35142
Cl =-1.47242
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.25367
US2 = 0.30389
US3 = 0.38495

255
C
C Data is non written into file SAMPLE4.DAT
C
OPEN(i,FILE=SAMPLENJATH.DAT,STATUS='NEW)
WRITE(1,(A3)') ELEMENT
WRITECl,*) WF
WRITECl,*) SD
WRITECl,*) A1
WRITECl,*) B1
WRITECl,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSEC1,STATUS=KEEP)
END

256
C
Q ftft ft ftftft ftftftft ft ftftft ftftftft ftftft
C *
C SAMPLENJBU.FOR *
C *
C i*********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample NJB-U, a non-homogenous
C Th and U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Weight Fraction, WF
C
WF = 0.87653
C
C Sample Density, SD
C
SD = 1.06198
C
C Hubble Fit Parameters, Al, Bl, St Cl
C
Al = 1.07694
Bl = 1.19446
Cl =-1.36489
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.25818
US2 = 0.30521
US3 = 0.34727

257
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(1,FILE=SAMPLERJBU.DAT,STATUS=NEW)
WRITE(1,'(A3)') ELEMENT
WRITECl,*) WF
WRITECl,*) SD
WRITECl,*) Ai
WRITECl,*) B1
WRITECl,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSEC1,STATUS=KEEP)
END

258
C
C *********************
C *
C SAMPLESJBTH.FOE *
C *
C i*********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample NJB-TH, a non-homogenous
C Th and U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH'
C
C Soil Weight Fraction, WF
C
WF = 0.87653
C
C Sample Density, SD
C
SD = 1.06198
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.07694
Bl = 1.19446
Cl =-1.36489
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.25818
US2 = 0.30521
US3 = 0.37231

259
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(1,FILE=SAMPLENJBTH.DAT,STATUS^'NEW)
WRITE(1,'(A3)') ELEMENT
WRITECl,*) WF
WRITE(1,*) SD
WRITE(1,*) A1
WRITECl,*) B1
WRITECl,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSEC1,STATUS=KEEP')
END

260
C
c *********************
c *
C SAMPLEUSA.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample USA, a non-homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH
C
C Soil Weight Fraction, WF
C
WF = 0.9221
C
C Sample Density, SD
C
SD = 1.4589
C
C Hubble Fit Parameters, Al, Bl, t Cl
C
A1 = 1.27985
Bl = 0.73205
Cl =-0.50038
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.23116
US2 = 0.24787
US3 = 0.29318

261
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(1,FILE='SAMPLEUSA.DAT,STATUS=*NEW*)
WRITE(i,(A3)) ELEMENT
WRITE(i,*) WF
WRITE(1,*) SD
WRITECl,*) A1
WRITEd,*) B1
WRITECl,*) Ci
WRITE(1,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSE C1,STATUS=KEEP)
END

262
C
C *********************
c *
C SAMPLEUSB.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program create a data file of input
C data pertaining to Sample USB, a non-homogenous
C Th sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = TH'
C
C Soil Height Fraction, HF
C
HF = 0.94997
C
C Sample Density, SD
C
SD = 1.4152
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.33008
Bl = 0.73746
Cl =-0.50040
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 93.3 keV
C
US1 = 0.21953
US2 = 0.23533
US3 = 0.27892

263
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(i,FILE='SAHPLEUSB.DAT',STATUS=NEW)
WRITE(1,'(A3)) ELEMENT
WRITE(1,*) WF
WRITEd,*) SD
WRITE(1,*) A1
WRITEd,*) B1
WRITE(1,*) Cl
WRITEd,*) US1
WRITEd,*) US2
WRITEd,*) US3
CL0SE(1,STATUS='KEEP *)
END

264
C
C *********************
c *
C SAMPLEUSC.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample USC, a non-homogenous
C U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Weight Fraction, WF
C
WF = 0.76647
C
C Sample Density, SD
C
SD = 1.6058
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.24604
Bl = 0.59428
Cl =-0.37477
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.24741
US2 = 0.26040
US3 = 0.29039

265
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(1,FILE=SAHPLEUSC.DAT',STATUS=NEW)
WRITE(1,(A3)) ELEMENT
WRITECl,*) WF
WRITECl,*) SD
WRITECl,*) A1
WRITECl,*) Bi
WRITE(1,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSE C1,STATUS='KEEP)
END

266
C
C ***#!*****************
c *
C SAMPLEUSD.FOR *
C *
c *********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample USD, a non-homogenous
C U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Height Fraction, WF
C
HF = 0.78909
C
C Sample Density, SD
C
SD = 1.6687
C
C Hubble Fit Parameters, Al, Bl, ft Cl
C
A1 = 1.25039
Bl = 0.61177
Cl =-0.33336
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.24413
US2 = 0.25768
US3 = 0.28921

267
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(i,FILE= *SAMPLEUSD.DAT,STATUS=NEW)
WRITE(1,(A3)) ELEMENT
WRITEd,*) HF
WRITEd,*) SD
WRITEd,*) Ai
WRITEd,*) B1
WRITEd,*) Cl
WRITEd,*) US1
WRITEd,*) US2
WRITEd,*) US3
CLOSE(1,STATUS=KEEP)
END

268
C
****************************
c *
c *
c *
c *
c *
c *
****************************
FILE PROGRAM
S2XRF.F0R
*
C
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = '[LAZO.DISS.S23S2XRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE #2 IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE #2 IS 87 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND PEAK AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1.S2B2.CNF; 1
C
D4(l) = 27.0
M5(l) = 5.0
Y5(l) = 87.0
HR(1) = 14.0
MN(i) = 33.0
RH(i) = 1.0
RM(1) = 22.0
RS(1) = 25.46
PH(1) = 264561.0
ER(1) = 2926.0

DATA FROM
XRF2J32B2. CNF; 1
D4(2)
=
27.0
H5(2)
=
5.0
Y5(2)
=
87.0
HR(2)
=
15.0
HN(2)
=
57.0
RH(2)
=
1.0
RM(2)
=
20.0
RS(2)
=
4.15
PH(2)
=
240028.0
ER(2)
=
2344.0
DATA FROM
XRF3J32B2.CNF;1
D4(3)
=:
27.0
M5(3)
=
5.0
Y5(3)
=
87.0
HR(3)
=
17.0
MN(3)
=
56.0
RH(3)
=
1.0
RM(3)
=
18.0
RS(3)
=
13.06
PH(3)
=
212015.0
ER(3)

2136.0
DATA FROM
XRF4.S2B2.CNF;1
D4(4)
=
27.0
M5(4)
=
5.0
Y5(4)
=
87.0
HR(4)
=
19.0
MN(4)
=
17.0
RH(4)
=
1.0
RM(4)
=
16.0
RS(4)
=
41.92
PH(4)
=
199047.0
ER(4)
=
1107.0

DATA FROM
XRF5J52B2. CNF; 1
D4(B)
=
27.0
M5(5)
=
B.O
Y5(B)
=
87.0
HR(5)
=
21.0
MN(6)
=
0.0
RH(5)
=
1.0
RH(5)
=
16.0
RS(B)
=
23.91
PH(B)
=
166260.0
ER(B)
=
1076.0
DATA FROM
XRF6J32B2. CNF; 1
D4(6)
=
28.0
MB(6)
=
B.O
Y6C6)
=
87.0
HR(6)
=
9.0
MN(6)
=
2.0
RH(6)
=
1.0
RM(6)
=
14.0
RS(6)
=
22.64
PH(6)
=
148666.0
ER(6)
=
1407.0
DATA FROM
XRF7 J52B2.CHF;1
D4(7)
=
28.0
MB(7)
=
B.O
YB(7)
=
87.0
HR(7)
=
10.0
MN(7)
=
18.0
RH(7)
=
1.0
RM(7)
=
13.0
RS(7)
=
26.42
PHC7)
=
127261.0
ER(7)
=
1422.0

271
C
C
C
DATA FROM XRF8_S2B2.CNF;1
C
C
C
D4(8)
M5(8)
Y5(8)
HR(8)
HN(8)
RH(8)
RH(8)
RS(8)
PH(8)
ER(8)
28.0
5.0
87.0
11.0
54.0
1.0
12.0
39.06
115378.
674.0
10
25
50
75
90
100
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS*'NEW')
WRITECl.5) NF
F0RMTUI2)
WRITE(i.lO) LH, LM, LS
FORHAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
FORHATdFlO.5, 112, 1F10.5)
WRITE(1,50) HR(I), HN(I)
F0RHAT(2F10.5)
WRITE(1,75) RH(I), RH(I), RS(I)
FORMAT(3F10.5)
WRITE(1,90) PH(I), ER(I)
F0RHAT(2F15.5)
CONTINUE
END

272
c *
C S3XRF.F0R *
C *
C FILE PROGRAM *
C *
£ $$$$$$$ $$$$$*$ $££££$$ 3f:it:3(c*stJ|c)|[
c
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, MB(20)
PKFIL = [LAZO.DISS.S3]S3XRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE #3 IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY SO. SAMPLE #3 IS 228 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRF1.S3B1.CNF;1
D4(l)
=
26.0
M5(l)
=
5.0
Y5(l)
=
87.0
HR(i)
=
16.0
MN (1)
=
54.0
RH(1)
=
1.0
RM(i)
=
19.0
RS(1)
=
41.51
PH(1)
=
541821.0
ER(1)
=
2133.0

DATA FROM
XRF2 JS3B1. CNF; 1
D4(2)
26.0
H5(2)
=
5.0
Y5(2)
=
87.0
HR(2)
=
18.0
MN(2)
s
44.0
RH(2)
=
1.0
RM(2)
=
17.0
RS(2)
=
39.50
PH(2)
=
479982.0
ER(2)
=
718.0
DATA FROM
XRF3 J33B1.CNF;1
D4(3)
=
26.0
M5(3)
=
5.0
Y5(3)
=
87.0
HR(3)
=
20.0
MH(3)
=
12.0
RH(3)
=
1.0
RM(3)
=
16.0
RS(3)
=
7.27
PH(3)
=
428292.0
ER(3)
968.0
DATA FROM
XRF4J53B1. CNF; 1
D4(4)
=
26.0
M5(4)
=
5.0
YS(4)
=
87.0
HR(4)
a
21.0
MN(4)
=
31.0
RH(4)
=
1.0
RM(4)
=
14.0
RS(4)
=
49.72
PH(4)
=
375253.0
ER(4)
=
999.0

274
C
C
C
C
C
C
C
C
C
DATA FROM
XRF5J53B1. CNF; 1
D4(5)
=
27.0
M5(5)
=
5.0
Y5(5)
=
87.0
HR(5)
=
9.0
MN(5)
=
3.0
RH(5)
=
1.0
RM(5)
=
13.0
RS(5)
=
44.87
PH(5)
=
334559.0
ER(5)
=
1110.0
DATA FROM
XRF6_S3B1.CNF;1
D4(6)
=
27.0
M5(6)
=
5.0
Y5(6)
=
87.0
HR(6)
=
10.0
HN(6)
=
26.0
RH(6)
=
1.0
RM(6)
=
12.0
RS(6)
=
53.39
PH(6)
=
301884.0
ER(6)
=
1151.0
DATA FROM
XRF7 _S3B1.CHF; 1
D4(7)
=
27.0
H5(7)
=
5.0
Y5(7)
=
87.0
HR(7)
=
11.0
HU (7)
=
41.0
RH(7)
=
1.0
RH(7)
=
12.0
RS(7)
=
6.67
PH(7)
=
261608.0
ER(7)
=
1037.0

275
C
C DATA FROM XRF8J33B1.CNF;1
D4(8)
=
27.0
M5(8)
=
5.0
Y5(8)
=
87.0
HR(8)
=
13.0
MN(8)
=
13.0
RH(8)
=
1.0
RM(8)
=
11.0
RS(8)
=
27.77
PH(8)
=
233651.0
ER(8)
=
1130.0
STORE DATA
ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS=NEW1)
HRITE(1,5) NF
5 F0RMAT(1I2)
HRITECl.iO) LH, LH, LS
10 FORMAT(3F10.5)
DO 100 I = i,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 F0RMAT(3F10.5)
HRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

276
C *********>>********>1!*********
c *
C S4XRF.F0R *
C *
C FILE PROGRAM *
C *
C ****************************
c
CHARACTER *25 PKFIL
DIMENSION D4(20),YS(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.S4]S4XRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE #4 IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE #4 IS 689 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRF1_S3B1.CNF;1
D4(i)
=
25.0
M5(l)
=
5.0
Y5(l)
=
87.0
HR(1)
=
17.0
MN(1)
=
24.0
RH(1)
=
1.0
RM(1)
=
18.0
RS(1)
=
27.82
PH(i)
=
1453181.0
ER(1)
=
2711.0

277
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MW(2) =
RH(2) =
RH(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MN(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2J53B1.CNF;1
25.0
5.0
87.0
19.0
23.0
1.0
16.0
30.31
1287314.0
2590.0
XRF3_S3B1.CHF;1
25.0
5.0
87.0
20.0
42.0
1.0
15.0
3.62
1148003.0
1957.0
XRF4J33B1. CNF; 1
25.0
5.0
87.0
22.0
3.0
1.0
13.0
53.55
1014348.0
2344.0

DATA FROM
XRF5J33B1. CNF; 1
D4(5)
=
26.0
H5(B)
=
B.O
YB(5)
=
87.0
HR(B)
=
10.0
MN(6)
=
23.0
RH(5)
=
1.0
RH(5)
=
12.0
RS(B)
=
SB. 03
PH(B)
=
899790.0
ER(5)
2317.0
DATA FROM
XRF6J33B1. CNF;1
D4(6)
=
26.0
MB(6)
=
6.0
YB(6)
=
87.0
HR(6)
=
12.0
MN(6)
=
13.0
RH(6)
=
1.0
RM(6)
=
12.0
RS(6)
=
7.9B
PH(6)
=
798214.0
ER(6)
=
2662.0
DATA FROM
XRF7_S3B1.CNF; 1
D4(7)
=
26.0
M5(7)
=
B.O
YB(7)
=
87.0
HR(7)
=
14.0
MN(7)
=
19.0
RH(7)
=
1.0
RM(7)
=
11.0
RS(7)
=
26.93
PH(7)
=
710364.0
ER(7)
=
1878.0

279
C
C DATA FROM XRF8_S3B1.CNF;1
C
C
C
C
D4(8) = 26.0
M5(8) = 5.0
Y5(8) = 87.0
HR(8) = 15.0
MN(8) = 33.0
RH(8) = 1.0
RM(8) = 10.0
RS(8) = 50.94
PH(8) = 636039.0
ER(8) = 2614.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
5 F0RMAT(1I2)
WRITE(1,10) LH, LH, LS
10 F0RMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), H5(I), Y5(I)
25 FORMAT(IF10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

280
C ****************************
c *
C U1XRF.FOR *
C *
C FILE PROGRAM *
C *
C ****************************
c
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
f PKFIL = '[LAZO.DISS.Ul]U1XRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE Ul IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE Ul IS 186 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
DATA FROM
XRF1JU1.CNF;1
D4(l)
=
2.0
M5(l)
=
6.0
Y5C1)
=
87.0
HR(1)
=
8.0
MN(1)
=
47.0
RH(1)
=
1.0
RM(1)
=
22.0
RS(1)
=
42.64
PH(1)
=
127598.0
ER(1)
=
774.0

DATA FROM
XRF2JUi.CNF;1
D4(2)
=
2.0
H5(2)
=
6.0
Y5(2)
=
87.0
HR(2)
=
11.0
MN(2)
=
63.0
RH(2)
=
1.0
RM(2)
=
20.0
RS(2)
=
59.48
PH(2)
=
118246.0
ER(2)
=
694.0
DATA FROM
XRF3_U1.CNF;1
D4(3)
=
2.0
M5(3)
=
6.0
Y5(3)
=
87.0
HR(3)
=
13.0
MN(3)
=
29.0
RH(3)
=
1.0
RM(3)
=
18.0
RS(3)
=
42.19
PH (3)
=
98117.0
ER(3)
=
767.0
DATA FROM
XRF4JUI.CNF;1
D4(4)
=
2.0
M5(4)
=
6.0
Y5(4)
=
87.0
HR(4)
=
16.0
MN(4)
=
8.0
RH(4)
=
1.0
RM(4)
=
17.0
RS(4)
=
17.48
PH(4)
=
96466.0
ER(4)
=
763.0

DATA FROM
XRF5_U1.CNF;1
D4(5)
=
2.0
M5(E)
=
6.0
Y5(5)
=
87.0
HR(5)
=
16.0
MN(5)
=
49.0
RH(5)
=
1.0
RM(5)
=
1B.0
RS(5)
=
35.92
PH(5)
=
82104.0
ER(5)
=
387.0
DATA FROM
XRF6_U1.CNF;1
D4(6)
=
2.0
M5(6)
=
6.0
Y5(6)
=
87.0
HR(6)
=
18.0
MN(6)
=
12.0
RH(6)
=
1.0
RM(6)
sr
14.0
RS(6)
=
4.84
PH(6)
=
67923.0
ER(6)
=
1109.0
DATA FROM
XRF7JU1.CNF;!
D4(7)
=
2.0
M5(7)
=
6.0
Y5(7)
=
87.0
HR(7)
=
19.0
MN(7)
=
28.0
RH(7)
=
1.0
RM(7)
=
13.0
RS(7)
=
30.73
PH(7)
s
63979.0
ERC7)
=
407.0

283
C
C DATA FROM XRF8_U1.CNF;1
C
C
C
C
D4(8) = 2.0
M5(8) = 6.0
Y5(8) = 87.0
HR(8) = 22.0
MN(8) = 56.0
RH(8) = 1.0
RM(8) = 12.0
RS(8) = 21.82
PH(8) = 56134.0
ER(8) = 450.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS='NEW')
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RMATC1F1O.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 FORMAT(2F15.5)
100 CONTINUE
END

284
C
I****************************
C *
c *
c *
c *
c *
c *
FILE PROGRAM
U1AXRF.FOR
*
C
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.UiA]U1AXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE U1A IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE U1A IS 186 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1JJ1A.CNF;1
C
D4(l) = 3.0
M5(i) = 6.0
Y5(l) = 87.0
HR(1) = 11.0
MN(1) = 3.0
RH(1) = 1.0
RM(1) = 23.0
RS(1) = 9.15
PH(1) = 141648.0
ER(1) = 599.0

285
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MN(2) =
RH(2) =
RH(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
HN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
H5(4) =
Y5(4) =
HR(4) =
HN(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2_U1A.CNF;1
3.0
6.0
87.0
12.0
28.0
1.0
20.0
22.14
123835.0
815.0
XRF3_U1A.CNF;1
3.0
6.0
87.0
13.0
51.0
1.0
18.0
22.25
111116.0
538.0
XRF4JJ1A.CHF; 1
3.0
6.0
87.0
15.0
21.0
1.0
17.0
0.37
100696.0
634.0

286
C
C DATA FROM
C
D4(5) =
M5(5) =
Y5(5) =
HR(5) =
MN(5) =
RH(5) =
RM(5) =
RS(5) =
PH(5) =
ER(5) =
C
C DATA FROM
C
D4(6) =
H5(6) =
Y5(6) =
HR(6) =
HN(6) =
RH(6) =
RH(6) =
RS(6) =
PH(6) =
ER(6) =
C
C DATA FROM
C
D4(7) =
H5(7) =
Y5(7) =
HR(7) =
HN(7) =
RH(7) =
RMC7) =
RS(7) =
PH(7) =
ER(7) =
XRF5_U1A.CNF;1
3.0
6.0
87.0
16.0
67.0
1.0
16.0
9.13
94625.0
728.0
XRF6JJ1A.CNF; 1
3.0
6.0
87.0
19.0
26.0
1.0
14.0
54.18
85532.0
367.0
XRF7JU1A.CNF;1
3.0
6.0
87.0
20.0
49.0
1.0
13.0
54.04
77306.0
425.0

287
C
C
c
DATA FROM XRF8JJ1A.CNF;1
C
C
C
D4(8)
M5(8)
Y5(8)
HR(8)
MN(8)
RH(8)
RM(8)
RS(8)
PH(8)
ER(8)
3.0
6.0
87.0
22.0
29.0
1.0
12.0
43.31
68731.0
530.0
10
25
50
75
90
100
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
F0RMAT1I2)
HRITE(l.lO) LH, LM, LS
F0RHATC3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
FORMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
F0RMAT2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
F0RMATC3F10.5)
WRITE(1,90) PH(I),ER(I)
FORMAT(2F15.5)
CONTINUE
END

J**********^*****************
* *
* TH1XRF.F0R *
* *
* FILE PROGRAM *
* *
****************************
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = >[LAZO.DISS.TH1DTH1XRF.DAT'
THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE TH1 IN
BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
GEOMETRY 50. SAMPLE #3 IS 130 PCI/GM TH-232 AND
WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
AND THE COUNT LIVE TIME, LH, LM, t LS. THEN FOR
EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
ERROR, ER(I).
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM XRF1_TH1.CNF;1
D4(l) = 15.0
M5(l) = 6.0
Y5(l) = 87.0
HR(1) = 9.0
MN(1) = 44.0
RH(1) = 1.0
RM(1) = 21.0
RSCl) = 40.53
PH(1) = 396916.0
ER(1) = 1708.0

289
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MH(2) =
RH(2) =
RM(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MN(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2_TH1.CNF;1
15.0
6.0
87.0
11.0
17.0
1.0
20.0
17.86
367607.0
1486.0
XRF3JTH1.CNF;1
15.0
6.0
87.0
13.0
27.0
1.0
18.0
26.36
333507.0
1647.0
XRF4-TH1.CHF; 1
15.0
6.0
87.0
15.0
4.0
1.0
16.0
58.22
298668.0
1629.0

DATA FROM
XRF5_TH1.CNF;1
D4(5)
=
15.0
M5(5)
=
6.0
Y5(5)
=
87.0
HR(5)
=
16.0
HN(5)
=
31.0
RH(5)
=
1.0
RM(5)
=
15.0
RS(5)
=
20.36
PH(5)
=
251310.0
ER(5)
=
2221.0
DATA FROM
XRF6JTH1.CNF;1
D4(6)
=
16.0
M5(6)
=
6.0
Y5(6)
=
87.0
HR(6)
=
9.0
MN(6)
=
28.0
RH(6)
=
1.0
RM(6)
=
14.0
RS(6)
=
30.19
PH(6)
=
232490.0
ER(6)
=
1121.0
DATA FROM
XRF7_THl.CNF;i
D4(7)
=
16.0
M5(7)
=
6.0
Y5(7)
=
87.0
HR(7)
=
10.0
MN(7)
=
54.0
RH(7)
=
1.0
RM(7)
=
13.0
RS(7)
=
3.79
PH(7)
=
196953.0
ER(7)
=
1430.0

291
C
C DATA FROM XRF8_TH1.CNF;1
C
C
C
C
D4(8) = 16.0
M5(8) = 6.0
Y6(8) = 87.0
HR(8) = 12.0
MN(8) =58.0
RH(8) = 1.0
RM(8) = 12.0
RS(8) = 17.70
PH(8) = 171638.0
ER(8) = 1446.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITEC1.5) NF
5 F0RMAT(1I2)
WRITE(l.lO) LH, LH, LS
10 FORHAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), H5(I), Y5(I)
25 FORHATdFlO.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 F0RMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 F0RMATC3F1O.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

292
C ****************************
c *
C TH1AXRF.F0R *
C *
C FILE PROGRAM *
C *
C ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),YS(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = '[LAZ0.DISS.TH1A3TH1AXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE TH1A IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE TH1A IS 130 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRFIJTHIA.CNF;1
D4(l)
=
18.0
M5(l)
=
6.0
Y5(l)
=
87.0
HR(1)
=
11.0
MN(i)
=
38.0
RH(1)
=
1.0
RM(1)
=
21.0
RS(1)
=
47.00
PH(1)
=
390175.0
ER(1)
=
2084.0

293
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MN(2) =
RH(2) =
RM(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
H5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RH(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MIi(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2JTH1A.CNF;1
18.0
6.0
87.0
9.0
19.0
1.0
19.0
41.40
359972.0
2600.0
XRF3JTH1A.CNF;1
17.0
6.0
87.0
16.0
50.0
1.0
18.0
9.68
331580.0
1750.0
XRF4JTH1A.CNF;1
17.0
6.0
87.0
15.0
27.0
1.0
16.0
42.01
298234.0
1383.0

294
C
C DATA FROM
C
D4(5) =
M5(5) =
Y5(5) =
HR(5) =
MN(5) =
RH(5) =
RM(5) =
RS(5) =
PH(5) =
ER(5) =
C
C DATA FROM
C
D4(6) =
M5(6) =
Y5(6) =
HR(6) =
MN(6) =
RH(6) =
RM(6) =
RS(6) =
PH(6) =
ER(6) =
C
C DATA FROM
C
D4(7) =
M5(7) =
Y5(7) =
HR(7) =
MN(7) =
RH(7) =
RM(7) =
RS(7) =
PH(7) =
ER(7) =
XRF5_TH1A.CHF;1
17.0
6.0
87.0
13.0
29.0
1.0
15.0
21.60
259990.0
1398.0
XRF6JTH1A.CNF;1
16.0
6.0
87.0
17.0
18.0
1.0
13.0
47.19
221465.0
831.0
XRF7JTH1A.CNF; 1
16.0
6.0
87.0
15.0
39.0
1.0
13.0
24.31
199931.0
1160.0

295
C
C DATA FROM XRF8_TH1A.CNF;1
D4(8)
=
16.0
M5(8)
=
6.0
75(8)
=
87.0
HR(8)
=
14.0
MN(8)
=
19.0
RH(8)
=
1.0
RM(8)
=
12.0
RS(8)
=
18.12
PH(8)
=
178059.0
ER(8)
=
1317.0
STORE DATA
ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS=NEW')
WRITE(1,5) NF
5 F0RMAT(1I2)
WRITE(l.lO) LH, LM, LS
10 F0RHATC3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), HN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 FORMAT(2F15.5)
100 CONTINUE
END

296
C ****************************
c *
C NJAUXRF.FOR *
C *
C FILE PROGRAM *
C *
c ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.NJA]NJAUXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE NJA-U IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY SA, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE NJA-U IS 171 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRFl_NJA.CNF;i
D4(l)
=
30.0
M5(i)
=
6.0
Y5(l)
=
87.0
HR(1)
=
17.0
MN(1)
=
37.0
RHCl)
=
1.0
RM(1)
=
14.0
RS(1)
=
48.70
PH(1)
=
70722.0
ER(1)
=
645.0

297
DATA FROM
XRF2 JIJA.CNF;1
D4(2)
=
1.0
M5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
10.0
MN(2)
=
36.0
RH(2)
=
1.0
RM(2)
=
13.0
RS(2)
=
23.13
PH(2)
=
67460.0
ER(2)

586.0
DATA FROM
XRF3JJJA. CNF; 1
D4(3)
=
1.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
14.0
MN(3)
=
59.0
RH(3)
=
1.0
RM(3)
=
12.0
RS(3)
=
48.61
PH(3)
=
65292.0
ER(3)
=
452.0
DATA FROM
XRF4 JIJA. CNF ;1
D4(4)
=
1.0
M5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
16.0
MN(4)
=
17.0
RH(4)
=
1.0
RM(4)
=
11.0
RS(4)
=
45.29
PH(4)
=
58533.0
ER(4)
=
503.0

298
C
C DATA FROM
C
D4(5) =
M5(5) =
Y5(5) =
HR(5) =
MN(5) =
RH(5) =
RM(5) =
RSC5) =
PH(5) =
ER(5) =
C
C DATA FROM
C
D4(6) =
M5(6) =
Y5(6) =
HR(6) =
MN(6) =
RH(6) =
RH(6) =
RS(6) =
PH(6) =
ER(6) =
C
C DATA FROM
C
D4(7) =
H5(7) =
Y5(7) =
HR(7) =
MN(7) =
RH(7) =
RM(7) =
RS(7) =
PH(7) =
ER(7) =
XRF5_NJA.CNF;1
2.0
7.0
87.0
9.0
53.0
1.0
10.0
58.11
51170.0
392.0
XRF6 JIJA. CNF ;1
2.0
7.0
87.0
14.0
31.0
1.0
10.0
10.59
44378.0
466.0
XRF7 JIJA. CNF; 1
2.0
7.0
87.0
15.0
54.0
1.0
9.0
43.16
39759.0
240.0

299
C
C DATA FROM XRF8_NJA.CNF;i
C
D4(8) = 7.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 9.0
HN(8) = 49.0
RH(8) = 1.0
RM(8) = 9.0
RS(8) = 4.26
PH(8) = 34988.0
ER(8) = 430.0
C
C STORE DATA ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS=NEW')
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 F0RMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,2B) D4(I), M5(I), Y5(I)
25 F0RMATC1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

300
C **** *****111 ****** ****** ******
c *
C NJATHXRF.FOR *
C *
C FILE PROGRAM *
C *
c ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, MS(20)
PKFIL = [LAZO.DISS.NJA]NJATHXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE NJA-TH IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE NJA-TH IS 2590 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1JTJA.CNF; 1
C
D4(l) = 30.0
M5(l) = 6.0
Y5(l) = 87.0
HR(1) = 17.0
MN(1) = 37.0
RH(1) = 1.0
RM(i) = 14.0
RS(1) = 48.70
PH(1) = 3062432.0
ER(1) = 1980.0

301
DATA FROM
XRF2 JIJA.CNF;1
D4(2)
=
1.0
M5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
10.0
MN(2)
=
36.0
RH(2)
=
1.0
RH(2)
=
13.0
RS(2)
=
23.13
PH(2)
=
2709169.0
ER(2)
2614.0
DATA FROM
XRF3 JIJA.CNF;1
D4(3)
=
1.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
14.0
MN(3)
=
59.0
RH(3)
=
1.0
RH(3)
=
12.0
RS(3)
=
48.61
PH(3)
=
2560958.0
ER(3)
=
2554.0
DATA FROM
XRF4 JIJA. CNF ;1
D4(4)
=
1.0
M5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
16.0
MN(4)
=
17.0
RH(4)
=
1.0
RH(4)
=
11.0
RS(4)
=
45.29
PH(4)
=
2245527.0
ER(4)
=
1712.0

302
DATA FROM
XRF5 JIJA. CNF; 1
D4(5)
=
2.0
M5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
9.0
MN(5)
=
53.0
RH(5)
=
1.0
RM(5)
=
10.0
RS(5)
=
58.11
PH(5)
=
2002194.0
ER(5)
=
2646.0
DATA FROM
XRF6 JIJA.CNF;1
D4(6)
=
2.0
MB(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
14.0
MN(6)
=
31.0
RH(6)
=
1.0
RM(6)
=
10.0
RS(6)
=
10.59
PH(6)
=
1742420.0
ER(6)

2638.0
DATA FROM
XRF7 JIJA. CNF; 1
D4(7)
=
2.0
M5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
15.0
MN(7)
=
54.0
RH(7)
=
1.0
RM(7)
=
9.0
RS(7)
=
43.16
PH(7)
=
1568213.0
ER(7)
=
3196.0

303
C
C DATA FROM XRF8JIJA.CNF; 1
C
C
C
C
D4(8) = 7.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 9.0
MN(8) = 49.0
RH(8) = 1.0
RM(8) = 9.0
RS(8) = 4.26
PH(8) = 1367233.0
ER(8) = 2223.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 FORMAT(1F10.5, 112, 1F10.6)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

304
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
****************************
* *
* NJBUXRF.FOR *
* *
* FILE PROGRAM *
* *
****************************
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, MB(20)
PKFIL = '[LAZO.DISS.NJB]NJBUXRF.DAT'
THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE NJB-TH IN
BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
IN GEOMETRY BA, AND A THROUGH I + 1 THROUGH 14, IN
GEOMETRY 60. SAMPLE NJA-U IS 2B90 PCI/GM TH-232 AND
WAS IRRADIATED BY C0-B7 SOURCES #3 AND #2.
LINE 101B CONSISTS OF THE NUMBER OF DATA POINTS, NF,
AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
EACH SPECTRA, COUNTING DATE, D4, MB, Y6, AND TIME,
HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
ERROR, ER(I).
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM XRF1JIJB.CNF; 1
D4(l) = 7.0
MS(1) = 7.0
YS(1) = 87.0
HR(1) = 11.0
MN(1) = 10.0
RH(1) = 1.0
RM(1) = 1B.0
RS(1) = 32.81
PH(1) = 63408.0
ER(1) = B19.0

305
DATA FROM
XRF2_NJB.CNF; 1
D4(2)

7.0
M5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
14.0
HN(2)
=
10.0
RH(2)
=
1.0
RM(2)
=
14.0
RS(2)
=
31.67
PH(2)
=
52018.0
ER(2)
=
453.0
DATA FROM
XRF3_NJB.CNF;1
D4(3)
=
7.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
16.0
HN(3)
=
8.0
RH(3)
=
1.0
RM(3)
=
13.0
RS(3)
=
3.41
PH(3)
=
45726.0
ER(3)
=
315.0
DATA FROM
XRF4 JJJB. CNF; 1
D4(4)
8.0
M5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
10.0
MN(4)
=
18.0
RH(4)
=
1.0
RM(4)
=
12.0
RS(4)
=
12.69
PH(4)
=
42182.0
ER(4)
=
435.0

306
DATA FROM
XRF6_NJB.CNF;1
D4(5)
=
8.0
H5(B)
=
7.0
Y5(5)
=
87.0
HR(5)
=
12.0
MN(5)
=
15.0
RH(5)
=
1.0
RH(5)
=
11.0
RS(5)
=
24.29
PH(5)
=
38196.0
ER(5)
=
378.0
DATA FROM
XRF6JJJB. CNF; 1
D4(6)
=
8.0
H5(6)
=
7.0
Y5(6)
=
87.0
HRC6)
=
14.0
MN(6)
=
42.0
RH(6)
=
1.0
RH(6)
=
10.0
RS(6)
=
36.35
PH(6)
=
34393.0
ER(6)
=
495.0
DATA FROM
XRF7_NJB.CNF;1
D4(7)
=
8.0
M5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
16.0
MN(7)
=
22.0
RH(7)
=
1.0
RMC7)
=
9.0
RS(7)
=
59.44
PH(7)
=
31229.0
ER(7)
=
295.0

307
C
C DATA FROM XRF8JTJABCNF; 1
C
C
C
C
D4(8) = 9.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 11.0
MN(8) = 27.0
RH(8) = 1.0
RM(8) = 9.0
RS(8) = 24.32
PH(8) = 25097.0
ER(8) = 327.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS='NEW)
WRITE(1,5) NF
5 F0RMAT(1I2)
WRITEC1.10) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

308
C ****************************
c *
C NJBTHXRF.FOR *
C *
C FILE PROGRAM *
C *
C ****************************
C
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.NJB]NJBTHXRF.DAT*
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE NJB-TH IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE NJA-TH IS 2590 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1JTJB.CNF; 1
C
D4(l) = 7.0
M5(l) = 7.0
Y5(l) = 87.0
HR(1) = 11.0
MN(1) = 10.0
RH(1) = 1.0
RM(1) = 15.0
RS(1) = 32.81
PH(1) = 2896677.0
ER(1) = 3378.0

309
DATA FROM
XRF2_NJB.CNF;1
D4(2)
=
7.0
H5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
14.0
MH(2)
=
10.0
RH(2)
=
1.0
RH(2)
=
14.0
RS(2)
=
31.67
PH(2)
=
2689680.0
ER(2)
=
2332.0
DATA FROM
XRF3JIJB. CNF; 1
D4(3)
=
7.0
H5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
16.0
MN(3)
=
8.0
RH(3)
=
1.0
RH(3)
=
13.0
RS(3)
=
3.41
PH(3)
=
2364069.0
ER(3)
=
2875.0
DATA FROM
XRF4.NJB. CNF; 1
D4(4)
=
8.0
M5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
10.0
MN(4)
=
18.0
RH(4)
=
1.0
RH(4)
=
12.0
RS(4)
=
12.69
PH(4)
=
2133681.0
ER(4)
=
3002.0

DATA FROM
XRF5 JIJB.CNF;1
D4(5)
8.0
M5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
12.0
MN(5)
=
15.0
RH(5)
=
1.0
RM(5)
=
11.0
RS(5)
=
24.29
PHC5)
=
1910431.0
ER(B)
=
2887.0
DATA FROM
XRF6 JIJB.CNF;1
D4(6)
=
8.0
M5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
14.0
MN(6)
=
42.0
RH(6)
=
1.0
RM(6)
=
10.0
RS(6)
=
36.35
PH(6)
=
1692538.0
ER(6)
=
1708.0
DATA FROM
XRF7 JIJB.CNF;1
D4(7)
=
8.0
M5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
16.0
MN(7)
=
22.0
RH(7)
=
1.0
RM(7)
=
9.0
RS(7)
=
59.44
PH(7)
=
1507566.0
ER(7)
=
3183.0

311
C
C DATA FROM XRF8JJJABCNF; 1
C
C
C
C
D4(8) = 9.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 11.0
MN(8) = 27.0
RH(8) = 1.0
RH(8) = 9.0
RS(8) = 24.32
PH(8) = 1336647.0
ER(8) = 2666.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
5 F0RHATC1I2)
WRITE(l.lO) LH, LH, LS
10 FORHAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RHAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORHAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORHAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RHATC2F15.5)
100 CONTINUE
END

312
C ****************************
c *
C USAXRF.FOR *
C *
C FILE PROGRAM *
C *
c ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = '[LAZO.DISS.USA]USAXRF.DAT'
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE USA IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY BA, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE USA IS 165 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRF1_USA.CNF;1
D4(l)
=
9.0
M5(l)
=
7.0
Y5(l)
=
87.0
HR(1)
=
14.0
MN(1)
=
8.0
RH(1)
=
1.0
RM(1)
=
17.0
RS(1)
=
56.43
PH(1)
=
386406.0
ER(1)
=
1848.0

313
DATA FROM
XRF2JUSA.CNF;1
D4(2)
=
13.0
M5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
9.0
MN(2)
=
21.0
RH(2)
=
1.0
RM(2)
=
16.0
RS(2)
=
16.45
PH(2)
=
351203.0
ER(2)
=
1525.0
DATA FROM
XRF3JJSA. CNF; 1
D4(3)
=
13.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
10.0
MN(3)
=
47.0
RH(3)
=
1.0
RM(3)
=
14.0
RS(3)
=
45.83
PH(3)
=
315751.0
ER(3)
=
1473.0
DATA FROM
XRF4_USA.CNF;1
D4(4)
=
13.0
M5(4)
=
7.0
YB(4)
=
87.0
HR(4)
=
15.0
MN(4)
=
35.0
RH(4)
=
1.0
RM(4)
=
13.0
RS(4)
=
30.71
PH(4)
=
275494.0
ER(4)
=
1688.0

DATA FROM
XRF5JJSA. CNF; 1
D4(5)
=
14.0
M5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
9.0
HN(5)
=
21.0
RH(5)
=
1.0
RH(5)
=
12.0
RS(5)
=
B9.74
PH(5)
=
252671.0
ER(5)
=
1573.0
DATA FROM
XRF6_USA.CNF;i
D4(6)
=
14.0
H5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
10.0
MN(6)
=
52.0
RH(6)
=
1.0
RM(6)
=
11.0
RS(6)
=
44.54
PH(6)
=
212386.0
ER(6)
=
983.0
DATA FROM
XRF7JUSA.CNF;1
D4C7)
=
14.0
H5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
14.0
MN(7)
=
2.0
RH(7)
=
1.0
RH(7)
=
10.0
RS(7)
=
54.16
PH(7)
=
184506.0
ER(7)
=
1017.0

315
C
C DATA FROM XRF8JJSA.CNF; 1
D4(8)
=
14.0
M5(8)
=
7.0
75(8)
=
87.0
HR(8)
=
15.0
MN(8)
=
19.0
RH(8)
=
1.0
RM(8)
=
10.0
RS(8)
=
20.85
PH(8)
=
164036.0
ER(8)
=
1041.0
STORE DATA
ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS= *NEW)
WRITE(1,5) NF
5 FORHATC1I2)
WRITE(l.lO) LH, LM, LS
10 FORHAT(3F10.5)
DO 100 I = 1,NF
WRITE(i,25) D4(I), H5(I), Y5(I)
25 FORMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
HRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

316
C ******** ***!(! ********** *****
c *
C USBXRF.FOR *
C *
C FILE PROGRAM *
C *
c ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.USB]USBXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE USB IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE USA IS 165 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1_USB.CNF;1
C
D4(l) = 14.0
M5(l) = 7.0
Y5(l) = 87.0
HR(1) = 16.0
MN(1) = 50.0
RH(1) = 1.0
RM(i) = 17.0
RS(i) = 43.05
PH(1) = 352365.0
ER(1) = 1565.0

317
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MW(2) =
RH(2) =
RH(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MN(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2JJSB. CNF; 1
15.0
7.0
87.0
10.0
5.0
1.0
15.0
50.74
310193.0
2039.0
XRF3JUSB.CNF;1
15.0
7.0
87.0
11.0
28.0
1.0
14.0
45.12
274348.0
1409.0
XRF4JJSB. CNF; 1
15.0
7.0
87.0
13.0
6.0
1.0
13.0
55.72
253452.0
738.0

318
DATA FROM
XRF5JDSB.CNF;1
D4(5)
=
15.0
H5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
15.0
MN(5)
=
45.0
RH(5)
=
1.0
RH(5)
=
12.0
RS(5)
=
29.33
PH(B)
=
216978.0
ER(5)
=
1043.0
DATA FROM
XRF6JJSB. CNF; 1
D4(6)
=
16.0
M5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
14.0
HN(6)
=
46.0
RH(6)
=
1.0
RM(6)
=
11.0
RS(6)
=
35.93
PH(6)
=
185294.0
ER(6)
=
1201.0
DATA FROM
XRF7JJSB. CNF; 1
D4(7)
=
16.0
M5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
16.0
HN(7)
=
44.0
RH(7)
=
1.0
RH(7)
=
10.0
RS(7)
=
48.83
PH(7)
=
157422.0
ER(7)
=
881.0

319
C
C DATA FROM XRF8_USB.CNF;1
C
C
C
C
D4(8) = 17.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 9.0
MN(8) = 53.0
RH(8) = 1.0
RM(8) = 10.0
RS(8) = 29.18
PH(8) = 153290.0
ER(8) = 1208.0
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS*NEW)
WRITE(1,5) NF
5 F0RHAT(1I2)
WRITE(l.lO) LH, LM, LS
10 F0RHAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RHATC1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 FORMAT(2F15.5)
100 CONTINUE
END

320
C ****** iii*********************
c *
C USCXRF.FOR *
C *
C FILE PROGRAM *
C *
C ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = CLAZ0.DISS.USC3USCXRF.DAT'
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE USB IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE USA IS 130 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1016 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1JJSC.CNF; 1
C
D4(i) = 17.0
M5(l) = 7.0
Y5(l) = 87.0
HR(1) = 17.0
MN(1) = 3.0
RH(i) = 1.0
RM(1) = 18.0
RS(1) = 15.57
PH(l) = 65157.0
ER(1) = 666.0

321
C
C DATA FROM
C
D4(2) =
M5(2) =
Y5(2) =
HR(2) =
MN(2) =
RH(2) =
RM(2) =
RS(2) =
PH(2) =
ER(2) =
C
C DATA FROM
C
D4(3) =
M5(3) =
Y5(3) =
HR(3) =
MN(3) =
RH(3) =
RM(3) =
RS(3) =
PH(3) =
ER(3) =
C
C DATA FROM
C
D4(4) =
M5(4) =
Y5(4) =
HR(4) =
MH(4) =
RH(4) =
RM(4) =
RS(4) =
PH(4) =
ER(4) =
XRF2JUCB.CNF;1
21.0
7.0
87.0
9.0
28.0
1.0
17.0
44.46
64825.0
575.0
XRF3JJCB. CNF; 1
21.0
7.0
87.0
10.0
59.0
1.0
16.0
5.22
61715.0
613.0
XRF4JJCB. CNF; 1
21.0
7.0
87.0
12.0
43.0
1.0
14.0
58.13
58935.0
398.0

DATA FROM
XRF5JUCB.CHF;1
D4(5)
=
21.0
115(5)
=
7.0
Y5(S)
=
87.0
HR(5)
=
14.0
HN(5)
=
24.0
RH(5)
a
1.0
RM(5)
=
13.0
RS(5)
=
31.03
PH(5)
=
50625.0
ER(5)
=
504.0
DATA FROM
XRF6JJSC. CNF; 1
D4(6)
=
21.0
H5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
16.0
MN(6)
=
13.0
RH(6)
=
1.0
RH(6)
=
12.0
RS(6)
=
17.21
PH(6)
=
43545.0
ER(6)
=
236.0
DATA FROM
XRF7JJSC.CNF;1
D4(7)

21.0
H5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
17.0
MH(7)
=
33.0
RH(7)
=
1.0
RH(7)
=
11.0
RS(7)
=
13.67
PH(7)
=
41045.0
ER(7)
=
495.0

323
C
C DATA FROM XRF8JJSC.CNF;1
C
D4(8) = 22.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) = 10.0
HN(8) = 29.0
RH(8) = 1.0
RM(8) =10.0
RS(8) = 36.56
PH(8) = 35238.0
ER(8) = 307.0
C
C STORE DATA ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS='NEW)
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 FORMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

324
C ****************************
c *
C USDXRF.FOR *
C *
C FILE PROGRAM *
C *
Q 3|E3fC9|e>|Ej|C3|C9|C3fe3fe3tC3|e3|e^i3|E3tC3te3|e9|e3|e3|C3fC|e)|E3fE3tG9tC3te3te
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN{20), LH, LM, LS
INTEGER NF, MS(20)
PKFIL = [LAZO.DISS.USD]USDXRF.DAT'
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE USB IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE USA IS 130 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
DATA FROM
XRF 1JJSD. CNF ;1
D4(l)
t=
22.0
M5(l)
=
7.0
Y5(l)
=
87.0
HR(1)
=
13.0
MN(1)
=
30.0
RH(1)
=
1.0
RM(1)
=
19.0
RS(1)
=
27.55
PH(1)
=
77305.0
ER(1)
=
743.0

DATA FROM
XRF2JJSD.CNF;1
D4(2)
=
22.0
H5(2)
=
7.0
Y5(2)
=
87.0
HR(2)
=
15.0
HH(2)
=
34.0
RH(2)
=
1.0
RM(2)
17.0
RS(2)
=
17.89
PH(2)
=
74508.0
ER(2)
=
467.0
DATA FROM
XRF3JJSD. CNF; 1
D4(3)
=
23.0
M5(3)
=
7.0
Y5(3)
=
87.0
HR(3)
=
9.0
MN(3)
=
27.0
RH(3)
=
1.0
RM(3)
=
15.0
RS(3)
=
19.36
PH(3)
=
66612.0
ER(3)
=
482.0
DATA FROM
XRF4JJSD.CUF;1
D4(4)
=
23.0
H5(4)
=
7.0
Y5(4)
=
87.0
HR(4)
=
13.0
MN(4)
=
40.0
RH(4)
=
1.0
RM(4)
=
14.0
RS(4)
=
47.99
PH(4)
=
63801.0
ER(4)
=
341.0

DATA FROM
XRF5JJSD. CNF; 1
D4(5)

24.0
M5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
12.0
MN(S)
=
48.0
RH(5)
=
1.0
RM(5)
=
13.0
RS(5)
=
8.51
PH(5)
=
56354.0
ER(5)
=
428.0
DATA FROM
XRF6JJSD.CNF;1
D4(6)
=
24.0
H5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
15.0
MN(6)
=
0.0
RH(6)
=
1.0
RH(6)
=
12.0
RS(6)
=
1.30
PH(6)
=
44377.0
ER(6)
=
510.0
DATA FROM
XRF7JUSD.CNF; 1
D4(7)
-
24.0
H5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
16.0
MH(7)
=
20.0
RH(7)
=
1.0
RH(7)
=
11.0
RS(7)
=
18.62
PH(7)
=
38989.0
ER(7)
=
373.0

327
C
C DATA FROM XRF8_USD.CNF;1
C
D4(8) = 28.0
M5(8) = 7.0
Y5(8) = 87.0
HR(8) =10.0
MN(8) = 45.0
RH(8) = 1.0
RH(8) = 10.0
RS(8) = 47.35
PH(8) = 32926.0
ER(8) = 534.0
C
C STORE DATA ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS=NEW)
WRITE(1,5) NF
5 FORMAT(112)
WRITE(l.lO) LH, LM, LS
10 FORMAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 FORMAT(1F10.5, 112, 1F10.5)
HRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
HRITE(1,75) RH(I), RM(I), RS(I)
75 FORMAT(3F10.5)
WRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END

LIST OF REFERENCES
1. Knoll, G. F., Radiation Detection and Measurement, John Wiley & Sons, New
York (1979).
2. Bureau of Radiological Health, U.S. Department of Health, Education, and
Welfare, Radiological Health Handbook, U.S. Government Printing Office,
Washington, D.C. (1970).
3. DOE Memorandum, U.S. Department of Energy Guidelines for Residual Ra
dioactive Material at Formerly Utilized Sites Remedial Action Program and
Remote Surplus Facilities Management Program Sites, Revision 2, Oak Ridge
Area Office, Oak Ridge, TN, March, 1987.
4. Woldseth, R., All You Ever Wanted to Know about X- Ray Energy Spectrom
etry, Kevex Corporation, Burlingame, CA (1973).
5. Prussin, S. G., Prospects for Near State-of-the-Art Analysis of Complex Semi
conductor Spectra in the Small Laboratory, Nuclear Instruments and Methods,
193 (1982), 121 128.
6. Evans, R. D., The Atomic Nucleus, McGraw-Hill Book Co., New York, 14th
printing (1972).
7. Scofield, J. II., Radiative Deca,y Rates of Vacancies in the K and L Shells,
Physical Review, 179 (1969), 9.
8. Gunnink, R., Niday, J. B., Siemens, P. D., UCRL-51577, Lawrence Livermore
Laboratory, Livermore, CA, April, 1974.
9. Salem, S. I., Lee, P. C., Experimental Widths of K and L X-Ray Lines, Atomic
Data and Nuclear Data Tables, 18 (1976), 233 214.
10. Wiesskopf, V., Wagner, E., Berechnug der naturlichen Linienbreite auf Grund
der Diracschen Lichttheorie, Z. Pliysik, 63 (1930), 54.
11. Gunnink, R., An Algorithm for Fitting Lorentzian-Broadened, K-Series X-Ray
Peaks of Heavy Elements, Nuclear Instruments and Methods, 143 (1977), 145
- 149.
12. Wilkinson, D. II., Breit-Wigners Viewed Through Gaussians, Nuclear Instru
ments and Methods, 95 (1971), 259 264.
13. Sasamoto, N., Koyama, K., Tanaka, S., An Analysis Method of Gamma-Ray
Pulse Height Distributions Obtained with a Ge(Li) Detector, Nuclear Instru
ments and Methods, 125 (1975), 507 523.
328

329
14. Baba, H., Baba, S., Suzuki, T., Effect of Baseline Shape on the Unfolding of
Peaks in the Ge(Li) Gamma-Ray Spectrum Analysis, Nuclear Instruments and
Methods, 145 (1977), 517 523.
15. Gunnink, R., Ruhter, W. P., GRPANL: A Program for Fitting Complex
Peak Groupings for Gamma and X-ray Energies and Intensities, UCRL-52917,
Lawrence Livermore Laboratory, Livermore, CA, January, 1980.
16. Phillips, G. W., Marlow, K. W., Automatic Analysis of Gamma-Ray Spectra
from Germanium Detectors, Nuclear Instruments and Methods, 137 (1976),
525 536.
17. Browne, E., Firestone, R. B., Table of Radioactive Isotopes, John Wiley &
Sons, New York, NY (1986).
18. Koclier, D. C., Radioactive Decay Data Tables, Technical Information Cen
ter Office of Scientific & Technical Information, United States Department of
Energy, DOE/TIC-11026, Oak Ridge, TN (1981).
19. ICRP Report No. 38, Radiological Transformations, Energy and Intensity of
Emissions, Pergamon Press, Oxford, England (1983).
20. Forsythe, G. E., Malcolm, M. A., Moler, C., Computer Methods for Mathemat
ical Computations, Prentice-Hall, Englewood Cliffs, New Jersey (1972).
21. J. Orear, Notes on Statistics for Physicists, Revised, Laboratory for Nuclear
Studies, Cornell University, Ithaca, NY (1982).
22. Chan, Heaug-Ping, Doi, Kunio, Physical Characteristics of Scattered Radiation
in Diagnostic Radiology: Monte Carlo Simulation Studies, Medical Physics, Vol
12, Mar/Apr (1985).
23. Hubble, J. II., Photon Mass Attenuation and Energy Absorption Coefficients
for 1 keV to 20 MeV, Int. J. Appl. Radiat. Isot., 33 (1982), 1269 1290.
24. Lindstrom, R. M., Fleming, R. F., Accuracy in Activation Analysis: Count
Rate Effects, Proceedings, Fourth International Conference on Nuclear Meth
ods in Environmental and Energy Research, University of Missouri, Columbia,
CONF-800433 (1980), 25 35.
25. Olson, D. G., Counting Losses in Gamma Ray Spectrometry Not Eliminated by
Dead Time Correction Circuitry, Health Physics, 51, No. 3 (1986), 380 381.
26. Ryman, J. C., Faw, R. E., Slmltis, K., Air-Ground Interface Effects on Gamma-
Ray Submersion Dose, Health Physics, Pergamon Press, New York, New York,
Vol. 41, No. 5 (1981), 759 768.
27. Kerr, G. D., Pace, J. V., Scott, W. H., Tissue Kerma vs. Distance from
Initial Nuclear Radiation from Atomic Devices Detonated over Hiroshima and
Nagasaki, ORNL/TM 8727, Oak Ridge National Laboratory (1979).
28. Brooks, R. A., Di Cliiro, G., Principles of Computer Assisted Tomography and
Radioisotopic Imaging, Phys. Med. Biol., 21, No. 5 (1976), 689 732.

BIOGRAPHICAL SKETCH
Edward (Ted, as in Teddy Kennedy) Nicholas Lazo was born 22 April, 1956, in Summit
New Jersey, where he lived the first three years of his life. In 1959, he moved with his
family to Milwaukee, Wisconsin, where he lived until he was eight years old. His first two
years of schooling were attended in Milwaukee at a Catholic grade-school where he learned
all he ever wanted to know about nuns. In 1964 he moved with his family to Lake Forest,
Illinois, in the Chicago suburbs, where he lived until he was 16. While in Lake Forest he
finished grade school and junior high school as well as his first two years of high school.
It was during this eight years that he became interested in science and math, proving to
be an above average student. His enjoyment of school and education, somewhat unusual
in the troubled times of the late 60s, was due partly to the sheltered affluence of life in
Lake Forest, but largely due to the active participation of his parents in his education and
in school affairs. His father, Dr. Robert Martin Lazo, was during this time president of
the High School Board of Education, while Ills mother, Rosemarie Lazo, was the president
of the Parent- Teachers Association. The values that his parents instilled supported him
throughout his education, eventually leading to the production of this dissertation. In 1972,
at the age of 16, he moved with his family to McLean, Virginia, in the Washington D.C.,
suburbs. His father had been a partner in a patent attorney firm in Chicago and had taken
a position on the Atomic Safety and Licensing Board of the Atomic Energy Commission,
resulting in the familys move to McLean. It was during this period that Edward became
interested in nuclear power. Both parents remained interested and active in his education.
330

331
In 1974 Edward entered the University of Virginia as a First Year student. Until en
countering organic chemistry that year, he had planned to study chemical engineering. The
organic experience, however, suggested that nuclear engineering would be a better choice.
During his four years at Virginia he again proved to be an above average student, partici
pated in student government and the local American Nuclear Society, and lived modestly in
apartments with affectionate names such as the Bungalow, the Cave, and the Farm.
He graduated with distinction in 1978 with a Bachelor of Science in Nuclear Engineering.
He moved directly into the Virginia graduate program in nuclear engineering, during which
time he spent a summer and a semester co oping with Bechtel Power Corporation, at the
Gaithersburg, Maryland, office. After graduating in December of 1979 with a Master of
Engineering degree, he went to work for Bechtel as a site liaison engineer stationed at the
then recently damaged unit 2 reactor at Three Mile Island (TMI).
He enjoyed his time at TMI very much and built a reputation for knowing how to get
things done properly. Over the 3.5 years that he worked at TMI his duties included site
specific review of home office documents, development of a data acquisition plan for the
removal items from the containment building, development and performance of decontam
ination experiments for the containment building, and development of work packages for
the Reactor Building Gross Decontamination Experiment.
In July, 1983, he left Bechtel to return to school to pursue his Pli.D. in health physics
at the University of Florida (UF). It was during this time that he met Corinne Ann
Coughanowr, who was working on her Ph.D. in chemical engineering at UF, and who he
would marry on 5 July, 1986. After four semesters of classes and one summer working
for Bechtel as a health physicist on the Formerly Utilized Sites Remedial Action Program
(FUSRAP), he completed his preliminary exams and was awarded a Laboratory Graduate
Participation Fellowship by Oak Ridge Associated Universities to perform his dissertation

332
research at; Oak Ridge National Laboratory (ORNL). He worked at ORNL for two years,
three months of which was spent working for Bechtel at Three Mile Island. During his time
at ORNL, he completed the experimental portion of his dissertation work. Upon completion
of his experiments, he took a position as a health physicist with the Safety and Environmen
tal Protection (S&EP) Division at Brookhaven National Laboratory (BNL). This choice of
jobs was driven by the fact that Corinne was at BNL finishing her Ph.D. research experi
ments. Over the course of a year at BNL the development of the mathematical model used
in Edwards dissertation research was completed.
Edward is currently at BNL with S&EP and, with his wife, has two lovely cats. He is
a member of the local and national Health Physics Societies as well as the local American
Nuclear Society. Edward has an older brother, Robert Linden, who is currently in Medical
School at the University of Virginia and has a wife, Theresa, and two sons Nicholas and
James; a younger sister, Lisamarie, who works for a nuclear consulting firm in Knoxville,
Tennessee, and is married to Steven Jarriel; and a younger brother, Thomas Christopher,
who works for NASA in Houston, Texas, and has a wife, Margerie.

I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Genevieve S. Roessler, Chair
Associate Professor of Nuclear Engineering Sciences
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
TS
Barry B erven
Section Head,
Environmental Measurements and Applications Section
Health and Safety Research Division
Oak Ridge National Laboratory
I certify that 1 have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Emmett W. Bolch
Professor of Nuclear Engineering Sciences
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosppliy.
Edward Carroll
Professor of Nuclear Engineering Sciences
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
David Hintenlang
Assistant Professor of Nuclear Engineering Sciences

I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Arthur Hornsby
Professor of Soil Science
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy
HenrFVan Rinsvelt
Professor of Nuclear Engineering Sciences
1 certify that 1 have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
G uvgn'Yalcintas
Director, Office of Technology Applications
Martin Marietta Energy Systems
This dissertation was submitted to the Graduate Faculty of the College of Engineering
and the Graduate School and was accepted as partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
December, 1988
iUlj-C. 6.
41* j
Dean, College of Engineering
Dean, Graduate School

UF Libraries:Digital Dissertation Project
Internet Distribution Consent Agreement
In reference to the following dissertation:
AUTHOR: Lazo, Edward
TITLE: Determination of radionuclide concentratins of U and Th in unprocessed
soil samples / (record number: 1130251)
PUBLICATION DATE: 1988
I, /K ,/ as copyright holder for the aforementioned
dissertation, hereby grant specific and limited archive and distribution rights to the Board of Trustees
of the University of Florida and its agents. I authorize the University of Florida to digitize and
distribute the dissertation described above for nonprofit, educational purposes via the Internet or
successive technologies.
This is a non-exclusive grant of permissions for specific off-line and on-line uses for an indefinite
term. Off-line uses shall be limited to those specifically allowed by "Fair Use" as prescribed by the
terms of United States copyright legislation (cf, Title 17, U.S. Code) as well as to the maintenance
and preservation of a digital archive copy. Digitization allows the University of Florida to generate
image- and text-based versions as appropriate and to provide and enhance access using search
software.
This grant of permissions prohibits use of the digitized versions for commercial use or profit.
Signature of Copyright Holder
Printed or Tvned Name of Convrisht Holder/Licensee
Personal information blurred
// i** f
Date of Signature
Please print, sign arid return to:
Cathleen Martyniak
UF Dissertation Project
PreservationDepartittent
University of Florida Libraries
P.O. Box 117007
Gainesville, FL 32611-7007
2 of 2
10-Jun-08 15:23



Counts


274
C
C
C
C
C
C
C
C
C
DATA FROM
XRF5J53B1. CNF; 1
D4(5)
=
27.0
M5(5)
=
5.0
Y5(5)
=
87.0
HR(5)
=
9.0
MN(5)
=
3.0
RH(5)
=
1.0
RM(5)
=
13.0
RS(5)
=
44.87
PH(5)
=
334559.0
ER(5)
=
1110.0
DATA FROM
XRF6_S3B1.CNF;1
D4(6)
=
27.0
M5(6)
=
5.0
Y5(6)
=
87.0
HR(6)
=
10.0
HN(6)
=
26.0
RH(6)
=
1.0
RM(6)
=
12.0
RS(6)
=
53.39
PH(6)
=
301884.0
ER(6)
=
1151.0
DATA FROM
XRF7 _S3B1.CHF; 1
D4(7)
=
27.0
H5(7)
=
5.0
Y5(7)
=
87.0
HR(7)
=
11.0
HU (7)
=
41.0
RH(7)
=
1.0
RH(7)
=
12.0
RS(7)
=
6.67
PH(7)
=
261608.0
ER(7)
=
1037.0


18
The x-ray fluorescent analysis system described in this paper uses its own peak shaping
program for the following reasons. First, since only the Kai peaks from U and Th will
be used, only two peaks at known energies, need to be determined. It is not necessary
to search the entire spectrum to shape each peak and to calculate the area of all possible
peaks since only the Kai peaks are of interest. This eliminates much of the computational
software necessary for large spectral analysis programs, thus decreasing processing time.
Since most processing programs are quite fast, this is not the most important reason to
have a separate peak shaping program. The second and more important reason is that
most spectral analysis programs perform Gaussian peak shaping, which is inappropriate for
x rays. This results in inaccurate area determination.
The spectral response of a detector system can be mathematically described as a con
volution of the detector systems inherent response function and the energy distribution of
the monoenergetic incident radiation (Knoll^ pp 732-739).
N{H) = f R{H,E)xS{E)dE
J OO
where
N (H) = the differential pulse height spectrum,
R(H,E) = the differential probability that a pulse of
amplitude II originates from a photon of
energy within dE of E,
5 (E) = the photon energy distribution.
Detector system response functions are typically Gaussian (Knoll^ pp 434-440). Mo
noenergetic gamma rays emitted by the de-excitation of a nucleus in an excited state are
actually not monoenergetic but are distributed in energy about a central value. This distri
bution is described by the function S(E). The width of this energy distribution is inversely


65
The value of this technique is that it measures 7-238 and Th-232 directly and without
relying on equilibrium with progeny. Neutron activation and its associated neutron source
was previously required to achieve this independence.
Error Analysis
Introduction
A soil contamination assay must be accompanied by an estimate of the error associated
with the measured contamination concentration. The assay system presented in this work
is based on fitting measured data to mathematical models using the least squares technique.
Least squares analyses lend themselves well to propagation of error from one curve fit to
the next, as well as to calculation of the chi-squared test statistic as a measure of goodness
of fit.
This work begins with measured spectral data and the error associated with each data
point. This data is fit to a mathematical model of an x-ray peak as viewed through a Ge
detector, and the peak parameters are determined. These parameters are used to determine
the area of the peak and the error associated with the peak area. This operation is repeated
for several different target configurations yielding several peak areas and their associated
errors. These areas are then fit to a mathematical model which predicts the detector
response as a function of target geometry and contamination concentration. The only
fitting parameter of this model is the contamination concentration in the target, which
is calculated by least squares fitting the previously calculated peak areas to the modeled
function. The error in the fitting parameter is extracted from the least squares fitting
process and the desired result, determination of the soil contamination concentration and
its associated error, is achieved.


FIGURE 3
Typical Th KaX Spectral Peak


165
240 N = LB + RF
245 FOR I = 1 TO N
250 PRINT X(I),Y(I)
260 NEXT I
265 PRINT
280 PRINT Points for Initial Parameters Guess
285 PRINT
290 PRINT X(I),Y(D
295 PRINT
300 S3 = INT (N / (M 1))
310 FOR I = 1 TO H
320 J = 1 + (I 1) S3
325 IF J > N THEN J = N
330 K1(I) = X(J)
340 K2(I) = Y(J)
345 PRINT K1(I),K2(I)
350 NEXT I
355 PRINT
360 FOR I = 1 TO H
370 FOR J = 1 TO H
380 AA(I,J) = (Kl(D) ** (J 1)
385 NEXT J
400 DT(I,1) = K2(I)
410 NEXT I
420 GOSUB 5000
430 FOR I = 1 TO M
440 V(I) = DA(I)
450 NEXT I
460 FOR I = 1 TO H
470 FOR J = 1 TO H
480 AA(I,J) = 0
490 NEXT J
500 DT(I,1) = 0
510 NEXT I
520 FOR I = 1 TO N
530 FOR J = 1 TO H
535 A(I,J) = (X(I)) ** (J 1)
540 TA(J,I) = A(I,J)
550 NEXT J
560 NEXT I
565 FOR I = 1 TO N
570 W(I,I) = 1
575 NEXT I
580 W = N
585 FOR I = 1 TO N
590 qi(I,I) = H(I,I)
595 NEXT I
600 FOR I = 1 TO H


33
Soil Attenuation Coefficient
It is well known that as monoenergetic gamma rays pass through any medium, the
fraction of uncollided gammas, as a function of thickness of the medium, is given by
Transmission Fraction = exp (p (E) px),
where
p (E) = mass attenuation coefficient at the
energy E, (cm/gm2) ,
p0 = density of the attenuating medium,
(gm/cc), and
x = thickness of the attenuating medium (cm).
For a monoenergetic point source, with emission rate A, the number of gammas which
strike and are detected by a detector of area AD located at distance r from the source is
A(E) =
A0 (E) xADx t;(E) x CT
47rr2
(1)
where
Aa (E) = source gamma emission rate at energy E
(Gammas/s),
AD = detector surface area (cm2) ,
t](E) = detector intrinsic energy efficiency at
energy E, (gammas counted in the full energy.
peak per gamma hitting the detector),
CT = pulse pileup corrected live time (s),
r = distance from source to detector (cm).


5
The drawback to this technique is that it relies upon the known sample, referred to as
the standard, being physically similar to each unknown sample counted. This is because the
density, moisture content, consistency, and elemental makeup of a sample will determine
that samples radiation attenuation properties. A homogeneous sample of given properties
containing 100 pCi of a radionuclide will attenuate a given fraction of the gammas emitted by
that radionuclide. A second homogeneous sample, of different properties but also containing
100 pCi of the same radionuclide, will attenuate a different fraction of the gammas emitted
by that radionuclide. Therefore two homogeneous samples containing the same amount of
a radionuclide can yield spectra with characteristic gamma energy peaks of different areas.
This makes it very important that the standards chosen match the unknowns as closely as
possible.
Unfortunately, the standards used for analysis are often significantly different in atten
uation properties from the unknown samples. Dry, ground, and homogeneous standards are
obviously different from unprocessed, wet, inhomogeneous unknown samples. And although
standards can be fairly similar to processed unknown samples, mineral content differences
do residt in differences in attenuation properties. Thus the process to be developed should
take the attenuation properties of each unknown sample into account in order to properly
determine radionuclide content.
Radionuclides of Interest
Two elements that are of particular interest to both FUSRAP and MAD are U and
Th. These are common contaminants at sites around the country. Many of the MED sites
of FUSRAP became contaminated while receiving, processing, or shipping U to be used
in the fabrication of the first atomic bomb. The Grand Junction, Colorado, site that the
MAD program is surveying is contaminated with mill tailings from U mining operations.


8510
8520
8525
8530
8540
8545
8550
8555
8560
8570
8580
8600
8610
8620
9000
171
TI = TI + ((DA(I)) ** 2) C0V(I,I)
FOR J = 1 TO H
IF J = I THEN GOTO 8540
T2 = TI + DA(I) DA(J) COV(I.J)
NEXT J
NEXT I
SIG(K) = (SqR(Tl + T2)) 5000
YFIT = O
FOR I = 1 TO H
YFIT = YFIT + V(I) ((XT(K) XT(1)) ** (I 1))
NEXT I
PRINT XT(K),(YFIT 5000),SIG(K)
NEXT K
RETURN
END


TABLE 26
Sample Physical Characteristics
Sample
Weight
(gm)
Density
(gm/ee)
Soil Weight
Fraction
(gm dry/gm wet)
Sample 2
190.0
1.66
1.0
Sample 3
125.4
1.37
1.0
Sample 4
120.0
1.31
1.0
U1
201.2
1.76
1.0
Ula
209.9
1.83
1.0
TH1
229.1
1.90
1.0
THla
208.8
1.82
1.0
NJA
132.5
1.18
0.93
NJB
142.2
1.24
0.89
USA
166.9
1.46
0.92
USB
161.9
1.42
0.95
use
183.7
1.61
0.77
USD
190.6
1.67
0.79


150
could be made to be independent by varying experimental conditions, but the changes
necessary would cause the measured peaks to drop substantially in size such that accu
rate measurement of peak areas would become impossible. The inhomogeneity analysis
technique, while theoretically possible, is not practically applicable.
To reiterate the theory of the analysis technique briefly, each jar of soil is measured
at eight positions relative to a detector. Each position is 3 mm farther from the detector
than the last. The target is broken into 3840 nodes, each of which acts approximately
as a point source. From the geometry of each position and the measured soil attenuation
properties, a Geometry Factor (GF) for each node is calculated. The sum of each GF times
the contamination concentration at each node is equal to the measured peak area for each
position. New GFs are calculated for each of the eight positions. The 3840 nodes are
grouped into eight zones; the GF of each zone is equal to the sum of the GFs of the nodes
in the zone. Assuming that each zone is contaminated uniformly, this yields a set of eight
equations in eight unknowns. This is the set of equations that is nearly singular. This arises
because the spacing between measurements is oidy 3 mm and the GFs are nearly the same.
This can be seen mathematically by looking at the Condition of the matrix.
G. E. Forsythe et al.^ define the Condition of a matrix as being similar to the inverse
of the matrix determinant. Thus a matrix which is singular, ie. determinant = 0, has a
Condition that is infinite. Practically speaking, the condition of a matrix should not be
much higher than 10 if the matrix is well behaved. Forsythe gives a fortran program for
solving a system of linear equations, using Gaussian elimination, which also determines a
lower bound for the matrixs condition. This is the program which was used to solve the
system of equations that I described above.
To study the effect of relative target separation, from position to position, on matrix
condition, the inliomogeneity analysis program was altered such that it looked at a target


175
2
REM
3
REM
*
*
4
REM
* PEAKFIT.BAS
*
5
REM
* with Error Analysis
*
6
REM
* and entire peak shaping
*
7
REM
*

8
REM
9
REM
15
PI =
3.141592653#
20
W1 =
1
30 DIM (25,15),TA(15,25),Ql(25,15),Q2(15,25),Q3(1S,15)
45 DIM T(25),0LDVAR(4)
40 DIM DT(25,1),DY(25),X(30),Y(30),F(30),SG(2,30),FIT(30),HLD(4,4)
50 DIM AA(15,15),TE(15),LI(2,50),VAR(10),DS(10),PK(3,25),BK(25)
60 DIM CH(2),VA$(3),DF(2),A1(3),B1(3),AM(5,5),DA(5),W(25,25),C0V(4,4)
85 PRINT Is this a II or Th K-alpha-1 x-ray peak?
90 INPUT EL$
95 PRINT
100 PRINT Input the name of the peak data file
105 INPUT FILE$
110 PRINT
150 FWHM = 7
170 IF EL$ = TH THEN GOTO 185
175 GA = .103
177 XB = 993
180 GOTO 190
185 GA = .0947
187 XB = 942
190 Al = 4.63217E-07
195 Bi = 9.986879E-02
200 Cl = .323665
203 EC = A1 ((XB) ** 2) + Bl XB + Cl
205 El = EC (GA / 2)
210 E2 = EC + (GA / 2)
215 CH(1) = ( Bl + SQR (Bl ** 2 4 Al (Cl El))) / (2 Al)
220 CH(2) = ( Bl + SQR (Bl ** 2 4 Al (Cl E2))) / (2 Al)
225 GA = CH(2) CH(1)
230 SIG = FWHM / (2 SQR (2 LOG (2)))
235 VA$(1) = SIG
240 VA$(2) = XB
245 VA$(3) = A
500 OPEN I,#1,FILE$
510 INPUT #1, NP
515 FOR I = 1 TO NP
525 INPUT #1, PK(l.I)
535 INPUT #1, PK(2,I)
537 INPUT #1, PK(3,I)
540 NEXT I


214
C
C STORE DATA IN FILE REV6.DAT
C
OPEN(1,FILE=DATFIL,STATUS=NEW')
DO 100 I = 1,12
100 WRITE(1,*) MTH(I)
DO 150 I = 1,4
150 WRITECl,*) E(I)
DO 200 I = 1,4
200 WRITECl,*) FA(I)
DO 250 I = 1,4
250 WRITECl,*) UA(I)
DO 300 I = 1,4
300 WRITECl,*) UB(I)
DO 350 I = 1,4
350 WRITECl,*) EDCI)
DO 400 I = 1,3
400 WRITECl,*) AOCl)
DO 450 I = 1,2
450 WRITECl,*) EOCI)
DO 500 I = 1,2
500 WRITECl,*) YICD
WRITECl,*) AD
DO 550 I = 1,4
550 WRITECl,*) JACD
CLOSEC1,STATUS=KEEP >)
END


216
C
C The following data is for Uranium
C
C PE interpolation energy, K-absorption energy, in MeV
C from data sent to me by Hubble.
C
DATA EKAB(l) /.1156061/
C
C Uranium Photoelectric Cross Section, (sq cm / atom), for
C .150 MeV and E(k-abs) from data sent to me by Hubble.
C
DATA PEi(l),PE2(1) /.9381E-21, 1.819E-21/
C
C Specific Atom Concentration, (Atoms U/gm Soil)/(pCi U/gm Soil),
C caluclated using a Uranium half life of 4.468E9 Y, from The
C Table of Radioactive Isotopes, by E. Browne and R. B. Firestone.
C
DATA EC(1) /7.5265E15/
C
C The following data is for Thorium
C
C PE interpolation energy, K-absorption energy, in MeV
C from data sent to me by Hubble.
C
DATA EKAB(2) /.1096509/
C
C Thorium Photoelectric Cross Section, (sq cm / atom), for
C .150 MeV and E(k-abs) from data sent to me by Hubble.
C
DATA PE1(2),PE2(2) /.8702E-21, 1.939E-21/
C
C Specific Atom Concentration, (Atoms Th/gm Soil)/(pCi Th/gm Soil),
C calculated using Th half life of 1.41E10 y, from The Table
C of Radioactive Isotopes, by E. Browne and R. B. Firestone.
C
DATA EC(2) /2.3752E16/


298
C
C DATA FROM
C
D4(5) =
M5(5) =
Y5(5) =
HR(5) =
MN(5) =
RH(5) =
RM(5) =
RSC5) =
PH(5) =
ER(5) =
C
C DATA FROM
C
D4(6) =
M5(6) =
Y5(6) =
HR(6) =
MN(6) =
RH(6) =
RH(6) =
RS(6) =
PH(6) =
ER(6) =
C
C DATA FROM
C
D4(7) =
H5(7) =
Y5(7) =
HR(7) =
MN(7) =
RH(7) =
RM(7) =
RS(7) =
PH(7) =
ER(7) =
XRF5_NJA.CNF;1
2.0
7.0
87.0
9.0
53.0
1.0
10.0
58.11
51170.0
392.0
XRF6 JIJA. CNF ;1
2.0
7.0
87.0
14.0
31.0
1.0
10.0
10.59
44378.0
466.0
XRF7 JIJA. CNF; 1
2.0
7.0
87.0
15.0
54.0
1.0
9.0
43.16
39759.0
240.0


DATA FROM
XRF5JUCB.CHF;1
D4(5)
=
21.0
115(5)
=
7.0
Y5(S)
=
87.0
HR(5)
=
14.0
HN(5)
=
24.0
RH(5)
a
1.0
RM(5)
=
13.0
RS(5)
=
31.03
PH(5)
=
50625.0
ER(5)
=
504.0
DATA FROM
XRF6JJSC. CNF; 1
D4(6)
=
21.0
H5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
16.0
MN(6)
=
13.0
RH(6)
=
1.0
RH(6)
=
12.0
RS(6)
=
17.21
PH(6)
=
43545.0
ER(6)
=
236.0
DATA FROM
XRF7JJSC.CNF;1
D4(7)

21.0
H5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
17.0
MH(7)
=
33.0
RH(7)
=
1.0
RH(7)
=
11.0
RS(7)
=
13.67
PH(7)
=
41045.0
ER(7)
=
495.0


207
COV = DAI
CHISQ(l) = CHI
600 WRITE(6,605)
605 F0RMAT(/,1X,In what file should results be stored?)
READ(5,(A10)) OUT
OPEN(i,FILE=OUT,STATUS=NEW)
WRITE(1,610)
610 FORMAT(/,IX,This is an ASSAY.FOR run)
WRITEC1,1030) PKFIL
1030 F0RMAT(/,1X,XRF Peak data from file ,A25)
WRITE(1,1040) GFFILE
1040 FORMAT(/,IX,Geometry Factor data form file ,A25)
WRITE(1,1045) CGFFILE
1045 F0RMAT(/,IX,Compton Geometry Factor data from file ,A25)
WRITE(1,1050) GEOH
1050 F0RMAT(/fIX,System Geometry data from file ,A25)
WRITE(1,620)
620 FORMAT(/,IX,Liniar Fit Coefficients,/,
1 IX,Y(I) = A X(I))
WRITE(1,630) Al.COV
630 F0RMAT(/,1X,A = Contamination Concentration (pCi/gm) =
1 ,F10.5, +- .F10.5)
WRITE(1,637) CHISq(l)
637 F0RMAT(/,IX,The Reduced Chi**2 value for the fit = .F10.5)
WRITE(1,640)
640 FORMAT(/,25X,Fit Results,//,
1 IX,Position,Ex,GF Sum,7X,DR Fit,7X,
2 DR Meas,7X, Del ('/,),/)
DO 650 I = 1,NP
DEL = 100.0 (Y(I) F(I)) / Y(I)
650 WRITE(1,660) I,X(I), F(I), Y(I), DEL
660 FORMAT(4X,I1,5X,F10.5,5X,F10.5,3X,F10.5,3X,F10.5)
9000 END


51
GF(P) = target geometry factor, or, the sum of
all point node geometry factors for a
target located at position P,
(counts/a) / (pCi/gm).
Using the contamination concentration, C, as the fit parameter, the data collected from
measurements made at several different geometries is then least squares fit to the above
equation. This yields a value for C, the contamination concentration in the target sample,
which is the desired result of the assay.
Compton Scatter Gamma Production of Fluorescent X Rays
The fluorescent x-ray production described by the previous equations is due to unscat
tered source gammas undergoing photoelectric interactions in the target. Since the target is
thick, gammas will also Compton scatter. If the scatter angle is small enough, the scattered
gamma will still be of sufficient energy to undergo a photoelectric interaction in the sam
ple and produce more fluorescent x rays. As will be discussed in the experimental results
section, approximately 15% of the fluorescent x rays produced are due to singly Compton
scattered ganunas. It is therefore important to calculate this production term and include
it in the model.
Compton scatter gamma model
Qualitatively, Compton scatter gamma production of fluorescent x rays is due to ex
citation source gammas which undergo a single Compton scatter interaction at point A
in a target, change direction and energy, and then undergo a photoelectric interaction at
point B in a target. Quantitatively, this is slightly more complicated to describe. Consider
two target points, A and B, as shown in Figure 7. Using equations similar to those used
previously, the flux, at scatter point A is calculated, the scatter flux and gamma energy of


191
C
READ(1,*) SD
WRITE(6,*) SD
C
C READ EXTRA DATA STORED IN SAMPLE FILE BUT NOT
C NEEDED BY THIS PROGRAM
C
DO 10 I = 1,3
10 READCl,*) QHLD
C
C INPUT THE SAMPLE LINIAR ATTENUATION COEFFICIENT (1 / CM)
C FOR 136.476 keV
C
READCl,*) US(1)
C
C FOR 122.063 keV
C
READCl,*) US(2)
C
C IF EL = TH, FOR 93.334 keV
C IF EL = U ', FOR 98.428 keV
C
READ(1,*) US(3)
C
C WHICH TWO CO-57 SOURCES WERE USED? (EX:3,2 OR 3,1 ETC.)
C
C0(1) = 3
C0(2) = 2
CLOSE(1,STATUS='KEEP)
DTFILE = [LAZ0.DISS.DATA3REV6.DAT
XRFFIL = '[LAZO.DISS.DATA]XRFDTA.DAT'
WRITEC6.70) DTFILE
70 FORMAT(/,IX,READING ATTENUATION DATA FROM FILE >,A10)
OPEN(1,FILE=DTFILE,STATUS=OLD')
DO 75 I = 1,12
75 READCl,*) IMNTH
DO 80 I = 1,4
80 READCl,*) FHOLD
E(3) = 0.0
E(4) = 0.0
DO 85 I = 1,4
85 READCl,*) FA(I)
FA(3) = 0.0
FA(4) = 0.0
DO 90 I = 1,4
90 READCl,*) UA(I)
UA(3) = 0.0
UA(4) = 0.0


231
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
* *
* GE0M5K.F0R *
* *
INTEGER NS, RT, CT, VT, RD, CD
CHARACTER *10 GEOH
DIMENSION X(2), Y(2), Z(2)
GEOM = GE0M5K.DAT
This program creats file GE0M5K.DAT.
This file contains the relative geometrical locations
of the sources, the target, and the detector.
Sources #3 and #2 were used. The target bottle
was supported by plastic rings A through I and by
target support 5.
NUMBER OF CO-57 SOURCES USED TO IRRADIATE THE TARGET
NS = 2
SOURCE #1 COORDINATES, XI, Yl, Z1
X(l) = 4.422
Y(l) = 0.0
Z(l) = 4.42
SOURCE #2 COORDINATES, X2, Y2, Z2
X(2) = 4.422
Y(2) = 0.0
Z(2) = -4.42
TARGET CENTER COORDINATES, XT, YT, ZT
FOR TARGET SUPPORTED BY 2 SUPPORTS (2 ft S)
XT = 12.0
YT = 0.0
ZT = 0.0
TARGET HEIGHT, TH, AND RADIOUS, TR
TH = 6.50
TR = 2.32


Counts


TABLE 23
Measured vs. Fitted Detector Response for
NJB-Th
Fitting Equation : DR = GF X CC
Where : DR = Measured Detector Response
GF Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 2267.0 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.462
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.863
1956.3
1907.0
2
0.760
1723.1
1753.9
3
0.672
1522.4
1520.0
4
0.595
1349.0
1363.2
5
0.529
1198.8
1211.4
6
0.471
1068.0
1065.1
7
0.421
954.4
943.2
8
0.377
855.1
833.2


265
C
C Data is now written into file SAMPLENJBTH.DAT
C
OPEN(1,FILE=SAHPLEUSC.DAT',STATUS=NEW)
WRITE(1,(A3)) ELEMENT
WRITECl,*) WF
WRITECl,*) SD
WRITECl,*) A1
WRITECl,*) Bi
WRITE(1,*) Cl
WRITECl,*) US1
WRITECl,*) US2
WRITECl,*) US3
CLOSE C1,STATUS='KEEP)
END


BIOGRAPHICAL SKETCH
Edward (Ted, as in Teddy Kennedy) Nicholas Lazo was born 22 April, 1956, in Summit
New Jersey, where he lived the first three years of his life. In 1959, he moved with his
family to Milwaukee, Wisconsin, where he lived until he was eight years old. His first two
years of schooling were attended in Milwaukee at a Catholic grade-school where he learned
all he ever wanted to know about nuns. In 1964 he moved with his family to Lake Forest,
Illinois, in the Chicago suburbs, where he lived until he was 16. While in Lake Forest he
finished grade school and junior high school as well as his first two years of high school.
It was during this eight years that he became interested in science and math, proving to
be an above average student. His enjoyment of school and education, somewhat unusual
in the troubled times of the late 60s, was due partly to the sheltered affluence of life in
Lake Forest, but largely due to the active participation of his parents in his education and
in school affairs. His father, Dr. Robert Martin Lazo, was during this time president of
the High School Board of Education, while Ills mother, Rosemarie Lazo, was the president
of the Parent- Teachers Association. The values that his parents instilled supported him
throughout his education, eventually leading to the production of this dissertation. In 1972,
at the age of 16, he moved with his family to McLean, Virginia, in the Washington D.C.,
suburbs. His father had been a partner in a patent attorney firm in Chicago and had taken
a position on the Atomic Safety and Licensing Board of the Atomic Energy Commission,
resulting in the familys move to McLean. It was during this period that Edward became
interested in nuclear power. Both parents remained interested and active in his education.
330


Dal a File Programs
These programs were written to create data files for the above listed data processing
programs. These programs are written in FORTRAN-77 and were run on a VAX Cluster
main-frame computer. REV6.FOR lists detector system calibration data. COMDTA.FOR
lists data used for the compton x-ray production calculations. XRFDTA.FOR lists data
used for direct gamma ray x-ray production calculations. And finally the GEOM5A.FOR
through GE0M50.F0R list data which describe the geometry of the experimental setup
used to count each soil target.


185
C
C ****************************
c *
C DIST.FOR *
C *
c ****************************
c
COMMON XT, YT, TR
INTEGER SLICE, RT, CT, VT, RD, CD
CHARACTER *1 Q
CHARACTER *10 GEOM, SPD, PDD
DIMENSION XS(2),YS(2),ZS(2)
DIMENSION DTR(24,3),AD(24),PTS(192,3),V0LT(192)
DIMENSION SP(192,4),PI(192,24),P2(192,24),V(21)
PI = 3.14159
SLICE = 1
Q = Y*
C
C DETECTOR COORDINATES, X, Y, Z, AND RADIOUS (CM)
C
XD = 0.0
YD = 0.0
ZD = 0.0
C
C DETECTOR RADIOUS, DR
C
DR = 1.8
WRITE(6,10)
10 FORMAT(/,IX,Enter the name of the System Geometry File)
READ(5,15) GEOM
15 FORMAT(AIO)
OPEN(1,FILE=GEOM,STATUS=OLD)
C
C NUMBER OF SOURCES USED
C
READ(1,*) NS
C
C SOURCE COORDINATES
C
DO 50 1=1,NS
READ(1,*) XS(I),YS(I),ZS(I)
50


32
TABLE 4
U anc
Th K-Sliell Absorption and Emi
17
3 sionJ'
Element
K-Sliell
Absorption
Ka i
Emission
Ka2
Emission
U
115.591 keV
98.434 keV
94.654 keV
Th
109.63 keV
93.350 keV
89.957 keV
TABLE 5
Co-57 and Eu-155 Emission Energies and Yields
Element
Emission Energy
Gamma Yield
Backscatter
Energy
Co 57
122.063 keV
.8559
82.6 keY
136.476 keV
.1061
89.0 keV
Eu 155
105.308 keV
.207 *
74.6 keV
86.545 keV
.309 *
64.6 keV
*: The gamma yields for Eu 155 are not known to the same precision as
those of Co57. Europium-155 sources, therefore, are described by gamma
emission rates, Activity (Ci) X Yield (gammas/s). The listed yields are for
estimation purposes only.
TABLE 6
Co- 57 and Eu-155 Physical C
aracteristics
Co-57
Eu-155
Activity
5 mCi 15%
2 mCi 15%
(1 October 1985)
(1 April 1986)
Half Life
271.7 d
1741 d
Soil Moisture Content and Attenuation Coefficients
In order to properly analyze spectral data, the soil attenuation coefficient as a function
of energy must be known. The details of their use are described in a subsequent section.
Since the goal of this assay is to determine the soil U and Th concentrations in units of pCi
per gm of dry soil, the water weight fraction is needed to determine the soil dry weight.
Fortunately, both of these parameters are easily measured.


187
C
C
C
WRITE(6,260)
260 F0RMAT(/,IX,Completed Target Node Points)
DETERMINE DISTANCE FROM SOURCE TO POINT
275 DO 350 II = 1,RT CT / 2
DO 300 A1 = 1,NS
A2 = 2 Al i
A3 = 2 A1
PX1 = XS(A1)
PY1 = YS(A1)
PZ1 = ZS(A1)
PX2 = PTS(Ii,l)
PY2 = PTS(I1,2)
PZ2 = PTS(I1,3)
CALL DISTANCE(PX1,PY1,PZ1,PX2,PY2,PZ2,DSTi,DST2,Ki)
IF (Kl .Eq. 10) GOTO 9000
SP(I1,A2) = DSTI
300 SP(I1,A3) = DST2
C
C
C
350
360
400
500
600
650
700
800
DETERMINE DISTANCE FROM POINT TO DETECTOR
DO 350 K = 1,RD CD
PX1 = DTR(K,1)
PY1 = DTR(K,2)
PZ1 = DTR(K,3)
CALL DISTANCE(PXi,PYi,PZ1,PX2,PY2,PZ2,DSTI,DST2,Kl)
IF (Kl .Eq. 10) GOTO 9000
P1(I1,K) = DSTI
P2(I1,K) = DST2
WRITE(6,360) SLICE
FORMAT(/,IX,'Slice #fAl, Completed)
IF (SLICE .HE. 1) GOTO 500
OPEN(1,FILE=SPD,STATUS=NEW)
OPEN(2,FILE=PDD,STATUS=NEW)
WRITE(6,400) SPD
FORMAT(/,IX,Writing Source Target data to file ,A15)
WRITE(1,*) XS(1),YS(1),ZS(1),XS(2),YS(2),ZS(2)
WRITE(1,*) XT,YT,ZT,TR,TH,RT,CT,VT
WRITEd,*) XD,YD,ZD,DR,RD,CD,NS
DO 600 II = 1,RT CT / 2
WRITEd,*) SP(I1,1) ,SP(I1,2) ,SP(I1,3) ,SP(I1,4) ,V0LT(I1)
IF(SLICE .GT. 1) GOTO 700
WRITE(6,650) PDD
FORMAT(/,IX,Writing Target Detector data to file ,A15)
DO 800 I = 1,RT CT / 2
DO 800 J = 1,RD CD
WRITE(2,*) P1(I,J), P2(I,J)


222
C
C TARGET RADIAL, CIRCUNFERENCIAL, AND VERTICAL
C SEGMENTATION: RT, CT, ft VT.
C
RT = 32
CT = 10
VT = 12
C
C STORE DATA IN FILE GE0M5A.DAT
C
OPEN(1,FILE=GEOM,STATUS='NEW)
WRITE(1,*) NS
DO 100 I = 1,NS
100 WRITE(1,*) X(I),Y(I),Z(I)
HRITEd,*) XT, YT, ZT
WRITEd,*) TH, TR
HRITEd,*) RT, CT, VT
CLOSE(1,STATUS='KEEP)
END


154
TABLE B-2
Target-Detector Distance vs.
Measured Peak Area
Target-Detector
Distance (cm)
Peak Area
(counts)
10.5
541821
10.8
479982
11.1
428292
11.4
375253
11.7
334559
12.0
301884
12.3
261608
12.6
233651
It can be seen from Table B-l and Figure B-l that as the separation between positions
becomes greater, the resulting matrix equations become more well behaved. This makes
sense intuitively since the relative GFs are also becoming much different as the relative
target separation increases. Then, if a truly well behaved matrix should have a condition
of approximately 10, the curve in Figure 1 can be extrapolated to determine the required
relative target separation. From the crude (and conservative) line drawn on Figure B1 it is
estimated that the matrix condition will be 40 at a target separation of 70 mm.
Moving now to Table B2 and Figure B2, it can be seen that the decline in detector
signal as the target moves away from the detector is very close to exponential. This line
may be fit to the curve,


TABLE A-2
NBS Source, SRM 4275-B-7, Emission Rates
129
Radionuclide
Energy
(keV)
Emission Rate
(Gammas/s)+
Uncertainty
(%)
Eu-154/Eu-155
42.8
1.102E4
1.3
Eu-155
86.6
6.320E3
0.8
Eu-155
105.3
4.365E3
1.1
Eu-154
123.1
1.510E4
0.7
56-125
176.4
1.626E3
0.6
+: Emission rates are for 1200 EST, 1 May, 1983
TABLE A-3
NBS Source, SRM 4275-B-7, Physical Characteristics
Radionuclide
Half Life
Decay Constant
56-125
1008.7 1.0 d
6.872E-4 d-1
FJu-154
3127 8
d
2.217E-4 d-1
Eu-155
1741 10
d
3.981E-4 d-1
The first step in efficiency calibration, then, was using the NBS source to determine
detector intrinsic energy efficiencies at the energies listed in Table A-2. The Physical setup
used to count the NBS source is shown in Figure A-l. The equation describing the situation
is
FL(E)=
ER(E) x AD x T) x CT
4xR\
x ATN(E),
(Al)
where
FL (E) = the gamma flux measured by the detector, ie., the
full energy peak area at energy E, (gammas),
ER(E) the emission rate of the source at energy E, (gammas/s),


64
It is also reasonable to conclude that all U and Th seen by XRF is C/-238 and Th-
232 respectively. Based on the above table, such large quantities of other isotopes would
be required before these isotopes could be seen by XRF, the radiation levels of the sources
would be too large for analysis using sensitive Ge detectors. It is also extremely unlikely that
such large quantities of other isotopes would be found. Even if U-238 were in equilibrium
with Th-234, 7-234, and Th-230, or if Th-232 were in equilibrium with Th-228, while the
curie contents of the sample would be high in these other isotopes, the ppm concentrations
of these other isotopes would be much to low to register using XRF. It would thus be safe
to assume that all of the signal seen at the detector was from U-238 or Th-232.
Prior knowledge of the nature of the process which lead to the contamination might
point toward high concentrations of other isotopes. For example, excavation near a plant
which previously processed Th-230 to remove Ra-226 would be expected to show high Th-
230 levels and natural Th-232 levels. Again though, unless the T/i-230 levels were extremely
high, XRF would not be of any use.
Unfortunately then, tills XRF technique is not useful in determining the concentrations
of isotopes other than U-238 and Th-232. If it were known that the contamination in
question was primarily U-238 and/or Th-232, progeny equilibrium with U-238 and Th-232
could be assumed thus establishing an upper limit of other isotopic concentrations. This
would not, however, constitute an adequate assay unless the upper limit were below some
lower bound of regulatory concern.
However, the analysis teclmique used, that is measuring the attenuation properties of
the sample at the energies of the gamma rays of interest, and the calculation of geometry
factors, could be applied to gamma spectroscopic techniques or to neutron activation anal
ysis techniques to improve their accuracy. This work is, however, beyond the scope of this
project.


FIGURE 9
Target in Place Above Detector


3
fudge factor being the average ratio of sample analysis results for processed vs. unprocessed
samples, the results of the analysis of unprocessed soil samples are accurate enough to use
and to guide further work. Even with the fudge factor, analysis of unprocessed soil samples
is not sufficiently accurate to prove, for example, that an area is free of contamination and
needs no further work. The second analysis, of the processed soil, is accurate but takes too
long to meet construction schedules.
The process in need of development, then, was an assay technique that was accurate but
could be performed on unprocessed soil samples. This would eliminate the time-consuming
step of sample drying and grinding.
Upon selecting this topic, I received a Laboratory Graduate Participation Fellowship
from Oak Ridge Associated Universities (ORAU) to pursue the research at Oak Ridge Na
tional Laboratory (ORNL). The Radiological Survey Activities section (RASA), currently
called the Measurement Applications and Development (MAD) section, of the Health and
Safety Research Division (HASRD) sponsored this work because it has been in the business
of performing radiological assessment surveys of various contaminated government sites
around the country. At the MAD lab at ORNL soil samples are processed in the same
method as used hy the FUSRAP analysis lab, and the standards comparison method of
gamma spectroscopic analysis is used to determine radionuclide concentrations. As with
the FUSRAP project, soil sample processing is a time-consuming endeavor.
Further research indicated that the processing of soil samples prior to analysis was
standard procedure at most soil assay labs. Thus a procedure that eliminated the processing
step would be universally useful.
My research also indicated that there was a second drawback to standard gamma spec
troscopic techniques. A description of the standards comparison method of gamma spec
troscopic analysis will help provide a better understanding of this problem.


302
DATA FROM
XRF5 JIJA. CNF; 1
D4(5)
=
2.0
M5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
9.0
MN(5)
=
53.0
RH(5)
=
1.0
RM(5)
=
10.0
RS(5)
=
58.11
PH(5)
=
2002194.0
ER(5)
=
2646.0
DATA FROM
XRF6 JIJA.CNF;1
D4(6)
=
2.0
MB(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
14.0
MN(6)
=
31.0
RH(6)
=
1.0
RM(6)
=
10.0
RS(6)
=
10.59
PH(6)
=
1742420.0
ER(6)

2638.0
DATA FROM
XRF7 JIJA. CNF; 1
D4(7)
=
2.0
M5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
15.0
MN(7)
=
54.0
RH(7)
=
1.0
RM(7)
=
9.0
RS(7)
=
43.16
PH(7)
=
1568213.0
ER(7)
=
3196.0


151
with only two zones, not eight as described above. In this analysis then, all that was
necessary was data from the target counted at only two positions. This would show what
effect relative target separation, from position to position, would have on the condition of
the resulting matrix. The measurements used for the analysis and the resulting matrix
conditions are listed in Table B-l. Figure B-l is a graphical representation of this data.
Table B-2 shows the measured peak area verses target-detector separation. Figure B-2
shows shows this data graphically.
TABLE B-l
Relative Sample Separation vs.
Solution Matrix Cone
ition
Positions
Relative Separation
(mm)
Matrix Condition
1 & 2
3
2680
1 & 3
6
1493
1 & 4
9
1112
1 & 5
12
932
1 & 6
15
834
1 & 7
18
778
1 & 8
21
746


318
DATA FROM
XRF5JDSB.CNF;1
D4(5)
=
15.0
H5(5)
=
7.0
Y5(5)
=
87.0
HR(5)
=
15.0
MN(5)
=
45.0
RH(5)
=
1.0
RH(5)
=
12.0
RS(5)
=
29.33
PH(B)
=
216978.0
ER(5)
=
1043.0
DATA FROM
XRF6JJSB. CNF; 1
D4(6)
=
16.0
M5(6)
=
7.0
Y5(6)
=
87.0
HR(6)
=
14.0
HN(6)
=
46.0
RH(6)
=
1.0
RM(6)
=
11.0
RS(6)
=
35.93
PH(6)
=
185294.0
ER(6)
=
1201.0
DATA FROM
XRF7JJSB. CNF; 1
D4(7)
=
16.0
M5(7)
=
7.0
Y5(7)
=
87.0
HR(7)
=
16.0
HN(7)
=
44.0
RH(7)
=
1.0
RH(7)
=
10.0
RS(7)
=
48.83
PH(7)
=
157422.0
ER(7)
=
881.0


215
C
c *
C COMDTA.FOR *
C *
c ********************
c
CHARACTER *10 DTFILE
DIMENSION E(2),CTRATI0(2),TF(2),UA(2),
1 A0(2),YI(2),EKAB(2),
2 PE1(2),PE2(2),EC(2)
REAL JA(2)
C
C Co-57 Gamma energies (MeV)
C
DATA E(l),E(2) /.136476, .122063/
C
C Compton Scatter to Total Liniar Attenuation Ratio for Soil
C as averaged for several soil types and calculated by XSECT.
C
DATA CTRATIO(l),CTRATI0(2) /.90712, .88048/
C
C Stainless Steel Co-57 Source end window attenuation fraction
C for the above energies as taken from REV.6 data.
C
DATA TF(1),TF(2) /.94598, .93925/
C
C Air mass attenuation coefficients (sq cm / gm)
C for the above energies as taken from REV.6 data.
C
DATA UA(1),UA(2) /.1406, .1459/
C
C Source Strengths (mCi) for Co-57 sources #3 and #2 as
C of 1 October, 1986, as taken from REV.6 data.
C
DATA A0(1),A0(2) /2.38809, 2.20737/
C
C Co-57 Gamma Yields for the above energies
C as taken from REV.6 data.
C
DATA YI(1),YI(2) /.1061, .8559/
C
C Bottle Transmission Fractions
C for the above energies as taken from REV.6 data.
C
DATA JA(1),JA(2) /.97190, .97110/


284
C
I****************************
C *
c *
c *
c *
c *
c *
FILE PROGRAM
U1AXRF.FOR
*
C
CHARACTER *25 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, M5(20)
PKFIL = [LAZO.DISS.UiA]U1AXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE U1A IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE U1A IS 186 PCI/GM U-238 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, ft LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1JJ1A.CNF;1
C
D4(l) = 3.0
M5(i) = 6.0
Y5(l) = 87.0
HR(1) = 11.0
MN(1) = 3.0
RH(1) = 1.0
RM(1) = 23.0
RS(1) = 9.15
PH(1) = 141648.0
ER(1) = 599.0


87
geometry due to unscattered gammas from the XRF activation sources. The total GF
for each geometry is stored for use by subsequent programs.
6. COMPTON.FOR is run once for each of the eight geometries and must he run for each
soil sample. This program uses the distances calculated by DIST.FOR and the atten
uation coefficients calculated by SOILTRANS.BAS to determine the sample Compton
GFs for each geometry due to singly scattered compton gammas from the activation
sources. The total compton GF for each geometry is stored for use by subsequent
programs.
7. ASSAY.FOR is run once for each sample. This is the final processing program and uses
the peak areas calculated by PEAKFIT.BAS and the GFs calculated by IMAGE.FOR
and COMPTON.FOR to determine the soil £7-238 and/or Th-232 concentration^) in
each sample. Errors and the resulting fitted line are reported.


205
C ************************
c *
C ASSAY.FOR *
C *
c ************************
c
CHARACTER *1 TEST, OS
CHARACTER *30 GEOM, GFFILE, CGFFILE
CHARACTER *30 PKFIL, SAMPLE, DRFIL, OUT
DIMENSION X(32),Y(32),A(32,7),TA(7,32),F(32),DY(32),V(9)
DIMENSION AA(7,7),AM(7,8),H2(7,7),ER(8)
DIMENSION qi(32,7),Q2(7,32),Q3(7,7),DT(7),DA(7)
DIMENSION GF(32,192), GFT(16), DR(32), CHISq(2)
DIMENSION CGFC3840), CGFT(16), GFT0T(16)
REAL MN, LH, LM, LS, LT, NCR, NLT, NF, NER(8)
INTEGER Wl, W, NP
INTEGER RT, CT, VT, q, P
PI = 3.14159
GEOM = '[LAZO.DISS.DATA]GE0M5A.DAT
WRITE(6,20)
20 FORMAT(/,IX,In what file is GF data stored?)
READ(5,25) GFFILE
25 F0RMAT(A25)
WRITE(6,45)
45 FORMAT(/,IX,In what file is the Compton GF data stored?)
READ(5,50) CGFFILE
50 F0RMAT(A25)
WRITE(6,55)
55 F0RMAT(/,1X,In what file is the XRF Peak Data stored?)
READ(5,57) PKFIL
57 F0RMAT(A25)
NP = 8
OPEN(1,FILE=GEOM,STATUS=OLD)
READ(1,*) AHOLD
DO 70 I = 1,AHOLD
70 READ(1,*) AHI, AH2, AH3
READ(1,*) AHI, AH2, AH3
READ(1,*) TH, TR
READ(1,*) RT, CT, VT
CLOSE(1,STATUS=KEEP)
100 q = 2
OPEN(1,FILE=GFFILE,STATUS=OLD)
DO 120 P = 1,NP
READd,*) GFT(P)
GFT(P) = GFT(P) 2
WRITE(6,115) P, GFT(P)
115 FORMAT(/,IX,GF Total for Position #,I1, is .F10.5)
120 CONTINUE


271
C
C
C
DATA FROM XRF8_S2B2.CNF;1
C
C
C
D4(8)
M5(8)
Y5(8)
HR(8)
HN(8)
RH(8)
RH(8)
RS(8)
PH(8)
ER(8)
28.0
5.0
87.0
11.0
54.0
1.0
12.0
39.06
115378.
674.0
10
25
50
75
90
100
STORE DATA ON DISK FILE
OPEN(1,FILE=PKFIL,STATUS*'NEW')
WRITECl.5) NF
F0RMTUI2)
WRITE(i.lO) LH, LM, LS
FORHAT(3F10.5)
DO 100 I = 1,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
FORHATdFlO.5, 112, 1F10.5)
WRITE(1,50) HR(I), HN(I)
F0RHAT(2F10.5)
WRITE(1,75) RH(I), RH(I), RS(I)
FORMAT(3F10.5)
WRITE(1,90) PH(I), ER(I)
F0RHAT(2F15.5)
CONTINUE
END


FIGURE 1
Typical Gamma Ray Spectral Peak and Background


159
The value of this equation will become clear from the ensuing discussion. The Mass
Attenuation Coefficient, /x, mentioned above, is a function of energy. It is also the sum of
the Mass Attenuation coefficients of its composite parts. That is
fl x p = flw x pw + fl, x p
where
fly, = mass attenuation coefficient for water at the
energy of interest {cm2 ¡gm of water) ,
pw water hulk density [gm of water/cm3 of sample),
fi, = mass attenuation coefficient for soil at the
energy of interest {cm2¡gm of soil),
p, = soil bulk density {gm of soil ¡cm3 of sample) .
But
P. = P~ Pvn
therefore
fi X p = fiw X pw + fi, X [p pw).
Since, for the energy of interest, the mass attenuation coefficient for water can be looked
up in a table, and p is a measured quantity, this is an equation in two unknowns; fi, at
the energy of interest (fi, (E)) and p0. This expression for fi X p can now be put into
the Equation 1, which describes the attenuation of gammas by some medium. A source-
attenuator-detector system can be set up and A(E) can be measured. Assuming that source
strength, relevant distances, and attenuator thickness can be accurately measured, again,
we have an equation in two unknowns. By taking the natural log of both sides of that
equation and rearranging tilings slightly, the equation becomes


161
In (us (E)) = A + B In (E) + C (In (E))2 ,
or
H, (E) = exp [A + B In (E) + C (In (E))2) ,
where A, B, and C are constants.
If this expression is put into Equation B-l, the result is one equation in four unknowns.
Since, however, the above expression is valid over a small energy range, four measurements
at four different energies (El < E2 < E3 < E4) can be made and that system of equations
can be solved for Row, A, B, and C. As with the peak fitting, this system is solved using a
least squares fitting technique such that the four unknowns are determined. A, B, and C are
then used to determine fi, (E) ,El account for sample inhomogeneity in the determination of U and Th concentrations. The
gamma rays chosen are from Co-57, 122 keV and 136 keV, and from Eu-155, 86 keV and
105 keV. This range encompasses both Kal energies from U and Th (see Table 4) and is
narrow enough such that /(E) can be modeled as a quadratic in In (E). The techniques
developed for processing this information into U and Th concentrations are discussed in the
next section.
Reasons for Soil Moisture Content Analysis Failure
The above described moisture analysis technique relies upon the solution of a set of
four simultaneous equations. As with the inhomogeneity analysis, this set of equations is
very close to singular and thus is not be solved explicitly. In this case, the energies of the
chosen gamma rays are too close together such that the attenuation coefficients are too close


300
C **** *****111 ****** ****** ******
c *
C NJATHXRF.FOR *
C *
C FILE PROGRAM *
C *
c ****************************
c
CHARACTER *30 PKFIL
DIMENSION D4(20),Y5(20),HR(20)
DIMENSION RH(20),RM(20),RS(20),PH(20),ER(20)
REAL MN(20), LH, LM, LS
INTEGER NF, MS(20)
PKFIL = [LAZO.DISS.NJA]NJATHXRF.DAT
C
C THE FOLLOWING XRF PEAK DATA IS FOR SAMPLE NJA-TH IN
C BOTTLE #1 SUPPORTED BY PLASTIC RINGS A THROUGH I,
C IN GEOMETRY 5A, AND A THROUGH I + 1 THROUGH 14, IN
C GEOMETRY 50. SAMPLE NJA-TH IS 2590 PCI/GM TH-232 AND
C WAS IRRADIATED BY CO-57 SOURCES #3 AND #2.
C LINE 1015 CONSISTS OF THE NUMBER OF DATA POINTS, NF,
C AND THE COUNT LIVE TIME, LH, LM, LS. THEN FOR
C EACH SPECTRA, COUNTING DATE, D4, M5, Y5, AND TIME,
C HR, MN, REAL TIME, RH, RM, RS, AND FINALLY THE
C PEAK FIT K-ALPHA-1 PEAK AREA, PH(1,I), AND THE AREA
C ERROR, ER(I).
C
NF = 8
LH = 1.0
LM = 0.0
LS = 0.0
C
C DATA FROM XRF1JTJA.CNF; 1
C
D4(l) = 30.0
M5(l) = 6.0
Y5(l) = 87.0
HR(1) = 17.0
MN(1) = 37.0
RH(1) = 1.0
RM(i) = 14.0
RS(1) = 48.70
PH(1) = 3062432.0
ER(1) = 1980.0


199
6 JA(1),JA(2)
qr = ja(i)
JA(1) = SQRT(q7)
q7 = JA(2)
JA(2) = SqRT(q7)
c
C Input data specific to U or Th. PE Cross Sections at 150 keV
C and Ekab, and EC
C
DO 300 I = 1,2
READ(3,*) EKAB, PEI, PE2, EC
300 IF (ELEMENT .Eq. U ) GOTO 310
310 CL0SE(3,STATUS=,KEEP>)
C
C Determine Target and Detector Node Points
C
II = 0
DO 350 I = 1,CD
DO 350 J = 1,RD
II = II + 1
T = (2 PI / RD) (J .5)
XD(I1) = (DR / CD) (I .5) COS(T) + XDC
YD(I1) = (DR / CD) (I .5) SIN(T) + YDC
ZD(I1) = 0.0
350 AD(I1)=PI*((I*DR/CD)**2-((I-1)*DR/CD)**2)/RD
II = 0
DO 400 K = 1,VT
DO 400 I = 1,CT
DO 400 J = 1,RT
II = II + 1
T = (2 PI / RT) (J .5)
XT(I1) = (TR / CT) (I .5) COS (T) + XTC
YT(I1) = (TR / CT) (I .5) SIN (T) + YTC
ZT(I1) = ( TH / 2) + (TH / VT) (K .5) + ZTC
VOL(Il) = PI*(TH/ VT) ((I TR / CT)**2
1 ((I 1) TR / CT)**2) / RT
DO 375 L = 1,2
CALL DISTANCE (XS(L),YS(L),ZS(L),XT(I1),YT(I1),ZT(I1),
1 U(L,I1),V(L,I1),W(L,Ii),
2 R1T(L,I1),R2T(L,I1),K7)
IF (K7 .Eq. 10) GOTO 9000
375 CONTINUE
DO 385 L = 1,24
CALL DISTANCE (XD(L),YD(L),ZD(L),XT(I1),YT(I1),ZT(I1),
1 HLD1.HLD2.HLD3,
2 RID(L,II),R2D(L,I1),K7)
IF (K7 .Eq. 10) GOTO 9000
385 CONTINUE


15
with the advent of high resolution semiconductor detectors. A good overview of current
theory and of the variety of functions available to fit peaks and backgrounds is provided by
Prussin.^ As an introduction to the theory of peak shaping he states that:
As is well known, the shape of a photopeak from monoenergetic photons
in spectra taken with semiconductor detectors is closely approximated by
a Gaussian with more or less severe tailing below the centroid. The peak
is joined smoothly to a lower-energy continuum of small curvature until it
meets the relatively sharp Compton edge. This continuum, which is pro
duced mainly by the loss of some of the energy of photoelectrons from the
sensitive volume of the detector, leads to the appearance of a step-like dis
tribution upon which the main intensity is superimposed. Under conditions
of low input rate, short counting times with stable electronics and negligi
ble background at higher energies, the high-energy edge is indeed found to
be nearly Gaussian. The low energy edge begins to deviate from Gaussian
form at fractions of the peak maximum in the range of .5 to .01 depending
upon the detector type, its quality and its history. While Gaussian shape
results from statistical spread due to fluctuations in electron-hole pairs
produced in the stopping process and random noise from the amplifying
electronics, the low energy tailing represents pulse-lieight degradation from
a number of phenomena including charge trapping and recombination, en
ergy loss of primary and secondary electrons in the insensitive volume of
the detector or by bremsstralilung.
Figure 1 shows a typical spectral gamma peak and its component parts; the Gaussian
peak and step function background. Typically, peak fitting programs will fit the background
to some function, subtract the background from beneath the peak, and fit the remaining
data to some peak function. The following sections will discuss the peak and background
fitting functions used in this work.
A Fitting Peak
Peak shaping and peak area determination are commonly done by gamma spectroscopy
systems in an efficient manner. Such systems usually contain long computer programs to
locate all spectral peaks, to determine and subtract the baselines from beneath those peaks,
and to determine peak areas by summing of channel counts or by least squares fitting to a
Gaussian shape.


179
1286 LPRINT X(I) ',1 Y(I) ', FIT(I)
1288 LPRINT
1290 FOR I = 1 TO 27
1292 LPRINT X(I),Y(I),FIT(I)
1294 NEXT I
1299 GOTO 9000
1490 REM
1492 REM Subroutine to calculate the fraction of the Viogt Profile
1494 REM area which lies beyond XB +- 13 Channels
1496 REH
1500 Al(l) = .4613135
1505 1(2) = 9.999216E-02
1510 Al(3) = 2.883894E-03
1515 Bl(l) = .1901635
1520 Bl(2) = 1.7844927#
1525 Bl(3) = 5.5253437#
1530 DT = XB X(l)
1535 TH = SIG SQR (2)
1540 FOR I = 1 TO 3
1545 TI = ATN ((2 / GA) (DT + TH SQR (B1(I))))
1550 T2 = ATN ((2 / GA) (DT TH SQR (B1(I))))
1555 FR = FR + (1 / SqR (PI)) A1(I) (PI (TI + T2))
1560 NEXT I
1565 AREA = AREA / (1 FR)
1570 RETURN
1990 REH
1992 REH Subroutine to calculate Voigt Profile data points
1994 REH
2000 AL = 1 / (2 SIG ** 2)
2020 GH = GA / (SIG SqR (2))
2040 Cl = 1 GH / SOR (PI)
2060 C2 = GH / (2 PI)
2080 C3 = .25 GH ** 2
2100 C4 = 2 GH / PI
2120 CHI = (X(I) XB) / (SIG SqR (2))
2140 F4 = 0
2160 F5 = 0
2180 FOR T4 = 1 TO 100
2200 FI = (T4 ** 2) / 4
2220 F2 = (T4 CHI) (T4 ** 2) / 4
2240 F3 = (T4 CHI) + (T4 ** 2) / 4
2260 F9=(EXP(-F1))/(T4**2)-(EXP(F2))/(2*T4**2)-(EXP(-F3))/(2*T4**2)
2270 F4 = F4 + F9
2280 IF ABS (F4 F5) < = .001 ( ABS (F4)) GOTO 2380
2300 F5 = F4
2320 NEXT T4
2340 PRINT DID NOT CONVERGE IN LINE 2340
2360 GOTO 9000
2380 BX = ( EXP ( (CHI ** 2))) F4


275
C
C DATA FROM XRF8J33B1.CNF;1
D4(8)
=
27.0
M5(8)
=
5.0
Y5(8)
=
87.0
HR(8)
=
13.0
MN(8)
=
13.0
RH(8)
=
1.0
RM(8)
=
11.0
RS(8)
=
27.77
PH(8)
=
233651.0
ER(8)
=
1130.0
STORE DATA
ON DISK FILE
C
OPEN(1,FILE=PKFIL,STATUS=NEW1)
HRITE(1,5) NF
5 F0RMAT(1I2)
HRITECl.iO) LH, LH, LS
10 FORMAT(3F10.5)
DO 100 I = i,NF
WRITE(1,25) D4(I), M5(I), Y5(I)
25 F0RMAT(1F10.5, 112, 1F10.5)
WRITE(1,50) HR(I), MN(I)
50 FORMAT(2F10.5)
WRITE(1,75) RH(I), RM(I), RS(I)
75 F0RMAT(3F10.5)
HRITE(1,90) PH(I),ER(I)
90 F0RMAT(2F15.5)
100 CONTINUE
END


198
WRITE(6,*) Cl
HRITE(6,190)
190 F0RMAT(/,IX,Input the Soil Liniar Attenuation Coefficients
1 for 136 ft 122 keV,/,
2 IX,136 keV)
READ(1,*) US(1)
WRITE(6,*) US(1)
HRITE(6,195)
195 F0RHAT(/,IX,122 keV)
READ(1,*) US(2)
HRITE(6,*) US(2)
IF (ELEMENT .Eq. TH) GOTO 220
C
C Natural K-alphal emission rate, (Kal/sec)/(pCi U238),
C from ICRP Report #38.
C
KA1NAT = 8.584E-5
WRITE(6,200)
200 F0RMAT(/,IX,98.428 keV)
READ(1,*) US(3)
GOTO 250
C
C Natural K-alphal emission rate, (Kal/sec)/(pCi Th232),
C from ICRP Report #38.
C
220 KA1NAT = .001584
WRITE(6,230)
230 F0RMAT(/,IX,93.334 keV)
READ(1,*) US(3)
250 WRITE(6,*) US(3)
CLOSE(1,STATUS=KEEP)
WRITE(6,260)
260 F0RMAT(/,IX,Compton Data will now be read)
COMDTA = $2$DUA14:[LAZO.DISS.DATA]COMDTA.DAT
OPEN (3,FILE=COMDTA,STATUS='OLD)
C
C Input the energies of Co-57 gammas (MeV), Compton-to-Total
C ratios for Soil, CTRATIO(l), CTRATI0(2), TF and Atten data
C for Steal and Air at 136 ft 122 keV, TF(1),TF(2),UA(1),UA(2),
C Source Strength data, A0(1), A0(2), Gamma Yields, YI(1), YI(2),
C and Jar Transmission Fraction data, JA(1), JA(2).
C
READ(3,*) E(1),E(2)
1
2
3
4
5
CTRATIO(l),CTRATI0(2)
TF(1),TF(2),
UA(1),UA(2),
A0(1),A0(2),
YI(1),YI(2),


92
in the slope of this fitted line is easily calculated using linear least squares statistics. As is
shown in Tables 11 to 25 and evidenced by the very low X2 values for the fitted lines, the
data points lie very close to the fitted line and thus small errors in the fitted slope of the
line would be expected. This is seen in the small errors in the resulting answers shown in
Tables 9 and 10.
Table 9 also lists soil U and Th concentrations as calculated by Oak Ridge National
Laboratory using gamma spectroscopic techniques. The errors associated with these con
centrations are larger than those calculated by the technique developed here. This is due
to several factors. Gamma spectroscopy, as described in Chapter I, uses gamma rays from
several progeny of U and Th to determine the contamination concentrations in a given soil
sample. The theoretical relative peak areas of all gammas, assuming equilibrium in the
decay chain, are used in an algorithm to calculate the contamination concentration in the
target soil sample using measured peak areas. The peaks which are used each have associ
ated errors and the error in the calculated contamination concentration is derived from the
proper propagation of those peak errors. In the Table 9 data, the peak areas used for the
ORNL calculated U and Th concentrations were smaller, in general, than the peak areas
used for the XRF calculations. Thus the errors associated with the ORNL gamma peaks
were larger than those associated with the XRF peaks. The algorithm used by the ORNL
gamma spectroscopic analysis system then propagates those peak area errors to determine
the U and Th concentrations. Beginning with errors larger than those of the XRF tech
nique and propagating those errors correctly thus yields resulting errors in contamination
concentrations which are larger for the gamma spectroscopic analysis than for the XRF
analysis.


42
Ri = distance from the source to the point, (cm),
H (E) p0 = sample mass attenuation coefficient at
energy E, /t (E) (gm/cm2), times sample
density, p0 (gm/cm?) and
iZ2 = that portion of the total distance that
lies within the attenuating sample, (cm).
The photoelectric reaction rate (RX) at the point, due to the above excitation gamma
flux, can be described by
RX (E) = FL (E) x PE (E) xfx AD,
(3)
where
and:
RX (E) = photoelectric reaction rate at the point,
(reactions/a) / (pCi/gm of dry soil),
FL (E) = excitation gamma flux at a point in the
target, (gammas/cm2s) ,
PE (E) photoelectric cross section for U or Th at
energy E, (cm2/atom),
V = volume of the point source, (cm3),
AD = atom density of U or Th,
(atoms/cm3of soil) / (pCi/gm of dry soil),
= .037 (dis/s) / (pCi) X A X /)
.037 = the number of disintegrations per second
per pCi of activity,


60
Electron density
The electron density used above is a parameter which will vary from sample to sample
due to changes in density, elemental makeup, and water content. Electron density must
therefore be calculated for each sample. This is accomplished in a simple fashion using the
transmission measurement described earlier.
The total linear attenuation coefficient is made up of an absorption coefficient, a pair
production coefficient, a Compton scatter coefficient, and a coherent scatter coefficient.
A conversation with John Hubble of the National Bureau of Standards and a follow-up
computer study indicated that for various soils, the ratio of Compton scatter coefficient
to total linear attenuation coefficient is approximately constant for a given energy gamma.
Appendix A details the computer study done to verify this and to arrive at an appropriate
average Compton to total ratio. Knowing this ratio, the measured total linear attenuation
coefficient can be used to calculate the electron density as follows
Hccaic = CTR x fira
where
Hccalc = calculated Compton linear attenuation
coefficient as ratioed from the total
linear attenuation coefficient, (cm-1),
^rneo measured total linear attenuation
coefficient, (cm-1), measured as
described in a previous section,
CTR = ratio of Compton linear attenuation
coefficient to total linear attenuation
coefficient,


220
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
Photoelectric cross sections, in sq cm/atom, from
U data sent to me by Hubble, for energies .136476 MeV
and .122063 MeV.
DATA PE(3),PE(4) /1.2284E-21, 1.6102E-21/
Jump Ratio (Rk) used to calculate the fractional K-shell
vaceincies per photoelectric interaction.
KS = (Rk 1)/Rk, was calculated from U cross sections
sent to me by Hubble. The fractional K x ray yield, KY,
is from, The Table of Radioactive Isotopes, by
E. Browne and R. B. Firestone, 1986, LLNL.
DATA KS(2),KY(2) /.7693, .4640/
The elemental concentration per pCi/gm, EC,
(Atoms U/gm Soil)/(pCi U/gm Soil), was calculated
using a U-238 half life of 4.468E9 y from, The
Table of Radioactive Isotopes, by E. Browne and
R. B. Firestone.
DATA EC(2) /2.3752E16/
Data files filled with correct values
DTFILE = XRFDTA.DAT
OPEN(1,FILE=DTFILE,STATUS=NEW)
WRITE(1,*) E(i)
WRITE(1,*) UA(1)
WRITEd,*) UB(1)
WRITE(1,*) ETA(l)
WRITEd,*) JA(1)
WRITEd,*) PE(1)
WRITEd,*) PE(2)
WRITEd,*) KS(1)
WRITEd,*) KY(1)
WRITEd,*) EC(1)
WRITEd,*) E(2)
WRITEd,*) UA(2)
WRITEd,*) UB(2)
WRITEd,*) ETA(2)
WRITEd,*) JA(2)
WRITEd,*) PE(3)
WRITEd,*) PE(4)
WRITEd,*) KS(2)
WRITEd,*) KY(2)
WRITEd,*) EC(2)
CLOSE(1,STATUS=KEEP)
END


45
Considering that ten degrees is the upper bound for scatters which will still hit the detector,
this 3% error can be ignored.
As evidence of this, if small angle scatter were a significant contributor to the total peak
area, peaks would be broadened on the low energy side of their centroids and would not be
well described by the peak fitting equations shown earlier. Data in Chapter III shows that
the measured peaks are fit very well by the previously described peak fitting equations. As
such it is concluded that small angle scatter of x rays is not a significant problem and need
not be accounted for here.
Finally, the fluorescent signal (FS), the number of Kal x rays that are counted in the
full energy peak at energy E, due to the above flux at the detector, can be described by
FS (E') = FD (E') x DE (£') x CT,
where
FS (E1) = the number of counts in the full energy peak at
energy E', ie. peak area,
(Kai rays) / (pCi/gm of dry soil),
FD (E1) the flux of fluorescent x rays of energy E' that
hit the detector,
((Kai rays) /s) / (pCi/gm, of dry soil),
DE (E') = the detector intrinsic energy efficiency at
energy E',
(x rays counted) / (x ray hitting the detector),
and,
CT = total counting time, (s), corrected for pulse
pileup as described in a subsequent section.
This equation can also be written in the following more useful form


TABLE 14
Measured vs. Fitted Detector Response for
NJB-U
Fitting Equation :DR = GFxCC
Where : DR = Measured Detector Response
GF = Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 142.0 pCi/gm U23S
Reduced X2 Value for Fitted Data : 0.071
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
0.268
38.0
35.2
2
0.236
33.5
33.9
3
0.208
29.6
29.4
4
0.185
26.2
27.0
5
0.164
23.3
24.2
6
0.146
20.8
21.6
7
0.131
18.6
19.5
8
0.117
16.7
15.6


DATA FROM
XRF2J32B2. CNF; 1
D4(2)
=
27.0
H5(2)
=
5.0
Y5(2)
=
87.0
HR(2)
=
15.0
HN(2)
=
57.0
RH(2)
=
1.0
RM(2)
=
20.0
RS(2)
=
4.15
PH(2)
=
240028.0
ER(2)
=
2344.0
DATA FROM
XRF3J32B2.CNF;1
D4(3)
=:
27.0
M5(3)
=
5.0
Y5(3)
=
87.0
HR(3)
=
17.0
MN(3)
=
56.0
RH(3)
=
1.0
RM(3)
=
18.0
RS(3)
=
13.06
PH(3)
=
212015.0
ER(3)

2136.0
DATA FROM
XRF4.S2B2.CNF;1
D4(4)
=
27.0
M5(4)
=
5.0
Y5(4)
=
87.0
HR(4)
=
19.0
MN(4)
=
17.0
RH(4)
=
1.0
RM(4)
=
16.0
RS(4)
=
41.92
PH(4)
=
199047.0
ER(4)
=
1107.0


TABLE 21
Measured vs. Fitted Detector Response for
Thla
Fitting Equation : DR = GF X CC
Where : DR = Measured Detector Response
GF Calculated Geometry Factor
CC = Fitted Contamination Concentration
Calculated CC : 144.1 pCi/gm Th232
Reduced X2 Value for Fitted Data : 0.346
Position
GF
DR Fit
(cts/s/pCi/gm)
DR Measured
(cts/s/pCi/gm)
1
1.800
259.5
260.1
2
1.586
228.6
235.0
3
1.401
202.0
212.9
4
1.242
178.9
188.8
5
1.104
159.1
162.4
6
0.983
141.6
135.9
7
0.879
126.7
122.3
8
0.788
113.5
107.7


CHAPTER II
METHODS AND MATERIALS
This chapter describes the theoretical basis for the U and Th assay technique. The
theory is divided into three sections: peak shaping, soil moisture content and attenuation
properties, and system modeling. Following this theory are descriptions of the error analysis
and the experimental procedure used in this work.
Peak Shaping
In order to determine the physical properties physical measurements must be made. In
the case of this soil sample assay technique, the induced fluorescent x rays emitted by the
target are the physical quality measured. The measurement takes the form of an energy
spectrum. The number of x rays emitted by the sample is proportional to the concentration
of U and/or Th in the sample. The areas of the Kal x-ray peaks are the number of x
rays that hit the detector and are counted in the full energy peak. These areas, then, are
proportional to the concentrations of U and/or Th in the soil sample. The details of the
proportionality are discussed in subsequent sections. This section describes the method
used to determine peak areas.
The fitting of spectral data to mathematical functions is known as peak shaping or
peak fitting. As stated above, the motivation for fitting peaks is to accurately determine
the peak area which is proportional, in this case, to the concentration of U and/or Th in a
soil sample. The art of peak fitting has been steadily perfected over the years, particularly
14


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DETERMINATION OF RADIONUCLIDE CONCENTRATIONS
OF U AND Th IN UNPROCESSED SOIL SAMPLES
By
Edward Nicholas Lazo
December, 1988
Chairman: Genevieve S. Roessler
Major Department: Nuclear Engineering Sciences
Work with systems used to assay soil samples for U-238 and Th-232 indicated that the
need existed to more directly measure the concentrations of these radionuclides. An x-ray
fluorescent analysis system was developed here to directly measure the concentrations of
these radionuclides in bulk (125 gm), unprocessed (not dried and not ground to uniform
particle size), soil samples. Tliis technique improves on gamma spectroscopic analysis be
cause progeny equilibrium is not required, improves on neutron activation analysis because
bulk samples are assayed, and improves on both methods because standard soil samples are
not needed for system calibration.
The assay system developed equates a measured KaX x-ray peak area to a calculated
Geometry Factor (GF) times the unknown soil sample radionuclide concentration. From
this equation the radionuclide concentration is determined. Spectral data are generated
by irradiating the soil sample with Co-57 gammas to induce fluorescent x rays which are
measured using an intrinsic Ge detector. The Co-57 sources, the sample, and the detector
are oriented to optimize the production of fluorescent x rays. Transmission gamma rays
are then used to determine the sample linear attenuation coefficient at the KaX energy of
interest.
xv


c
c
c
c
c
c
$**$**$$**£$£******$***$*
* *
* IMAGE.FOR *
* *
Hi#******#******##***#**
INTEGER RT, CT, VT, RD, CD, IV(3), CO(2)
CHARACTER *2 EL
CHARACTER *10 SMPLE, CTO
CHARACTER *30 GFFILE, DTFILE, XRFFIL
CHARACTER *30 SPFILE(8), PDFILE(8)
CHARACTER *30 SFILE
DIMENSION US(3),E(4),FA(4),UA(4),UB(4)
DIMENSION ED(4),YI(2),A0(3),E0(4)
DIMENSION SP(192,4),P1(192,24),P2(192,24)
DIMENSION AD(24),V(21),V0L(192)
DIMENSION PE(2),XS(2),YS(2),ZS(2),RX(2),IT(4)
DIMENSION GF(12,192), GFT0TAL(8)
REAL JA(4), KS, KY
PI = 3.14159
q9 = 0.0
WRITE(6,25)
25 F0RMAT(/,1X,What sample is being counted ?)
READ(5,30) SMPLE
30 FORMAT(AIO)
WRITE(6,40)
40 F0RMAT(/,1X,In what file should the Geometry Factor,/,
1 IX,results be stored? (Ex: Dr:File.Ext))
READ(5,45) GFFILE
45 F0RMAT(A3O)
WRITE(6,50)
50 FORMAT(/,IX,In what file is the Sample data stored?)
READ(5,55) SFILE
55 FORMAT(A30)
OPEN(1,FILE=SFILE,STATUS=OLD)
C
C INPUT THE TARGET CONTAMINATION, U OR TH
C
READ(1,60) EL
60 F0RMAT(A2)
WRITE(6,60) EL
C
C INPUT THE SAMPLE DRY SOIL WEIGHT FRACTION
C
READ(1,*) WF
WRITE(6,*) WF
C
C INPUT THE SAMPLE DENSITY (GM/CC)


256
C
Q ftft ft ftftft ftftftft ft ftftft ftftftft ftftft
C *
C SAMPLENJBU.FOR *
C *
C i*********************
c
CHARACTER *3 ELEMENT
C
C This program creats a data file of input
C data pertaining to Sample NJB-U, a non-homogenous
C Th and U sample.
C
C
C Sample contaminant, ELEMENT
C
ELEMENT = U
C
C Soil Weight Fraction, WF
C
WF = 0.87653
C
C Sample Density, SD
C
SD = 1.06198
C
C Hubble Fit Parameters, Al, Bl, St Cl
C
Al = 1.07694
Bl = 1.19446
Cl =-1.36489
C
C
C Soil Liniar Attenuation Coefficients
C at 136 keV, 122 keV, and 98.4 keV
C
US1 = 0.25818
US2 = 0.30521
US3 = 0.34727


218
C
C ********************
c *
C XRFDTA.FOR *
C *
c ********************
c
CHARACTER *10 DTFILE
DIMENSION E(2),UA(2),UB(2),ETA(2),
1 PE(4),EC(2)
REAL JA(2),KS(2),KY(2)
C
C The following data is for U
C
C
C K-alpha-1 X-Ray energy (MeV) for U
C from Data Tables, by Kocher
C
DATA E(l) /.098428/
C
C Air mass attenuation coefficients, sq cm/gm,
C from, Photon Mass Attenuation and Energy
C Attenuation Coefficients from 1 keV to 20 MeV,
C by Hubble.
C
DATA UA(1) /.1550/
C
C Be transmission fractions as measured using a
C Be window similar to that actually used with
C the detector.
C
DATA UB(i) /.1314/
C
C Intrinsic detector efficiency as calculated by
C NBS.EFF and EFFICIENCY.
C
DATA ETA(l) /.84931/
C
C Transmission fraction for an average jar
C calculated using TRANSMISSION and REV.6 data.
C
DATA JA(1) /.96901/
C
C Photoelectric cross sections, in sq cm/atom, from
C U data sent to me by Hubble, for energies .136476 MeV
C and .122063 MeV.
C
DATA PE(1),PE(2) /1.2845E-21, 1.6B36E-21/