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## Material Information- Title:
- Determination of radionuclide concentratins of U and Th in unprocessed soil samples
- Creator:
- Lazo, Edward Nicholas
- Publisher:
- Edward Nicholas Lazo
- Publication Date:
- 1988
- Language:
- English
## Subjects- 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 )
## Record Information- Source Institution:
- 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.
- Resource Identifier:
- 001130251 ( alephbibnum )
20139548 ( oclc )
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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 |

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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/ \ ^ ((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 Tj7Â¡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 = Â£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) = FÂ¡(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) = 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, {cm2Â¡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(Â£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 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(Â£) 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) = 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 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_Â¡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 * Â£ $$$$$$$ $$$$$*$ $Â£Â£Â£Â£$$ 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 , 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(Â£!)), 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, 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 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 = Â£(*(*<),-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 'XT(I) ,BR(I) ,*SIG(I)* FOR I = 1 TO DP PRINT XT(I),F(I),SIG(I) NEXT I 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 977 980 FOR I = 1 TO M 985 PRINT VA$(I); = '>;VAR(I) 987 990 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 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 1165 PRINT S = ;S 1166 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'/ ((Â£ 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) = YÂ¡. 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 DRÂ¡ (E1) and GFÂ¡ {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<Â¡xÂ¡,(-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_Â¡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 Â¡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' (Â£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 cÂ¥ 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 Â£ $$$Â£$$$$$$$$$$$$$$$$$ 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 Tj7Â¡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'/ ((Â£ 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/ \ ^ ((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' (Â£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 cÂ¥ 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(Â£!)), 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<Â¡xÂ¡,(-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 (Â£') 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 DRÂ¡ (E1) and GFÂ¡ {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, 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 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 , 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 = Â£(*(*<),-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 = Â£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) = 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 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) = YÂ¡. 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) = 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) = FÂ¡(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 Â£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(Â£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(Â£) 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, {cm2Â¡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_Â¡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 Â¡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_Â¡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 Â¡gm of water) , pw water hulk density [gm of water/cm3 of sample), fi, = mass attenuation coefficient for soil at the energy of interest {cm2Â¡gm of soil), p, = soil bulk density {gm of soil Â¡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 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 'XT(I) ,BR(I) ,*SIG(I)* FOR I = 1 TO DP PRINT XT(I),F(I),SIG(I) NEXT I 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 977 980 FOR I = 1 TO M 985 PRINT VA$(I); = '>;VAR(I) 987 990 NEXT I 995 FOR I = 1 TO N 1000 SIG = VAR(l) 1005 XB = VAR(2) 1008 A = VAR(3) 1010 PRINT X;I; = ' ;X(I), Y;I; = ;Y(I) 1015 GOSUB 2000 1020 F(I) = F6 1025 PRINT X;I; = ;X(I), F* ;I; = ';F(I) 1030 1035 FOR 11 = 1 TO H 1040 DF(2) = 0 1045 FOR 12 = 1 TO M 1050 DS(I2) = 0 1055 NEXT 12 1060 DS(I1) = VAR(Il) .001 1065 SIG = VAR(l) + DS(1) 1070 XB = VAR(2) + DS(2) 1080 A = VAR(3) + DS(3) 1085 GOSUB 2000 1090 DF(1) = (F6 F(I)) / DS(I1) 1095 TE = DF(1) DF(2) 1100 IF ABS (TE) < = ABS (.001 DF(1)) GOTO 1120 1105 DS(I1) = DS(I1) .5 1110 DF(2) = DF(1) 1115 GOTO 1065 1120 A(I,I1) = DF(1) 1125 TA(I1,I) = DF(1) 1130 NEXT 11 1135 DY(I) = Y(I) F(I) 1140 S = S + (DY(I)) ** 2 1143 CHISQ = CHISq + ((DY(I)) ** 2) / (F(I) * (N M)) 1145 NEXT I 1150 IF S > SI THEN GOTO 1176 1151 IF ABS (S SI) < (S / 1000) THEN GOTO 1180 1152 SI = S 1153 ochisq = cHisq 1155 GOSUB 6500 1160 1165 PRINT S = ;S 1166 1167 PRINT CHISq = CHISq 1170 W1 = W1 + 1 1175 1176 1177 1178 1179 1180 1181 1182 1183 1185 1186 1187 1188 1190 1192 1194 1196 1198 1200 1205 1207 1210 1215 1219 1221 1223 1225 1230 1235 1240 1245 1247 1248 1249 1251 1252 1253 1254 1255 1256 1257 1259 1260 1265 1270 1272 1282 1284 GOTO 970 S = SI FOR I = 1 TO H VAR(I) = OLDVAR(I) NEXT I SIG = VAR(l) XB = VAR(2) A = VAR(3) CHisq = ocHisq AREA = 0 FOR I = 1 TO 27 X(I) = INT (XB) 13 + (I 1) FOR J = 1 TO NP IF X(I) = PK(1,J) THEN GOTO 1198 NEXT J Y(I) = 0 GOTO 1200 Y(I) = PK(2,J) GOSUB 2000 FIT(I) = F6 IF F6 < 0 THEN FIT(I) = 0 PRINT X(I),Y(I),FIT(I) AREA = AREA + FIT(I) NEXT I GOSUB 8000 GOSUB 1500 REM LPRINT This is a WHOLEPK.BAS run' LPRINT LPRINT The Peak Data was obtained from disk file ;FILE$ 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 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 $**$**$$**Â£$Â£******$***$* * * * 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 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 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 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 = 2.32 224 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 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 = 2.32 226 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 Â£ $$$Â£$$$$$$$$$$$$$$$$$ 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 * Â£ $$$$$$$ $$$$$*$ $Â£Â£Â£Â£$$ 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 Â£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 Â¡gm of water) , pw water hulk density [gm of water/cm3 of sample), fi, = mass attenuation coefficient for soil at the energy of interest {cm2Â¡gm of soil), p, = soil bulk density {gm of soil Â¡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 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 (Â£') 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 $**$**$$**Â£$Â£******$***$* * * * 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/ |