• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 General introduction
 Nuclear reaction studies
 Apparatus
 Experimental methods and resul...
 Energy loss studies
 Experimental procedure
 Results
 Discussion
 Reference
 Biographical sketch
 Copyright














Title: interaction of tritons with matter.
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Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
    List of Tables
        Page iv
    List of Figures
        Page v
        Page vi
    General introduction
        Page 1
    Nuclear reaction studies
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Apparatus
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
    Experimental methods and results
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
    Energy loss studies
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
    Experimental procedure
        Page 48
        Page 49
        Page 50
        Page 51
    Results
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
    Discussion
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
    Reference
        Page 89
        Page 90
        Page 91
        Page 92
    Biographical sketch
        Page 93
        Page 94
    Copyright
        Copyright
Full Text












THE INTERACTION OF TRITONS

WITH MATTER












By

WILLIAM NEWBERRY BISHOP


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










UNIVERSITY OF FLORIDA
June, 1961













ACKNOWLEDGEMENTS




I am grateful to Dr. Robert L. Wolke, Dr. Eugene Eichler,

and Dr. Noah R. Johnson for their direction of this work. I also

wish to thank Dr. H. H. Sisler for assuming the chairmanship of my

committee after Dr. Wolke left the University of Florida. I wish to

express my appreciation to various members of the Oak Ridge National

Laboratory staff for their assistance in this work, and especially to

Dr. G. D. OtKelley, who, although he was not officially on my committee,

cheerfully gave much helpful advice.

This research was supported by the Oak Ridge Graduate Fellow-

ship program of the Oak Ridge Institute of Nuclear Studies and was

carried out in the Chemistry Division of the Oak Ridge National

Laboratory.







-iii-


TABLE OF CONTENTS



Page

ACKNOWLEDGEMENTS------------------------------ ii

LIST OF TABLES--------------------------------------------- iv

LIST OF FIGURES-------------------------------------- v

GENERAL INTRODUCTION 1

PART I NUCLEAR REACTION STUDIES ----------------------- 2

Chapter

I. INTRODUCTION------------------------------------ 2

II. APPARATUS--------------------------------------- 11

III. EXPERIMENTAL METHODS AND RESULTS---------------- 28

PART II. ENERGY LOSS STUDIES-------------------------- 38

Chapter

I. INTRODUCTION---------------------------------- 38

II. EXPERIMENTAL PROCEDURE-------------------------- 48

III. RESULTS---------------------------------------- 52

IV. DISCUSSION-------------------------------------- 81

LIST OF REFERENCES----------------------------------------- 89






-iv-


LIST OF TABLES



Table Page

1 Mean Range of 2.736-Mev Tritons 53

2 Contributions to the Error in the Range of 54
2.756-Mev Tritons

5 Triton Ranges in Xenon 55

4 Triton Ranges in Krypton 56

5 Triton Ranges in Nickel 57

6 Triton Ranges in Argon 58

7 Triton Ranges in Aluminum 59

8 Triton Ranges in Air 60

9 Triton Ranges in Nitrogen 61

10 Triton Ranges in Polystyrene 62

11 Energy Loss of Tritons in Xenon 66

12 Energy Loss of Tritons in Krypton 67

15 Energy Loss of Tritons in Nickel 68

14 Energy Loss of Tritons in Argon 69

15 Energy Loss of Tritons in Aluminum 70

16 Energy Loss of Tritons in Air 71

17 Energy Loss of Tritons in Nitrogen 72

18 Energy Loss of Tritons in Polystyrene 75

19 Conversion Factors for Energy Loss 76

20 Values of Parameters in Empirical Equation 83

21 Values of Coefficient a when b = 1.50 in 84
Empirical Equation










LIST OF FIGURES


Figure Page

1 Typical Potential Barrier Shapes 4

2 Excitation Function for Bi209(dp)Bi211 and 7
Bi209(d,n)Po211

5 Detector and Source Geometry 10

4 Shielding at Experimental Facility 12

5 Experimental Chamber 15

6 Silicon Diode Barrier Equation Nomograph 19

7 Simplified Diagram of Fast Coincidence Circuit 22

8 Simplified Diagram of Slow Coincidence Circuit 25

9 Overall Diagram of Experimental Arrangement 26
Used in Reaction Studies

10 Ungated Triton and Alpha-Particle Spectrum 29
Using a Cesium Iodide Detector

11 Coincidence Spectra of Tritons and Alpha 30
Particles Using Cesium Iodide Detector

12 Ungated Triton and Alpha-Particle Spectrum 31
Using Gas Flow Counter

15 Ungated Triton and Alpha-Particle Spectrum 33
Using a Silicon Semiconductor Radiation
Detector

14 Coincidence Spectra of Tritons and Alpha 34
Particles Using Silicon Semiconductor
Radiation Detectors

15 Spectrum of Al27(tp)Al29 and Al27(t,)Al28
Reaction Products Using Silicon Semi-
Conductor Radiation Detectors







-vi-


LIST OF FIGURES (CONT'D)



Figure Page

16 Lindhard-Scharff Plot of Energy Loss 44

17 Range Curve for Tritons in Air 51

18 Triton Ranges in Xenon, Krypton, Nickel, 63
and Argon

19 Triton Ranges in Aluminum, Air, Nitrogen 64
and Polystyrene

20 Atomic Stopping Cross Section for Tritons 74
in Nickel, Aluminum, Air, and Poly-
styrene

21 Atomic Stopping Cross Section for Tritons in 75
Xenon, Krypton, Argon, and Nitrogen

22 Comparison of Energy Loss Results for Tritons 77
with Literature Values in Xenon and
Krypton

23 Comparison of Energy Loss Results for Tritons 78
with Literature Values in Argon and
Nitrogen

24 Comparison of Energy Loss Results for Tritons 79
with Literature Values in Air and Poly-
styrene

25 Comparison of Energy Loss Results for Tritons. 80
with Literature Values in Nickel and
Aluminum

26 Stopping Cross Section as a Function of the 85
Atomic Number of the Stopping Material
for Particles Having an Energy Equiva-
lent to a 1.5-Mev Triton

27 Stopping Cross Section as a Function of the 86
Atomic Number of the Stopping Material
for Particles Having an Energy Equiva-
lent to a 60-Mev Triton

28 Comparison of Experimental Results with 88
Empirical Relations







- 1 -


GENERAL INTRODUCTION







The interactions of charged particles with matter may be divided

into two categories, energy loss and nuclear reactions. When a. charged

particle passes through a substance, it loses energy primarily through

interactions with the atomic electrons of that substance, while the much

more rare and very short range interactions of the particles with the

nuclei of the atoms are classified as nuclear reactions.

These experiments investigate the interactions of tritons with

matter using tritons produced by the reaction Li + n -- He + H3.

Although these phenomena of energy loss and nuclear reactions are

related, they are more conveniently discussed separately. In Part I

the attempts to study nuclear reactions induced by the tritons are

discussed; from these experiments it was possible to set upper limits

on the reaction cross sections. The energy loss studies, discussed in

Part II, yield considerable information on the range and energy loss of

tritons in various substances.







-2 -


PART I

NUCLEAR REACTION STUDIES

CHAPTER I


INTRODUCTION



Nuclear reactions are in many ways similar to chemical reactions.

Chemical reactions, resulting from interactions between the electrons

of atoms, are characterized by relatively small energy changes, while

nuclear reactions, are accompanied by much greater energies. Nuclear

reactions may be either exoergic or endoergic as is the case with-

chemical reactions. For endoergic reactions energy must be supplied in

order for the reaction to occur.

An obstacle which must be overcome by an incident particle is the

potential barrier which is given by

ZZe 2
S ax h2( + 1) (1)
r 82 M r

where Z and Z are the charges of the particle and target nucleus
a x
e is the electronic charge, 4.8 x 10 esu

r is the distance between the centers of the particle and target
nucleus in cm

h is Planck's constant, 6.625 x 1027 erg-sec

M is the mass of the particle in g

I is the angular momentum quantum number for the system: projectile
plus target, about their center of mass

The first term represents the coulombic repulsion between the particle

and the nucleus, and the second term gives the centrifugal contribution







-3-


which is also repulsive. The centrifugal barrier results from the

angular momentum of non-central collisions. For central or "head-on"

collisions A = 0 and there is no centrifugal contribution. When the

particle penetrates to a distance of the order of a nuclear diameter,

very large, short-range attractive forces cancel the repulsive forces.

Figure 1 shows the shapes of some typical potential barriers.

Figure la illustrates the case for central collisions by neutrons where

there is neither a centrifugal nor coulomb barrier, while the barrier in

Fig. Ic, with only a centrifugal contribution, is applicable for non-

central collisions by neutrons. Charged particles experiencing head-on

collisions would encounter a barrier arising only from the coulombic

repulsion as shown in Fig. lb. The barrier illustrated in Fig. Id has

contributions from both coulombic and centrifugal forces and represents

the obstacle for a charged particle undergoing non-central collisions

with a nucleus. The centrifugal force is of lesser magnitude and of shorter

range than the coulombic force.

The fact that the energy of an incident particle is less than the

barrier height does not preclude the possibility of penetration of the

barrier and the initiation of a nuclear reaction. The probability of

barrier penetration increases for increasing particle energies.

The probability of a nuclear process is usually represented by a

cross-section a, which is analagous to the rate constant of a second

order chemical reaction. The cross section is defined by the equation


N = I nx










UNCLASSIFIED
ORNL-LR DWG. 57656




U U

0----- 0---- ----------------



r r
(a) (b)





U U

0 ----I- o



r r
(c) (d)

Fig. 1. Typical Potential Barrier Shapes.
(a) Coulomb Barrier = 0 ; Centrifugal Barrier=O.
Za Zx e2
(b) Coulomb Barrier = Z ; Centrifugal

Barrier = 0.

(c) Coulomb Barrier = 0 ; Centrifugal Barrier =
.h2.1 (1+1)
8 72r2 z2 Z 2
zo zx e
(d) Coulomb Barrier = r ; Centrifugal
rh2 1(-+4)
Barrier h
8r2M/r2


- 4 -






-5-


where N is the number of reactions

I is the number of incident particles

n is the number of target atoms/cm5

x is the target thickness in cm
2
a is the cross section in cm

The cross section is usually expressed in barns (1024 cm ) or

millibarns (10-27 cm2).

The cross section of a nuclear reaction varies greatly with the

kinetic energy of the bombarding particle. A plot of the cross section

as a function of particle energy is called an "excitation function,"

and numerous experiments have been performed to determine the excitation

functions of nuclear reactions. Of the various mechanisms which have

been proposed to explain these data, two principal models are in current

use: compound nucleus formation and direct interaction. To better

understand these mechanisms the nuclear reaction X(a,b)Y is written

a + X --4 --- Y + b (3)

where a is the bombarding particle

X is the target nucleus

Y and b are the products

C is an activated intermediate

When the lifetime of C is long compared to the time necessary for the
-22
particle to traverse a nuclear diameter ( 1022 sec.), the mechanism is

termed the "compound nucleus" process, with C the compound nucleus. If
-22
the reaction is complete in the order of 102 sec, the process is called

"direct interaction."






-6-


The compound nucleus process, first postulated by Bohr (1) and

later extended by Weisskopf and many others (2), proceeds in two

distinct phases. First, the energy of the incident particle is rapidly

distributed among the nucleons comprising the compound nucleus. The

second step, decay of the compound nucleus, is independent of the mode

of formation, and may take place by the emission of one or more nucleons,

the emission of gamma rays, or by fission. As a particle leaving the

nucleus encounters a potential barrier, neutron emission is expected to

be favored over proton emission at low energies.

In the direct interaction process the particle enters the nucleus,

collides with a nucleon usually near the nuclear surface, and transmits

a large fraction of its kinetic energy to that nucleon, which then

escapes from the nucleus. Thus the reaction is complete with little

excitation of the residual nucleus.

A special type of direct interaction is encountered when deuterons

are used as the bombarding particle. Much higher cross sections are found

for (d,p) reactions than would be expected for energies below that of

the potential barrier. This effect is illustrated in Fig. 2 which shows

the excitation functions of (d,p) and (d,n) reactions on Bi209 as found

by Segre and Kelly (3).

Oppenheimer and Phillips (4) first advanced an explanation for these

phenomena based on the structure of the deuteron. The deuteron is a

relatively large and loosely bound particle having a binding energy of

only 2.2 Mev. When a deuteron nears a nucleus the coulombic repulsion






- 7-


UNCLASSIFIED
ORNL-LR-DWG. 57657


6 8 10 12 14 16 48
E (Mev)
d


Fig. 2. Excitation
Bi209(d,n) Po21. (3)


Function for Bi209(d,p) Bi211 and


120


400



80


60


40


20



0






-8-


orients the deuteron with the neutron closest to the nucleus. This

allows the neutron to interact with the target nucleus without the

proton having to completely penetrate the barrier, and because of

the low binding energy, the neutron can be stripped off easily.

For low energy particles this mechanism is called the Oppenheimer-

Phillips process. The general term for this type of interaction is

"stripping." It is also possible for the deuteron to enter the nucleus

leading to a more conventional compound nucleus formation or direct

interaction. The converse of stripping in which for example, a proton

picks up a neutron from a nucleus to become a deuteron is called a

"pick-up" reaction.

The unique behavior of the deuteron led to speculation on the

possibility that the triton possessed similar properties. Numerous

reactions of the (t,p) type, corresponding to the capture of two

neutrons, have been noted at energies below the potential barrier; for

example, Cu (tp)u67 Rh10(t,p)Rh105, and AlOg (t,p)Ag11 (5).

To determine whether (t,p) reactions proceeded in a manner similar to

(d,p) reactions, efforts were made in this work to measure the relative

cross sections of (t,p) and (t,d) reactions in various substances.

At the time this work was started the only quantitative data on

(t,p) and (t,d) reactions were for reactions on N (6) and Li (7). The

paucity of studies using tritons was mainly due to the lack of accelerators

for tritons. Experimenters strongly object to using tritons in an

accelerator which is also used for other particles because of the contami-

nation of the accelerator with tritium. When experiments using tritons






-9-


are followed by those using deuterons, 14 Mev neutrons produced from

the high cross section H3(d,n)He4 reaction are a hazard to both the

experiment and experimenter. Accordingly attempts were made to investi-

gate triton reactions using the Li (n,a)H3 reaction as a source of tritons.

The measurement of some (t,p) and (t,d) cross sections was to be accomplished

by placing a detector on each side of a Li foil which is being bombarded

by a beam of thermal neutrons. (See Fig. 5.) Detector 1 is set to count

only the alpha particles. If a (t,p) or (t,d) target is placed in front

of detector 2, the resultant protons or deuterons can be counted by this

detector. Since the alphas and tritons from the Li (n,a) reaction are

produced in coincidence and 1800 apart, the protons or deuterons seen

by detector 2 will be in coincidence with alpha particles in detector 1.

If the geometry is properly arranged, the number of alpha counts in

detector 1 gives the number of tritons incident on the target and an

absolute (t,p) or (t,d) cross section can, in principle, be obtained.





- 10 -


UNCLASSIFIED
ORNL-LR-DWG. 57658


NEUTRON
BEAM


DETECTOR 2


\
\\b/


a-


-LI6


DETECTOR 1


Fig. 3. Detector and Source Geometry.
Event a Both Particles are Detected.
Event b Only One of the Particles is Detected.


- ~,-v--






- 11 -


CHAPTER II


APPARATUS

Triton Source


A collimated neutron beam from facility HB-1 of the Low Intensity

Test Reactor was used to produce the tritons. A diagram of the shielding

and collimator is shown in Fig. 4. The insert, an eight-foot length of

concrete with a tapered bore, served as a rough collimator. By filling

this tube with water the beam was shut off at the end of an experiment.

For further collimation the neutrons passed through the one inch diameter

hole in 2 two-foot "W plugs," which are fabricated from alternating

layers of two inch thicknesses of iron and micarta. The neutrons passed

through the experimental chamber and then down a 30-foot evacuated pipe

and were stopped in a mass of borated paraffin.

The high level of background radiation due to scattering from the

beam and streaming around the insert in the reactor shield requires

extensive shielding for both experimental and biological reasons. Blocks

of an iron oxide-paraffin mixture were used to absorb the scattered neutrons.

The large movable concrete shield and lead bricks attenuated the gamma

rays to a safe level. After preliminary experiments a boron liner with

a 1/8-inch wall thickness was inserted in the hole through the second

W-plug in an attempt to reduce the number of gamma rays produced by

neutron capture in the W-plug. Subsequent experiments proved this

unnecessary as the primary source of the gamma rays was the reactor core.








UNCLASSIFIED
ORNL-LR-DWG. 57659


Fig. 4. Shielding at Experimental Facility.

^I BORON-PARAFFIN, LEAD, E CONCRETE Fe304 PARAFFIN, M[- COLLIMATOR.






- 13 -


The location and intensity of the neutron beam was determined by

foil activation. Two sets of gold foils were activated, one bare and

the other shielded by 40 mils of cadmium to remove the neutrons below

0.5 ev in energy. The activity induced in the unshielded foils showed
8 2
a total neutron flux of 1 x 10 neutrons/cm /sec, and the activity

induced in the shielded foils indicated that only 20 per cent of the

neutrons had energies above 0.5 ev.

The lithium source foil was prepared by evaporating either lithium

or lithium fluoride (enriched to 99.3 percent Li ) onto 50- Ag/cm formvar

films supported by aluminum rings. As the chemical reactivity of lithium

made its use in the metallic form impractical, the lithium metal was

allowed to oxidize after evaporation. Different thicknesses of the

evaporated layer were used varying from 100-500 Pg/cm2. The area of the

foils was chosen to be the same as the area of the detectors with which

they were used, for reasons which will be discussed later. To prepare

foils of 1-1/4-inch diameter the lithium metal evaporations were used.

Wnen small area foils were required, it was found that the thick layers

of oxidized lithium flaked badly. Consequently lithium fluoride was used

to prepare the small area foils.

The LiO(n,a)H3 reaction has a tnermal-neutron cross section of

930 barns. Above the thermal region the cross section decreases mono-

tonically with increasing neutron energy until a resonance of 20 barns

is reached at 255 key (8). Above this resonance peak the cross section

again decreases with increasing neutron energy. Except for the region






- 14 -


of the resonance peak, the variation in the cross section is inversely

proportional to the change in neutron velocity. A typical triton flux

obtained was 5 x 104 tritons/cm2/sec at a distance of 1 cm from a.

500-pg/cm2 Li foil 0.25 cm in area.

For thermal neutrons the reaction is exoergic by 4.788 Mev giving a

triton energy of 2.756 Mev and an alpha particle of 2.052 Mev (9). As

thermal neutrons contribute essentially zero momentum, the triton and

alpha particle are correlated at 1800 in the breakup of the compound

nucleus.

Due to this angular correlation the useful area of a source foil is

no larger than the area of the detectors with which it is used. This is

illustrated in Fig. 5 where the detectors are of the same sensitive area

and are alined equidistant from the source. The pair of particles

indicated by "a" in Fig. 5 will each be detected, but in the event

marked "b," only one particle can be detected.

Experimental Chamber

The detectors and source foil were situated in an evacuated chamber.

The chamber used with the surface barrier detectors is shown in Fig. 5.

The distance between the detector holders marked A and B and the source

holder C may be varied. Holder A can be moved without opening the

chamber. The source holder has provision for two sources and either can

be used without opening the chamber. Electrical connections were made

through kovar seals D. The neutron windows E were made from 4 mil aluminum

foil.






- 15 -


Fig. 5. Experimental Chamber.

A,B-Detector Holders
C Source Foil Holder
D- Kovar Seals
E- Aluminum Window






- 16 -


The materials used as targets were aluminum, boron, and carbon

(in the form of polystyrene.) Two thicknesses of aluminum targets

were used, 1.7 mg/cm2 and 10.4 mg/cm The polystyrene and boron

targets were 15.5 mg/cm2. The aluminum and polystyrene targets were

prepared by punching discs slightly larger than the detector size from

commercial sheet foils. A boron target was prepared by making a slurry

of amorphous boron in a solution of polystyrene in benzene. After

evaporation of the solvent, a fairly durable foil of approximately

50 percent boron resulted. The targets were placed in the slot in

detector holder A.

Detectors

In the course of the experiments, several types of detectors

were tried in attempts to reduce background interference. The detectors

are discussed below in the order in which they were tried.

Cesium Iodide

Two thallium activated cesium iodide scintillation crystals, 5 mils

thick and 1-1/4 inch in diameter, cemented to 1/4 inch thick lucite discs

were obtained from Harshaw Chemical Company. These detectors were optically

coupled through lucite light pipes to Dumont 6292 photomultiplier tubes.

Cesium iodide has been shown to have a linear response to protons of

energies greater than 0.9 Mev with an energy intercept near zero. In the

region of linear response the relative light output for particles of the

same energy is protons 1.0, deuterons 0.9 and alpha particles 0.6 (10).

From the relative response to protons and deuterons, it is estimated that






- 17 -


the relative light output for protons and tritons of the same energy

would be 1.0:0.8.

Gas Flow Proportional Counter

A cylindrical proportional counter of 1-1/4-inch diameter was

constructed. A circular loop of 1/4-inch diameter was fashioned from

1-mil stainless steel wire to form the central electrode. Aluminized

mylar of 1 mg/cm2 thickness served as the window and methane at atmos-

pheric pressure was the counting gas.

Silicon Surface Barrier Semiconductor Radiation Detectors

Semiconductor radiation detectors may be correctly called solid

state ionization chambers. When ionizing radiation passes through the

detectors, electron-hole pairs are formed analogous to the electron-ion

pairs formed in a gas-filled ionization chamber. A space charge or

depletion layer is established by applying a reverse bias across the

diode. Electron-hole pairs formed within the depletion layer are collected

at the electrodes. The depth of the depletion layer X in microns is given

by

X = (1.33 x 1015 V p p e)1/2 (4)

where V is the total potential drop across the depletion region in

question in volts

p is the resistivity of the silicon in ohm-cm

p is the mobility of the majority carriers in cm2/volt-sec

e is the electronic charge, 1.6 x 109 could






- 18 -


A nomograph shown in Fig. 6 (11) enables one to solve the equation

graphically and determine the maximum particle energy for which the

detector response is linear. For example, for 3600 ohm-cm, n-type

silicon with 45 volts reverse bias the depletion layer is 200 microns,

corresponding to the range of a 5-Mev proton.

An undesirable property of semiconductor radiation detectors is

the leakage current, randomly fluctuating in magnitude, which causes

low pulse-height noise and poor resolution. As this current increases

with increasing surface area, the fabrication of large area detectors

with good resolution is very difficult. At the time of these experiments
2
good detectors of area greater than 1 cm were not available.

These devices have several advantages over the gas counters which

were previously used for precise charged particle spectroscopy. Since

the average energy required to produce an electron-hole pair in silicon

is only 3.5 ev compared to 30-35 ev for an ionization event in a gas

counter, a greater number of ionization events occur, decreasing the

statistical fluctuation and improving the inherent resolution. The

mobility of the hole is approximately one-half that of the electron while

the mobility of the ion in a gas counter is orders of magnitude lower than

that of an electron. The high mobility and short distance between electrodes

gives a very fast response.

Various workers (12) have shown that for particles ranging from

electrons to fission fragments the response of the detectors varies

linearly with energy if the entire energy of the particle is deposited

within the depletion layer. In the linear region the response is the same







- 19 -


UNCLASSIFIED
ORNL-LR-DWG 45902B


BARRIER
DEPTH
X
406 METERS


RANGE-
ENERGY (Mev)

PROTON
1 mm)OOO-
2-- 900-
41- 800-
40-- 700
600-
9--
500-
8--
400-
7-
300-
6--

5- ----200-


4-
4-OO
100 -
90-
80-
ALPHA 70-
40 60 -
-50-
2- 8 40-
7 -
6- 30-:
-T-J
5-


4 -


3- 40-


CAPACITANCE
C/cm2
40-12 f


IMPURITY
CONCENTRATION
N/cm3


-10




-20


-30




-60
-70
-80
-90
- 100




- 200


-300

-400

-500
-600
-700
-800
--900
4-000


412
40


400-

300-


200

450


00-
90-
80-
70-
60-
50-

40-

30-


X = V.-. 4.326 x 405, C/A= 4.064 x 404, i P

PN=4200 cm2/volt-sec, pp= 450 cm2/volt sec


Fig. 6. Silicon Diode Barrier Equation Nomograph.


VOLTAGE
APPLIED
(v)


3-

4-

5-
6-
7-
8-
9-
x4013 -


1.5-

2-


3-

4-

5-
6-


20-

15-


40-
9-
8-
7-
6-
5-

4-

3-


RESIS
N TYPE
PN


o0,000
-9000
-8000
-7000
-6000
-5000

-4000

-3000


-2000

--4500


-1000
-900
-800
-700
-600
-500

400

-300


-200

--450


- 00


'IVITY
P TYPE
Pp


- 40,000

-30,000


- 20,000

-45,000


10,000
-9000
-8000
-7000
-6000
-5000

-4000

-3000


-2000

-4500


-4000
-900
-800
-700
-600
-500

400

-300


I






- 20 -


for all particles of the same energy. As gamma rays deposit very little

energy in a thin layer of silicon they do not contribute greatly to

the background.

There are two kinds of silicon semiconductor radiation detectors

in current use. The surface barrier detector is fabricated by treating

the surface of n-type silicon to produce a p-type inversion layer

containing a high density of electron traps. The diffused-junction

detector is made by diffusing some electron donor such as phosphorus

into p-type silicon giving a thin region of n-silicon.

The detectors used in these experiments were the surface-barrier

type fabricated by J. L. Blankenship and C. E. Ryan of the Instrumenta-

tion and Control Division of Oak Ridge National Laboratory.

Amplifiers and Preamplifiers

The linear amplifiers used in these experiments were ORNL Type A-l,

slightly modified to obtain a lower noise level (13). The amplitude of

the positive output pulse, which may be from 0 to 100 volts, is proportional

to the input pulse height: hence the term "linear" amplifier. A second

output is the "PHS" pulse, which is a. negative spike of about 25 volts

amplitude across a 1000 ohm load, having a very fast rise time.

The low-noise, high-gain preamplifiers were designed by Edward

Fairstein of Oak Ridge National Laboratory for use with semiconductor

radiation detectors. The high gain is necessary because of the low

signal levels from these detectors.

Coincidence Circuit

The coincidence system was designed by Harris and Kelley of the






- 21 -


Oak Ridge National Laboratory. A simplified diagram of the coinci-

dence circuit used is shown in Fig. 7. The PHS pulse from each

amplifier is fed to a fast coincidence unit. A time delay, Z1, is

inserted in one channel to compensate for timing differences in the

circuitry of each amplifier and preamplifier. The PHS pulse passes

through a coupling diode to the grid of a limiter tube. The pulse

shuts off the normally conducting tube, causing a very rapid rise in

plate voltage and giving a very nearly square pulse. The shorted

delay line Z2, by reflection, clips this pulse of 4 volts to a width

of 10 sec, and if a pulse from each tube arrives within this time,

they add to a height of 8 volts. The pickoff bias is set so that

only pulses slightly greater than 4 volts will be passed, corresponding

to a coincidence event. These pulses are shaped by the univibrator
-7
to a square shape of 4 volts and 5 x 10 sec wide.

The time interval mentioned above is referred to as T and the

circuit is said to have a resolving time of 27. The reason for using

2T is that if a given pulse arrives any time within the interval T

before a second pulse until the interval T after the second pulse they

will add. The resolving time of the circuit used was 2 x 107.

The fast coincidence output signal and the output of the signal

channel analyzer are supplied to the slow coincidence circuit shown

in Fig. 8. Both diodes, D1 and D2, are normally conducting. When a

positive signal arrives at the cathode of one of the diodes, the diode

is cut off. If only one diode is cut off, point A remains at some low

positive voltage due to the conduction of the other diode. When a











UNCLASSIFIED
ORNL-LR-DWG. 57825


PHS SIGNAL
FROM
AMPLIFIER 4








PHS SIGNAL Z,
FROM r-I
AMPLIFIER 2 --T


LEVEL


PICK OFF
DIODE


J.-- FAST
COINCIDENCE
OUTPUT


Fig. 7. Simplified Diagram of Fast Coincidence Circuit.









UNCLASSIFIED
ORNL-LR-DWG. 57826


OUTPUT
FROM FAST T-L
COINCIDENCE
UNIT


OUTPUT
FROM
SINGLE -
CHANNEL
ANALYZER


COINCIDENCE
GATE
-0
OUTPUT


Fig. 8. Simplified Diagram of Slow Coincidence Circuit.






- 24 -


signal is supplied to the cathode of each diode, both are shut off,

the voltage at point A rises rapidly and diode D-3 begins to conduct,

supplying a signal to the output univibrator. The pulse is shaped and

an output coincidence gate signal is generated.

Multichannel Analyzer

A multichannel pulse-height analyzer enables one to determine

the height distribution of a series of voltage pulses arriving at a

rapid rate. Various multichannel analyzers capable of a high degree

of amplitude resolution have been developed. The Oak Ridge type used

in these experiments will be described briefly.

In this analyzer design a. biased, nonoverloading window amplifier

expands a selected portion of the spectrum, which is then analyzed by

a series of 20 voltage discriminators. Successive portions of the

pulse-height distribution are analyzed by shifting the bias at the

input of the expander. This analyzer requires that the discriminators

give no output to the scaler units until after the peak of a pulse.

This is achieved by a pulse stretcher circuit placed after the expander,

which lengthens the pulse and generates an inspector pulse at a fixed

time after the beginning of a. signal. The inspector pulse causes the

highest of the discriminators which was triggered by the signal to send

an output pulse to its scaling unit. A simple anticoincidence arrange-

ment suppresses the lower discriminators.

Two multichannel analyzers were used in these experiments. The

ungated spectra were displayed on an analyzer manufactured by El Dorado






- 25 -


Electronics. An Oak Ridge twenty-channel analyzer designed by Bell,

Kelley and Goss of Oak Ridge National Laboratory was used to record

the coincidence spectra.

General

An overall diagram of the experimental arrangement is shown in

Fig. 9. The signal from detector 2 was fed through a preamplifier

and a linear amplifier to the signal input of two multichannel analyzers.

The alpha-particle signal from the detector 1 went through a preamplifier

and amplifier to a single channel analyzer whose window was set to accept

pulses corresponding to the energy of the alpha particles.

The PHS signals from each amplifier went to the fast coincidence

unit. The output of the fast coincidence circuit and the output of

the single channel analyzer were supplied to the slow coincidence unit,

and the coincidence signal from this circuit was fed to the gate input

of one of the multichannel analyzers. This analyzer recorded events

only when a gate signal was supplied by the coincidence system, while the

other analyzer recorded all of the pulses it received.

The spectra taken on the coincidence analyzer from detector 2 were

due to tritons when no target was used and to the reaction products when

a target was in place. The ungated analyzer was used to measure the

singles spectrum in order to calculate the number of random coincidence

events. These random coincidences occur when the detectors respond to

events which arrive within the resolving time of the coincidence unit






- 26 -


UNCLASSIFIED
ORNL-LR-DWG. 57660


NEUTRON
BEAM


Fig.9. Overall Diagram of Experimental
Arrangement Used in Reaction Studies.






- 27 -


but are not time-correlated. The expected number of random coincidences

may be calculated by the relation


Nr = N1N2(2T) (5)

where N is the number of random coincidences
r
N1 and N2 are the number of events recorded by detectors one and

two respectively

2T is the resolving time of the coincidence circuit

The probability of a pulse being observed in a random coincidence with

a given gate signal from the detector 2 is just proportional to the

counting rate at that pulse height, thus the random coincidence spectrum

has the same shape as the ungated spectrum.






- 28 -


CHAPTER III

EXPERIMENTAL METHODS AND RESULTS

To begin an experiment the water was blown out of the rough

collimator with helium, allowing the neutron beam to fall on the Li6

foil. The spectra were recorded using the techniques previously

described. The ungated spectrum taken without a target in place, is

shown in Fig. 10 and illustrates the response of cesium iodide to the

tritons and alpha particles. The gamma-ray background from the reactor

completely obscures the alpha-particle peak. The effect of coincidence

techniques is illustrated by the spectra shown in Fig. 11, where the

single-channel window was set to accept the tritons for the alpha-

particle spectrum and to accept the alpha particles for the triton

spectrum.

Due to the high background it was decided to use thick targets to

maximize the counting rate of the reaction products. With an aluminum

target of 10.4 mg/cm2 in place the spectrum showed a much higher counting

rate than was expected for the reaction products. A spectrum recorded

with the lithium source foil removed, proved to be identical to the

spectrum with the lithium foil present. This indicated that both spectra

were due to random background coincidences and prompted the use of

another detector.

The results obtained with the proportional counter were somewhat

worse than those with cesium iodide as illustrated by the ungated triton

and alpha-particle spectrum in Fig. 12. Here the triton peak is little





- 29-


UNCLASSIFIED
ORNL-LR-DWG. 57661


EXPECTED
POSITION
OF
ALPHA-PARTICLE
PEAK
t


TRITON
PEAK

t


4021 I I I I I I
PULSE HEIGHT, arbitrary units
Fig. 10. Ungated Triton and Alpha-Particle Spectrum
Using a Cesium Iodide Detector.


104






- 30 -


UNCLASSIFIED
ORNL-LR-DWG.57662


PULSE HEIGHT, arbitrary units
Fig. 11. Coincidence Spectra of Tritons and Alpha-
Particles Using Cesium Iodide Detector.
o Single Channel Window Set to Contain Alpha Particles.
A Single Channel Window Set to Contain Tritons.


402















UNCLASSIFIED
ORNL-LR-DWG. 57663


40 31 I I I I I I
PULSE HEIGHT, arbitrary units

Fig. 12. Ungated Triton and Alpha-Particle Spectrum
Using Gas Flow Counter.


.J
I-
D




0

I-
z
3
0











more than a shoulder on the background spectrum. As the triton and

alpha-particle peaks were even more swamped by the background than

with cesium iodide, the next attempts were with the semiconductor

radiation detectors.

The ungated spectrum of tritons and alpha particles shown in

Fig. 13 indicates the superior performance of the surface barrier

detectors. The use of coincidence techniques reduces background effects

to a negligible contribution as shown in Fig. 14 where the single channel

window was set to accept alpha particles for the triton spectrum and

to accept tritons for tne alpna particle spectrum.

Due to the small angle subtended by these detectors the counting

rates were much lower than with other types of detectors. To increase

the counting rate lithium fluoride foils of the maximum usable thickness

were prepared, and the detectors were moved as close to the source foil

as practicable. The limitation on the thickness of lithium fluoride

was set by the range of the alpha particle. It was decided that 0.5 mg/cm

was the optimum thickness to give the maximum number of tritons without

degrading the alpha-particle energy to a point where coincidence techniques

could not be applied. It was found that at distances less than 1 cm from

the source foil the background counting rate increased greatly as the

detector was then in the beam of neutrons and gamma rays. This increase

in background was proportionate to the increase in the triton counting

rate.

Attempts were made to investigate the (t,p) and (t,d) reactions on


- 32 -






- 33 -


UNCLASSIFIED
ORNL-LR-DWG. 57664


PULSE HEIGHT, arbitrary units
Fig. 13. Ungated Triton and Alpha-Particle Spectrum
Using a Silicon Semiconductor Radiation Detector.






- 34 -


UNCLASSIFIED
ORNL-LR- DWG. 57665


S- a

It
z

U-1
i

a_






100
(n
I-
z






40-











PULSE HEIGHT, arbitrary units

Fig.14. Coincidence Spectra of Tritons and Alpha
Particles Using Silicon Semiconductor Radiation Detectors.
o Single Channel Window Set to Contain Alpha
Particles.
A Single Channel Window Set to Contain Tritons.






- 35 -


aluminum, boron and carbon using the semiconductor detectors. When

a 1.7 mg/cm2 aluminum target was used, the spectrum showed peaks at

2.4 and 4.8 Mev and a shoulder at 7.2 Mev. The 2.4-Mev peak was the

most prominent, with the 4.8-Mev peak a factor of 10 lower, and the

7.2-Mev shoulder reduced by another factor of 10 The peak at 2.4

Mev was attributed to the tritons penetrating the target, because

1.7-mg/cm2 aluminum target would degrade their energy to that figure.

As the 4.8-Mev peak was approximately three orders of magnitude higher

than would be expected for the reaction products, and from the ratio

of the energies of the peaks, it was thought that the 4.8-Mev peak

might be due to two tritons being detected within the resolving time

of the electronics. Using a resolving time equal to the width of the

amplifier pulse the counting rate of random sum pulses was calculated

using Eq. 5. Not only did the calculated result for the sum of two

events agree with the observed spectra, but the shoulder at 7.2 Mev

was shown to be due to the sum of three triton pulses. As few reaction

products were expected to have energies greater than 7.2 Mev, thick

targets were used.

The spectrum obtained from a 10.4 mg/cm2 aluminum target is shown

in Fig. 15. The solid line corresponds to the measured coincidence

spectrum while the circles give the counting rate calculated for random

coincidences with background pulses. The results indicate that the

spectrum can be entirely accounted for by random events. It is there-

fore obvious that the (t,p) and (t,d) reactions which were being sought






- 36 -


UNCLASSIFIED
ORNL-LR-DWG.57827


PULSE HEIGHT, arbitrary units
Fig. 15. Spectrum of A127( f,p) A129 and A127(t ,d) Al28
Reaction Products Using Silicon Semiconductor Radiation
Detectors. Smooth Curve Is the Observed Coincidence
Spectrum. Circles Indicate the Calculated Random Coinci-
dence Spectrum.


401






- 37 -


must occur with too small a probability to be observed above the

random coincidence background, at least in runs of reasonably

short duration.

Recently, several papers reporting differential cross sections

for triton-induced reactions have appeared in the literature (14).

By using particle accelerators with special tritium-handling equip-

ment, these investigators were able to overcome many of the problems

encountered in using the Li (n,a) reaction. Using these recent

reported differential cross sections and the ratio of total cross

section to differential cross section for (d,p) reactions, one can

calculate the proton counting rates to be expected in the geometry

of the present experiment. Such a calculation shows that in order

to reduce the statistical error of the counting rate to a point where

the reaction products could be noticed above random background, the

experiment would require at least ten days of continuous operation.

Since the reliability of the equipment would cast doubt on any results

obtained from an experiment of this duration, further work was not

attempted.

From the experimental data it was possible, however, to set an

upper limit of 500 mb for the (t,p) cross section on B, C, and Al.

The maximum expected cross section for these reactions estimated from

the differential cross sections of Ref. 14, was 100 mb.

Although no quantitative results were obtained from the reaction

studies, the experience in charged particle spectroscopy in the presence

of a high neutron and gamma ray environment was most helpful in carrying

out the energy loss experiments described in Part II.






- 38 -


PART II


ENERGY LOSS STUDIES

CHAPTER I


INTRODUCTION



The probability that a charged particle passing through a

substance will experience interactions resulting in the loss of kinetic

energy is much greater than the probability that it will initiate a

nuclear reaction; thus the measurement of energy loss of charged particles

is of interest not only as a means of studying that phenomenon but also

to determine energy corrections for nuclear reaction experiments. The

need for reliable experimental data is greatest for particles having

energies less than a few mev. In this energy region the literature

values are often in poor agreement, and a detailed theoretical treatment

is difficult.

The four types of interaction by which a charged particle may lose

kinetic energy are: (1) inelastic collisions with atomic electrons, (2)

inelastic collisions with nuclei, (3) elastic collisions with atomic

electrons and (4) elastic collisions with nuclei. Inelastic collisions

with electrons result in one or more electrons experiencing a transition

to an excitated state or to an unbound state. Particles undergoing

inelastic collisions with nuclei are deflected from their path

with a resultant loss of energy. In some of these deflections a quantum







- 39 -


of electromagnetic radiation is emitted. The energy lost through

an elastic collision between a particle and a nucleus is just that

necessary for the conservation of momentum. The energy transferred

to an atomic electron through an elastic collision is insufficient to

raise the electron to an excited state; again momentum and energy are

conserved.

This discussion will be confined to the energy loss of swiftly

moving, heavy charged particles such as protons, deuterons and alpha

particles. The adjective, heavy, indicates that the mass of the

particle is much greater than the rest mass of the electron, and by

swiftly moving, it is meant that the particle velocity is much greater

than the velocities associated with thermal motion. The predominant

mechanism by which these particles lose energy is inelastic collisions

with atomic electrons.

While the physical processes involved in the loss of energy by

charged particles have been understood for some time, a detailed

theoretical treatment is complicated by the mathematical difficulties

encountered in an accurate collision theory.

In order to develop a mathematical relation several simplifying

assumptions are made. The region through which the particle passes is

considered to be made of many isolated atoms. The contribution of a

single particle-atom collision is calculated and then summed over all of

the atoms. This approximation is appropriate for particles of the






- 40 -


velocities which this paper considers. A difficulty with this approach

in any region of particle velocity is that this sum is an average value,

as the collisions do not lead to one discrete final state but to many

states which must be described by some kind of probability function.

A complicating process is the pick up of orbital electrons by the

particles. Correcting for this electron pick up is rendered more

difficult by the possibility that the particle may later be stripped

of that electron.

Bethe (15) has derived the following expression for the average

energy loss of a particle

4r z e Z 2mv
E 2 I (6)
my
The atomic stopping cross section e is expressed in units of 10-15 ev-cm

and is defined by


e = (-dE/dx) (7)

where N is the number of atoms of the stopping medium per cm3

-dE/dx is the energy loss in ev/cm

z is the particle charge

e is the electronic charge, 4.8 x 10 esu

Z is the atomic number of the stopping material
-28
m is the electron rest mass, 9.11 x 10 gm

v is the particle velocity in cm/sec

I is the mean excitation potential of the stopping material in

ev and may be expressed as

1 Zfi Ii (8)
i






- 41 -


where fi is the contribution of the i th electron to the stopping power

Ii is its ionization potential

Bloch (16) found that the mean ionization potential may be expressed

as

I = KZ (9)

where K is a constant having a value of 10-15 ev for all stopping

materials.

The validity of the expression derived by Bethe depends on two

conditions: (1) the particle must have its full charge or the particle

velocity must be much greater than the velocity of its orbital electrons

which has been expressed by Williams (17) as


v >> 2> z e2/h

and (2) the velocity of the particle must be great compared to

velocity of the most energetic electron of the stopping medium


(10)

the

or


E > > M- I (11)
p m e

where E is the kinetic energy of the particle

M is the particle mass

m is the rest mass of the electron

Ie is the ionization potential of the most tightly bound electron of

the stopping medium

The second of these conditions is the more restrictive as it

necessitates a higher particle energy in order to be fulfilled. The

physical manifestation of this restriction is that the more tightly






- 42 -


bound electrons of the stopping material cease to contribute to the

stopping, as the particle velocity becomes comparable to the velocity

of these electrons. This is reflected as a gradual change in the

mean ionization potential. In order to compensate for the effect due to

K electrons, Bethe and others (18), from theoretical considerations,

evaluated a term CK, and Eq. 6 becomes

2 4 2
47 z e Z 2mv
E z 2 (in CK) (12)
my I
Using the same approach Walske (19) derived the values for CL to

correct for the effect of L electrons.

The application of this technique to the other electron shells

becomes very cumbersome and tedious. Bichsel (20), through an empirical

approach, has developed a method of evaluating these correction terms,

but the calculations are extremely time consuming unless done by a

computer.

Other workers have taken a different approach to the calculation

of energy loss at low energies. In a qualitative manner Bohr (21) has

derived an expression which shows the energy loss to be inversely

proportional to the particle velocity and directly proportional to the

cube root of the atomic number of the stopping material. This relation

gives values of energy loss which show the same velocity dependence as

the experimental data, but the quantitative agreement between the

calculated and experimental values is poor. This is not surprising due

to the qualitative approach of the derivation.






- 43 -


From dimentional considerations based on the Fermi-Thomas atomic

model, Lindhard and Scharff (22) advance a general function which is

applicable at all energies. Their argument that the quantity e v2/Z

is a function only of v2/Z. Thus Lindhard and Scharff write

2 4
47z e(1
E = 2 ZL( ) (15)
m v


where v = v2/Z v2 (14)


with vo = 2 e2/h (15)

2
The factor vo is introduced to make and thus L a dimensionless quantity.

It is apparent that the value of is a measure of how well Eq. 11

(which stipulates that the particle velocity be great compared to the

most energetic electron velocity of the stopping material) is fulfilled.

When t > > 1, this condition is satisfied and the Bethe equation should

apply. Thus for large values of t, L(t) --> In t, giving an
EE
expression essentially the same as the Bethe equation. If -- is
Z
plotted against In E/Z all points corresponding to large values of 5
2 4
should lie on a. straight line whose slope is z e with an
m4m
intercept of In -- Figure 16 illustrates this behavior where the

data is plotted in terms of triton energy. The solid line corresponds

to a value of K = I/Z = 13 ev. The data of Burkig and MacKenzie (25)

give the energy loss of 20-Mev protons (corresponding to 60-Mev tritons;

this comparison will be discussed below) in various substances. The

results of Brolley and Ribe (24) are for 4.4-Mev protons. The energy






- 44 -


UNCLASSIFIED
ORNL- LR-DWG.57824


0.01 0.1 4.0
E, /Z


Fig. 46.
Ribe (24) o


Lindhard- Scharff Plot of Energy Loss. + Brolley and
Burkig and Mackenzie (23) Green et a.(25).


eEf
Z






- 45 -


loss of protons below 1.0 Mev determined by Green, Cooper and Harris (25)

deviate from the straight line as is expected as the restriction of

Eq. 11 is not satisfied.

In this low energy region Lindhard and Scharff state that L -- 1/2

From an empirical fit to experimental data these authors found that L =

1.36t1/2 0.0163/2. More recent experiments have shown that some of

the data used in the evaluation of L were 10-15 percent low. These later

results would not alter the velocity dependence, but only change the

values of the constants.

In all of the expressions for energy loss given above, the stopping

cross section for a given absorber is a function of only the charge and

velocity of the particle. It follows that the relative energy loss of

two different particles having the same velocity is given by the ratio

of their relative charges

z m
E(E) = -1 (--E) (16)

where e1 and e2 are the stopping cross sections of particle 1 and 2

respectively

z1 and z2 are their charges

mi and m2 are their masses.

The only restriction on this conversion is that the particles be completely

stripped of their electrons, which is the condition represented by Eq. 10.

This relationship is verified by the experimental data.

From the Bloch relation (Eq. 9) and the theory of Lindhard and Scharff











(Eq. 13), the energy loss of a particle is expected to be a smooth

function of the atomic number of the stopping material, and to a first

approximation this is true. This aspect will be discussed in greater

detail in Chapter IV. The stopping cross section for compounds is

obtained by adding the atomic stopping cross sections of its constituent

atoms. This ignores the effect of chemical binding on the ionization

potential, but Thompson (26) has shown that the binding contributes less

than 1 percent to the stopping power.

The mean range, or average distance which a particle will travel

before it is stopped may be found from the stopping cross section by


R(E) = --" -- E (17)
0
if e(E) is known throughout the span of integration. As the energy loss

is not known at very low energies some known range is used as a lower

limit



E
R(E) = 0(Eo) + I/Nj -dE (18)


The range of one particle in a substance may be calculated from

that of another particle in the same substance if the particles have

the same nuclear charge; for example, protons, deuterons, and tritons.

From Eq. 16 it follows that

R1(E) = (2 E) (19)
m2 M1


- 46 -






- 47 -


The conversion of data for particles of different nuclear charges does

not follow a simple rule, due to the differences in electron pick up by

the particles. This effect does not lend itself to theoretical treat-

ment and is usually compensated for by an empirical constant or



R(--- E) = Rt(E) + C (20)

Accurate calculation of the range of a particle in one element from its

range in another element is precluded for reasons which will be discussed

in Chapter IV.

In the region where the condition given by Eq. 11 (that the particle

velocity must be greater than the electron velocities in the stopping

material) is not fulfilled, the energy loss of a particle cannot be

evaluated from theoretical considerations and must be determined

experimentally. In some cases, no experimental results have been

obtained, and even in the cases where data exists, frequently either

the results are unsubstantiated or multiple determinations show poor

agreement. As particles having the same charge and velocity lose energy

at the same rate, and as tritons have the greatest energy for a given

velocity of the hydrogen-type particles, triton energy loss can be

measured with the greatest accuracy. In these experiments the ranges

and energy loss of tritons are measured in various substances.







- 48 -


CHAPTER II

EXPERIMENTAL PROCEDURE


Apparatus


The experimental facilities used in the energy loss studies were

essentially the same as those previously described for the reaction

studies. The vacuum chamber mentioned in Part I was used to house

the detectors, source foil and absorbers. The triton pulse-height

spectrum was recorded for each thickness of absorber through which

the particles had passed. The coincidence techniques discussed in

Part I were used to reduce background and scattering effects. The

mean range of the tritons was determined by counting the coincidence

pulses as a function of absorber thickness. From these data, range-

energy and energy loss values were obtained.

Absorbers

The solid absorbers were prepared by accurately punching one inch

diameter discs from commercial sheet foils. These discs were weighed

to determine the surface density. The thickness of the gaseous absorbers

was varied by changing the gas pressure, and was calculated from the

pressure, temperature and the distance between the source and detector.

Detectors

Silicon surface barrier detectors of 16 mm sensitive area. were

used for particle detection. The triton detector was placed 6.8 cm

from the source. The alpha particle detector was also situated 6.8 cm






- 49 -


from the source for measurements with the solid absorbers. Due to the

very short range of these alpha particles, the detector for these

particles was moved to a distance of 0.5 cm from the source foil in

the experiments using gases since the gas filled the entire chamber.

Triton Source

The source of tritons was the same as discussed in Part I. The

source foil was a 100-pg/cm2 layer of LiF covering an area of 25 mm .

Electronics

The electronics system was very similar to that shown in Fig. 9,

the difference being that only the Oak Ridge type multichannel analyzer

was used.

Experimental Method

The triton spectra, which were recorded for each absorber thick-

ness, showed a gaussian-shaped peak. The mean position of the peak

was determined by fitting the spectrum with standard shapes of the
244
appropriate width. The 5.80-Mev alpha particles of Cm2 and the

undegraded tritons and alpha particles from the Li (n,a)H3 reaction

were used for energy calibration. In order to check the linearity of

the detector and ancillary equipment, the energy of the Cm244 alpha

particles was degraded by air and the pulse height spectrum was

recorded for various gas pressures. The range-energy curves of

Bethe (27) were used to determine the alpha-particle energy for each

gas pressure. The resulting plot of energy vs pulse height was linear






- 50 -


with a zero energy intercept. The range in air of the Cm244 alpha

particles was found to be 4.42 cm which compares favorably with the

value of 4.40 from the curve of Bethe.

The mean range of the tritons was determined by counting the

gate pulses due to coincidences between the tritons and alpha particles,

at each absorber thickness. The range curve for air is shown in

Fig. 17. The half point of the counting rate is taken as the mean

range. To find the range of tritons of lower energy, one subtracts

the thickness of absorber necessary to degrade the tritons to the

desired energy from the range of the undegraded tritons


R(E) = R(2.7) A(E). (21)

In this manner range-energy tables were constructed.

The energy loss is the ratio of the differences in the energy and

range of two points, or


E2 1-E AE/AR dE/dx. (22)
R2- R1


This energy loss corresponds to the average energy of the interval

(E2 El), provided this interval is a small fraction of the particle

energy.








UNCLASSIFIED
ORNL-LR- DWG. 57823


2500




2000



en

_i
0
a

z 1000
UL
0
Z
O5
o 500


5.0 5.5


6.0 6.5 7.0 7.5 8.0
EQUIVALENT THICKNESS OF AIR (mg/cm2)

Fig. 17. Range Curve for Tritons in Air.


8.5


9.0






- 52 -


CHAPTER III

RESULTS


The mean ranges of 2.756-Mev tritons in xenon, krypton, nickel,

argon, aluminum, air, nitrogen and polystyrene are given in Table 1

along with associated error. The factors which contribute to this

error and their approximate contributions are listed in Table 2,

and the total error is the square root of the sum of the squares of

these contributions. The only experimental triton range reported in

the literature is for air and the results of B ggild and Minnhagen (28),

7.56 0.07 mg/cm2, and of Cooper, Crocker, and Walker (29), 7.32 + 0.06

mg/cm2, are in excellent agreement with the present work.

The range-energy data are shown in Tables 5-10, Fig. 18 and

Fig. 19. The estimated error of these points increases from approxi-

mately .one percent at 2.7 Mev to three percent for the lowest energies.

The only additional contribution to these errors is the determination

of the energy of the emergent tritons (- 5 Kev). The behavior of these

curves at low energy (below 0.5 Mev) is due to the fact that the particles

spend part of the time in an uncharged state and consequently the rate

of energy loss is lower.

In an attempt to determine the degree of non-uniformity of the

foils, duplicate sets of absorbers were prepared for aluminum. The

variation in the energy of the degraded tritons after passing through

different sets of absorbers of the same thickness was approximately

twice the estimated error in the measurement of the energy.






- 53 -


TABLE 1



MEAN RANGE OF 2.756-MEV TRITONS


Substance

Xenon

Krypton

Nickel

Argon

Aluminum

Air

Nitrogen

Polystyrene


Range

20.56 0.20

17.85 0.18

15.15 + 0.15

11.40 0.09

10.10 0.10

7.54 t. 0.06

7.26 + 0.06

6.12 + 0.10






- 54 -


TABLE 2


CONTRIBUTIONS TO THE ERROR IN THE RANGE OF 2.736-MEV TRITONS


Factor

Determination of Half Point of Counting Rate

Energy Loss in Source Foil

Energy Loss in Gold Layer on Detector

Non-Uniformity of Foils

Distance Between Source and Detector
*5*
Gas Pressure

Gas Temperature

Absorber Purity

Total Error Solid Absorbers
Gaseous Absorbers


Approximate Percentage Error

0.75

0.05

0.01

0.60

0.50

0.05

0.01

0.01

1%
0.8Wo


*Solid Absorbers Only
* Gaseous Absorbers Only






- 55 -


TABLE 5


TRITON RANGES IN XENON


Range (mg/cm2)

20.36

19.97

18.57

17.51

16.58

15.50

14.51

13.13

12.22

11.44

10.46

9.592

8.821

7.961

6.946

5.992

5.448

4.766

4.072

3.340

2.619

1.759

1.010


Energy (Mev)

2.756

2.700

2.552

2.460

2.348

2.260

2.149

1.996

1.900

1.802

1.689

1.574

1.476

1.364

1.216

1.078

0.998

0.888

0.775

0.659

0.525

0.341

0.165






- 56 -


TABLE 4


TRITON RANGES IN KRYPTON


Range (mg/cm2)


Energy (Mev)


17.83

17.47

15.79

14.50

15.64

12.49

11.48

10.35

9.514

8.130

6.993

6.107

5.344

4.230

5.425

2.774

2.152

1.399

.710


2.756

2.700

2.509

2.328

2.255

2.120

1.989

1.843

1.717

1.548

1.383

1.254

1.156

0.942

0.810

0.679

0.542

0.543

0.146






- 57 -


TABLE 5



TRITON RANGES IN NICKEL


Energy (Mev)


2.756

2.700

2.670

2.640

2.555

2.480

2.468

2.55

2.500

2.285

2.210

2.180

2.097

2.020

1.960

1.910


Range (mg/cm )


9.01

8.71

7.92

7.72

6.60

5.61

5.52

5.96

2.42

0.92

0.75


Energy (Mev)


1.858

1.791

1.660

1.642

1.430

1.240

1.188

0.917

0.590

0.190

0.150


15.15

14.89

14.66

14.40

13.82

13.24

15.14

12.28

12.07

11.82

11.39

11.18

10.67

10.20

9.76

9.45






- 58 -


TABLE 6



TRITON RANGES IN ARGON


e (mg/cm 2)

1.400

1.180

0.960

0.669

0.338

9.807

9.418

9.051

8.582

8.127

7.711

7.303

6.904

6.432

5.867

5.478


Energy (Mev)

2.756

2.700

2.662

2.619

2.566

2.471

2.413

2.354

2.265

2.197

2.120

2.044

1.973

1.880

1.776

1.690


Range (mg/cm 2)

5.040

4.580

4.127

3.686

3.300

3.063

2.749

2.360

2.053

1.888

1.715

1.568

1.421

1.152

0.859

0.646


Energy (Mev)

1.606

1.511

1.402

1.298

1.216

1.150

1.069

0.961

0.876

0.815

0.753

0.708

0.645

0.524

0.396

0.288






- 59 -


TABLE 7




TRITON RANGES IN ALUMINUM


e (mg/cm )

10.10

9.70

8.28

7.98

7.70

7.37

7.16

6.62

6.17

5.70

5.21

4.72

4.20

5.78

5.24

2.74


Range (mg/cm2)

2.21

1.69

1.57

1.18

1.04

0. 6

0.80

0.75

0.69

0.59

0.47

0.58


Energy (Mev)

0.866

0.680

0.568

0.492

0.433

0.548

0.321

0.510

0.286

0.240

0.186

0.154


Energy (Mev)

2.756

2.666

2.580

2.518

2.255

2.189

2.142

2.024

1.922

1.818

1.699

1.578

1.445

1.326

1.178

1.033






- 60 -


TABLE 8



TRITON RANGES IN AIR


2
e (mg/cm )

7.344

7.209

7.156

6.986

6.511

6.255

6.223

5.655

5.192

4.902

4.824

4.776

4.536

4.111

4.042

3.555


Energy (Mev)

2.756

2.700

2.685

2.646

2.550

2.475

2.459

2.519

2.200

2.126

2.100

2.090

2.025

1.900

1.892

1.672


Range (mg/cm )

3.232

3.000

2.679

2.479

2.344

1.827

1.716

1.447

1.570

1.555

1.201

0.998

0.794

0.587

0.508

0.579


Energy (Mev)

1.652

1.571

1.450

1.380

1.550

1.116

1.065

0.927

0.890

0.865

0.800

0.679

0.540

0.380

0.352

0.231






- 61 -


TABLE 9



TRITON RANGES IN NITROGEN


age (mg/cm2)


Energy (Mev)


7.257

7.141

6.857

6.380

6.124

5.791

5.624

5.470

5.315

5.245

5.061

4.736

4.221

4.072

4.007

3.599


2.736

2.700

2.634

2.514

2.449

2.361

2.321

2.279

2.236

2.219

2.171

2.080

1.930

1.900

1.862

1.750


Range (mg/cm2)



3.104

2.790

2.458

1.962

1.587

1.183

0.823

0.592

0.345


Energy (Mev)



1.588

1.480

1.360

1.172

1.000

0.796

0.573

0.406

0.224






- 62 -


TABLE 10




TRITON RANGES IN POLYSTYRENE


Range (mg/cm 2

6.120

5.996

5.752

4.928

3.861

3.384

2.783

2.269

1.985

1.526

0.649

0.243


Energy (Mev)

2.736

2.700

2.630

2.390

2.038

1.867

1.638

1.419

1.278

0.941

0.504

0.195







UNCLASSIFIED
ORNL-LR-DWG. 55054A
22 II I I

20-

18-

16-

E 14-


XENON KRYPTON NICKEL ARGON 0o

o 10-
z
n" 8 -


1 2 0 1 2 0 1 2 0 1 2
TRITON ENERGY (Mev)
Fig. 18. Triton Ranges in Xenon, Krypton, Nickel, and Argon.






UNCLASSIFIED
ORNL-LR-DWG. 55055A


TRITON ENERGY (Mev)
Triton Ranges in Aluminum, Air, Nitrogen, and Polystyrene.


Fig. 19.






- 65 -


The ranges of protons below 250 key in energy, measured in

nitrogen, argon and air by Cook, Jones and Jorgensen (30) are in

agreement with the triton data. The triton ranges in aluminum agree

with the proton results of Bichsel (31: and the deuteron data of

Wilcox (32), but are not in agreement with the proton ranges of

Parkinson, Herb, Bellamy and Hudson (33).

The measured values of the stopping cross section of the various

substances are shown in Tables 11-18, Fig. 20 and Fig. 21. Table 19
-1 2
lists the factors used to convert the energy loss from kev-mg -cm to
-14 2
10 ev-cm The error estimate of the data is approximately 5

percent; no additional sources of error contribute to this value.

The present experiments are the first extensive measurements of the

energy loss of tritons, the only published report is by Phillips (37)

for tritons below 80 key in hydrogen.

Two excellent sources of information on the energy loss of charged

particles are a review article by Whaling (34) and a bibliography of

range and energy loss data by Brown and 4armie (35).

Figures 22, 23, 24, and 25 show the data from the present experiments

and the literature values for other particles (converted to the equivalent

triton energy) in the substances. The smooth curves are drawn through

the triton points. The only serious discrepancies are for polystyrene

where one of the triton points falls below the values of Lorentz and

Zimmerman (40), and for nickel below 1.5 Mev where the triton data fall

between the proton results of Bader (41) and Osetinskii (42).






- 66 -


TABLE 11




ENERGY LOSS OF TRITONS IN XENON



E (Mev) E (10-15 ev-cm2)

2.718 20.1

2.580 20.7

2.404 21.6

2.304 21.8

2.020 23.7

1.745 25.1

1.525 27.7

1.420 28.5

1.183 51.6

0.943 35.1

0.830 36.2

0.594 40.6

0.433 46.7

0.265 51.2

0.082 35.5












TABLE 12


ENERGY LOSS OF TRITONS IN KRYPTON


E (10-15 ev-cm2)


15.0

15.5

16.4

16.85

17.9

19.0

20.0

22.6

24.0

27.9

30.5

55.6

36.5

39.6

28.5


E (Mev)


2.718

2.605

2.380

2.120

1.921

1.665

1.465

1.195

1.039

0.745

0.610

0.468

0.442

0.248

0.073


- 67 -






- 68 -


TABLE 13



ENERGY LOSS OF TRITONS IN NICKEL


E (10-15 ev-cm2)


15.2

15.4

14.2

14.9

15.6

16.1

16.2

16.7

17.0

17.6

18.6

19.5

20.8

22.7

25.0

25.4

24.4

19.5


E (Mev)


2.704

2.557

2.317

2.076

1.92

1.755

1.725

1.585

1.545

1.410

1.225

1.030

0.824

0.585

0.450

0.350

0.170

0.060






- 69 -


TABLE 14



ENERGY LOSS OF TRITONS IN ARGON



E (Mev) e (10"15 ev-cm2)

2.680 10.6

2.440 11.26

2.200 11.77

2.082 12.28

1.962 12.56

1.785 13.23

1.504 14.7

1.350 15.7

1.110 17.1

0.911 19.9

0.761 22.5

0.670 23.9

0.460 29.0

0.270 33.4

0.072 26.6






- 70 -


TABLE 15




ENERGY LOSS OF TRITONS IN ALUMINUM




E (Mev) (10-15 ev-cm2)

2.698 8.50

2.520 8.80

2.352 9.20

2.249 9.60

2.150 9.7

1.924 10.1

1.761 10.9

1.640 11.0

1.508 11.6

1.253 12.3

1.105 13.0

0.952 14.0

0.700 15.9

0.531 17.2

0.528 18.2

0.451 17.9

0.255 20.3

0.145 19.8

0.050 16.3






- 71 -


TABLE 16



ENERGY LOSS OF TRITONS IN AIR


E (10-15 ev-cm )


5.95

5.97

6.14

6.49

6.54

7.24

7.50

8.15

9.40

11.1

12.2

13.6

17.5

18.1

17.4

13.2


E (Mev)


2.678

2.635

2.490

2.260

2.150

1.995

1.785

1.560

1.275

0.995

0.845

0.690

0.305

0.280

0.180

0.067






- 72 -


TABLE 17




ENERGY LOSS OF TRITONS IN NITROGEN


S(10-15 ev-cm2)


5.74

5.88

6.10

6.29

6.56

7.04

7.60

8.21

8.84

10.1

11.8

15.4

17.0

17.4

16.8

15.6


E (Mev)


2.686

2.585

2.298

2.158

1.998

1.855

1.670

1.474

1.266

1.010

0.898

0.685

0.405

0.515

0.165

0.050






- 73 -


TABLE 18



ENERGY LOSS OF TRITONS IN POLYSTYRENE



(10-15 ev-cm2/C H8)


50.2

49.7

57.0

61.9

65.8

73.7

80.4

88.9

111.5

147.6

158.6


E (Mev)

2.718

2.665

2.214

1.952

1.752

1.529

1.348

1.110

0.722

0.502

0.098







UNCLASSIFIED
ORNL-LR-DWG. 55056A


I I I I I


I II I I I


I I


z
0



0 -
on

0
(DE
2 >
-a
CL
0O -




Io
0


NUM


POLYSTYRENE N
(10-14ev-cm2/CH8 )


I I I I I I


I I I I I I I


4.0


5.0


TRITON ENERGY ( Mev)

Fig. 20. Atomic Stopping Cross Section for Tritons in Nickel,
Aluminum, Air, and Polystyrene.


50


5 h


ICKEL


,I II


0.05


0.1


I I I I I I .,..


1 I I







UNCLASSIFIED
ORNL-LR-DWG. 55057A
- -- .____


_ I I I I


I I I I I I I I


I I I -


XENON


z
0

0
L)

co

0 C

-In

O-
0L
0


I-


I I I I I I11


I I


5.0


TRITON ENERGY (Mev)

Fig. 24. Atomic Stopping Cross Section for Tritons in Xenon,
Krypton, Argon, and Nitrogen.


10C


5h


0.05


" "


I I I


I I I I


10


1






- 76 -


TABLE 19


CONVERSION FACTORS FOR ENERGY LOSS

(1015 ev-cm ) = Factor x (kev mgl -cm2)


Substance


Xenon

Krypton

Nickel

Argon

Air

Nitrogen

Polystyrene (e for C8H8)

Polystyrene (e for CH)


Factor


0.218

0.159

0.0971

0.0663

0.0240

0.0255

0.175

0.0216








UNCLASSIFIED
ORNL-LR-DWG. 57819


o0
0o


50-


40h-


301-


201-


40L
0


0.5


I I I I I


2.0


2.5


1.5
E, (Mev)


Fig. 22. Comparison of Energy Loss Results for Tritons with
Literature Values in Xenon and Krypton. Present Work o Dunbar
et al (Protons) (36), Phillips (Protons) (37) o Chilton (Protons)
(38).


3.0







UNCLASSIFIED
ORNL-LR-DWG. 5782


300-


e 20-


ARGON


10o-


NITROGEN
NITROGEN


0.5


1.5
(Mev)


2.0


2.5


3.0


Fig. 23. Comparison of Energy Loss Results for Tritons with
Literature Values in Argon and Nitrogen. Present Work, o Dunbar
etal (Protons) (36) A Phillips (Protons)(37), a Weyl (Protons) (39),e
Chilton (Protons) (38).







UNCLASSIFIED
ORNL-LR-DWG. 57822


AA
-A
A -e.


POLYSTYRENE





AIR
AIR


1.5
Et (Mev)


Fig. 24.
Values in Air


Comparison of Energy Loss
and Polystyrene. Present


Results for Tritons with Literature
Work, o Weyl (39) (Protons),


a Dunbar et al (37)(Protons), a Lorents and Zimmerman (40) (Protons).


30


20-


40-


-4


I

E
20

20









0
0




o


U-
'-
W


0.5


2.0


2.5


3.0


I







UNCLASSIFIED
ORNL-LR-DWG. 57820


1.5
Ef (Mev)


Fig. 25. Comparison of Energy Loss Results for Tritons with
Literature Values in Nickel and Aluminum. Present Work, o Bader
(Protons) (41) a Osetinskii (Protons) (42), o Gobelli (Alpha
Particles) (43) Chilton (Protons) (38), x Kahn (Protons)(44),
Warshaw ( Protons) (45), + Wilcox (32)( Protons and Deuterons).


CN 20
E



0
_10
w


3.0






- 81 -


CHAPTER IV


DISCUSSION



The velocity of the 2.736-Mev tritons did not fulfill the condition

that the particle velocity be large compared to the velocity of the

most energetic electron of the stopping medium, placing these experiments

in the region in which a rigorous theoretical treatment is most

difficult. As no theoretical expression, from which the energy loss

could be calculated, had been derived, it was decided to fit an

empirical relation to the data, and as the range values were of greater

internal consistency, they were chosen rather than the more basic energy

loss data.

Rather than become involved in the uncertainties and complexities

of shell corrections, the relation chosen was based on the energy loss

being inversely proportional to the particle velocity as had been pointed

out by Bohr and by Lindhard and Scharff. The range would then be given

by

1 -dE 1 -dE 1 1/2
R- 5_ fE dE
R N E(E) N kE-1/2 kNf

R = KE3/2 + C (22)

The equation R = aEb + C was fitted to the data for each absorbing

material by a computer least squares program. The parameters and the







- 82 -


region in which they fit the data are given in Table 20. For triton

energies above 1.2 Mev the exponent b has values near 1.5 for each

absorber except polystyrene. The value for polystyrene may be

attributed to the presence of hydrogen atoms and chemical bonding.

The particle velocity is greater than the velocity of the hydrogen

electrons and even though the effects of chemical binding are small,

the average ionization potential may be sufficiently affected to

produce this effect. The apparently unsystematic behavior of the

coefficient a is largely removed if b is taken as 1.50 for each

absorber. The values of a then show an increase with increasing

atomic number of the stopping medium as shown in Table 21. The

lower values of the exponent b for the lower energy region is due

to the pick up of electrons by the tritons in this area.

In Chapter I the variation of stopping power with the atomic

number of the stopping material was mentioned and Fig. 26 shows the

values for a triton energy of 1.5 Mev. These data represent the

best values of proton energy loss in the literature and the triton

results of the present experiments. It is apparent that there is

some variation from a smooth function of the atomic number, particular-

ly in the region of Z = 22 50 where the electrons are being added in the

3d orbitals. Figure 27 shows a similar plot for 20-Mev protons; the

variations are still present but are not as pronounced as at the lower

energies. Brandt (46) has shown the trend of the mean ionization






- 85 -


TABLE 20



VALUES OF PARAMETERS IN EMPIRICAL EQUATION

R(mg/cm2) = a.105E(kev)b + C


bstance

non

ypton

ckel

gon

uminum



trogen

lystyrene

non

:ton

kel

on

ninum



rogen

ystyrene


Energy Span (Mev)

1.3-2.7

0.8-2.7

1.4-2.7

1.0-2.7

1.0-2.7

1.2-2.7

1.5-2.7

1.4-2.7

0-1.4

0-0.8

0-1.4

0-1.2

0-1.1

0-1.2

0-1.2

0-1.4


Z

54

56

28

18

15

7.2

7

3.5

54

36

28

18

15

7.2

7

3.5


a.

8.43

24.0

12.0

4.98

7.17

2.81

2.61

0.67

49.5

40.6

62.6

1.96

40.7

6.34

5.78

11.2


b

1.55

1.42

1.47

1.56

1.49

1.57

1.59

1.72

1.33

1.33

1.27

1.67

1.26

1.44

1.46

1.55


c

1.66

0.51

1.27

0.13

0.51

0.12

0.o6

0.44

0.57

0.41

0.40

0.41

0.19

0.25

0.20

0.10











TABLE 21


VALUES OF COEFFICIENT a WHEN b = 1.50 IN EMPIRICAL EQUATION

R = a-105"E1'50 + C


Substance Z a

Xenon 54 12.52

Krypton 36 12.26

Nickel 28 9.47

Argon 18 7.70

Aluminum 15 6.68

Air 7.2 4.89

Nitrogen 7 5.30

Polystyrene 3.5 2.54






- 85 -


UNCLASSIFIED
ORNL-LR-DWG. 57829


100


1 10
Z


Fig. 26. Stopping Cross Section as a Function of the Atomic
Number of the Stopping Material for Particles Having an Energy
Equivalent to a 1.5-Mev Triton. Data Represents the Best Litera-
ture Results.






- 86 -


UNCLASSIFIED
ORNL-LR-DWG. 57830
I I I I 1 111


I I I I I I


0-


4F


I I I I 11 I


I I I I I I I I


10
Z
Fig. 27. Stopping Cross Section as a Function
Number of the Stopping Material for Particles Having
Equivalent to a 60-Mev Triton. Data of Burkig and
(23) for 20-Mev Protons.


400


of the Atomic
an Energy
MacKenzie


400


I I I I I I I I I I III






- 87 -


potential for the 3d region follows the variations in the square

root of the electron density but in the 4d region the agreement is

very questionable. These variations in the mean ionization potential

are probably due to the effects of the electron shells and the metallic

bonding, and vary with the relative velocities of the particle and

the electrons.

Figure 28 contains the triton energy loss data plotted as a function

of E/Z with the empirical relation of Lindhard and Scharff represented

by a broken line. The considerable variation between the triton data

and the Lindhard and Scharff equation is due to their use of energy

loss values which have later been shown to fall 10-15 percent below the

accepted values. A more representative relation, shown by the dashed

line, is


S= 4(Z/Et)1/2 (Et/Z)1/2 (25)

The shell corrections given by Bichsel were applied to the

triton energy loss data in order to calculate the mean ionization

potentials. These calculated values agree with the ionization

potentials determined from the energy loss of particles having sufficient

energy to obviate the use of shell corrections.











I I I I I1 1


100
lr-





XE
Kf




40






0.004


UNCLASSIFIED
ORNL-LR-DWG. 57828


I I 4I 1 1 11 I I I I I
4 E,/Z


NITROGEN


LINDHARD-SCHARFF EQUATION


I I I I II,11


I I I I 11111I


0.04


I I


0.1


E, /Z


Fig. 28. Comparison of Experimental Results with Empirical Relations.


NICKEL-
ALUMI


1.0


- '-'' ` '






89 -

LIST OF REFERENCES


(1) N. Bohr, Nature 137, 344 (1936).

(2) J. M. Blatt and V. F. Weisskopf, "THEORETICAL NUCLEAR PHYSICS,"
(John Wiley and Sons, Inc., New York, 1952).

(3) E. Segre and E. Kelly, Phys. Rev. 75, 999 (1949).
(4) J. R. Oppenheimer and M. Phillips, Phys. Rev. 48, 500 (1935).

(5) M. L. Pool, Physica 18, 1504 (1952).
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(7) T. P. Pepper, K. W. Allen, E. Almqvist, and J. T. Dewan, Phys. Rev.
85, 155 (1952).
(8) D. J. Hughes and J. A. Harvey, Neutron Cross Sections, BNL 525
(U.S. Government Printing Office, Washington, D. C., 1955).

(9) A. V. Tollestrup, W. A. Fowler, and C. C. Lauritsen, Phys. Rev.
76, 428 (1949).
(10) A. Galonsky, C. H. Johnson, and C. D. Moak, Rev. Sci. Inst. 27,
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(11) J. L. Blankenship and C. J. Borkowski, I.R.E. Trans. Vol. NS-7,
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(12) S. S. Friedland, J. W. Mayer, and J. S. Wiggins, I.R.E. Trans.
Vol. NS-7, No. 2-5, 181 (1960).

J. M. McKenzie and J. B. S. Waugh, I.R.E. Trans. Vol. NS-7, No. 2-3,
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(15) E. Fairstein, Oak Ridge National Laboratory Physics Division
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(14) J. Muto, F. De S. Barros, and A. A. Jaffe, Proc. Phys. Soc. 75,
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- 90 -


(14) Cont'd
H. D. Holmgren and L. M. Cameron, Bull. Am. Phys. Soc. 6, 36
(1961).

H. D. Holmgren, R. L. Johnson, and E. A. Wolicki, Bull. Am.
Phys. Soc. 4, 403 (1959).

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G. D. Gutsche, H. D. Holmgren, and R. L. Johnson, Bull. Am.
Phys. Soc. 4, 321 (1959).

(15) H. A. Bethe, Ann. Physik 5, 525 (1950).
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(17) E. J. Williams, Rev. Mod. Phys. 17, 217 (1945).
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(1950).
L. M. Brown, Phys. Rev. 79, 297 (1950).

M. C. Walske and H. A. Bethe, Phys. Rev. 83, 457 (1951).

M. C. Walske, Phys. Rev. 88, 1283 (1952).

(19) M. C. Walske, Phys. Rev. 101, 940 (1956).

(20) H. Bichsel, Bull. Am. Phys. Soc. 6, 46 (1961).

H. Bichsel, University of Southern California, Linear Accelerator
Group, Technical Report No. 2 (1961).

(21) N. Bohr, Kgl. Danske Videnskab. Selskab. Mat. Fys. Medd. 18,
No. 8 (1948).

(22) J. Lindhard and M. Scharff, Kgl. Danske Videnskab. Selskab. Mat.
Fys. Medd. 27, No. 15 (1953).

(25) V. C. Burkig and K. R. McKenzie, Phys. Rev. 106, 848 (1957).

(24) J. E. Brolley and F. L. Ribe, Phys. Rev. 98, 1112 (1955).






- 91 -


(25) D. W. Green, J. N. Cooper, and J. C. Harris, Phys. Rev. 98
466 (1955).
(26) T. Thompson, UCRL 1910 (1952).

(27) H. A. Bethe, Rev. Med. Phys. 22, 213 (1950).
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(50) C. J. Cook, E. Jones, and T. Jorgensen, Phys. Rev. 91, 1417
(1953).

(31) H. Bichsel, Phys. Rev. 112, 1089 (1958).
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Phys. Rev. 52, 75 (1937).

(34) W. Whaling, Handbuch der Physik, 34, 193 (1958).
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(45) S. D. Warshaw, Phys. Rev. 76, 1759 (1949).






92 -




(46) W. Brandt, "Penetration of Charged Particles in Matter,"
National Academy of Science National Research Council,
Publication 752 (1960).









BIOGRAPHICAL SKETCH


William Newberry Bishop was born June 18, 1950, at Chattanooga,

Tennessee. In May 1948, he was graduated from Tyner High School.

In June 1951, he received the degree of Bachelor of Science from the

University of Chattanooga, and in June 1955, he received the degree

of Master of Science from the University of Tennessee. In 1954, he

enrolled in the Graduate School of the University of Florida. From

1954 until 1958 he served in the United States Navy, returning to

the University of Florida upon separation from active duty. In

June 1959, he accepted an Oak Ridge Graduate Fellowship under which

the research for his dissertation was performed

William Newberry Bishop is a member of the American Chemical

Society, Theta Chi, Gamma Sigma Epsilon, and Sigma Xi.










This dissertation was prepared under the direction of the

chairman of the candidate's supervisory committee and has been

approved by all members of that committee. It was submitted to

the Dean of the College of Arts and Sciences and to the Graduate

Council, and was approved as partial fulfillment of the requirements

for the degree of Doctor of Philosophy.



June, 1961




Dean, College' o Arts andkScSices



Dean, Graduate School

S rvisory o ittee:


Chairman I


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