THE INTERACTION OF TRITONS
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
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
TABLE OF CONTENTS
LIST OF TABLES--------------------------------------------- iv
LIST OF FIGURES-------------------------------------- v
GENERAL INTRODUCTION 1
PART I NUCLEAR REACTION STUDIES ----------------------- 2
I. INTRODUCTION------------------------------------ 2
II. APPARATUS--------------------------------------- 11
III. EXPERIMENTAL METHODS AND RESULTS---------------- 28
PART II. ENERGY LOSS STUDIES-------------------------- 38
I. INTRODUCTION---------------------------------- 38
II. EXPERIMENTAL PROCEDURE-------------------------- 48
III. RESULTS---------------------------------------- 52
IV. DISCUSSION-------------------------------------- 81
LIST OF REFERENCES----------------------------------------- 89
LIST OF TABLES
1 Mean Range of 2.736-Mev Tritons 53
2 Contributions to the Error in the Range of 54
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
LIST OF FIGURES
1 Typical Potential Barrier Shapes 4
2 Excitation Function for Bi209(dp)Bi211 and 7
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
14 Coincidence Spectra of Tritons and Alpha 34
Particles Using Silicon Semiconductor
15 Spectrum of Al27(tp)Al29 and Al27(t,)Al28
Reaction Products Using Silicon Semi-
Conductor Radiation Detectors
LIST OF FIGURES (CONT'D)
16 Lindhard-Scharff Plot of Energy Loss 44
17 Range Curve for Tritons in Air 51
18 Triton Ranges in Xenon, Krypton, Nickel, 63
19 Triton Ranges in Aluminum, Air, Nitrogen 64
20 Atomic Stopping Cross Section for Tritons 74
in Nickel, Aluminum, Air, and Poly-
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
23 Comparison of Energy Loss Results for Tritons 78
with Literature Values in Argon and
24 Comparison of Energy Loss Results for Tritons 79
with Literature Values in Air and Poly-
25 Comparison of Energy Loss Results for Tritons. 80
with Literature Values in Nickel and
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
- 1 -
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.
NUCLEAR REACTION STUDIES
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
S ax h2( + 1) (1)
r 82 M r
where Z and Z are the charges of the particle and target nucleus
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
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
ORNL-LR DWG. 57656
0----- 0---- ----------------
0 ----I- o
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 =
8 72r2 z2 Z 2
zo zx e
(d) Coulomb Barrier = r ; Centrifugal
- 4 -
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
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
particle to traverse a nuclear diameter ( 1022 sec.), the mechanism is
termed the "compound nucleus" process, with C the compound nucleus. If
the reaction is complete in the order of 102 sec, the process is called
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
6 8 10 12 14 16 48
Fig. 2. Excitation
Bi209(d,n) Po21. (3)
Function for Bi209(d,p) Bi211 and
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
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
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 -
Fig. 3. Detector and Source Geometry.
Event a Both Particles are Detected.
Event b Only One of the Particles is Detected.
- 11 -
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.
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
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
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.
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
- 15 -
Fig. 5. Experimental Chamber.
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.
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.
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
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
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 -
40 60 -
2- 8 40-
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.
- 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
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.
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
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
PHS SIGNAL Z,
AMPLIFIER 2 --T
Fig. 7. Simplified Diagram of Fast Coincidence Circuit.
FROM FAST T-L
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.
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.
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 -
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
N1 and N2 are the number of events recorded by detectors one and
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 -
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
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
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
4021 I I I I I I
PULSE HEIGHT, arbitrary units
Fig. 10. Ungated Triton and Alpha-Particle Spectrum
Using a Cesium Iodide Detector.
- 30 -
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.
40 31 I I I I I I
PULSE HEIGHT, arbitrary units
Fig. 12. Ungated Triton and Alpha-Particle Spectrum
Using Gas Flow Counter.
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
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
Attempts were made to investigate the (t,p) and (t,d) reactions on
- 32 -
- 33 -
PULSE HEIGHT, arbitrary units
Fig. 13. Ungated Triton and Alpha-Particle Spectrum
Using a Silicon Semiconductor Radiation Detector.
- 34 -
ORNL-LR- DWG. 57665
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
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 -
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-
- 37 -
must occur with too small a probability to be observed above the
random coincidence background, at least in runs of reasonably
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
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 -
ENERGY LOSS STUDIES
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
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
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)
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
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)
- 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
I = KZ (9)
where K is a constant having a value of 10-15 ev for all stopping
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
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)
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
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
E = 2 ZL( ) (15)
where v = v2/Z v2 (14)
with vo = 2 e2/h (15)
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
expression essentially the same as the Bethe equation. If -- is
plotted against In E/Z all points corresponding to large values of 5
should lie on a. straight line whose slope is z e with an
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 -
0.01 0.1 4.0
Ribe (24) o
Lindhard- Scharff Plot of Energy Loss. + Brolley and
Burkig and Mackenzie (23) Green et a.(25).
- 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
E(E) = -1 (--E) (16)
where e1 and e2 are the stopping cross sections of particle 1 and 2
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)
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
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)
- 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 -
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.
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.
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.
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 .
The electronics system was very similar to that shown in Fig. 9,
the difference being that only the Oak Ridge type multichannel analyzer
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
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)
This energy loss corresponds to the average energy of the interval
(E2 El), provided this interval is a small fraction of the particle
ORNL-LR- DWG. 57823
6.0 6.5 7.0 7.5 8.0
EQUIVALENT THICKNESS OF AIR (mg/cm2)
Fig. 17. Range Curve for Tritons in Air.
- 52 -
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 -
MEAN RANGE OF 2.756-MEV TRITONS
15.15 + 0.15
7.54 t. 0.06
7.26 + 0.06
6.12 + 0.10
- 54 -
CONTRIBUTIONS TO THE ERROR IN THE RANGE OF 2.736-MEV TRITONS
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
Total Error Solid Absorbers
Approximate Percentage Error
*Solid Absorbers Only
* Gaseous Absorbers Only
- 55 -
TRITON RANGES IN XENON
- 56 -
TRITON RANGES IN KRYPTON
- 57 -
TRITON RANGES IN NICKEL
Range (mg/cm )
- 58 -
TRITON RANGES IN ARGON
e (mg/cm 2)
Range (mg/cm 2)
- 59 -
TRITON RANGES IN ALUMINUM
e (mg/cm )
- 60 -
TRITON RANGES IN AIR
e (mg/cm )
Range (mg/cm )
- 61 -
TRITON RANGES IN NITROGEN
- 62 -
TRITON RANGES IN POLYSTYRENE
Range (mg/cm 2
22 II I I
XENON KRYPTON NICKEL ARGON 0o
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.
TRITON ENERGY (Mev)
Triton Ranges in Aluminum, Air, Nitrogen, and Polystyrene.
- 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
lists the factors used to convert the energy loss from kev-mg -cm to
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 -
ENERGY LOSS OF TRITONS IN XENON
E (Mev) E (10-15 ev-cm2)
ENERGY LOSS OF TRITONS IN KRYPTON
E (10-15 ev-cm2)
- 67 -
- 68 -
ENERGY LOSS OF TRITONS IN NICKEL
E (10-15 ev-cm2)
- 69 -
ENERGY LOSS OF TRITONS IN ARGON
E (Mev) e (10"15 ev-cm2)
- 70 -
ENERGY LOSS OF TRITONS IN ALUMINUM
E (Mev) (10-15 ev-cm2)
- 71 -
ENERGY LOSS OF TRITONS IN AIR
E (10-15 ev-cm )
- 72 -
ENERGY LOSS OF TRITONS IN NITROGEN
- 73 -
ENERGY LOSS OF TRITONS IN POLYSTYRENE
(10-15 ev-cm2/C H8)
I I I I I
I II I I I
I I I I I I
I I I I I I I
TRITON ENERGY ( Mev)
Fig. 20. Atomic Stopping Cross Section for Tritons in Nickel,
Aluminum, Air, and Polystyrene.
I I I I I I .,..
1 I I
- -- .____
_ I I I I
I I I I I I I I
I I I -
I I I I I I11
TRITON ENERGY (Mev)
Fig. 24. Atomic Stopping Cross Section for Tritons in Xenon,
Krypton, Argon, and Nitrogen.
I I I
I I I I
- 76 -
CONVERSION FACTORS FOR ENERGY LOSS
(1015 ev-cm ) = Factor x (kev mgl -cm2)
Polystyrene (e for C8H8)
Polystyrene (e for CH)
I I I I I
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)
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).
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).
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).
- 81 -
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
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
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 -
VALUES OF PARAMETERS IN EMPIRICAL EQUATION
R(mg/cm2) = a.105E(kev)b + C
Energy Span (Mev)
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 -
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-
- 86 -
I I I I 1 111
I I I I I I
I I I I 11 I
I I I I I I I I
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.
of the Atomic
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
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
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
I I 4I 1 1 11 I I I I I
I I I I II,11
I I I I 11111I
Fig. 28. Comparison of Experimental Results with Empirical Relations.
- '-'' ` '
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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.
Dean, College' o Arts andkScSices
Dean, Graduate School
S rvisory o ittee:
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