Table Of ContentCOPYRIGHTED
BY
CYRIL DEAN CURTIS
1952
CROSS SECTION FOR BREMSSTRAHLUNG PRODUCTION
IN LEAD BY SIXTY MILLION VOLT ELECTRONS
BY
CYRIL DEAN CURTIS
B.S., McKendree College, 1943
M.S., University of Illinois, 1947
THESIS
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSIOS
IN THE GRADUATE COLLEGE OF THE
UNIVERSITY OF ILLINOIS, 1951
URBANA, ILLINOIS
UNIVERSITY OF ILLINOIS
THE GRADUATE COLLEGE
September 15, 1951
I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY
CYRIL DEAN CURTIS
SUPERVISION BY.
ENTITLED CROS'^-SECTION FOR BREMSSTRAHLUNG PRODUCTION IN LEAP BY
SIXTY MILLION VOLT ELECTRONS
BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OT7 DOCTOR OF PHILOSOPHY IN PHYSICS
dm In Charge of Thesis
Head of Department
Recommendation concurred inf
44H
^ . ^ < f c M ^.
Committee
^(^^W^^ahy^v-
on
Final Examinationf
t Required for doctor's degree but not for master's.
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TABLE OF CONTENTS
CHAPTER PAGE
I. INTRODUCTION . 1
A. Theory . . .. • . . . . . « • • • • • • • • .. 1
B. Previous Experimental Work . . . . . . . . . . . . . . . . . .. 3
II. EXPERIMENTAL PROCEDURE . « . .. 7
A. Experimental Arrangement • • • • • • • • • • • • • • • • • • •• 8
1. Source of Electrons . . . . . . • • • • • • • • • • • • •• 8
2. Detection of Radiation Straggling . . . • • • • • • • • •• 8
B. Analysis of Tracks . • • • • • • • • • • • • • • 19
IH. TREATMENT OF DATA 25
A. Primary Electron Energy Distribution • • • • 25
1. The Energy Distribution . . . . . . • • • • • • • • • • •• 25
2. Effects on the X-ray Spectrum . . . . . . . . « . • . . .. 25
B. Calculations of the Cross Section .. . . . . . . . . . . . . . 28
C. Corrections • • • • • • • • • • • • • • • • • • • • • 30
1. Discrimination . . .. • • • • • • • • • • • • • • • • • • • 30
2. Energy Loss . . . • • • • • • • • • • • • • • • • • • • • • i ll
IV. RESULTS AND CONCLUSIONS • • •• kl
A. The X-ray Spectrum and Cross Section . .. • • • • • • • • • •• hi
B. Conclusions . . . . . . . . . . . .. • • • • • • • l i°
APPENDIX A . 58
APPENDIX B 60
REFERENCES 62
VITA 6U
iv
ACKNOKVLEDGMENTS
The author wishes to acknowledge with gratitude the advice, suggestions, and
encouragement of Professor Donald W, Kerst who directed this work.
He also wishes to express his appreciation to Dr. H. William Koch, now of
the Bureau of Standards, under whose auspices the project was begun. Much of the
cloud chamber equipment was designed and previously used by hian. The performance
of this experiment was in part a culmination of early interest in radiation
straggling stimulated at this laboratory by Dr. L. S. Skaggs.
The collecting and analysis of the data were carried forward with the able
assistance of P. C. Fisher, J. W. Henderson, J. H. Maloriberg, and G. Modesitt.
To the betatron shop personnel, the author is indebted for their careful
workmanship in the construction of much of the apparatus.
The project was assisted by the joint program of the ONR and the AEC,
CHAPTER I
INTRODUCTION
When an electron passes through matter, it loses energy principally in two
ways. It may experience inelastic collisions losing energy to the atoms by
excitation and ionization. This collision loss is effective at all energies of
the incident electron. The electron may be deflected in the field of an atom
and emit a quantum by radiation. The radiation or bremsstrahlung can result
from the interaction of the electron vri-th the nuclear field screened by the
orbital electrons or from interaction with the field of one of the orbital
electrons, the latter interaction being much less probable. At about ten Mev for
lead, collision loss and radiation loss are comparable. Below this energy,
radiation loss becomes much smaller while above this energy, radiation loss
becomes greater. Near five-tenths Mev the radiation loss increases proportion
ately to the primary energy of the electron, while at higher energies it
increases even more rapidly (1). At the same time the collision loss rises very
slowly with energy so that at high energies of several million volts, radiation
loss is the predominant effect. This report will be concerned chiefly with
measurements of the radiation or bremsstrahlung process.
A. Theory
Classically, the deflection of an electron means an acceleration and conse
quently a radiation of energy. Quantum mechanically, there exists a probability
that the electron will emit a certain energy quantum of radiation when passing
through the field of a nucleus. The theory in either case leads to a continuous
energy spectrum of x-rays, however different the spectrum is in other respects
2
for the two treatments.
For the low energy region of electrons, Sommerfeld, Sommerfeld and Maue,
and Weinstock (2, 3, U) developed a non-relativistic wave-mechanical treatment
of bremsstrahlung production. The theory gives a step function for the number of
quanta at the high energy end of the x-ray spectrum for monoenergetic electrons
striking a thin target.
For the relativistic region, Bethe and Heitler (5> 6) developed a theory for
electrons using quantum electrodynamics. It is a perturbation calculation valid
to the extent of the Born approximation. The validity conditions are
Ze2/fiv « i, Ze2/nv «1 where Ze is the charge on the target nucleus, ft is l/2 11
0
times Planck' s constant and v and v are the electron speeds before and after
Q
collision. From these conditions, the theory is not expected to be accurate for
heavy elements and for the high energy tip of the x-ray spectrum where v 4< c.
At high energies when E , E » mc2, where E , E and mc are initial, final, and
0 Q
rest energies of the electron respectively, the above conditions become
Ze2/nc SS Z/137. For lead this is approximately six-tenths. Parzen (?) has
pointed out that the error in the integral cross section (integrated over all
angles) when the Born approximation is used should not be greater than (mc2/E )^.
0
This is a result of the fact that although the number of large angle quanta is not
predicted accurately, little error should result in the small angle quanta, which
comprise most of the total radiation. The mean angle between the emitted quantum
and the initial electron direction is 0*v(mc /E ),
0
The correct expression for the probability of bremsstrahlung production in
the field of a nucleus is different from that for a pure coulomb field because of
the screening by the extra-nuclear electrons. Assuming a Fermi-Thomas model for
the atom, Bethe and Heitler (5) give for the cross section integrated over all
angles of the emergent electron and x-ray quantum
M M Tsgt
t'K)'*®il(Hffl* -*''<*>-& '* l
y=ioo^rf
The energy of the emitted quantum is represented by "k." The quantity Y is
a measure of the amount of screening by the atomic electrons. The numerical
values of the functions (p, ( y ) and <p ( )f ) are given in a graph by Bethe and
x
Heitler (5). For values of Y « 1, the screening is important. This corresponds
to high initial energies, high Z elements and the lower energy quanta. For the
case of y=o, called complete screening, <j> (o) = 1; log 183 sxid ^(o) = <P,(o) -H/6.
t
When y » l, 02=^* f and <P approximately equals (p, when ¥ £ O.U. It is
2
apparent that for fixed E , the screening has a very small effect upon the higher
Q
energy quanta but reduces the number of lower energy quanta more and more from
that of the unshielded case as the quantum energy decreases.
B. Previous Experimental Work
Experiments of Nicholas (8), Kulenkampff (?), and Harworth and Kirkpatrick (10
confirmed the non-relativistic theory of Sommerfeld with regard to the shape of
the bremsstrahlung spectrum and the existence of a finite number of quanta at the
high energy tip. Clark and Kelly" measured an absolute value for the cross
section of an isolated continuous band of the spectrum. They checked the theo
retical value within an experimental uncertainty of 33$.
In 1936 KLarman and Bothe (11) measured the energy loss of /3 -particles
with a mean energy of 3.5 Mev in xenon and krypton in a cloud chamber. They
reported energy losses from three to five times greater than those predicted by
the Bethe-Heitler theory. Their statistics were poor, however,
Guth (12) applied a correction to remove the error due to the Born
* Reported by Weinstock (3)
h
approximation at the high energy end of the spectrum."3*" His prediction of a
finite number of quanta at the high energy tip was in agreement with the results
of the Notre Dame group (13-110 who used energies near two Mev from an electro
static generator. They found a constant intensity of radiation within several
hundred kilovolts of the tip by using a monochromatic detector and varying the
primary electron energy.
Ivanov et al. (l5) measured the radiation loss of electrons from an electro
static generator by calorimetric detection. At 2,1+8 Mev they observed 16% less
loss than that calculated from the Bethe-Heitler theory.
Van Atta et al, (16) used monokinetic electrons and ion chamber detection
and found losses from 12% lower at nine-tenths Mev to 20% higher at 2.35 Mev than
those given by theory.
Several cloud chamber experiments (17-21) determining the total energy loss
of (3 -particles passing through foils were performed during the 1930's. The
energies ranged from a few tenths of an Mev to 13 • 5 Mev mean energy. Most of
these were difficult to interpret, however, because of excessive energy loss due
to multiple scattering in the foils. Those experiments using thinner foils gave
energy loss values at least 1+0% higher than theory.
At much higher energies, Blackett (22) measured the energy loss of cosmic
ray electrons when they passed through lead plates in a cloud chamber. Two
energy intervals extending to two hundred Mev showed energy losses in agreement
with the Bethe-Heitler theory within an experimental uncertainty of nearly 20%.
In similar experiments, Anderson and Neddermeyer (23) found the energy losses at
all energies up to />/ three hundred Mev to be >-v 1$% less than theory in general.
The statistical accuracy was poor, however.
Within the past five years, attempts were made to measure the x-ray spectra
* See also Jaeger (lU)
5
from betatrons. Various methods used involved Compton recoil electrons (2h)>
electron-positron pair production and photo-protons from deuterium (25). In
19h9 Koch and Carter (26) made a careful measurement of the energy distribution
s
of electron-positron pairs produced in the air of a cloud chamber by x-rays from
19,5 Mev electrons striking a platinum target five-thousandths of an inch in
thickness in a betatron. They obtained the shape of the complete x-ray spectrum.
It was in fair agreement with the Bethe-Heitler theory although giving relatively
somewhat more quanta in the middle energy region of the spectrum in the vicinity
of ten Mev. Within a range of one Mev of the tip, the statistics were too poor
to show definitely that the intensity spectrum was flat, but the experimental
points did not contradict such a conclusion,
Powell, Hartsough, and Hill (27) measured the shape of the complete x-ray
spectrum from 322 Mev electrons striking a similar platinum target in a syn
chrotron. They measured the energy distribution of pairs formed in lead foils
one mil thick in a cloud chamber. The shape of the spectrum including the high
energy tip was in good agreement with the Bethe-Heitler theory within the
statistical error.
Recently Lanzl (28, 29) investigated the bremsstrahlung production of mono-
kinetic electrons extracted from a betatron. He made various types of measurement
of the Z dependence of the radiation using threshold detectors, the absolute
radiation cross section with ionization chamber detectors, and angular distri
bution of the radiation talcing into account the multiple scattering of electrons.
He found the radiation cross section to be proportional to Z for the unscreened
nucleus to within 1% for the upper portion of the spectrum with a maximum energy
of 16.93 Mev. This was in agreement with the Born approximation. At the same
time, collisions gave seven-tenths of the radiation produced by electron-proton
collisions in comparison with a value of 0.5U from the Bethe-Heitler theory. The
absolute total yield of x-rays with maximum energy of 16.9 Mev was in rough
