Calhoun: The NPS Institutional Archive
DSpace Repository
Theses and Dissertations
Thesis and Dissertation Collection
1970
Energy loss of high energy electrons in tin,
lead, and gadolinium
Mosbrooker, Michael Lee
Monterey, California ; Naval Postgraduate School
http://hdl.handle.net/10945/14987
Downloaded from NPS Archive: Calhoun
ENERGY LOSS OF HIGH ENERGY ELECTRONS
IN TIN, LEAD, AND GADOLINIUM
by
Michael
Lee Mosbrooker
United States
Naval Postgraduate School
THESIS
ENERGY LOSS OF HIGH ENERGY ELECTRONS
IN TIN, LEAD, AND GADOLINIUM
by
Michael Lee Mosbrooker
and
Davi d Lee Sandquist
June 1970
Tki6 documznt hn6 bee/i appJiove.d Ion pubLLc tzIza&e. and 6atz; <Lt& di&&u.bution am untmutzd.
T136107
Energy Loss of High Energy Electrons
in Tin,
Lead, and Gadolinium
by
Michael Lee.^Mosbrooker
Major, United States Army
B.S., California State Polytechnic College, 1960
and
David Lee Sandquist
Major, United States Army
B.S., Iowa State University, 1961
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN PHYSICS
from the
NAVAL POSTGRADUATE SCHOOL
June 1970
.
ABSTRACT
The LINAC at the Naval
Postgraduate School
,
Monterey, was used
to accelerate electrons to energies ranging from 52 to 92 MeV in
order to study the energy distributions of high energy electrons
before and after passing through layers of tin, gadolinium, and
lead.
The thickness of these materials ranged from 0.8 to 5.9 g/cm
2
.
The most probable energy losses agreed with the theory of Blunck
and Westphal for all materials used, while distribution half-widths
agreed only for absorbers of thickness less than 3.0 g/cm
thickness at which theory and experiment began to exhibit
2
.
a
The
notice-
able discrepancy was found to be dependent on the atomic number of
the material
Where comparison was possible, results of this experiment generally
agreed with the findings of similar works concluded previously.
LIBRARY
NAVAL POSTGRADUATE SCHOOL
MONTEREY, CALIF. 93940
TABLE OF CONTENTS
Page
I.
II.
III.
IV.
V.
11
INTRODUCTION
—
THEORETICAL CONSIDERATIONS
17
EXPERIMENTAL PROCEDURE
19
-
TREATMENT OF DATA
-
RESULTS AND OBSERVATIONS
APPENDIX A.
Tables
APPENDIX
B.
Figures
APPENDIX
C.
Beam Folding Technique
APPENDIX
D.
Computer Program
FORM DD 1473
21
23
-
-
—
-
26
64
68
-
-
BIBLIOGRAPHY
INITIAL DISTRIBUTION LIST
13
-
81
82
83
LIST OF TABLES
Table
I.
II.
III.
Title
Page
Energy Loss Distribution Characteristics of Tin
Energy Loss Distribution Characteristics of Gadolinium
Energy Loss Distribution Characteristics of Lead
23
—
24
25
LIST OF FIGURES
Appendix
Figure
B
Title
Page
1
Most Probable Energy Loss Vs. Tin Absorber Thickness
26
2
Half-Widths Vs. Tin Absorber Thickness
27
3
Most Probable Energy Loss Vs. Gadolinium Absorber
Thickness
28
4
Half-Widths Vs. Gadolinium Absorber Thickness
29
5
Most Probable Energy Loss Vs. Lead Absorber
Thickness
30
6
Half-Widths Vs. Lead Absorber Thickness
31
o
7
Energy Distribution, Tin Absorber, T = 1.485 g/cm
E. = 52.51 MeV
8
Energy Distribution, Tin Absorber, T
E.
9
Energy Distribution, Tin Absorber, T
E.
2.970 g/cm
= 52.51 MeV
=
4.455 g/cm
= 52.51 MeV
=
10
Energy Distribution, Tin Absorber, T = 5.940 g/cm
E. = 52.51 MeV
11
Energy Distribution, Tin Absorber, T
=
E.
=
Energy Distribution, Tin Absorber, T
=
12
E.
13
Energy Distribution, Tin Absorber, T
E
1.485 g/cm
74.95 MeV
2.970 g/cm
= 74.95 MeV
4.455 g/cm
= 74.95 MeV
=
32
2
33
2
34
2
35
2
36
2
2
37
38
i
14
Energy Distribution, Tin Absorber, T = 5.940 g/cm
E. = 74.95 MeV
15
Energy Distribution, Tin Absorber, T = 1.485 g/cm
E. = 94.32 MeV
16
Energy Distribution, Tin Absorber, T
E
j
2.970 g/cm
= 94.32 MeV
=
2
39
2
40
2
41
Figure
17
Title
Page
Energy Distribution, Tin Absorber, T
-
=
E
4.455 g/cm
94.32 MeV
2
42
i
18
19
20
Energy Distribution, Tin Absorber, T
=
E.
=
5.940 g/cm
94.32 MeV
Energy Distribution, Gadolinium Absorber, T
=
E.
=
Energy Distribution, Gadolinium Absorber, T
E.
21
22
23
E.
=
Energy Distribution, Gadolinium Absorber, T
E.
0.814 g/cm
53.16 MeV
1.610 g/cm
= 52.78 MeV
=
E.
43
=
Energy Distribution, Gadolinium Absorber, T
Energy Distribution, Gadolinium Absorber, T
2
g/cm
52.78 MeV
3.221
4.026 g/cm
= 53.16 MeV
=
= 4.831
= 53.16
g/cm
MeV
24
Energy Distribution, Gadolinium Absorber, T = 0.814 g/cm
E. = 74.96 MeV
25
Energy Distribution, Gadolinium Absorber, T
=
E.
=
26
Energy Distribution, Gadolinium Absorber, T
=
27
Energy Distribution, Gadolinium Absorber, T
=
E.
=
Energy Distribution, Gadolinium Absorber, T
=
28
1.610 g/cm
74.96 MeV
3.221 g/cm
E. = 74.96 MeV
E
4.026 g/cm
74.96 MeV
4.831 g/cm
= 74.96 MeV
44
2
45
2
46
2
47
2
48
2
49
2
50
2
51
2
52
2
53
i
29
Energy Distribution, Gadolinium Absorber, T
E
0.814 g/cm
= 91.74 MeV
=
2
54
i
30
31
Energy Distribution, Gadolinium Absorber, T
=
E.
=
1.610 g/cm
91.74 MeV
Energy Distribution, Gadolinium Absorber, T
=
3.221
Energy Distribution, Gadolinium Absorber, T
=
E.
=
4.026 g/cm
91.74 MeV
Energy Distribution, Gadolinium Absorber, T
=
E.
=
E.
32
33
g/cm
= 91.74 MeV
4.880 g/cm
91.74 MeV
2
55
2
56
2
57
2
58
Title
Figure
34
35
36
37
38
Appendix
1
Page
Energy Distribution, Lead Absorber, T = 2.825 g/cm
E. = 53.17 MeV
59
2
Energy Distribution, Lead Absorber, T = 4.236 g/cm
E. = 53.17 MeV
60
2
Energy Distribution, Lead Absorber, T = 2.825 g/cm
=
E.
74.97 MeV
61
2
Energy Distribution, Lead Absorber, T = 4.236 g/cm
E. = 74.97 MeV
62
2
Energy Distribution, Lead Absorber, T = 2.854 g/cm
E. = 91.76 MeV
63
C
Beam Folding Technique
65
,
I.
INTRODUCTION
The theoretical energy distribution for an initially monoenergetic
electron beam which has passed through an absorbing material was de-
termined by Blunck and Westphal
[1].
Their work modified previous
theoretical calculations of Landau [2], Eyges [3], Bethe and Heitler
[4], and Blunck and Leisegang [5] by adding radiation losses to the
previous predictions of ionization losses for electrons when passing
through thin absorbing layers.
small
The distribution assumes energy losses
compared to the incident beam energy.
is presented in Section
The theoretical treatment
II.
Several measurements of energy losses by high energy electrons
passing through various materials have been performed in the 10 MeV
Of note are the works of Breuer on aluminium [6];
to 150 MeV range.
Bumiller, Buskirk, Dyer, and Miller on aluminum [7,8]; Goodwin on
copper [9]; and DeLeuil and Raynis on aluminum, copper, and lead [10].
Except for Breuer'
work on the Darmstadt linear accelerator, the
s
experiments were performed on the LINAC at the Naval Postgraduate School
These experimental results are in general agreement with theory for thin
o
absorbers
(<
2
g/cm
),
but discrepancies with theoretical predictions
are reported for the thicker absorbers.
Such discrepancies are expected
for the thicker absorbers since the energy loss is no longer small
compared to the initial beam energy.
In this thesis the
energy loss measurements are extended to include
tin (Z = 50) and gadolinium (Z = 64).
These metals were chosen to
provide experimental results for materials with atomic numbers between
11
copper (Z
=
29) and lead
(Z = 82).
It was thought that analysis of
these materials would provide more conclusive information on the
effects of atomic number on the agreement between experimental and
theoretical half-widths as reported by DeLeuil and Raynis [10].
Thicknesses used ranged from 1.485 to 5.940 g/cm
0.814 to 4.831 g/cm
2
for gadolinium; nominal
2
for tin and from
beam energies were 52,
Thick lead absorbers (2.825 and 4.236 g/cm
75, and 92 MeV.
2
)
were
investigated as an extension of the work of DeLeuil and Raynis, and,
in addition, their thickest aluminum absorber (5.574 g/cm
investigated as
a
2
)
was
continuity check between the two experiments.
The energy loss distributions are characterized by the most probable
energy loss and the half-width.
The half-width is the full width of
the distribution curve at half maximum.
These quantities, obtained
from experiment and theory, are the basis for comparison between experimental and theoretical results.
12
THEORETICAL CONSIDERATIONS
II.
The Blunck and Westphal
theory of the distribution for the energy
loss of a beam of monoenergetic electrons in passing through a layer
of absorbing material assumes that the energy loss Q is small compared
to the initial
beam energy,
E.
Let W(Q)dQ be the probability of
.
energy loss between Q and Q + dQ, and
X
be that portion of the loss
Hence, the ionization loss is Q
Q due to radiation.
-
Considering
X.
these two loss processes, the probability of energy loss is
Q
W(Q)dQ =
W T (Q-X)W<;(X)dXdQ
/
where W, and
IaL
(1)
3
l
o
are the energy loss distributions for ionization and
radiation respectively.
The Landau equation [2], as modified by Blunck and Leisegang, is
used for the energy loss distribution due to ionization.
bution is expressed as
A
a
The distri-
function of Landau's dimensionless parameter
as follows:
,2
C y
=
W (Q)dQ = *(x) dx
z
T
—
where
^
=
A
aK
4aK
-
^
rS-S
f
E.
+ In
:
+
exp
h2 +
I
b
y,
L
2
y
dA
(2)
n
1.116
(3)
The terms used in equations (2) and (3) are defined as follows:
C
,
y
s
and
x
are constants given by Blunck and Leisegang [5] and
are used to fit Landau's distribution to a sum of gaussian functions.
R is the
absorber thickness in cm.
13
The quantity "a" is a function of the atomic number Z, the atomic
weight A, and the density
p
of the absorber; and b(=v/c) of the
electrons:
Z
0.154
~
rf
:
A
P
r
MeV/cm.
(4)
f
is a correction to Landau's theory given by Blunck
The quantity b
and Leisegang [5]:
b
2
=
3^0
aR
z
Vm_
2
E.
ln
yi
m
(5)
-
.
*>.
where the summation is over the ionization potentials of the atomic
electrons, and N
is the number of electrons with ionization potential
m
Q is the average energy loss due to ionization
electrons of incident energy E.
(no radiation) for
and is given by Sternheimer [11,12,
s
and 13] as follows:
-
V
m
B +
0.43 + In
/
-
E
i
wh ere t is the thickness in g/cm
,
-
C - a
(X-,
-
and the constants A
log
,
10
B,
p/mc)
C,
MeV
(6)
X,, a
(
and m
are parameters of the absorber material.
These parameters for
tin, lead, and various other material are listed in reference [13],
The
parameters for gadolinium are not listed but were determined by the
following method.
A
vs.
for gadolinium was obtained by extrapolating from a plot of A
Z/A for the absorber materials listed in reference 13.
was A
B vs.
I
=
I
graph.
0.0624.
B for
gadolinium was found in
(ionization potential) plot where
The result was B = 13.3.
14
C
I
a
The result
similar manner from
a
was determined from a Z vs.
was determined from a semi-log plot
\
2
of
X,
I
,
C =
A/pZ vs. -C, and the result was
-6.80.
,
were more difficult to determine, but fortunately they
and m
contribute little in determining
determined.
These constants were numerically
m
The values for the term a (Xn-log-, (p/mc))
were
calculated for tin (Z
=
Q.
50) and tungsten
(Z = 74)
in the p/mc range
momentum, and m is the rest mass of the electron) of the energies
(p is
used in the experiment.
Using Z as a basis of interpolation, the cor-
responding values for gadolinium (Z
=
64) were estimated for two
representative p/mc values (100 and 150).
arbitrarily set to be 3.0, and the
from
The values for a
a
The value
values were determined
and m
a
for X, was
simultaneous algebraic solution based on the interpolated values,
The results were a„
=
0.418 and
tion of
Westphal
The error in the determina-
2.10.
s
using these values was estimated to be 1% or less.
Q"
For W
=
rn
s
s
,
the energy loss distribution due to radiation, Blunck and
[1] give:
W (Q)dQ = BaR(Q/E.)
aR
^
s
(7)
where
3
a = 1.4 x 10"
^
4/3 In
and B is a normalizing factor =
,
1&R +
,
+
]
/9
cm"
1
(8)
.
The distribution of total energy loss according to Blunck and
Westphal
(1)
is
obtained by putting equations (7) and (2) into equation
and performing the required integration.
The result is the energy
loss distribution for a single electron of incident energy E.
.
For
comparison of theoretical and experimental values, this distribution
15
function was used, with corrections to account for the finite energy
width of the incident electron beam.
Section IV and Appendix
C.
16
This treatment is described
in
EXPERIMENTAL PROCEDURE
III.
The LINAC of the Naval Postgraduate School was used to obtain
electron beam energies from 52 MeV to 92 MeV.
scattered at 90° from
a
This beam was elastically
thin (3.5 mil) aluminum scattering foil, passed
through the absorber, and finally analyzed by a 120° magnetic spectro-
meter described by Kenaston, Luke, and Sones [14].
This general experimental arrangement was similar to that used by
Miller [7,8] and DeLeuil and Raynis [10] with the exception of the
removal
of a 3.5 mil aluminum window and the installation of a ten
channel
coincidence counting system.
These changes are discussed below.
The aluminum window removed was located just before the scattering
chamber.
Since the presence of the window caused a broadening of the
incident electron beam distribution, its removal decreased the energy
width of the incident beam for this experiment, as compared to previous
works done at the NPS.
The ten channel counting system consists of ten front counters and
a
single backing counter operated in coincidence with the front counters.
The entire ten channel system has an energy spread of about 3%.
The absorbers were positioned approximately 3 cm. from the scattering
foil
as recommended by DeLeuil
Absorber thicknesses for
and Raynis [10].
tin were 1.485, 2.970, 4.455, and 5.940 g/cm
2
;
were 0.814, 1.610, 3.221, 4.026, and 4.831 g/cm
for lead were 2.825 and 4.236 g/cm
thicknesses for gadolinium
2
;
absorber thicknesses
2
.
A thick aluminum absorber (5.574 g/cm
)
was used to correlate the
results of this experiment to the results of DeLeuil and Raynis [10],
17
.
which were obtained before the ten channel countin., system Wa
.
called.
The results agreed within experimental accuracy.
Since the electron beam scattered into the absorbing matei
was
not monoenergetic, the energy distribution was determined both before
and after passing through the absorber.
Various thicknesses of absorber
material, including no absorber, were positioned on a remotely controlled
ladder device.
For measurement of the distribution before passing through
the absorbers (called a zero peak), the ladder was positioned such that
After measuring the
the beam passed only through the scattering foil.
zero peak spectrum, the various absorbers were moved into the beam to
determine the energy distribution of the beam after passing through each
absorber.
In the case of tin and lead all
absorber thicknesses could be measured
without turning oft the accelerator and thus possibly altering the character of the beam.
This was not possible for gadolinium.
cost, only a small quantity was purchased.
Because of its
Hence, only two gadolinium
absorbers could be run without turning off the accelerator and rearranging the gadolinium on the ladder.
a
Since the beam character could change,
zero peak measurement was made whenever absorbers were replaced.
The data represented the number of electrons detected by the coin-
cidence counting system at the exit of the magnetic spectrometer.
stream Secondary Emission Monitor was used as
a
standard for normalization
purposes, in that each data point corresponded to
current, i.e.,
a
A down-
a
given integration
certain number of electrons passing through the absorb-
ing material
18
IV.
TREATMENT OF DATA
The data reduction for the ten channel counting system is standard
for multi -channel systems and is on file in the NPS LINAC computer
library.
In this reduction process, three characteristics of the
counting system are required.
The characteristics are:
(1)
the energy spread of the counting system,
(2)
the energy seen by each front counter,
(3)
the relative efficiencies of the front counters.
With this information the actual energy corresponding to the front counter
data is calculated.
Counting rate and background corrections are also
performed during this computerized process.
In the lower
energy regions of the spectrum, where all counter read-
ings should be nearly equal, a counting discrepancy was noted in that the
lower energy front counters read consistently higher than those on the
higher energy portion of the counting spectrum.
This effect occurred at
energies lower than required to obtain distribution half-widths and thus
did not affect the data reported.
However, it made confirmation of the
shape of the distributions at
low energy
\/ery
(<
20 MeV) impossible.
The electron beam energy is not monoenergetic as required by Blunck
and Westphal theory.
To compare experimental and theoretical results,
the zero peak data must be used to modify the theoretical
predictions.
With no data treatment, the theory will predict half-widths which are
too small and, in the case of asymmetric zero peaks, erroneous most
probable energy losses.
Removal of the aluminum window noted in Section
III narrowed the zero peak to the extent that it could be treated as a
19
symmetrical gaussian distribution.
The IBM 360 computer of the MPS
was used to unfold the zero peak energy distribution into the theory.
A histogram method described in Appendix C was used for this unfolding.
The computer program used to accomplish the unfolding is Appendix
In the
D.
comparison of experiment with theory, the measured incident
energy distribution was unfolded as previously described, properly
normalized to the experimental data, and plotted.
the theoretical
determined.
From these plots
half-widths and most probable energy losses were
The experimental data were plotted along with the correspond-
ing theoretical
curve, and measurable parameters were compared.
are shown in figures
1
through 38 of Appendix
20
B.
The curves
RESULTS AND OBSERVATIONS
V.
*
The values predicted by theory and the experimental results for the
most probable energy loss and half-width for tin, gadolinium, and lead
are shown in Tables I, II, and III respectively.
In these tables, BW
refers to Blunck and Westphal theoretical predictions, Q
represents
the most probable energy loss, and
Data are given
Hw*
is the half-width.
for predictions with and without beam folding.
On comparing the theoretical
predictions with beam folding and the
experimental results, it is seen that good agreement exists for target
thicknesses less than about 3.0 g/cm
probable energy loss.
2
for both half-width and most
At thicknesses greater than this, the agreement
in most probable energy loss is still
agreement in half-width.
reasonably good, but there is poor
The greatest variation in most probable energy
loss is 8% while the average variation is 3%.
These percentages, while
averaged over all material, are typical and not material dependent.
The
average half-width variation is 9% where half -widths were obtained.
As
can be seen from Appendix B, figures
predict a half-width for
a
2,4, and
6,
the theory does not
certain target thickness for each element.
This cutoff thickness is smaller as the atomic number increases.
For
o
example, the theory would predict
but not for 4.2 g/cm
2
a
half-width for 5.6 g/cm
aluminum,
lead.
It is concluded from these results that the Blunck and Westphal
theory
predicts correctly the most probable energy loss for all targets used and
predicts satisfactorily the half-widths for the thinner targets.
21
Thin
targets can be defined empirically as those satisfying the
relation
T(Z)
1
/3
<
13.5, where T is the absorber thickness
the absorber atomic number.
22
(g/cm
2
)
and
Z
is
<
:
——
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1
/
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S-
APPENDIX
C
-
BEAM FOLDING TECHNIQUE
The theory of Blunck and Westphal
[1] assumes that the beam of
electrons striking the absorber is monoenergetic.
The beam of electrons
produced by the NPS LINAC, or any other linear accelerator, for that
matter, has
a
finite energy spread about
energy point.
a
maximum or most probable
The fact that monoenergetic electrons are not avail-
able to strike the absorber must be taken into account in computing
theoretical predictions if a meaningful comparison with experimental
results is to be made.
This has been done here by a technique termed
"beam folding".
Beam folding is accomplished by
a
number of well defined steps.
Energy distribution curves may be approximated by histograms.
histograms consist of
a
These
series of "bins" of area W(Q)aQ, where Q is
the energy loss and W(Q)aQ is the probability of loss between Q and
Q + aQ.
scale.
Thus, each bin has an "address", Q, on an energy coordinate
To accomplish beam folding, the beam distribution must be known.
This is observed experimentally and approximated in the computer by
gaussian curve of appropriate half-width.
a
The energy at which the
maximum occurs is established by the energy of the beam and the magnitude
of energy loss incurred by elastic scattering of the beam as it impinges
on the thin aluminum scattering foil
prior to striking the absorber.
The width aQ is then selected for the predicted distribution.
be a small, but finite number where numerical
This must
techniques are to be used.
This same width is used to break the beam distribution into a histogram.
This is illustrated in figure 1(a) of this appendix.
The reason the
same width is used for both distributions is to facilitate computer
programming.
64
(a)
Beam Distribution
(b)
Energy Distribution of E
(c)
Energy Distribution of
Energy
Energy
E,-
Energy
(d)
Total energy Distribution
Energy
Figure
65
1
Each bin of the beam distribution is now treated as
a
monoenergetic
beam with energy commensurate with its center location on the energy
scale.
Each bin also has a definite magnitude, or weight, with the
magnitude of the center bin being unity.
The formulae of Blunck and
Westphal is now applied to each of these beams and an absorber distri-
bution curve results for each, with
a
maximum amplitude proportional
to the height of the appropriate beam distribution histogram.
Each of
the absorber distribution curves thus obtained may be thought of as
being plotted and added to previously determined curves, using the
energy of the electrons as
1
(b),
a
correlation point, as depicted in figures
(d) of this appendix.
(c), and
This is accomplished on the
computer by adding the contents of each bin of the same address and
plotting the cumulative total.
figures
1
(b),
(c), and (d).
The bin of address E
is depicted in
Note that the beam distribution for histo-
gram E4 is centered over the maximum point of the distribution.
This
is important as a false picture could easily be presented if the histo-
gram were not symmetrical as the distribution would then appear skewed.
Since the half-width for a particular absorber increases as the
thickness (g/cm
)
increases, the beam folding technique is affected in
that thick target energy distribution, whose half-width is large, will
be affected much less by the finite beam distribution than will
energy distribution of
more than
2 or 3
a
the
thin target whose predicted half-width is not
times the size of the beam distribution half-width.
Thus, in selecting bin width (aQ), it is desirable to make the width
proportional to the target thickness so as to apply the beam folding
technique in greater detail to thin as opposed to thick targets.
The
computer program (Appendix D) applies the target thickness in direct
66
proportion to establish
calculations.
a
bin width for subsequent beam folding
Thus aQ is much smaller for the thinner absorbers
compared to thick ones.
67
APPENDIX
C
C
f.
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
D.
Computer Program
PURPOSE: THIS program ACCEPTS p<\damptF"<; F^3 m c M r Pr,v
fxp c rt mpnts roNnurTFn on the
compute
injaf a mo wtli
THEORETICAL HALFWIOTfi AMD MOST PRORABLF =N C RGY L n SS AVH
WILL PLOT ROTH THE FXP ER MFNT AL AND THEOR F T C AL c N r °r,v
DISTRIBUTION FOR THF EXPFrimfnt,
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SCOpF: THE PROGRAM TS SPT UP TO MAKP C OMPUT A T on
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TO C XPFR TM<=MTATin\! W I TH ALUM* NUM C opp c r t N, GADO!
AND LEAD,
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METHOD: THE PROGRAM PL nT ^ A Theory HPVE RASED n N THE C T
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TWO GRAPHS ARF PL°TTFD; ON r "FOQ^^FS T HF
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DISTRIRU T ION FOLDFO IN,
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THIS PROGRAM IS WRITTEN USING FORTRAN TV IANGUAG C ANO tm c
TOTAI RUNNING
NPS COMPUTFR FACILITY PLOTTING PACKAGE,
TIMF IS ABOUT 25/T "MINUTES, WHFR F T IS THF ARSDRB r R
THICKNESS IN OM/SO CM,
IMPLICIT REAL*P( A-H.O-Z)
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lWUFnO^) XUF(^n^),ExyCOO) rxY(POO) t iyY(?CO) T'>(^)
EXTFRNAL FCT,RFAM WIOMtWRAD
D01200 J=1,eo
,
(
t
t
f
f
t
E( J)=0
1?00 WF(J)=C
D01201 J=1,?oq
FXX( J)^0
FXY( J)=0
1201 IXY(J)=0
DO1202 J=I t^OO
WOT( J)=0
HW( J)=o
XX( J)=0
WUF( J)=0
120? XUF(J)=o
r
C
r
C
C
C
I
I
1
C
C
C
C
C
"> «;
c;
\
PFAO TN PAPAMFTE^S FOR EXPERIMENT-.
BEAM cnjproy
FB
ATOMir numrer
7
ATOMIC WEIGHT
A
TARGFT THK^NESS: C,m/sq CM
T
SPFfTPnMFTPP INDICATION OF LOCATION np rc^M
07EP0
DISTRIBUTION (Mcy)
NUMBER TO WHICH e X ppdjmfnTAL COUNTS WILL RE
CTSNnR
N0RMALI7EH
HALFWIDTU OF BEAM DISTRIBUTION
HT
68
RC
C
C
C
AP(5,
11
EB, Z,A, T,OZERO,CTSMOR,HT
)
^
7 C RP
PEAK INTO "RIMS"
PTVIDE
WIPTH
INCREASES WITH TAPGFT thtCKM«=SS,
C
DE|_X,
BT*
1
WIPTH
D C LX=.03 J'T
IF(T,LT !„
PELX=, Of>*T
OAVF IS THF RFCPTL LOSS OF ^t c rTP1MS STRIKING AllJMINUM
NUCIETT OF TH«= SCATTER tng fpil,
IONI7ATIPN LOSS TN
SCATTFRF" IS NFGlECTEO„
)
C
C
C
C
C
QAVE=FB*EB/(931,4*A)
c
C
C
c
r n RR
IS th p rnPRrr.TinM to be aop c o to- exper I mcnjtal
TO OORRFCT FOR SP r r.TRHMFTPR C RPPR,
CPRP=0?FPP-QAV
12 FORMAT
c
C
C
C
C
I
"=m ci ?ry
,=
5(1 X,Pfl.-,?,l X, 16)
)
READ IN UP TP ?^P FX»FR TMFMTA! POINTS; C XX IS ENERGY (« r VI
THERE MUST RE ^0 OATA CAROS AMP the
AND IXY TS COUNTS,
LAST E XX MUST BE 7Fon,
READ (5,1?) (EXX(J) TXY(J), J= 1,200)
ESTABLISH PAPAMFTERS FPP SCATTFRINO FOIL-,
,
C
C
C
FOTL=,0">4
1
ZFOIL=13„
KSIG=0
00 1 J=l,200
EXY( J)=TXY( J)
M=
C
C
C
p
C
c
c
c
c
c
c
THF FOLLOWING portion pF THE PR3GRAM UNFOLDS BFAM OtsTdTBUTTON,
ICENT IS AM TNTE0E3 VALUE ASSIGNED to t H c
HISTOGRAM CFNTerfo nyr-o. the PFAK OF THE 8 c Am DTSToip.iiFACH HISTOGRAM IS D C MOTPO RY ITS C M C RGY e AMP
TIOM,
MAGNITUDE RELATIVE Tn th^ p^AK OF THF n I STR I BUTT PM, WF„
I
IS VALUE
OF
BEAM ENERGY INCIDENT PM TARG C T,
FI=EB-PAVF
TEMP=PI
ICPNT=(HT+PELX)/PELX
J
PELX
20? X=X+PFLX
IF(X.GT„ (EI+HT)
X = EI-ir.FNT
)
GPTO 1003
M = M+1
F(M)=X
C
C
C
C
C
C
cvjcp^y
FUNCTION B r AM REPLICATES TH C P T STo TRUT I PN or BEAM
AS A SIMOLF GAHSSTAM CURVE BASEO PM THE EX P c R T ^ r M T ALl Y
PBSFPVFO HALFWIOTH ANO TS IPCAT C P RELATIVE Tn THE r^am
ENERGY BY THE COMPUTED AVERAGE RECOIL LOSS,
WF(M) = REAM( EI, HT,X
GOTP?0?
)
1003 WRITER,??) 0AVE,HT,EPH
DO 100f L-] ,M
DX =
t
7EPjL,EI
N=
10C^ N = N+1
C
C
f
C
C
C
C
USING EACH HISTOGRAM AS \ "B C AM", THF EP|_LOWTNO PnuTl^j OF
the PRPG^AM fpMPUTES AM FNFRGY niSTRTBUTIOM F^R FAfH
OF THESE "RF\ms« AMD STORES THFM IN "BINS" LARFLEP RV
The CUMULATIVE AMPUNIT PE F!_ef t ppm COUNTS IM
EWFPGY, XX,
TS T HE ENERGY LPSS PVER WHICH TH r R-W
THE BIN TS WQT,
PPFDTCTIPN IS INTEGRATED AMD OX IS THE AMOUNT BY WHICH
69
)
c
r
TS
T
E
)
CHANGES FOP EACH Sljrr.FSSTV" TN TFT,o ATION.
CAPPED OUT IN SUBROUTINE DOG 3?*
TMT C GP ATI™)
C
O=3«0*TM7/13,
T
)' •>, ^-r>X
IP(Q 9 L ^EI JGOTO1O04
N=
GDT01005
100^ IF(0,LT o n)r,OTni0O6
EI=F(L)
VALIM=„?5*Q
CALL D003?(0, XL
FCT,7A,F Ot T A,Z>
CALL nOG3? XL, VALI M, FfT, 7B, P
Of f A, 71
CALL DOG^?( VALI M ,0 ,f=CT, ZCtE
0»T, A, 7
WQ=ZA+ZB+7C
WQTCL+N-1 )=WQT (I + N-1 )+WO*WF(L)
XXU + N-1 )=F(L)-0
J=L+N-1
t
,
t
(
C
r
C
r
THE DISTRIBUTION fna TH<= HISTOGRAM nnpR PSPHMDTNG Tn thp
CFNT p R OP T Hf BFA^ niSTP TBIJT irjw IS PPMoy/FD A NO ST1R r
IN
WUF A\in XI IF AS THE UNFOLDED CDUN TS AND ENERGY
RESPECTIVELY,
C
c
IF(! ,NF„
WMF(
M)
ICFNT)G0T01005
=W0
XUF<N)=FI-0
K=N
GOTH 1005
1006 CONTINUE
On 1717 1=1,7
C
c
c
c
FLIMINATP LOW NUMBEBFD "RTNS" AS
LEO ANO ARF NOT P E PP S P NTATI VF
DISTRIBUTION,
T H<=y ARF ONLY
1 F THE CUMULA'
PARTLY
I
F!!.-
Vp
c
WUF( I)=W!)F(8)
1717 WOT( I)=WQT( «)
D n 6 1=1,4
6
T3(
I
)
= T6(
I
)
Goth 77P
777 D0778 N = 1,K
C
PPHCPSS THP UNFOLDED THEORY CURVE.
SETTING EXXC M c OUAL
TO ZEPO ALLOWS PLOTTING HP THIS TH^OPY CUPVE WITHOUT ANY
EXPERIMENTAL DATA„
C.
c
c
c
WQTf N)=WUF<N)
XX
(
N =X
)
JF
!
(
N
)
KSIG=1
J=K
778 CONTINUE
EXX( 1)=0
nn 5 i = i ,4
5 T3( I = T5t I
>
)
77Q WQTMX=0
001007 N=3,J
nn th^ HI STP RUT ION, WOT MX,
DFT r RMT\]P 7H n MAXIMUM pniNT
AND THUS c STAPLISi-< TH C ^OST PPOB ABLE >=N c ROY LOSS, QP,
GE WOT N-?
TF(WOT{ M)„ c wO T (N-l )o ANO, WQT(M-i
1GOT01003 7
GOTn loo*
10O8 IF(WOT( M-l ,| T, W0TMX)r,OTP 10^7
WQTMX=WQT( N-l
EI=TEM°
QP=F T-XY(N-T
1007 CONTINUE
NORVALIZF ALL POINTS OP DTSTPIBUTT n N AND ST^PF TN HW,
I
1
)
n
)
)
i
70
,
.
(
)
)
)
j
,
on ioqc m=i j
HW( M )=WOT( M) 7WQTMX
?
^C° CONTINUF
J = J-1
HWI=0
DFTFRMIMP HALFWIDTH hf TH c TH^HRPtICM
no 1010 Mai,
IF(HW( M*i ,GT. ,*, ANP, HW( Ml
1HW(M) '•nr?LX/(HW( v +1 )-HW( V)
)
)
.,
I
T,
>
5
n
I
STR T RUT
)HWI =XX ( M ) +(
I ni\) t
,
HWA
5-
)
1
IF(M,FQ, J„ 4MD,HWI„ Pf),0 )r,nTf)iiq
GnTni2l
\o WPITP(6,?0)
HWA = n
GOTOIOi n
?0 FORMAT (/ ,?X, NO HAL r WIDTH OBTAINFrv)
1
?
•
1
I
c
(
HW M
(
)
o
GT
, „
5
,
A
MO „ HW m + ]
(
)
3
LT >0 «5)HWA
=
XV{M)-f(HW{M)
1-*5)*DELX/<HW(M)-HW(M+] ))-HWI
010 CONTINUE
ESTABLISH CUTOFF SIGNAL COR PLOTTING SUBROUTINE-!
XX( J+l )=0
ESTABLISH CORRECT GRAPH TITLES FPR ABS^RFR USED,
IF(Z.GT,13, l)G0Tn2Q
DO 3 1=1 ,4
3 T2(I = T3U
)
)
GOT01011
?P IF(Z„GT,?Q^! )GHTH50
DO 101=1,4
10 T?(
I
)
= Ti 0(
I
)
GOT01011
50 IFC7»GT,50.3 l)GOTn64
On 8 1=1,4
8 T2<I )=T9
I
GOTH in ii
64 IE(Z«G T *A4,nG0Tn8?
00 9 1=1,4
I
9 T2(I )=TQ
G0T0101!
p? no 7 1=1,4
(
(
7 T2<
I
)=T7
(
I
SEND DATA TO PLOTTING SUBROUTINE FOR PROCESSING..
1
CALL GRAPH(XX,WQT, EXX,EXY,T4,T3,T2,T1,HWA,EI,T,
lCOPR,CTSNHR t OP)
PRINT RESULTS OF COMPUTATIONS IN TABULAR F0RM o
Oil
WRITE(6,22) 0P,HWA T,7t'
IFfKSIO^O^) GOTO ^77
11 FORMAT (7^1.0,0)
,F*. i
0°: •,F7,4,» HAL C WIDTH:
22 FORMAT{ /,2X,
1' T(GM/SO-CM): »,F6-,4,« 7:
INCIDENT EN-PGY:
2,F6«2,/)
STOP
r
I
t
•
•
1
END
c
c
c
c
c
c
c
c
c
c
c
r
C
71
•
(
(
)
nOG32(XLfXUtFCT,Y,F I,0,T,Dt7)
PI) RPOSF: T HIS SUBROUTINE pfpftpmS THF INTEGRATION RFQUIPFO
IN THF R-W THEORY.
SUBPntJT INF
c
C
c
c
IMPL ICTT
oom
A = ,*
B = XU -XL
P raL*-8(
xu + XL
A-H,n-7
)
)
C = «4 Op A3"» Q
3C9?474O7Pn0 + R
Y=,3 50Q7oe; iA4^c;oiQ5n-')*
KFCT (( A+0) ,7,n,T,FI,0)+FCri( A-C)
C = *4 P?«05T ^57 7?f 34] 700 ''R
Y = Y + •8137! Q"M A646? P3RO-?
! (FCT ((A+C)
7,D T,c Tf 0)+FCT
A-C)
C = ,4 823811 ?77Q77^3? ?oo*R
Y=Y + ol ?6 C"S n*? 654 6"* 1^300-1 *
1(FCT ((A+C) iZtOtT.EIf 0>+FCT( A-C)
C = *4 ^,7^5 30^7Q6PP^Q« 4HO *R
Y=Y + «!71?6 Q^l 4^*^! 07170-1 *
l
,n
f
(
,Z ,n
t
1
t
t
z
t,fi
t
Q)
<r
(
t
1
(FCT (( A+C) ,7. 0,T t FT r O)+FC,T(
c=,,4 4R16^577RR"*0?69An(y~B
Y = Y + ,21417940 011
3340D-1*
(
H
1
(FCT ((A+C) t 7 f n,T,FI, 0)+FC T
C = *4 246R8R 'V 366? R49900 V'R
Y = Y + „?K4Q9 n?q5^i flpnsgn-]
(FCT ((A+C) 7,0, T ,FI t Q)+FCT
97?
R 0795-3071 ?onn -n,
C=
^ M
Y ,?Q34?0£*73Q?f,77 74n-'i*»
Y=
(
((
FI,0)
7,O t T,ET,0)
A-C) ,7
,n,T,n
f
Q|
A-C) ,Z tO» T,c !f0
)
A-C) ,Zt0,T,FI,0)
+
A+ C
,7.n,T CT t 0)+FCT
C=.3 66^ C»10S°37<"-1 44R40O*R
Y = Y + -,^ 7c5]11113R »lR^ r)2^n-l^
ci 0)+Fr.T
1 (FCT ((A+C) t7,0,T
C = ,3 315221 334651 0760m*R
Y = Y + ,-5 c,17?pQ7 0S4^?^?53 r»-l»A + C .7,D»T,EI,0)+FCT
1 (FCT
C = ,2 93P5787»620^116nr»*R
Y = Y + 3 90 96 947893535 15^0-1 *
0)+FCT
1 (FCT ((A+C) ,7»n T FI
C = ,2 5344995^4661 14' C0^ R
Y = Y + .4165596?ll?47 3*7*n-l*
Z,D,T,ET,0)+FCT
1 (FCT ((A+C)
C = ,2 106756 3B06531 76700 B
Y=Y + a 43R'>6 94£ qn??r^i9n^n-i*
KFCT ((A+C) 7t0,T FT,0)+FCT{
C=.l 65°^4^ 01141 ^6"*R?nO*R
Y = Y + « 45 5 86 O3qr>A7RRlO4^0-l
1 (FCT ((A+C) •7tDtT.FI. 0)+PCT(f
C = „l 1Q64 36R112 6^6R5400 & R
Y = Y + e 46°??l QO 5^ r>4n??fl30-1*
T »EI,0)+FC^(
1 (FCT (( A+r) ,7,0t
50-1 ^R
=
598
07913982
C .7 723
Y = Y + ,47 RIO 2 AO0?°6'*7 4'^0-! *
1 (FCT ((A+C) ,7»6|T f F I, 6) +FC.T(
1
t
•-
i
1
(
T
(FCT
( (
)
(
t
7,0, T, CT,Q)
A-C)
,
A-C)
,Z
c
t
(
t
(
tO,T f FI,0)
(
( (
)
t
t
t
7
,
(
A-C) tZ»n,T,Fi,o)
(
A-C) ,7 f D,T,
(
A-C) »Z ,D f T, Fit 0)
c Tf q)
*?
,
?;
7,0,T,EI,Q)
A-C)
f
A-C)
,Z ,O
(
A-C)
,7
f
(
A-C)
7tOtT,Ei,o)+FCT( A-C)
t
4-
C = ,2 41 5 3 33 ?P4^ R69] 50Q-'' * R
Y=R* (Y + „4R?79 44?67T6^Q A nr)-l
KFCT
r
R
((A+C)
TU RN
,
(
END
c
c
c
c
c
c
c
c
c
c
c
c
72
Tt
t
0)
O,T,FI,
0)
»Z
,0»T,fi,
Q)
,7
t
O
t
t
T
t
<=I
FI,0)
)
T
/
,
REAL FUNCTION WI ON *B X r
7
A
PURPOSE: THTS FUNCTION CALCULATES THAT PART n E THE enfrqy
DISTRIBUTION OF AM H c f.T^N OUT Tn L^^S HF emcqry «Y
IHMIZATI^N WHILF PASSING THROUGH AN ABSORBER,
I ,
(
IMPLICI
IL
T
,
f
,
)
R^AL*R( A-H,0-Z)
ON T 7 AT T nri POTENTIALS PEP ^LTTRHM FOP
AR C THE AVERAGE
LEAD FOR EACH SHELL, BEGINNING WITH T HE K ^HCLL,
I
NPOTL
Thf NUMBER °F
IS
inNI7ATin\j POTENTIALS USED
TN THIS CONTEXT, L=LEAO,
AND A=ALUMINU M
G=GADOL IN IUM,
r "iP
!
c /\o
C=COPPER,
S=TIN,
->
REAL** IL( 6)/. 0380 00, » 01 4700,, 003200, 000490,
1*000076,., 00 0002/
->
RFAL*R NL(6)/2-»,8,,lR n ,*?,,lR,,4,/
AL*R IG(5)/,OSO?4 ,no7=?5,or ^l Q 9 ,O r)^?4, .00 00?!/
REAL* 9 NGI 5)/2, R a ,l«, ,2 5, Q,/
0007?,,on*062,,'^00m/
R C AI *8 TS{ c )/,o?o? ,'>n44
REAL*R NSf *)/?„ ,o, ,1°, ,!««, ,4./
RFAL*R IC( > )/, oorqr ,ooooo nnn^R/
REAL*R NC(3)/2, ,8„ 1»,
R C AL*B T A( ?)/,001 56, >OO0^R Q /
REALMS NA( > )/?,, «, /
NP0TL=6
NPQTG=5
npots=e
NP0TC=3
NPOTA=?
P C
>
t
f
,
f
t
t
.,
t
t
,
,
SB
IS THF SUMMATION OF IONIZATION POTENTIALS
EXPERIMENTAL ATRM,
F
0°
THE
SR = 0»
XMASE
THE REST MASS OE AN ELECTRON IN mfv,
IS
XMASE= 511006
BETA TS THE NORMAL V/C USED
GAMMA
THE NORMAL TFRM USED
IS
RELATIVISTTC CALCULATIONS*
IN
I
RELATIVISTIC CALCULATIONS
N
'
BETA=DSORTUE! '-'El + ^o^EP XMASE) /(EI *EI+?, * c I* XMASE
1+XMASE ^XMASE)
GAMMA=U/( l.-BETA**2)**(l*/2o)
thf PRnr.RAM MiJST ehmphte the proper CONAT THIS °OINT
A SFPIFS ^e LOGIC STATFSTANTS FOR THF FXPFPIMCN T AL Z„
MENTS SELECT TH r CORRECT FORMULAE,
)
c
c
c
c
c
t
13
c
c
c
c
IF(7«GT,13*l)GOT02 c
>
COMPUTE SB FOR cxp c R Mp NTAL
TIAL FROM n^c SHELL.
T
I=1,NPHTA
B=IA(I) J'NA(n j'nLOG("
71 SB=SB+B
DO 71
>
^
c
Z,
B
THE
IS
IONIZATION POTEN-
I/{IA(n-<'(l,-B TA*^?)))
,r
THESF A p c MATFPIAI DEESTABLISH VALUES FOP R?r AND Al ,
COMPUTE
THE AV^AQ^ FM«"pr,Y
TO
D
PENDENT TONSTANTS US
C D BY Tf|r <;TFPNHEIMCp
LHS C BY T0MI7ATinN AMD A ?? SUPPLT
THESE ARE B AND A, R«=SP C C T V El. Y EOPM HI C PAPED,
PAP £ P,
1
I
,
r? = ] ft,77
Al
=.07^0
OFLT IS
A
PART OF THE EXPRESSION) BY
73
c T
poNH c IMrp cno THE
T
I
AVFPAGE FN C RGY n SS DU C TO ionization,
NiJMRFRS Hedptn
PPPPFSFNT OTHER STFPMHPIMFO CONSTANTS AS FOLLOWS:
SMALL A „oqr>6
SMALL w 3*510
X!
3.000
-C
4*210
0ELT=4-, fi^ + nLnr,i oj bcta*GAMma)-4,21 -, 0906*
1 (3„-nL0G10(RFTA"GAMMA) )"*3
^1
!.
,
GO TO 11!
? Q IF(7.GT ^q,! )GnTn^O
on 72 I=1,Npotc
B = IC
U
)*NC(n*DL0G(2* *EI/{
72 SR=SR+R
ICC
I
)*( 1„
-BETA**?
)
)
)
lh-RFTA^?)
I
)
)
)
)
)
B?=! 5,oq
Al=.07^1
DELT=4„606*OLOG10( BETA*GAMMA )-4-,74+ a 11QQ*
H3«-0LQG10< PFTA*GAMMA) )**3,^8
50
73
GO TO ill
IF(7eGT,50,1 )G0TO64
00 7? 1=] ,NPOTS
B=ISU >*NS< I )*DLOG( ?**-EI/< ISin
+
SB=SB+B
B? = 13» 93
Al=,0647
OFLT=4,606''OLOG10( RET A *GAMMA -6 2R
10L0G10( BETA' GAMMA)
)
-,
+3
404*
(
3
,
-
)
GO TO 111
64 IF(Z,GT,64^nGnTnfl?
DO 74 I=l,NPOTG
B=TG(I )*NG< >*DLOG(?,*Fl/( IG(I)*(1
74 SR=SP+R
B2=13.3
Al=,06?4
OfLT=4-, 606*DLOG1 0( R^TA*GAMM a
IOLOG10( BETA J GAMMA)
)
-
(
I) * (1
6-,
,
-BFta**2)
8+<,418*<
3
.
-
)
1+*?. 10
GO TO 111
R2
TF(7.GT,R?„1 JGPTnqnrj
DO 75 I="» NPOTL
B=IL (I )*NL( )*DLOG(?,*FI/(
,
IL
,
-BETA**
2
)
75 SB=SB+B
B 2=12.81
Al=,06OR
DFLT=4 9 606*OLGG10( BETA^GAMMA )-6
lf 4.-DL0G10C RETA*GAMMA )**3,41
,0 3 + ,
65
2^-
J
GO TO 111
c
c
r.
c
c
c
c
c
IS TH^ QUANTITY SMALI A, FROM R| UNCK ANn W c STPHALt
MULTIPLIED BY R, the TARGFT THICKNFSS IN CENTIMETERS,
111 AR=0, 154*7 *T/A/RFTA/RFTA
AR
COMPUTE RS?, TH^ SMALI
LFIS^GANG PAPER,
R
SQUARED FROM THE BLUNFK AND
BS2=3.*SB/( 7*AR)
c
c
c
c
c
VAP1, VAR?, ANO VAR"* A R c CONVENIENCE STORAGE LOCATIONS
USFO TO STORE COMPUT c O PORTIONS Hf" S T r R MH C I M FR S 4V c t?^ c
ENERGY LOSS,
'
VAR1=A1*T/BETA**2
VAR7=R? + A 4^ + ?„*DL0G(RETA GAMMA)
VAR3=DL0G( C )-RETA** ?
QAVF IS THF FINAL VALUE FOR THF AVERAGE FN^PGY LOSS.
Q^V^ = VAR1*(V^R' + VAR -DEL'^
B1=DSQRT(BS?J
X IS THF PORTION OF SOME TOTAL ENERGY LOSS Q OIF T^
J-
I
:
:,
)
74
s
)
PEAL FUNCTION WR An *<M
c
c
c
c
r
p
I ,
T
,
7
t
A
)
,
RAOTA T I0N WHILF PASSING THROUGH AN ARSORRrp,
U
IS
AN
ALPHA*
R c At + R(
A-H,n-7
)
TNTFPMEDIATF STORAGE LOCATION USFO IN
U=183.0/Z**U.
c
c
c
c
c
f
pljPPDSF: THIS FUNCTION CALCULATES THAT PART or THF c NFROY
ISTRIPtJT I ON n F AN F| PfT^N HUE T n LOSS IF PW^r,Y «Y
IMPLICIT
c
c
c
c
X
COMdijtc VALUE or AtRHA^R fop TAPG C T THTCKN C SS, ATOvjr
NUMBFR AMO ATiVIC WEIGHT HP ^XP^R I MENT Al ars^RCr,
THE TARGFT THICKNESS FXPRESSFD TN CENT I m^TFP
c
c
c
IS
,
ALPHR^^OO 4*T*Z*7/A*{ 4„0/3.>0*QL0G(U)+!
COMPUTE VALUE for
R=
c
n MPUTIMH
/3 9 0)
n
1
c
c
c
C
p
f
a
,
/°>°)
NORMALIZING CONSTANT,
K /DGAMMA(ALPHP+!»
)
OF
COMPUTP WRAO, TH^ NIJMRFP np COUNTS c XPPCTFn AS A RFSUI
PAOTATION PN C PGY L n SSESo
X P c PR c S r NTS THAT pni<TT™N 0«"
Spmt TOTAL ENERGY LOSS
WHICH IS NOT LHST BY IONIZATION
WRAO=( R*ALPHPt (X**ALPHO
RETURN
ENO
)
/
(
F
I
** ALPHP
))
/X
c
c
C
c
c
c
c
c
c
c
c
c
RFAL FUNCTION BFAM*8 ( FI HW, X
IMPLICIT PFAL*«( A-H f O-Z)
Y=?,
ALFA =4, *OLOGC Y )/(HW HW)
BEA^=D'XP(-( IHII*"I ^ALFA)
RETURN
ENn
fc
c
r
c
c
r
c
c
c
c
c
c
r
f.
R C
c
c
r.
c
c
AL
FUNCTION FCT* 8
(
X» 7
1
A» T, E
\ ,
o
)
PURPOSE: THTS FUNCTION mijl t pl I AT T VH Y Jhjms TOGETHER th c
PRFnfCTinN OF c^cp^y |O^S DUF TO IONIZATION AMO TMP LOSS
DUE TQ RADIATION,
i
I^PLirTT RFAL*«( A-HtO-71
FCT=WRAn(x,FI ,T, 7, A.Q * WI ON
RFTU°N
)
END
76
(
X
,
F
T ,
T
f
7
,
A
,
)
c
c
c
c
SlRRntJTTNP GRAPH (THX.THV, FXX, C XY,T! ,TM^,Ti,HW f n ,T,
ICORRfCTSNORtQP)
PUPPOS c THIS SURPnUTIN c PL^TS THF RFSULTS oc TH^npy CALCULATIONS AND FXP^PI MENTAL RESULTS.
:
IMPLICIT rcai *Q( A-H,n-7)
/• mfv
RFAl *P TITL^Xt
r
R^AL*3
THL
Y(
«
/
1
)
1
)/»M1RMALI7Fn COUNTS
RC&I ^q TTTL^Ot ?) /» Roy
i
i
DIMENSION T1(^),T?<4|,TM^),TM^I, T HX( 1 ^) ,THY(30O)
1FXX(?00) ,PXY{?oo| CTSUfM?^ »C TSDNHOO
,
c
c
c
DFTERMINF SCALING FACTORS AMD CHANGE DATA Tn DISPLACEMENT
X=8,
Y=5.
SIXIN=( C I-QP)*?
ISIXIN = S!XIN + ,
SIXIN?= I SI XIN
)
e;
SIXIN=SIXIN?/2>
IF(HW. EO.0JGOT090
XNCR2>i 5*HW
INCR2=XNCR?+*5
IFCINC2»LT«1 )INCR?=1
XINCR2=INCR2
XINCR=XINCR7/2^
SP=SIXIN-6,*XINCR
IF(SP«LT.O)GOT090
G0T091
oo SP= n
INCR = (EI-l<.5*T)/6.+o5
XINCR=INCP
N=0
1=0
20 1=1+1
TF(EXX(
91
I
|,GT,1,
)
GOT021
GOTO??
21 N=N+1
GOTO ?n
22 IF(N.F0,0)GOTO100
DO 23 J = 1,N
EXX< J)=<EXX( J1-SP) /XINCR+CORR/XINCP
IF(J.EQ.N)G0T073
23 CONT INUE
100 1=0
M=
30
1=1+1
IFCTHX! I)«GT.l
)
GOTO 31
GOT032
31
M=M+1
G0T030
37 On 3^ J=l f M
THX( J)=(THX(J)-SP)/XINCR
IF( j ro»M)r.cTn^?
IF(THY( J+l KGT -,TUY(
J)
)
THYM A
X=
THY
(
J +1
33 CONTINUE
IF(N.EO.O) GHT010!
SCALF=4„
IF(T.GT 4„ R) SCALF = 3o
on 40 j=i,n
FXY<J1=EXY(J)/CTSN0R*SCALE
^0 CONTINUF
101 DO 50 J=^fM
SCALE**..
IF(T^GT,4,
q)
SCA!.F = ^,
THY( J)=THY(J)/THYMAX*SCALE
^0 CONTINUE
C
c
,
)
)
SORT EXX AND ELIMINATE VALUES OFF GRAPH
77
)
K1
IF( NoEQ,^)
K = N -1
I)
GOTniO'
on 60 1=1 ,k
I
PI =
on
T
+
1
I P
c ( FXX( T ),l
T C M P=FYX( T )
T C M = PXY( T )
PXX ( I)= C XX(
C XY ( I)= r XY(
6
J=
I
FXX J)=Tf MP
EXY J)=T=M
60 COM TINUE
»N
c
,
PXX(J
)
)
GHTP 60
J)
J)
:
(
i
J=
KK
=
K=N
on 61
I=1,K
TF< KK,F0„1 IG0T061
IF( C XX( I )oLT„0)00T06i
J=J+
1
N=J
EXX J)=^XX(
C XY J)= r XY(
(
(
1F( C XX(
GOT
61
I
I
J),GT„X)GOTnA?
62 N=J
KK = 1
61
CON TINUE
10? KK =
J=0
K=M
on 71
I =1 ,
IF( KK.FQ^l )0nTn71
IF( THX( I ),L T ,0)r,nTn7i
J=J+
M=J
1
THX J)=THX( T
THY ( J) -THY(T)
IF( THX( I ),, GT, XIG0T07?
GOT 071
7? M=J -1
KK = 1
71 CON T INU C
(
DFTFRMINE PRROR BAR MAGNITUDE
TF(N,P0,0)GnTOin3
OH 700 1=1 t N
CTSON( T)=FXY(I)-n ;0RT(rxY(l) -?C^,)/?0 o
CTsUP(M = FXY(n + n<;QRT(FXYfn'-?O v )/?or
7°0 CONTINUE
A
<
r
>
INITIALIZE "LOT AND
WR IT^
I
DENT
T
r
I
CAT
103 CALL PLOTS
CALL SYMBOL (0, 0, ,?°,TTTL r ^»r»l 6)
CALL PL0T(0,2.t-3)
DRAW OUTLINE n^ GRAPH
7
=
CALL PI nT(
CALL PLOT(
CALL PLOT(
CALL PI PT
(
»Y,
»Y,
,7,
tZ,
DRAW ^UTLIM C OF TITLE BOX
Bl=„^
B? = ^ ,A
84=4.6
78
I
">N
,
5=R
*=R
!
+ >!
3+,
I
ALL PI 0T{ 81 , B*,"M
ALL PLHT( *?, RR, ">)
ALL PI ~>T( R?,R4, ?)
ALL PI. OT( B1,B4,?)
ALL PI HT( R1I, R3, 2)
ALL SYMRH L(B5,B6,,14,
Tl f 0>^,3^)
5 = R 5+„ 2^
ALL Nll^RE P(B«5,B6,„14,T,0,0,3)
^ = R 54-1 „ 32
6 = R 6 + -,!
XP =
ALL NDMRP D (85,86,
J
07,FXP,0o0,-1
)
5=R
6=P
6-.1
ALL NUMRF R(B5,R6,.,14,FT ,0,0,2
5=R
6=P
6+o 2^
ALL SYMRO L
70!
)
5-2*76
(
R5
,
P6
,
,
F(N) ,EO*0)
6=B 6+o n 7
5 = R 5+„ R2
7 = R S+ 3 c ^
GDT0701
ALL PLOT
ALL PLHT
6 = B 6-. 07
(85,86,3)
(P7,RA,2)
1
4
T?
,
0,0,3^)
5 = R 5-, R?
A = B (S+o ">4
ALL SYMRP L(B5»B6,ol4,
6+,2^
ALL SYMRO L (B5,R6,,
T3,0»0,32)
6=R
1.4,
PL^T TIC MARKS
Y-,1
ALL PL
G,Y» 3
ALL PL 0T( G,H, 2)
=
1
S7n
)
= G + ,1
p <G„L F..X1G0
= X-»1
l
5
BO
TO 1S70
ALL PL 0T(G,H,3)
ALL PL 0T(G,0 o t 2)
= G-»l
F(G.GT •0. )G0 TQ 1580
o2
ALL
=
lf>70
PL
0T(G,H,3)
ALL PL QT(G,0,2)
= G+1.
F G , L T , X) GO T
1670
=Y-.2
ALL PL 0T( G,H,R)
ALL PL 0T( G,Y,?)
= G-1„
F(G,GT Oo
GO TO 16R0
(
1
690
)
= •1
= Y-,1
1
K 71
ALL PL 0T( G,H, 3)
ALL PI. 0T( 0o,H,2)
= H-»!
GO TO
F(H.GT ,0.
)
1
*71
= ,1
!5 Q 1
ALL PL GT( G , H
ALL PL 1T( X,H,
= H+.l
F(H„LT
Y)
3 )
3)
GO Tn 15B1
= X-,2
= Y-1,
79
T4, 0,0, 32)
167]
CALL PlOT(G,H f ^l
CALL PLnT(X,H ?)
?
IF(HoGT.O) OH Tn ]A7i
G-m?
H=l.
!**! CALL PLnT(G f H ">)
CALL PLGT(0,H ^>)
t
f
IF(H a LT,Y)
c
C
C
GO TT l^qi
LAB^L AXIS
CALL SYMRPL(3,5,-^ t ,}'M T TTiex f %4)
1,'56>t>14,TTTLFY,o?,,?4»
CALL SYWRnL(- e ?
e;
f
C
C
NU M RFR
ENERGY AXIS
C
1050 G=-e2P
FLO=SP
1^60 CALL NMMRPPCG, H,,l^ FLn,n,->)
f
G=G+U
IF(G GT,X)
GH
Tn
1070
FLO=FLO+XJNCP
GO TO 1^60
C
C
c
C
c
C
PLO T FXPERIMFN T AL OATA
1070 if(n,F0o0) nnmioA
CALL LINEC EXX, Eyy,
N
f
?,-M
PLOT ERROR FLAG^
nn 101 o 1=1 f \i
ES!=FXX( I >-*05
c5? = c X x( I +
r
CALL PLOT( c Sl,CTSnP( I) ,3
CALL PI nT( r S?,CTSUo( I t?)
CALL PLO T (FXX(n ,CTSUP< I ,3
CALL PLn T (EXX( I) ,CTSOM( I ),?)
CALL PL0T(FS1 ,CTSON( T) ,3)
CALL PLGT( ES?,CTSOM< I) ,3)
>
,
r>
)
)
)
1010 CTNTINU C
c
c
c
c
c
c
PLOT THEORY CURVE
104 CALL LINE(THX, THY, M, 2,11
FINALIZE PLOT
CALL PLDT(0«,,8 a ,-3)
CALL PLO T F
RFTIJRN
END
80
)
BIBLIOGRAPHY
1.
Blunck, 0., and K. Westphal
page 641, (1951).
2.
Landau, L., Journal of Physics, USSR, Vol. 8, page 201, (1944).
3.
Eyges, L., Physical Review, Vol. 76, page 264,
page 81, (1950).
4.
Bethe, H., and W. Heitler, Proc. Roy.
Vol. 146, page 83, (1934).
5.
Blunck, 0., and S. Leisegang, Zeitschrift fur Physik, Vol. 128,
page 500, (1950).
6.
Breuer, H., Zeitschrift fur Physik, Vol. 180, page 209, (1964).
7.
Bumiller, F. A., F. R. Buskirk, J. N. Dyer, and R. D. Miller,
Zeitschrift fur Physik, Vol. 223, page 415, (1969).
8.
Miller, R. D., Energy Loss of High Energy Electrons in Aluminum,
Master's Thesis, Naval Postgraduate School, (1968).
9.
Goodwin, J. C, Energy Loss of High Energy Electrons in Aluminum
and Copper, Master's Thesis, Naval Postgraduate School, (1968).
,
Zeitschrift fur Physik, Vol. 130,
(1949); Vol. 77,
Soc, London, Series
A,
10.
DeLeuil, W. R., and J. B. Raynis, Energy Loss of High Energy
Electrons in Aluminum, Copper, and Lead, Master's Thesis,
Naval Postgraduate School , (1969).
11.
Steinheimer,
R.
M., Physical Review, Vol. 88, page 851,
12.
Steinheimer,
R.
M., Physical
Review, Vol. 91, page 156, (1953).
13.
Steinheimer,
R.
M., Physical
Review, Vol. 109, page 511, (1956).
14.
Kenaston, G. W., C. T. Luke, Jr., and W. C. Sones, A Multichannel
Electron Detection System for Use in a Stabilized Magnetic
Spectrometer, Master's Thesis, Naval Postgraduate School, (1965)
81
(1952).
INITIAL DISTRIBUTION LIST
Copies
No.
1.
Defense Documentation Center
Cameron Station
Alexandria, Virginia 22314
2
2.
Library
Postgraduate School
Monterey, California 93940
2
Naval
3.
Professor John N. Dyer
Department of Physics, Code
Naval Postgraduate School
Monterey, California 93940
4.
Major Michael L. Mosbrooker
16944 Hart! and Street
Van Nuys, California
91406
5.
Major David L. Sandquist
1019 Hacker Avenue
Joliet, Illinois 60432
10
61
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body of abstract and indexing annotation must be entered when the overall report
(Corporate author)
Naval Postgraduate School
Monterey, California 93940
is
classified)
2».
REPORT SECURITY CLASSIFICATION
2b.
GROUP
Unclassified
REPORT TITLE
3
Energy Loss of High Energy Electrons in Tin, Lead, and Gadolinium
DESCRIPTIVE NO T E S (Type
4.
ol report and. inclus ve dates)
i
Master's Thesis. June 1970
AUTHORiS)
5-
(First name, middle initial, laat
name)
Michael L. Mosbrooker
David L. Sandquist
REPOR T DATE
CONTRACT OR GRANT
•a.
NO.
OF PAGES
7a.
TOTAL
0a.
81
ORIGINATOR'S REPORT NUMBER(S)
June 1970
NO.
76.
NO. OF REFS
14
N/A
b.
PROJEC
NO.
T
N/A
N/A
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this report)
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DISTRIBUTION STATEMENT
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This document has been approved for public release and sale; its distribution
is unlimited.
SUPPLEMENTARY NOTES
It.
12.
SPONSORING MILITARY ACTIVITY
Postgraduate School
Monterey, California 93940
Naval
13.
ABSTRAC
T
The LINAC at the Naval Postgraduate School, Monterey, was used to accelerate
electrons to energies ranging from 52 to 92 MeV in order to study the energy
distributions of high energy electrons before and after passing through layers of
tin, gadolinium, and lead.
The thickness of these materials ranged from 0.8 to
5.9 g/cm 2
.
The most probable energy losses agreed with the theory of Blunck and Westphal
for all materials used, while distribution half-widths agreed only for absorbers
The thickness at which theory and experiment
of thickness less than 3.0 g/cm 2
began to exhibit a noticeable discrepancy was found to be dependent on the atomic
number of the material.
.
Where comparison was possible, results of this experiment generally agreed with
the findings of similar works concluded previously.
DD
>/N
"""
t
NOV
65
1473
"T I Sj
I
OIOI -807-681
1
(PAGE
1
83
UNC1ASSTFTFD
Security Classification
A-3M0G
UNCLASSIFIED
Security Classification
key wo ROS
ROLE
W
T
Energy loss in tin, lead, and gadolinium
Half-width
Energy distribution
tost probable energy losses
*
I
NOV
69
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0101 -807-682
^t /
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UNCLASSIFIED
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A-
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27
Thesis
M8405
c.l
AUC74
22<*83
21629
Mosbrooker
Energy loss of high
energy electrons in
tin, lead, and gadolinium.
22483
7AUG74
Thesis
M8405
c.l
121629
Mosbrooker
Enerqy loss of hiqh
energy electrons in
tin, lead, and gadoinium.
1
thesM8405
Energy loss of high energy electrons
3 2768 001 91740 4
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