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N PS ARCHIVE1967GIBBONS, F.
SPACE AND ENERGY DEPENDENT
NEUTRON SLOWING DOWN TIME IN
GRAPHITE by FRANCIS W GIBBONS
Course XXII Sept 1967
V
ft SPACE AND ENERGY DEPENDENT NEUTRONr
SLOWING DOWN TIME IN GRAPHITE
by
Francis W. GibbonsEnsign, United otates Navy
B.S. , United States Naval Academy(1966)
SUBMITTED IN PARTIAL FULFILLMENT OF THE "
REQUIREMENTS FOR THE DEGRE2 OF
MASTER OF SCIENCE
at thei
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September, 1967
Signature of Author,
Department of Nuclear EngineeringSeptember, 1967
Certified by
Thesis Supervisor
/i
i
i
KTS
LIBRARYNAVAL POSTGRADUATE SCHOOL PUOUTEREY, CALIF. 93940
I
ABSTRACT
SPACE AND ENERGY DEPENDENT NEUTRON
SLOWING DOWN TIME IN GRAPHITE
Submitted to the Department of Nuclear Engineering onSeptember 26, 1967 in partial fulfillment of the requirementsfor the degree of Master of Science.
A 4 foot cube, graphit^ moderating assembly was con-structed at the M.I.T. Rockefeller Van de Graaff accelerator.Using the pulsed neutron experimental installation, a neu- .
tron burst of 200 nsec width was injected into the centerof the assembly. Prompt gamma radiation from a neutronresonance capture by an indicator foil in the moderatorwas measured, with a 3 inch x 3 inch sodium iodide scin-tillation detector, as a function of time after the neu- ;
tron pulse. The energy dependence of slowing down timewas experimentally measured by using resonance absorber
;
foils of cadmium, indium, and gold with isolated reson-ances of 0.2, 1.46 and 5*0 eV respectively. By vary-ing the distance of the foil from the source, the spatialdependence of slowing down time was also investigated.'Comparisons are made with slowing down theory. The experi- :
mental results, together with their estimated uncertainties,'are tabulated below:
tm (usee)
r(cm) 0.2 1.46 3.0
12.5 47s
. 50 + 3.00 19.75 + .50 11.25 + .25
18.0 47.25 + 2.25 19.37 + .25 10.10 + .25
28.0 47.25 + 2.25 19.00 + .50 10.87 + .25
37.5 - 20.00 + .50 11.13 + .37
44.0 - - 12.50 + .25
44.5 49.75 + 2.25 21.62 + .50
Thesis Supervisor: Franklyn M. Clikeman
Title: Assistant Professor of Nuclear ' Engineering
-3-
TABLE OF CONTENTS
1. Introduction 5
References for. Chapter 1 8
2. Theory
2.1 General '
'
9
2.2 Space Independent Slowing Down Theory 11
2.3 Space Dependent Slowing Down Theory 13
References for Chapter 2 .18
3. Experimental Equipment
3.1 General Description 19ii
3.2 The Mechanical Layout 21
- 3.3 The Neutron Source 23
3.4 The Moderating Assembly 26
3.5 Electronic Systems ,26
3.5.1 Beam Pulsing System 26
3.5.2 The Detection System 28
3.5.3 The Analyzing System 30
3.5-4- The Monitoring and Normalizing System 33
References for Chapter 3 . * 36
4-. Experimental Results and Discussion
4-.1 The Use of Resonance Absorbers as NeutronDensity Indicators 37
4.2 Performance of the Experiment 38
4-. 3 Normalization, Background Subtraction, DeadTime Correction and Smoothing 4-0
-Ci-
table OF CONTENTS (Continued)
4.4 Space and Energy Dependent Slowing Down 44Time Measurements
4.5 Conclusions 73
References for Chapter 4 78
Appendix A. Computer Program Listings
A.l Normalization, Dead Time Correction, andBackground Subtraction Code Listing • 79
A. 2 Data Smoothing Code Listing Including Normal-ization, Dead Time Correction, and BackgroundSubtraction 81
Acknowledgements • 87
-5-
CHAPTER 1
Introduction
In his.M.I.T. Ph.D. thesis, Adamant iades (l) demon-
strated that the pulsed neutron technique using a resonance
absorber as a point indicator could be used to measure sys-
tem transient effects such' as the slowing down time. He
designed- and installed an experimental installation for
pulsed .neutron experiments, and made some measurements in
water. Vaughan (2) refined Adamant aides' system, and measured
the spatial dependence of slowing down time in water for
three different resonance absorbers. Moller has carried
out extensive experiments in the field of neutron slowing
down for both light (5,4) and heavy (5) water. However,
there does not appear to be any published measurements of
the slowing down time for heavier moderators. Therefore,
in this present experiment, the pulsed technique has been
expanded to investigate slowing down time in graphite.
In the pulsed neutron method, a short monoenergetic
burst of neutrons is injected into the moderating medium
at a point. The neutrons, originally high energy, gradually
slow down by elastic collisions with the moderating medium.
If a neutron indicator is incorporated into the moderating
medium, it is possible to measure the time difference between
pulse injection and neutron arrival at the indicator. A
aac
i
-6-
time distribution is formed from many time differences,
measured under the exact same conditions./
Since most materials emit prompt gamma rays upon the
capture of a neutron, detection of these gamma rays pro-
vides one method by v/hich the time behavior of neutron
captures may be followed after the pulse. If an absorber
with a strong, isolated neutron capture resonance is incor-
porated into the moderating system as a point indicator,
then the- reaction rate of the neutron flux with the absorp-
tion resonance is proportional to the time dependent flux
at that point, for neutrons with energies equal to the
resonance energy. That is, the neutron density (or flux)
N(r,E t)
N - neutron density
r - distance from source
E - energy of absorber resonance
t - time
can be measured. Thus, variation of the position of the
absorber and the use of different resonance absorbers should
yield the time, space, and energy variation of the neutron
density following the pulsing of the assembly.
By using the M.I.T. Rockefeller Van de Graaff accelera-
tor as a source of high energy protons, high energy neutrons
7 7were obtained by the Li' (p,n)Be^ nuclear reaction. The lithium
target was located at the center of a large assembly of
graphite, thus approximating a point source in an infi-
nite medium. The accelerator beam was pulsed by an external. _'.
-7-
pulsing system after the protons had been accelerated. The
pulse width used in these experiments v/as 200 nsec. Enough
time was . allowed: to elapse between pulses so that all tran-
sient neutron effects from one pulse would die out before
the next pulse was injected. Absorber foils of cadmium,
indium, and gold, with isolated resonances located at 0.2 eV,
1.46 eV, and 5«0 eV respectively, were used to sample the
neutron flux at these energies. A detecting and analyzing
system was assembled that was capable of indicating the
time difference between pulse injection and the resonance
capture of a neutron. The most probable time difference
from injection to resonance capture was assumed to be the
neutron slowing down time for that energy at that position.
The material in this thesis is organized as ; follows:
Chapter 2 is concerned with slowing dov/n theory} the
experimental facilities are described in Chapter 3| the
performance of the experiments is described in Chapter' 4-*
and the results are presented and discussed.
-8-
References for Chapter 1
1. A.G. Adamantlades, Ph.D. Thesis, Department of Nuclear
Engineering M.I.T., (1966).
2. J.E. Vaughan, M.S. Thesis, Department of Nuclear
•, Engineering M.I. T. , (196?).
3. E.- Moller and Sjostrand, N.G., Report RFX-248,
Chalmers University of Technology, Sweden (1963)
»
Proc. Ins. Conf. Neutron Thermalization, BNL-719,
pp. .966 - '976.
4. E. Moller, Measurement of the Neutron Slowing-Down
Time Distribution at 1.46 eV and Its Space Dependence
in Water, Arkiv for Fysik, j>l, 253 (1965).
5. E. Moller, Report AE-216, Aktiebotaget Atomenergi,
Sweden, (1962).
-9-
.CHAPTER 2 i
Theory
|'
I
2.1 Genera l ^
The analytical treatment of pulsed neutron assem-
blies requires a mathematical solution of the general
transport equation. If an' expression representing the neu-
tron density as a function of time, energy, and space, and
satisfying the Boltzmann transport equation with its source
and "boundary conditions can be found, the behavior of neu-
trons in the "system can be completely described.
Unfortunately, no exact solution of the Boltzmann
equation, in all its generality, has ever been found^
but approximate solutions are available. Of these solutions,
', only-.a few may be verified because not all quantities can
be measured experimentally.
The quantity most readily measured experimentally
in the slowing down region is the neutron slowing down
time (t ). This is the time at v/hich the neutron densitym
at some energy (E) is maximum and can be found by setting
the derivative of N(r,E,t)
N - neutron density
r- distance from source
E - neutron energy
t - time •
•
.
>- 4
- .
-10-
with respect to time equal to zero.
It is also possible to measure the mean slowing down
time (<t>) which is also defined at the first time moment.
The time moments are integral quantities defined as:
^(r.v^-J^t 11 N(v,t) dt/f^N(v,t) dt (2.1.1)
lT(v,t) -neutron density as a function of space
and energy (velocity)
t - time
Both the time to maximum or the slov/ing down time,
and mean slov/ing down time may "be measured experimentally as
a function of space and neutron energy.
In this experiment, the source may be considered
isotropic and a delta function in time, energy, and space.
Although the neutron source energy does vary with the angle
in the laboratory system, this source term can be neglected
because it appears in the denominator of the expressions
for the time distributions, and it is much greater than the
energy at which the time distribution is measured. For
example, one expression for the neutron slowing down flux
in hydrogen is:
cp(v,t) = S.(vt/ys
)
2• exp(-vt/Y
s)•(l-v/v
o +2Y s/v
ot)+
2S.vo/v.5(v-v
o).exp(-v
ot/Y
s) (2.1.2)
cp - neutron flux
v - neutron velocity
S - source strength
-11-
Y - scattering mean free path
v - neutron source velocityo J
t - time
However, because v »v, equation (2.1.2) simplifies to:
cp(v,t) = S.(vt/YJ 2. exp(-vt/yj (2.1.3)
Except for positions closer than three mean free
paths away from the physical boundary of the assembly, the
spatial boundary conditions are those of an infinite medium.
For positions closer than three mean paths, leakage must
be taken into account.
In the energy region lying above a few tenths of an
eV, the nuclei of the moderating assembly can be considered• "!
i
free and at rest. For lower energies, however, the molecularI;
structure of the moderator becomes important.
Any absorption which occurs in the moderating assembly
will effect the time distribution. Those neutrons which
take longer to slow down, i.e. have more collisions, to
energy (v) will have a greater probability of being absorbed.
Thus, absorption contributes to a decrease in t . In'
.• m
graphite, the absorption cross section is very small^ and
absorption effects may be neglected.
2.2 Space Independent Slowing Down Theory
If, in addition to an infinite medium, we assume a
uniformly distributed source instead of a spatial delta
function source, the spatial dependence is removed from the
5k i
-12-
Boltzmann Equation. The equation reduces to:
.l/v-.6(p(v,t)/6t = -[s (v) + s(v)]cp(v,t) +
is ci
• Jcp(v',t).e(v'—>v) dv'+S-6(v-v )-6(t) (2.2.1)
cp(v,t) - neutron flux as a function of space and
energy (velocity)
•,' e macroscopic scattering cross section
e - macroscooic absorption cross sectiona "
. e - removal cross section
s -. source strength (n/cm -sec)
v - source energy
6( ) - Dirac delta function
Unfortunately, for a heavier than water moderator,
it is very difficult to obtain an expression for the flux,
and hence, for the slowing down time. Using a method
introduced by Marshak (1) the time moments can be obtained
exactly. A few of the moments, in terms of the moderator
mass number, obtained by Adamantiades (2) are given in
Table I, of his thesis. Once the time moments have been
determined, trial functions can be found to fit these
moments.
Marshak and vonDardel (3) suggest using the function:
<p(x) = A.x" 1+2/(l~p2)
.exp(-x-b/x) • (2.2.2)
A - normalization constant
x = vt/y where y - scattering mean free path
r = (M-m)/(M+m)
M - mass of moderator
-13-
m - mass of neutron
"b - a parameter
which gives the right asymptotic dependence for the higher
positive moments. vonDardel varies the parameter (b) with
(r) wh'ile Marshak treats it as a constant.
For heavier elements, the time dependent neutron den-
sity distribution approaches a narrow Gaussian in shape.
Thus, for heavier elements, t should approximately equal
<t>.
Adamantiades gives a complete discussion of the time
moment method in Chapter II of his thesis. He also men-
tions other methods, and gives a number of references deal-
ing with the problem of a heavier than water moderator.t:
None of these references, however, specifically give results
for graphite assemblies.
2.3 Space Dependent Slowing Down Theory
When the neutron source is localized, as in this
experiment, the effects of diffusion during moderation must
be taken into account. The problem becomes much more com-
plicated since the transport equation is now a function of
three, rather than two variables.
As in the space independent case, Adamantiades in Chap-
ter II of his thesis discusses the theoretical work which
has been done in this area. This concludes a solution by
Dyad'.kin and Batalina (4) , for the space-energy-time neu-
tron density distribution assuming no absorption, constant
-14-
scattering cross section, and isotropic scattering. The
expression involves three factors which are complicated^
and require coefficients which are dependent on the medium
being examined. The authors also give a simplified expres-
i sicn for t , which is:m*
tmax= 2Y
s/vn.(2-3u/YFT^r).
.
'
[l-2a/3.(l-puAr
rrTpl7")']"
1(2.3.1)
i>
Y - scattering mean free path
v - neutron velocity
7i - average logarithmic energy decrement
u - neutron lethargy
a - parameter which depends on the moderating medium
p - parameter which depends on the moderating medium
r - distance from source
Results are given for sand and water mixtures. /
Claesson (5) has also determined the space dependent
neutron density distribution for both a point and plane
source assuming zero absorption, isotropic scattering,
and constant mean free path. Although his method can be
extended to moderators of arbitrary mass, curves are only
given for the case of water at the indium resonance. These
curves show however, that past 10 cm the slowing down time
is strongly dependent on neutron energy at birth.
Adamantiades also develops a method of calculating,
time moments using an iterative solution of the stationary
transport equation. The nth time mpment is expressed
-15-
as
:
. <tn> = cp
(n)/cp
(0) .(2.5.2)
HcpCo)
= -S(r,v, U ) (2.5.3)
H (p(n)
+n/v.cp(n- 1}
= (2.3.4)
H = [-u^-Et+/dv'/dvL' e
s(v'—*v,v.'—»u)] (2. $.5)
r,v,ji - vectors for position, velocity and solid
angle, respectively
e. - total macroscopic absorption cross section.
Any calculational method suitable to solve the steady state
can be used to solve for the flux moments.
David Diamond, a graduate student at M.I.T., has
kindly supplied -theoretical time distributions at the gold
and indium resonances for a number of spatial points,
using the diffusion approximation. A distribution for each
foil at a distance from the source of 18 cm is shown in
Figure 2.1 (a) and (b)
.
-16-
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References for Chapter 2
1. R.E. Marshak, Review of Modern Physics, 12, 185 (194-7).
2. A.G. Adamantiad.es, Ph.D. Thesis, Department of Nuclear
Engineering, M.I.T., (1966).
5. G.F. vonDardel, Trans, Roy. Inst. Techn. , Stockholm,
75 (19540-
4. I.G. Dyad'kin and E.P. Batalina, Atomnaya Energiya
10, No. 1,5 (1961); Reactor Sci. Techn. 16, 105 (1962)
5. A. Claesson, Report AE-71, Aktiebotaget Atomenergi,
Sweden (1962).
-19-
CHAPTER 3
Experimental Equipment
3»1 General Description
The equipment necessary for measuring neutron transient
effects by the pulsed source method can be grouped into six
categories:
1) The neutron source.
2) A method for pulsing the source.
3) The moderating assembly.
4) A system for -detecting, analyzing and storing data.
5) A system to monitor the experimental equipment.
6) A normalizing system to insure consistent data.
The general layout of the experimental system showing I
the major components is given in Figure 3.1.
The neutron source consisted of a target of natural
lithium, located approximately in the center of the modera-
ting assembly, bombarded by 2.4- MeV protons to produce the
Li'(p,n)Be' reaction. The high energy protons were produced
by a Van de Graaff electrostatic accelerator. The pulsing
system electrostatically deflected the proton beam off the
lithium target, allowing it to strike the target for a short
time.
Thus, the pulse of fast neutrons produced at the target
was ejected into the center of the moderating assembly.
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These neutrons were then slowed down by elastic collisions
in the medium, and their time distribution was measured
by the detecting and analyzing system. This system con-
sisted of the conventional detector-preamplifier-amplifier
array, plus electronic equipment for pulse height discri-
mination and tine analysis combined with a multi-channel
analyzer to store the data. There was a common link betv/een
the pulsing and the analyzing system which provided a zero
time reference.
The monitoring system was used to control the perfor-
mance of the pulsing system, and thus to optimize the quality
of the neutron pulse. The normalizing system yielded the
time integrated neutron flux for each experiment performed.
This information was necessary to properly carry out back-
ground subtraction.
A more detailed description of the experimental equip-
ment will be given in the sections to follow.
3.2 The Mechanical Layout
A plan view of the mechanical layout of the system is
given in Figure 3*2. Only a brief description of the sys-
tem will be given here since a thorough, detailed descrip-
tion of the system will be given by Adamantiades (1), who
actually constructed the system.
Since the experimental apparatus, was positioned on
the floor below the accelerator, the protons were accelerated
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downward and bent into the horizontal bean tube by a bend-
ing and 'analyzing magnet. The beam tube was kept under a
high vacuum by the diffusion pump of the accelerator, and
by a small Vac Ion pump located close to the target.
The deflecting plates delivered a high voltage pulse
which deflected the beam. The water-cooled chopping slits
were mounted after the deflection plates for the purpose
of intercepting the beam when it was swept off the target.
The distance between the slits, the shape of the high vol-
tage pulse, and the deflecting plates configuration deter-
mined the shape of the pulse reaching the target.
A remotely controlled pneumatic shutter valve was
interposed between the chopping slits and the target.
The beam could thus be cut off from the target, enabling
work to be done around the assembly. The target tube itselfi
was constructed of aluminum and was 23 inches long, 3/8i
inch O.D., with a 1/16 inch wall thickness. The targeti
assembly was located at the end of the target tube.
It was decided to cool the target in order to protect
it from deterioration. This was done by sealing the end cap,i
which presses the target disc directly against the O-ring
vacuum seal, with a plate into which short lengths of tubing
had been brazed. (See Figure 3. 3) V/ater' forced through
the cap removed the heat from the target disc.
?j
3.3 The Neutron Source-
As in previous experimental measurements of neutron
sfe,
.. a»iti-.gB»avg.j
-24-
-2
slowing down time (1,2), the Li'(p,n)Be' reaction was used
as the neutron source mainly on the basis of its high
yield and relatively good homogeneity. For a given. angle
from the target and for laboratory proton energy up to 2.34-
MeV, the reaction is monoenergetic. The threshold of the
7 7^fLi'(p,n)Be' reaction is shown in Figure 4.6 of Adamantiades'
thesis. Because of neutron intensity considerations,' a
proton energy of .2.4 MeV was used in this experiment.
The target used in these experiments consisted of a
layer of natural lithium 0.8/cui2
thick deposited through
evaporation on a circular tantalum disc 0.055 inches thick
and 13/16 inch in diameter. Although the thickness of the
target is less than 1/10 of the range of 2.5 MeV protons
in lithium, some protons will undergo slowing down colli-
sions before undergoing nuclear reactions. The energy
spread of the actual beam of protons incident on the tar-
get, however, is very small in the Rockefeller Van de Graaff
accelerator.
To summarize, there were three major sources of neutron
energy inhomogeneity in this experiment:
1) Angular dependence of neutron energy.
2) Excited product nucleus reaction.
3) Energy spread of the reacting protons.
As mentioned in section 2.1, this energy inhomogeneity
could be tolerated since the slowing down time is relatively
insensitive to the source energy.
c
•26-
3.4 The Moderating; Assembly
The moderating assembly (see Figure 3«4) consisted of
reactor-grade graphite stringers, approximately 4.0 inches
by 4.25 inches and 4.0 feet long, stacked so that alternate
JLayers were at right angles to each other. The overall
dimensions of the assembly was 3.6 feet by 4.0 feet by
4.0 feet. The entire assembly was covered with aluminum
foil to shield the monitoring and detection, systems from
R.F. pickup coming from the pulsing system, although this
pickup was never entirely eliminated.
In a stringer located at the center of one face of
the pile, a hole was bored so that the target, along with the
cooling water tubes and the cables of the monitoring sys-
tem, could be inserted into the center of the assembly.
"At a right angle to, and on the same horizontal plane
as the beam tube was an open channel, 4.0 inches wide,
4.25 inches high, and 19.3 inches long, which led from the
target to one face of the assembly. It was through this
channel that the detector, foil, and graphite spacers were
inserted or removed (see Section 4.2).
3.5 Electronic Systems
3.3«1 Beam Pulsing System
Although the Rockefeller accelerator has a terminal
pulsing capability, its single sweeping frequency was much
too high for this experiment. Therefore, a post-accelera-
tion system was used which had the advantage of a variable
-?27-
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pulse width and repetition, rate (see Figure 3.5). A
detailed discussion of the system is given in Reference (1).
A repetition rate of 2kc/sec was used, allowing 500 usee
between pulses, which was enough time to allow all tran-
sient neutron levels to die out. A pulse width of 200 nsec
was used in this experiment.
The pulsing system was triggered by the general Radio
wave generator (type no'. 1217-A) , which was also used to
start the timing circuits of the analyzing system (see
Section. 3. 5«3) • The output pulse of the G.R. pulser'
triggered an E-H Research Laboratories Model No. 130 pulser.
The variable width output pulse of the E-H pulser was
the input for the driver circuit which is essentially a
pulse amplifier. An extensive discussion of the driver
circuit is given by A.E. Waltar' (3)» who designed it.
Vaughan modified the circuit somewhat to give a narrower
pulse. In this experiment the driver circuit delivered a
2.9 KeV pulse to the deflection plates.
3>5»2 The Detection System
The object of these experiments was to detect neutron
capture gamma rays as a function of time, so an efficient
gamma-ray detector was required. A Harshaw Integral Line
Scintillator Assembly, consisting of a 3 inch x 3 inch
Nal(Tl) crystal attached to a 6363 DuMont photomutiplier
tube, was used. The crystal and tube are hermetrically
sealed within an aluminum housing, making the detector
-29-
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a sin: plug-in unit. A thermal neutron shield, consisting
of 3 mm. thick boron carbide enclosed "by aluminum, was pro-
vided to' keep activation of the sodium at a minimum.
The solid state preamplifier, v/hich plugged into the
-end of the detector assembly, was designed and built in a
cylindrical can having the same diameter as the detector.
Vaughan gives a schematic diagram of the preamplifier in
Figure 4.6 of his thesis.
The high voltage for the phototube was provided by
a 2 KV power supply, while the preamplifier was powered by
a small solid state power supply. The entire detector
'was wrapped in -aluminum foil, and all leads to and from
the detector were enclosed within copper braid to eliminate
R.F. pickup. .
$.5.3 The Analyzing; System
The main features of the time analyzing system were:
1) A start pulse providing a time reference, derived
from the beam pulsing, network.
2) A stop pulse indicating the time at which an event
of interest took place, derived from the detector.
3) A timing unit, used in conjunction with a multi-
channel analyzer, which produced a count in the channel
corresponding to the time interval between the arrival of
the start and stop pulses. Conventional, commercially
available equipment was used in the entire analyzing system
(see Figure 3.6)
.
-31-
10 VPov/erSupply
2 kVPov/erSupply
\'
Pre ampCrystal
andPhototube\
\ / \ /
Ortec410
Amplifier
Ortec410
Amplifier
GeneralRadioTrigger
0/7 000
V ' \ / \ / i: N/
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TMC Model 211 Time ofFlight Logic Unit
TMC Model CN-110256 Channel Pulse Analv-
•
Pigure 3»d Analyzing System
32-
The start pulse was obtained from the General Radio
trigger (see Section 3. 5.1). This pulse was fed through
a General Radio 1392-A Time Delay Generator which provided
a stable, variable tine delay. Unfortunately, the .output
pulse of the G.R. delay was too narrow to trigger the tim-
ing unit', and an integrating circuit was employed to
stretch the pulse.
The detector output signal was fed to two Ortec 4-10
Strobbed Discriminator, with the strobe input coming from
an Ortec 40? Zero Cross-over Pickoff Unit. The cross-
over pickoff v/as fed by the other Ortec 4-10, whose time con-
stants had been optimized for a stable cross-over point.i
A positive logic signal was provided by the discriminator !
i
when the incoming detector signal met minimum energy require-i
ments. The strobe assured a constant time relation between
the detector input and discriminator output. The positivej
logic pulse was attenuated by a resistor network before iti
was fed into the timing unit.
The timing unit consisted of a TMC Model 211 Time of
Flight Logic Unit which plugged into the TMC Model CN-110
256 Channel Pulse Analyzer. The 211 unit converted the time
difference between the trigger input and a detector signal
to an appropriate channel number, depending on the scale
factor which could be varied from 0.25 to 64. p.sec/channel.
This information was then stored in the multi-channel analy-
zer.
The TMC 211 Unit could handle more than one stop pulse
•33-
(detector signal) per cycle. However, 16 y/sec were
needed to analyze an L record each incoming signal. A
correction for this deadtime was included in the computer
program used to process the data (see Section 4. 3). More
de bailed information on the 211 unit and the multi-channel
analyser is give?n in Reference (4-).
3.5.4- The Monitoring and Normalizing System
To insure that the pulsing system was operating under
the best possible conditions at all times a beam pulse
monitor v/as provided.
The beam pulse monitor was necessary due to the pro-
blem of focusing the proton beam from the accelerator.
Because of various changes and drifts in the accelerator,
the setting for optimum focusing changed from day to day,
and had to be constantly adjusted. In pulsed operation,
the only practical method of focusing was to use an electri-
cal signal from the target itself and to observe the signal
with a fast oscilloscope. The system employed is sketched
in Figure 3.7. Notice that the target was insulated from
the beam tube with a glass ring which enables the signal
to be picked off the target. The monitoring system was
especially susceptible to R.F. pick-up from the pulser.
All cables of the system were shielded against pick-up^
but the 'problem was never completely eliminated. A typical
target puis") can be seen in Figure 4.11 of Vaughan's thesis.
The electronic pulse being delivered to the deflection platen
i
/
34-
Tektronix53$ oscillo-
scopeK plug-in
Control area
Experiment area
Probe
-F=V
Glass Insulation
Pi
Tektronix583 oscillo-
scopeL plug-in
200 ri
200 -n.
460 ARHewlett Packard
Amplifier
;7
)
460 AE
Hewlett Packard
Figure 5-7 The Monitoring Systems
35-
could also 1 ' litored.' This system, is also shown in
Figure 3»7«
A neutron monitor was used as a means of normalization
for comparing different runs and subtracting background.
A detailed discussion of normalization is given in Chapter
5 of Reference (1). As in previous experiments, this author
concluded that total neutrons produced during an experiment
would be the most reliable quantity to use of normalization.
A boron triflouride counter was placed between the graphite.
stringers of the assembly about 13 inches from the target
and on the side opposite the absorber foil and detector.
Thus, with the output 'of the BF^. tube going to a scaler,
the time integrated neutron • flux as seen by the detector
could be reco, led.
•36-
References for Chapter 3
1. A.G. Adamantiad.es, Ph.D. Thesis, Department of
Nuclear Engineering M.I.T., (1966).
2.' J.E. Yaughan, M.S. Thesis, Department of Nuclear
Engineering M.I. T. , (1967).
3. A.E. vYaltar, S.M. Thesis, M.I.T., Department of
Nuclear Engineering, (1962).
4. Transistorized Multi-Channel Pulse Analyzer System
Model CN-110, Technical Measurement Corporation,
• North Haven, Connecticut. j-.
-37-
CHAPTER 4
Experimental Results and Discussion
•4.1 The Us e of Resonance Absorbers as Neut ron Density
Indicators
Resonance absorbers were used in this experiment to
sample neutron population' at the resonance energy. The
most suitable materials for this purpose are those .which
exhibit a strong isolated absorption resonance. The
higher and narrower the resonance, the better it approxi-
mates a delta 'function. Table II of Reference (1) gives
a list of absorbers which exhibit strong isolated reson-
ances. The energy and peak cross section of the reson-
ance" is also given.
Another important consideration in choosing a suit- :
able absorber was its prompt neutron capture gamma-ray
•spectrum. This did not prove to be a problem since the
de-excitation gamma rays of most materials are spread
over a wide range of energy. Reference (1) gives capture
gamma-ray spectra for the three absorbers used in these
experiments: cadmium, indium, and gold. The capture gamma
spectra of these materials extends from the KeV region
to energies exceeding 7 MeV.
Indium and gold were chosen for their strong isolated.
resonances at 1.46 eV. and 5*0 eV respectively. Cadmium,-
•38'
broad resonance that reaches a maximum at
: about C.2 eV, was also used, although it was expected that
the time- resolution for these measurements v/ould not be
as good as that for indium and gold.
4.2 Performance o f the Experiment
In order to insure a constant geometric relationship
between the foil and detector, a foil holder was used.
The fori holder consisted of a one inch thick slab of gra-
phite, which was^sized to fit into" the channel of the assem-
bly and was bonded to the end of the detector with epoxy
cement. The foil was taped to this slab, and the whole
detector-foil array was inserted into the graphite assem-
bly through the channel (see Figure 4.1). n
To measure the spatial dependence of the slowing down
time, it was necessary to be able to move the detector-
foil array along the channel. Graphite slabs of varying
thickness, which v/ere inserted in the channel between the
source and foil, assured that there would always be solid
moderating material in front of the foil.
Before performing the actual experiments, short- runs ,
were made while varying the discriminator of the Ortec
413 Strobbed Discriminator. For each foil, the discrimin-
ator setting which resulted in the best foil counts to
background .counts ratio was determined.
A typical set of experimental data is shown in Figure
4.2(a). .These results are for a 7 cm x 7 cm x 0.05 cm gold
«:..-
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foil positioned 28 cm away from the target. The beam
pulse width was 200 usee,, and the time interval between
bursts was ^>Q0 usee. The channel width was 2^0 nsec.
A time distribution with the gold absorber in place was
taken, and a distribution without the absorber was taken
immediately afterwards. The BF-, counts for the gold foil
was 251,111 and for the background was 259,992. Notice
the very prominent peak around channel 20. This peak is
called t.he prompt peak and occurs when the burst of pro-
tons hits the lithium target. This peak was used as an
accurate zero time reference in the experiment. The right
half of the graph (notice the change of scale) shows the
region in which the most probable slowing down time occurred
No peak is discernible from the raw data.
4.3 Normalization, Background Subtraction, Dead Time
Correction and Smoothing
As mentioned in Section 3«5«4, the time integrated
neutron flux, as derived from a BF-, tube, was used for
normalization. The number of 31? counts registered by
the scaler was recorded for each experiment. A factor
obtained by taking the ratio of background-run BF^ counts
to foil-run BF-, counts was aoolied to the foil data.
In order to obtain the net effect of neutron cap-
tures in the foil, the counts originating from all other
events must be subtracted when the time distribution is
taken. These sources of parasitic gamma rays include:
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-42-
1) Inelastic scattering by the target, the absorber
foil, and the detector.
2) Absorption in materials other than the absorber*
foil.
3) Reactions coincident with the neutron burst.i
4) Overlapping events from preceding bursts.
5) Steady state background.
All these items were taken into account by taking
a time distribution without the absorber foil in place,
and then subtracting it from the distribution taken with
the foil.
As mentioned in Section 3»5»3i there was a 16 "usee
dead time associated with each count registered in the
multi-channel analyzer. In Appendix C of Reference (2)
,
a theoretical discussion of the dead time correction for
the TMC Model 211 Unit is presented. The correction fac-
tors derived in that reference were used in this thesis.
Computer programs which normalized, subtracted the
background, and applied dead time corrections to the raw
data are listed in Appendix A.
Figure 4.2(b) shows the time distribution resulting
from processing the raw data in Figure 4.2(a)'. It is
obvious from this graph that there is a maximum in the
time distribution occurring roughly at channel number 60.
It is also obvious, however, that the fluctuations in the
curve prevent an accurate determination of the maximum
point. To reduce this uncertainty, a computer program
/
/
-43-
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at M.I.T. (3)' which applied a smoothing tech-
nique to the corrected data was used. Effectively, the
program -fits a Fouier series curve to the data points.
Smoothing is accomplished by choosing not to fit the ser-
les toj&igh frequency waves, which correspond here to sta- .
tisticfu fluctuations. The frequency . cutoff , above which
all hiwher frequencies will be thrown away, is under the
contriJr of the programmer. Thus, any desired degree of
smooti"»rg can be effected to a set of data points. In
this experiment, all frequencies less than four channels
wide were dropped. Figure 4.2(c) is the smoothed version
of Figure 4.2(b). Using this smoothed distribution^ it
was estimated that the maximum point of the time dis-
tribution occurred in channel 62.5+1. Since the prompt
peak is in channel 20, the slowing down time is: (43.5+1)
x (.25 ]isec/channel) = 10. 87+. 25 usee. The smoothing
program is listed in Appendix A.
4.4 Space and Energy Dependent Slowing Down Time Mea-
surements
If various absorbers with resonances located at
different energies are used and if the distance of these
absorbers from the source is varied, the time dependent
neutron distribution can be measured as a function of
space arid neutron energy.
Figures 4.3 to 4.6 represent time distributions to
the cadmium resonance', Figures 4.7 to 4.11 represent time
-45-
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distribution to the indium resonance^ and Figures 4.13
to 4.16 represent time distributions to the gold reson-
ance. In each Figure, (a) represents the distribution
before smoothing and (b) after smoothing. Notice that
the scale for the cadmium curves is 500 nsec/channel
,
while it is 2f?0 nsec/channel for the indium and gold
curves.
The- results. of this experiment, together with their
probable errors, are graphically presented in. Figures
4.17 to 4.19. The experimental uncertainty associated
with each point reflects the broadness in the time dis-
tribution- around the maximum value. As expected, the
peaks of the cadmium distribution were much broader than
those of gold or indium'. The solid line in the gold and
indium figures has been constructed from theoretical time
distributions (see Section 2.3), based on diffusion theory
(4).
The experimental results for. the slowing down time
to 5«0 eV appear to be in good agreement with the theo-
retical calculations. The agreement with theory for
1.46 eV is not as good. The experimental results indi-
cate that there is little, if any, spatial dependence of
the slowing down time for distances closer than about
30. cm from the source. For distances greater than 30 cm,
the experimental results show a sharp rise in t with dis-m
fcance, indicating a strong spatial dependence. Theore-
tical calculations do not predict as sharp a rise of
-47-
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-73-
t as shown by the experiments.
This disagreement "between theory and experiment was
probably due to the breakdown of the infinite medium
boundary conditions, since the foil was only 9 cm from
the outer edge of the assembly at the last spatial point.
The absence of moderating material surrounding the foil
meant that the neutrons took a longir time to slow down
to a given energy. More measurements need to be taken
at greater distances to resolve this question.
A few measurements were made with the detector separ-
ated from the foil by about 10 cm of graphite in order
to determine if the perturbation caused by the detector
had any effect on the slowing down time. These ^.results
are marked by triangles in the Figures. It can be seen
that, the gold and cadmium results agree, within the limits
of experimental uncertaintity, with previous measurements.
The indium point, however, falls far- below the original
measurements. The author can give no explanation for the
contradiction of this" point with either the original results
for indium or the close agreement between the first and
second measurements for the gold and cadmium. Further
measurements, with the detector and foil separated, need
to be performed to clear up this contradiction.
4-. 5 Conclusions
There was some agreement between the spatially depen-
dent slowing down time measurements made in these experi-
ments and theoretical calculations using diffusion theory.
• 74-
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-77-
No measurable spatial dependence of the slowing down time
was observed for distances less than 30 cm. Spatial depen-
dence was observed for distances greater than 30 cm, although
this dependence was much more promounced in the experiments
than predicted by slowing down theory. More space depen-
dent measurements at distances greater than 4-4- cm should
be made in a larger graphite assembly to determine the
true spatial dependence. Measurements to determine 'if
the perturbation of the detector had any effect on the
slowing down time were inconclusive and should be repeated.
-73-
References for Chapter 4-
1.- A.G. Adamantiades, Ph.D. Thesis, Department of
Nuclear Engineering M.I.T., (1966).
2. S.G. Oston, Ph.D. Thesis, Department of Nuclear
Engineering M.I. T. , (1966).
3. T. Inouye and N. C. Rasmussen, A Computer Method for
the Analysis of Complex Gamma-Ray Spectra, Trans-
actions of the American Nuclear Society, Illinois,
10 (1967).
4. D. Diamond, private correspondence, September
(1966).
•79-
Appendix A. Computer Program Listings
A.lC FORMALIZATION, DEAD TIME CORRECTION, AND BACKGROUNDC SUBTRACTION CODE LISTINGC
DIMENSION T8M(2 55),CHAN(255) , BACK { 255 ), FOIL! 255) f ANORM( 255 )
,
1C8ACK(255),CF0IL(255),X(255) , Y ( 2 55 ) , TBAC 20 6 ) , ACHAN t 206) ,B{800)COMMON TBM, CHAN, WIDTHEQUIVALENCE(TBM(50J t TBAtl)!t ( CHAN ( 50 ), ACHAN ( 1 )
)
READ 2 00, WIDTH200 FORMAT(F6.2)
READ 99,8C0UNT,FCQUNT99 FORMAT <2F 10.0) /
NUM=0 /
103 NUM=NUM+1READ 100, (BACKt I ) ,1 = 1,255;
100 FORMAT (3X,10F7.0)READ 101, (FUIKI ), 1=1, 255)
101 FORMAT (3X,10F7.0)READ 98,3BUR,ABUR i
98 FORMAT 12F10.0)PRINT 701,BC0UNT,FC0UNT
i
701 FORMAT (3X,2F10.0>PRINT 100, (BACKd ) ,1 = 1,255)PRINT 101»IFOILU ), 1 = 1, 255)PRINT 702,BCUR,ABUR
702 FORMAT 13X,2F1Q.Q)L = -l
420 L = LHIF ID419, 419,417
419 DO 418 1=1*255'\
\
418 X( I )=BACK(I)BUR=BBURGO TO 415
417 DO 416 1=1,255416 X(I )=FOIL(I)
BUR = ABUR :.\, !
415 0UM = 1.6. /WIDTH •
'
N = DUMYM)=BUR*LQGF(BUR/(BUR-X(1) ) )
\
SUM=0.,
DO 610 I=2,NSUM=SUM+X( 1-1) •
i
-30-
610
615
414413
412All
906
306
50
Y{ I )
SUM =
NMDQ 6
Y(I)K = I-
SUM =
IF {
DO 4
CBACGO
DQ 4CFOIi = BCDO 9
AN ORTBM(CHANCONTprinFORM
= BUR
15 I
=our<
N
SUM +
LJ4113 I
K( I )
TO 4
11 I
L( I )
OUNT06 I
MmI)=A(I) =
INUET 30AT I
»L0GF( { BUR-SUM) /(BUR-SUM-XI I)) )
X t N
)
=MM,255»L0GF( ( BUR-SUM) /(BUR-SUM-X( I )>
)
X(
I
)-X(KJ4,414,412=1,255=YU)20=1,255= Y(I)/FCOUNT=1,255= Z»CFQ[L(I )
NORM (I J-CtJACK(I)floa'tfu)
6, ITBM(I), 1=1,255)1H ,10F10.1)
CALCOMP ROUTINES
CALL PL0TS1(B,800)CALL SYM3L5(3.0,9.0,D.2,20H ID NO. = M3994-5788, 0. , 20
)
CALL NUMBRl{4.0,8.5,0.2,NUM f 0«.t-UCALL PICrUR[8.5,4.2,15H CHANNEL NUMBER,15,19H COUNTS PER CHANNEL , 19, ACHAN, TBA, 206, 0. , )
END FILE 10
700
READ 99, 3C0UNT, FCOUNTIF (BCOUNT)700,700,103CALL EXITEND
-01 -
A.
2
C
C
c
DATATIME
SMOCOR
OTHING CODERECTI ON, AND
LISTING INCLUDING NORMALIZATION, DEADBACKGROUND SUBTRACTION
200
102
201
205
203
99
103
100
101
98
701
702
420
419418
417416
OlMENSIO1XC0S413728ETA(75)3CBACM25COMMON T
UIYALEREAD 200FORMAT {
READ 102FORMAT (
PRINT 20FORMAT (
15H CRT=,PRINT 20FORMAT (
PRINT 20FORMAT (
READ 99,FORMAT {
NUM-0NUM=NUM+READ 100FORMAT {
P.E\D 101FORMAT (
READ 98,FORMAT (
PRINT 70FORMAT (
PRINT 10PRINT 10PRINT 70FORMAT {
L=-lL=L+1IF U)41DO 418 I
X(I )=BACt=BBUR
GO TO 41DO 416 I
I )=FOIBUR^ABUR
N TBJ,TB,GAM5) ,C8N,XNCE(tlW,I 4 , E
, IWT12F61 , I W
1H1,F6.05
1H ,
3 , I W
1M ,
BCQU2F10
N(37MI 25MA (7
FOILS IN
,
tb:<{
OMEG10.4(I),.3),OME9H N
tiX,
GAH,-OME8H F
CRT, FACTR, WIDTHGA=,I4,1X,9H D-QMEGA=,E1Q.4,1X,ACT0R=,F6.3,7H WIDTH=,F6.2)
20X,16HTf 11,1*15E15.7)NT,FCOUN.0)
WEIGHT> IW>
FUNCTION)
, [BACKCI > t 1=
3X,10F7.0),{FOILU) ,1=3X»10F7.0JBBURf ABUR2F10-0)1,BC0UNT,FC03X,2F10.0)0, (BACMI) ,1
1, (FOIL* I ) ,1
2,B8UR,ABUR3X,2F10.0)
9,419,417=1,255K[ I)
5
=1,255LCI)
1,255}
1,255)
UMT
=1,255)=1,255)
.*
-82-
415
610
615
4L4413
412411
905
902901
903
906
DUM =
N = DUYd)
DO 6
SUM=y •:
i )
SUM =
NM00 6
Yd
)
K=I-SUM =
IF {
on 4
CBACGO
DO 4
CFOIDO 9
YKAKXCOSCONTDO 9
DO 9
XKAKSEIGCONTCONTDO 9
ALPH1C0SFBETA
1SEIGGAMMCONTDQ 9
Z = 3C
TBM(CONTDO 1
16'I
= B
0,
10
su— p
su
=N15= B
N
SU
L)
13
K(
TO11
L(
05U441
IN
0102U=ENIN
Ih03A{
A{
(T
(J
EN'
IN
06OUHi
I)
IN
./WIDTH
UR*.LOGFIBUR/(BUR~Xm )
)
1 = 2, NM + X( I- I)
LOGF{ (BUR-SUM) /{BUR-SUM-Xt I ) )
)
H*-X(NJ«]
I=NM,255UR*LOGFl (BUR-SUM)/(BUR-SUM-XU ) )
)
M+X{ r )-XlK)414,414,4121=1,255
I )=Y( I
)
4201=1,255
I)=Y(I)1=1,37
=C"EGAH*FL0ATF(IW-1)»FL0ATFU)I )=C0SF(YKAKU4)UE1=1,37J=1,IW
OMEGAH*FLOATF { I ) *FLOATF{ J-l
)
(I, J)=SINF(XKAKU)UEUEJ=1,IW
J ) =ONEGAH*FLOATFl J-l
)
JI=THETA{ J)**l-3)*ITHETA(J)*«2*THETA{ J ) »SEIGEN C
1
, J
HETA(J))-2.*SEIGEN(1.J)«*2))=2.*THETAIJ)»*(-3)*(THETA( J)*(1.*C0SF(THETA( J) )**
U,J)*COSF{THETAU)) )
J)=4.*THETA(J) »*t-3)*(SElGEN<l f J)-THETA( J)*C0SFITHUE1=1,255
NT/FCOUNT '
.
n-z»CFoiLm=ANORM(I)-CBACK{I J
UE1=1,27
i
2)-2.*
ETAU) )
)
-83-
90 \
511
517
DO 904YKAKU1YKAKUXCQSKXC0S21CO NT IN
5 1
1
YA=ALP
YOGAMSXG4=0sicDO 1 N
SIG3=SDO 2 N
SIG4=SXA=YA*XSINUCONTINDO 517YA=ALPYB=BETYC=GAHSIG^OSIG3=0NY=IW-DO 3 N
SIG3=SNY=IW-DO 4 NSIG4=SXAOMEIN=IXTSK.i IN
CHANt
I
CONTINDO 914YKAKU1YKAKU2XCOSKXCOS2(
J=1,IW= 0,MEGAH*FLDATF(J-1)=27.»YKAKU1J)=COSF(YKAKUI)J)=C0SF{YKAKU2)UE1=1, IWHAinA( I )
MAI I )
«5MTBNm*SEIGENU,I)+TBNI27)*SEIGEN{27,I>)N=3,25,2IG3+TBN(NN}»SE!GENINN,I)N=2,26,2IG4 +TBN(NN)»SElGEN(N.M,n '
(T8N{1)»XC0S1( I)-TBN(271*XC0S2( I ) ) *YB»S I G3*YC*S I G4J=XA*WT(I)UE li
IX=1,16HA(IX*1)A( IX+1)MAUX+1)
.5*IXSIN(1) *SEIGEN(IX, U + XSINl I W
)
*SE I GENt IX, I W ) )
2
N=3,NY,2IG3+XSIN(NN)*SEIGENCIX,NN)1
N=2,NY,2IG4+XSIN(NN)*SEIGENl IX,NN)GAH»iYAMXSlNt l}-XSINUVn*XC0S4(IX) ) +YB*SIG3+YC*SI G4 )
)=Q.63662*XAN)=FLQATFC IN)UEJ = 1 , I W
=OMEGAH*FLOATF(J-l)=37„«YKAKU1J)=C0SF(YK4KU1)J)=C0SF(YKAKU2)
-84-
914
525
521
527530
535
c o n r i ^DO 530DO 525K-16«(TBN1 I )
DOYA=ALPYB =
YC=GAMSiG4=0
3 =
DO 5 N
SIG3=SDO 6 N
S1G^=SXA=YA*XSIN{ I
CONTtNDC 5 27YA=ALPYB=BETYC=GAMSIG4=0SIG3=0NY=IW-DQ 7 N
SIG3=SNY=IW-DO 3 NSIG4=SXA-QMEIN=16»TBxt IM
CHAN t
I
CONTIMTIN
DO 535K=230+I ::
-85-
92'+ CONTINUEDO 531 1 = 1, I
W
YA=ALPHA(I)YB-BETAU)YC =GAMMAU)SIG'^0.SiG3 = 0.5*{TBN(l) »SEIGENU,I)«-TBN(25)*SEIGEN{25,I 5 )
DO 9 NN=3,23,29 SIG3=SIG3+TBN{NN)«SEIGEN(NN,n
DG 10 NN=2,2Vt 2
10 SIG4=SIG4+TBN(NN)*SEIGEN(NN, I)XA = YAMTBNC 1)«XC0S1U ) -TBN { 2 5 ) *XC0S2 ( I) ) «-YB*S IG3*YC*SI G4XSINU>=XA*WT<I)
531 CONTINUEDO 537 IX=ll,25YA&ALPHA1 IX+1)
A IX+1)YC=GAMMA(IX+1)
j
SIG4=0.SiG3 = 0.5*{XSINll)*SEIGENMXf 1)*XSIN( IW)*SEIGEN( IX, IW) )
NY*lW-2DO 11 NN=3,NY,2
' 11 SIG3 = 5IG3 + XSIN{NN)*SEIGENUX f NN)NYsIW-1DO 12 NN=2 t NY,2 !
12 SIG^=SIG^+XSIN(NN)*SEIGEN(IX,NN)j
XA =0MEGAH*IYAMXSIN{1>-XSIN(IW)»XC0S*IIX) ) + YB*S I G3*YC*S I G4
)
IN=23Q+IX I
TBK( In)=0.63662*XACHANUN)*FLOATFtIN)
53 7 CONTINUEPRINT 307
307 FORMAT (1H1,1SH SMOOTHED FUNCTION)PRINT 306, ITBXil ), 1=1, 255)
306 FORMAT UH , 10F10.1)C
C CALCOM? ROUTINESC
50 CALL PLOTS! (Br 300)CALL NUMBRH<r.0,8.5,0-2tNUM,0. ,-1)
LL SYMBL5I3.0,9.0,0.2»20H ID NO. = M3994-5788, 0. , 20
)
CALL PICTUR(8.5,4.2, 15H CHANNEL NUMBER,115.28H SMOOTHED COUNTS PER CHANNEL , 28 , ACHAN, TBA, 21 6, 0. , )
END FILE 10C
READ 99tBC0UNT,FC0UNTIF tBCOUNT) 700,700,103
-85-
700 CALL EXITEND
-87-
Acknowle&gements
This thesis was made possible through support by the
National Science Foundation of the M.I.T. Rockefeller
Generator Group, the direction of which was shared by
Dr. Leon Beghian and Professor Franklyn Clikeman. The
author wishes to express his deep appreciation to Pro-
fessor Clikeman, who was the supervisor of this thesis.
Thanks- go to Mr. James Vaughan for his helpful advice
and assistance with the experimental equipment and com-
puter programs}" to Mr. Daniel Sullivan v/ho operated the
accelerator and contributed his years of valuable exper-
ience to the experimentJ
and to Mr. Anthony Luongo for
preparing the lithium target } and Mr. Vernon Rodgers,
who also operated the accelerator.
The author is grateful to his wife, Carlene, for
typing the thesis', for preparing the diagrams} and last
but not least, for her moral support.
The author gratefully acknowledges a Special Fellow-
ship in Nuclear Science and Engineering granted him by
the United States Atomic Energy Commission through its
contractor, the Oak Ridge Associated Universities.
F.W.G.
C amb r i d g e , Massachusetts
September, 1967
thesG373
Space and energy dependent neutron slowi
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