Title: Proton radiative capture by tritium below 30 MeV
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00099393/00001
 Material Information
Title: Proton radiative capture by tritium below 30 MeV
Physical Description: vii, 93 leaves : ill. ; 28 cm.
Language: English
Creator: McBroom, Robert Chism, 1947-
Copyright Date: 1977
Subject: Tritium   ( lcsh )
Protons -- Capture   ( lcsh )
Physics thesis Ph. D
Dissertations, Academic -- Physics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Statement of Responsibility: by Robert Chism McBroom.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 87-92.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00099393
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000207918
oclc - 04080406
notis - AAX4722


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This project was conducted under the guidance of

Dr. H. R. Weller. His patience and direction are deeply

appreciated. A special thanks to Dr. N. R. Roberson and the

members of the Duke Capture Gamma Group for the privilege of

working with them. The author is especially grateful for

the Group's assistance with the acquisition of the experi-

mental data. Thanks to Dr. C. P. Cameron for the use of

some of his computer programs. Also, thanks to Mrs. M.

Bailey for her care in drafting the figures, Mr. D. Turner

for the photography, and Mrs. J. Ogden for the typing. The

author is thankful to Mr. D. C. Pound and The General

Atomic Company for their support during the final stages

of the dissertation.

Financial support for this study was provided by the

University of Florida.

Final and most heartfelt thanks to the author's

wife, Mrs. Karen McBroom, for her love throughout all the




LIST OF TABLES . . . . . .

LIST OF FIGURES . . . . . .

ABSTRACT . . . . . . . .

INTRODUCTION . . . . . . . . .




Experimental Details . . .
Experimental Data . . . .

III. DATA ANALYSIS . . . . . .

Kinematics . . . . . .
Excitation Curve Analysis . .
Angular Distributions . . .
Results . . . . . . .


APPENDICES . . . . . . . . .

A . . . . . .

B . . . . . .


BIOGRAPHY . . . . . .


S . . . . 85

. . . . 87









Table Page

1.1 4He Photodisintegration Reactions . . .. 11

1.2 Sum Rules for 4He and Their Shell Model
Representations . . . . . .. 13

1.3 He Experimental Studies . . . . .. 16

1.4 Relations Between the Legendre Polynomial
and Sin 6, cos 6 Angular Distribution
Expansions . . . . . . .. 26

2.1 Measured Differential Cross Sections . . 47

3.1 Direct and Resonance Strengths of E2
Interactions . . . . . . ... 70

3.2 ai Coefficients of Measured Angular
Distributions for 3H(p,y)4He ..... . 73

3.3 Cross Sections Integrated from 22 to 44
MeV Excitation . . . . . ... .77


Figure Page

1.1 Excited States of 4He. . . . . .. 7

1.2 4He Photodisintegration Cross Sections . . 24

2.1 Detector Assembly for 25.4 x 25.4cm.
Cylindrical NaI(Tl) High Resolution
Detector . . . . . . . .. .32

2.2 Detector Assembly for 10.2 x 17.8cm.
Cylindrical NaI(Tl) Detector for
Small Angle Measurements . . . ... .35

2.3 Electronics Block Diagram for High
Resolution Detector . . . . . 38

2.4 Electronics Block Diagram for Small
Angle Experiment . . . . . .. 41.

2.5 3H(p,y) He Center of Mass Cross Section
for l1ab = 900 . . . . . ... .46

2.6 H(p,y) He Center of Mass Cross Sections
of 8 = 550 and 1250 . . . ... .46

2.7 3H(p,y)4He Angular Distributions . . .. .53

3.1 Laboratory and Center of Momentum
Coordinates . . . . . . ... .56
3 4
3.2 Asymmetry of the H(p,y) He Angular
Distribution . . . . . . .. .72

3.3 Coefficients of the Legendre Expansion
of o(6) . . . . . . . ... 75

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



Robert Chism McBroom

June 1977

Chairman: Henry R. Weller
Major Department: Physics

The 3(p,y) 4He reaction is studied for incident

proton energies from 8-30 MeV. The experimental data is

composed of excitation functions measured at the angles of

550, 90 and 125 in the center of mass system in 1 MeV

steps from 8-15 MeV proton energy and in 0.5 MeV steps from

17-30 MeV proton energy. These data measured the energy

dependence of the cross section and its deviation from the

sin 6 angular dependence of the electric dipole (El)


Additional angular distributions were taken at

selected energies in the range from 13-30 MeV with up to

nine angles measured between 200 and 1420 in the laboratory.

This number of angles was taken to insure statistical signi-

ficance for determining the coefficients of the Legendre

expansion of the differential cross section through a4.

The experimental data is shown to be consistent with the

assumption that the observed radiation is primarily El with

an additional electric quadrupole (E2) component and

negligible contributions from higher order multipoles. The

E2 radiation is shown to be consistent with a model of the

E2 cross section composed of the sum of a direct interaction

component, and two Breit-Wigner resonances. A resonance of

width 12 MeV at a 4He energy of 35 MeV is observed in agree-

ment with previous experimenters and a second previously

unobserved resonance is observed with a width of 3.8 MeV

at a 4He energy of 39.5 MeV.


Investigations of the properties of the 4He nucleus

are an important method of improving the understanding of

the nuclear force. Consisting of four nucleons, 4He falls

in a transition region between describing the nuclear

interaction in terms of nucleon-nucleon interactions and

statistical descriptions of many nucleon interactions. The

properties of the 4He nucleus show a number of differences

from predictions based on the two-nucleon interaction and

the assumption that the two-nucleon forces are additive.

Similar difficulties are observed with models that are

based on systems with a large number of nucleons.

The application of models of the nuclear inter-

action to 4He seeks to predict the observed properties of

this nucleus. One of these properties is the fact that 4He

is the most tightly bound of all the nuclei.1 Another

property to be considered is the root-mean-square (rms)

charge radius measured using the elastic scattering of

electrons.2-4 Indications of the presence of many body

forces are obtained in measurements of the charge distri-

bution of the nucleus by electron scattering. The charge

distribution deviates significantly from a Gaussian shape.4

Also to be considered in a description of 4He is evidence

that the ground state is not a pure spin zero (S=0) shell

model state.5

Many models have been presented to describe the

observed properties of 4He. Their success has been varied.

In general the models proceed by incorporating short range

correlations and non-central forces into the interaction.6-7

Further information on the importance of ground state

correlations is sought from the angular distributions of

4He photonuclear reactions.9

Several measurements of the 4He photonuclear

reactions have been made. A number of inconsistencies were

observed in the early works, some of which have been

resolved by more recent measurements. The behavior of the

angular distributions has been interpreted to give suppor-

ting evidence for the presence of ground state correlations.1012

In addition, evidence exists for the presence of resonant

excited states in 4He whose influence should be considered
in a complete description of the angular distributions.1314

Evidence for excited states in He is presented in

the analysis of many experiments. This evidence is derived

primarily from reactions in which 4He is formed as the

compound nucleus.15 Evidence for several states has been

obtained from phase shift analyses of nucleon scattering

data. Other states are seen in inelastic electron

scattering.16,17 All of these states have positive energy.

There exists no evidence for bound states of 4He. Isospin

selection rules indicate that the photodisintegration of

4He can be useful in the investigation of negative parity,

J = 1 isospin T = 1 states and positive parity J7 = 2,

T = 0, 1 states. Some studies of the He (y,p) H reaction

have exhibited resonance-like structures, but 3H (p,y)4He

measurements have failed to confirm the existence of the

proposed levels. 18-21 Measurements of the He (y,n)3He

reaction present evidence for a J = 2 T = 0 resonance at

a gamma energy of E, 35 MeV.22 It will be shown that the
present work provides additional evidence for the existence

of this level at 35 MeV in 4He.

Most of the 4He photodisintegration experimental

efforts for excitation energy in the range from 20-40 Mey

have been devoted to the He (y,n) He reaction. The early

studies of the 4He (y,p) 3H reaction suffered from diffi-

culties due to poor statistics. For energies below 35 MeV

where the triton tract becomes too short to measure, the

diffusion chamber and cloud chamber measurements have

difficulty distinguishing protons which arise from multi-
particle final states.112 Studies of the inverse

reaction 3H (p,Y)He have been conducted for limited

excitation energy ranges from 20 MeV to 34 MeV. In the

present experiment measurements of the energy and angular

dependence of the 3H (p,y) He reaction were taken for

excitation energies from 26 to 42 MeV.

The proton beam from the Triangle Universities

Nuclear Laboratory Cyclo-Graaff was used to provide

incident protons in the energy range from 8 to 30.5 MeV.

The beam was incident on a 5p self-supporting tritiated

titanium foil target containing about 0.14 mg/cm2 of

tritium. The emitted photons were detected with a thallium

doped sodium iodide NaI(TI) detector for up to nine labora-

tory angles between 200 and 1420. It will be shown that

these measurements indicate the existence of a previously

unobserved level in 4He at about 40 MeV excitation having

a J7 of 2+ and a width of about 3 MeV in the center of mass.

An appendix is included which describes a peak

fitting program. This program was designed to extract the

low energy tail of the Nal detector response curve from

beneath the peaks due to gamma rays from transitions to

states other than the ground state. The shape of the Nal

response curve was based on the measured response to the
3 4
H (p,y) He reaction.


The 4He nucleus has been the subject of intense

interest. The resulting body of literature is extensive

in both experimental and theoretical studies. This body

of literature is reviewed in a number of recent works,

particularly the survey by Fiarman and Meyerhof (1973).15

Many different theoretical models have met with qualitative

success in describing the observed ground state properties

of 4He, but have been unable to satisfactorily describe all

the observed properties. Further input for model deter-

mination is provided by experimental studies of the excited

states of He. While there are no bound states of He,

experimental evidence exists for virtual states as shown in

Figure 1.1. Particular consideration is given here to the

photon excitation states having spin and parity (JI) and

isopin (T) quantum numbers as follows:

J= = = 1 1 and

Jr = 2+, T = 0,1

These states have been studied by photodisintegration and

the inverse photonuclear reaction. The experimental

results to date have not definitively established the

Figure 1.1 Excited States of 4He. The energy levels of
He and the general form of the cross sections for the four
reactions, which form He as the compound nucleus, are shown
(Fiarman and Meyerhof5).

b: 7



c 4-


CI d

existence of any of these states; although studies of the

4He(Y,n)3He reaction indicate the existence of a Jn = 2+,

T = 0 state for an excitation energy of 35 MeV.22 In

addition to the question of the existence of excited states,

there are fundamental questions regarding the observed

shapes of the photoproton and photoneutron angular distri-

bution as a function of the gamma ray energy. The (y,n)

distribution is predicted to be backward peaked while

experimentally it is observed to be forward peaked for

excitations less than 27 MeV and then to become backward

peaked between 27 and 35 MeV excitation.22 For energies

greater than 35 MeV excitation the angular distribution of

the (y,n) reaction is forward peaked and the asymmetry

approaches the asymmetry of the (y,p) reaction channel.0-12

The (y,n) forward peaking may be interpreted to be due to

correlations in the ground state wave functions.23

The experimental observations of the photodisinte-

gration reaction have limited resolution. These

measurements are averaged quantities in a given energy

interval. One method of relating these averaged quantities

to the properties of the Hamiltonian and the ground state

wave function is the sum rule approach.24 The theory of

sum rules has undergone extensive development starting from

the study of atomic photoabsorption processes. For the

electric dipole (El) radiation in the long wave length

approximation the integrated cross section is given by the

sum rule

El = fo(E))dE
int (1.1)
= k ek <01 [Zk' [H, Zk]]10>
1 60 NZ ( = 60 MeV mb for 4He).24

The wave vector 0 > is the ground state wave function, H is

the nuclear Hamiltonian, Zk the position operator, and ek

is the effective charge for the kth nucleon. The equality

in the last term is satisfied if the position operator com-

mutes with the potential energy operator. This condition

is violated by Majorana or Heisenberg exchange forces or

velocity dependent forces. Each of these three interactions

would tend to increase o El Electron scattering experi-
ments indicate that the contribution due to exchange

currents may be included as follows:

El 25-27
S. = 60 NZ(1 + a), a = 0.40. (1.2)
(= 84 MeV-mb for 4He)
Under the assumption that the ground state is spatially

symmetric and including the charge radius of the proton,

the Levinger, Bethe (28) bremsstrahlung-weighted cross

section is related to the nuclear radius by the following

dipole sum rule:

El "I1 El
b = foE (E)dE
b oE

S0.096 (R2 R2)
A-i z p

( = 2.48 mb for he)

where R and R are the nuclear and proton rms radii
z p


The quantity Ea (E) referred to in the sum rules

is the total cross section for all electric dipole photo-

disintegrations. For the 4He reactions there are five

competing reactions. The yields for these five reactions

were measured by Gorbunov and co-workers.10, A 170 MeV

Bremsstrahlung beam incident on a cloud chamber was used

in the study. Their results for the relative yield of the

various reactions are shown in Table 1.1.

The measured angular distributions indicated that

the El interaction comprises r94% of the total integrated

cross section up to 170 MeV. Approximating oE by the

total cross section, integration of Gorbunov's data for

the reactions of Table 1.1 gives:

El El
int = 95 7 MeV mb and = 2.4 .15 mb

This value is larger than that predicted by the simple

sum rules (Eq. 1.1-1.3) indicating contributions due to

exchange and velocity dependent forces. When these forces

are considered as in the sum rule analysis of Quarati34



1) I


U 0

4 1O

r >




E-1 0



'd +

>- 0)

- 3






'd >
U U rN 0)

o o C N o C )





00 >
g 0

(N 'd
rl H

H H x
Cd 'd

- 0


H 'd H C H O
Cd 0 d C d

S H rl ) H
- '4 -
> 0 r 0 d r.

l Ca a3 n O
O Q 0 .0 4- 0
Cd .0 Cd a) 'd U

for the shell model (Table 1.1), the experimental cross

section up to 170 MeV excitation exhausts 95% of the sum


These results indicate the usefulness of sum rules.

This usefulness may be increased by the removal of the

approximation that the total cross reaction is due to the

El interaction. In Table 1.2 are listed the sum rules

commonly appearing in the literature along with their

representations in the shell model formulism. The results

of these equations for the shell model parameters are

11 1 -'
=1.75 fm2, kEl 1 fm = 36 MeV and kE2 -fm

These values give the rms charge radius of 4He to be

= 1.62 fm. It has been suggested by Leonardi and

Lipparini38 that the final entry in Table 1.2, a be
measured, as the E2 sum rule for the electric quadrupole

strength is dependent only on the ground state wave function.

These features of the four nucleon system have

received extensive theoretical treatment. Many different

models have been successful to varying degrees in descri-

bing these features. The common factor in most of these

analyses is an attempt to develop a method to properly

account for the contributions of many body and velocity

dependent forces in an orderly way. Many of the models

are based on "realistic" potentials that are derived from




S E Ln
0 r-- 0 +
SICo co

ul --l ro -4i

c* 00 +1
S 0H 1 L (D 0
C Qir in CM o
0 X n o o
+- r- oo o< o
O H I o o


aJ C



4 -I

a N
0 j H -0

H I -c
0 c0 I 0

SrQll 0 -N T

) ( : 1
.0 '0 43 -4 +
H : 0) r: W ar

Url E
N , m
a) I I 0
rl -) C cD (0 I Q) 5-

ID 13 *D
- + I + + I H
3Q I ( 441
C OC H o aI c -
ra d l -(N N N cv
1) rHl (1) I 40D *Il
H() r( rM fM (U
00 I N N. r-I
H c N oJ c- 3 0' X
0 a) N dc NM H (

I II i i 3

M0 3 +
3 3 -d 3 3
TV V 3 V 3
) f 33 3 3 3 33 3

U l 4J
0 N 3
o o o I o


-1 4J

00 0
4> O 4H

( OO
Qa 00

O Q) m 1 a)
04,-4 u1 0

0 p
4J 4J
o) a

S0 0
G 0
0 1 4 o 0
0 O0 0 '.
o3 o e0

0 0

0 4-4

.0 0

0O1 0
O-0 0

-r-I H --4 -1
* ei -1 2 0

0 d o 0
H I 0-
Qo 0 c0 () c (C

co r- a)) e

0 4-' 0

H 0
1- (0 -3

04-1 (di I H
0rl 0 0
Ul (H) a) 4-4
14 0 0
Q 0 a U3 )4 U)

014 7 4 H *
a-)c1 (1) *H *H (c

H 0 0 0 I g
-4 1)4 00 I
4 (a r- 0
w o a

c! 0 0

n -Y ca + 4
3 ~ ~ ^ a ; .

the nucleon-nucleon scattering phase shifts.7,8,39,40 These

potentials fit the on-shell matrix elements equally well.

Their differences are embodied in their treatment of off-

shell matrix elements. One such potential is the Sussex

potential which was used by Szydlik, et al.36 to calculate

the spectrum of 4He.

Photodisintegration studies of the 4He nucleus span

the excitation energy range from threshold to 500 MeV. The

reaction is characterized by the asymmetries in the proton

and neutron angular distributions. At low excitation

energies the asymmetries exhibit structure which has been

interpreted as being due to interference between the electric

dipole (El) and electric quadrupole (E2) absorption ampli-

tudes.22,41 For excitations above 100 MeV the (y,n) and

(y,p) asymmetries approach one another.2 The absorption

of photons of energies of 100 MeV or higher is expected to

occur predominantly by the quasideuteron mechanism discussed

by Levinger.9 Recent calculations by Gari and Hebach account

well for the total cross section and asymmetry in the range

50 < E < 140 MeV.23

Many measurements have been made of the various 4He

photodisintegration processes. An overview of these experi-

ments is shown in Table 1.3. The history of the experimental
measurements is one of controversy. The early measure-

ments gave the general character of the energy and


co ~

00 '.0
CM (


O m
4- .4J


* a

0 H

0 >




4-) -O
0) 0

0) 1_
r -4-)


M x

en en en a }. 4-e
ao ) 0) Q) ) 0 -I
n >1 > r >1 ><1 r 4

14 0

0 0
C)' C)

4 p4

0 0
rO --l H r r m U u en
F m H1 H U l E h 4 E 4 -1 4
.0 fft r-1 .00 H H -f H .0
, 0 ) 4 0 r .,- ,40
0 4p 0 4J -J n^J a oa R: 4u4-,

- 0

2n 0
en >1 4

> w
7 ^ h



4-) 0 0 t3
S i m 0
-- 0
1 P Q

m ,- C o

r-l r-1



AI --I



0 U
03 m N
()0 4-) ;4 o In D

0 H H 0H


s: >
o- m O r v m o uo

r O r> M \
4- o) 0W N N 0 C o C i
- r- 4m C C

wO w CN (N NN r (( N CN

rN ) Na S rfl o H
0 C I I II C I I

*H --4 -. *. 10
n -4 -1 r1 -r "-1 . .
0 4 44 44 LI 44 ir 4- 4) 4.) 1
4-p T3 Lr i 4 n 1 U n Er -
-H -- rl rl 0

0)0 ( E F E 4 n Lf H Hi H H
.1i *H i -rH A -H -H m 0 0 (a
4j 4- 4j 4+j 1 'OH z z 2Z Z

in r-H
r- 1 CH N (N r (o
0o M Ln LA (N r' r0 0 -
4- P - LO n Ln ri fl L- (N (N
-H o CN - rN w. -
N N N m LI) l LI m -
r- NN i n O LI)
HQ 1 ---- ^ - - -N

00.0 0 0 0 0
a04 0 0 4 .0 ro 4) i u >1 0
213 E u u) in rd p H 3

m(U x H H U) P4
(QCQg HIH~ i P; almQ ft


0 mU

Sa) c l-- --1



o m

O >I I I I I 0 I I

Pa H H > Ol
0 QL

o o 4 o o o o c c-n N
, -- o I

. ) N O ) O .
Uo O u u u 4J U

P )C H H H H O Qi 4-H I C) C) 0
aC rd rd OH rl .11 Q) 04 D4 0
z a z z u u Lan pm Un w)

H 0 H-I
co In 1 -
H-4 I In 0o COO Hl NM C
ra N o CN -n k 4 H
0 -- In -. N
14 0 N n
Hc n N -
) -- H -l 0 0 W

l)) -Hl C) H 0 (UI 0

StC) )
a~C C)m



N Nm


4 4-1 r4
O u




41 01
-4 H

ci a

H $



4-4 0 -
O m

4 -) ff

a u 1

o 0 0

o m

a r, a a4
4O1 -P g. 41O
11 to (n a) Q) a) c a z r E 2 O 0 0 04

o 0 0 0 0 0 0 0
.H a l 4 4 ) 4 UW C
3 3 ci) c) 3H 44 ( I 3rzH

Qi 41 4 M u1 41 to in $44.)

N '.0

Inr C-

co CO

S o

> >
0 0
a) o

3 0
. ci

n N\

- N

(d 0






a) 20
u > a

O t
-4 U

0 0
o 3- --

0 Q)
rt X M

-r-I E

I4J tn I c 0 in
-H an) LO I N m
O N I o I I
*X* N 0 N

00 C4

O 1 0 0
. I C) Cg C c C

0C i 0 ) in fa rd n
O 4 U ) 4 H -H -H .
-- 00 1)0 1) 0 0 0 0
,-1 O O- O OO O
r H .H O 0 ) rI O IC

S' 0O 00 O
LC )

H 4 Em
( o m -. -
N N -p i
H 4 U 0 i -H -O H

00 O H 0 0O
4)4r 4.1 0 (1 i -
NI LI r0
a- r' n P-

angular dependence of the excitation. For the cloud chamber

and diffusion chamber results there are difficulties relat-

ing to small numbers of events in a given excitation range

and in analyzing the tracks of the product particles for

excitations below 30 MeV. Particular difficulty is associ-

ated with the measurement of the 3He recoil for the (y,n)

measurement. All the photodisintegration experiments suffer

from difficulties associated with the spectral distribution

of the photon beam. These early measurements indicated the

existence of a number of structures in the cross sections,

but could give little definitive information concerning the

(y,n) assymmetry.

The measurements by the different experimenters are

in general agreement concerning the magnitude of the (y,p)

cross section. However, the (y,n) cross section is quite

variable. Charge independence considerations support the

results obtained by Gorbunov that the (y,n), (y,p) cross

sections are the same.11,77-80 The measurements are in

agreement for an excitation energy greater than 35 MeV.
The results reported by Berman, et al. and
Busso, et al.4849, give a lower (y,n) cross section for

energies between 23 and 35 MeV. In the case of Berman's

results, the cross section would agree with the measure-

ments of Gorbunov0 if multiplied by a factor of 1.8.41

This disagreement has been clarified by a series of experi-

ments by Irish, et al.53'54 which show that the variation was

due to a reduced target thickness from bubble formation in

liquid He.80 Measurements with liquid targets by Malcom,

et al.22give the (y,n) cross section in agreement with

Gorbunov. The 5 atm diffusion chamber measurements by Busso

agree with other experimenters for excitations above 30 MeV

but fall below the (y,p) cross section at lower excitation.

Recent 1.5 atm diffusion chamber measurements by Arkatov,

et al.55 with improved accuracy in the low energy 3He

recoil measurement give the (y,n) cross section in agreement

with the (y,p) cross section. These results for the 4He (y,p)

and (y,n) cross sections give experimental evidence for the

charge independence of the nuclear force.79

The existence of evidence for excited states of 4He

has been reported by many experimenters as seen in Table 1.3.

There is little agreement in the structure seen by various

early experimenters. The recent experiments with better

statistics exhibit much less structure than seen previously.

The experimental cross sections are shown in Figure 1.2. The

significant features are the peak of the cross section for an

excitation energy of 26 MeV and a broad peak for 28 MeV exci-

tation. Peaks in this region are consistent with the

existence of two states with angular momentum, parity JT = 1

and isospin T = 1. These states correspond to a mixture of

the spectroscopic states singlet P1 and triplet 3P13

Figure 1.2 He Photodisintegration Cross Sections.
This figure is a compilation of the results reported by
the indicated authors.

20 30 40 50 60 70

Evidence for a third excited state at 35 MeV excitation

with angular momentum, parity J" = 2+ and isospin T = 0 is

obtained from (y,n) asymmetry measurements.22

The (y,n) and (y,p) angular distributions are given

in terms of the Legendre polynomial expansion as

= Ao ( + jk k (cos 6)).81 (1.4)

The coefficients contain contributions from photons of

multipolarity L for k < 2L, k even and k < L + L k odd

where L is the multipolarity of an interfering photon.

The equivalent expansion in terms of sin e and cos 6

prevalent in the literature is

do = B(a + sin2 B + B sin2 6 cos 8 + 6 sin2 6 cos2 +

cos 6 + . .) (1.5)

The coefficients Ba, B, B3, B6 and Be correspond to ampli-

tudes and cross terms for multipolarities of 0, 1, and 2.

The respective relations between the coefficients of the two

expansions are shown in Table 1.4. Electric operators in-

volve only space coordinates and magnetic operators only

spin coordinates in the central force approximation. For a

pure IS ground state the allowed final states of the out-

going particles are 3S1, 1P, and 1D2 for angular momentum

changes less than two. The admixture of D states in the

ground state indicated by variational calculations and

Table 1.4

Relations Between the Legendre Polynomial and
sin 6, cos 6 Angular Distribution Expansions

-3 5
B = A (3 + a)

a= 1+ a2 + a4 +

3 5
2 8 a4 + .

S= -2 a3 7a5 +
23 5
-3 5

6 = -3 a4 +

-3 5
2 a2 8 4 +

-3 5
= a + a a4 + .
-3 a 5 a +
2 a2 8 a4

4He (p,p) He measurements complicates the interpretation of

the coefficients of the angular distribution. Possible

additional contributions may be observed as an increase in

the isotropic component from El transitions from the D state

to P and F states and a contribution from the cos 0 term

which arises from interference between El and non-spin-flip

Ml transitions.41 The angular distribution measurements by

Wait12 Gorbunov 10 and Meyerhofl3 yield negligible

values for the coefficients a and E. Their results are

dominated by the El term B.

The asymmetry (as) of the angular distributions about

9 = 900 can be defined in terms of the difference between the

cross section at 550 and 1250. This quantity, as will be

shown in Chapter II, can be written as

a = al P (cos 55 a= a .68 a3

for the Legendre polynomial expansion (or equivalently the

term for the sin 6, cos 8 expansion) where P2(cos 550) = 0

eliminating a2. These terms arise from interference between

the electric dipole and quadrupole interactions. At low

energy the observed angular distributions are very close to

a pure sin 6 distribution.56 This distribution indicates a

predominately dipole interaction. The isotropic terms were

observed by Gorbunov to be small for photon energies up to

170 MeV providing a basis for the assumption that only El, E2


radiation contribute significantly to the yield. The

interference terms producing the asymmetry are more

sensitive to smaller amounts of E2 interaction than the

E2 amplitude itself under these conditions. This result

is due to the fact that the coefficients al and a3 are

proportional to the product of the dipole and quadrupole



This study consists of a series of experimental

measurements designed to obtain the electric quadrupole E2

strength as a function of the excitation of the compound
3 4
nucleus for the reaction H(p,Y) He. The methods used to

determine the E2 strength consisted of measuring the asym-

metry of the angular distribution about 90 and the measure-

ment of the detailed angular distributions of the outgoing

Y-rays. Shell model calculations predict a number of states

of angular momentum and parity J" = 2+ with isospin T = 0,1

in the energy range from 30-50 MeV excitation. The proton

energies available from the Triangle Universities Nuclear

Laboratory (TUNL) Cyclo-Graaff allow study of the energy

range from 22 to 42 MeV excitation of the compound nucleus.

Experimental Details

Using a 15 MeV isochronous Cyclotron as a source,

the TUNL FN Tandem provides a pulsed 25 MHz proton beam.

The beam energy is continuously variable from 17-31 MeV.

The beam pulse width is 2 ns and the energy spread is 30 KeV.

The root-mean-square beam current delivered to the target

was kept in the range of 20 to 100 nanoamperes depending on

the total count rate in the sodium iodide detector. The

count rate in the detector was kept below 350k counts per

second because pile-up problems and a deterioration of the

resolution occurred for higher count rates.

Two separate detector assemblies were used in the

experiment. The first detector assembly was a high resolu-

tion system and was used for the yield curve measurements

and the angles of the angular distributions between 420 and

1420. The second detector assembly allowed measurements to

be obtained for angles between 100 and 900 although with

reduced resolution. The experimental arrangement was

designed in both cases to minimize the background events

that were not associated with the target.

The detector assembly is based on a cylindrical

25.4 x 25.4 cm thallium doped sodium iodide crystal. This

crystal is surrounded by a well type Ne 110 plastic scintil-

lator. The center crystal is viewed by six RCA-8575 photo-

multiplier tubes and the plastic scintillator by eight XP1031

photomultiplier tubes.82 A schematic of the detector arrange-

ment is shown in Figure 2.1. Active shielding is provided

by detecting coincidences between the plastic detector and

the center-crystal detector which were processed by the

electronics to reject cosmic ray events. Passive shielding

for the detector is provided by four inches of lead and eight

inches of paraffin loaded with lithium carbonate (%50% by

weight). The detector is mounted on a carriage that allows

Figure 2.1 Detector Assembly for 25.4 x 25.4 cm Cylindrical
NaI(T1) High Resolution Detector. This illustration shows
the arrangement of the active and passive shielding from the
cosmic rays and beam associated background. The collimator
arrangement that was used to restrict the cone of gamma rays
to that just illuminating the back face of the detector
crystal is shown (Weller, et al.82).


radial and angular positioning about the target location.

Two radial positions of the detector were used in the

experimental series. These distances placed the rear face

of the NaI crystal at the positions of 82 cm and 106 cm

respectively. Collimators were provided which restricted

the observed solid angles to those subtended by the rear
crystal face corresponding to solid angles of 7.42 x 10-2 Sr

and 4.46 x 10-2 Sr respectively. Excitation curves were

measured with the detector at the 82 cm distance in the

interest of higher yield rates. The angular distributions

were measured with the detector at the 106 position to allow

the inclusion of measurements of the angles at 420 and 142 .

To determine the angular distribution as the labora-

tory angle approaches zero, additional measurements were

taken for the laboratory angle of 200 using a separate

detector system. This system was based on a 10.2 x 17.8 cm

NaI(Tl) crystal surrounded by a 22.9 x 22.9 cm NaI(Tl)

annulus for active cosmic ray rejection. The experimental

arrangement is shown in Figure 2.2. Passive shielding is

provided by a 20.3 cm thick copper annulus and 4.4 cm of

lead. A cadmium sheet was located between the lead and

copper for thermal neutron absorption and the collimator was

filled with paraffin loaded with lithium carbonate. The

distance from the target to the crystal front face was

93.3 cm. The collimator restricts the photon flux to the

Figure 2.2 Detector Assembly for 10.2 x 17.8 cm Cylindrical
NaI(Tl) Detector for Small Angle Measurement. The active
and passive shielding for cosmic rays and beam associated
background is shown. The beam stop shielding for measurements
at 61ab = 200 is shown.


z z

- I-
:) z
z i
z L

6.57 x 10-3 Sr solid angle subtended by the back face of

the crystal. The entrance aperture was formed from tungsten

for attenuation of fast neutrons. The remainder of the

collimator was lined with lead.

Further measures to minimize the background events

not associated with the target consisted of the use of a

single insulated collimator close to the target and adequate

shielding of the beam dump. The insulated collimator allows

monitoring of the beam current striking it. This current

was kept to a minimum by adjustments of the focusing of the

beam transport system. The beam stop for the large crystal

arrangement is located three meters beyond the target.

Originally this beam stop was shielded by about 10 cm of

lead and 70 cm of paraffin. The shielding was changed to

about 10 cm of copper and 40 cm of lithium loaded paraffin

to more effectively attenuate neutrons produced in the beam

stop. For the small crystal assembly, the beam stop was

located 33 cm behind the target. The shielding was provided

by the copper shield of the detector itself and a tungsten

shadow bar.

The electronics for the two detector systems were

similar; however, the use of the Nal annular cosmic ray

detector on the smaller crystal required a different elec-

tronic arrangement than the plastic shield of the 25.4 x

25.4 cm system. The electronic arrangement for the large

crystal is shown in Figure 2.3 and that for the small crystal

Figure 2.3 Electronics Block Diagram for High Resolution
Detector. This diagram illustrates the signal routing used
to determine the coincidences between the active shield
detector and the center detector. The additional electronics
used to determine the number of coincidences are not shown
(Weller, et al.82)


C- C -




L .Ln .-cn

c C


x w 0: c
0O C:)
< x

Z o -1-

clo ZMO (

in Figure 2.4. Typically, the count rate due to low energy

events is several orders of magnitude greater than the count

rate due to events of interest. Common to both systems is

the arrangement of the electronics to minimize the events

due to the pileup of lower energy events. This minimization

is accomplished by time-clipping the detector signals. The

signal is then passed through a fast linear gate (250 ns)

before processing. During the 10 ps processing time, the

gate is held closed.

Further reduction of the background due to unwanted

events was possible in this experimental series due to the

pulsed nature of the Cyclo-Graaff beam. A time of flight

requirement (TOF) was set up between a signal derived from

a radio-frequency inductive pick-up loop at the Cyclotron

and the gamma ray events in the center crystal. The R-F

signal was used for the stop signal for a time to amplitude

converter (TAC). The TAC start signal is derived from the

linear signal of the Nal center crystal. The TAC was gated

by the pile-up rejection circuitry to be active only for

the time during which the linear gate was open. Both

detectors are pulse stabilized by a calibrated light emit-

ting diode flash into the crystal. This pulse was used to

correct for slow changes in the system gain due to thermal

drifts. The pulse stabilization was found to be unnecessary

for the large detector system. The cosmic ray rejection was

accomplished differently for the two detector systems. The

Figure 2.4
to determine
detector and

Electronics Block Diagram for Small Angle
Illustrated here are the electronics used
the coincidences between the active shield
the center detector for the yield measurement

at 68ab = 200. The electronics associated with the pulse
stabilization, accidental monitoring and beam time of
flight circuits are also shown.


L) w
W 14 LL 14 Z

0Z J Wlj

1414 14 4 I -

z, z
ui m


1 4 Z1 1401
UJ >.
0 W W Fia
I in Lnn -

M 0- 0
0 z4 0

L) o )
F-C1 -

r -I
In W

o ILZ ~ c IL



uw~1 4Z 4
7 >

~-z z

0 Lj
a- 0


3W cn z ~


ocr z

M W; ( W 0 -- cr 03

0 Ej
W ulW I I
co JW

r P
th a

:3 UZ
(L cr cr
in ,o W

response of the plastic scintillator is faster than that of

Nal. For the large detector with the plastic shield, the

shield signals were delay line clipped and timed for an

overlap coincidence with the center crystal events. When

a coincidence occurs, a routing signal is sent to the

computer for storage of the event in a coincidence spectrum.

The small crystal system utilizes the linear signal from the

center crystal as the start signal for a time to amplitude

converter. The shield pulses are then the stop signal for

the TAC. The TAC output goes to two single channel analyzers,

one of which is set to provide a signal for events occurring

in the peak of the coincidence TAC spectrum. The other

analyzer is set off the peak to determine the counts due to

accidental coincidences. In each case the resulting signals

are processed by two analog to digital converter's (ADC's)

in coincidence and passed to the on-line computer. For

maximum resolution, the threshold of the coincidence circuit

could be set to give a coincidence for events due to annihi-

lation y-rays from events in the center crystal.

The information stored in the computer consisted of

eight 512 channel spectra. A window light-penned on the

y-flash in the TAC spectrum separated the Y-ray events into

three pairs of spectra. These pairs were stored as short

time events, true data events and long time events. Each

pair corresponds to center crystal events and coincidences

respectively. The eighth spectrum stored was used with the

large crystal system to store the elastic proton spectrum

from a 500p silicon surface barrier detector located at a

laboratory angle of 1600

The targets used in this experiment were tritiated

titanium foils. The foils were 5p thick and the activity
was 6 Curies/in This activity corresponds to an atomic

ratio of approximately one between the tritium and the

titanium. The tritium contained in the foils was deter-

mined by comparing the yield obtained by the solid state

detector with the known yield of 3H(p,p) 3H. The measured

tritium values for the two targets used were 0.14 mg/cm2
and 0.11 mg/cm The error in these concentrations is

determined by the uncertainty in the experimental geometry

and is estimated to be 10%. The errors associated with the

statistics, the H(p,p) H cross section and the beam charge

measurement combined contribute about 1% to this error.

Experimental Data

The experimental data were taken in four series. The

first series consisted of a set of excitation curves which

were utilized to determine the experimental asymmetry of the

angular distribution. The second series consisted of angular

distributions measured at eight angles between 42 and 1420

These measurements were extended in the third series to in-

clude a measurement at an angle of 20 The fourth series

was an extension of the excitation curve data to lower

energies than covered in the first series. This data was

then analyzed to determine the effects due to contributions

from the electric quadrupole interaction.

In the first series, the excitation curves were

measured for laboratory angles that transform approximately

to the center of mass angles of 550, 930, and 1250 (Figures

2.5, 2.6). The measurement was taken in 500 keV steps over

the energy range from 17-30 MeV. The resulting cross sections

are shown in Table 2.1. The center of mass angle in the for-

ward direction (bf = 550) and in the backward direction

(eB = 125) were chosen to be approximately the zeros of the

second order Legendre polynomial P2 (cos 0). This condition

on Of and OB requires that OB = 180-6f which yields the

following results for the Legendre polynomials:

P1 (cos 6B) = -P1(cos )

P2 (cos (cos = P2( O ) = 0

P3 (cos 6B) = -P3(cos )

P4 (cos B ) = P4(cos f )

The observed yield as a function of angle can be written as

an expansion of Legendre polynomials,

Y(8,) = Ao(l + ,akPk(cos 9)).

3 4
Figure 2.5 H(p,y) He Center of Mass Cross Section for
6 ab = 900. The data from this series of experiments is
shown as the solid dots. The error bars represent the
statistical error associated with the data points. The
data is plotted both as a function of the laboratory energy
of the incident proton and the center of mass energy of the
emitted gamma ray. The experimental cross section reported
by Meyerhof, et al.13 is included as the open squares. The
solid curve is a least squares fit of the data in the proton
energy range from 5 to 30.5 MeV to a cubic polynomial. The
cross section was obtained by normalizing to the data of
Meyerhof.13 The measured target thickness, solid angle
and collected charge was combined with the normalization to
obtain the detector efficiency. The value of 27 + 3% obtained
is consistent with the efficiency 26 6% reported by Weller,
et al.82

3 4
Figure 2.6 H(p,y) He Center of Mass Cross Sections for
o = 550 and 125. The experimental data is shown as the
solid dots with the error bars indicating the associated
statistical error. The data is plotted both as a function
of the laboratory energy of the incident proton and the
center of mass energy of the emitted gamma ray. The solid
lines are fits to the data in terms of the model discussed
in Chapter III.

o Meyerhof
- Polynomiol Fil

5 10 15 20 25 30
E (MeV)

20 25 30

E (MeV)

35 40


o a


















CM 0





3 r1
H c

r- N
H (N

o 0 0 0 0 0 0

i-I r-4 i-i i-l ri-
0 1 0 (N m
H H H H Hmp

N4 N
+1 +1

o 0
+1 +1

Hl r
+1 +-

+1 +1
co m
m CN

. (N

+1 +1

l m
m m
r- ,-

c; o
+1 +1


+1 +1
co Ln
0 1n
N~ \D

r( r- NO m ( -

cO Ln
N4 (N
+1 +1

lN r-

NO o
o o

+I +l

o 10

+1 +1

* *
l e
CM r--
H n
H o

+1 +1

m m
+1 +1
o 10

a N

0 0

+1 +1
10 r
mn CM
(1 (N

In 0




F: ) C

n O 11 CO C 048
C. ko in In %0 In 'T 48
+1 +1 +1 +1 +1 +1 +1 +1
in Co uI in fm CO I rN
co Ln o m c) r Ln C o
O o N m Co Co co co
o I rH H

m c t rm N m No N

+1 +1 +1 +1 +1 +1 +1 +1
rI 0 n r H O CD D

+1 +1 +1 +1 +1 +1 +1 +1

0) C m Co in N r- -z
rN co N- o In Ln '

+ + + +1 +1 +1 +1 +1 +1
0 i l l l ^

rl 0o < 0 0
C D CM r H H 9 In 9 O N

+ 1] +i +i +i +i +i +i +i
So ril i-i ro in co r-
4N CN CO o T rm H- (O

8 In In In m m r ^ u,

CN co In In In In NM C LI
Q) 'I r IV m- c m
S+I +i +1 +1 +1 +1 +1 +1
Q I 'm CO N C C O
n r rN H In co D
co rN r r rN N In In

H V m m n Cl N Co

+1 +1 +1 +1 +1 +1 +1 +1
CN rN CN CN N 'T m co

In In In T Ln IV -V -'

CO H! I n cO CN CO O
C mn rn fn r "r in

mo 00o 0 co mo o o c

l rl l rl l Cl I CD


SH r-H H r-H H 'IN N

S m ,' r 49

+1 +1 +1 +1 +1 +1

00 r r A I LA
o 0 0 0 w in

mr-- N N N m
0 I r i -1 r-I I I

+1 +1 +1 +1 +1 +1

c N C CO in
(N ( 0 C r-H

NM r N N N N
+1 +1 +1 +- +1 +1
-i- IT -T 0 r-- .D
'Z 'IT ) CM4 N N N

+1 +1 +1 +1 +1 +1

oa o N D LA

D0 0 0 0 0
+I +I +I +I +I +I

J 00 -IT Cl CO C CN
r! ml 0 r- ko LO n
0 H H r H O N


a 0 0 0
+1 +1 +1 +I +1 +1

-I re m l ClI C

0l l Cl Cl C al Cl

in inl il in a0 0

( N N C N

co 0 o cD O N

(N (N NM C






0O CO O 0co 0o co
0\ ^ 0) '^ 01 ^
ll 1 lo lo
m 'T LO LA I'D
(N (N (N (N CN (N

0 LA 0 LA
(N (N (N -4

+1 +1 +1 +1 4- +1

- C r H H H
-l rl rH- H- H- -

+1 +1 +1
rN Ln 10

Sm m

o o 0

+i +1 +I
m r- a

+1 +1 +1
0 0 0
,' C )




n0 0

+1 +

0 O0

co rl
(N CN m

+l +i +i

o 0o HD

+I +I +I

(N H1 M

N cN (N

iA 0 Ln
n 0 o
NM en m

Under the assumption that multipolarities of L > 2 contri-

bute negligibly to the cross section, the sum of the yields

for the angles 6f and B reduces to

Y(Of) + Y(OB) = 2Ao(l+a4P4(cos 6f)). (2.2)

where a and a4 are defined in equation (1.4). The dif-

ference between the yields is then

Y(f )-Y(gB) = Ao(alP(cos )+aos f)+ s f)-alP (cos gB)

-a3P3(cos GB)) (2.3)

= 2Ao(alPl(cos f )+a3P3(cos a )).

Therefore, assuming the condition a4P4(cos f)<
should be expected if the E2 intensity is small compared to

the El intensity, the total cross section is given by

at = 4nAo = 2n(Y(Of)+Y(6B)) (2.4)
Ao = (Y(f)+Y( B)). (2.5)

Under these conditions, the experimental asymmetry in terms

of the yields Y( f) and Y(B ) is equivalent to that defined

in terms of the coefficients of the Legendre expansion of

the angular distribution (Figure 2.7). This equivalence is

shown by the following relations:

S Y(e ) Y(B) = 2Ao(alPl(cos f)+a3P3(cos 9f))
s P1(cos 6 )(Y( )+Y(OB)) P1(cos f)(2Ao(l+a4 4(cos Of))
= a1 + P3(cos )a3 a4P4(cos ef)<<1.
P1(cos f)

Figure 2.7 3H(p,y) 4He Angular Distributions. The
experimental data is shown as the solid dots with the
error bars indicating the associated statistical error.
The solid lines are least squares fits to the data in
terms of the Legendre Polynomials as discussed in
Chapter III. The measured values for the cross sections
are included in Appendix B.

0 V ( .




L) 0)



0 .0

As will be shown in Chapter III, the measured asymmetry and

the measured cross section can be used to obtain an experi-

mental E2 cross section.

The El cross section is obtained by observing that

the terms of the multiple expansion (equation 1.5) for
multipolarities up to L = 4 reduce to = B (a +1) at

6 =900
Therefore, taking a<< 1 (no spin-flip or magnetic

dipole radiation) the yield at this angle is the El cross

section.13'19'33 The angle measured was 8lab = 900 so that

the results could be readily compared with those of previous


A second experimental series was conducted to con-

firm the energy behavior of the E2 cross section and to

provide a direct measurement of the E2 amplitude. This

series consisted of a set of angular distribution measure-

ments taken every 2 MeV between 17 and 27 MeV incident

proton energy, and included angular distributions measured

for proton energies of 13 and 30 MeV. For each angular

distribution, yields were measured for a minimum of seven

angles in the range 420-142 covered by the detector.

Additional angles were included as needed to define the

shape of the peak and the slope of the sides of the angular

distribution. The minimum number of measurement points was

chosen so that the number of degrees of freedom associated

with-a Legendre polynomial least squares fit to four

coefficients is greater than zero. The amount of charge

collected was varied so that a minimum of 200 counts was

observed for the 1420 measurement. The yield was larger

for all other angles observed (Figure 2.7).

The third series of measurements was conducted

using the 10.2 x 17.8 cm Nal detector. The purpose of

this experimental series was to determine the shape of the

angular distribution as the angle approaches zero. Measure-

ments were made every 2 MeV in the proton energy range

17 < E < 27 MeV. Yields were measured for three laboratory

angles including 200, 900 and an intermediate angle corres-

ponding to an angle at each energy for which the yield was

measured in the second series. These measurements were

normalized to the data of the second series, and an effective

yield for the 25.4 x 25.4 cm detector at the laboratory angle

of 200 was obtained. This yield was incorporated into the

angular distributions used to determine the Legendre

expansion coefficients.

The fourth series of measurements extended the

asymmetry data to lower energy. The TUNL FN tandem was used

to measure the fore-aft asymmetry every 1 MeV in the proton

energy range from 8 < E < 15 MeV. This information was
p -
obtained for comparison with the published results of

earlier experimenters.13



The kinematics of the reaction 3H(p,y) He for

proton energies above 10 MeV are subject to relativistic

corrections. Therefore, the kinematics were explicitly

treated according to special relativity following the treat-

ment by J. J. Jackson.84 The reaction coordinates in the

laboratory and center of momentum frames are shown in

Figure 3.1.

Laboratory Center of Momentum

P qY

m m )6z m m
yp pt y P 7t
-+ q

Figure 3.1 L-aboratory and Center of Momentum Coordinates

The conservation equation for the square of the four momen-

tum of the alpha particle in its rest frame and in the

laboratory system is

(0,j cmac2)2 = ( 2p -1 m ck-T, j/c (ypmc2+ 2 2-E ))2 (3.1)

where y. is the Lorentz transformation parameter. For the

proton in the laboratory, this parameter is y = //l-v2/c2.
p p

Solving the conservation equation for the laboratory gamma

ray energy as a function of laboratory angle gives

E (E')2- m2c4
S (3.2)
2(ypmc 2+m tc2- yl m C2COSO)
pp t p p Y

where the energy

E' = (m2c4+m2c4+2ypm2mc2 ) (3.3)
p t p p t

is the total energy in the center of mass system.

The gamma ray energy in the center of mass is

S (E') 2 _m2 c
E = a (3.4)

The excitation energy of the compound nucleus is found by

subtracting the alpha particle rest energy from the total

center of mass energy

E = E' -m c2 (3.5)

The relationship between the angle in the center of

momentum and in the laboratory is given by
I 2 -1
sin G p
G' = tan ( Y ) where -= p (3.6)
y (cos -8) Y2
cm ( P

where the Lorentz transformation parameter for the center of

momentum ycm is related to the total laboratory energy and

the total energy of the compound nucleus by

y = y m C2 + mtc2
Ycm yp mpc +t (3.7)

These relations were incorporated in the computer programs

used for data analysis.

The relationship between the measured cross section

in the laboratory reference frame and that of the center of

momentum reference frame is also necessary for comparison of

the experiment to theory. This relation can be obtained

from the equality of the yield in the two frames following

Marion.85 This equality is

lab (6y)dQ = Qcm (0')df'. (3.8)

Using the kinematic relations between 6 and 6' with the

definitions of the solid angle increments, which are

dQ = 2r sin9 d6 and dQ' = 2n sine'dO' the relation be-
tween the two differential cross sections is found to be

as follows:

sin36' cos6'cos6y+ c) (3.9)
S, (9 ) = o (9') ( y+ y ). (3.9)
lab y cm sin9 sin'sin cm

This form of the relation between the two frames was con-

venient to use as the analysis programs calculated 0' and

ym for measured gamma ray angle 6 .

Excitation Curve Analysis

Assuming only El and E2 radiation with the

additional assumption that the El and E2 spin-flip terms

are negligible, the cross section may be written in terms

of the spherical harmonics Y11 and Y21. The interaction is

modeled by assuming that it consists of direct and resonance

terms. The center of mass cross section expression is

do (8) i61 i62 i(Di+ni)
'P- =|eDie Y11 + ( e2D2e + Rie
+R2e )Y211 2

This expression for the cross section implicitly includes

the relations a3 = -a and 1 + a2 + a4 = 0 between the coef-

ficients in the Legendre expansion. The first term of the

cross section is due to a direct El interaction. The

second term is due to a direct E2 interaction, The factors
e1 and E2 are the kinematic effective charges. The third

and fourth terms are resolved Breit Wigner resonances cen-

tered around energies E1 and E2 respectively. Each term of

this expression will be examined further in the following


The expressions for the resonance terms in the

center of mass are

= g() p (3.11)
((E' ) 2+F/4)


R2 = g2(EI)/2 p/2
p2 (3.12)
((E' E )2+r /4)
Y 2

The energy dependence of the resonance partial widths is

explicitly included in these expressions where P is the

proton penetrability calculated by the method of B. Buck,
et al. and

2L+l F
(E ( (B') p
(E k2 ) E

describes the energy dependence of the transition amplitude

(F ) of a L = 2 multiple. The resonance strength for the

gamma ray resonant absorption is then

C2 C2(2L+1) F F 4g2(E) P (3.13)
ty p (3.13)
(E') 2 (E') 2

The energy dependence of the total width of the resonance

is included by using the proton and neutron penetrabilities

and their respective reduced widths, i.e.

r = F + F = 2yn + 2yp (3.14)
n p n n pp

The deuteron and gamma partial widths are assumed to be

negligible with respect to the neutron and proton partial

widths. The reduced widths are solutions to the equations

(E) = 2y2Pn(E) + 2y Pp(E) (3.15)
n n pp


Yn Yp

for the resonance centered about the energy E. The neutron

and proton contributions are here assumed to differ only by

coulomb effects. The phase 4 in each case is the resonance

phase, given by

n = tan E i) (3.16)

The phases n1 and n2 account for the relative phases be-

tween the resonances and the direct terms.

The functional form for the direct terms was taken

from the analysis of Flowers and Mandl.88 They assume

gaussian type wave functions and obtain relations of the


i -bE i6
DE e = a(EQ E 6 e P e (3.17)
Da e = (y) p


i62 3E -bE i62
D e = Ca (E )2E / e e (3.18)
2 -y p

The gaussian wave functions parameters are chosen to fit

the 4He rms. radius of 1.61 fm. given by electron scatter-

ing giving = .101 (mb/MeV/2), a2 = 5.13 x 10-5

(mb/MeV ) and b = .043 MeV .41 For comparison to the

experimental data, the direct El term was replaced with an

empirical function and the strength of the E2 term, a2, was

allowed to vary. The phases 61 and 62 were varied to ob-

tain the relative phase between the direct El and E2 terms

that best fit the data.

The above expression for the differential cross

section is in the form of products of spherical harmonics.

These products are expanded in terms of single spherical

harmonics. The product expansion is

+' L
Y ()Y () = (-1)m i (2t+1) (2i'+1)
L= I -'I M=-L 4- (2L+1) (3.19)
Cooo m' M M

where the Clebsh-Gordon coefficient CmmM is zero for

M / m'-m. The resulting expansion is in terms of the YLO

functions alone. The functions YL0 are simply related to

the Legendre polynomials by the function

YL0(6,) = -- PL (cose) (3.20)

Collecting the terms of the polynomials and comparing with

the Legendre expansion of the angular distribution allows

identification of the expansion coefficients in terms of the

direct and resonance contributions of the model. In order

to make this identification the following three definitions

are made:

B = (EcDI)2

B1 = [2EDIE2D2Cos (6-62)-2c1DI (Ricos (i.+ni-61)+R2COS(42+ 2-6) ]

B2 = [(C2D2) 2-2e2D2(Rlcos(4l+nl-5c2)+R2cos(2+r 2-62)) +12

+2R1R2cos(01+qi-r2-n2) + R2].

In these definitions B appears in terms of only El ampli-

tudes, B1 appears in terms of products of El and E2

amplitudes, and B2 appears in terms of E2 amplitudes only.

The coefficients of the cross section expansion may then be

written as follows:

1 3 1 5
A = (B +B2), A a = B, A a2 (-Bo+ B)
4x/5 o 4 o

Aoa3 = -A .a, Aa4 = -1 B2
0 6a 7(4[) (3.22)

In this form the El and E2 contributions are explicitly


The Legendre expansion gives the differential cross

section as a function of angle 6 in the limit of infinitesmal

solid angle; however, the actual detector solid angle is

finite. In order to compare the model to experiment, it is

therefore necessary to transform to finite geometry. This

transformation introduces geometric correction factors Q.

(Ferguson 89 ) into the expansion. The resulting expression

for the experimental cross section is

yI = A (Qo+aiQ1Pi(cos6)+a2Q2P2(cos9)
0A (3.23)

+a3Q3P3 (cose)+a4Q4P4(cos6))

The yield from the 3H(p,y)4He reaction is converted

to the photonuclear reaction 4He(y,p) 3H by the principle of

detailed balance. The relationship between the cross

sections is given by

1 ( ( H)+1)(21I(3H)+1) 2m cpE (p90
y,p 2 (2I(4He)+l) E2 pY

where I(A) is the nuclear spin of nucleus A.

Using these relations, a computer program was de-

veloped which plotted the model cross sections against the

measured cross sections as a function of energy and angle.

The model parameters for the curves that best represented

the plotted experimental data were used to obtain the

resonance parameters and the integrated strength of the

various components of the model. These results are

presented at the end of this Chapter.

Angular Distributions

The angular distribution data were measured in an

attempt to obtain a direct measurement of the E2 strength

through a determination of the coefficient a4. The magni-

tude of the cross section for e = 0 180 also provides a

determination of the contribution of spin-flip interactions

to the cross section. The experimental data are fit by

linear least squares to the first four terms of the Legendre

cross section expansion for finite geometry as discussed in

the previous section. For some measurements, the resulting

fits were negative for 6 = 0, 1800. A non-linear least

squares search with the additional requirement that the cross

section be positive was then used to obtain the values for

the coefficients Ao, al, a2, a3, and a4. The error associa-

ted with each coefficient is then obtained from the

curvature of the Chi-square space.

The assumption that the El and E2 spin flip is

negligible is tested by the angular distributions. The

truncated Legendre expansion reduces to

d (6) = Ao(l+a +a +a3+a,) (3.25)

at 8 = 00 and

dg (0) = Ao(l-a1+a2-a3+a4)

at 6 = 1800. The cross section is equal at these two angles for

a3 = -al and zero if in addition l+a +a4 = 0. Assuming only El

and E2 radiation, the coefficients Aoa, and Aoa3 can be

written in terms of the complex vectors Ijj JJ> for total

angular momentum (p3) coupling where + S is the

total angular momentum of the incident particle, = S

is the total angular momentum of the target and J = 3 + 8

is the total angular momentum of the system. The nuclear

spins are S and S of the projectile and target respec-
tivelywhile a is the orbital angular momentum. The R
matrix elements () for radiation of multi-

polarity e? and compound nucleus of ground state spin I = 0

are the following for El and E2 radiation:

<011 ITI 1> = Pe 2, <011 T i3/21/21> = P3/ e
i2Q2/ 1
<022 [TI1 //2/2> = d/2e /2, <022 TI 5/'/2 = d5e

The resulting expression for the coefficients are as follows:

i(23 11/2 ))
Aoa1 = {/f0 Re(Pd /2 e2

3 /2 1 3/2) (3.28)
5 Re(Pd/2

+33/3 i(25/2-1/2)
3 Re (P d 5/2d ,/ e

A a3 = { 15 Re(Pd3/2 e )
+o i3i2 3/Y)

5 Re(P2d 3/2 e13/) (3.29)
-5 3 /2/2

5 Re(P 32dse /)

The relationship a3 = -al can be obtained from these equa-

tions by imposing the following conditions on the phases

13/2 = '1/2 + nm
/2 /2
n = 0,2,4, ... (3.30)

2 2 + nT

With these conditions there are two possible classes of

solutions to equations 3.28 and 3.29 that lead to the

result a3 = -al. One class is obtained when the ratio be-

tween the magnitudes d3 and ds/ equals -/6/3 in which

case the ratio between the magnitudes Pi/ and P3 is

indeterminate. The other possible class of solutions is

obtained when the ratio between the magnitudes P1/ and P/2

equals -/2/2 in which case the ratio of the magnitudes d/2

and d/2 is indeterminate.

Alternatively the system may be described in terms

of the (A-S) coupling vectors ( i S X S LSJ>). The total

angular momentum is + = A + and the total spin is

A = A + B. The total angular momentum is then + = A + A.

These vectors can be related to the 3-3 coupling vectors

of equations 3.27 by the use of the 9j symbols.9 The

relationship is as follows:

IL S -LSJ> = I(2S+1) (2L+1) (2j +1)(2j +1)]

SL I ja(3.31)

ja J J

The results for total angular momentum and parity J' = 1


10I 1 101 > = -7 1 1 > + /I 3/,1/ >
3 3

0 1 111 > = /j 1 > + 3/21/2
3 3

The results for total angular momentum and parity J" = 2+

10 2 202 > = -/S /21/22 > + /T15 21/22 >
5 5

10 2 212 > = /1 3/2'/22 > + /I [ 5/21/22
5 5

The two cases leading to the relation a3 =-al are obtained

by either I01111> or I02212> being equal to zero.

Studies with polarized protons indicate that I01111> is
92 15,19,33
non-zero. As seen by previous experimenters 15,19,33

the contribution of the spin flip terms 101111> and

1.02212> to the un-polarized cross section is zero to

within the experimental error. The data in this experiment

are consistent with neglecting spin-flip as can be seen in

Figure 2.7 and 3.3. Therefore, these terms were not

included in the analysis.


The experimental data is consistent with the

assumption that the reaction is dominated by the electric

dipole radiation. Considering only electric dipole and

quadrupole radiation, the magnitude of the cross section

for 6 = 900 is a measure of the electric dipole strength
if the angular distribution of the quadrupole radiation is

of the form of the spherical harmonic Y21 (which vanishes

at 900). Using these assumptions, an empirical equation

for the electric dipole strength was derived from the ex-

perimental data, using a linear least squares fit to the

experimental 3H(p,y) 4He cross section between 23 and 42 MeV

excitation. The cross section in this energy range was

found to be best represented by a cubic polynomial with a

reduced chi-square of 0.02. The resulting expression for

the El radiation in the model is
3 5 2 -7 3
2 4m c2E {1.518x10 +3.953x10 E -3.921x10 E +5.419x10 E }
D= p p x x x
Y (3.34)

This expression gives the 90 cross section shown as the

solid curve in Figure 2.5. Using this result for D1 the

model parameters were obtained to produce the solid curves

in Figure 2.6 for the angles cm = 530, 1230. The asymmetry

(as) resulting from this calculation is displayed as the

solid curve in Figure 3.2. The parameters of the calculation

are shown in Table 3.1 for the resonances observed in the


Table 3.1

Direct and Resonance Parameters of the E2 Cross Section

E(Mev)* r (keV) F (MeV) n 6 a(mb )
p 2 MeV

35. 2.6 12.8 500 -650 1.24x10 -46

39.5 0.60 3.2 350

*all energies are cm

The least squares fits to the angular distributions are shown

in Figure 2.7 as the solid lines. The coefficients for the

Legendre polynomials as a function of the incident proton

energy at the center of the target are displayed in Table 3.2.

The Legendre coefficients obtained from the excitation curve

analysis are shown as the solid curves on Figure 3.3 overlaid

with the experimental results. The experimental results are

shown to support the hypothesis that a3 =-al and l+a2+a4=0 to

within experimental error at all measured energies with the

exception of E = 23.0 MeV. The agreement between

3 4
Figure 3.2 Asymmetry of the H(p,y) He Angular Distribution.
The asymmetry data from the measurements at cm = 550 and
1250 are the solid dots with the error bars showing the
statistical error. The asymmetry from the angular Distri-
bution of Figure 2.7 are shown as x's with arrowheads
indicating the error propagated from al and a3. The results
reported by previous experimenters is also plotted.136058









>,- >
M (U

Figure 3.3 Coefficients of the Legendre Expansion of
o(9). The a. coefficients from the angular distributions
of Figure 2.7 are shown as x's in the upper plot. The
error bars are the errors of the coefficients a. obtained
from the least squares fit of the data to the Legendre
expansion. The lower plot shows the experimental A
obtained from the cross sections of Figure 2.6. The
solid curves in both plots are the results obtained from
the model (Equation 3.10). The energy E is in the center
of mass.







the experimental data and the model of direct E2 and two E2

resonances superimposed on a dominant El background inter-

action is seen to be quite satisfactory.

For comparison to theoretical calculations in the

literature, the integrated cross sections due to the indi-

vidual components of the model were evaluated. The total

photonuclear cross section is obtained by integrating the

Legendre polynomial expansion of the angular distribution

(Equation 1.4) over all solid angleS. The result is

Fl E2
IdQ do = 47A = B + B = o + o

where Bo and B2 are defined by Equation 3.21. As seen in

Equation 3.21, the individual contributions of the direct

and resonance terms used in the model may be evaluated

separately. The results of this evaluation are shown in

Table 3.3.

Table 3.3

Cross Sections Integrated From 22 to 44 MeV Excitation

fa dE = 30.6 mb MeV / E1 dE = 29.6 mb MeV

foE2 dE = 1.01 mb MeV

I Rk2 dE = 0.226 mb MeV

/ R22 dE = 0.047 mb Mev

f 2 dE = 0.969 mb MeV

I/ E2 dE = 8.12x10-4 mb/Me

S^R1 dE = 1.78x10- inb/


R2 -4

/ R dE = 3.07x10 mb/



S= 6.69x104
dE = 6.69x10 mb/Me


The TUNL Cyclo-Graaff was used to obtain data from

the H(p,y) He reaction for protons of energies from 8-30

MeV in the laboratory. The data were taken as a series of

excitation curves and angular distributions. The data

obtained can be adequately accounted for if the radiation

is viewed as being predominantly electric dipole with an

admixture of direct and resonant electric quadrupole radia-

tion. Two electric quadrupole resonances are observed and

the resonance width obtained for each. The resonance at a

compound nucleus excitation of 35 MeV with a width of 12

MeV is in good agreement with the result reported by Malcom,

et al.22 in the 4He photoneutron experiments at the

Saskatchewan Linear Accelerator Laboratory. A second,

previously unobserved, resonance is seen with a width of

"3.2 MeV at an excitation energy of 39.5 MeV. A survey of

the experimental literature shows a possible indication of
4 2
structure at this energy in the He(y,d) H reaction measure-

ments reported by Skopik and Dodge69 and in 4He(y,p) H

assymetry measurements by Arkatov, et al.,19 thus lending

credibility to the result reported here.

The observed resonances are in good agreement with

the (JC,T) = (2+,0) and (2+,1) levels reported by Szydlik,

et al.36 for shell model calculations with modified Sussex93

potentials, where T is the isospin quantum number.94 This

reference quotes levels of (2+,0) located at about 34 MeV

and (2+,1) located at about 44 MeV excitation. The inte-

grated strengths of these two levels are reported as 0.86

and 0.96 mb MeV respectively giving a total E2 strength of

1.86 mb MeV from threshold to 50 MeV. This strength com-

pares with 0.23 and 0.047 mb MeV for the two levels observed

and 0.97 mb MeV for the E2 direct term. The total E2

strength from this experiment is found to be 1.01 mb MeV

(Table 3.3).

The above reference would imply that the newly

observed level at 39.5 MeV would have an isospin assignment

of T = 1. A definite assignment of the isospin quantum

number can not be made from this experiment as both T = 0

and T = 1 quadrupole states can be formed in the H(p,y)4He

reaction. The narrow width, however, suggests the T = 1

assignment since fewer decay channels are available.

A recent microscopic continuum calculation by

Bevelacqua and Philpott9 indicates a (2 ,0) resonance

of 3.8 MeV width at about 39 MeV in 4He. Bevelacqua and

Philpott compare this level to the experimental data of

Lin, et al.96 Using inelastic scattering of deuterons from

4He and 6Li, Lin and Associates suggest the existence of a

level of width from 2.8 to 5.6 MeV at an excitation energy

of 31.7 MeV to fit the trend of their data at the upper end

of their observed energy range. Since the data of Lin, et al.

includes only the low energy tail of this resonance, their

width assignment of this level must remain questionable.

While it is tempting to associate this narrow level with the

level observed at 39.5 MeV in this experiment, the level at
35 MeV observed both here and by Malcom, et al. cannot be

ignored. If the level in the reported calculation of

Bevelacqua and Philpott corresponds to the 35 MeV resonance

observed here, then their level corresponding to the 39.5

MeV resonance would be at an energy beyond the range of their


It is apparent that further theoretical work is

necessary in order to explain and understand the existence

of the 2+ level at 39.5 MeV observed in this experiment.

This series of experiments extends the energy range covered

by the 3H(p,y)4He reaction measurements from 18 to 30 MeV

incident proton energy. The (p,y) reaction lends itself to

better resolution and simpler analysis than the 4He(y,p)3H

or 4He(e,e'p)3H experiments that comprise the data in the

literature in this energy range. The effects of an E2

component in the radiation are seen in the measured angular



The spectra for each energy and angle measurement

were written on magnetic tape for off line computer analysis.

The spectra were fit to the response curve of the detector

for monochromatic y-ray. This response curve was obtained
3 4
by accumulating a H(p,y) He spectrum with 2741 counts in

the full width at half maximum of the peak. A least squares

fit to the spectrum was obtained for the composite function

F(x) = (l-0(x-Cg+e)exp (C1+C2X+C3X2+C4x3)

+ 8(x-C9-C)exp (Cs+C6x+C7X2+C8X3)

o x < x
6(x-x ) = 1{ x > x

and xo = C9 is the channel where the two functions have equal

magnitude and slope.97 The first term is the low energy tail

of the peak and the second is the peak and high energy edge

of the spectrum. The coefficients Ci obtained from this fit

determined the standard curve shape. The experimental

measurements were then fit to the equation

F(X) = B (l-9(X-C9+c)exp (CI+C2X+C3X2+C4X3)

+ 6(X-Cg-E)exp (C5+C6X+C7X2+CsX3)

where X = + X The fitting parameters are the
R max

amplitude B, the gain R and the peak position P. The

variable x corresponds to the channel numbers, and the term

X is the peak of the standard spectrum. The fitting is

done by a parabolic extrapolation of the chi-squared hyper-

surface routine that is a modification of the routine Chifit

described by Bevington. This routine was found to be

reasonably fast while yielding reproducable fits to the

experimental spectra. The coefficients of the fitting

equation are as follows:
Cl = 3.6393 C5 = 1.4269x10

2 1
C2 = 8.9808x10 C6 = 1.4674x10
2. 2
-4 2
C3 = 4.8943x10 C7 = 5.0242x10

7 5
C4 = 9.1427x10 C = 5.7104x10
4 8

Xax = 312.5 C = 294.
R = (x2-xl) 2.5x10 B = N/95.

The peak channel counts N, and half width x2 xl are

initially selected by the operator using a light pen on

the displayed spectrum.

A sample fit is shown in Figure A.1 for the gamma

ray emitted at the laboratory angle of 650 for an incident

proton energy of 30 MeV.

3 4
Figure A.1 H(p,y) He Spectrum for 30 MeV Incident Proton
Energy. The full energy peak, first escape peak, and
second escape peak are indicated. The solid curve indi-
cates the fit obtained using the peak fitting program





Table B.1

Experimental Angular Distributions*

E 29.5 32.4 33.9 35.4

8 26. 21. 21.
o(6) 2.34 + .18 1.57 .15 1.41 .14

6 44. 44. 44. 44.
0(6) 4.95 .20 4.48 .15 4.42 .15 4.14 .14

8 52. 52. 52.
a(6) 5.63 .17 5.93 .17 4.80 .16

8 57.
0(8) 7.59 .25

0 72. 73. 73. 73.
o(6) 8.50 .27 7.17 .19 6.28 .18 5.47 .14

8 82.
o(6) 7.99 .27

8 92. 93. 93. 93.
0(e) 6.70 .24 6.02 .18 5.19 .17 4.78 .27

6 112. 113. 113. 113.
a(6) 6.19 .24 4.86 .16 4.36 .16 3.85 .15

6 127. 132. 132. 127.
0(6) 4.28 .20 2.80 .13 2.69 .12 2.50 .12

6 143. 144. 144. 144.
a(6) 2.17 .14 1.74 .07 1.74 .10 1.33 .07


Table B.1 (continued)

E 36.8 38.3 39.8 42.0
8 21. 21. 21.
o(e) 1.31 .13 1.42 .14 .86 .11

o 44. 44. 44.
0(o) 3.43 .11 3.68 .11 3.18 .11

6 50. 50. 51. 51.
0(8) 3.86 .12 3.96 .12 3.45 .11 4.09 .18

9 58. 58. 58. 61.
o(6) 4.80 .13 4.70 .13 3.92 .12 4.66 .14

e 73. 73. 73. 68.
o(8) 6.68 .17 6.15 .17 5.00 .15 4.71 .14

6 84.
a(6) 5.33 .22

8 93. 93. 93. 97.
0(8) 4.34 .13 3.42 .11 3.29 .11 3.38 .19

o 113. 113. 113. 113.
S0() 3.24 .11 2.63 .10 2.86 .11 3.01 .12

o 128. 128. 128. 128.
Co() 2.28 .10 1.72 .08 1.68 .08 2.01 .10

o 144. 144. 144. 144.
o0() 1.32 .06 .99 .04 1.04 .05 .96 .07

* all entries are center of mass, cross sections are pb


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The place of my birth is Magdalena, New Mexico, and

the date was May 24, 1947. I am the eldest of four children.

I attended the Quemado, New Mexico, grade school until the

seventh grade when my family moved to Robert Lee, Texas,

where I completed my primary and secondary education in the

Robert Lee Schools. I played the flute in the high school

band and was elected to the Beta Club National Honor Society.

In May, 1964, I graduated second in a class of twenty-two.

After graduating from high school, I entered San Angelo

College, later to become Angelo State University. I was a

member of the college band, was elected into Alpha Chi

National Honor Society, and was awarded a Certificate of

Scholastic Excellence. In June, 1968 I was awarded the

degree of Bachelor of Science with a major in physics. Upon

being awarded a NASA Traineeship by Illinois Institute of

Technology, I entered Graduate School. While attending IIT,

I met my wife to be. When I had completed the requirements

for the degree of Master of Science at IIT, I transferred

with my new bride to the University of Florida to complete

my education.

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