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thesis entitled

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1€0(p,d)150 AND l“m(p,d>lun RPACTIAXC

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James Lewis Snelgrove

has been accepted towards fulfillment
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Ph.D degree in Physics

55/777,; {2%

Major professor

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ABSTRACT

ENERGY DEPENDENCE AND SPECTROSCOPY
IN THE
l60(p,d)150 AND 15N(p,d)14N REACTIONS

By James Lewis Snelgrove

A systematic study of the extraction of spectroscopic
factors for the (p,d) reaction on light nuclei and the
difficulties encountered in obtaining reasonable DWBA fits
to the shapes of the angular distributions has been made.
Deuteron spectra and angular distributions were obtained for
the 16O(p,d)150 reaction over an angular range of 10°
to 165° in the center-of—mass frame for 25.52, 31.82, 38.63,
and 45.34 MeV incident protons using the variable energy
proton beam of the Michigan State University sector focused
cyclotron. Partial angular distributions were obtained for
other proton energies between 21 and 36 MeV. The elastic
scattering of protons from 16O was measured over the same
energy range and used to obtain proton optical model
parameters. Deuteron Optical model parameters for the
l6O(d.d)160 reaction were obtained from the literature for

use in the DWBA exit channel calculations.

 

 

 

code
0.0
Opti

Obta

James Lewis Snelgrove

DWBA calculations were performed using the Oak Ridge
code JULIE, and spectroscoPic factors were extracted for the
0.0 MeV, 1/2_ and 6.18 MeV, 3/2- levels of 150. Unadjusted
Optical model parameters were used with a 3 F cutoff to
obtain some agreement between the shapes of the experimental
and theoretical angular distributions. The absolute values
of the extracted spectrOSCOpic factors were found to depend
strongly on the value of the neutron bound state well radius
used in the DWBA calculations. The best absolute values of
the spectrOSCOpic factors were obtained when the neutron
bound state well radius was set equal to the proton real
well radius,whereas relative spectroscopic factors were
found to depend much less strongly on this parameter. The
energy dependence of the differential cross section was
reproduced by the DWBA calculations for deuterons in the
exit channel having a center-of—mass energy greater than
22 MeV. The variable energy feature of the MSU cyclotron
was used in a scheme to eliminate part of the Q-dependence
from the relative spectrOSCOpio factors. The lack of any
improvement indicates that the problems with the DWBA
calculations are probably not in the deuteron channel.

At least 30% of the lp3/2‘strength.appears to be missing
from the 6.18 MeV._3/2- leve1._with approximately 12%

of the missing strength_appearing in the 9.60 MeV and

—__—-—-——-— fi“

 

 

 

 

1C

0v:
fre
39 .

worj
l4

bei

The

James Lewis Snelgrove

10.46 MeV levels. Small 25—1d admixtures and a possible

1g7/2 admixture were observed in the ground state of 160.

Energy spectra and angular distributions were obtained
over an angular range of 10° to 145° in the center-of—mass

14
15N(p,d) N reactions at

frame for the 15N(p,p)15N and
.39.84 MeV. Using the method determined by the l6O(p,d)150
work, spectrOSCOpic factors were extracted for the levels in
4N populated by £n=l pickup. These values were found to
be in excellent agreement with intermediate coupling predicticnns.

14N at 9.17 and 10.43 MeV were found to

14

The 2+, T=1 levels of
be strongly mixed. The 13.72 MeV level of N was unambigu-
ously assigned Jfl=l+, T=1 on the basis of comparison with
theoretical predictions, and a width of 210 i 30 keV has
been determined for this level. Angular distributions for
all the 14N levels pOpulated in the 15N(p,d)l4N reaction

are shown.

ENERGY DEPENDENCE AND SPECTROSCOPY
IN THE

14
16o(p.d)150 AND l5N(p,d) N REACTIONS

BY

James Lewis Snelgrove

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Physics

1968

 

 

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ACKNOWLEDGMENTS

My deepest appreciation goes to Dr. Edwin Kashy for

the advice and counsel he hasgiven me throughout my

_graduate study and particularly during the preparation

of this thesis.

The assistance of Dr. Barry Preedom and Miss Thelma
Arnette in the use of the optical model and DWBA codes
was invaluable. I also acknowledge many helpful discussions
with other members of the professional staff of the
Michigan State University Cyclotron Laboratory.

I am grateful to Phillip Plauger and Craig Barrows
for their assistance in data acquisition and to Bryan
Horning for his help in analyzing the data.

To the members of the Cyclotron Laboratory technical
staff go my thanks for their assistance in building and
maintaining apparatus used in the experiments for this
thesis and for their help in running the cyclotron itself.

I also acknowledge the financial support of the
experimental program provided by the National Science
Foundation and the personal financial support provided by
a three-year National Aeronautics and SpaceAdministration

TraineeShip and a one—year National Science Foundation

Graduate Fellowship.

ii

 

 

LJ
Li
Ch

Ch.

Cha}

Acknowledgments
List of Tables

List of Figures

TABLE OF CONTENTS

Chapter I. INTRODUCTION

Chapter II. NUCLEAR THEORY

II.AO
II 0A. 10

II.A.Z.

II.A.3.

II.B.

Distorted-Wave Born Approximation

ii

vi

vii

DWBA Expression for Differential Cross

Section

Finite-Range and Non-Locality
Corrections

Extraction of Experimental Spectro-
scopic Factors

Intermediate Coupling Model

Chapter III. EXPERIMENTAL APPARATUS AND METHODS

III.A.

III.A.l.
III.A.Z.
III.A.3.

III.A.4.
III.B.

III.B.l.
III.B.Z.
III.B.3.
III.C.

III.C.l.
III.C.Z.

III. C-. 3 .l

III.C.4.

Proton Beam Production and Handling
Cyclotron

Analysis System

Alignment of Beam to Scattering
Chamber

Charge Integration

Scattering Chamber Set-Up
Scattering Chamber

Targets

Counter Systems

Electronics

16O(p,p)160 Experiments
l6O(p,,d)150 EXperiments

15

15
15
16

18
20
20
20
21
25
26
26
27

15N(p,p)15N and 15N(p,d)14N Experiment 32
Comparison of the Systems for Particle"

Identification

iii

33'

 

 

Che

Chap

Chapt

III.D.
III.D.1.
III.D.2.
III.B.
III.E.1.

III.E.Z.

Data Acquisition and Analysis

Data Acquisition

Data AnalysiS'

Analysis of Experimental Uncertainties
Beam Energy and Energy-Level
Determination

Differential Cross Sections

Chapter IV. ELASTIC SCATTERING DATA AND OPTICAL MODEL

PARAMETERS
IV.A. Proton Elastic Scattering
IV.A.l. 160(plp)15o
IV.A.2. 15N(P:P)15N
IV.B. Optical Model Analysis of the Proton
Eéastic Egattering Data
IV.B.l. O(P:P) O
IV.B.2. 15N(PIP)15N
IV.C. Deuteron Optical Model Parameters

Chapter V. EXPERIMENTAL RESULTS

<l< < <.< < <
unfilw'?'> w >
thH

O
H
O

<=F
who
him

160(p,d)150

Simple Model Predictions

Energy Spectra

Negative Parity Levels

Positive Parity Levels

15u(p,d)14N

Simple Model Predictions and Energy
Spectra

Levels Reached by £n=l Pickup
Levels Reached by £n#l Pickup

Chapter VI. DWBA ANALYSIS, EXTRACTION OF SPECTROSCOPIC
FACTORS, AND COMPARISON TO THEORY

VI.A.
VIOAOIO

VI.A.2.

VI.B.

VI.B.1.

VIOBOZO

160(p,d)150

DWBA Calculations and SpectrOSCOpic
Factors for the 0.0 and 6.18 MeV
Levels

SpectrOSCOpic Factors for Other
Levels,ang the Ground State of 16O
l5N(p.d) N

DWBA Calculations and Experimental
SpectrosCOpic Factors

Comparison to the Intermediate
Coupling Theory

iv

,35

35
36
41

41
42

46

46
46

47

50
53
58

60
64

64
64
67
74
79

86
86
87
92
99

99

100

116
121

121

127

Chapter VII. SUMMARY AND CONCLUSIONS 133

Appendix A. TABULATION OF 16O(p,p)16o AND 160(p,d)150

DIFFERENTIAL CROSS SECTIONS 135
15
Appendix B. TABULATION OF 15N(p,p)15N AND N(p,d)l4N
DIFFERENTIAL CROSS SECTIONS 154

References 163

 

Tab
III

III-
IV—

IV-.

VI—J

VI-z

VI~3.

VI-4.

VI‘S.

Table
III-1 o

III-2.

IV-1.

IV-2.

VI-l.

VI-2.

VI-3.

V1-4.

VI-5.

LIST OF TABLES

Contributions to the energy resolution obtained
with the three methods of particle identification

Estimated uncertainties in quantities involved
in the calculation of absolute cross sections

Optical model parameters describing proton
elastic scattering from 16O and 15N

Deuteron Optical arameters used in the DWBA
analysis of the 1 O(p,d)15O and l5N(p,d)14N
reactions

Experimental spectrOSCOpic factors for the 0.0
and the 6.18 MeV levels of 150 from the
l6O(p,d)150 reaction induced by 25.52-45.34
MeV protons

Ratios of experimental spectroscopic factors for
the 0.0 and 6.18 MeV levels of 150 from the
160(p,d)150 reaction induced by 25.52-45-34

MeV protons

Peak cross sections and spectroscoPic factors
for the levels observed in 150 with 45.34
MeV incident protons

Peak cross sections and spectrOSCOpic factors
for the levels observed in 14N with 39.84
MeV incident protons

Intermediate coupling predictions of coefficients
of fractional parentage and spectrOscopic
factors for lp neutrOn pickup from 15N. Also
included are the spectrosCOpic factors predicted
in jj-coupling

vi

43

44

57

62

114

114

117

125

128

 

Fig
II]

III
III
III-
III~
III~.
IV~j
IV~2

IV~3

IV~4.

IV~5.

Iv~6 .

Figure
III-1.

III-2 o

III-3.

III-4.

III-5.

III-6.

IV-1.

IV-2 o

IV-3.

IV-4.

IV-5 o

IV—6 0

LIST OF FIGURES

Experimental area of the Michigan State
University Cyclotron Laboratory

Section of the beam system leading to the
36—in. scattering Chamber

Diagram of the 3-in. gas cell used in the
experiments

Block diagram of the electronics for the
Goulding method of particle identification

Block diagram of the electronics for the time-
of—flight method of particle identification

Block diagram of the electronics for the pulse
multiplication method for particle identification

16O(p,p')160 spectrum at SLAB = 29.2° for
Ep=25.46 MeV

16O(p,p)160 experimental angular distributions
for Ep = 25.46--45.13 MeV.

Effects of variations of individual Optical
model parameters on the calculated 16O(p,p)160
angular distributions

Optical model fits to the 16O(p,p)160 angular
distributions using an average set of parameters

Optical model fits to the 16O(p,p)160 angular
distributions using energy-dependent sets of
parameters

Optical model fit to the 15N(p,p)15N angular
distribution

vii

17

19

23

29

30

48

49

52

55

.56_

59

IV-7.

V-6.

V'8.

V-9.

v-10 0

Optical model parameters describing the
elastic scattering of deuterons from 160
between 11.8 and 52 MeV

Simple shell model configurations of the 160
ground state and the 150 1/2‘ and 3/2’ states

Energy level diagram of 15O displayed beside
a deuteron energy Spectrum from the 16O(p,d)150
reaction for Ep=45.34 MeV and GLAB=20.1°

Deuteron energy Spectra at 8 =61.9° and
118.0° from the 16O(p,d)150 Eégction for
E =45.34 MeV

P
Deuteron energy spectra at 8 =20.0° and
60.1° from the l6O(p,d)150 reggtion for Ep=
38.63 MeV

Deuteron energy spectra at 0 =20.l° and
20.0° from the 16O(p,d)150 rgégtions at
Ep=3l.82 and 25.52 MeV, respectively

High resolution energy spectrum of reaction
products at GLAB=17.5° for 32.00 MeV protons‘
incident on - 160, obtained by use of
time-of-flight techniques for particle
identification

Deuteron angular distributions for the 0.0
MeV, l/2' level of 15O from the 160(p,d)150
reaction for incident proton energies between
21.27 and 45.34 MeV.

Deuteron angular distributions for the 6.180
MeV, 3/2' level of 150 from the l6O(p,d)150
reaction for incident proton energies between
25.52 and 45.34 MeV

Dependence of the 2 =1 peak cross section
of the 0.0 MeV, 1/2- and 6.180 MeV,
3/2- levels of 150 from the 16O(p,d)150
reaction on the incident proton energy

Deuteron angular distributions for thIGQ'GO
and 10.46 MeV levels of 150 from the O(p,d)
reaction for Ep=45.34 MeV

15O

viii

61

66

69

7O

71

72

73

75

76

77

'82.

V—ll.

V-12.

V-13.

V-l4 o

V-lSO

V-16.

V-17.

V-18.

V-19.

V-20.

V-Zl.

Deuteron angular distributions for the 5.188—
5.240 MeV doublet of 15o from the 15O(p,d)150
reaction for incident proton energies between
25.52 and 45.34 MeV

Deuteron angular distribution and DWBA fit
for the 7.284 MeV, (7/2 ) level of 150
from the 16O(p,d)l5O reaction for Ep=45.34
MeV

Deuteron an ular distributions for other levels
excited in 50 from the l6O(p,d)150 reaction
at Ep=45.34 MeV

Simple shell model configurations of the 15N
ground state and the l N levels, based only
on ls-lp nucleons

Energy level diagram of 14N displayed beside a
deuteron energy spectrum from the 15N(p,d)14N
reaction for E =39.84 MeV and 6 =19.9°

p LAB
Deuteron energy 5 ectra at 8 =59.8° and
ll9.6° from the 1 N(p,d)14N LABreaction for
Ep=39.84 MeV

+
Deuteron angular distributions for the 0 and
1+ levels of 14N strongly excited in the
15N(p,d)l4N reaction for Ep=39.84 MeV

Deuteron an ular distributions for the 2+
levels of 1 N strongly excited in the
15N(p,d)l4N reaction for Ep=39.84 MeV
Deuteron angular distributions for the 2—
and 3‘ levels in 14N excited by the
15N(p,d)14N reaction for Ep=39.84 MeV

Deuteron angular distributions for the 0-,l—,
3+, and 4+ levels in 14N excited by the
15N(p,d)14N reaction for EP=39.84 MeV

Deuteron angular distributions for other levels

of 14N weakly excited by the 15N(p,d)14N
reaction for Ep=39.84 MeV

ix

83

84

85

88

89

90

94

95

96

97

98

VI—l.

VI-2.

VI-3.

VI-4o

VI-5.

VI-6.

VI-7o

VI-8.

VI-9.

VI-lO.

VI-ll o

V1-12 o

VI-13.

DWBA fits to the l6O(p,d)150, E =45.34 MeV,
E =0.Q MeV, J"=1/2‘ angular disEribution for
different values of the deuteron imaginary
well depth

Dependence of calculated zn=l and 2 =2 peak
cross sections from the l6O(p,d)150nreaction
for E =45.34 MeV on the value of the lower
radiaI integration cutoff used in the DWBA
calculation

DWBA fits to the 160(p,d)150, E =45.34 MeV,
Ex=0.0 MeV, J"=l/2' angular dis ribution for
different values of the lower radial integration
cutoff '

DWBA fits to the l50(p,d)150, E =45.34 MeV,
EX=6.18 MeV, J"=3/2’ angular digtribution for
different values of the lower radial integration
cutoff

Basis for the selection of incident proton
energies for the 16O(p,d)150 experiments

DWBA fits to the l6O(p,d)15O, E =38.63 MeV,
Ex=0.0 and 6.18 MeV angular dis ributions

DWBA fits to the 16O(p,d)150, E =31.82 MeV,
Ex=0'0 and 6.18 MeV angular disgributions

DWBA fits to the l6O(p,d)15(2, E =25.52 MeV,
Ex=0’0 and 6.18 MeV angular disgributions

DWBA fit to the 16O(p,d)150, E =45.34 MeV,
E =5.188-5.240 MeV (doublet) aRgular

X . . ‘
dlstrlbutlon

DWBA fits to the 15N(p,d)14N, E =39.84 MeV,
Ex=0.0 and 2.311 MeV angular di tributions

DWBA fits to the 15N(p,d)l4N, E =39.84 MeV,
Ex=7.03 and 13.72 MeV angular dIstributions

DWBA fit to the l5N(p,d_)14N, =39.84 MeV,
Ex=5.lO MeV angular distribution

Theoretical and eXperimental 2n=l spectrOSCOpic

factors for the l5N(p,d)14N reaction

X

103

104

105

106

109

110

111

112

119

122

123

124

130'

CHAPTER I

INTRODUCTION

For a number of years the (p,d) reaction has proven
to be a pOpular and valuable tool in nuclear SpectrOSCOpy.
The selective way in which the (p,d) reaction populates
the levels of the residual nucleus provides information
about these levels and about the ground state of the
target nucleus, which can be compared to the predictions
of various models used to describe certain prOperties of
the nuclei. The direct reaction picture provides a
correlation between the shape of the deuteron angular
distribution and the angular momentum transferred to the
picked-up neutron. This enables one to make parity
(and sometimes, spin) assignments for the levels of the
residual nucleus. The most widely used theory of direct
reactions is the distorted—wave Born approximation (DWBA),
and from comparisons of experimental and theoretical
angular distributions one can also determine the overlap
of the target wavefunction with the wavefunctions of the
states in the residual nucleus. The overlap for a given

state is related to the SpectrOSCOpic factor,_an

2

experimental quantity extracted from comparison of the

data to theoretical calculations. The meaningfulness of

the SpectrOSCOpic factors, however, depends on the degree

to which the DWBA calculation represents the actual reaction.
mechanism. The distorted waves in a DWBA calculation are
assumed to be those which describe the elastic scattering

of the proton and deuteron by the appropriate nuclear
states, and are calculated from optical model potentials.

In studies of (p,d) reactions on nuclei in the 1p and ZS-ld
shells, difficulty has been encountered in obtaining
reasonable agreement of the experimental and theoretical
angular distribution shapes when Optical potentials which
best describe the elastic scattering are used in a standard
DWBA calculation (no integration cutoffs, etc.). The
theoretical shapes have been improved by somewhat artificial
means (e.g., adjusting potentials or using cutoffs), but
then one must question the accuracy of the SpectrOSCOpic
factors extracted on the basis of such calculations.

The present work was undertaken first to study the
extraction of (p,d) SpectrOSCOpic factors for light nuclei,
then to apply this knowledge to the analysis of data from
the 15N(p,d)l4N reaction, which had not been previously
studied. The target nucleus for the study of spectrosc0pic

16 x ” .
factors, 0, was chosen for several reasons. It Is a

nominally "closed-shell" nucleus on which numerous theoretical
studies have been done. One feels confident, then, in
making certain predictions about the values of the spectro—
scopic factors which should be obtained. These predictions
could be used as a guide in evaluating the results of a
_given DWBA calculation. Since, as will be shown, the
16O(p,d)150 peak cross sections Show a strong energy
dependence, it was possible to test the DWBA calculations
over a wide (WZOMeV) energy range. During the course

of the study considerable SpectrOSCOpic information was
Obtained on the levels of 15O and is. presented in some

4

detail. Similar studies have been made for the 0Ca(d,p)4lCa.

4OCa(d,3He)39K

reaction (Le 64) and for the 16O(d,3He)150 and
reactions (Hi 67).

Although the 14N levels have previously been studied
extensively by means of other reactions, the selective
nature of the (p,d) reaction made it possible to obtain
much new SpectrOSCOpic information about this nucleus.

The extracted SpectrOSCOpic factors are compared to those
predicted by the lp shell intermediate coupling calculations

of Cohen and Kurath (Co 67), which had previously proven

valid for lighter 1p shell nuclei (Ku 67).

CHAPTER II

NUCLEAR THEORY

II.A. Distorted-Wave Born Approximation

 

A direct reaction is defined as a reaction in which
only one degree of freedom is excited in the target nucleus
(Au 63). The (p,d) reaction is considered to be direct
if the proton picks up a neutron from the ground state of
the target nucleus in a simple one-step process. The
most distinctive characteristic of the direct reaction
process is a strong forward peaking of the angular
distribution and its subsequent oscillation with increasing
angle. Earliest attempts to describe the direct reaction
(Bu 51) used the plane wave Born approximation, but
recently the distorted-wave Born approximation (DWBA)
has been used exclusively. Extensive discussions of the
DWBA theory have been presented by Tobocman (To 61)
and Satchler (Sa 64). The most salient features of the
DWBA theory and the approximations employed in it are

discussed in the following sections.

5
II.A.l. 'DWBA Expression for Differential'Cross Section

The differential cross section for the reaction

A(a,b)B is given (Sa 64) by

I I Z ITI2
d0 =. “.3in . . kb MamaMbmb

* 2 2 -- (11.1)
d9 (Zwfi ) ka (2JA+1)(Zsa+1)

 

 

where the transition amplitude is

(-)*

+
T =de£afd£bxb (15b.£b)<B,bIVIA.a>xa( )(lga.§_a). (11.2)

Here J is the Jacobian of the transformation to the relative
coordinates Ea (the displacement of a from A) and Eb
(the displacement of b from B), and “a and “b are the
reduced masses of a and b. The functions xa and Xb
are the distorted waves and are taken to be the elastic
scattering waves which asymptotically describe the
relative motion of the a,A and b,B pairs before and after
the collision, respectively. The distorted waves are
usually calculated from an Optical potential of the form
shown in Chapter IV.

The remaining factor in (II.2) is the matrix element
of the interaction causing the inelastic event, taken
between the internal states of the colliding pairs, and

it contains all of the nuclear structure information.

Thus, the inelastic event is treated aS‘a perturbation to

the elastic scattering. The matrix element can be
expanded into terms corresponding to the transfer to the
nucleus of a definite angular momentum j, comprised of

an orbital part 2 and a spin part 5. These can be defined by

“frag-EA: §_=‘§b-§av £=l~ar

where sa, Sb are the intrinsic spins of particles aqb;
and JA' JB are the nuclear spins of A,B. The transition

amplitude becomes

2

.-2
> = .
J<JBMB,sbmbIVIJAMA, Sama 2531 Gflsjm(£b'£a)
5 -mb

_ ' _ _ _ >
x( ) <JA3MA,MB MAIJBMB><sasbma, mbls,ma mb
X<£sm,ma-mblj,MB-MA>. (II.3)
The term Glsjm(£b’£a) 15 called the radial form factor

and contains all of the information about the radial part
of the interaction. In general, it is convenient to
separate Gisjm as a product of a spectroscopic coefficient

and a form factor:

= . II.4
Gflsjm(£b'£a) ~Alsjf12,sjm(£b'-r-a)’ ( )
where A , contains such quantities as fractional parentage

28:

coefficients. 'Ibr the case of the (p,d) reaction, these

are the coefficients of the eXpansion of the ground state

.7

wavefunction of the target nucleus in terms of the wave-
functions of the final states in the residual nucleus

coupled to the wavefunction of a single neutron.

The evaluation of T (11.2) involves a six-dimensional
numerical integration, which is quite difficult. A
simplification usually used is the zero—range approximation,
in which the outgoing particle b is emitted at the point

at which the incoming particle is absorbed. This results in

*
, . N m _
fgsjm(rh'ra) — fgsj(ra)Yz (8a,cba)<3(rl MP r ), (II.£5)
B

3

where fgsj(ra) is the radial wavefunction of the picked—up
neutron for the (p,d) reaction. It now contains all of the
information of nuclear structure. Under the zero range
approximation, (II.3) implies an allowed parity change of
(—)" (Sa 64).

If only one value each of s and i are allowed, as
in the (p,d) reaction where s = 1/2 and R is determined
by the parity change, the value of the differential cross

section becomes (Sa 64, Ba 62)

' §g_='23' +’l st Sksjofisj(e) mb/sr. (II.6)

d9 25a + 1

Thus, with sa = 1/2, sb = l, and s = 1/2, the differential

cross section, since only onez and j are allowed,_is

£151 _~;s£.o£.(e), (11.7)
dB " 2 3 3

where O£j(8) is the cross section computed by the Oak
Ridge code JULIE (Ba 62, Ba 66). The effect of using zero
range rather than an effective range can be approximately
removed by multiplying O£j(9) by a factor of 1.5 (Au 64).

Thus, the final expression for the differential cross section

is

§%'= 2.2580DWBA(8) (mb/sr) (II.8)

where the subscripts have been drOpped.

II.A.2. Finite~Range and Non-Locality Corrections

 

The neglect of finite—range effects has been investi-
gated by Austernet a1. (Au 64) and proved to be most
important in reactions which involve large momentum
transfers. The inclusion of exact finite-range calculations
is difficult, but the effects are approximated by the
local energy approximation (Bu 64, Pe 64) as a correction
factor which multiplies the zero-range radial form factor
flsj(ra)' The effect is to lessen the contribution of the
nuclear interior. A further correction to the calculation.
can be made by the inclusion of non—locality in the Optical

potentials. This can also be calculated in the local

9
energy approximation, resulting in a further lessening

of the contribution of the nuclear interior.

II.A.3. ExtraCtion of Experimental SpectrOSCOpic
Factors

In the ideal case one would find that the calculated
DWBA angular distribution would reproduce the shape Of the
experimental angular distribution and would, therefore,
differ at each point by a constant factor, as shown in
(II.8). The SpectrOSCOpic factor S would, then, be
unambiguous. Although the DWBA and experimental angular
distribution shapes are Similar in many cases, the
application Of (II.8) at different points of the distribution.
will not give unique results. A method for the extraction
of spectroscopic factors which has been successfully
applied for (£n#0) (Ku 67, Ko 67a) is to use (II.8) at
the characteristic forward peak of angular distribution.
One might expect that the assumption of a direct reaction
is more valid for forward angle scattering. On a semi-
classical picture, the impact parameter for forward
angle scattering is much larger than for backward angle
scattering, so the incoming particle tends to interact
less with the nucleus and thus is less likely to excite

more than one degree of freedom. It is also thought (Au 63)

that exchange terms, which were not included in the

lO

transition amplitude, are unimportant at forward angles,
but they might make noticeable contributions at the
backward angles. Also, the fit of the DWBA calculations
to the data at the forward angles, where most of the
integrated cross section is contained, is usually best.

Thus, (II.8) has been applied to the forward peak
of the £n#0 angular distributions to obtain the corresponding'
SpectrOSCOpic factors given in this work. The situation for
the extraction of 2n=0 SpectrOSCOpic factors is not clear,

“0°.

since the characteristic forward maximum occurs at 8c m —

In these cases approximate SpectrOSCOpic factors might
be obtained by matching the DWBA calculations and the
experimental data at several forward angles. However,
owing to the uncertainties involved in such a procedure,
no attempt was made to extract 2n=0 spectroscopic

factors on this basis.

II.B. Intermediate Coupling Model

 

The two models used extensively to describe phenomena
involving the interaction of particles having both angular
momentum and intrinsic spin are the jj-coupling model and
the LS-coupling model. The jj-coupling model (the nuclear
shell model) has been very successful in explaining many
features observed in heavy nuclei (Ma 50). In this model

the spin—orbit force causes the orbital angular momentum

11

‘£_and the intrinsic s for each nucleon to couple to

form a resultant angular momentum i. Then, the 1's

of the individual nucleons interact to produce a character-
istic set of energy levels. The resulting wavefunctions
can be used to predict various nuclear prOpertieS. In

the LS-coupling model, which has been widely applied in

the study of atomic spectra, the spins of all the particles
are coupled to form a resultant spin S, and the orbital
angular momenta are coupled to produce a resultant angular
momentum L, These are then coupled by the spin-orbit
interaction to produce a total angular momentum J. The
energy level schemes predicted by the two models are
different, but the total number of states which can be
formed in each case are the same.

The success of the jj-coupling model for heavy nuclei
has not been repeated for the light nuclei, particularly
the 1p shell nuclei (Ku 52). The LS—coupling model
has not had much success for these nuclei either (Fe 37).
The concept of intermediate coupling, of which jj- and
LS-coupling are the two extremes, had been applied to the
theory of complex atomic spectra (€0.35) and was used
by Inglis (In 53) in an attempt to explain the energy level

sequences of the 1p shell nuclei.

12

Since the energy level sequence and spacing is
expeCted to depend upon the interactions of the 1p
nucleons, the interaction between any two of the nucleons
must be considered (this, of course, ignores the effects
of many—body forces). The central interaction is generally
considered to be a central interaction V(rij) multiplied

by an exchange Operator Oij usually approximated (R0 48) by

Oij

IZ

0.8P + 0.2Q, (II.9)

where P is the Majorana space-exchange Operator and Q is the
Bartlett spin-exchange Operator. A Simple form of the

Spin-orbit coupling Operator
HI = Za£.s (11.10)

is usually assumed as a perturbation term in the Hamiltonian.
In the early works (In 53) the parameter a was assumed to

be constant for a given nucleon shell. The diagonalization
of the unperturbed Hamiltonian, which gives the energies of

the levels, results in integrals of the form

L = fl” (ri)¢* (rj)v(rij)\Y(ri)¢(rj)d£id£j

and

(II.ll)

N
II

I)?" (ri) (if (rj )V (rij) (b (ri) 1b (rj )dgi'dgj .

 

 

upon
is r
prov
ener
isot

for

Pond

Pict

COup
and

data

13

The integral L is commonly called the ordinary, or direct,
integral,and K is called the exchange integral. The
energies calculated are a linear combination of L and
K, so that the Splitting of the degeneracy by the
perturbation can be expressed in terms of the parameters
a,K, and L.

It has been found that the ratio L/K depends only
upon the range of the nuclear forces; the value L/K = 6.8
is reasonable for the 1p shell (Ku 56). The ratio a/K
provides a measure of the relative Spin-orbit and central
energy contributions. In general, a/K=:2 for the Li
isotopes, whereas a/K 2 5 or 6 gives reasonable agreement
for masses 13 and 14. This effect is primarily due to
a (Ku 56). The large values of a/K imply a close corres-
pondence between the intermediate coupling and jj-coupling
pictures. The value of K itself is usually determined from
the known energy spacings. Once the parameters have been
fixed, wavefunctions can be calculated and used to predict
experimentally observable phenomena, such as radiative
transition widths (Ku 57).

The most extensive application of the intermediate
coupling model to 1p shell nuclei has been made by Cohen
and Kurath (Co 65, ,Co 67). 'From the available eXperimental

data they derived single particle energies and an effective.

 

interac
was the:
determil
wavefun<
parentag

be derix

l4

interaction for the lp shell. The effective interaction
was then used in intermediate coupling calculations to
determine wavefunctions for the levels. From these
wavefunctions they extracted coefficients of fractional
parentage (CFP), from which SpectrOSCOpic factors can
be derived.

The theoretical tn=l SpectrOSCOpic factors for the
15N(p,d)l4N reaction were extracted from the CFPS

calculated by Cohen and Kurath (Co 67). They are_given by

S = n|<T'1/2Mél/2|TMT>|ZZCFPjZ,
3

where n is the number of nucleons in the 1p shell of the
target (n = 11 for 15N), and <I> is a Clebsch-Gordan
coefficient which accounts for the amount of strength
going into the neutron pickup reaction as Opposed to the
proton pickup reaction. T,T' and MT' M& are the isotOpic
spins and their projections for the target and residual
state, respectively. The first 1/2 in the Clebsch—
Gordan coefficient is the isotOpic Spin of a nucleon, and
the second 1/2 is the isotOpic spin projection of the

neutron. The summation is over all values of j possible

for a given energy level.

CHAPTER III

EXPERIMENTAL APPARATUS AND METHODS

III.A. Proton Beam Production and Handling

 

III.A.l. Cyclotron

 

The proton beams for these experiments were produced
by the Michigan State University sector-focused cyclotron
(B1 66). Two methods of acceleration and extraction were
used during the course of this study. In one, negative
hydrogen ions were accelerated to extraction radius,
then stripped of their two electrons by a 700 ug/cm2
aluminum foil. The Lorentz force on the ions is thus
reversed, and they are deflected out of the cyclotron.

The second method entailed the acceleration of positively
charged hydrogen ions (protons) to extraction radius

where they were extracted using an electrostatic deflector
and a magnetic channel. This latter method is preferred
owing to the higher intensity and better beam quality,

i.e., higher phase space density. However, when the voltage
on the electrostatic deflector necessary to deflect protons

of a given energy was higher than conditions of the day

15

16

allowed, or when modifications were being made on the

deflector, the former method was used successfully.

III.A.Z. ‘Analysis System

 

The philOSOphy and construction of the beam transport
system has been described previously (Ma 67). A schematic
diagram is Shown in Fig. III-1. Momentum analysis is
accomplished by the 45° magnets M3 and M4. The resolution
of the beam is determined by the widths of the apertures
81 and 83, while its divergence can be limited by the
aperture 82. These apertures are remotely controlled
and have been described previously (Be 68a). For equal
widths of $1 and 83 the energy resolution of the transmitted
beam is 1 part in 104 per 0.013 in. of opening. Typical
apertures used in these experiments varied between 0.060 in.
and 0.100 in., corresponding to energy resolutions of 5
to 8 parts in 104. The distance between $1 and 82 is
approximately 44 in., so a typical width of 82 of 0.40 in.
_gives a beam divergence of i9 mrad. The energy of the
beam was determined from the values of decapot settings
of the magnet power SUpplieS reached by a well-defined
cycling procedure. The energy reproducibility of this
system is believed to be 1 part in 15000, if the central
fields of M3 and M4 are reproduced as indicated by

nuclear magnetic resonance fluxmeters (Sn 67).

 

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noon noon 000R
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Figure III—1. Experimental area of the Michig State University Cyclotron L oratory.

18
III.A.3. Alignment of Beam to Scattering Chamber

A schematic diagram of the beamline leading to the
scattering chamber is shown in Fig. III-2. After having
been deflected through 22.5° by the switching magnet (M5),
the beam was focused by a quadrupole doublet. A 0.375 in.
square aperture was placed at the intermediate focus. A
second aperture 0.40 in. wide and a third aperture
0.250 in. wide and 0.375 in. high were positioned immediately
outside the scattering chamber and approximately 6 in.
from the center of the chamber, respectively. A second
quadrupole doublet focused the beam at the center of the
chamber. The size and position Of the beam spot on a
0.010 in. thick piece of Pilot 3* plastic scintillator was
viewed by closed-circuit television, and currents on the
various apertures were monitored during the alignment.

The excitation of M5 and the quadrupole doublets were

adjusted to give minimum current readings on the apertures
and the best possible beam spot on the scintillator. Beam
spots were typically rectangular with a width of 0.100 in.

and height of 0.150 in.

 

*Pilot Chemical, Watertown, Mass.

 

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20
III.A.4. Charge Integration

 

Protons passing through the target were collected by
a Faraday cup located outside the rear wall of the chamber.
The insulated cup is 2.88 in. in diameter and 11.5 in,deep.
In previous studies (Ku 67 ) little change in the collected
charge was detected when permanent magnets were placed
near the entrance of the cup to prevent the escape of
secondary electrons.

The beam current and integrated charge were measured
using an Elcor model A310B current indicator and integrator.
The accuracy of the instrument has been found to be within
1% using both internal and external calibration sources
(Ku 67 ). The calibration of each scale was checked against
the internal calibration source at the end of most
experiments. These tests showed the calibration to be
within 1.1%; the integrated charges were subsequently

corrected for deviations in calibration.

III.B. Scattering Chamber Set-Up

 

III.B.l. Scattering Chamber

 

A 36 in. diameter scattering chamber was used in these
experiments. The chamber contains a counter arm which can
be remotely positioned over a useful angular range of 1 165°,
the upper limit being determined by the geometry of the

beam and counter collimators used in the experiment. The

21

digital readout has been calibrated against an internal
protractor, and this calibration curve was used to correct
the digital readout values. To eliminate errors due to
backlash in the mechanism, care was taken to set all angles
in a consistent manner. It is felt that these procedures

led to a relative angular accuracy of better than i0.2°.

The chamber also contains a target post which can be remotely
positioned in height and in angle. Ports are available

in the side of the chamber through which electrical leads,

etc., can be passed.

III.B.2. Targets

All data presented were taken using gas targets. For
the 160 experiments, natural oxygen gas, which has an
isotOpic abundance of 16O of 99.76%, was used. An enriched

15 15N experiment.

gas consisting of 99% N was used in the

The gases were contained in gas cells during the experiments.
Two different cells were used, each having certain

advantages and disadvantages. Most of the l6O(p,d)150 data

was taken with a 5 in. diameter cell whose tOp and bottom

plates were held apart by two struts placed 180° apart.

The window of the cell was 0.0005 in. Kapton* clamped

against an O-ring seal. Gas was introduced from outside

 

*E.I. DuPont de Nemours, Wilmington, Del.

22

the chamber until a pressure of 30 cm Hg, as measured by
a mercury manometer, was attained. The pressure in the
cell was continuously monitored by viewing the manometer
with remote television. The temperature of the cell was
assumed to remain at room temperature.

Certain problems and disadvantages were encountered
while using this cell. The method used in sealing the
window made replacement quite difficult: clamping a
0.0005 in. foil against an O-ring around a circular cell
without causing a leak-producing wrinkle is extremely
difficult. In fact, the cell was never completely tight.
This method certainly was unacceptable for an eXpensive

15N. Also, the volume of such a large

gas such as
cell is impractical for expensive gases. Finally, it

was necessary to keep track of the relation of the
supporting strut and counter positions in order that the
counter would not inadvertantly be allowed to pass behind
the strut.

All of these objections were removed by using a 3 in.
diameter cell designed for the 15N eXperiment. The cell
(Fig. III—3) was machined from a solid piece of brass;
the top and bottom were quite thick to reduce flexing,
since there is support only on one side. The counters

could be positioned from —40° to the limit of 165° previously

mentioned without moving the cell. The window was 0.0005 in.

l
-—.———

 

TAR

0.(

23

m

 

 

 

 

 

 

 

 

 

 

 

III/Xilljllil
/
/ PROTECTIVE
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KFOIL TARGET
/HOLDER
,POST H
d
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L l T l l .R...
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ii:
TARGET POST MOUNT {m \ EPOXY SEAL
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SET SCREWS GAS INLET
0.0005" KAPTON
WINDOW
SUPPORT
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f \
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F---4
3-INCH GAS CELL

Figure'III—3.
experiment.

Diagram of

the 3—in. gas cell used in the

 

 

 

24

Kapton attached with an epoxy resin. The only disadvantage
of a small cell is that the forward angle limit is determined
by the scattering angle at which the counter "sees" the
beam spot on the wall of the cell-—the smaller the cell
the larger this angle. However, with this cell data were
taken as far forward as 10° in the laboratory frame with
no difficulty. The smaller cell is helpful from the stand-
point Of resolution in that the incident and scattered
particles travel through less gas and thus experience less
energy straggling.

Kapton was chosen for the windows on the basis of
its great strength, radiation resistance, and low density.
Other foils which have been used in this laboratory are
Havar* (successfully) and mylar (unsuccessfully). Kapton
windows have taken hundreds of nanoampere-hours of 45 MeV
protons in an 1/8 in. square spot without showing any signs
of weakening. In contrast, a mylar window developed a
bulge and leak after less than 50 nanoampere-hours.
Beam currents as high as 300 nanoamperes have been used
with the Kapton, and recent studies with 42 MeV alpha

particles indicate that proton currents up to 500 nanoamperes

could be used. Straggling from Kapton and mylar are

 

*Hamilton Watch Company, Lancaster, Pa.

25

comparatfle. Mylar was tried because a 0.00025 in. window
was desired, and pinhole-free Kapton of that thickness was
not available. On the other hand, Havar is stronger than
Kapton, but has a higher effective Z and a higher density,

so the straggling introduced is considerably worse.

III.B.3. Counter Systems
16

 

The counter used in the O(p,p) experiments was a
0.25 in. square, 0.50 in. thick CsI(T1) crystal mounted on
the face of a photomultiplier. All other data were taken
using commercial silicon surface barrier or lithium-
drifted Silicon detectors. The AE counters ranged in
thickness from 54p to 770p depending on the incident proton
energy. The E counters ranged from 270D to 4000p (two
2000p counters in parallel) in thickness. All counters
were cooled by circulating alcohol cooled to dry ice
temperature (-78°C) through the counter mounts.

When using a gas target, two collimators are necessary
to define the solid angle. A brass collimator having a lip
thickness of 0.067 in. and an aperture 0.126 in. wide and
ml.0 in. high was placed near the gas cell. This collimator
was thick enough to st0p all deuterons and to degrade
elastic protons sufficiently in energy so that they were
well-separated from the elastic protons passing through the

aperture, Brass plates extended back from this collimator

26
to shield the detector from particles produced at the walls
Of the cell. A second collimator was placed immediately in
front of the detector. In all of the (p,d) experiments,
except the one using time-of-flight for particle identification,
a 0.063 in. thick tantalum collimator with an aperture of
diameter 0.1575 1 0.001 in. was used. In the exception,
an oval aperture 0.208 f 0.001 in. long and 0.104 t 0.001
in. wide in 0.060 in. thick tantalum was used. The second
collimator for the 16O(p,d) experiments was 0.125 in.
thick tantalum with an aperture diameter of 0.125 1 0.001 in.
The rear collimator was placed from 9.1 to 14.7 in. from
the center of the cell, with the corresponding distances
between the two collimators ranging from 5.9 to 12.7 in.
Angular acceptances corresponding to these collimator

placements ranged from ml.2° to m0.6°, respectively.

III.C. ElectrOnics

 

III.C.l. 160(pypll60 Experiments

 

Light from the CsI(Tl) crystal was detected by a
photomultiplier tube. The signal was amplified with a
Landis preamplifier and an ORTEC multimode amplifier. The
signal was then analyzed, and events were stored in a
256 channel subgroup of a 4096 channel analyzer (Nuclear

Data 160D). A window was set around the elastic group

27

using a single channel analyzer, and the resulting gate

pulses were scaled.

15
III.C.2. l6O(p,d) 0 Experiments

 

Most of the data were taken using two counters in a
AE—E telescOpe arrangement, and particles were identified
by a Goulding system. Early experiments were done using
a system constructed at Michigan State University; later,
an ORTEC modular system was used. A block diagram of the
modular system is shown in Fig. III-4. Pulses from the
detectors were amplified by Tennelec 100B charge-sensitive
preamplifiers and by ORTEC selectable active filter ampli-
fiers. The gains of the amplifiers had to be precisely
matched since the E and AE pulses are added after amplifi-
cation to produce a sum pulse which must be prOportional
to the total energy of the particle. A slow coincidence
was required between the AE and E signals. Those pulses
in coincidence were stretched and presented to the identifier
module, which produced an energy pulse equal to E + AE and
a "mass" pulse prOportional to

(E + AE)l.73 _ El°73.

The "mass" pulse was fed into a timing single channel
analyzer (TSCA) set to select pulses corresponding to

deuterons. A linear gate was Opened to let through only

those energy pulses which corresponded to deuterons. These

28

pulses were analyzed and stored in a 1024 channel group
of the ND-l60D analyzer. The contents of the memory
were punched on paper tape or "dumped" into the memory
of the Laboratory's Scientific Data Systems Sigma 7
computer.

Another technique for particle identification was
used quite successfully. It depended on the difference in
flight times between the target and the detector for
particles of different mass.. A block diagram of the
electronics is shown in Fig. III-5. Two counters were
used--an E counter and a veto counter. The E counter
thickness was sufficient to stOp the deuterons of interest.
Any particles passing through the E counter produced an
anticoincidence pulse in the veto counter. An event in the
E counter was detected by a time pickoff unit (TPO), and
the resulting signal was used to start a time-to-amplitude
converter (TAC), which was stOpped by the cyclotrOn RF
pulse. Since deuterons are the only stable mass 2 particles,
their identification by time-of—flight was unambiguous.
The time resolution was approximately 0.8 nsec. The
E signal was amplified with an FET preamplifier and a
selectable active filter amplifier. A slow coincidence
was required between the energy and time signals which were
input to the ND-l60D analyzer used in the 64 x 64 channel

mode. A window was then set, using a timing single channel

29

 

 

 

 

 

 

 

 

 

 

 

 

 

TSCA
E AMP h 1 TSCA n
PREAMP N
SLOW
COflL
LJN. lJN. r‘1
GATE GATE

 

f)

ImTj 7P «1

PARTICLE . I

IDENTWHHQ

 

 

 

 

 

 

 

E+AE MASS
£11 TSCA ]

Figure III—4. Block diagram of the electronics for the
Goulding method of particle identification.

 

 

 

[ANALYZER

 

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TWP. 22?: . F
Em OATH 1%”. GATE]

DATE
LIMGATEjv—a—[TSOA ]

MI I

Figure III-5. Block diagram of the electronics for the time-
of-flight method of particle identification.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure I]

31

“V j' AMP HTSCATD

.| PREAMP k

. :5” H Ann—L T... J
n

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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PULSE
[NAATPUER
* - - e T
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L... I l W | I
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7 [1
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NALYZER

 

 

 

 

 

 

Figure III-6. Block diagram of the electronics for the
pulse multiplication method for particle identification.

 

analy zer,
the deute:
pulses wh;

dimension.

III.I

In t
but the p
Goulding
A block d
pulses we
Preamplif
by V. Rad

has the f

which Car

The

32

analyzer, to include only time pulses corresponsing to.
the deuterons. (This signal was used to gate the energy
pulses which were analyzed in the 1024 channel one-

dimensional mode of the analyzer.

l5 4
III.C.3. 15N(p,p) N and 15N(p,d)1 N Experiment

 

In this experiment an E-AE teleSCOpe was again used,
but the particle identification was not done with a
Goulding system. Instead, a pulse multiplier was used.
A block diagram is shown in Fig. III-6. The E and AE
pulses were amplified using Tennelec 100B charge-sensitive
preamplifiers, then were fed into a pulse multiplier designed
by V. Radeka and G. Miller (Mi 63). The pulse produced
has the form

AE(E + K AE + K2)

1

2 of

which can be shown to be roughly prOportional to M2
the particle (G1 65).

The E and AE signals were summed at the detectors by
placing a 5 megohm resistor between the normally grounded
sides of the detectors and ground. The sum signal was
amplified with an FET preamplifier and a Tennelec TC-200
amplifier and then was delayed by the amount of time necessary
to place it in coincidence with delayed E and AE signals and
the output of the pulse multiplier. The energy and mass

signals were fed into the two sides of the ND-160D

analyzer used in the 64 x 64 channel mode. By adjusting the

33

gains of the E and AE amplifiers in the pulse multiplier
and the values of the constants K1 and K2, the different
mass groups could be made to appear as straight bands in
the two-dimensional spectrum. Windows were then set to
include all the deuterons and the elastic protons (which
were not stOpped by the detectors and thus produced a mass
pulse smaller than those of protons which were stOpped)
using two timing single channel analyzers. The proton
pulses were sent through a biased amplifier to reduce their
heights to values less than that of any deuteron pulse

and then added to the deuteron pulses. Since these pulses
did not arrive in coincidence, the sum signal contained
either a proton pulse or a deuteron pulse. This signal
was then input into a 4096 channel analyzer (Nuclear

Data NDZQOO). The spectra were stored in 1024 channel
groups and contained both the elastic protons and the

deuterons.

III.C.4. Comparison of the Systems for Particle

Identification

 

Each of the systems described offers some advantages
and disadvantages. With the exception of the pulse multi-
plier, all components necessary for each system are available
in standard modular form. The Goulding system has a

greater mass range than the multiplier system. A disadvantage

34
for high resolution work is the necessity of matching
gains of the E and AE amplifier systems to high precision.
This is especially true if one uses the E + AE output of
the identifier module. It was quite difficult to have the
gains match well over the energy range of the incoming
particles. Also, the E and AE pulses must pass through a
relatively large number of stages before being added
and analyzed. The electronic noise using this system was
typically 45 to 50 keV. This figure could undoubtedly
be imprOved if one were to sum the E and AE pulses at the
detectors, as was done with the pulse multiplier system.
Then one could use the Goulding system only to produce mass
pulses. Electronic noise in the sum pulses was approximately
30 keV for the pulse multiplier system. All noise values
quoted were measured with the detectors cooled and under
bias.

The best overall resolution was obtained with the time-
of-flight system. Here again, the energy pulse passed through
only a preamplifier, amplifier, and linear gate. Perhaps
the greatest advantage of this system is that one gets the
energy information from a single detector. Thus, the
particle passes through only one detector "dead" layer
instead of three. Also, the Single, thick E counter has
a much lower capacitance than the relatively thin AE

counters that must be used for low-energy particles, thus

35

introducing less noise. The electronic noise for this
system was approximately 20 keV. Of course, an Obvious
disadvantage of time-of-flight is its inability to distin-

3H and 3He.

guish between particles of the same mass such as
However, deuterons, being the only stable mass 2 particles,
are well-separated from protons and from the mass 3 particles.
Another disadvantage is the fact that the mass lines are
curved in an E vs t plot. This means that a linear "time"
gate may not be sufficient to separate pulses corresponding

to particles with different masses. If not, one must

rely on the Q-values of the different reactions involved

to keep clear the energy region of interest. This problem

can be eliminated if an on—line computer such as the Sigma

7 is available. At present (but not when the data using
time—of-flight were taken) one can use the computer as an

analyzer and have it store events appearing in a curved

band in the E—t plane.

III.D. Data Acquisition and Analysis

 

III.D.l. Data Acquisition

 

After the initial alignment of the beam and the initial
adjustment of mass gates, etc., angular distributions were
begun at forward angles. In order to minimize the dead time
of the electronics and analyzer, the beam was kept at such

a level that pileups seen on an oscillOSCOpe monitoring the

36
output of the E amplifier were few. In all of the (p,d)

work using the Goulding system, pulses corresponding to
elastic protons were eliminated before reaching the
identifier by requiring that the energy lost by a particle
in the AE counter begreater than that lost by the elastics.

Zero corrections to the scattering angles indicated by
the digital readout system were obtained by comparing
values of the differential cross sections measured on
both sides of the beam at angles where the slope of the
angular distribution was steep. Progress of the experiment
was monitored by calculating and plotting a relative
cross section for one of the strongly excited states
(usually the ground state). Often, as a check on consistency,
at least one angle would be repeated. At periodic intervals
the mass gate was checked and adjusted if necessary.

Angular distributions were generally taken from 10° to
approximately 160° in the laboratory frame. Five-degree
steps were used to approximately 70°, and then 7.5° steps
were used. At times, additional intermediate points were
taken between 10° and 20° to determine better the first

peak of the angular distribution.

III.D.2. Data Analysis

 

The data stored in the analyzers were dumped either on

paper tape or into the memory of the Sigma 7 and then punched

37

on computer cards for use by analysis programs. All
Spectra were plotted using the CALCOMP plotting routine
of P. J. Plauger. Each peak was then identified by the
channel numbers corresponding to each edge, and a back-
ground value was assigned at each edge on the basis of
counts in neighboring "clear" regions of the spectrum.
These data, along with the cards containing the Spectrum,
were input to the program PEAKSTRIP (written by R. A.
Paddock) which computed a linear background under the peak,
the centroid of the peak, the width of the peak (assuming
a caussian shape), and the net area and background. The
program punched all of these data on cards to be used in
other programs. Also available were several data analysis
routines which use the display oscillOSCOpe connected to
the Sigma 7. They allowed one to fit backgrounds of
various polynomial orders either to an individual peak or
to groups of peaks. Analyses with these programs were
compared to those using PEAKSTRIP and were found to agree
very well. Linear backgrounds under each peak were
satisfactory. The SCOpe analysis programs were not used
extensively since that would have involved many hours of
computer time.

The excitation energies of the peaks were determined
by using the program GASCELCAL written by R. A. Paddock.

Input data consisted of the PEAKSTRIP output data for all

.38

angles at a given incident proton energy and data giving
information about the target gas,scattering angles, and
excitation energies of peaks to be used as calibration
points. The program then produced a calibration curve of
channel number vs particle energy at the detector by
calculating the apprOpriate reaction kinematics and the
energy losses Of the incident and scattered particles in
the gas and in the walls of the gas cell. Generally, a
quadratic fit was used. The program then calculated the
excitation energy of each peak in each run and listed-it
according to peak number. Since the energy levels of

15O and 14N are quite well-known, these calculations

served mainly to identify the peaks. A useful Option of

this program allowed one to find, according to the calibration
curve, the position of peaks corresponding to levels not
observed in a particular spectrum. This method was used

to search for peaks correSponding to the (p,d) reaction on

the most likely target contaminant, 14N. In those cases in

f 14

which a measurable amount 0 N contamination was found

15 f 16

[the N(p,d) data and one set 0 O(Pld) data], the

amount present was calculated by comparing the differential
cross sections of one of the strongly excited states of 13N
to the values measured by Kozub et a1. (KO 67). at 33 MeV.

Once the amount had been determined, the number Of counts

in any peak which overlapped a 13N peak was corrected.

.39

In the l6O(p,p) eXperiments two additional corrections
to the number of counts were made. A dead—time correction
was made on the basis of a comparison of the scaled proton
counts to those analyzed. This correction was significant
only at laboratory angles smaller than 30°, and in most
cases was less than 2%. However, the data taken at 38.43
MeV showed an 8% correction at 10°, but this number had
drOpped to 2% at 20°. The other correction was for
counting losses due to reactions in the CsI(T1) crystal.
This correction was based on the following empirical
expression deduced from data on NaI (Ca67):

% Loss = 0.001062 E2 + 0.01392 E - 0.1554. (111.1)
This correction was approximately 2% at forward angles and
decreased with the kinematic drOp in energy of the scattered
protons. These numbers agree well with results of a
calculation in which the cross section for a reaction is
assumed to be the geometrical cross section, so that the
total probability of a reaction can be determined from
range and density data.

Dead-time corrections were not necessary for the (p,d)
data owing to the much smaller counting rates. Using the
,geometrical approximation described, calculations of counting
losses for deuterons in silicon were made. These were less
than 1% owing to the smaller range of deuterons in the

silicon. Hence, no correction was made to the data.

40.

When all necessary corrections were made, the yields
and backgrounds were fed into a prOgram which calculated
the differential cross section for each level at each angle
at which it was observed. The expression for the cross
section in the laboratory frame can be written as

dO/dQ = YsinO/nNG, (III.2)
where Y is the yield, n is the number of incident particles,
and N is the number of target atoms per cm3. The quantity
G is a geometrical factor, to be found in a paper by
Silverstein (Si 59), which contains terms accounting for
effects due to a finite beam size and finite collimator
apertures. The calculations of Silverstein have been
extended by R. A. Atneosen (At 67) to include the case of
an oval rear collimator. The G-factor can be written as

G = 2Ab (1 + A + o'A + o"A + ...), (III.3)
———-_ O —— 1 —» 2
Roh o 0

where A is the area of the rear collimator aperture, b

is the half—width of the front collimator aperture, Ro is
the distance between the rear collimator and the center

of the cell, h is the distance between the front and rear
collimators, and the A1 are correction terms depending on
the geometry of the beam and collimators. Inclusion of the
A0 and Al terms have made differenceS" of less than 0.1%

at all angles. The A0 term has been included in all

calculations. The program calculated cross sections in the

41

laboratory and center-of—mass frames and computed the statistical
error according to the formula

e = /Y + 23, (111.4)
Y

where Y is the net yield and B is the background. A total
error was also computed in which the statistical error

was added, in quadrature, to errors associated with other
quantities in the calculation. An option allowed the angular

distribution to be plotted on the CALCOMP plotter.

III.B. Analysis of Experimental Uncertainties

 

III.E.1. Beam Energy and Energy—Level Determination

 

The beam energy was determined from the values of the
decapot settings of the analyzing magnet power supplies,
which were calculated from the measured field values.
Extensive checks of the energies thus determined have not
been made over the range from 20 to 50 MeV, but a check at
33 MeV using the range-energy method described by Kull
(Ku 67.) and Kozub (KO 67 a) was consistent with an uncertainty
of i100 keV.
The energy resolution for the 16O(p,d) data was typically
100 keV, except for the data taken using the single counter
and time-of—flight, where the resolution was approximately
60 keV. The resolution for the 15N(p,d) data was approximately

90 keV. Major contributions to the resolution are given

 

 

nITable I
the energy
detectors 6
detectors,

The e:
upon the er.
in the cent
peak and to
from adjace
related to
from the um
negligible.

an uncertair

 

 

Overall Cali
had a typica
Um POints,

excitation e
Mmber refle
Thus

’ an err

each excitat

III.B.;
The maj

III~2.

42
in Table III—l. The quantity labelled "Other" includes

the energy spread involved in charge collection in the
detectors and straggling in the dead layers of the
detectors, as well as other unknown sources.

The error in the energies of the excited levels depends
upon the energy resolution to the extent that the error
in the centroid of the peak is related to the width of the
peak and to the extent that some peaks could not be resolved
from adjacent peaks. The error in the centroid is also
related to the number of counts in the peak. The contribution
from the uncertainty in the absolute beam energy was
negligible. Thus, for the relatively weak excited states
an uncertainty as great as 15 keV could be expected. The
overall calibration curve calculated by the code GASCELCAL
had a typical uncertainty of 15 keV owing to scatter in
the points. The average deviation of the calculated
excitation energies was typically 20 keV. Of course, this
number reflects the uncertainty in the calibration curve.
Thus, an error Of at least 20 keV should be attached to

each excitation energy measured.

III.E.Z. “Differential Cross Sections
The major sources of error in the determination of
the absolute differential cross sections are shown in Table

III-2.

 

43

.msououm unopflocfl >oz Nmo
.maouonm ucoowocw >02 ova
.msououm ucoowocfl >oz mvo

 

 

>ox om >ox om >ox oaa fleece
.mm .wm .mm umcuo
ma mm mm GOHDDHOmou Boom
mm mm om msecopooun owuofiosfim
mm ea mm who
CH mswammonum couousoc
om ma ha Hamz Haoo
ca mcflammonum conouaon
m m NH mom :H mafiammouum Gogoum
m h m Hao3 Haoo
CH mcflammonum cououm
>ox mm >ox mm >ox om omaoc oasonuooam
UEOPmMm EODmMm oEoummm
Dcoeam uoIoEHB hone specs chasm oceoacoo coeucbeuucoo mo oousom

 

 

.GOHDMOHMHPGDCHUHUHuHom.mo moocuoe
mourn Dru EDHB oocwmuno noHuoaomou hmuoco Dru Op mCOHusanusoo .HIHHH Tahoe

44
Table III-2. Estimated uncertainties in quantities
involved in the calculation of absolute
cross sections for 6LA 230°. The uncertainties
are to be treated as sIandard deviations.

 

 

Type of Uncertainty Value
Target temperature 1.5%
Target pressure 1.0%
Charge integration 1.5%
Solid angle determination 2.2%
Scattering angle (0.2°): [dO(8)/d6] 1.6%
Total Measurement Uncertainty 3.6%

 

Although not shown, the uncertainty in the determination
of the background counts for each peak was considered. This
uncertainty was negligible for large peaks, but became
significant for small peaks superimposed on rather large
backgrounds. Even for those, however, this error was
still smaller than the corresponding statistical error.
Other sources of uncertainty not listed include those in
the dead-time and counting loss corrections, which were
themselves small. The effect of the uncertainty in beam
energy was negleCted since the differential cross sections
changed slowly with incident proton energy (see Chapter V)-
An-additional contribution to the uncertainty in the

differential cross sections is the statistical error,

45

which must be added, in quadratUre, to the measurement

error. The statistical error was different for each data
point, and ranged from 0.2% upward, depending on the strength
of the level. The error bars shown on all data points
represent the total error. Statistical and total errors

are tabulated with the data in the appendices for the more

strongly excited levels.

CHAPTER IV

ELASTIC SCATTERING DATA AND OPTICAL MODEL PARAMETERS

IV.A. Proton Elastic Scattering

 

16 16
IV.A.l. O(p,p) O

 

Differential cross sections for the elastic scattering

160 were measured at incident energies

of protons by
(corrected for losses in the cell window and gas) of

25.46, 32.07, 35.10, 38.43, and 45.13 MeV over an angular
range of 10° to 170° in the center-of—mass frame. Details
of the experimental apparatus and procedures were discussed
in Chapter III. At the end of each angular distribution
the differential cross section at the position of the
second maximum (SO-60°) was measured over an energy range
of 1300 keV around the bombarding energy to detect the
presence of any sharp resonances in the cross section. No
significant fluctuations were found. As a check on the
efficiency of the counter system, differential cross
sections for the elastic scattering of protons by

protons were measured at several angles between 15° and 22°

in the laboratory frame. These were compared to those

46

47

measured by Johnston and Swenson (Jo 58) and were found to
agree within the experimental errors.

A sample spectrum is shown in Fig. IV-l, and the five
eXperimental angular distributions are shown in Fig. IV-2.
They exhibit a rather smooth energy dependence, with the
25.46 MeV angular distribution showing a Slightly different
behavior beyond 60°. These data are in quantitative agree-
ment with those of Cameron et al.(Ca 68), whose measurements
covered the energy range 23.4—-46.l MeV. These authors
found that the behavior of the cross sections below 30 MeV
indicated the existence of broad resonances or intermediate
structure in the p-l6O system. The behavior of the 25.46
MeV data is consistent with such a conclusion. These
resonances were too broad to have been detected during the
search for sharp resonances within 300 keV of the original

proton energy.

IV.A.2. 15N(p,p)15N

 

Differential cross sections for the elastic scattering
of protons by 15N were measured simultaneously with the
15 14 . . .
measurement of the N(p,d) N differential cross sections
as has been described in Chapter III. The incident proton
energy was 39.84 MeV, and an angular range of 10°to 145° in.
the center—of—mass frame was covered. The data are shown

in Fig. IV—6 with the optical model fit discussed in

48

.Houmawaaoo usonm onp mo

med may amoousu common o>o£ :wflnz msououm UMMmoHo on one mum on Hossono osoono mucsoo

mo Hones: momma one

m

.>oz ov.m~n m how om.m~u e no esuuoodo OoHA.m.choH .HI>H ounces

nXuN

 

 

 

mmmEDZ ...mzz<Io
09

 

 

.mom . 93o

>22 boom . em
02%;: 0o.

-

 

 

 

 

‘IBNNVHO /S.LNOOO

 

 

 

no. no

49

 

tuna: r
I I I I IE5 I “£5 I

O (p.p) O
25.46 MeV
32.07 MeV
35.20 MeV

38.43 MeV
45.|3 MeV

@QOU’O

 

ILIo —- \ //‘ ‘ \'\egI

 

 

 

M, I I I I l I I I

6 (degrees)

Chfll

Figure IV-2. 16O(p,p)lGO eXperimental angular distributions
for Ep=25.46--45.l3 MeV.

50
Section IV.B.2. This angular distribution is very similar
to the oxygen angular distributions in the apprOpriate

energy range.

IV.B. Optical Model Analysis of the Proton Elastic

 

Scattering Data

 

In the Optical model of elastic scattering it is
assumed that the interaction of the two nuclei involved can
be represented by scattering from a one-body complex
potential having the form

Vopt(r) = VC(r) - Vf(x) - i(WS - 4 WD_d_)f(x')

 

dx'
2
+Vso(fi)1df(X) (_1_° g).
(mflcfir dr
._ I2
where Vc(r) — ZZ e , r = RC (IV.1)
r
2 2
= ZZ'e (3 - r )/2R , r = R
R2 C C
c
1 3
R =rA/,
c c
_ X ’1
and f(X) - (e + 1) ,
. 1/3 _ _ 1/3
With x = (r - rRA )/aR’x' — (r rIA )/aI.

V is the potential felt by a point charge (Ze) interacting
c
with a uniformly charged sphere of radius (RC) and charge

(Z'e).

51

Optical model analyses were performed with the Perey
search code GIBELUMP*, which runs on both the CDC 3600
and the SDS Sigma 7 computers. The potentials and geomet—
rical parameters could be varied singly or in combination.
In general, the spin—orbit radius and dflfuseness were
set equal to the corresponding parameters of the real well,
although this condition was not imposed by the code. The

code sought to minimize the quantity

2? _ . . . . 2
x /N — (l/N)iZ{[oth(i) - oeXPIIIJ/Acexpun , (1v.2)

where N is the number of experimental data points, oth(i)
and Oexp(i) are the theoretical and experimental cross
sections at angles Si in the center—Of—mass frame, and
Aoexp(i) is the error in oexp(i).

As is well-known, the optical parameters exhibit
certain ambiguities, such as the one represented by a
constant value of Vrz. To determine the effect of
changing a given parameter and hence to determine which
combinations of parameters would produce unambiguous
results, the calculations represented in Fig. IV-3 were

performed. The solid lines represent the standard

calculation using the parameter values listed. Each

 

*Unpublished FORTRAN-IV computer code written by F. G.
Perey and modified by R. M. Haybron at Oak Ridge National
Laboratory.

52

.pomomuocw mnouoEoHom osu no

oco ruwz cofiumaooaoo o mucomoumou OPMSO pormmp or» can .poumfla muouoeonom Dru means
cowuoaaoamo o musomonmon oPHso uflaom one .mGOADSQHHDme uoasmso o Am.m00ma umpoaaoaoo
or» so muouoeonom Hopoe amoeumo Honua>eocfi mo chHuoHHDP mo mMOOmmm .mI>H ousmfim

 

       
 

 

       
   

 

 

glaze. :30
o
e!
.0
a.
9 “HI
. ...w
u
%.
15:06.29 mWW
.9 I quoLo m:
have...
Lsaos.4s . a
«o. I >596...» >22Nmmu u no.
33.8010 023.30..
.2 - 32.3.... i. 30:58.26 .2
>8. 3...;
mmm...m.2<m<n_l Jun—0.2 132.50 .
2 _, p _ r _ r. r _ .IP e _ p _ _ _ P -%.

 

53

dashed curve represents the effect of changing one parameter.
It is interesting that a sizable change in Vso has very

little effect on the calculated angular distribution.

1
IV.B.l. 60(pgp)160

 

In the initial phase of the calculations an effort
was made to obtain the set of parameters which gave the
best overall fit to the five experimental angular distri-
butions. Unambiguous combinations of parameters were
searched on until the average xz/N was a minimum. The
parameters and fits are shown in Fig. IV-4. The fits
are only fair at forward angles and completely out-of—phase
at the back angles. The relatively low value of 1.12 F for
RR was chosen on the basis of better fits.

Owing to non-locality effects not included in the
optical potential, one expects the parameters to be some-
what energy-dependent. Starting from the average parameters,
searches were made allowing the parameters to vary with the
energy of the incident proton. It was found that the real
radius and diffuseness parameters tended not to vary, so
they were fixed at 1.12 F and 0.69 F, respectively.

Owing to the lack of polarization data to be fitted simul-
taneously with the elastic scattering, no effort was made
to search on V50. As was pointed out earlier, the

calculation was not sensitive to variations of VS A

o.

54

value of 7.0 MeV for V was chosen on the basis of
so
parameters found by Cameron (Ca 67) during preliminary

analyses of elastic scattering (Ca 68) and polarization

data (El 68). Cameron (Ca 67)had also measured reaction

 

cross section data at incident proton energies apprOpriate
to his work. Since these varied smoothly with energy,
values of the reaction cross section (OR) for the incident
proton energies of the present work were extracted by

graphical interpolation. These were used as a guide in

 

Ev
choosing between sets of Optical parameters which gave

essentially identical values ofxz/N.

An effort was also made to keep as smooth as possible
the variation of the parameters with energy. Thus, a set
of parameters producing a much better value of iz/N for the
38.43 MeV data was judged unacceptable because the value of
aI was much smaller than those obtained for the other data.
The final set of parameters is shown in Table IV-l, and
the corresponding fits are shown in Fig. IV—5. It was
found that the inclusion of a volume imaginary potential
was necessary above 32.07 MeV, with its strength increasing
with energy. This is probably due to the deeper penetration
of the more highly energetic protons. The forward angle
fits are improved,although the improvement is slight for

the 25.46 MeV data. The back angle fits are very poor for

 

 

 

 

  
  
    
  
 

   

 

   

 

 

  
 

 

 

 

55
s
'0 Il6 I I IGI I I I I I '05
O(p,p) 0 v - 46.8 MeV
. r ' r-I.HZF
IO‘ OptICOI Model " ’° .. .04
F'Is w,- 0.80 MeV
r,- l.35 F
'0‘ 0,- 0.48 F '02
v”: 7.0 F -
- I.I5 F
Io“ - Io'
'5 +
\
4 O
.0 IO F 4 IO
E
V5.
0 3 O
A _
bla '0 IO
on
v
IOZ- ~ I0°
I ' I
IO - _. IO
2
0 25.46 49.0
b 32.07 60.5
I0"- 0 3520 63.7 — I0"
0 38.43 l9.3
e 45.I3 43.3 t
l l i l l l l l
0 20 40 60 80 I00 I20 I40 I60 IBO
9c.m(degrees)

Figure IV—4. Optical model fits to the l6O(p,p)lGO angular
distributions using the average.set of parameters listed.
The average value of x /N is 47.2.

 

.—

IC
IC
’2 IC
0')
\
.0
es ..
/\0'
bl q
33 .c
IC
IO
l0
lgure IV
diStributh
listed in m

 

 

 

56

 

   
    

4
I0 I I I ['6 I I I6] I l '04
' O(p.p) O

.04 -- Optical Model Fits _ '03
0 25.46 MeV
b 32.07 MeV

'04 c 35.20Mev 2
a 38.43 MeV ‘ '0
e 45.I3Mev

   

 

 

I I l 1 l I I I
O 20 4O 60 80 IOO l20 I40 I60 IBO

 

 

OM; degrees)

Figure IV—5. Optical model fits to the l6O(p, p)160 angular
distributions using the energy-dependent sets 2of parameters
listed in Table IV-l. The average value of x 2/N is 27.1. ‘

 

 

 

 

 

 

zx x Abucmc «onocmo ou> Hm H 0 m m m

N am

.H \w «ONTO.» m Umvmhmvpfi

II/I
II/

.ZmH USU 00H EOHH OCHHUUDMUT UHHMUHU COHOHQ DCHQHHUMUD UHUUUEHMQ HQUOE HMUHUQO

 

 

IHII>H @Hhflmofi

 

 

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.mm on .mom CH endow open so oomome

 

57

 

 

 

.m mH.H H OH .mo H 0mm .mu n OmH
m.m mme III o.m mme.o ~4.H mm.m em.e ooo.o mH.H m.me em.mm ZmH
o.e see new o.e mae.o mm.H mo.m Ha.m oae.o ~H.H e.me ma.me ooH
m.oa owe Hes o.e ome.o oe.H mm.e oo.m omo.o NH.H e.ve me.mm OoH
m.me was mme o.e ome.o me.a oe.m Hm.o oom.o NH.H o.me o~.mm ooH
m.~m ewe mes o.e ome.o ce.a Hm.m o.o omo.o ~H.H m.me eo.~m OoH
5.6m mmm pom o.e omm.o mH.H om.o o.o omo.o ~H.H «.me oe.m~ Ooa
Ange “nee x>ozc has Ame A>osc A>osc Ame Ame A>ozc “>620
m
Z\mx Annexe «Amxovmo Om> Hm HH 03 m3 mm mm > Amway m ummuma
.ZmH can 03 Eonm mcwuouuoom owumoam couonm mcwnfluomoo.WMTDDEUMdm.AUUOE Howflemo ..HI>H manna

58
all but the 45.13 MeV data. This behavior is consistent

with that found by van Oers and Cameron (Va 68) over the
energy range of 23-53 MeV, by Barrett; et al. (Ba 65)

at 30.3 MeV, by Kim et a1. (Ki 64) at 31.0 MeV, and by
Fannon et a1. (Fa 67)at 49.48 MeV. It has been found in
other work (Fr 67) that the use of a spin—orbit radius
parameter Of 10% to 15% smaller than the real radius
parameter was helpful in obtaining fits to the back angle
data. This was tried with no significant improvement.
Thus, it appears that the Optical model gives a poor
description of proton elastic scattering from 160 below
30 MeV where resonances occur, that between 30 and 40

MeV the description is poor beyond 100° in the center-of-
mass frame, and that the Optical model describes the

scattering very well for incident protons above 40 MeV.

lSNIPIPIISN

IV.B.2.
Similar procedures were followed to obtain a set of
parameters which describe the elastic scattering of protons

from 15N. The parameters are listed in Table IV—l, and the

16
fit is comparable to that for the 38.43 MeV 0 data, as
was expected owing to the similarity of the incident proton

energies. 'The Optical model fit to the data is shown in

Fig. IV-6.

 

( mb kr)
C. m.

(5'2?)

distributio;

59

 

 

 

 

 

 

 

'04 T I I I I
I5 l5
N (v.0) N
'03 I- ED =39.84M6V—
-OPTICAL
MODEL .4
IOZ - .:
‘e’
v . I0I ...
E
Ad
b
‘1!
“ IO°—
IO" P-
I62 I I l I l
0 30 60 90 I20 ISO I80

Gamldegl

IFligure IV—6. Optical model fit to the 15N(p,p_)15N angular
distribution. The parameters used are listed in Table IV—l.

60
IV.C.' Deuteron Optical Model Parameters
Since it is impossible to measure the elastic
15

scattering of deuterons by the unstable nucleus 0, data

. l .
for deuteron scattering by 6O was used. Sets of optical

model parameters have been found for deuteron elastic

scattering by 16O for incident deuteron energies between

11.8 and 52 MeV (Fl 67, Ng 66, Co 66, Ho 66, Te 64,
Ne 67, Du 66). Many studies have been done with lower

energy deuterons, but the applicability of the optical

Inodel is questionable in these cases. The parameters for

this work are based on the 11.8 MeV parameters of Fitz et

al. (F1 67), the 16.8 MeV parameters of Hodgson (Ho 66),

'the 34.4 MeV parameters of Newman et a1. (Ne 67), and the

552 MeV parameters of Duelli et a1. (Du 66). Each of these
sstudies used a derivative surface absorption and included

srpin-orbit effects. These parameters are shown in Fig.

JTV-7. The solid curves were drawn with the constraint

that they pass through the 34.4 MeV points. Very little

‘VVEeight was placed on the 16.8 MeV parameters since they

c‘iziffered significantly from the general trend of the other

IE>Earameters in several cases.

Since the 16O(p,d)150 data covered a wide range of
j~11cident proton energies, and since for each incident energy

‘leere existed a wide range of Q—values, it was necessary to

 

0.8l
(II

04

 

6.0
(MeV)

I20

(MeV)
60

 

I20

80
(MeV)

40

 

Figure IV‘
from 16¢
”eSt"

E){t

UEA

61

OPTICAL MODEL PARAMETERS FOR BOId,d)BO

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I2 l2
0. - . - - 0.8 . ,
(f) (f) .
0.4 CJR‘OSO 0.4 0.
0 0
6'0 . . ; . "6 K.—
(W V50
0 l2
'20 . (f)0.8
(MeV) / r
6.0 0.4 I
W0
0 0
I20 \— I2
0 W—
80 0.8
(MeV) (f)
40 V 0.4 I}; [’30
0 0
0 20 40 6O 0 20 40 60
ELAB (MeV) ELAB (MeV)

Figure IV-7. Optical model parameters from references quoted
in the text describing the elastic scattering of deuterons
131‘0m 150 between 11.8 and 52 MeV. The curves represent the
"best" values of the parameters, from which those used in
tlfle DWBA exit channel calculations were taken.

mi

 

62

oo Om .m Om .m Om

 

om OMoH H .H ~>mz “Moh N > M H M .H H .H
oe.o mo.H oo.m oe.o om.e o.ome ~o.ea- mm.m~ m.e
ee.meu mm.mm
oe.o em.e ee.o ee.e ma.e e.eHH Amo.aau mm.em~ e.oH
oe.o mm.a ee.o em.e em.e o.oeH mm.-l em.mm m.ea
ee.mau me.am
oe.o em.H mo.e ee.e mm.o e.eee imo.ael mo.em~ e.oH
ee.o oe.e em.e em.o eo.e m.oo eo.men em.am e.e~
ee.mHI me.mm
oe.o me.H ma.» em.e eo.H e.mm imo.oeu em.me~ m.o~
oe.o He.e ee.e ee.o mo.H m.mm Ho.mu em.mm o.~m
ee.o He.a ee.m om.o mo.e e.~m ee.mal em.me «.mm.
“my Ame A>ozc its Ame i>ozv i>ozc A>ozc x>ozc
Ho HA 63 mo mu > o am pm

 

 

.GOADUMOH map mo ODHOPIO on» can cououm osm souopsop Tau mo
woemnoco muouononoa on» an COHUQDH who moose .msoHDUMOH ZvHAU.mVZmH can

038663 05 m0 mfimfimcm «man ofi 5 wow: mumumsgmm Hmowumo coumuzmg .NIE. gag

63
have deuteron parameters corresponding to incident deuteron

energies between 33.2 and 5.1 MeV. These were taken from
Fig. IV-7; the ones of major interest (see Chapter VI) are
listed in Table IV-2.
. 15 14 .

For the ana1y51s of the N(p,d) N data, Optical
model parameters for deuteron elastic scattering on 14N
at 32.8 MeV and lower were required. Very little data
is available in the literature, and that which is available
(Ng 66, Vi 66) corresponds to lower deuteron energies
and was analyzed using simplified forms of the optical
model potential. Thus, it was again decided to use

. 16 16

parameters derived from O(d,d) 0 data. Newman et al.
(Ne 67) have shown that the variation of the parameters with
Z and A is rather slow, so these parameters should be

quite valid. Table IV-2 also lists the deuteron parameters

1
used in the SN(p,d)14N analyses.

 

CHAPTER'V

EXPERIMENTAL RESULTS
Deuteron energy spectra and angular distributions
. . 16 15
are presented in this chapter for the O(p,d) O and
15 14 . .
N(p,d) N reactions. Some of the concluSions reached
about possible spin and parity assignments are based
upon the distorted wave Born approximation (DWBA)
calculations discussed in Chapter VI; however, unless
otherwise noted, the curves shown with the angular
distributions represent only the general trend of the data.
The error bars shown in the figures represent the total

error in the differential cross section. Those not shown

were smaller than the size of the data points.

V.A. l6O(p,d)lso

 

V.A.l. Simple Model Predictions

Before discussing the data it would be instructive
to determine which levels of 150 should be populated in

16

the O(p,d) reaction. Considered as a direct reaction,‘

the (p,d) reaction involves the removal of a single neutron

from the target nucleus, which is assumed to be in its

64

ground state
ground state
energies are
44.0, and 45
and 251/2 pa;
were consider
would be bour
Thus, one wou

neutron to be

 

 

 

would be Very
Since the gro
Conservation

Spin and pari

Picked-up neu

Shell model 1:
hole in the 1

One 3/2- P8 a}

It is k:

much too nai‘

10w~lying de:

(M9 56' ED 61

65
‘ground state. The simple shell model picture of the 160

ground state is shown in Fig. V-l. The single particle
energies are given by Jolly (Jo 63) as 0.0, 27.0, 33.0,
44.0, and 45.0 MeV for the 151/2' lp3/2, lpl/Z' ldS/Z’

and 251/2 particles respectively. If the lpl/2 neutrons

were considered to be barely bound, the lp3/2 neutrons

would be bound by 6 MeV and the 181/2 neutrons by 33 MeV.
Thus, one would expect either a lpl/2 or a lp3/2
neutron to be picked up; the pickup of a 131/2 neutron
would be very unlikely owing to its strong binding.
Since the ground state of 16O is known to have JTr = 0+,
conservation of angular momentum and parity require the
spin and parity of the final state to be that of the
picked-up neutron, i.e., l/2' or 3/2'. The simplest
shell model picture of 15O is that of a single neutron
hole in the 160 core. These are also shown in Fig. V-l.
On the basis of these simple pictures one would expect
the deuteron energy spectra to contain one 1/2— peak,
one 3/2- peak, and no others.

It is known, however, that the simple shell model is
much too naive, even for the case of a ”closed" shell
nucleus such as 160. One should consider the effects of

low-lying deformed states in the closed shell nucleus

(M9 56, En 65, Br 66a, Br 66b).when using that nucleus as

F"

 

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

"1i p n 2j+l
2592 2
”5,2 6
'95 oo 0. 2
:93/2 0000 0.00 4
s'IZ oo o. 2
'60 9.3.

P n p n
00 0 OO O 0
P000 0000 0000 00.
[co oo oo oo

'50 V2‘ '50 3/2"

Figure V-l. Simple shell model configurations of the 160

_ground state and the 150 1/25 and 3/2' states. The value

2j+l is the number of protons or neutrons required to fill
a given nlj subshell.

67

a core. Such effects are known as core polarization.

Brown and Shukka(Br 67) have performed such calculations
for 150 and 15N. They predict, in addition to the strong
0.0 MeV, 1/2‘ and 6.18 MeV, 3/2- levels, the existence

of a 3/2- level between 10.0 and 11.0 MeV of excitation

and a 1/2‘ level approximately 1.0 MeV lower. Bertsch

(Be 68) has predicted that core polarization could result
in many highly fragmented states with excitation energies
of approximately 20 MeV. Hence, core polarization can
result in the sharing of the lpl/2 and 1p3/2 strengths
among several states. One would also expect the 160 ground
state to be more complex. Calculations have been performed
(Br 66a) in which 2 particle-2 hole and 4 particle-4 hole
admixtures have been considered. If such admixtures
existed, one would eXpect to pickup some 1d and 25

5/2 1/2

neutrons, leading to positive parity levels in 15O.

V.A.2. Energy Spectra

 

Fig. V-2 shows an energy level diagram of the 15O

nucleus beside which has been placed a deuteron spectrum
taken at a laboratory angle of 20.1° with 45.34 MeV
incident protons. All of the known levels below 11 MeV
are shown. All energies, spins, and parities for the
levels below 9 MeV were taken from the gamma—ray work

of Warburton et a1. (Wa 65), those of the levels between

68
9 and 10 MeV from the work of Lambert and Durand (La 67),

and those of levels above 10 MeV from Lauritsen and
Ajzenberg-Selove (La 62). One immediately notices the
presence of the two very strong peaks corresponding to

1p and 1p3/2 neutron pickup. All other states excited

1/2

are much weaker. It is interesting to note here the

surprisingly good agreement with the simplest shell model ”—
picture discussed in the preceding section.

Additional deuteron energy spectra obtained for incident :3

1...;

 

 

protons of energies 45.34, 38.63, 31.82, and 25.52 MeV are
shown in Figs. V-3-—V-5. The Goulding particle identifi-
cation system was used in obtaining each of these spectra.
Fig. V-6 shows a spectrum obtained using the time-of-flight
system for mass identification. The peaks corresponding

to 14N levels are due to 3He particles from the 16O(p,3He)14N
reaction which reached the detector within the accepted
time window. The closely spaced levels near 5.2 and

6.8 MeV are partially resolved here. The other spectra
obtained between 12.4° and 30° in the laboratory frame
using time-of-flight showed comparable resolution. This
data will be discussed in Section V.A.4. A tabulation of
the peak cross sections for the levels excited is contained

in Table VI—3.

69

 

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Aw.mv0ma may scum

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Hmcm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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70

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in: Julio

 

 

 

m

meg w>mz vm.mwu m mom coauomou
pcm om.Hmu o um muuommm mmuozo noumudma

 

 

 

 

 

egg of £% 9N oo
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a m
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m m
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9:

WHO I SlNflOO

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71

 

‘0(p.d)"o ?
E £58.63
750. p o i
6m=200 T
500- .

 

g

COUN T8 / CHANNEL
CL
o—noss
«(949-9561
7 «7.204
F .. [spa-5240]
1 .
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‘—0.0

    

“(Em-6.57]

E ‘—'[5.m- 5.240]
r
i

o—nac
.— [9.49-9.66]
o—[ans-asaoa
*— 1284

   

   

 

 

 

 

 

\J
250 500 I000
CHANNEL Human
Figure. V—4- Deuteron energy spectra at .e =20.0° and 60.1°
fT-‘om the '160(p,d)150 reaction for E =3¥8.6§Afiev. ' '

P

72

 

300
'60 (p,d) “o g.
Ep=3l.82 MeV l
200L. SLAB: ZOJO g .,
l

 

     

0—[5188- 5.240]

 

 

 

 

 

 

5'; J i ii
:2»
3 3
8 400 .. Ep 3 25.520MeV l .-
9m=200
W a _
200- S _
‘5 '5'
1
loo— 2 _
J
A _J L

 

 

 

01 e - 4 ,
50° 75° I000
CHANNEL NUMBER

 

Deuteron energy Spectra at,e =zo,19 and 20-00

Figure V-S.
1150 reactions at Ep=31.85‘“Band 25.52 MeV. .

from the 150(p,a
reSpectively. ..'

73

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Zvahomm.mVOmH may Eoum mcouopsop ou mom who mxmom Zea one .GOflpMOHMHquQH oaoflunmm How.
mosvwcgoou ucmflamumolofiwu mo own man an Uoc«Mpbo .Oma :0 unopwocfl mcououm >02 oo.~m

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mum—>52 szz<Io
ooo. omm

g _ E _ _4_ ____.

 

 

 

 

 

 

 

 

 

 

 

 

m
_ 4.0. n
N
R NH O: Om Qu. n/J
3 ¥/ m .9 .9 a W
a. a. g a m w M
.9 c. :8.
w .2 .2736 _I
my >3. E1 f
>22 83.3..
_ 20:3...Ezme

w...oFm<a mou— PIG...“—

umo.m§£H wzmflg q_*nr&.900~

 

 

 

74
V.A.3. Negative Parity Levels

 

Below an excitation energy of 16.5 MeV the existence
<31? one 1/2- and three 3/2- levels have been confirmed
(Wa 65, La 67, La 62). The 1/2- level at 0.0 MeV and the
3/2- level at 6.180 MeV are those predicted by the
ssijnplest shell model. Angular distributions measured for
tilease states are shown in Figs. V-7 and V-8. The
existence of a first maximum between 10° and 20° in the
cxariter-of-mass frame is characteristic of £n=1 pickup.
ITI€3 angle at which the first maximum occurs decreases
ass the incident proton energy increases. J-dependence
.111 this reaction exhibits itself in the generally steeper
Slepe and more pronounced oscillation of the Jv=1/2-.data.

The magnitude of the differential cross section at

me first £n=1 maximum is used in the extraction of spectro-
SCOPic factors (see Chapters II and VI). This quantity
143 shown as a function of the incident proton energy in
5:15;. V-9. Included in this figure are points from other
Eituldies of the 16O(p,d)lSO reaction between 18.5 and 100
Mev (Ch 67, K0 67a, Le 67, Le 63, Sh 67). The dashed
C311:I:~ves are drawn to accentuate the general trend of the
data. The 3/2- peak cross section becomes larger than

tire 1/2- peak cross section at some point between 45

axui 100 MeV. At 100 MeV it is interesting to note that

the ratio of the. 3/2- to the' 1/2— cross section is'bl.3.

75

 

I,
'0 I I I I I I I I

'60 (p. d ) l5O
EX=O.O MeV

J'=l/2"

 
    

O 20 4O 60 80 IOO lb F416 b |80

6Qmfldeg.)

 

 

Figure V—7. Deuteron angular distributions for the 0.0 MeV,
1/2‘ level of 150 from the l6O(p,d)l50 reaction for incident
proton energies between 21.27 and 45.34 MeV.

 

3h 1"

 

76

 

 

   
   

I
'0 I I 'SoIppII'So I
it \- Ex=6.|80MeV
IO' J'=3/2' ..
Ep=25.52MeV

 

 

 

 

l l I l I
O 30 60 90 l20 ISO ISO

90mm”)

 

Figure Ve8. Deuteron angular distributions for the 6.180

MeV, 3/2- level of 150 from the 16O(p,d)150 reaction for
incident proton energies between 25.52 and 45.34 MeV.

77

ENERGY DEPENDENCE OF '60(p,d)'50 In=l

I8~ PEAK CROSS SECTIONS .
I6- /,/’/+ i
M- //’/// 4
I2- 4”]: """"""""" + _

 

O'PENémb/sr)
S5
\
ea»:
\\
\x
\

 

 

 

b
OWW,V2.’1'I + 9 c
4" [I /+ X d "I
I
‘ "fiswmmae' ' e
2- #0‘ -
*1
O l ’1 l l l l l l l I
OI02030405060708090lOO
Ep (MeV)

Figure V-9. Dependence of the £n=l peak cross section of the
0.0 MeV, 1/2— and 6.180 MeV, 3/2- levels of 150 from the
16O(p,d)150 reaction on the incident proton energy. The data
represented by symbols a—-e are found in Refs. Ko 67a, Ch 67,
Sh 66, Le 63, and Le 67, respectively.

78

In an attempt to explain the phase of the E2/Ml
mixing ratio for the (6.18 MeV, 3/2_ + 0.0 MeV, 1/2')
transition in 150, Rose and Lopes (R0 65, Lo 66) proposed
that only 40% of the lp3/2 hole strength was contained
in the 6.18 MeV state, and that much of the remaining
strength was contained in the 8.98 MeV level. However,

l6O(3He,cx)150 data (Wa 65a)

16O(p,d)lSO data (Ba 64) and
indicated that there was no appreciable (110%) 1p3/2
component at excitation energies between 6.5 and 13 MeV.

The deuteron energy spectra in Figs. V-2--V—5 indicate

that the excitation of the 8.98 MeV level is very weak,

the peak cross section being less than 0.1 mb/sr. However,
there are two relatively strong deuteron groups corresponding
to levels of higher excitation energy. The first corresponds
to the levels at 9.49, 9.53, 9.60, and 9.66 MeV, which have
J1T = 5/2', 1/2+, 3/2', and (7/2, 9/2)‘ respectively (La 67).
Careful examination of the energy spectra showed that all
four levels were excited, but that approximately 70% of

the area of the peak was due to excitation of the 9.60 MeV,
3/2- level. The other deuteron group comes from the
excitation of the 10.46 MeV level, which was resolved

from the 10.28 MeV level. Angular distributions for

these levels are shown in Fig. V—lO. The angular

distribution labeled 9.60 contains contributions from the

other three close—lying levels. The curves represent

79
empirical £n=l shapes corresponding to the Q—values of
the reactions leading to these states, obtained by
graphical interpolation between the shapes of the 0.0 and
6.18 MeV angular distributions for 45.34 and 38.63 MeV
incident protons. Both levels are seen to be 2n=1 in
character. On the basis of shape, the assignment of
3/2- to the 10.46 MeV level is preferred. The data
certainly do not disagree with the previous 3/2- assignment
for the 9.60 MeV level. Estimates of the lp3/2 hole
strength in these levels will be given in Chapter VI,

where spectroscopic factors will be discussed.

V.A.4. Positive Parity Levels

 

As was noted in Section V.A.1., the only way in

15
which a positive parity level can be reached in O

16

by the direct pick-up of a neutron from O is for the

16Oground state to contain an admixture of even-2 neutrons.

The most likely admixtures being 1d5/2 and 251/2 neutrons,

one would look for 5/2+ and 1/2+ levels. The levels at

5.188, 7.550, 8.735, and 9.53 have previously been shown

to be l/2+. The level at 5.240 MeV has an assignment of

5/2+, and the (3/2, 5/2) level at 6.857 MeV appears to

be the mirror level of the 7.15 MeV, 5/2f level in 15N.
Examination of Figs. V—2—+V—6 shows that the 5.188—5.240

MeV doublet has considerable strength. Angular distributions

80

for the unresolved doublet are shown in Fig. V—ll. The
time-of-flight data taken with 32.00 MeV incident protons
had sufficient resolution to allow a Gaussian peakshape
analysis to be performed to separate the states. Using
a non-linear least squares method, a skewed Gaussian was
fitted to the single 6.18 MeV level to determine a peak
shape. Then the areas and centroids of two Gaussians
having this shape were adjusted, keeping a fixed
separation corresponding to the known separation of the
levels, until the fit to the 5.188-5.240 MeV group was
judged best. The ratios of the areas were applied to the
31.82 MeV data to obtain partial angular distributions,
also shown in Fig. V—ll. The large errors (m30%) are due
to the poor statistics of the data and the uncertainty in
the ratios of the areas. The shape of the 5.188 MeV
angular distribution is characteristic of £n=0 pickup,
whereas the occurrence of the first maximum near 30° for
the 5.240 MeV angular distribution indicates an 2n12,
consistent with the 5/2+ assignment. This data disagrees
with the 16O(d,t)150 data of the Rochester group (quoted
in W0 68), which showed no direct reaction pattern for the
1/2+ member of the doublet.

Excitations of the other 1/2+ and 5/2+ levels are

very weak, with the exception of the 7.550 MeV, 1/2+ level,

which does not exhibit the characteristics of ln=0 pickup

 

81
(Fig. V—13), Wong (W068) in a study of centroids and sums of

16

direct reaction strengths with O as a target, has found that

central force (e.g., Rosenfeld, Soper) calculations imply that
most of the ld5/2 strength is in the 5.24 MeV level, whereas
calculations using realistic forces (e.g., Brueckner—Gamel-
Thaler,Hamada-Johnston) imply that the dominant part of the
1d5/2 strength will be in a higher 5/2+ state. Thus, the

present data tend to support the use of central forces.

Weak excitation of the 3/2+ levels at 6.789 and

 

8.283 MeV has been found, which could be due to the pickup

of a ld3/2 neutron. The shapes of the angular distributions

(Fig. V-l3) are not inconsistent with such a pickup.

A very interesting angular distribution was measured

for the level at 7.284 MeV, which had been assigned

a spin of :9/2 and appears to be the mirror level of

the 7.56 MeV, 7/2+ level of 15N. If it were excited by a

direct reaction, it would correspond to the pickup of

a 197/2 neutron. The angular distribution for this

level obtained with 45.34 MeV incident protons is shown

in Fig. V-12. The curves are DWBA calculations with and

without a lower integration cutoff (to be discussed in

Chapter VI). The zn=4 shape fits the data well. An

alternative process for the excitation of this level is a
16

two-step one in which the 6.13 MeV, 3“ level of O

is first excited,_with the pickup of a 1p neutron

82

 

 

  

 

 

 

|.O —- l6O(p,d) "’0
Ep = 45.34 MeV
"’17 Empirical shapes to
_ 3" '
\‘ . 1- motch deuteron energues
o.I —
15
.0
353
A
£5 '° '
O-I - [5x = IO.46 MeV
0.0I ~— \ , , "
\\//’
o L 62) I I50 I I80
echdeq.)

Figure V-lO. Deuteron angular distributions for the 9.60 and
0- 46 MeV levels of 150 from the l6O(p,d)lSO reaction for

p=45.34 MeV. The contributions of the 9.49, 9.53, and 9.66
MeV levels have not been separated from the 9.60 MeV angular .

iStribution. The curves were obtained empirically from the ‘
45 . 34 and. 38.63 meV data.

83

 

l
'°IIIIIIII

 

l6 l5
0 (p,d) o
E x =[5.|88-5.240] MeV
O
| —
° W, J” = [V2+ — 5/2*]
05 Ep= 25.52 MeV
IO — _
A Io" — _
(D
B I) f .
S , ”I - 5.|88MeV,l/2 } TIMEOFFUGHT
/_7§5 O f I 5.240 MeV, 5/2+ DATA
3&1: '° ‘ —

 

 

 

'62 l l I l l l I l
O 20 4O 60 80 IOO l20 I40 |60 ISO

9 ch deg.)

 

F,igure V—ll. Deuteron angular distributions for the 5.188—
.5- 240 MeV doublet of 150 from the l6O(p,d)lSO reaction for
incident proton energies between 25.52 and 45.34 MeV. The
Solid symbols represent a decomposition of the 31.82 MeV

a‘Ilgular distribution based on a Gaussian peakshape analysis ‘
of the time—of—flight data.

84

 

0
'0 I I I I I

'GOIp,d) l5O
Ep= 45.34 MeV

Ex= 7.284 MeV
1,, = 4

I0"- ++

) (mb/sr)
c.m.

 

IO'

 

 

"- 7/2: ’zRCUIOff O F
DWBA {— 7/2 Rcutoff= 3 F

 

 

ICfB I I I I I
O 30 60 9O IZO I50 IBO

90. m ( Degrees)

Deuteron angular distribution and DWBA fit for
150 from the l6O(p, d)l5O

 

Figure V—12.
the 7.284 MeV, (7/2+) level of

reaction for Ep=45.34 MeV.

85

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Eoum woGHMon oum3 poumoflpcfi mofluflumm paw mcflmm .>oz vm.mvn m um coauomon Omaap.mVOoH
ozu Eoum OmH ca pmufloxo mHo>oH Honuo How mcoflusnflnumflp smasmcm couwpsoa .mHI> ousmflm

 

 

 

 

 

 

 

 

 

air o
a q . T + q 1 q q a q q +e O
2: i . e is . is . i:1
I . I. . :e . + . 1.5 I w . 5:: o
+ :2 + . 11+; . 2+: . + see
2... i - .2. . s eh... . es ..
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e i . i i .3. I
:1 . +3: + .2 Ezemoeuem
.Ns . .NBNEJNB + 19.0 093.30!
>02 000K >£ TOOGIGQNOH

 

 

86
(probably a lpl/2 neutron) following. Evidence for such

a process has been found in the 12C(d,3He)llB*(6.67, 7/2‘)
reaction (Du 68). A 5/2+ level could also be excited

by the pickup of a lp3/2 neutron in a two-step process.
The other angular distributions shown in Fig. V-13 exhibit
little character. However, the 12.30 and 13.79 MeV levels

are quite strong (0.12 mb/sr).

15 14
V.B. N(p,d) N

 

 

V.B.l. Simple Model Predictions and Energy Spectra

 

The simplest shell model configuration for the 15N

ground state is that of one lpl/Z proton hole in a

160 core. Thus, the neutron configuration is the same as

15

that of 16O. The spin and parity of the N ground state

is 1/2', so the pickup of a lpl/2 neutron populates

14 + +

N states having J" = 0 , 1 , and the pickup of a 1p3/2
neutron leads to states having JTr = 1+, 2+. Based upon
the simplest shell model, using only 1p nucleons, one

l4N configurations shown in Fig. V414.

can construct the
The isotopic spin quantum number (T) is good for all of the
states shown. The particular combinations of the two

terms of (c) were necessary in order that T be good. The

T=1 states are those in which a neutron could be transformed

into a proton, or vice versa, without violating the Pauli

87
principle. There are nine levels which could be reached

by 1p pickup from 15N, the pOpulation of the 3+ level
being forbidden by angular momentum conservation. The
three other levels having configuration (b) are not
pOpulated in the simplest model since they require the
excitation of one of the protons in 15N. Thus, one would
expect to see six strong levels (one 0+, T=1; two 1+, T=0;
one 1+, T-l; one 2+, T=0; and one 2+, T=1) whose relative
strengths are discussed later.‘ .
There are over fifty known levels in 14N between 0.0
and 14.0 MeV, sixteen of which have been identified as

+, 1+, or 2+. All energies, spins, and parities have been

0
taken from (Za 67) and the references therein. An energy
level diagram of 14N, displayed beside a deuteron energy
spectrum obtained at GLAB=20° for an incident proton

energy of 39.84 MeV, is shown in Fig. V-15. It is seen that
many levels are excited to some extent. However, the
strongly excited levels are seen to be either 0+, 1+,

or 2+ (the assignment for the 13.72 MeV level coming from

the present work). Other deuteron energy spectra obtained

at eLAB=59.8° and 119.6° are presented in Fig. V-l6.

V.B.2. Levels Reached by‘£n=l Pickup
Six of the sixteen levels which could be reached by

1p neutron pickup had peak cross seCtions of 40 ub/sr or

88

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

III] p n 2]+|
2892 2
Ides,2 6
lpyz o co 2
Ip3,2 0000 000. 4
”ya 00 co 2
'SN 9.3.
(a) "‘N (b)
p n p n
II)”2 ° 0 oo 00
lpwoooo 0000 000 000
"I12 00 no 00 co
J;=O*,T=I J'=o*,Ta-I
J=I+,T=o J;'l*,T=O
(c) J 'v'T"
IJ"=3*.T=0I
P n p n
_I_ °° ' + _I_ o o o
4:2- 000 o... onoo .00
oo 0. Foo on

 

 

 

fame” Ito H
J”-I*,2* hi «I

Figure V—l4. Simple shell model configurations of the 15N
‘ground state and the 14N levels based only on ls—lp nucleons.
The J"=3+ level cannot be reached by 1p neutron pickup because
of angular momentum conservation. The other levels of

configuration (b) will not be reached by the direct pickup
of a 1p neutron from 15N.

89

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91

less. Angular distributions for the ten remaining levels
are presented in Fig. V-l7 and Fig. V—18. They all
exhibit the characteristics of £n=l transfer. J-dependence
is again seen in the steeper lepe of the 0+ angular
distribution (pl/2 pickup) as compared to the 2+ angular
distributions (p3/2 pickup). A Q-dependent effect is
seen in the decreasing lepes of the 2+ angular distributions
with increasing excitation energy. The lepes of the 0.0
MeV, 1+ and the 2.311 MeV, O+ angular distributions are
very nearly the same, indicating, on the basis of J-
dependence, that the ground state is populated mainly by
lpl/2 pickup, as one might expect from energy considerations.
The other l+ angular distributions exhibit less steep
slopes, indicating 1p3/2 pickup. The 15N(p,d)14N and
l6O(p,d)lSO 2n=l angular distributions are very similar.
The broad level at 13.72 MeV is particularly
interesting. Its angular distribution (Fig. V-l7)
definitely exhibits an £n=l shape, contradicting the
previous assignment of J=3 (La 62). The strong excitation
is also indicative of 1p neutron pickup, with the lepe of
the curve indicating lp3/2 pickup. The width of the state
has been determined from the.Various energy spectra by
subtracting (in quadrature) the resolution from the

measured width of the state. This value is 210r30.keV.

92

Angular distributions for the other levels which have

. . + . .
been preViously ass1gned J =0 , 1+, 2+ are shown in Fig.
V—21. These levels are weakly excited, and their angular

distributions do not contradict the assignments.

V.B.3. Levels Reached by £_#l Pickup

 

The presence of levels other than 0+, 1+, or 2+
is an indication of admixtures in the ground state of 15N.
As for the 160 ground state, the most likely admixtures are
ld5/2 and 251/2, leading to the excitation of 2’ or 3-
and 0- or 1- states, respectively. Angular distributions
for those levels having previous spin and parity assignments
of 2- and 3_ are shown in Fig. V-l9. Most of the levels
are very weakly excited. The level at 12.52 MeV had no
previous assignment. It is rather strongly excited,
especially for a state with such a high excitation energy,
and its angular distribution is consistent with 1d pickup.
Levels having previous spin and parity assignments of 0-
and l- are shown in Fig. V-20. These levels are also
weak, in general, with the angular distributions of the
levels at 4.91, 5.69, and 8.06 displaying the rise of the
cross section toward a maximum at 6c m =0°, which is

characteristic of zn=0.pickup. If the 11° point is

ignored, the shape of the angular distribution of the 13.17

93

MeV level is consistent with £n=0 pickup. The 1- level
at 10.213 MeV could be 0 ulated either b 25 or 1d
P P Y 1/2 3/2
pickup.
Also shown in Fig. V-20 are angular distributions
3+ 21+

for levels having previously been assigned JTr = or

These would require 1f neutron pickup in the direct reaction
picture. The angular distributions for the 12.61 and

12.80 MeV levels may contain contributions from other
close-lying levels. Again, the cross sections are small.
The existence of a level between the 10.55 and 11.06

MeV levels has been reported at 10.71 MeV (Pe 65), at

10.78 MeV (Ma 67a), and at 10.85 MeV (Ha 66), and at
10.8510.02 MeV (Za 67). The Spin and parity of this level
have been given as (4+) (Ma 67a). In the present work

this level was very weakly excited, with an average excitation
energy of 10.80i0.05. The angular distribution is shown

in Fig. V-20. Several other levels were weakly excited.
Spins and parities cannot be assigned by inspection of

the angular distributions, which are shown in Fig. V-21.

The peak cross sections for all levels excited in the 15N(p,d)

reaction are listed in Table VI-4.

94

 

   
      

 

 

 

 

 

 

 

   
    

 

 

IO 1 I I I l '0 I I I I I
IS
N(p,d) ”N
IO -
,. Ex=3.945MeV
3
\ V = '4'
a | J .-
55
A E =Il.06MeV
3'3 I‘M“
V -
- . +
'0' I— J I&F— Q J —
,0 Ex=2.3ll MeV
.J'E0+ (f
d
IOOII' _, I0 1+ -*
Ex=62l MeV
- J'=I*
IO' - -‘ IOZF i I 1
IO 1 1 l l. I I6” 1 l 71
0 3K) 60 90 20 I50 KI) C) 30 (K) 90 20 I83 EX)
echdeq)

Figure V-l7. Deuteron angular distributions for the 0+ and 1+
levels of 14N strongly excited in the 15N(p,d)l4N reaction
for Ep=39.84 MeV.

95

 

I
I0 I I I I I

 

  
   
  

 

 

 

'5N(p.d) MN
Ep= 39.84Mev
1n 3 I
I0 .-
Ex= 7.03 MeV
.0 J'=2+
E [0° E =9.l7MeV _-
13 X
S E
b'fiéd
13
"’ . Ex=|0.43 MeV
Id' _ 00 J": 2+ —
lOz- ...
E x: I0.09 MeV
J'=2*
.53 l w I I l l
0 30 606 90 IZO ISO ISO

(1fl1( ° +
Figure V-18. Deuteron angular distributions £14 the 2 .
levels of.14N strongly excited in the 15N(p,d) N reaction

for Ep=39.84 MeV.

96

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CHAPTER VI

DWBA ANALYSIS, EXTRACTION OF SPECTROSCOPIC FACTORS,

AND COMPARISON TO THEORY L

16
VI.A. ' O(p,d)lSO

 

As was stated in Chapter I, one of the major purposes

 

of this work was to study the extraction of spectroscopic
factors (discussed in Chapter II) for neutron pickup

from a light nucleus. The nucleus 160 was chosen as a
target because one has some feeling about the values of
the spectroscopic factors for the reaction. The simplest
shell model predicts spectrosc0pic factors of 2 and 4 for
the 0.0 MeV, 1/2’ and the 6.18 MeV, 3/2" levels of

150, respectively. These are just the numbers of lpl/2
and lp3/2 neutrons available for pickup. If, however,
some of the lp strength lies in other 150 levels of
higher excitation, the spectroscopic factors for the

0.0 and 6.18 MeV levels will be reduced, but the sum

of the lp spectrosc0pic factors will still be 6. However,

160 were to contain admixtures of

if the ground state of
neutrons from other shells,_the total number of lp neutrons

available for pickup would be less than 6, and since the'

99

100

neutrons are less stron l bound than the 1
1/2 '9 Y p3/2

neutrons, one might expect the lpl/Z subshell to be

19

depleted more than the lp3/2 subshell. Thus, one would
expect the ratio of the summed lp3/2 Spectroscopic factors
to the summed lpl/Z spectrosc0pic factors to be greater
than 2. These conditions were considered when evaluating
the results of a DWBA calculation.

A FORTRAN version of the Oak Ridge code JULIE,*
running on the CDC 3600 computer at the Michigan State

University Computer Center, was used for all DWBA calculations.

VI.A.l. DWBA Calculations and Spectrosc0pic Factors

 

for the'0.0'and 6.18 MeV Levels

 

Initial DWBA calculations were made for 45.34 MeV
incident protons. Optical model parameters for the
entrance and exit channels are listed in Tables IV-l and
IV-2. The parameters for the bound state well were
ron = 1.12 F, an = 0.69 F, and A = 25. The geometric
parameters are the same as those of the real proton well,
and the value of the spin-orbit strength is the one

normally used for nucleons. No lower integration cutoff

was used in initial calculations. As can be seen in

 

.*JULIE is described in Refs. Ba 62 and Ba 66.

101

Fig. VI—l, the shape of the calculated angular distribution
does not match the data. However, in studies of (p,d)
reactions in lp shell and Zs-ld shell nuclei, Kull (Ku 67)
and Kozub (Ko 67a) found that an increase in the imaginary
well depth (WD) of the deuteron Optical potential led to
shapes which were in better agreement with the data.

They found that increases of from 200 to 300% produced
changes in the magnitude of the first peak of the differ-
ential cross section (hereafter referred to as Opeak) of
less than 20%. This was important since the value of

the experimental spectroscopic factor depends on the value

of o k (see Chapter II for a discussion of the extraction

pea
of experimental spectrosc0pic factors). The same
procedure was followed in the present case; the results
are presented in Fig. VI—l. The shape does improve as
WD increases, but the shape of the data still is not
well-reproduced. The worst feature, however, is that

the magnitude of 0 decreases from 1.5 mb/sr to

peak
0.6 mb/sr as WD increases from WD0 to 4WD0. These values
give spectrosc0pic factors of 3.6 and 8.9, respectively,
much too large for lpl/2 pickup.

Siemssen (Si 67) also encountered the difficulty of

reproducing the shape of the data from (d,p) reactions with

lp shell nuclei. He obtained reasonable fits by using a

 

102

lower integration cutoff in the DWBA calculation. Following

a similar procedure, W was kept at the value found from

D

Optical model calculations, and a series of DWBA calculations
was made with different values of the lower integration

cutoff radius (Rcutoff)' The effect of the cutoff radius

on g is shown in Fig. VI-2. Two maxima exist, one at

peak

Rcutoff = 0 F and one at R = 3 F. For R = 0 F

cutoff cutoff
the SpectrOSCOpic factor for the 0.0 MeV level is 3.2,
whereas for Rcutoff = 3 F it is 1.8, a much more acceptable
value. For the 6.18 MeV level there is no appreciable
difference in the spectrosc0p1c factors for Rcutoff = 0 F
and Rcutoff = 3 F. Figures VI-3 and VI—4 show the DWBA

angular distributions for the ground and 6.18 MeV states.

The shape for R 3 F is better than that for Rcutoff =

cutoff
0 F, but is still not very good. However, the first
maximum is reasonably well-reproduced, so the prescription
of using the measured Optical parameters with a lower
integration cutoff of 3 F was adOpted for all of the DWBA
calculations.

Fixing the Optical parameters and the integration
limits left only the parameters of the bound state well to
13e investigated. Since the value of 1.12 F for the radius

IParameter (ron) was somewhat smaller than that generally

Ilsed, calculations were performed for ron = 1.25 and 1.35 F.

103

 

 

 

 

 

2
'0 I I I I I
'60(p,d) '50
Ep=45.34MeV
a Ex= 0.0 MeV
' .o. . _
'0 \ J"=I/2‘
’5, . C — DWBA
B 7 d
g 000
A0 IO d
C: 0
file °.
9
¢
-|_ WOO: 884MeV 0
IO a Mr woo ¢ . e
b wo=2wDo
C WD: 3WDO ¢ o
d wD=4wDo ¢ 4» 1? °
K52 I l I l
O 30 60 9O IZO ISO I80
ecum(deg)

Figure VI—l. DWBA fits to the 150(p,d)150, _E =45.34 MeV,

Ex=0..0 MeV, J"=l/2" angular distribution for ifferent values
of the imaginary well depth. All curves have been nornalized
to the first maximum of the eXperimental angular distribution.

104

 

 

   
 
 

    

 

   

 

 

 

 

I6 I5
O(p,d) 0
Ep =45.4 MeV
I
3.0- I -
I
I
I '9
2‘0 I Va 1
: E; 0.0MOV
I
I.o i ..
I
I> : 2
2.0 . I
I
'9
LG I we a
: Ex-SJB mv
1
2.0I- I e
I D
, I
I Id
LQL I 3/2 ..
: Ex-8.28 MeV
I
I
O I l l L I I
O I 2 3 4 5 6 7
Rcutofl IFI
Figure VI-2. Dependencel of the calculated in :1 and 'Q'n =2 peak
CrOss sections from the 16O(p, d)150 reactionn forE =45. 34

MeV on the value of the lower radial integration cutoff used
in the DWBA calculations.

105

 

 

'02 I I I I
'60 (M) '50
Ep=45.34MeV
EX=O.O MeV
IOI r .. —
I ° J = I/Z
\ — DWBA

ICS|_' 4I¢é I“\\ -4
o RW=OF
b R =3F II
cumfl’ 0 ¢
c Rcmfl=5F +°

 

    

 

I I I I

 

I02

60 90 I20 I50 I80
Sc.m.(deg,)

DWBA fits to the 160(p,d)150, E =45.34 MeV,~

jEx=0.0 MeV, J"=l/2’ angular distribution for gifferent values
of the lower radial integration cutoff. All curves have been
normalized to the first maximum of the experimental angular

distribution.

106

 

 

 

2
'0 I I I I I
Emma) '50
Ex=6.l8 MeV
I
'0 .I' =3/2' ‘
:5 —DWBA
.0
E E
d
A
a; -

 

 

 

 

c -
IOL I I I I I
0 3O 60 90 I20 I50 ISO
SQmIdeg.)

Figure VI-4.- DWBA fits to the 16O (p,d)lSO, (E =45.34 MeV, .
Ex=6.18 MeV, ‘J"=3/2" angular distribution for different values"
of the lower radial integration cutoff. All curves have been
normalized to the first maximum of the experimental angular
distribution.

107
The shapes of the angular distributions were essentially

unaltered, but Opeak for the. ground state rose from its

value of 2.68 mb/sr for ron = 1.12 F to 4.35 mb/sr for

ron = 1.35 F. This represents a lowering of the ground

state spectrosc0pic factor, the value being 1.51 for ron=

IL. 25 F. This value of the spectroscopic factor is reasonable,

but that for the 6.18 MeV, 3/2- level seems much too small
since the ratio of the lp3/2 to the lpl/2 spectrosc0pic
factors is essentially unchanged by the change in 1on-
Owing to the lack of significant improvement in the
shape and magnitude of the angular distributions with a

higher value of ron' the value of ron was kept at 1.12 F

for the subsequent calculations.

It was noted in Chapter II that the inclusion of
finite-range and non-locality effects in the DWBA calculations
tends to reduce the effect of the nuclear interior.

Since this is also the effect of a lower integration
c31.1toff, a set Of calculations including these effects was
made. The code FANLFR2* was used to obtain the bound state
form factor which was then used by JULIE in the DWBA
cIalculation. Since the shape Of the angular distribution

Was little improved from that calculated using the zero-range

*Oak Ridge Computer code 'FANLFRZ, written by J.K. Dickens.

approximation and Rcutoff =' 0 F, and a value Of 3.0

vvziss Obtained for the ground state spectrosc0pic factor,

the use of finite-range and non-locality was abandoned.
Having decided to use a lower integration cutoff with

the normal deuteron Optical model parameters, calculations

were performed for the 0.0 MeV, 1/2- and 6.18 MeV, 3/2- t

levels for incident proton energies of 25.52, 31.82,

38 -62, and 45.34 MeV. The Optical parameters used were

those which described elastic scattering at the appropriate

 

energy. This means that the deuteron parameters used for
the 0.0 MeV level were different from those for the 6.18
MeV level. The method used in choosing the four proton
energies is illustrated in Fig. VI-5. For an incident
proton energy Ep (e.g. , 25.52 MeV) the deuterons leaving
150 in the 0.0 MeV, l/Z- state have the same energy in the
Center—Of-mass frame as those leaving 150 in the 6.18
MeV, 3/2- state when the incident proton energy is E '

P
(e_-g., 31.82 MeV) . Thus, deuteron parameters used in the

DWBA calculation for the 6.18 MeV level for 45.34 MeV
incident protons are the same as those for the 0.0 MeV
calculation for 38.62 MeV incident protons.

The results of these calculations are presented in
Figs. VI—3—s-VI-4, VI—6——VI—8, and in Tables VI—l and VI-2.

The shapes are reasonable for the higher energies, but are

109

BASIS FOR SELECTION OF
IN CIDENT PROTON ENERGIES

 

 

 

 

 

-l3.44 -I3.44
l60+p_d l60+p_d

 

 

E'igure VI—S. Basis for the selection of incident proton
energies for the l6O(p,d)lso experiments.

110

 

 
  
 

 

'02 I I I I I
'60 (p,d) '50
Ep=38.63 MeV
'0' 1n= | .,
—DWBA,Rcu,off=3F
’5
\
.0
13, E. EX=O.O MeV
0' '0 J”: V? -

 
  

Ex = 6.I8 MeV

  

 

 

 

1r_ -
J -3/2 0
6
I0" 1 1 1 1 1
O 30 60 90 IZO ISO I80

9cm (deg)
Figure VI—6. DWBA fits to the 160(p,d)150, Ep=38.63 MeV, ,
Ex=0.0 and 6.18 MeV angular distributions.

111

 

'02 I I F I 5 I
'60(I>.d)l 0
Ep=3l.82MeV
' Inn
IO -—

 

I:x = 6J8 MeV

 

 

  

— DWBA ,Rmfis "F"

 

 

 

J": 3/2‘
|CT JL .1 I I I
o 30 60 90 I20 I50 l80

Figure VI-7. DWBA fits to the 6O(p,d)lso, Ep=3l.82 MeV,,

EX=0.O and 6.18 MeV angular

ecm. (deg)

l

distributions.

 

112

 

      

2
'0 I I I I I
l6O(p,d) I5O
Ep=25.52 MeV
'0' " In = I d It
—DWBA,

Rcquff :3 F .
IEX=(1C"WQV' I

 

 

 

 

 

IO'I I I J I I
O 30 60 90 IZO I50 I80

ecmjdeg.)

 

FigureVI—B.“ DWBA fits to the l6O(p,d)150, Ep=25.52 Mev,~
EX=0.0 and 6.18 MeV angular distributions.

113
significantly worse for the 25.52 MeV data. The rather

low deuteron energies for this latter case made the
assumption of a direct reaction questionable. Spectro-
sc0pic factors and ratios of spectrosc0pic factors for the
0.0 and 6.18 MeV leVels are given in Tables VI-l and VI-2,
where the errors reflect only the errors in the values of
OeXp° The extracted spectrosc0pic factor for the ground
state is constant for the two higher bombarding energies,
but it increases for lower values of the incident proton
energy. The spectrosc0pic factor for the 6.18 MeV level
rises as the energy of the incident protons decreases from
45 MeV. Table VI-2 shows that the ratios of the spectro-
sc0pic factors for these levels is reasonably constant for
incident proton energies greater than 30 MeV. The ratios
given in the last column are based upon use of the proton
energy scheme shown in Fig. VI-5 to reduce any Q—dependent
effects. Only the ratios for the 45.34 MeV data remain
unchanged. These data indicate that if reliable spectro-
sc0pic factors are to be extracted from the (p,d) reaction
on light nuclei, the incident proton energy must be
sufficient to produce deuterons having an energy greater
than 22 mev in the center—of—mass frame. Relative spectro-
scOpic factors appear to be reliable even for 10wer incident

proton energies or, conversely, for higher excitation energies.

114

Table VI—l. Experimental spectroscopic factors for the

0.0 and the 6.18 MeV levels of 150 from the

16O(p,d)150 reaction induced by 25.52-45.34
MeV protons.

 

 

 

 

 

Ex J” E Oexp ODWBA 5

(MeV) (MeV) (mb/sr) (mb/sr)

0.0 1/2- 25.52 6.8:0.5 0.94 3.2:0.2
31.82 8.5:0.6 1.66 2.3:0.2
38.63 9.710.5 2 38 1.8¢0.l
45.34 ll.0:0.8 2.68 1.8:O.l

6.18 3/2' 25.52 2.2:o.2 0.12 8.liO.7
31.82 4.5:0.5 0.57 3.5:O.4
38.63 7.6i0.6 1.14 3.0:0.3
45.34 10.0i0.7 1.72 2.6:0.2

Table VI-2. Ratios of experimental spectroscopic factors

for the 0.0 and 6.18 MeV levels of 150 from
the l6O(p,d)15O reaction induced by 25.52-
45.34 MeV protons.

 

 

 

Ep+ Ep’ S3/2(EP+)/Sl/2(Ep+) S3/2(Ep+)/Sl/2(Ep
(MeV) (MeV)

25.52 --- 2.53:0.25 ——-

31.82 25.52 1.54:0.15 1.09:0.11

38.63 31.82 1.63:0.16 1.30:0.13'

45.34 .38.63 1.41:0.14 1.41:0.14

 

115
It is interesting to note the similarity of the ratio of

spectrosc0pic factors for the 6.18 MeV, 3/2- and 0.0 MeV,
1/2- transitions from the 45.34 MeV data to the ratio of
the peak cross sections Of these levels from the 100 MeV
data.

It is possible to Obtain better agreement between the
DWBA calculations and the shapes of the experimental
angular distributions. Chant et al. (Ch 67) freely
adjusted the deuteron optical model parameters to obtain
the best fit to the ground state angular distribution
from their 30-3 MeV 16O(p,d)lSO data. The imaginary well
depth was increased by a factor of approximately 3,
with changes of 5-20% being made in the other parameters.
The fit was very good for the ground state angular distri-
bution below 78° in the center—Of—mass frame, where the
data ended, but the 6.18 MeV fit was not as good. They
did not calculate SpectrOSCOpic factors, so the quality
of the fits could not be judged by that criterion.
However, the calculations of the present work showed that
an increase Of the imaginary well depth led to spectrosc0pic
factors which were much too large. Thus, the value of
such a fit is questionable.

A study similar to that of the present work has been

16

made by Hiebert et a1. (Hi 67) for protOn pickup from O.

116

The l6O(d,3He)15N reaction was employed with an incident

deuteron energy of 34.4 MeV. Satisfactory fits to the
data were obtained using standard optical model potentials.
They found that the local finite—range form of the DWBA
theory gave the most reliable spectrosc0pic factors.

- 15
These values were 2.14 for the 0.0 MeV, 1/2 level of N

and 3.72 for the 6.33 MeV, 3/2- level. These are not in
good agreement with the present values for neutron pickup
from 160 presented in Table VI-l, and probably reflect more
the uncertainty in the extraction of spectroscoPic factors

than a dissimilarity of the proton and neutron configurations

of the 16Oground state.

VI.A.Z. Spectroscopic Factors for Other Levels, and

 

the Ground State of 16O

 

Using the criteria established in the previous section,
DWBA calculations were performed for other levels in the
45.34 MeV data. The results are similar to those for the
strong levels shown in the previous sections. Spectro-
scopic factors for these levels arquiven in Table VI-3.
Again, the errors quoted reflect only the errors in the

exPerimental value of the 0 An estimate of the spectro-

peak.
sc0pic factors for the 5.188 and 5.240 MeV levels was

Obtained b addin to ether 25 and 1d DWBA angular
Y g g 1/2 5/2 .

 

Peak cross sections and spe
for the levels observed in
cross section over the indicated angular

117

O.

igrosc

opic factors
The average

range is given for weak levels having angular

distributions showing no characteristic maximum.

The uncertainties quoted in the spectrosc0pic
factors represent only the uncertainties in

 

 

 

 

Opea‘k’.

EX J“ Opeak epeak S

(MeV) (mb/sr) (deg)

0.0 1/2‘ 11.0 1 0.8 12 1 1 1.8 1 0.1
5.188 1/2+ 0.02 1 0.01
5.240 5/2+ 0.11 1 0.01
6.180 3/2’ 10.0 1 0.7 15 1 1 2.6 1 0.2
6.789 3/2+ 0.08 1 0.03 20 1 2 0.02 1 0.01
6.857 (3/2,5/2) 0.08 1 0.03 20 1 2 0.02 1 0.01
7.284 (9/2+,7/2+) 0.12 1 0.02 45 1 3 0.03 1 0.01
7.550 1/2+ 0.08 1 0.03 30 1 3

8.283 3/2+ 0.05 1 0.02 24 1 3 0.01 1 0.005
8.915 3/2+ 1

8.980 3/2' — 0.08 1 0.04 21 1 s 0.04 1 0.02
9.49 5/2‘ a

9.53 1/2+ 0.57 1 0.05* 15 1 1

9.60 3/2‘ 0.40 1 0.07** 15 1 1 0.18 1 0.03
9.66 (7/2,9/2)‘ a

10.28 0.06 1 0.02 lO--—46

10.46 (3/2‘,1/2‘) 0.58 1 0.06 15 1 1 0.28 1 0.03
10.94 0.08 1 0.03 lO—-46

11.02 0.06 1 0.02 18--46

11.70 0.06 1 0.02 24--—46

12.30 0.12 1 0.05 24 1 3

13.79 0.12 1 0.05 9--*46

 

peaks between 9.49 and 9.66 MeV.
**This number represents the estimated contribution of
the 9.60 MeV level alone.

*This number represents the combination of the four

118

distributions in varying combinations. The results are

1/2

in the ratio 10 to 1 appears to give the best overall

shown in Fig. VI—9. A combination of ld5/2 and 25

fit. The spectrosc0pic factor for the 7.284 MeV, 7/2+
level assumes that its excitation is due only to a direct
process. It thus represents an upper limit.
It is interesting to determine the total 1p strength
. 16 15 . .
seen in the O(p,d) 0 reaction at 45.34 MeV. By summing
the spectrosc0pic factors for all of the 1/2- and 3/2-

levels listed in Table VI-3, we get

1 = 1.80, 1 = 3.10,
{S( pl/z) [SI p3/2)

hence

ZS(lp) 4.90.
The relatively low value for the total lp3/2

strength indicates the possibility of higher 3/2-

levels, as predicted by Bertsch (Be 68). The 3/2- levels

at 9.60 and 10.46 MeV might comprise the 3/2- level

predicted by Brown and Shukla (Br 67) to be between 10

and 11 MeV. If it were at 10 MeV, they predict it would

have a spectrosc0pic factor 3% of that of the 6.18 MeV

level. Experimentally, the ratio is 18%. An estimate

16

Of the 23-1d admixtures in the ground state of O is

Ill-It 'Jv

119

 

I0' I I

6o (p,d) '50
Ep=45.34MeV
E =5. l88-5. 240

dO'
(mb/sr)
(an)...

 

 

 

 

IC)() GK) I2!) IEK)
90m. (deg)

Figure VI—9. DWBA fit to the 150(p,d)150,
Ex=5° 188—5. 240 MeV (doublet) angular distribution.
and 2 n=2 angular distributions are added in the ratio 1:10

to produce the solid curve.

=45.34 MeV,
The 2 n=0

120

contained in the SpectrOSCOpic factors for the l/2+,

+

5/2 , and3/2+ levels.

zazsl/Z) = «0.02, 25(ld5 ) = 0.15, ZS(1d = 0.04.

/2 3/2’

The present results can also be compared to those
calculated from the 160 ground state wave function of

Brown and Green (Br 66a). This wave function has the form

16

0 g.s.> = 0.874|0p-0h:>+ 0.469l2p-2h>-+ 0.13o|4p-4h>,

where p is for particles and h is for holes. In the 2p-2h
and 4p-4h admixtures one can assume that on the average
half of the particles and holes are neutrons, and half
protons. Thus, the Op-Oh portion represents six 1p
neutrons, and the 2p-2h and 4p-4h portions represent five
and four 1p neutrons, respectively. One would then expect

the summed 1p spectrosc0pic factor to be

II
U1
0
\l
U'I

Xfilp) = 6(0.874)2 + 5(0.469)2 + 4(0.130)2

and

2 2 2
ZS(Other) =- ‘0(0.874) + l(0.469) + 2(0.130) 0.25.

The sum of the experimental Zs—ld spectroscopic factors
agrees well with this prediction. It appears, then, that.
as much as 15% of the lp strength could be in levels

above 10.46 MeV.

121

VI.B. 15N(p,d)l4N

 

VI.B.1. DWBA Calculations and Experimental

SpectrOSCOpic Factors

 

14
The DWBA calculations for the 15N(p,d) N reactions
_ 16 15
were made in the same manner as those for O(p,d) O. A
lower integration cutoff of BF was used, which represented

a peak in the 0 vs R curve. The parameters

peak cutoff
of the bound state well were the same also. The optical
model parameters were discussed in Chapter IV.
The shapes of the calculated angular distributions
agreed with the data to approximately the same degree

as those for 160. Those for some of the £n=l levels

are shown in Figs. v1-1o and VI-ll. The 0', 1 , 2 ,
and 3- levels represent ZS-ld admixtures in the 15N
ground states. DWBA calculations for mum: of these levels
are shown in Fig. VI-12. The eXperimental spectroscoPic
factors extracted for the levels are given in Table VI—4.
Again, the errors quoted reflect only the experimental
error. The decision as to whether a 1+ level was formed
by lpl/Z or lp3/2 pickup was made on the basis Of shape
Of the angular distribution (J-dependence) and on the

predictions of Cohen and Kurath (CO 67), to be discussed

in the next section. The amount of Zs—ld admixture in

122

 

I I I I If

'5N (p,d) "‘N _
Ep=39.84 MeV

zen=4
— DWBA

 
   
 
  

 

° Ex =0.0 MeV

 

E J”=I*
3
" 5: 10°

’6ch‘

'U U,

Io"—

IIIII ..

 

 

 

9cm(deg.)

Figure VI-lO. DWBA fits to the 15N(p,d)14N, Ep=39.84 Mev,_
Ex=0.0.and 2.311 MeV angular distributions, assuming lpl/2
neutron transfer.

123

 

    
     
   

 

 

'0 I I I I I
l5N(p,d) ”N
Ep=39.84MeV

I0 0000 In = I '1

2 .e —DWBA

«‘5 E =7.03MeV

1 \ "

" El

/'\"

b 0

eIS I0

 

 

 

Ex= l3.72 MeV I’ '—
0”: I+
“52 I I I I I
O 30 60 90 I20 I50 I80

Ochdeg.)

Figure VI-ll. DWBA fits to the 15N(p,d)14N, E =39.84 Mev,,
Ex=7.03 and 13.72 MeV angular distributions,_assuming lp3 2
neutron transfer. /

124

 

IO . I
'SNIp,dII4N
IEIJ=ENBIBAIIW€“/
Ex =5.|O MeV
I0° — 1r _
J =2-
ln= 2

I — DWBA

  

A
s.
In
‘x
E -.

  

 

 

 

. '0 -I
E ¢
0
’ b| c'.‘ WI
13 13,
IOZ— I _
I03 1 l
0 60 120 I80

9c.m.(deg.)

Figure VI-12. DWBA fit to the 15N(p,d)14N, EU=39.84 MeV,

L

Ex=5'10 MeV angular distribution, assuming ld5/2 neutron
transfer.

125

 

 

 

Table VI—4. Peak cross sections and spectrosc0pic factors
for the levels Observed in 14N. The average
cross section over the indicated angular I
range isgiven for weak levels having angular
distributions showing no characteristic
maximum. The uncertainties quoted in the
spectrosc0pic factors represent only the
uncertainties in o .

peak
‘TT

Ex J T 0peak 6peak 8

(MeV) (mb/sr) (deg)

0.0 1+ 0 11.1 1 0.8 12 1 1 1.27 1 0.09

2.311 0* 1 3.4 1 0.2 14 1 1 0.50 1 0.03

3.945 1+ 0 3.3 1 0.4 14 1 1 0.60 1 0.07

4.91 (0)’ 0 0.06 1 0.02 12- -15

5.10 2' o 0.22 1 0.06 18 1 2 0.06 1 0.02

5.69 1' 0 0.12 1 0.03 12- -15

5.83 3; 0 0.15 1 0.05 21 1 3 0.04 1 0.01

6.21 1 o 0.15 1 0.04 15 1 2 0.03 1 0.01

6.44 3+ 0 0.01 1 0.006 14- -34

6.70 + <o.01

7.03 2 0 4.7 1 0.3 15 1 1 1.02 1 0.07

7.40 0.02 1 0.01 18 1 3

7.60 <o.01

7.97 2’ 0 0.05 1 0.02 15 1 2

8.06 1‘ 1 0.06 1 0.03 12- —15

8.63 0+ 1 0.02 1 0.01 21 1 2

8.91 3‘ (1) 0.04 1 0.02 12— -29

8.963 (5*) o 1

8.98 2+ 0 0.05 1 0.02 21 1 2

9.17 2+ _ 1 1.7 1 0.2 15 1 1 0.49 1 0.06

9.388 (2',3 ) o 0.12 1 0.05 30 1 3 0.05 1 0.02

9.508 2‘ 1 0.06 1 0.02 9- -18

9.71 1+ 0 <0.01 9- -45

10.09 2+ 0 50.10 1 0.03 16 1 2 0.03 1 0.01

10.43 2+ 1 1.16 1 0.15 16 1 1 0.39 1 0.05

10.85 (4*) o <o.01 ‘

11.06 1 0 0.09 + 0.03 16 1 2 0.04 1 0.01

11.23 .3“ 1 ]

11.29 2‘ 0 0.05 1 0-03 15 1 3 0.02 1 0.01

11.39 (1+) 0 o 02 1 0.01 14- —24

126

 

 

 

Table VI-4. (continued)
TI
EX J 0peak epeak S
(MeV) (mb/sr) (deg)
11.51 3+ 0.03 1 0.01 30 1 3
11.66 0.05 1 0.03 12 1 3
11.74 1* 3
11.80 (2*) 0.03 1 0.02 12- ~40
12.21 (3’) ]
12.29 0.01 1 0.01 14- ~25
12.52 0.32 1 0.05 24 1 3
12.61 3: 0.06 1 0.03 11- ~23
12.80 4 ]
12.83 4‘ 0.07 1 0.03 11- ~30
13.17 (0‘,1 I 3
13.23 0.15 1 0.05 12- ~15
13.72 1+ 1.38 1 0.1 15 1 1 0.81 1 0.06

127

15
the Nground state appears to be similar to that in the

160 ground state.

VI.B.Z. Comparison to the Intermediate Coupling Theory

Comparisons Of the experimental data to the inter-
mediate coupling predictions Of Cohen and Kurath are made
in this section. This model and the method of computing
spectrosc0pic factors from the coefficients of fractional
parentage deduced from it were discussed in Chapter II.
These predictions are given in Table VI-S; they show
six strong levels below 12.0 MeV, with three weak levels
lying quite a bit higher. Included in Table VI-S are
the spectrosc0pic factors expected in the jj—coupling
limit. Pickup of a lpl/2 neutron leads to states having
configuration (a) in Fig. V-l4, whereas 1p3/2 pickup leads
to states having configuration (c). For a given config-
uration the predicted SpectrOSCOpic factor for 1p pickup

leading to a state of angular momentum J is given by
Slj(Ji) = nlj(2Ji + 1)/]Z<(2Jk + 1),

where nlj is the number of lpj neutrons in the ground
state configuration of 15N. The summation is over all

states Jk of a given configuration. The jj—coupling and

intermediate coupling descriptions are very similar.

128

 

 

 

Table VI-5. Intermediate coupling predictions of coeffi-
cients of fractional parentage and spectro-
sc0pic factors for lp neutron pickup from
15N. Also included are the spectrosc0pic
factors predicted in jj—coupling.

E(ca1c.) (J",T) nzj CFP ZCFPZ S 3..

(MeV) j 33

0.0 (1+,0) lp3/2 0.0542

pl/2 -0.3601 0.1326 1.459 1.500

2.690 (0+,1) 1151/2 0.3376 0.1140 0.418 0.500

3.616 (1+,0) lp3/2 0.2434

1pl/2 0.0642 0.0633 0.696 0.750
6.991 (2+,0) lp3/2 ~0.3371 0.1136 1.250 1.250
9.524 (2+,1) 1133/2 ~0.5704 0.3255 1.192 1.250
11.783 (1+,1) lp3/2 -0.4523

1p1/2 0.0000 0.2046 0.750 0.750
15.238 (1+,0) lp3/2 -0.0776

1p ~0.0505 0.0086 0.095 0.000

1/2
+

16.323 (0 ,1) 1pl/2 0.1497 0.0224 0.082 0.000
17.879 (2+,1) 1p -0.1246 0.0155 0.057 0.000

129

A graphical comparison of the theoretical and
experimental results is given in Fig. VI—13, where the
lengths of the lines are prOportional to the SpectrOSCOpic
factors. The extensions of the theoretical lines represent
the jj—coupling predictions. Seven strong levels were
observed in the present experiment, all of which have
angular distributions characteristic of 2n=l pickup,
whereas the Cohen and Kurath calculations predict only
six levels. It appears that the 1p strength in the 2+, T=1
level predicted to be at 9.524 MeV is shared by the 2*, T=1
level at 9.17 MeV and the 2+, T=1 level at 10.43 MeV
(Wa 60, Ka 61). The mixing of these levels is also supported
by the values of the M1 transition strengths of the (9.17
MeV+0.0 MeV) and (10.43 MeV+0.0 MeV)transitions. Warburton
and Pinkston (Wa 60) indicate that a single 2+, T=1
level having a (ls)4(lp)lo configuration is allowed in
the 10 MeV region (the one predicted by both jj—coupling
and intermediate coupling). A 2+, T=1 level having a
(ls)4(1p)8(ls)(ld) configuration is eXpected in the same
region. The predictions for the relative Ml strengths for
ground state transitions from these levels are ~12 and 0,
respectively. Since the observed Ml strengths for the 9.17
MeV and 10.43 MeV ground state transitions are 4.1 and 5.5,

respectively, Warburton and Pinkston suggest that these two

130

I5
N(p,dI'4N Ip SPECTROSCOPIC FACTORS

THEORETICAL EXPERIMENTAL
2*,7 -I

021-1

'5 l*.TsO _

 

 

Ex (MeV)

 

 

O 0.5 |.O I5 0 0.5 I.O I5
5

Figure VI—13. Theoretical and experimental 2 =1 SpectrOSCOpic

factors for the 15N(p,d)14N reaction. The soIid theoretical
bars are the intermediate coupling predictions of Cohen and
Kurath (CO 67). Where different, the jj—coupling predictions
for the six strong levels are represented by the Open extensiOls

of the bars.

131

levels are mixtures of the two configurations. The ratio
of the (ls)4(lp)10 components of the two levels is given
by the ratio of the M1 strengths, and can be obtained from

the present work as the ratio of the 1p spectroscopic

factors for these levels. The ratios are

[(ls)4(lp)lo,(9.l7 MeV)]/[(ls)4(lp)lo,(10.43 MeV)] = 0.75

from the M1 strengths, and

[(ls)4(lp)lo,(9.l7 MeV)]/[(ls)4(lp)lo,(10.43 MeV)]'=l.25 i 0.15_

from the spectroscopic factors. Thus, both the work of
Warburton and Pinkston and the present work suggest strong
mixing Of the two levels, but disagree somewhat about the
division of 1p strength between them. The sum Of the
spectrosc0pic factors for the 9.17 and 10.43 MeV levels
is slightly less than that predicted for the 9.524 MeV
level, but the overall agreement is good. These data thus
support the 2+, T=1 assignments for the 9.17 and 10.43
MeV levels.

This leaves the predicted 1+, T=1 level to correspond
to the previously unassigned broad level observed at 13.72
MeV. The T=1 assignment for this level is consistent with
the 12C(a,d)14N data shown by Zafiratos et a1. (Za 67), where

no level of appreciable strength was observed in the 13.7

I51

 

132

MeV region. The several weakly excited £n=l levels observed
in the present experiment probably result from small
admixtures Of the wavefunctions of the strong levels having

the same J7T

and T. NO levels of measurable strength were
observed above 13.72 MeV. The three weak levels predicted
by Cohen and Kurath probably appear at much higher excitation
energies and may be mixed with other levels. The strongest
of these levels would be expected to have a peak cross
section of only 50 ub/sr, and since the levels are well
above the particle threshold and therefore expected to

be broad, there would be little hOpe for being able to
separate them from the background. The good overall
agreement of the Cohen and Kurath intermediatecoupling
predictions and the experimental spectroscopic factors is

further evidence for the validity of this model for 1p

shell nuclei.

CHAPTER VII

SUMMARY AND CONCLUSIONS

This work has provided valuable information about the
use of DWBA calculations in the extraction of spectroscopic
factors for the (p,d) reaction on light nuclei. While
it is not possible to provide a definite guide for performing
meaningful calculations, the effects Of variations of
certain parameters of the calculation can be pointed out.
The most immediately obvious problem, the inability of
a straightforward DWBA calculation to reproduce the shape
of the angular distribution, was treated by the use of a
lower integration cutoff, rather than by changing the
deuteron imaginary well depth, which resulted in too-large
values of the extracted spectroscopic factors. The 3 F

cutoff used was a max1mum 1n the Opeak vs R

. l/3 16
and is close to the value of 1.2A for

curve

0 and 15O.

cutoff

In addition to improving the shape of the distribution,
the value of the spectrosc0pic factor became more reasonable.
The radius parameter of the bound state well (ron)

Offers a special problem. This study indicates that the

133

134
value of the calculated peak cross section, and hence the
SpectrOSCOpic factor, is a strong function of ron. One
should be aware of this problem in any attempt to extract
absolute spectroscopic factors; however, relative spectro—
sc0pic factors appear to depend much less strongly on ron.

In the present work a value of r equal to the real proton

on
well radiusgave reasonable SpectrOSCOpic factors.

It also was found that the energy dependence of the
peak 2n=l cross sections for the two strongly excited
levels of 15O was not reproduced for a deuteron energy
in the center-Of-mass frame of less than 22 MeV. Thus,
if a (p,d) reaction on a light nucleus is to be performed
at a single energy, the proton energy should be as high

as practicable. In the 16

0 experiment some of the
difficulties with the 25 MeV data could be due to the
resonance structure observed by Cameron et a1. (Ca 68)

in the p-l6O system below 30 MeV. The relative spectrosc0pic
factors showed much less energy dependence than the absolute
spectrosc0pic factors. The use of a method to eliminate

some of the Q-dependence in the relative SpectrOSCOpic
factors did not result in any significant improvement and
indicates that the problems involved are probably not

in the deuteron channel. It may instead be that the high

penetrability of the proton is not well—accounted-for in

the DWBA calculation.

135

The spectrosc0pic factors extracted from the 45.34
MeV l6O(p,d)lSO data indicate that at least.30% of the lp3/2
strength is missing from the 6.18 MeV, 3/2- level, which
disagrees with previous work (Ba 64, Wa 65a). Approximately
12% of this missing strength is contained in the 9.60 MeV,
3/2' and 10.46 MeV (3/2-, 1/2’) levels, the latter assignment
being made on the basis of the shape of the angular
distribution. The 8.98 MeV, 3/2- level contains less than
1% of the lp3/2 strength. The remaining strength may
reside in many highly fragmented states in the 20 MeV
region of excitation (Be 68). Small Zs-ld admixtures and
a possible lg7/2 admixture were Observed in the ground
state of 16O.

The spectrosc0pic factors from the 15N(p,d)l4N data
were found to agree very well with the intermediate coupling
calculations of Cohen and Kurath. The 2+, T=1 levels at
9.17 and 10.43 MeV both appear to contain large mixtures
of the (ls)4(lp)lo configuration. The intermediate
coupling predictions have been used to assign values of
Jfl=l+ and T=1 to the 13.72 MeV level. The high degree of
agreement between the experimental data and the theoretical
predictions in the case of 15N(p,d)l4N strikes an

encouraging note about the present state of our understanding

of nuclear structure.

$134.. and;

APPENDIX A

15
TABULATION OF l6O(p,p)l6o AND l6O(p,d) o
DIFFERENTIAL CROSS SECTIONS

The following pages contain listings of the laboratory
and center-of-mass differential cross sections with the
corresponding statistical and total errors for the elastic

. 16 15
scattering of protons from O and for the levels of O
. . 16 15 . .

strongly exc1ted in the O(p,d) 0 reaction for various
proton energies between 21.27 and 45.34 MeV. A discussion
of the estimated errors is found in Chapter III (Section
III.B.). The values of the cross sections are to be read as

2.1393+o3 2 2.139 x 103.

136

137

on». o. o 0. on». o
V7MCWP7WHWFOWHWCUF}WHWCW01M’#-#UDU)QF\GJO\w\OU)mLOU3

¢NHOOHM¢QNN #013000 01¢¢\OI\I\CCO\OI'\I\I\~OLD

.Hzmuxmnv

mmmmm .kmp

mmmam

o oc’o‘oo o oo o o. o 01-. 0‘00 0 o
OCDCHDC30v4vHUr+HudthrUQlN(W3W3U)OF\F~NIO#N$4f#

03MLDF7¢CBU)BJBU3¢l§d*htbu1()flb¢r\u3mr\CFU7hr\h~0€fl

Ahzmummdv

>mz Cwo.0

.»<»m

oo+wamm.a
oo+m:on.a
on+mmmw.n
oo+mnmm.a
oo+wm:o.«
“ouwfimm.o
Houmm:m.o
Honwm¢m.m
oo+mw:m.a
Oo+m0¢mca
oo+wamw.m
oo+mmmm.m
oo+mmmfl.m
oo+mmmm.m
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APPENDIX B

TABULATION OF 15N(p,p)15N AND 15N(p,d)l4N
DIFFERENTIAL CROSS SECTIONS

The following pages contain listings of the laboratory
and center-of-mass differential cross sections with the
corresponding statistical and total errors for the elastic
scattering of protons from 15N and for the levels of 14N
strongly excited in the 15N(p,d)l4N reaction for 39.84
MeV protons. A discussion of the estimated errors is
found in Chapter III (Section III.E.). The values of the
cross sections are to be read as

1.492E+03 2 1.492 x 103.

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