awn. V d.
, '4«.

 

 

lililllllllllllllllllllllllllilll '

3 1293 01055 9825

This is to certify that the

dissertation entitled

INVESTIGATION OF HIGH LYING STATES
USING SINGLE NUCLEON TRANSFER
REACTIONS

presented by

Gwang Ho Yoo

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Physics

(.7
~01th
r fl Major professor /

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

Date February 26, 1992

 

 

 

LEBRAEY
signifier: State
Waivers“)!

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.

TO AVOID FINES return on or before due due.

  

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An Affirmative Action/Equal Opportunity Institution
eMMuns-M

J
l l—I

 

INVESTIGATION OF HIGH LYING STATES
USING SINGLE NUCLEON TRANSFER
REACTIONS

By

Gwang Ho Yoo

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1992

{7 7- 795’?

ABSTRACT

INVESTIGATION OF HIGH LYING STATES USING SINGLE
NUCLEON TRANSFER REACTIONS

Gwang Ho Yoo

The reactions (7Li,6Li), (7Li,6He), (7Li,8Li), (12C,13N) and (‘20,13C) have been mea-
sured at 30 MeV/n on the targets 90Zr, 91Zr, 89Y, 2O‘BPb, 2093i and 2("Pb in order
to investigate high lying states. Particles were analyzed using the S320 magnetic
spectrograph. In each reaction, the measured spectra were plotted both as a function
of the reaction Q — value and as a function of the excitation energy. A preference
for the excitation of high spin states with no spin flip was observed. Broad reso-
nance like peaks were observed in both proton and neutron stripping reactions at
excitation energies close to the excitation energy of the giant quadrupole resonance.
Comparison of reaction Q — values and the excitation energy spectra suggests that
these broad peaks are due to the excitation of single particle states rather than a
collective giant resonance. The existence of an extra particle or hole outside closed
shell nuclei does not change the strengths of these broad peaks significantly, but does
change the excitation energies significantly in some cases. Shell model calculations
carried out in the 2(”Pb region support this conclusion. Substantial backgrounds were
observed in these stripping reactions. Calculations of these underlying backgrounds

were carried out with the Serber model and with a semi-classical theory developed

i

by Brink and Bonaccorso. The Serber model calculations do not match the shape of
the experimental spectra except at the very high excitation energies ( > 35 MeV) in
proton stripping. The Brink-Bonaccorso model, does match the shape of the exper-
imental spectra for neutron stripping reactions very well although it does not agree
with the shape for the proton stripping case. The Brink-Bonaccorso model, also,
predicts that for these bombarding energies, only 20% of the continuum arises from
projectile breakup and 80% arises from the excitation of compound states in the resid-
ual nucleus. Strong peaks observed the (120,13C) reaction on both 9"Zr and 208Pb
region targets appear to arise from the mutual excitation of bound 2.31/2, 1p3/2 and
1d5/2 excited states in 13C along with low lying states of the residual nuclei. Broad
peaks are observed for the (12C,13N) reaction on the 2("BPb, 209Bi and 2(”Pb targets at
excitation energies about 18 MeV. The origins of these structures are not understood

clearly.

ACKNOWLEDGEMENTS

I would like to thank my advisor Professor G. M. Crawley for his guidance and
direction. His constant advice and support played the most important role to complete
this thesis. Professors P. Danielewicz, B. Lynch, P. Schroeder and D. Stump are also

thanked for their guidance and support.

There are many people whom I would like to thank: Prof. J. Finck for his reading
and correcting my writting, Dr. J. S. Winfield for his help to prepare the experiment
and for many discussions about the analysis, Profs. D. Brink and A. Bonaccorso for
their help to calculate the background for the continuum states, Prof. A. Brown for
his help to understand and use the Shell Model code and Prof. D. Cha for the fruitful
discussions about the contents of my thesis, Dr. S. Gales, Dr. N. Orr and J. Yurkon
for their help during the experiment. L. Zhao is thanked for the discussions on several

questions. This work would have been impossible without the help of these people.

I would also like to thank all my friends, K. Joh, J. Kim, J. Yee and D. Jeon for

their encouragement to finish my work at the N SCL.

I owe a large debt to my family, especially my parents, my wife’s parents and
my brothers who loved, encouraged and helped me to study throughout the years.
Finally, I am specially grateful to my two children, Sung Hyun and Seok Hyun, and

my wife, Soo Gyung for their endless understanding, patience and love.

iii

Contents

LIST OF TABLES
LIST OF FIGURES

1 Introduction

1.1 Motivation .................................
1.2 Selection of Targets and Projectiles ...................
1.3 Outline ...................................

2 Experimental Setup and Procedures

2.1 Target Preparations ............................
2.2 S320 Spectrograph ............................
2.3 Focal Plane Detectors ...........................
2.4 Electronics .................................
2.5 Magnetic Field Setting ..........................
2.6 Particle Identification ...........................
2.7 Energy Calibration ............................
2.8 Cross Section Determination .......................

3 Shell Model Analysis for 2("BPb Region Nuclei
3.1 Introduction ................................
3.2 Energy Level Calculations ........................

3.3 Results and Discussions .........................

4 Single Particle States and Giant Resonance States

4.1 Introduction ................................
4.2 Predictions for Single Particle States ..................
4.3 Predictions for Giant Resonance States .................

iv

vi

vii

«luv-0H

9
10
11
15
17
19
22
25
31

32
32
33
36

43
43
44
49

5 Results of Single Nucleon Stripping Reactions

5.1 Introduction ................................
5.2 9"Zr, 91Zr, 89Y (Li, 6Li) Reactions ...................
5.3 2me, 209Bi, 207Pb (7Li, 6Li) Reactions .................
5.4 9°Zr, 91Zr, 89Y (7Li, 6He) Reactions ...................
5.5 208Pb, 209Bi, 207Pb (7Li, 6He) Reactions .................
6 Analysis of Background
6.1 Introduction ................................
6.2 Projectile Breakup Background .....................
6.2.1 3 - Body Kinematics of Projectile Direct Breakup Process
6.2.2 Projectile Breakup Cross Section Calculations Using Serber
Model ...............................
6.2.3 Comparison of Serber Model Calculations with Experimental
Data ................................
6.3 Single Nucleon Transfer to Continuum States Using a Semi-Classical
Theory ...................................
6.3.1 Kinematics of Single N ucleon Transfer to Continuum States
6.3.2 Cross Section Calculations of Projectile Breakup and Com-
pound States ...........................
6.3.3 Comparison of Semi-Classical Calculations with Experimental
Data ................................
6.4 Coincidence Measurement ........................
7 Results of Single N ucleon Pickup Reactions
7.1 Introduction ................................
7.2 90Zr, 91Zr, 89Y (”C,‘3C) Reactions ...................
7.3 9"Zr, 91Zr, 89Y (7Li,8Li) Reactions ....................
7.4 208Pb, 209Bi, 2(”Pb (12C,13C) and 208Pb("Li,8Li) Reactions .......
7.5 9"Zr, 91Zr, 89Y (12C,‘3N) Reactions ...................
7.6 2“Pb, 2°9Bi, 207Pb (12C,13N) Reactions .................
8 Summary
8.1 Summary .................................

LIST OF REFERENCES

55
55
56
64
71
78

85
85
86
86

89
91

97
97

101

105
114

119
119
120
126
129
135
139

144
144

149

List of Tables

2.1
2.2

3.1

3.2

5.1
5.2
5.3
5.4

6.1
6.2

7.1
7.2
7.3
7.4

Parameters of the QQDMS S320 spectrograph .............

Energy losses of the reaction products in the targets ..........

Energy levels obtained using shell model calculations for neutron tran-
sitions ...................................

Energy levels obtained using shell model calculations for proton tran-
sitions ...................................

Output parameters for 90Zr, 91Zr, 89Y (7Li, 6Li) reactions .......
Output parameters for 2“Pb, 209Bi, 20"Pb (7Li, 6Li) reactions .....
Output parameters for 9°Zr, 91Zr, 89Y (7Li, 6He) reactions ......

Output parameters for 208Pb, 209Bi, 207Pb (7Li, 6He) reactions

Coefficients D(j,-, j I) ...........................

Optical input parameters for the neutron scattering reactions on 9°Zr
region and 2“Pb region targets .....................

Output parameters for 9(’Zr, 91Zr, 89Y (”C, 13C) reactions ......
Output parameters for 2“Pb, 207Pb, 209Bi (”C, 13C) reactions . . . .
Output parameters for 9°Zr, 91Zr, 8S’Y (12C,13N) reactions .......

Output parameters for 2("’Pb, 209Bi, 2me (12C,13N) reactions .....

vi

13
30

58
66
73
80

103

104

123
131
137
141

 

List of Figures

1.1

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8

3.1
3.2
3.3

4.1

4.2
4.3

4.4

5.1
5.2
5.3
5.4
5.5
5.6
5.7

Broad peaks obtained by a neutron transfer reactions ......... 4
Schematic view of the S320 spectrograph ................ 12
Schematic view of the focal plane detector ............... 16
Schematic view of the S320 electronics ................. 18
Flow diagram of on-line data taking system .............. 20
Flow diagram for off-line data taking system .............. 21
A sample of particle identification in two dimensional spectra ..... 24
Calibrations on 6Li, 6He and 12C particles ............... 27
Schematic diagram depicting the kinematics in the target ....... 28
Experimental single particle and hole energy levels in 2("IPb ...... 35
Energy levels obtained using shell model calculations ......... 38
Comparison of shell model calculations with experimental spectra . . 41

Predictions for the excitation energy shifts of single particle states in
20an region nuclei ............................ 47

A schematic representation of E1 and E2 single particle — hole transitions 50
Giant resonances in 9°Zr, 91Zr and 89Y nuclei with 12C (Egnc = 30

MeV/n) inelastic scattering ....................... 51
Giant resonances in 208Pb, 2”Bi and 2("Pb nuclei with 12C (Em = 30

MeV/ n) inelastic scattering ....................... 52
Energy spectra of 9"Zr, 91Zr, 89Y (7Li, 6Li) reactions .......... 57
Comparison of the neutron transfer spectra on 9"Zr region nuclei . . . 59
Energy spectra of 2“Pb, 209Bi, 2("Pb (7Li, 6Li) reactions ....... 65
Comparison of the neutron transfer spectra on 20‘;ng region nuclei . . 67
Energy spectra of 9(’Zr, 91Zr, 8"Y (Li, 6He) reactions ......... 72
Comparison of the proton transfer spectra on 9"Zr region nuclei . . . 74
Energy spectra of 2°8Pb, 209Bi, 20"Pb (7Li, 6He) reactions ....... 79

vii

5.8

6.1

6.2
6.3
6.4

6.5
6.6
6.7
6.8

6.9

6.10

6.11
6.12
6.13

7.1
7.2
7.3
7.4
7.5
7.6
7.7

Comparison of the proton transfer spectra on 208Pb region nuclei . . . 81

Schematic diagram for the projectile direct breakup processes with 3
body kinematics .............................. 86

Calculated breakup cross sections of 7Li into 6Li + n using Serber Model 92
Calculated breakup cross sections of 7Li into 6He + p using Serber Model 93

Breakup cross section calculations of 7Li into 6He + p on 90Zr target

using Serber Model ............................ 95
Coordinate system for transfer amplitude ................ 98
Single neutron transfer cross sections to continuum states ....... 106
Single proton transfer cross sections to continuum states ....... 107
The contributions for each angular momentum component to the total

cross sections in (7Li,6Li) reaction .................... 109
The contributions for each angular momentum component to the total

cross sections in (7Li,6He) reaction ................... 112
Breakup cross section calculations of 7Li into 6He + p on 9"Zr target

using Brink-Bonaccorso model ...................... 113
T0p view for the coincidence measurement of 6He and p ........ 115
Spectra from the forward array and particle identification ....... 116
Spectra from the backward array as functions of energy and time . . 117
Single particle energy levels of 9"Zr and 20st ............. 121
Energy spectra of 9"Zr, 91Zr, 89Y (12C,13C) reactions .......... 122
Energy spectra of 9°Zr, 91Zr, 89Y (7Li,8Li) reactions .......... 127
Energy spectra of 208Pb, 209Bi, 207Pb (12C,I3C) Reactions ....... 130
Energy spectrum of 208Pb("Li,8Li) reaction ............... 132
Energy spectra of 9°Zr, 91Zr, 89Y (”C,‘3N) reactions .......... 136

Energy spectra of 2“Pb, 2093i, 20"Pb (12C,13N) reactions ....... 140

viii

 

it

V6

Chapter 1

Introduction

1 .1 Motivation

The study of deep lying hole states and high lying particle states has been an inter-
esting area of research and many investigations have been carried out particularly for
nuclei near closed shells. These studies provide information on the strength distribu-
tion (position and width) of high lying single particle states, deep lying single hole
states, and the mechanism that spreads these states. Such information is useful for
calculations of more complicated excitations, such as giant resonances (GR) and mul-
tiple particle / hole excitations. The single particle transfer reaction is a simple method
for studying hole states in heavy target nuclei compared to knock out reactions such
as (e, e’ p) and (p, 2p) which require coincidence measurements, and is the only way of
observing particle states at high excitation in heavy nuclei. This method has proved
successful particularly at lower excitation energy for light ion induced reactions such
as (p,d), (3He,‘He) and (‘He,3He) [Kasa 83, Gerl 75, Mass 86]. These experiments
found single particle and single hole state strengths ranging from discrete peaks at
low excitation to large broad peaks at high excitation energy. The couplings to more
complicated collective excitations such as phonon excitations were found to play a

very important role in spreading the strength of the simpler states [Gale 85].

Unfortunately, in light ion reactions the poor peak to background ratio makes
it difficult to use these reactions to study highly excited states. The major source
of the background at high excitation energy is the breakup of the projectile. This
background must be subtracted to obtain the strength of the peaks of interest, and has
usually been estimated empirically. Several theories have been proposed to calculate
the background. For example, the Serber Model [Serb 48] explains the background
very well in light ion induced nuclear reactions, but it does not explain the background
well in heavy ion induced reactions. A semi-classical theory developed by Brink and
Bonaccorso [Bona 85, Bona 88] explains the shape of the background very well in a
number of neutron stripping reactions, although it does less well in proton stripping

reactions. Both of these models will be discussed in more detail in chap. 6 [Wu 78,

Wu 79, Bona 91].

Heavy ion reactions at high energies are expected to be more selective of high spin
states which might therefore become stronger relative to the background [Brin 72]
than in light ion induced reactions. However, to make use of these reactions for
studying high lying states, some questions remain to be answered. Recently, it has
been reported in the 208Pb(2°Ne,19Ne) and the 90Zr("’°Ne,19Ne) reactions at 25, 30, 40
MeV/n [Fort 90, Fras 87] and in the 208Pb(12C,"C) reaction at 40 MeV/n [Merm 88],
that large broad peaks were observed at excitation energies which are close to the
excitation energies of the giant quadrupole resonance (GQR), viz. 10.5 MeV for 2("E‘Pb
and 13.5 MeV for 90Zr. A broad peak was observed at a similar energy in the (‘He,3He)
reaction at 46 MeV/n on a 2°8Pb target [Mass 86] and in the (160,150) reaction at
20 MeV/n on a 19l’Au target [Olme 78]. However, the broad peaks in the vicinity of
the GQR were not observed in the (7Li,6Li) and (160,150) reactions at 20 MeV/n on
a 208Pb target [Becc 87, Olme 78] nor in the (‘He,3He) reaction at 46 MeV/n on a

120Sn target [Gale 85]. When these broad peaks are observed in transfer reactions,

they have excitation energies, widths and strengths consistent with the known GR
states [Fort 90, Fras 87, Fras 89, Duff 86, Olme 78, Gale 91]. (Some experimental
transfer reaction spectra with broad peaks are shown in fig. 1.1.) Whether these
peaks are from the excitation of GR states or from broad single particle states is not

clear.

The GR is known to be a 1p— 1h excitation in which many nucleons are involved.
Most information on GRs has been obtained through the inelastic scattering of light
ions [Youn 76], and heavy ions [Fra887a, Suom 89, Suom 90]. So far the evidence for
the excitation of GR states by transfer reactions is less convincing. According to RPA
theory, however, closed shell nuclei may contain some admixtures of p — It states in
the ground state [Ring 80]. When a nucleon is transferred to these closed shell target
nuclei, this nucleon may couple to the existing hole state in the target by a single
step mechanism and thus excite a component of a GR. A similar processes of forming
a GR may be possible by a pickup reaction on a closed shell target plus one nucleon
[Fras 89, Chom 86]. The formation of a CR state in a transfer reaction was mentioned
by Olmer et a1. [Olme 78]. But the experimental data were not enough to provide a
convincing identification of the broad peaks observed in the transfer reactions as GR

states.

Giant resonance states and single particle states have different properties, and it
may be possible to distinguish between them. In GR excitations, the motion is highly
collective and many particles in the nucleus are involved. The excitation energies of
GR states change very smoothly with the mass of the nucleus. On the other hand, for
single particle states, only a few particles are involved and the excitation energies of
similar single particle states may change substantially even for neighboring nuclei. For
a closed shell target, both proposed explanations lead to similar behavior, therefore

it is difficult to distinguish between these two explanations by measurements on only

 

 

   

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

9°Zr(’°Ne,wNe)°‘Zr me(’°Ne,‘°Ne)’°°Pb
T Em = 600 MeV ,, Em = 600 MeV
9m = 95° ‘7 9m = 5.3"
20 - l
20 ' A
>.. . E"-
2, c.
E to h E w '
43 E
e vs
a: 55
“c
c w c a
'o T E: o = 500 MeV a
E ’ 0‘-115° b to» l E'“=5OOM°V
'0 m - . “U 9m = 6.4"
.. q .
tot ¢ .
b 1 .
0 o 29 so an
Ex. (MeV)
N . r‘"
”Zr(’°Ne,"Ne)°‘Zr ”‘Pb(a,3He)3°’Pb r-M
Em = 300 MeV E. = 183 MeV '
1250‘ 2. S 0'“ S 6. 1 91.5 = 8°

1000 ‘

 

750i

 

 

250 ‘

 

 

 

 

 

 

 

 

43%....

2'0 10 0
Ex. (MeV) Ex. (MeV)

40 30 20 10

Figure 1.1: Broad peaks obtained by a neutron transfer reactions. The properties
of the broad peaks (marked with arrows) are very similar to those of GR states
[Fort 90, Fras 87, Mass 86].

Q;

21

boil

closed shell targets. However, if the spectrum from a closed shell nucleus is compared
with spectra from the same reaction for neighboring even — odd targets, one can
distinguish the two models, because in this case one expects that the differences are

large enough to be observable.

In this thesis, heavy ion transfer reactions have been investigated on even and
odd A targets to try to resolve the question as to whether the broad peaks observed
these reactions arise from GR excitation or from the excitation of single particle
states. In addition, the underlying background observed in stripping reactions has
been calculated using different models and the calculations have been compared to

the experimental data.

1.2 Selection of Targets and Projectiles

The choice of targets was based on the following considerations. Consider a neutron
stripping reaction on the even — even target 20st leading to the residual nucleus
2(’S’Pb. The low lying states formed in 2(’S’Pb are the well known single neutron states
which lie above the closed N =126 core. If the same reaction is carried out on the
neighboring nucleus 209Bi which has an extra lhg/g proton outside the 2:82 core,
multiplets of states are formed from the coupling of the 1119/2 proton with the afore-
mentioned neutron states. These multiplets occur at about the same excitation ener-
gies in 21"Bi as the corresponding single neutron states in 2”Pb. However a different
situation arises if a 20"Pb target is used. The 2""Pb nucleus has a 3p1/g neutron hole
state in the closed N =126 shell. Therefore the 0* ground state of 2”Pb is formed
when a neutron is added to this hole. As a neutron is added to other higher lying neu-
tron particle states, multiplets are produced due to the coupling of the 3111/2 neutron

hole with the neutron particle states. The excitation energies of these multiplets are

shifted to higher excitation approximately by the difference between the 0+ ground
state and the first multiplet. Such effects arise from rather general properties of single
particle transfer reactions on neighboring nuclei. In contrast, the excitation energies
of collective states like the GR change by much less than 0.1 MeV with a change of
one in the mass of the target. Thus one may distinguish between collective and single
particle states by measuring stripping reactions on 2“Pb, 2”Bi and 2”Pb. Similar
behavior is expected for stripping reactions in the vicinity of closed shell target 9°Zr

where one may perform a similar study using 90Zr, 89Y and 91Zr targets.

Thus, reactions were measured for two even — even nuclei 208Pb and ”Zr and their

nei hborin nuclei, four even — odd nuclei 20I’Pb, 2°9Bi, 89Y and 91Zr as targets.
5 g

In choosing the projectiles, two conditions were considered. First, the ejectile
excitations should be minimized to prevent the occurrence of spurious peaks in the
spectrum from ejectile excitation. The problem of ejectile excitation may be reduced
by using unbound or very weakly bound ejectiles such as (1, 6He, 6Li, 8Li and 13N .
Since the ejectiles excited above their “breakup threshold” decay into two or more
fragments, they will not contaminate the spectrum at energies above this threshold.
Second, the projectile energy should be high enough to excite the high lying states.
However, as the projectile energy increases, the resolution becomes worse and the
cross section for the breakup process increases faster with bombarding energy than
the cross section for transfer reactions. To excite a high spin state, heavy ions are
better than light ions, but the resolution is not as good as for light ions at the same
projectile energy per nucleon. Thus, a compromise had to be made in choosing the

projectiles and bombarding energies.

For the nucleon stripping reactions (7Li,6Li) and (7Li,6He), the projectile was
chosen because the resultant 6He and 6Li ejectiles have threshold energies for breakup

which are lower than the energies of their first excited states. In this case, one

expects ejectile excitation to be negligible. However projectile breakup still remains
a dominant source of background at high excitation energies. The 7Li beam is not
suitable for measuring the proton pickup reaction (7Li,8Be), because 8Be has a life-
time which is too short to be detected in the focal plane of the S320 spectrograph.
Instead, the proton pickup reaction was measured with a 12C beam, which again
produces an ejectile 13N for which the threshold energy for breakup is lower than the
energy of the first excited state. For neutron pickup, both the (7Li,8Li) and (12C,13C)

reactions were measured in order to estimate the contributions from ejectile excitation.

These reactions were measured at a projectile energy of 30 MeV/ n because at this

energy a large bump has already been seen in the 208Pb(2°Ne,19Ne) reaction [Fort 90].

1.3 Outline

In chapter 2, the experimental setup and procedures are described. These include the

target preparation, detection system, electronics, and the method of calibration.

In chapter 3, shell model calculations useful for the description of one nucleon
transfer reactions on 2("Pb and 2°QBi nuclei are presented. These calculations provide
information on the energy levels of the multiplet states, such as the excitation energies,
spectroscopic factors, and the shift of the centroid energy of the multiplets. The

calculations are compared with the experimental data.

In chapter 4, the characteristics of the single particle states and GR states, and the
method used to distinguish between the two states are described. The data obtained
at the same kinematic conditions on even — even targets and even — odd targets for
9"Zr region and 208Pb region are compared as a function of both the reaction Q —

values and the excitation energies.

In chapter 5, the results for the one nucleon stripping reactions are presented. The

spectrum from the closed shell target nucleus is compared with the spectra from the
neighboring targets. The relative strengths between the states are explained by the
angular momentum transfer matching conditions. Evidence relevant to the nature of

the broad peaks is presented.

In chapter 6, the background for the stripping reaction is described. Two theories
for calculating the background: the Serber Model, and the Semi-Classical theory
developed by Brink and Bonaccorso, are outlined and the corresponding calculations
are compared with the experimental measurements. In addition, a test run for a

coincidence measurement aimed at providing more information on the background is

described.

In chapter 7, the results for the one nucleon pickup reactions are described. Ejec-
tile excitation is shown to present significant problem for the interpretation of the

neutron pickup reactions. The nature of the high lying peaks is discussed.

In chapter 8, a summary of this thesis and suggestions for future work are described

briefly.

Chapter 2

Experimental Setup and
Procedures

The transfer reactions (7Li,6Li), (7Li,6He), (7Li,8Li), (”CPC) and (12C,‘3N) were
carried out at a bombarding energy of 30 MeV/ n using the K500 superconducting
cyclotron at Michigan State University. The average beam current was between 10
and 20 particle nA (pnA). The targets used in this experiment, 89Y, 9°Zr, 9‘ Zr, 2”Pb,
2“Pb and 209Bi were all self supporting and had thicknesses of about 5 mg/cm2. The
thicknesses were chosen on the basis of the transfer reaction cross sections, counting
rate, and the energy resolution for the given beams. The reaction products were
analyzed with the S320 broad range magnetic spectrograph [S320 90] and detected
by the focal plane detector system. In each reaction, the ejectiles were measured at
the grazing angles to give large cross sections. The energy resolution was about 500
keV full width at half maximum (FWHM) for the 6Li and 6He spectra, and about
1 MeV F WHM for the 12C, 13C and 13N spectra. In this chapter, the experimental

equipment, procedures and analysis methods are described.

10

2.1 Target Preparations

Six targets, 89Y (5.30 mg/cmz, 100%), 9°Zr (5.06 mg/cm’, 97.62%), 91 Zr (5.01 mg/cmz,
88.5%), 2(”Pb (4.95 mg/cmz, 92.40%), 208Pb (5.84 mg/cm’, 99.14%) and 2”Bi (6.50
mg/cmz, 100%) were used in this experiment. The 89Y target was purchased from the
Johnson Matthey Company. The original thickness of the yitrium target was 11.18
mg/cm2 when it was purchased. A target of thickness, 5.3 mg/cm’, was obtained
by using a rolling machine. The thickness was determined by measuring the energy
loss of a-particles emitted from an 2“Am source. The uniformity was $0.2 mg/cm2
over the central region of the target. This method was verified by weighing the tar-
get. There was about a 10% difference between the two methods. This caused an

uncertainty up to 10% in the absolute cross section.

The 209Bi target was fabricated at Michigan State University using vacuum evap-
oration. When pure 209Bi metal was heated in the furnace in a vacuum chamber,
209Bi molecules evaporated and were deposited on a glass plate which was coated
with detergent and placed about 15 cm above the 209Bi source. The growth rate was
dependent on the temperature of the furnace. The on-line measurement of the thick-
ness of the target using a quartz crystal vibrator provided a rough indication of the
thickness. The thickness was measured again after the target was floated off the glass
slide. The exact thickness was obtained by measuring the energy loss of a-particles.

The uniformity of the target was within 104 mg/cm’.

The other targets, 9°Zr, 91Zr, 20"Pb and 208Pb were purchased from the Micro
Matter Company. No noticeable sign of oxidation of the targets was observed in the

data.

5F

ar

be

0(

is

an.

11

2.2 S320 Spectrograph

The reaction products were analyzed with the S320 magnetic spectrograph and charged
particles were detected in a standard focal plane detector. This spectrograph has a
K-parameter of 320, where K is defined by the equation E /A = K (q/A)2, where E/A
is the maximum allowable kinetic energy in Mev per nucleon, and q is the charge of a
reaction product [S320 90]. The S320 spectrograph is designed to be operated in the
dispersion matched mode. The kinematic effects due to the finite angular acceptance
of the spectrograph are compensated by refocusing the quadrupole doublet according
to the kinematic parameter of the reaction. The particles scattered from the target
into a given solid angle and having the same momenta could be focused on the same
position of the focal plane detector. The dynamic range in momentum covered by
the spectrograph in a single setting is AP/ P = 10%, the maximum solid angle is 0.67
msr and the angular range is from - 4 to 55 degrees. A schematic view of the S320
spectrograph is given in fig. 2.1 and some important parameters of the spectrograph

are given in table. 2.1.

The S320 spectrograph is composed of a target chamber (or a scattering cham-
ber), QQDMS (Quadrupole, Quadrupole, Dipole, Multipole (which is predominantly
Octupole) and Sextupole) magnets and focal plane detectors. The target chamber
is a precision scattering chamber with a sliding seal. The inner diameter is 39 cm
and the inner height is 15 cm. The upper part of the chamber, including the lid, is
braced to the wall and does not move. At the center, there is a target ladder with
a circular platform. The target ladder can move up and down, and the ladder and
the platform assembly may be rotated together independently of the spectrograph
rotation. A total of 6 targets could be mounted in the target ladder at a same time.

One target position was used for a scintillator of 031 crystal as a beam viewer. An-

12

Focal Plane
Detector

 

Figure 2.1: Schematic view of the S320 spectrograph.

Ktjn

Bl

Ce

Re
PO
Be
Me

Ce
Dis
Dis
Dis

13

Table 2.1: Parameters of the QQDMS S320 spectrograph.

 

Quad(Y) - Quad(X) - Dipole — Octupole - Sextupole

 

Dispersion: D = 1.6 cm/% (Ap/p)
Magnification: Mx = —0.67 (D/M = 2.4)
My = -2.5
Max. solid angle: A0 = 12 mr

Ad = 12 mr
0 = 0.67 msr

Beam spot on target (assumed):

0.5 mm incoherent width

3 mm tall. dispersion matched

2.4 mm dispersed beam width for 0.1% energy spread
Calculated line width (ray tracing):

AE/E = 0.1%. 0.8 mm
Range: (Em-EmVE = 20%
Focal plane: Normal incidence. 18 cm long x 2.6 cm tall
Bend angle: 34.4"
Max rigidity: Bp (max) = 2.57 T-m O 1.47 T

p (max) = 1.75 rn

Central ray radius: p (mean) = 1.70 m
Distance target -v aperture: 1.965 111
Distance target -> focal plane: 6.75 m
Distance target -+ scintillator: 7.12 rn
Angular range: -4° to 55°

Cl

3n
:0

.0 r.

14

other was used to hold a blank target to check the target frame contribution to the
background, and a third one was used for a thin 12C target for calibration. Therefore
only three targets for reactions would be mounted at the same time in the ladder
during the experiment. Two monitor detectors (bare photodiodes) were used. They
were mounted on the lid of the chamber which is stationary and were located at a
distance of 15 cm from the target. The distance between monitors was 1.5 inches
and they were located at the lower left and lower right from the beam path. The
aperture of the spectrograph is located at a distance of 196.5 cm from the target.
Four different types of apertures, round holes of 8 mm and 25 mm diameter, a square
50 mm X 50 mm aperture and a 19 mm X 40 mm rectangular slit could be inserted

remotely depending on the counting rate required.

There are two kinds of Faraday cups mounted in the S320 spectrograph. These
cups stop the beam and accumulate the charge passing through the target. One is
mounted in the wedge chamber for small angles, ranging from 1.5 to 9.5 degrees. The
other one is mounted on the lid of the target chamber and is therefore independent
of the spectrograph rotation. The minimum spectrometer angle such that this latter
Faraday cup does not obscure the aperture is about 2.9 + W/2 degrees, where
W is the full opening angle of the spectrometer aperture. The biggest width of the
aperture used in this experiment was 5 cm. In this case that W would be 1.46 degree
and the minimum spectrometer angle possible would be 3.63 degree. Because the
spectrometer angles used in the present experiments are 6 and 9 degrees, only the

target chamber Faraday cup was used in this experiment.

The main role of the QQDMS magnet system is to separate the particles spatially
on the focal plane where they are detected by a position sensitive detector according
to the momentum and charge state of the particles. One of the quadrupole magnets

focuses the particles in the Y - direction and the other one in the X - direction. The

15

dipole magnet bends the particles according to their magnetic rigidity ( B - p = P/ q),
where P is the momentum and Q is the charge of the particle, B is the magnetic field
and p is the orbit radius. The multipole and sextupole magnets are used to help focus

the particles at the focal plane of the detector and to minimize the aberrations.

2.3 Focal Plane Detectors

The focal plane detection system of the S320 spectrograph is composed of three mod-
ular units: position sensitive counters, ion chambers, and scintillators. A schematic
view of the detector system is given in fig. 2.2. A position sensitive single wire pro-
portional counter (SWPC) is followed by two ionization chambers (1C), then another
SWPC and scintillator (SCNT). All the gas detectors operate with the same gas
volume and thus have the same pressures and are separated from the spectrometer
vacuum by a Kapton window of thickness 25 microns which can hold a pressure dif-
ference of one atmosphere. Depending on the charges and the energies of the reaction
products, different types of gases and pressures were used. For the 12C beam, 100%
isobutane gas was used at 70 torr, and for the 7Li beam, a mixture of 20% of isobutane
gas and 80% of freon gas was used at 140 torr. The mixed gas does not have as large
a gain as the pure isobutane gas. However the uniformity in the mixed gas is better
than that of pure Isobutane gas and less sensitive to poisoning. With the 7Li beams,
because there was no difficulty in particle identification, the mixed gas was used for

better uniformity.

The SWPC detector enables one to obtain the position spectra using the charge
division method (the relative ratio of the pulse heights from the two ends of the
resistive wire). For precision measurement of the particle position, the gains of the

amplifiers ( front wire left and front wire right, back wire left and back wire right )

16

 

  

FIE-D m PLASTIC
KAP'I'ON rCATHODI -\ SCINI'ILLA‘I‘OR \
WINDOW ‘ _ _ If
BEAM mom ION BACK ION

CHAMBER CHAMBER

 

 

 

 

 

 

 

............................... .
.........'.-.. ..............
LVN! J ~ 1' \
RESISTIVB ANOD‘ mm mm
m W m
DETECTOR DETECTOR

Figure 2.2: Schematic view of the focal plane detector [Moha 91].

17

were matched using a test signal. Adjustments for all the other amplifiers were also
done before taking the data and the initial settings were not changed until the end of
the experiment. A stopping scintillator is mounted behind the gas detectors. This is
composed of a thin (0.51 mm) fast scintillator and thick (10 cm) slow scintillator. The
output signal is the sum of the fast and slow scintillator signals and this signal was
used as a start signal. The time of flight of the particles was obtained by measuring

the difference between the cyclotron RF and the scintillator signal.

2.4 Electronics

The electronics used for the data taking is displayed in fig. 2.3. The same electronic
setup is used for most experiments with the S320 spectrograph. Ten signals were
obtained from the various detecting modules and were recorded after they were pro-
cessed by the electronics. A S320 spectrograph event was normally defined by the
total scintillator signal (fast + slow) above a constant fraction discriminator (CFD)
level. The signals from the scintillator left and scintillator right passed through the
coincidence checking circuit. When the two signals were above a CFD level and coin-
cident, a true event was assumed and the output signal from the coincidence checking
circuit was used as a start signal (or a S320 master signal). This signal was used
to open the gates of the ADC and QDC modules, and as a start input of the TDC
and the TAC. The signals detected from the two wire counters, two ion chambers
and two monitors were digitized with an ORTEC AD811 analog to digital converter
(ADC) and the signals obtained from the scintillator were digitized with a LECROY
2249W charge to digital converter (QDC). From the left and right signals from each
wire counter, the position was calculated, and the difference between the two de-
tected positions of the wires was used to measure the scattering angle relative to the

central angle of the spectrograph. The TDC signals were used for the time of flight

18

Pre Amp Main Amp

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BIC ADC 6 _
TAC
t
5 0p , ADC 4
TFA CFD “a"
QDC [2'2] STROBE
CFD _/ LJ ’ 315258
ScR » start 2323
[— —\ 222
J I + bit 1
QDC _ J
NIM
CFD start 92
ScL ,
stop
RF

Figure 2.3: Schematic view of the S320 electrOnics [S320 90].

19

(TOF) information. For the TOF relative to the cyclotron RF, the TDC was started
by either the left or the right scintillator delayed CFD output and was stopped by
the cyclotron RF signal. A time to pulse height converter (TAC) signal was used to
find the vertical position in the front ion chamber by measuring the drift time of the
electrons. The TAC was started by the S320 master signal and stopped by one of the

front ion chamber signals. The TAC signal was read by an ADC.

The signals which were digitized by ADC, QDC or TDC were recorded by the
program ROUTER in the VME bus front ends based on multiple M0680x0 architec-
ture processors as part of CAMAC data acquisition system [Fox 85, Fox 89, Sher 85].
The flow diagram of the data taking system is given in figs. 2.4 and 2.5 [Winf 91].
This system blocks the recorded events into 8192 byte buffers and then sends them
back to the VAX / VMS system for on-line event recording and analysis. The buffered
data are read by the program ROUTER and sent to specified subprocesses. There are
three main subprocesses. One is a scaler display task which sums and displays scaler
totals, and another is a tape writing task which writes the data buffers to tape. The
other one is a data analyzing program, SARA [Sara 90], which identifies the particles
and creates displays on the terminal. During the experiment, a fraction of the total
data was displayed on the terminal and analyzed on-line as a check on the progress

of the experiment.

2.5 Magnetic Field Setting

There are five magnets (QQDMS) which need to to be set to focus the particles on
the focal plane. The functions of these magnets were described in section 2.2. The
values for the field settings were obtained by executing the program nscIJibrary :

[setup.s320]s320.e2:e with the inputs such as reaction formula, lab. angle, energy/n

20

CAMAC CRATE
wrm VME
MICRO Processor

l DATA

ROUTER

 

 

 

 

I I l- | I lsurrsn STORAGE

 

 

 

TAPE SCALER
SARA WRITING DISPLAY
TASK TASK

 

 

 

 

 

 

 

I

a
m
7%

 

DISPLAY
WINDOW

Figure 2.4: Flow diagram of on-line data taking system [Winf 91].

21

 

 

l‘ MAGNETIC
SARA TAPE
AED
TASK

DISPLAY
WINDOW

 

 

Figure 2.5: Flow diagram for off-line data taking system. [Winf 91]

22

and excitation energy of the residual nucleus. This program calculates the kinetic
energies of the reaction products, magnetic fields of 5 magnets, grazing angles, C.M.
angles for the given lab angles and time of flight. The masses of the particles were
taken from the mass table of nsclJibrary : [mass86] mass86obj/lib. The magnetic
fields were calculated with fully relativistic kinematics and were based on empirical
calibrations. For each reaction, the fields were reset because of the different kinemat-
ics. The dipole field was measured with the SEN TEC N MR system. When the dipole
field strength was higher than 14 kGauss as was the case for the (7Li,8He) reaction,

the field measured by the N MR probe was not very stable.

The calculated field settings focus the highest energy particles of interest on the

middle of the focal plane single wire proportional counter (SWPC).

2.6 Particle Identification

The particle identification was done using the program SARA which allows gate
and contour setting, and histogramming with or without conditions [Sara 90]. The
gates can be set on the AED terminal by marking two points on a one dimensional
histogram or by drawing a contour on a two dimensional plot which is composed of
two parameters out of energy loss in ion chamber (AE), light out of scintillator (E),
time of flight (TOF), and position in the focal plane (P03). The ion chamber was
filled with a mixed gas of freon (80%) and isobutane (20%) at a pressure of 140 torr
for the 7Li beam and 100% isobutane gas at pressure of 70 torr for the 12C beam.
The energy loss in this chamber is proportional to Z 2 / v”, where Z is the charge state
and v the velocity of a detected particle. The particles separate cleanly when Z is
different at a similar energy per nucleon. TOF is proportional to M /Z where M is

a mass of a particle. This permits good separation of a particle which has a different

23

mass from particles which have the same charge states. The program SARA was
used for both on-line and off-line data analysis. In the on~line analysis, this program
was used to display a sample of the collected data on the AED terminal. By setting
the gates or contours on the spectra of the terminal while taking the data, spectra
of specific reaction products could be checked to see if the data acquisition process

was working correctly. In most of the reactions, two contours were used on the two

dimensional spectra of AE.vs.E and TOF.vs.P0.S'.

In the off-line analysis, clearer particle identification was possible. In the (7Li,“Li)
reactions, because any single contour was not enough to separate “Li particles clearly,
two contours on the AE.vs.E and TOF.vs.POS spectra were used. The particles
of charge state 3 were separated using the AE.vs.E spectrum and “Li particles were

separated using the TOF'.vs.POS spectrum.

In the (7Li,“He) reactions, only “He, and 3H which came from the direct breakup
of 7Li—i‘1He + 3H were detected. Because of big differences of Z 2 / v2 between the two

particles, “He particles were cleanly separated in the AE.vs.E spectrum.

In the (”C,‘3C) reactions, because the magnetic rigidity (P/q) of 1“C is not much
different from that of 12C, the elastically scattered 12C particles were also detected at
the focal plane corresponding to excitation energies of about 25 MeV in the residual
nuclei. Because the counting rate of elastically scattered 12C particles was much larger
than 13C particles, the 12C particles were blocked by using a “finger”. The particle

identification was done with two contours on the AE.vs.E and TOF.vs.P0.S' spectra.

In the (”CPN) reactions, elastically scattered 12C particles did not disturb the
detection of 1“N particles and no blocking finger was used. The particle identification
was done with the same method as for the 13C particles. Some typical two dimensional

spectra and contours for particle identifications are shown in fig. 2.6

24

 

AEIFIC)

 

TOF

 

 

 

 

Figure 2.6: A sample of particle identification in two dimensional spectra for 9“Zr +
12C reaction.

25

2.7 Energy Calibration

Energy calibration enables one to find the relation between the energies and the
channel numbers of various particles detected in the focal plane detector. From
magnetic rigidity, B - p = P/q , the orbit radius p in a known magnetic dipole
field B can be calculated for a detected particle of momentum P and charge state
q. The orbit radius may be expressed in terms of a channel number using a simple
polynomial of specified order. Normally a second order polynomial is sufficient. Then
the relation between the calculated orbit radius p and the measured channel number
:1: is given as

p=a+b~x+cmrz. (2.1)

To obtain the coefficients a, b and c at least 3 different settings of B and a: are required.
For the calibrations of this experiment, channel number x was obtained by changing
the magnetic field B, with the same target at a fixed scattering angle. Once the
calibration is done for a specified particle, the momentum and the related physical
quantities can be extracted from the measured channel number, and this calibration
may be applied to calibrations of energy spectra for other particles which have similar
mass and energy. The calibration obtained for the “Li spectra may be applied to the
calibration of “He or 8Li spectra, but may not be acceptable for the calibration of
13C or 13N spectra because of the big differences in energies and momenta, and the

nonlineality of the energy calibrations.

In this experiment, the “Li and “He spectra were calibrated using the reactions
12C(7'Li,“Li) and u'C(7Li,“He). To minimize the uncertainty in the calibration due to
the energy loss in the target, a very thin 1"'C target (0.48 mg/cm’) was used. For
calibrations of 13C and 13N spectra, 12C spectra on a target of ““Zr of thickness 5.3

mg/cm2 were used with elastic scattering reactions. The reason that 12C spectra were

 

75

en
1h.
de
IIE
an
the
an.
new

the

U)
r (.4
(II

Bt-

26

used instead of 1“C or 13N spectra is that the ground state of ““Zr or ”Y was not
separated cleanly from the excited states. The calibration coefficients were obtained
by executing the program NSCLJIBRARY : [SETUP.CALLIB]CAL88.EXE.
A detailed description is given in ref.[S320 90]. The fitted calibration curves for the

“Li, “He and 12C spectra are given in fig. 2.7.

The relativistic momentum P can be calculated for a given reaction, with known 1:,
B and q. Then it is possible to predict the location or the channel number of a known
state, or determine the excitation energy, reaction Q - value and particle’s kinetic
energy for a given channel number. To find the excitation energy corresponding to
the ejectile’s kinetic energy some relativistic kinematics are required. A diagram
depicting the initial, intermediate, and final systems involved in the kinematics of
transfer nuclear reaction is given in fig. 2.8. En, Mn and Pn are kinetic energy, mass
and momentum of the n“ particle just before and after the reaction. It is assumed
that the reaction happened at the middle of the target. As the particle’s momentum
and the position are measured after the reaction using the S320 spectrograph, it is
necessary to compensate for the energy loss in the target. Thus the final form for
the residual nucleus’s excitation should be expressed in terms of the initial and final
system’s known parameters. The x and y — components of the momentum must be
conserved, i.e.

P1 = P3-c030 + P4-coszl), (2.2)
P3-sin9 = P4-sintl). (2.3)

By eliminating the term which has 11),

P42 = P12 ‘1' 1332— 2P1'P3°C080, (24)

 

P1 = «E? + 2M1°E1, (2.5)

P / BatQ (Cm)

27

Calibrations for 12c,

 

180 _
12C
175

errrIrr

170

UTTI

165 '

I I l I I l U I I I' F r I I I T

    

 

180 E
175 L

170 '_"

 

180}-
175 _"

170 -

 

L 1 1 l l 1 L 1 I l l l l

 

l L

 

 

600 600 1000
Channel #

Figure 2.7: Calibrations on 12C, “Li and “He particles. Uncertainty is about 0.1%.

1200

 

'flIEM

Eo

 

 

 

 

 

TARGET

Figure 2.8: Schematic diagram depicting the kinematics in the target.

where E, = E0 -- Elam-n and P3 can be calculated easily using the measured channel

number (p), Emma, Elossout and P31,

 

P3} = B-p-q/3.3356, (2.6)
E; = E31 + Elossout

= W — M. + Elm...“ (2.7)
Pa = \/1332 + 2143.533, (2.8)

where momenta are expressed in a convenient unit (MeV/c) rather than an MKS
unit, B is the magnetic field strength in 1:0, q is the charge state and p is the orbit
radius in cm. Exam-n and Egon“, are the incident particle and ejectile’s energy loss in
the first half and second half of the target. Now P, can be calculated from eq.2.4 by

using P1, P3 and the scattering angle 0. The recoil energy is,

E4 = VP: + M} - M4. (2.9)

Then the excitation energy of the residual nucleus is

Ea: = E0 _ E3} — E4 '1' Q - Elana (2-10)

29

where Q is a reaction Q — value and E10,, is the total energy loss in the target, sum
of Elous'n and Elossout- The energy losses in the targets were calculated by executing
the program nsclJibrary : [setup.eloss]donna.exe. This program calculates the
energy loss of any particles in any medium or series of media. The input parameters
are, incident energy, proton number and nuclear mass of the projectile, and electron
number, atomic mass, mass density and thickness of the target particles. In heavy
targets, most of the energy loss is caused by inelastic collisions between the projectile
and the atomic electrons of the target making an ionization or excitation of the
target atoms. To determine the Elossfn and Elam“, it was assumed that the reaction
happened at the middle of the target. Elossin is the energy loss of the projectile for
the one half thickness of the target and Elmo,“ is the energy loss of the ejectile for
the other half thickness of the target. Elosss'n is independent of residual nucleus’s
excitation, but Emu,“ is, because the kinetic energy of the ejectile, dependent on the
excitation of the residual nucleus. In case when the residual nucleus was in an excited
state after the reaction, Elam“, was adjusted using the linear relation between the
two cases of energy losses at E = 0 MeV and E = 60 MeV of a residual nucleus.
Of course the exact excitation is not known in this step. But a small difference in
excitation energy does not affect Elam“, very much. If the excitation of the residual

nucleus is E, then

B

Elossout,Ez=E = Elossout,Ez-=0. + E ' (Elossout,E:t-=60. '" Elossout,Ex=0.)- (2-11)

When the residual nucleus is in an excited state, the reaction Q - value is the sum
of the excitation energy E and the reaction Q - value for the ground state of the

residual nucleus,
Q = E + QE:=O. - (2.12)

The calculated energy losses in the targets for the projectiles and the reaction products

are given in table. 2.2.

30

Table 2.2: Energy losses of the reaction products in the targets at E = 30 MeV/n.
Units are MeV. Numbers in parenthesis are target’s thicknesses in mg/cm’. Reac.Pro.
represents ”Reaction Products”. Uncertainty is about 10%.

 

 

 

 

 

 

 

 

 

 

 

Target 9°Zr 91Zr 89Y 20813b 2093i 20713b
Reac.Pro. (5.06) (5.01) (5.30) (5.84) (6.50) (4.95)
7L1 0.493 0.493 0.512 0.422 0.472 0.359

6L1 0.440 0.437 0.457 0.382 0.426 0.322
6H6 0.199 0.198 0.204 0.172 0.191 0.146
1""C 1.976 1.973 2.052 1.690 1.888 1.439

13C 2.134 2.109 2.214 1.800 2.012 1.531
13N 2.903 2.900 3.006 2.467 2.736 2.099

 

 

(J1

tar.
ELL-g
Gm:

027

31

The uncertainty of the calibration is about 0.15 MeV for 6Li and 6He, and about
0.3 MeV for 13C and 13N. The main uncertainties are from the inaccurate thickness
of the target and the intrinsic uncertainty of the focal plane detecting system‘of
S320 spectrograph. The final determination of the excitation energies was made by
subtraction from the energy of the ground state which was set at Ex. = 0 MeV. The
shifts to make E2. = 0. were less than 0.3 MeV for 6Li and 6He, and less than 0.5

MeV for 13C and 13N.

2.8 Cross Section Determination

The differential cross sections for the single nucleon transfer reactions were obtained

by using the parameters measured in the laboratory frame. The formula used is

(If—0' _ N3?“ Z‘Tflg DTC
do " 3.74.103 Q~T An’

 

(2.13)

where ch is the number of the reaction products detected by the spectrograph per
channel number, Z is the average charge number of the projectile after it passed
through the target, Q is the integrated beam current in 7:0, m, is the mass of the
target nucleus in amu, T is the thickness of the target in mg/cmz, A9 is the solid
angle of the aperture in msr and DTC is the dead time correction coefficient. The
cross sections are in mb/sr. The uncertainty for the cross section appears to be about

10% due to the the uncertainty of the target’s thickness.

rn

Chapter 3

Shell Model Analysis for 208Pb
Region Nuclei

3.1 Introduction

In single nucleon transfer reactions on targets which have an extra hole or particle
outside a closed shell nucleus, the interaction between the transferred nucleon and the
target’s hole or particle is the main factor that splits the single particle states and pro-
duces a multiplet of states. At low excitation energies, the shift in excitation energy
and a slight broadening of the peak due to this interaction were observed and discussed
extensively on lead region nuclei using light ion transfer reactions [Alfo 70, Craw 73].
But at high excitation energies, the density of states is so high that individual states
are not resolved. If the changes in excitation energies and widths of the multiplets
due to the presence of an extra particle or hole can be predicted by theoretical meth-
ods, it would give us confidence in predicting the shifts in excitation energies at high
excitation energy. One of the methods to calculate these changes is the shell model.
This calculation provides us very useful information on the splitting of energy levels
due to an extra particle or hole state, including the spectroscopic factors and the
excitation energies by solving the Schrodinger equations for the given conditions as-

suming that nucleons inside the core nucleus are in the same average potential. From

32

th

sin
fac

Du:

33

this information, the shift and the broadening of the multiplet states from the single

particle or single hole states can be obtained.

Shell model calculations have been very successful in the vicinity of the closed
shell nuclei, especially in the lead region nuclei [Ma 73, Herl 72, Mcgr 75, Warb 91].
One problem with the shell model calculation is that there are many low lying single
particle orbits which are potentially important. Thus very large matrices need to be
diagonalized which requires too large a working area and cpu time for the available
computers. Thus the number of particle states and hole states must be limited in

these calculations.

For the chosen two target nuclei, 20713b and 2093i which have an extra single
particle or hole outside the closed shell core nucleus 208Pb, the energy levels and
spectroscopic factors for the single nucleon stripping reactions were calculated. The
purpose of the shell model calculation is to observe how the characteristics of the
single particle states in the multiplet, such as excitation energies and spectroscopic
factors, are changed by the presence of a single particle or hole outside a closed shell
nucleus. But the single particle states at high excitation energies are not well known
and it is therefore difficult to calculate the changes for the high lying particle states.
But by calculating the changes for low lying particle states which are known well,
one can assume that the results are applicable to high lying single particle states,
since the interactions between the p — p or p — h states are not very dependent on the

excitation energies.

3.2 Energy Level Calculations

For the single nucleon stripping reactions on targets of 2”Pb and 209Bi, the energy lev-

els, and their parameters such as excitation energies, wave functions and spectroscopic

Th'
tro

am

34

factors were calculated using the N SCL version of the program OXBASH[OXBA 88].
This can handle up to 3 particle orbits and 4 hole orbits in both proton and neu-
tron shells. The targets were assumed to be a composite of the 20an core nucleus
and a single proton particle for the 2098i nucleus or a single neutron hole for the
2(”Pb nucleus. Energetically the highest 4 hole orbits and the lowest 3 particle or-
bits were considered to be the available particle and hole states both for proton and
neutron shells. The experimental single particle energy levels in 2“Pb are given in
fig. 3.1 [Ma 73]. (proton particle ; 1h9/2,2f7/2, 11°13”, proton hole ; 1h11/2,3s1/2,
2d3/2,2d5/2, neutron particle ; 299/2,1in/2, 1j15/2, neutron hole ; 1i13/2,3p1/2,
3P3/2, 2f5/2)

The matrix elements of the Hamiltonian operator H between the many particle

basis functions were obtained by using the second quantized operators 0" and a

[OXBA 88]. The Hamiltonian H can be written as
H = Hcore + Z Eiafa.‘ + Z vijkzafafakaz, (3.1)
i i>j,lc>l

where e,- is the energy of a single particle state, and
12in = (ilelkf), (3.2)

and Ii j ) is an antisymmetrized two particle m-scheme state. The values for the both 6,-
and 12ng are inputs in the code OXBASH. The single particle energies e; are adjusted
to fit the experiment and the two body terms v.3“ were based on the Kuo-Herling
G-matrix [Warb 91]. By applying this Hamiltonian operator to the wave function
Ii j ) and diagonalizing the matrix elements, the eigenvalues and eigenfunctions can be

obtained. Here, the eigenvalues are the energies of the final states.

In the 207Pb(+n) reaction, when the transferred neutron occupies one of the 3

neutron particle states, the neutron hole which is initially in the 3p1 ,2 state can be

F3,
516

be:

35

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. 1i13 2 1.601
1115/2 1.428 I

_ 2f7/2 0.892
1111/2 0.781

3.44 MeV 4.26 MeV
3p 112 i 0.0 381/2 0.0
- 0.350

2g,2 - 0.570 2d”

3 - 0.897

p3” 1h11/2 -1.34O
1113/2 '1-633 2d5/2 -1.670

Neutron Proton

Figure 3.1: Experimental single particle and hole energy levels in 20‘313b [Ma 73]. In
shell model calculation, the lowest 3 particle states and the highest 4 hole states for
both proton and neutron shells were used.

loc:

she

init
pro

ofl

C00

rea
tior
sta'
low
stem.
add
frm
the

do:

36

located in any one of the 4 neutron hole states in the final state while the proton
shell was assumed to remain closed. (The notation (+n) stands for adding a neutron
to the target by a neutron stripping reaction). So 12 combinations of one particle
- one hole states were used in the calculations. If the neutron occupies the target’s
initial hole state 3p%-1, the neutron shell becomes a closed shell. In this case the
proton shell was assumed either to be a closed shell or a proton can be excited to one
of the 3 proton particle states from one of the proton hole states, which makes 13
(1+12) combinations. Thus a total of 25 combinations of particle and hole states were

considered. Each combination has many different states due to the p — h couplings.

The same procedures were also used for the other reactions. In the 209Bi(+n)
reaction, since the target nucleus has a proton in the lhglg orbit, the main interac-
tion is between the transferred neutron and an outmost shell’s proton. Three particle
states are available for both proton and neutron shells, thus 9 combinations are al-
lowed. In the 207Pb(+p) reaction, three proton particle states and 4 neutron hole
states are available, thus total 12 combinations are allowed, where (+p) represents
adding a proton to the target by a stripping reaction. The main interaction comes
from the coupling of the transferred proton and the target’s neutron hole state. In
the 209Bi(+p) reaction, there are two protons in proton particle states outside the

closed me core nucleus. A total of 9 combinations are possible.

3.3 Results and Discussions

The results for the energy levels are expressed as an excitation energy, spectroscopic
factor S, j’r of the residual nucleus and a transferred nucleon’s final orbit quantum

numbers n,l and j. The cross section a; is defined as

2Jf+1
2Jg+1

 

0’] = 0th

El‘g

neu

Whj

37

where at}. is the cross section calculated theoretically and may be assumed to be
constant for the same orbit. j f and j; are the total angular momentum of the final
and initial state respectively, and 5' f is the spectroscopic factor of the final state.
The single particle states in the 209Pb and 2098i nuclei are independently normalized
to the experimental data, and the energy levels of each multiplet are plotted as
a function of excitation energy after the strengths are normalized to those of the
single particle states in the 2°9Pb and 209Bi nuclei (fig. 3.2). The average energies of
each multiplet are obtained by averaging the energies weighted by the cross section.
They are compared with the present experimental data, and the centroid energies are

compared with the single particle states of the 209Pb and 209m nuclei in tables. 3.1

and 3.2, and fig. 3.3.

In the 20"Pb(+n) reaction, the energy levels except the ground state are shifted to
higher excitation, which agrees very well with the experimental result. The ground
state is formed when a transferred neutron fills a target’s hole, 3p1 ,2 state. As the
final state is doubly closed, the shift of the ground state to lower energy (3.564
MeV) is much larger than in the odd - odd (2°7Pb(+p) or 209Bi(+n)) or non — closed
even - even (2°93i(+p)) residual nuclei’s ground states. The couplings between the
neutron’s particle state j1r and the ground state 3p;l allow only two j I of j + % and

j - §. Thus each multiplet is dominated by these two levels out of numerous levels

which are not seen in the figure due to the very weak spectroscopic strengths.

In the 209Bi(+n) reaction, each multiplet is represented by many levels which have
similar spectroscopic strengths, and the widths of the multiplets (about 500 keV) are
somewhat bigger than those (100 ~ 300 keV) of the multiplets in the 207Pb(+n)
reaction. The reason is that the ground state of 1mm, has a large angular momentum
(lhg/g) and the coupling with the neutron particle states allows many j I ranging from

I j.- - 3| to j,- + 33. But the ground state is not shifted much (about 0.35 MeV) from

38

Figure 3.2: Energy levels obtained from shell model calculations. The relative
strengths of single particle states of 209Pb and 2""Bi are normalized to the experi-
mental data of (7Li,6Li) or (7Li,6He) reaction. Each bar represents the strength of
a specific configuration and the dashed lines are calculated spectra obtained using
the gaussian distribution with the 0.3 MeV FWHM. The overall renomalization is
arbitrary. The same colored lines originate from the same single particle state.

809... 207,-__

208 r) in

C653 mmuocm .xm

 

 

 

 

 

 

 

w w N o
W- - .1 --.----,o.o
.W
. , _.
H W x/ W
.. \ W .
m. / W .quo
W / W .
. / W:
m l1]1 T l a \ 1‘11 1W. 0.0
W / W W .
W. :mo
\\ 4.0
W. W 90
Mr Omofim /. Wmd
W W .
_ < - q a < . 1400
W x... \ Wmd
W W \ W
.1 \ .30
m ,, W .
W. .. W W3
. 6.0
. Wmmom We;
all r r 1 p r _ - - - p L .b Nin

 

o a. N o
/.-: - a“. 1N1 a -
W \

W.

W

h.

 

. l fI—\l1la. 0.0

Nd

/
\
. I “~qu

 

.vd

 

/
\
/
\

. 0.0
md

Nd

/-
\
,0
0..
Q
C
N
WWIAJWAI

 

 

1

 

vIv Vfr‘i‘r

6.0

'0".
\

AAAlAW‘WJJAL44

I
/
\
/
\
AWL

. 0.0

0H
m
o
H
N
/
\
K

Wad
0.0
No
no
md
ad
on
rm;
Ac+v 0.3.8 Wmmom macaw

 

l
l
..(
4

I
/
/
\
‘\

 

 

vYIvvvvrv v—vlv
/
/
\
l
\
\

 

 

vvvivv

 

 

uouoag $80.13

Figure 3.2

39

Table 3.1: Average excitation energies obtained using shell model calculations for
the peaks 1, 2 and 3 of neutron stripping reactions on targets of 2(”Pb and 2"”Bi are
shown with the experimental data. Each peak is a multiplet between target’s state
and single particle states where a neutron transferred. The values in parenthesis are
the reaction Q — values for the corresponding excitation. Energy levels for the single
particle states of the 208Pb(+n) reaction are also given to measure the energy shift
from the particle - particle or particle - hole interactions. Experimental errors are

about 0.15 MeV.

 

 

 

 

 

 

 

 

 

 

 

 

Single State Shell Model Calculations This Experiment
(7Li, 6Li)
Peak 208Pb(+n) 2°7Pb(+n) 2°98i(+n) 2°7Pb(+n) 209Bi(+n)
# (MeV) (MeV) (MeV) (MeV) (MeV)
1 0. 3.557 0.414 3.30 0.65
(-3.313) (—3.400) (-3.060) (-3.11) (-3.30)
”(gs/2) l’(1’1/2)"1 ‘3’ ”(gs/2) 1r(he/2) 18’ ”(gs/2)
2 0.779 4.281 1.201 4.14 1.51
(-4.092) (-4.164) (-3.832) (-4.02) (-4.16)
”(in/2) "(Pi/2)-1 ‘3’ ”(in/2) 1"(he/2)® ”(in/2)
3 1.423 4.939 1.760 4.70 2.01
(4.736) (-4.712) (-4.406) (4.58) (-4.66)
”(jis/zl "(Pl/2)"l ‘3 ”firs/2) 1r(he/2) ® ”(115/2)

 

 

 

 

 

5i]

 

40

Table 3.2: Average excitation energies obtained using shell model calculations for the
peaks 1, 2 and 3 of proton stripping reactions on targets of 2("Pb and szi are shown
with the experimental data. Each peak is a multiplet between target’s state and
single particle states where a proton transferred. The values in parenthesis are the
reaction Q - values for the corresponding excitation energies. Energy levels for the
single particle states of the 208Pb(+p) reaction are also given to measure the energy
shift from the particle - particle or particle - hole interactions. Experimental errors

are about 0.15 MeV.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Single State Shell Model Calculations This Experiment
(7Li ,cHe)
Peak 2°81” 501*?) 2MP 5( +1?) 2091311+?) ”7P 5( +19) 2093441?)
(MeV) (MeV) (MeV) (MeV) (MeV)
1 0. 0.098 1.479 0.03 1.39
(-6.716) (-6.366) (-6.270) (-6.27) (-6.38)
7r(he/2) ”(Pl/2)-l ® 1r(he/2) “(he/2) ® fl'(hs/zl
2 0.897 1.134 2.354 0.90 2.12
(-7.073) (-7.402) (-7.324) (-7.17) (~7.11)
1r(fr/2) V(P1/2)-l 8’ 1r(fm) 7r(he/2) 3 1'’(fm)
3 1.609 1.718 3.002 1.52 2.73
(-7.715) (-7.987) (-7.980) (-7.79) (-7.72)
1r(1i13/2) l’(PI/zl-1 ® 7rfirs/2) 1r(ks/2) ‘3 1r(I'm/2)

 

 

 

41

Figure 3.3: Comparison of shell model calculations with experimental spectra. Each
vertical bar represents the strength of a specific configuration and the solid lines are
experimental data and the dashed lines are calculated spectra obtained using the
gaussian distribution with the 0.3 MeV FWHM. The same colored lines originate
from the same single particle state. Calculated values are normalized to the experi-
mental data. The average excitation energies of the shell model calculations for each
multiplet are marked with short arrows on the horizontal - axis while the centroid of
experimental peaks are marked with long arrows on the spectra.

809”; 2071_)1\/7T 1'. 6T 1'\ ZOBT‘JL 809,3; 207111W17r : 6r1W\

CEEV kmpodm .Nm

 

 

 

 

    

 

 

 

 

  

 

 

   

 

 

 

 

w .v N O m an N o
e a a e a.
Ml I’M/.4 l: OO ./1: 4 -\.\.4 «jc
. W
W. 25.43 ., .Wm O W \ Wm
L... i . W a 1
4.: w L .4: W 1443.1 W.
m \ W Wmé w. /& WW it 1
r can} .u v D um
58m W: W W W. _ W amoom W
4 , ON H . Wma
_. 14;. l -13;
W. um
/ W / n 4
4 / \ Woe WigsajfiJJa / W
.5: W... W :3...
.r > , _
W 0&on .W. D .4 “max... 44 Wm
W W W 3 5.
W . Am 1W W . )M \w
W: Dr .Wmd W. 4.: N
41:316.... .. m \ .W o H 7545—2137.: Fr. W my)? 1 m
H KR W . W. s e. 1
l i i. m H 4. ’2: L Wm
H.mmom W W amoom W.
a Wow 4 WOW
Filillrlll.-lil-l»l r r r l I? l .1. v - L i p > r j r h - 1 l lrikllllru

 

 

 

 

 

Ammmgqpvnmgm .Wmaom .nmmom

Cdo .wdbvfinmfiom .wmmON .Qnmmom

(AaW—uS/qun spup/np

Figure 3.3

anc

311C

42

the centroid of the u(lgg/2) ® 7r(1h9/2) multiplet because of the weak strength of the
odd — odd coupling. Even if a single proton in the 2g9/2 state in the target can occupy
any of its available states after the reaction, the most dominant state is the initial
state. Similar phenomena are seen in proton stripping reactions. In the 207Pb(+p)
reaction, two dominant levels appear in each multiplet as in the 20"Pb(+n) reaction.
Because of the very weak odd— odd coupling strength between the 3P7: state of 2”Pb
and the proton’s single particle states, the widths of the multiplets are about 70 keV

and there is about a 0.1 MeV shift of the whole spectrum to higher excitation.

In the 209Bi(+p) reaction, due to the Pauli exclusion principle and the smaller
j -values of the proton’s single particle states, the numbers of energy levels domi-
nantly contributing in each multiplet are less than those of the 2°98i(+n) reaction.
Thus the widths, about 300 keV, of the multiplets are not as large as the widths of
the multiplets in the 209Bi(+n) reactions, about 500 keV. The ground state of the
even — even residual nucleus 210P0 is shifted from the centroid of the 1r(1h9/2)2 mul-
tiplet to lower energy by 1.34 MeV, due to the pairing interaction in the #0129”)2
j = 0"“ state. This shift is much larger than that of the ground state for the even—odd

residual nucleus of the 2(’i’Bi(+n) reaction, namely 0.36 MeV.

As is shown in fig. 3.2, even though the energy levels in the multiplets are spread
up to 4 MeV, the relative excitation energies for the centroid of each multiplet do not
differ significantly from those of the single particle states in the 209Pb or 2("’Bi nucleus
(at most by a few hundred keV). When the reaction Q — values of the multiplets
are compared with those of the single particle states, no significant differences are
observed. However, when the excitation energies are compared, significant differences
are observed in some cases. From these comparisons, it is evident that the existence
of an extra hole or particle in the target does not change the reaction Q — values

significantly, but it may change the excitation energies significantly.

Chapter 4

Single Particle States and Giant
Resonance States

4. 1 Introduction

In some recent heavy ion transfer experiments, broad peaks have been observed with
properties (excitation energies, widths and strengths) which are similar to those of
the giant quadrupole resonance (GQR) [Merm 87, Fras 87, Fort 90]. Whether these
broad peaks are giant resonance (GR) states or simply broad single particle states
is not clear and remains a question (see fig. 1.1). The possibility of GR excitation
by transfer reactions was mentioned in a paper by Olmer et al.[Olme 78] and also
by Frascaria et al. [Fras 89]. Broad peaks in single particle transfer reactions have

been found in many nuclei over a wide range of the mass, from A = 60 to A = 208

[Fras 87, Duff 86, Fras 89, Fort 90, Gale 88].

This chapter attempts to address the nature of these broad peaks by discussing
what differences one might expect in transfer reactions on different targets. For this
purpose, 2 even — even nuclei targets, 90Zr and 208Pb, and their neighboring nuclei,
4 even — odd targets 91Zr, 89Y, 209Bi and 2°7Pb were chosen. The reason that these

targets were chosen is described in section. 1.2.

In this chapter, the characteristics of single particle states and GR states, and the

43

44

method of distinguishing GR states from the single particle states are described.

4.2 Predictions for Single Particle States

A single particle state is a state in which a nucleon occupies one of the shells outside
the non-excited core. The nucleon’s orbit is characterized by shell model quantum
numbers. A single particle state can be formed by adding a nucleon to an outer shell

using a transfer reaction.

If this state couples with the target’s ground state which has an extra hole or
particle outside the closed shell core, a multiplet of states will be formed which are
spread over a few MeV in excitation energy. The total cross sections for exciting the
multiplet states in a transfer reaction will be nearly the same as the cross section of
the single particle state. If the energies of the multiplet states are weighted by the
spectroscopic factors, the centroid of the multiplet behaves in a systematic way from
one nucleus to the next and it does not change significantly in absolute energy. Shell
model calculations show that the change of the centroid is about a few hundred keV

in the lead region [Ma 73] (and see chap. 3).

The excitation energy of a specific orbit’s single particle state depends upon the
ground state energy and may change significantly from one nucleus to the next. In
neutron stripping reactions, a significant change in excitation energy is expected for
similar single particle states between targets consist of a closed shell and targets which
have a single neutron hole, such as 208Pb and 2”Pb. The ground state energy of the
2°7Pb(+n) reaction is lower than the ground state energy of the 208Pb(+n) reaction
by 3.43 MeV which is the difference in binding energy of the outmost neutron in
209Pb and 208Pb, where (+n) denotes a neutron stripping reaction. Except for the

ground state, the spectrum of the 207Pb(+n) reaction is shifted to higher excitation

45

energy compared to the spectrum of the 208Pb(+n) reaction. Similar results may
be expected in proton stripping reactions for closed shell targets and targets which
have a single proton hole, such as 90Zr and 89Y. The difference between the outmost
proton’s binding energy in 91N b and in 9"Zr is 3.2 MeV, and this shifts the spectrum
of the 89Y(+p) reaction to higher excitation energy by about 3.2 MeV compared to
the 9°Zr(+p) reaction, where (+p) represents a proton stripping reaction. Thus the
excitation energies for similar single particle states may be changed significantly (up

to 3 or 4 MeV) between two neighboring nuclei.

But the reaction Q — values for transferring a nucleon to the same shell of the
neighboring nuclei are not very different from each other. At most a few hundred keV
difference results from the coupling between a single particle state and a core state.
For example, in neutron transfer reactions to the same V(2gg/2) shells of the me
and 20713b targets, the difference between the two reaction Q - values is about 0.1
MeV, due to the coupling of V(299/2) ® u(3p1/2)’1. As was shown in the shell model
calculations (chap. 3), 1p - 1 p or 1p — 1h couplings convert the single particle state
into a multiplet of 2 j + 1 states. Thus, for the single particle states, an extra hole or

particle in the target changes the reaction Q — values by a few hundred keV at most.

These ideas may be applied to the broad peaks observed in single nucleon stripping
reactions on targets of 9"Zr and '3me region. If the broad peaks are single particle
states, they should appear in the spectra of neighboring targets. There may be a
slight broadening in the peaks but the total strength should be similar. The broad
peaks shown in the 9°Zr(+n) reaction [Fort 90, Fras 87] at excitation energy about

13.5 MeV should also appear in the 91Zr(+n) and 89Y(+n) reaction.

In the 91Zr(+n) reaction, the ground state will shift to lower energy by 1.34 MeV
compared to the ground state of the 9°Zr(+n) reaction. The broad peak is expected

to appear at higher excitation energy than in the 9(’Zr(+n) reaction by 1.34 MeV,

46

where 1.34 MeV is the outmost neutron’s binding energy difference between 92Zr and

91 21'

Similarly in the 89Y(-{-n) reaction, the ground state of 9°Y will shift to lower energy
compared to the ground state of the 90Zr(+n) reaction by about 0.39 MeV. The broad
peak is expected to appear at about 0.39 MeV higher excitation energy than in the

90Zr(+n) reaction, where 0.39 MeV is the outmost neutron’s binding energy difference

between ”Y and 91Zr.

However, there should be no significant differences in reaction Q — values for the
broad peaks in these reactions. If the spectrum of 90Zr(+n) reaction is compared
to the spectra of the 91Zr(+n) and 89Y(+n) reactions as a function of reaction Q -
values, all the broad peaks except the ground state are expected to appear at almost

the same positions, within a few hundred keV.

Broad peaks observed in the 208Pb(+n) reactions [Fort 90, Merm 88, Mass 86] at
excitation energy about 10 MeV should also appear in the 209Bi(+n) reaction and

207Pb(+n) reactions.

In the 20"Pb(+n) reaction, the ground state will shift to lower energy by about
3.43 MeV compared to that of the 208Pb(-+-n) reaction. The broad peak is expected
to appear at excitation energy higher than in the 2f’st(+n) reaction by about 3.43
MeV.

Similarly in the 209Bi(+n) reaction, the ground state will shift to lower energy but
only by about 0.66 MeV. The broad peak is expected to appear at higher excitation
energy than in the 2osl’bH-n) reaction by about 0.66 MeV. But there will be no

significant difference in reaction Q — values for the broad peaks in both reactions.

Schematic depictions of the prediction for the single particle model for single

neutron transfer reactions on 20"’Pb region targets are given in fig. 4.1. In this figure,

 

 

 

 

 

 

47

 

208 Pb + n I
89/2\;0—
gs
A . A .
209Bi + n \

._.__.
g9\

l2—o—

 

119/2 _.._

 

 

 

 

 

A

94—":
D

 

 

2"71,134.11 \T"
P1/2 —— _ o

 

 

 

 

 

 

fl

 

gs

 

m
—>

‘Q

—’ Ex. Energy

Figure 4.1: Predictions for the excitation energy shifts of single particle states in
208Pb nucleus and its neighboring nuclei. If the broad peaks are GR states, they
will have almost the same excitation energies.

48

only two peaks in the 208Pb(+n) reaction are considered, the ground state where
a neutron is transferred to the 299/2 shell, and a broad peak corresponding to some
excited state. These peaks are expressed as a function of both the reaction Q — values
and excitation energies. If the same procedures are applied to the 2°93i(+n) reaction,
the situation is very similar to the 208Pb(+n) reaction. The two peaks, multiplets of
the «(hg/g) state and the same single particle states, appear at similar positions in
both the reaction Q — value and excitation energy, with somewhat broad widths. In
the 2o"Pb(+n) reaction, the two doublets resulting from the couplings between the
neutron hole state and the single particle states will appear at the same reaction Q -—
values. But the ground state will appear at lower energy by as much as the outmost

neutron’s binding energy difference between the 208Pb and 209Pb nuclei.

If all the peaks are compared as a function of reaction Q — values as in fig. 4.1.(a),
they will appear at almost the same reaction Q - values except the ground state of
the 20"Pb(+n) reaction. If they are compared as a function of excitation energies as in
fig. 4.1.(b), the two peaks of the 20"Pb(+n) reaction will appear at higher excitation

energies than the peaks of 208Pb(+n) and the 209Bi(+n) reactions.

In general, if the peaks, which are obtained by transferring a neutron to the same
shell, have similar reaction Q — values but show a shift in excitation energies, then
they can be assumed as single particle states. Whereas, if the broad peaks have the
similar excitation energies whatever reaction Q - values they have, then the broad
peaks can be assumed as GR states. This method may also be applied to the reactions

with the 9"Zr region targets to distinguish GR state and single particle state.

49

4.3 Predictions for Giant Resonance States

A giant resonance is a highly collective mode of nuclear excitation in which many
nucleons move together in a correlated way. The motion is so collective it may be
treated as the oscillation of a liquid drop. The resonance in which neutrons and
protons move in phase is an isoscalar resonance, while the one in which neutrons and
protons move out of phase is an isovector resonance. Similarly, the one in which spin
up and spin down nucleons move in phase yield S=0 modes (electric modes) and the
one in which spin up and spin down nucleons move out of phase yield S=l modes

(spin flip, magnetic modes). Giant resonance have been observed in many nuclei

[Youn 76, Woud 87].

The properties of GR such as excitation energies, widths and strengths change
very smoothly as the nucleus’s mass changes and the total cross section for the GR
is generally large compared to the cross section for the typical single particle state.
Microscopically, GR may be described as a coherent superposition of many 1p — 1h
excitations resulting from applying the electromagnetic interaction force to the ground
state [Woud 87]. A schematic representation for a single particle - hole transition
between shell model states is shown in fig. 4.2 [Bert 81]. The transitions shown
represent some of the collective vibrational modes that may occur by exciting one
nucleon from the core to a higher orbit. The centroid of the GR peaks is dependent
on the nucleus mass [Youn 76]. The centroid of the GQR excitation energy may
be expressed approximately as Ea: = 63/A1/3 MeV, where A is the mass number
[Bert 76, Youn 76]. A mass number difference of 2 or 3 in heavy nuclei does not shift

the centroid energy of the GR significantly.

The giant quadrupole resonances obtained by inelastic scattering reactions in this

experiment, using a 12C beam at 30 MeV/n, on 9°Zr and 208Pb region target nuclei are

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(
”+2
«45:»
”+1 1 l .
(l
f
f
«41501
~ 1]
I
\..w_a n..~__u 55,...)
All/=1 AN=O AN‘Z
L Y J
[1 [2

Figure 4.2: A schematic representation E l and E2 single particle - hole transitions
between the shell model states of a hypothetical nucleus.

Counts / Channel

51

”zr(m0,lac)’ e = 60 '12r(12C,12C), a = 60 50Y(12C,12c)' e = 60

 

 

 

 

 

 

’71 IVY'YI'I'I’IYI’V'I‘ 10000 7" VIr'V‘IVIT'rT'fV‘I I Yl'V'VlV—TYYIfo‘Ifi'J
h 4 ’
P 1
. 0000- 4
0000- 4 l . . .
» < 80004 4 L l
D d h 1 h 1
3 I- 4
‘ _ 1 0000—
0000r- 1 _
b : p
4 4000-
4000 1 -
‘ 2000

 

 

   

2000

h
h
P
i L
" L
b
r 1'
L
h P
b h
L r
o AAAAAAAAAAAAAAA o AALAIALLAILAAAILAWJW
0

010203040 10203040
2:. energy (MeV)

 

 

 

 

 

 

 

 

 

 

 

Figure 4.3: Giant resonances observed with inelastic scattering by a 12C (Em = 30
MeV/n) beam on 9"Zr, 91Zr and 89Y nuclei. The excitation energies are about 13.5
MeV and the widths are about 6 MeV. Small peaks at about Ex. ~ 27 MeV are
not understood in this experiment. Similar peaks were observed on these nuclei in

ref. [Ture 88, Yama 81, Bert8la].

Counts / Channel

 

 

 

 

 

 

52

 

 

 

 

 

 

 

 

 

 

 

a""1>i:(“'c,“'C). a = 9° mm(“c.“C), e =- 9° all"’r>b(“'c,”'c). a = 9°
.VIV YI'VTf'foVIY‘rVrI‘ P"'V VIYYYV'VVIVIVVT 1 P 'V VIV'V'IVVTYIVYT
. . , 3 . .
* ‘ 0000 h "‘ ‘
3000 " "‘ . 1 i <
r 4 C 1 500° " ‘
l 4 . J h ’
eooo - J °°°° ' ‘ C 1
D ‘ g 4 L 1
. GQR I . GQR . 4000 - R ~
P 4 L ‘ I GQ 4
m :- 1 mo p q i 4
i I 1 . ’ i
> 1 1 2000 ' ‘
2000 - 4 2000 - 'j 4 <
i l - ’ ‘
fA‘J p F
0’ ....1.WL.W1.-..|‘ 0' ..-.i...-i...-1-...i’ O .
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

Ex. energy (MeV)

Figure 4.4: Giant quadrupole resonances observed with inelastic scattering by a 12C
(Egnc = 30 MeV/ n) beam on 208Pb, 209Bi and 207Pb nuclei. The excitation energies

are about 10.5 MeV and the widths are about 6 MeV.

53

shown in figs. 4.3 and 4.4. From these figures, no recognizable differences are seen in
the excitation energies and widths between the giant resonance peaks for neighboring

nuclei.

Most of the studies of GRs to date have been done using inelastic scattering
reactions. N 0 GR has been observed using a transfer reaction. Theoretically, GR may
be obtained through the two step processes by transfer reactions (inelastic scattering
followed by transfer process). But GR with this mechanism seems to be very difficult
to be produced at grazing angles with high incident beam energy. Another mechanism
suggested [Chom 86, Fras 89] is that the particle - hole states are excited by a single
step mechanism through particle or hole components in the ground state of the target
nucleus. According to this explanation, for example, the giant quadrupole resonance
in 208Pb or 9°Zr would be formed by coupling the transferred neutron with a hole
state of the appropriate j " in the 208Pb or 9°Zr target. It is suggested that the broad
peaks shown in neutron stripping reactions on these targets might be produced by

the giant resonance excitations.

If the broad peaks obtained by nucleon transfer reactions in any process (by one
step or multi step process) are GR states, then the excitation energies of the peaks
should be the same with those of the GR states formed by inelastic scattering re-
actions. There should be no noticeable differences in the excitation energies among
the similar peaks obtained on targets of 208Pb, 20"'Pb and 209Bi with single nucleon
transfer reactions. One more nucleon or hole in heavy nuclei does not change the
excitation energies of the GR significantly. If the spectra of single nucleon transfer
reactions on these targets are compared as a function of excitation energy, the centroid
of the peaks should appear with a few hundred keV deviations as in figure 4.1. The
extra nucleon or hole in the target does not change the GR excitation energies (see

figs. 4.3 and 4.4). The same results may be expected in a nucleon transfer reactions

54

on targets of 9°Zr, 91Zr and 89’Y.

But, the cross section for the GR may vary dramatically depending on the struc-
ture of the target’s ground state, angular momentum transfer matching conditions
and on the number of the available configurations which can be coupled. For the
nucleon stripping reactions on targets of 207Pb and 89Y which have a hole in the p1,;
state, the contributions of the GR to the broad peaks are expected to be very small
compared to the single particle states because only a few configurations are available.
In this case the cross sections for the GR will be little larger than those of the nucleon
stripping reactions on the closed shell targets 208Pb and 9"Zr. For the same nucleon
stripping reactions on targets of 209Bi and 91Zr which have no fixed hole in the ground
states, no contribution of GR due to an extra particle to the broad peaks is expected.
Thus the cross scections for the broad peaks are expected to be the same with those

in the nucleon stripping reactions on the closed shell targets.

On the other hand, for the proton pickup reaction on the 209Bi target which has
a proton particle in the [lg/2 state, sevaral configurations are available for the GR. In
this case the cross sections for the GR are expected to be somewhat larger than the
cross section for the closed shell target 208Pb. A similar phenomenon is expected for

the neutron pickup reaction on the 91Zr target which a neutron particle in d5/2 state.

 

tir
0e

Ch

Chapter 5

Results of Single Nucleon
Stripping Reactions

5.1 Introduction

In this chapter, the one nucleon stripping reactions (7Li,6Li) and (7Li,°He) at 30
MeV/n on targets of 9°Zr, 9’ Zr, 89Y, 20f’Pb, 209Bi and 20"Pb are discussed. In each
reaction, the ejectiles were measured at grazing angles to obtain large cross sections
and to avoid multi-step transfer processes. The ejectiles, 6Li and 6He, are so weakly
bound that the threshold energies for breakup are lower than the first excited state’s

energies, and thus no ejectile excitations contribute to the energy spectra.

The spectra of the same reactions for the different targets are plotted as a func-
tion of both the excitation energies and reaction Q - values and the spectra from
neighboring targets are compared. The purpose of the comparison is to observe the
changes of the positions, widths and strengths of the peaks, and to understand the
phenomena in the spectra due to the interactions between the single particle state and
the target’s ground state. In each energy spectrum there is substantial background

at high excitation.

Strong peaks are observed when the final states have high spin and there is no spin-

flip process. A preference for transfer to high spin and no spin-flip states is understood

55

56

due to the large angular momentum transfer from the incident projectile to the target
at the grazing angle [Brin 72]. The selectivity for exciting high spin states has been
observed in recent experiments which used (a,3He) [Mass 86], (12C,"C), (”Cf’B)

[Merm 88], (2°Ne,‘9Ne) [Fort 90], and (160,150) [Merm 87] reactions.

The angular momentum transfer in the (7Li,6Li) reaction at the grazing angle at
a bombarding energy of 30 MeV/n on targets in the 9°Zr region is about 6h and
about 87': on targets in the 208Pb region. For the (7Li,6He) reaction under the same
conditions, it is about 5)": and 8h on the 9"Zr and 208Pb region targets respectively.
When a neutron or a proton which is initially in the 1p3/2(I,- = 1, j.- = I.- + %) state in
the projectile 7Li is transferred to the target nucleus, the favoured transfer appears
where the final state has j I = I f + %, and I f - I.- is similar to the angular momentum

transfer between the entrance channel and the exit channel.
5.2 90Zr, 91Zr, 89Y (7Li, 6Li) Reactions

The energy spectra for (Li, 6Li) reactions on the targets of 9°Zr, 91Zr and 8SW at
Em = 30 MeV/ n are shown in fig. 5.1. The dotted lines represent the background
drawn by hand and the arrows at the bottom represent the centroid of the peaks
analyzed. The peaks which have the same peak number are formed by transferring a
neutron to the same orbit. The ejectile, 6Li was measured at the grazing angle 0,0,, =
6°. Parameters for the peaks are shown in table 5.1. In fig. 5.2, they are plotted as
a function of both the excitation energies of the residual nuclei, and the reaction Q -

values.

Eight peaks at low excitation (less than 10 MeV) are observed in each reaction.
The first four peaks at low excitation in the 90Zr("Li, 6Li) reaction are well resolved,

but the peaks are not so clearly resolved in the 91Zr(7Li, 6Li) and 89Y("Li, 6Li)

r>QS~lLU\ I PC.» EUCU\.DU

57

l
CD
0

90 91 89 7 .6 .
Zr, Zr, Y ( L1, L1), @151,

 

. 1 r
15 " 2 alzr

'f‘i“ V

10

..e
.p

673

 

 

0' -°/ WA. .. ‘” . ....

f h l: 1| M h Ii “11 n

15}

 

9221,

10'-

do / dOdE (mb/sr—MeV)

 

 

 

Ex. Energy (MeV)

Figure 5.1: Energy spectra from 9°Zr, 91Zr, 89Y (7Li, 6Li) reactions (Em = 30
MeV/n). The dotted lines represent the background and the under lying spectra
are obtained after the background is subtracted. Arrows at the bottom of each spec-
trum represent the centroid of the peaks.

58

Table 5.1: Excitation energies for the resolved peaks for (Li, 6Li) reactions on targets
of 9°Zr, 91Zr and ”Y. I‘ is the full width at half maximum, Q is the reaction Q-Value
for a corresponding excitation energy and the units are MeV. The uncertainty is about
0.15 MeV. o is the cross section in mb/sr and the uncertainty is about 20%. Peak 0
in the spectrum is the ground state which is shifted to lower energy due to the p — p
interaction.

 

9°Zr(7Li,6Li)9‘Zr 9’Zr(7Li,6Li)9’Zr 89Y(7Li,6Li)9°Y

 

Peak Ex. I‘ -Q 0 Ex. I‘ -Q 0 Ex. I‘ -Q a

 

 

 

 

 

# r]

0 0.00 0.6 -1.39

1 0.00 0.7 0.06 1.34 0.9 -0.05 0.1 0.7 0.49
2 2.13 1.0 2.19 3.60 1.2 2.21 2.22 1.1 2.61
3 3.58 1.0 3.64 4.67 0.9 3.28 2.84 0.8 3.23
4 5.12 1.0 5.18 5.53 1.0 4.14 3.70 1.1 4.09
5 6.29 1.2 6.35 6.83 1.6 5.44 4.92 1.6 5.31
6 7.58 1.2 7.64 8.84 1.2 7.45 6.87 1.4 7.26
7 8.57 0.7 8.63 9.97 0.8 8.58 8.25 1.0 8.64
8 9.20 0.5 9.26 10.63 0.5 9.24 9.19 0.7 9.58
9 14.40 6.0 14.46 8.0 15.80 6.0 14.41 8.3 14.0. 6.0 14.39 9.9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A>0zlum\n5v Mucv\bv

Figur

abOVe

Sectio

59

er,”Zr,”Y(7Li,°Li), 81.1,:60 ”zr'glzr’B°Y(7u’oLi). 81.b=6°
'vtvrllivvivrrrltil‘ rvl.vvu1fiuurlrxuwlvu
l5 _—

 

 

10E-

 

 

 

'T"

0‘

'l
lLLlJWll
0‘

r1

V I

 

do/deE (mb/sr—MeV)
8
. . I .
3
r.

 

 

....
0'1

1" 1
l

 

 

 

 

 

o nannlnnnllananl W1

 

 

O 10 20 3O
- Q Value (MeV)

(60

 

Figure 5.2: Comparison of the neutron transfer spectra on 9"Zr region nuclei. Spectra
are plotted as functions of reaction Q - values and excitation energies. Broad peaks
above the assumed background are shaded to help to compare the positions and cross
sections.

60

reactions. Two broad peaks are seen at excitation energies about 14 MeV and 24

MeV.

The 9°Zr target has a j”=0+ ground state. If the core nucleus 9°Zr remains in
the ground state after the reaction, then in the residual nucleus 91Zr, only the single
particle states are formed by the transfer reaction. The single particle states of 91Zr
at low excitation are 0.0 MeV (2d5/2), 1.2 MeV (3.91/2), 2.04 MeV (2d3/2), 2.17 MeV
(lhn/g) and 2.2 MeV (197/2). But the ground state of the core may be broken and
the core states may couple with the single particle states and split the single energy

level into many levels [Zism 73].

The 85’Y target nucleus has one less proton in the 2p1/2 shell than the 9°Zr nucleus
and can be regarded as a composite of 9"Zr and a proton hole state (2p1/2)". The 91Zr
target nucleus has one extra neutron in the Ids/2 shell compared to the 9(’Zr nucleus
and may be treated as a composite of 9"Zr and a neutron particle state (1d5/2). When
a neutron is transferred to the target nucleus, the residual nucleus’s wave function

may be written as

|91 Zr) =|90 Zr) In), (5.1)
|92 Z?) =|90 Zr) I l’(ds/zll In), (5.2)
190 Y) =19° Z") I "(PI/2)”) l n), (53)

where I n) is the transferred neutron’s particle state. As the interesting physical
quantities are obtained from the comparison of each reaction, only the relative values
will be compared in the analysis. So the common term, I”0 Zr) may be neglected in
the residual nucleus’s wave function for simplicity. Then the couplings of the core
state with the neutron’s single particle states may be simplified without losing any
important physical characteristics. In many experiments, the Q - value of the centroid

of the particle states; weighted by spectroscopic factor, shifts about 0.2 to 0.3 MeV

61

due to a single particle or a hole state [Hodg 80].

In the 90Zr(7Li, 6Li) reaction, the first four peaks are strongly populated, where
the main contribution comes from a single state in each peak. The favoured angular
momentum transfer in this reaction is about 67': and a transition with no spin-flip is
more favoured. The ground state 2d5/2(I, = 2, j I = I f + -;-) is strongly populated, but
a single particle state 331/2 (1.21 MeV, I I = 0, j j = %) is so weak due to the small
angular momentum transfer compared to the favoured angular momentum transfer
and the small value of 2 j +1 that it is not seen at all. The second peak at 2.13 MeV is
composed of2d3/2 (2.04 MeV, If = 2,jf =1 —%), 1h11/2(2.17 MeV, If = 5,j; = lf+%)
and 1g”; (2.20 MeV, I, = 4,j, = I, — %), where 1h“); is probably the most dominant
because of a similar angular momentum transfer to the favoured angular momentum
transfer 6)": and no spin-flip process. These 3 states are not resolved in this experiment.
The third and fourth peaks (3.58 MeV and 5.12 MeV) probably have a contribution
mainly from the lhulg state, and a little from the 197/; state [Bing 70]. The first
four peaks are resolved clearly, because the density of states is small in this excitation
energy region and the transfer conditions favour only one state in each peak. But,
as the excitation energy increases, the density of states become larger and the states
overlap each other. Thus peaks 5 to 8 show up very weakly above the substantial

underlying background and the components are not well known.

In the 91Zr("Li, 6Li) reaction, the spectrum is similar to the spectrum of 9°Zr(7Li,6Li)
reaction. But the relative strengths and positions are changed a little due to the cou-
plings of single particle states with the target’s §+ state. The ground state of 92Zr(0"’)
is shifted to lower energy by about 1.34 MeV from the strong 4+ state which corre-
sponds to the ground state of the 9°Zr(7Li,6Li) reaction where a neutron is transferred
to the 2d5/2 state. This is caused by the coupling between the two neutrons in the g1-

state. If a neutron is transferred to the 2d5/2 state, then there will be two neutrons

62

in the same state. Because of the two identical particles in the same state, only even
values of j are allowed and the possible states are 0* (ground state), 2+ (0.93 MeV)
and 4* (1.50 MeV). The first peak has j’r = 0+ which is the ground state and the
second peak (1.34 MeV) is a mixture of 2+, 0+ and 4+ states, where the 4+ state
is the most prominent. The (2jf + 1) dependence of stripping reaction cross section
is a probable explanation for the weak ground state population. The two neutrons
in the same shell are very similar to the two protons in the same shell, as in the
209Bi(7Li,"He) reaction. Shell model calculations for the two protons in the 1119/;
state in 210Po show that the ground state, 0*, is shifted to lower energy by 1.33 MeV
(see chap. 3), which is a very similar value to the 1.34 MeV shift of the ground state
for the two neutrons in the 2d5/2 state. The reaction Q — values of the centroid of the
peaks, except the ground state, are shifted very little from the reaction Q - values
of the similar peaks seen in the 9°Zr(7Li,6Li) reaction (fig. 5.2). In most of the cases,
except for peaks 4 and 5, the differences of the reaction Q — values from the 9°Zr(7Li,
6Li) reaction are less than 0.5 MeV. For peaks 4 and 5, the differences are about
1 MeV. This is probably caused by the insufficient energy resolution, rather than a
particle — particle interaction. All the peaks in the spectrum of the 92Zr nucleus are
broadened because of the couplings with the Ids/2 state of the 91Zr nucleus. However,
the total strengths of the peaks in the 92Zr spectrum are not very different from those
in the 91Zr spectrum, within 10% in most of the cases. The peaks beyond peak 4 are

not clearly resolved as in the 91Zr spectrum.

In the 89Y(7Li,"Li) reaction, the spectrum is similar to the previous two spectra.
The ground state of 89Y is y. A neutron transferred to a 2d5/2 state couples with
the -;-- state of the target, and produces 2" and 3‘ states, which are present in peak
1. These two states are not resolved due to the small energy difference (~ 0.2 MeV).

The reaction Q - value of the centroid of these two peaks is shifted from that of

63

the 90Zr("Li,6Li) reaction by about 0.4 MeV. All the peaks in this reaction, except
peak 1, are broadened and overlap with their neighboring states due to the couplings
between the single particle states and a proton hole state, 1r(2p1 /2)“. These coupling
strengths are not big enough to change the shape of the peak, as is shown in peak 1.
But it makes the states overlap with each other, and thus the peaks beyond peak 4

are not resolved clearly.

In fig. 5.2, all 3 spectra are plotted as functions of reaction Q - values and excita-

tion energies. At high excitation, two broad peaks are seen in all 3 reactions at about

Ex. ~ 14 MeV and ~ 24 MeV.

The broad peaks seen at Ex. ~ 14 MeV, are so broad that it is difficult to compare
the centroid of the peaks. Instead, the starting points of the peaks are compared.
In the figure expressed in reaction Q — values, the broad peaks in all 3 reactions
appear almost at the same positions and the deviations are less than 0.3 MeV. But
in the figure expressed in excitation energies, the peak in the 91Zr("Li,"Li) reaction
is shifted to higher excitations by 1.5 MeV compared to the peak in the 9oZr(7Li,"Li)
reaction, while the peak in the 89Y(7Li,6Li) reaction is shifted to lower energy by
about 0.3 MeV. The broad peaks have very similar reaction Q - values but have
different excitation energies, which shows that the peaks have the characteristics of

single particle states rather than those of GR states.

The other peaks are seen at excitation energies about 23 ~ 26 MeV. Broad peaks
at similar excitation energies were also observed in the 9°Zr(2°Ne,’9Ne) reactions at
Em =25, 30 and 40 MeV/n [Fras 87, Fort 90], where the excitation energies are
somewhat dependent on the incident projectile’s energies. One of the possible ex-
planations is that they are from the projectile direct breakup processes. Consider
the 90Zr(7Li,"Li) reaction. The threshold energy for breakup of 7Li -v 6Li + n is

7.25 MeV and the recoil energy of 9°Zr is about 0.2 MeV for elastic scattering of 7Li

64

at 6°. Thus the kinetic energy of 6Li from the breakup process may be as large as
202.55 MeV, which corresponds to 7.15 MeV excitation energy in 91Zr where the ki-
netic energy of 6Li from the transfer reaction of 9°Zr(7Li, 6Li)91 erd is 209.7 MeV. In
many experiments the centroid of the peak of the breakup particles has been observed
at the energy corresponding to the incident beam velocity, but always less than the
beam velocity [Wu 78, Mats 80]. The energy corresponding to the beam velocity for
6Li is 180 MeV, which corresponds to 29.7 MeV in excitation energy. This excitation
energy is higher than the observed peak by about 5 MeV so that it is unlikely this

peak is from the projectile breakup process. This remains a puzzle.

5.3 208Pb, 209Bi, 207Pb (7Li, 6Li) Reactions

The energy spectra for the (Li, 6Li) reactions on targets of 208Pb, 209Bi and 2("Pb
are shown in fig. 5.3. Parameters for the peaks are given in table 5.2. In fig. 5.4,
they are compared as a function of both the excitation energies and the reaction Q
- values. The scattered ejectile, 6Li was measured at the grazing angle. Eight peaks
were resolved at low excitation in each spectrum. Two broad peaks at excitation

energies about 10 MeV and 20 MeV are observed in all 3 reactions.

The 208Pb nucleus is a doubly closed shell nucleus and has j’r = 0* in its ground
state. The single particle states formed by a neutron stripping reaction on the 208Pb
target are 0.0 MeV (299/2), 0.78 MeV (lin/g), 1.42 MeV (1j15/2,3d5/2) and 2.49 MeV
(mainly 297/2) at low excitation. The 209Bi nucleus has one more proton in the 1119/2
shell than the 208Pb nucleus, and the 20"Pb nucleus has one less neutron in the 3p1 ,2
shell than the 2o‘SPb nucleus. For neutron stripping reactions on these targets, the

residual nuclei’s wave functions may be written as

65

. 7 -6 .
208Pb, 20981, 207Pb ( L1, L1)

 

I,

12.5
10.0
75} 1
so}

2°°Pb, 0 = 6°

23 6 9 ...............
45 78 .~ “'

 

00; ‘ l . ‘ t
12.5 :-

10.0 r
:- 1 9 .....................
7.5E 23 ”a

25} (A ~“”

005 " ‘ i
125?

10.0;-
75} 1234 9 ,-”"i 1
5-0i- 5 ‘2
25} d '”' 1

J' . L . . . -
00

O 10 20 30
Ex. Energy (MeV)

 

uti—
4

do / dfldE (mb/sr—MeV)

AAAlJL

 

 

 

Figure 5.3: Energy spectra from 208Pb, 2""Bi, '3me (Li, 6Li) reactions (Em = 30
MeV / n). The dotted lines represent the background and the under lying spectra are

obtained after the background is subtracted. Arrows at the bottom of each spectrum
represent the centroid of the peaks.

66

Table 5.2: Excitation energies for the resolved peaks for the (Li, 6Li) reactions on
targets of 208Pb, 209Bi and 2""Pb. I‘ is the full width at half maximum, Q is the
reaction Q — value for a corresponding excitation energy and units are MeV. The
uncertainty is about 0.15 MeV. a is the cross section in mb/sr and the uncertainty
is about 20%. Peak 0 in the spectrum is the ground state which is shifted to lower
energy due to the p - p interaction.

 

2°8Pb(7Li,6Li)’°9Pb 2°98i(7Li,6Li)”°Bi 2°7Pb("Li,°Li)’°8Pb

 

Peak Ex. P -Q 0 Ex. P -Q 0 Ex. I‘ -Q a

 

#
0 0.00 1.2 -012
1 0.00 1.1 3.13 0.65 1.0 3.30 3.30 1.0 3.18
2 0.78 0.6 3.91 1.51 0.7 4.16 4.14 0.8 4.02
3 1.32 0.7 4.45 2.01 0.8 4.66 4.70 0.8 4.58
4 2.39 0.7 5.52 3.06 0.8 5.71 5.75 0.7 5.63
l 5 [3.78 0.8 6.91 4.36 1.0 7.01 7.13 1.0 7.01
[ 6 4.60 0.7 7.73 5.56 1.0 8.21 8.10 1.0 7.98
7 5.44 1.0 8.57 6.29 0.7 8.94 8.68 0.8 8.56
8 6.61 0.7 9.74 7.20 1.0 9.85 9.39 1.0 9.27
9 10.0 5.0 13.13 4.6 11.01 5.0 13.66 4.4 13.29 5.0 13.17 3.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- . 1..........2LJIHPLLtfrrLerLihLLlFEtLIEtLLIEIEE .. 4L V &|_
050500505005050 3.3mm...
075200752007520 Spams
41 4.1 4... ee .1
rrsc
flak
.WQaQN

r

A>92Ium\nEv MpCU\bU F t n. a

 

 

 

do/dfldE (mb/sr-MeV)

 

"Ir 1

. . . ., . .
10.0 —
...;
5.03
2.5
0.0
10.0
7.5

5.0

2.5

0.0
10.0 :—

7.5 ~"—-

I'IY'IV

5.0

2.5

 

VTV‘I"

0.0 W..l.
0 10 20 30

—- Q Value (MeV)
(30

 

a"“1915. em=9°
l A A l l l 1 l l 1 L

 

10.0
7.5
5.0
2.5
0.0

10.0
7.5
5.0
2.5

0.0 ’*

10.0
7.5
5.0
2.5

0.0

IIITTIII'I

[r11

UVIUTYVIIVU'

TIIYYVTWVIY'I I

“Pb, e,,.,=6°

 

21°1=31. em=9°

 

 

YV'V

'l

 

VVTqY—TVUITTTTIYT'

 

Figure 5.4: Comparison of the neutron transfer spectra on 2""Pb region nuclei. Spec-
tra are plotted as functions both of reaction Q - values and excitation energies. Broad
peaks above the assumed background are shaded to help to compare the positions
and cross sections.

 

|
The com
because

different

1n the

 

PEak (1.3
MeV, 11',
POPUlate<
of afigula
angular r.
[Merm 8:
relat‘n-e ¥
(299/2. 1,
than the

a Spin-Hi

68

|209 Pb) =.-|2°8 Pb) I n), (5.4)
|210 311=|2°8 Pb) | 4(hg,,)+) I n), (5.5)
l’08 Pb) =l208 Pb) I 1702172)") I n)- (5.6)

The common term |208 Pb) may be neglected for simplicity as in the previous section,
because the physics of interest results from the comparisons of the spectra for the

different targets.

In the 208Pb("Li, 6Li)"'°9Pb reaction, the ground state (299/2, peak 1) and the third
peak (1.33 MeV, mainly 1j15/2, 3d5/2) are strongly populated, whereas the second (0.78
MeV, 1711/2) and the fourth peaks (2.24 MeV, mainly 297/2) are relatively weakly
populated. The relative intensities of these peaks can be explained by a combination
of angular momentum transfer and spin-flip processes. In this reaction, the favoured
angular momentum transfer for good matching is about 81‘: and no spin-flip is favoured
[Merm 88]. If these two matching conditions are applied to the first four peaks, the
relative populations can be understood easily. In fig. 5.3, the ground state of 209Pb
(299/2, I f = 4, j I = I f + %) which is formed by a no spin-flip transition, is stronger
than the fourth peak (2.24 MeV, 2g7/2, I, = 4, j, = I —- %) which is formed by
a spin-flip transition. The second peak (0.78 MeV, lill/g, If = 5, j, = If - %) is
relatively weak compared to the third peak, mainly a lj15/2 state (1.33 MeV, I, = 6,
j f = I; + -;-), which has a similar orbital angular momentum but is formed by a no
spin-flip transition. In these two cases, the spin-flip processes played an important
role in the transition strengths. Above 4 MeV of excitation energy, peaks are not
resolved as individual states but appear as a combination of many single states above

the substantial background.

In the 209Bi("Li, 6Li)21°Bi reaction, the kinematics and the transfer matching

69

conditions are very similar to those of the 208Pb(7Li,6Li) reaction, except that 209Bi
has one more proton in the 1h9/2 shell than 208Pb. This «(lhg/g) state couples with
the single particle states of the 209Pb nucleus and forms multiplets. The 1" ground
state of 210Bi results from one of the couplings between the 77(1h9/2) state and the
14299”) state, whereas the other coupled states, arising from the coupling of these
two states, make a large peak at 0.65 MeV (peak 1), a composite of many states. The
ground state is very weak and it is not seen as a separated peak. Peak 2 is also not
seen as a separated peak due to the overlap with peaks 1 and 3. Peak 3 is somewhat
broader than the comparable peak in the 209Pb nucleus. The strengths for peaks 2
and 3 are almost the same as those of the comparable peaks in 209Pb. Overall, the
shape of the spectrum looks very similar to that of the 209Pb nucleus except that the

spectrum is shifted to higher excitation energy by about 0.65 MeV.

If the spectra are plotted as functions of reaction - Q values as in fig. 5.4.(a),
the centroid of the each peak in 21"Bi appears at almost the same position as the
comparable peak in 209Pb. The existence of an extra proton in the 209Bi target
changed the widths of some peaks slightly, but the total strength of the comparable
peaks remained the same. In chap. 3, the contribution of an extra particle or hole in
the target to the transition probability of each final state is discussed. For the three
lowest orbits (295/2, 1311/2, 1j15/2), the average excitation energies for the [u(2gg/2) ®
«(Mg/2)], [vain/2 ® «(mg/2)] and [u(1j15/2) ® 7r(lgg/2)] multiplets due to coupling
with the target’s lhg/g state are calculated using the shell model (see chap. 3). The
excitation energies and reaction Q - values of the centroid are compared with the
experimental measurements for the 3 multiplets after the energies of individual states
in each multiplet are weighted by their cross sections (see tables 3.1, 3.2 and fig. 3.3).
The results show that the shell model calculations agree with this experiment very

well and one extra proton outside the closed shell of a heavy nucleus does not change

 

11

’5

I}
Stf

llt‘

1181
this

Stat

70

the reaction Q - values much, at most by 0.3 MeV at low excitation.

In the 207Pb(7Li, 6Li)"'°8Pb reaction, the conditions are the same as with the
208Pb("Li,6Li) reaction, except that 20"'Pb has a neutron hole state in the 3111/2 shell.
The 0+ ground state of 208Pb results when a transferred neutron fills the 3p1/2 hole
state. This state is shifted by about 3.3 MeV to lower energy from peak 1, a compos-
ite of 5‘ and 4‘ states resulting from the couplings between 3111/2 and 299/; states
(fig. 5.4). This 3.3 MeV is very similar to the outmost neutron’s binding energy differ-
ence (3.43 MeV) between the 208Pb and 2°9Pb nuclei. The ground state is extremely
weakly populated compared to the other states. This is because first this transition
involves a spin-flip process, and second the angular momentum transfer, 177, is much

smaller than the favoured angular momentum transfer, 7h.

At about 10 MeV excitation energy in all 3 spectra, broad peaks whose nature
has been questioned are seen. In the present experiment, these peaks are very weak
compared to the data obtained by using the 2"Ne or 12C beam [Fort 90, Merm 88].
However, the peaks may still be recognized above the large underlying background.
The starting points of the peaks are compared. All 3 broad peaks appeared at almost
the same reaction Q — values. But, when expressed in excitation energies, the peak of
209Bi("Li,6Li) reaction is shifted to higher excitation by about 0.6 MeV and the peak
of 207Pb(7'Li,"Li) reaction is shifted to higher excitation by 3.5 MeV. The broad peaks
have same reaction Q - values, but have different excitation energies. The result of
this comparison also suggests that the peaks have the characteristics of single particle

states.

At about 20 MeV of excitation energy in the 209Pb and 210Bi nuclei, another
broad peaks are observed. The peak is seen at about 25 MeV excitation energy in the

208Pb nucleus. The broad peaks at these excitation energies are also observed in the

experiments of 20’3Pb(2°Ne,19Ne) with Em = 40 MeV/n and 208Pb(36Ar,35Ar) with

71

Em = 41 MeV/ n [Chom 90]. However the reaction Q - values of these broad peaks
are nearly the same (within 1 MeV difference). From the comparison of the excitation
energies and the reaction Q — values, these peaks show the characteristics of single
particle states rather than GR states. The energy of the beam velocity of the projectile
breakup particles (180 MeV, 6Li) corresponds to 26.6 MeV excitation energy in 209Pb.
The excitation energy of the centroid is somewhat higher (by ~ 6.6 MeV) than the
beam velocity. In light ion projectile breakup experiments [Wu 79, Mats 78, Mats 80],
the projectile breakup processes are peaked at near or smaller than the energy of the
beam velocity. Thus it seems unlikely that these broad peaks are from the projectile
breakup processes. As in the previous section for (7Li,6Li) reactions on 90Zr regions

targets, their nature is not clearly understood.
5.4 90Zr, 91Zr, 89Y (7Li, 6He) Reactions

The energy spectra for the (7Li,6He) reactions on targets of 9"Zr, 91Zr and 89Y with
Em = 30 MeV/n are given in fig. 5.5. The 6He particles were measured at the
grazing angle 01“, = 6°. Parameters for the peaks are given in table 5.3. Eight
peaks are resolved at low excitation. In the 6He nucleus, as the threshold energy
for breakup into 5He + n is smaller than the excitation energy for the first excited
state, no ejectile excitation is possible. All the peaks, except peak 1, appear above
a substantial background in all three reactions. In fig. 5.6, they are compared as a
function of both the excitation energies of the residual nuclei, and the reaction Q —

values.

In the 90Zr("Li,"He)9’N b reaction, peak 1 is strongly populated. This peak is a
composite of the two states which are not resolved, the lgg/g (0.0 MeV) and 2191/;
(0.105 MeV) states [Fink 73, Knop 70, Vour 69]. The main contribution to the peak

72

90 91 69 7 . 6
Zr, Zr, Y ( L1, He), ®lab = 6°

 

 

 

 

 

 

 

 

 

 

5' I ‘ V ' fl ‘
6- _
; '1 ”Nb .
47 -
2r

A I

:5 o.

3f E

h 4}

m .

\ I

.0 3:
p

E 2;

a: .

o :

c: 17

Q :

b 0:

'U :
4?
3C-
2}
1}
0’

 

0 1 0 20 30
Ex. Energy (MeV)

Figure 5.5: Energy spectra of 9°Zr, 9‘ Zr, 89Y (Li, 6He) reactions (Em = 30 MeV/ n).
The dotted lines represent the background and the under lying spectra are obtained
after the background is subtracted. Arrows at the bottom of each spectrum represent
the centroid of the peaks.

73

Table 5.3: Excitation energies for the resolved peaks for (7Li, 6He) reactions on targets
of 9"Zr, 91Zr and 89Y. F is the full width at half maximum, Q is the reaction Q-Value
for a corresponding excitation energy and units are MeV. The uncertainty is about
0.15 MeV. a is the cross section in mb/sr and the uncertainty is about 20%. Peak 0
in the spectrum is the ground state which is shifted to lower energy due to an extra

 

 

 

 

 

 

 

 

 

 

 

 

 

 

hole state.
9(’Zr(7Li,"He)9‘N b 91Zr("Li,"He)”"’N b 89Y("Li,"He)"°Zr
Peak Ex. I‘ - Q 0 Ex. F - Q 0 Ex. F - Q a'
#
0 0.00 0.86 1.62
l 0.00 0.8 4.82 0.42 1.0 4.53 2.44 1.0 4.06
2 1.67 0.6 6.49 2.22 0.5 6.35 4.13 0.5 5.75
3 3.13 0.6 7.95 3.48 0.9 7.61 5.75 0.9 7.37
4 4.93 1.2 9.75 5.13 1.2 9.26 7.75 1.3 9.37
5 5.96 0.8 10.78 6.39 1.3 10.52 9.02 1.3 10.74
6 6.85 1.2 11.67 7.48 1.5 11.61 9.91 1.3 11.53
7 9.10 3.0 13.92 .72 9.35 3.0 13.48 .79 11.88 3.0 13.50 .68
8 11.86 0.6 16.68 12.52 0.8 16.65 15.02 1.0 16.64

 

 

 

 

”Zr,"2r,°°v("1.i.‘ne), 8m=6°

74

 

 

6.—
4i-
2}-
E :
3 O
1 5
t;
\ 4
.0
E 3
E3 2
C
v 1
\
b
“o 0
5
4
3
2
1
0

V V

Frer

 

 

 

 

ALlJWLl

1 l l

rTIWTrVIY'UYfi

Ole

L I I

-4

 

 

l l l l l

 

0

10

20

3O
— Q Value (MeV)

(a)

T r1 V V T rfilfir U T V I Y jf' I IiTq

6 1— —.

i 01 I

_ Nb ,

~ 1

4 - -«

F 3

2.

2 h J

- 1

0 :

5 ”Nb ‘1

4 -Z
3
2
1

O 2‘

5 ‘2

90 1

4 Zr -3

3 d

2 .

3

1 -.

0 1 I 1 A n 1 L r L 1 L 1:

”Zr,°‘Zr,°'Y("L1,°He). e,,,=6°

 

 

 

 

 

 

 

 

 

 

O 10 20 30
Ex. (MeV)

(b)

Figure 5.6: Comparison of the proton transfer spectra on 9"Zr region nuclei. Spectra
are compared as functions of reaction Q - values and excitation energies. Peaks 7
above the assumed background are shaded to help to compare the positions and cross
sections. Note that the small peaks near 32 MeV excitation energy arise from end
effects in the counter. Similar effects are seen in many other spectra.

75

is very likely from the 199/2 state. The 9°Zr target’s ground state has j’r = 0*,
a mixture of about 65% of «(2191/2)’, which is a closed shell, and about 35% of
«(2p1/2)‘21r(199/2)2, which has two proton holes in the 2121/2 state and two proton
particles in the 1g9/2 state [Baym 58]. Defining the closed shell as I O), the ground

state of the 9°Zr target can be represented by
I90 ZT)0+ = V0.65 I 0) + V0.35[W(2p1/2)-27r(lgg/g)+2I I 0). (5.7)

The ground state of the 91N b nucleus, j " = %+ is formed when a proton is transferred

to the 199/2 shell and can be written as
I91 NbI9/2+ = V 0-65l7'(199/2)l I 0) + V0-35l7'(2P1/2)_27’(199/2)+3l I 0)- (5-8)

The first excited state j’r = %- (0.105 MeV) results when a proton is transferred
to the 2p”; shell and forms a state with the combination [1r(2p1 /g)"‘1r(1g9/2)+2] I 0)
[Knop 70]. The weak population of this state may be eXplained by using the two
matching conditions for transfer reactions. First a spin-flip process is involved in a
transition to the 2121/; state, whereas it is not involved in a transition to the 199,;
state. It was evident in neutron stripping reactions that a non spin-flip transition is
preferable to a transition where a spin-flip process is involved. Secondly, the favoured
angular momentum transfer, 5”: is much larger than that of a transition to 2p1/2(l =
1), while the angular momentum transfer to the ground state (299ml = 4) is closer

to the favoured transfer condition.

In reactions with low incident energies, the angular momentum mismatch between
the entrance and exit channel is small and the favoured angular momentum transfer
becomes small, and thus the relative ratio of the population for the 2121/2 state will
be increased. In the 9°Zr(3He,d) experiment done at an incident energy of 6 MeV/ n,
where the favoured momentum transfer is about 2h, the 2121 ,2 state is much more

strongly excited than in the present reaction [Knop 70].

76

Peak 3 (3.25 MeV), which is strongly populated, is mainly a 2d5/2 state. The an-
gular momentum transfer to this 2:15,; state is 271 and no spin-flip process is involved,
while the angular momentum transfer to the ground state is 4’2 and no spin-flip is
involved. The smaller angular momentum transfer is a good reason for the relatively
weaker strength for peak 3 than that of the ground state. Peaks of 4, 5 and 6 are
the sum of many single particle states which were resolved as separate states in a low

energy experiment [Zism 73].

A large peak is seen at 9.1 MeV (peak 7). When the reaction Q - value and
the excitation energy are compared with those of peaks 7 of other spectra, peaks
7 appeared at similar reaction Q - values but different excitation energies. The
comaprison suggests that peaks 7 seem to be single particle states. The sharp peak
seen at 11.9 MeV (peak 8) is an isobaric analog state [Pink 73]. No recognizable peak
is observed above 12 MeV. The spectrum stays fairly flat from 15 MeV excitation

energy up to about 30 MeV excitation energy.

One spectrum was measured out to 50 MeV excitation energy (see fig. 6.4). No
large broad peak is observed at around 13 MeV of excitation energy in this reaction,
whereas a large broad peak was observed in neutron stripping reactions on the 9°Zr
region targets. This suggests that the broad peaks seen in (7Li,6Li) reactions are from
one step processes rather than multi-step processes. If they were made by multi-step
processes (GR excitation followed by transfer reaction), they also should be seen in
(7Li,6He) reactions, because the cross sections and mechanisms for both reactions are

very similar.

In the 91Zr("Li, 6He) reaction, the proton single particle states form multiplets
when coupled with the target’s ground state u(d5/2). For example, the «(99/2) state
couples with the u(d5/2) state and forms a («(99/2), V(d5/2)) multiplet with j "' ranging

from 2+ to 7+, which makes up most of peak 1. Similarly, «(m/2) couples with V(d5/2)

77

and forms a (7r(p1 l2), V(d5/2)) multiplet, 2’ and 3‘, which is a small fraction of peak
1. The ground state of the 92Nb nucleus, j = 7* is so weakly excited that it is not
separated from peak 1. The centroid of peak 1 is positioned at an excitation energy

of 0.42 MeV, 0.3 MeV lower than the comparable peak in the 90Zr(7Li,6Li) reaction,

due to the coupling between the 1r(g9 fl) and V(d5/2) states.

Peak 2 and peak 3 appear to be weaker than the corresponding peaks in the
9°Zr(7Li,6He) reaction. This results from the broadening of the peaks due to the
couplings with the u(d5/2) state. Overall, all the peaks, except peak 1 in this spectrum,
are broadened and the ratio of peak to background is not as good as in the 91Nb
spectrum. Peak 8, which is very sharp in 91Nb, is almost hidden in the background
and is not seen clearly. The interactions between the V(2d5/2) state and the proton’s
single particle state are very similar to the interactions between the «(299/2) state
and the neutron single particle states in the 209Bi("Li,6Li) reaction. Peak 7 which is
shifted to higher excitation energy by 0.25 MeV from the comparable peak of 91Nb

appears to be the sum of many single particle states.

In the 89Y("'Li, 6He)9°Zr reaction, the spectrum is very similar to that of the
90Zr(7Li,6He) reaction except that the ground state is shifted to lower energy. As the
ground state of 89Y is j’r = f, proton single particle states couple with this state
to form multiplets. The ground state of the residual nucleus 9"Zr is formed when a
transferred proton fills the 2p”; hole state. This transition is very similar to that
of the 207Pb(+n) reaction where the ground state is formed when a neutron fills the
neutron hole state, u(3p1/2). In both cases, the ground states are very weakly excited

because of small values of 2 j + 1, and the poor transfer matching conditions.

Peak 1 is a composite of many states and is mainly populated when a proton is
transferred to the 199]; shell. This lgg/g state couples with the 7r(2p1/2)"l state and

forms 4' and 5‘ states, where the 5' state is more strongly populated. The reaction

78

Q - value difference between the ground states of the 90Zr("'Li,6He) and 89Y(7Li,6He)
reactions is 3.2 MeV, which is the same as the proton’s binding energy difference in
”Zr and 91N b nuclei. While in peaks 1 of these two reactions, a difference in reaction
Q - value of about 0.76 MeV is observed. This results from the coupling between the
«(199/2) and 1r(2p1/2)‘1 states in the 89Y(+p) reaction, but the strengths of peaks 1
in each of the 3 spectra are almost the same. Similar differences are also observed in

peaks 2 and 3.

Peak 7 is seen with the same strength as in the other two reactions but is shifted
to higher excitation as in peaks 1. The interactions between the proton single particle
states and the proton hole state does not change the positions of the peaks plotted
versus reaction Q - values significantly as were expected from the shell model cal-
culations. The deviations of the peaks in reaction Q - values ranged from 0. to 0.9

MeV for the peaks in the 91Nb spectrum.

5.5 208Pb, 209Bi, 207Pb (7Li, 6He) Reactions

The spectra for the (7Li, 6He) reactions on targets of 208Pb, 2093i and 2”Pb with
Egnc = 30 MeV/n are shown in fig. 5.7. The ejectile, 6He was measured at the
grazing angle, 010;, = 9°. Parameters for the peaks are given in table 5.4. Seven peaks
are resolved at low excitation energies in each spectrum and they are plotted as a
function of both excitation energies and reaction Q - values in fig. 5.8. All the peaks

are seen above a substantial underlying background.

In the 208Pb("Li,6He)2°9Bi reaction, the first 4 single particle states lhg/g (ground
state), 2f7/2 (0.71 MeV), 1i13/2 (1.4 MeV) and 2f5/2 (2.63 MeV), and 3 composite
states at excitation energies 4.03 MeV, 5.22 MeV and 8.35 MeV are resolved. The

ground state (j1r = g-) of 209Bi is not separated clearly from peaks 2 and 3 which have

79

 

: ""rr' 1 , WI
2.5,- 20931

2.0:- 2 .
1.5?
1.0:-
o.5§- '

0'03 M “U n ...$‘e#=“‘i“”'iI-h~hfl1~flllmndd
2.5} .
2.0:-
1.5}
1.0;-
o.5:- .- '
0.0: ,. ,.,: , “fi-mxwuuauummmum

M h

  

ZIOPO

Q
o
I
.
LlJLAJlAAHl-AA

l

 

da/dfldE (mb/sr—MeV)

 

#iLAA

2.5- 2°°Bi
2.05
1.5:-
1.0:-
o.5} .
0.0; _ .f . ... ' ‘ ‘3‘— -5 Ad's tub-[Ln lHflalli...”

 

 

Ex. Energy (MeV)

Figure 5.7: Energy spectra of 2°8Pb, 2093i, 20“'Pb (7Li, 6He) reactions (Em = 30
MeV/ n). The dotted lines represent the background and the under lying spectra are
obtained after the background is subtracted. Arrows at the bottom of each spectrum
represent the centroid of the peaks.

80

Table 5.4: Excitation energies for the resolved peaks for (7Li, 6He) reactions on targets
of 208Pb, 2”Bi and 20"Pb. F is the full width at half maximum, Q is the reaction Q
— Value for the corresponding excitation energy and units are MeV. The uncertainty
is about 0.15 MeV. 17 is the cross section in mb/sr and the uncertainty is about 20%.
Peak 0 in the spectrum is the ground state which is shifted to lower energy due an
extra hole state.

 

208pb(7Ll,6He)2ogBi 2093i(7Ll,6He)210P0 II 2°7Pb(7Li,°He)’“Bi

 

Peak Ex. I‘ -Q 0 Ex. P -Q 0 Ex. I‘ -Q a'

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

#

0 0.00 0.3 4.99 I

1 0.00 0.8 6.18 1.39 0.8 6.38 0.03 0.9 6.30

2 0.71 0.6 6.89 2.12 0.7 7.11 0.90 0.9 7.17

3 1.40 0.7 7.58 2.73 0.7 7.72 1.52 0.6 7.79

4 2.63 0.8 8.81 4.10 1.0 9.09 2.70 1.0 8.97

5 4.03 1.1 10.21 5.48 0.8 10.47 4.30 1.0 10.57

6 5.22 0.8 11.40 6.32 0.7 11.31 I520 0.9 11.47

7 8.35 4.0 14.53 .71 9.66 4.0 14.65 .80 8.41 4.0 14.68 .75

 

81

 

 

”Pb.”ai.‘"Pb('u.°He). ewes“ “Pb.”Bi.'°"Pb('u.'He). em=9°
2.5}H'HH'HH'HH" 2.5;.,....,....,....,._.€
2.03 2.0 — -
1.5 E 1.5 — 1
1.0 I 1.0 .- -5

0.5 0.5 ;- 2093i

111.leLAA

 

 

 

3..1...1.. 3 i.
0.0. II I [VIII I IIIJ 0.0

da/dndE (mb/sr—MeV)

 

2.5 .— —:- 2.5. '
2.0} - 2.0:
1.5} -: 1.5 1:—
1.0.— — 1.0:
0.5%— zropo - 0.5
I 4
g:g;:4I::::I¢::4I::::I:E 3%
2.0.— — 2.0:
1.5— -3 1.5__
1.03— —‘ 1.0:
0.5:— 266Bi — 0.55

 

 

 

 

 

 

l l L l L l L I L 1_L j l I A : l
0.0 l 0.0
10 20 30 40

— Q Value (MeV)

(80

 

Figure 5.8: Comparison of the proton transfer spectra on 208Pb region nuclei. Spectra
are compared as functions of reaction Q — values and excitation energies. Peaks 7

above the assumed background are shaded to help to compare the positions and corss
sections.

82

'1?

J = - and 1331+ respectively. It was extracted only by using a curve fitting program.

”IN

Peak 4 appears above a substantial background and is separated clearly from peaks
2 and 3. The relative strengths of these single particle states may be explained by

using the two matching conditions which were described in previous sections.

The ground state, 1179/2, has a high angular momentum Sh and a spin-flip is
involved in the transition, whereas peak 3, 1i13/2, has a similar value of angular
momentum 615 but no spin-flip is involved. The favoured angular momentum transfer
between the entrance channel and exit channel of this reaction is about 671. Thus

peak 3, which has I = 6 and no spin-flip transition is stronger than the ground state.

As another example, consider peak 2 and peak 4, which have the same angular
momentum. Peak 2 (2 fig), which has an angular momentum I = 3 with no spin-
flip transition, is more strongly populated than peak 4 (2 f5”), which has the same
angular momentum! = 3 with a spin-flip process. In this case, the difference between
the two transition strengths results only from the spin-flip process. Similar examples
explaining the relative transition strength using the matching conditions for transfer
processes were given for the (12C,“B) and (160,15N) reactions on the 2”Pb target

[Merm 88].

In the 209Bi("Li,6He)21°Po reaction, the energy spectrum of 210P0 is very similar
to that of the 2°8Pb(7Li,6He) reaction. The target has one more proton in the 1119/2
state than the 208Pb nucleus and this state couples with the proton single particle
states and makes many multiplets. When a proton is transferred to the 1179/; state,
as there are two protons in the same state, only even value of j (from 0* to 8+)
are allowed. The ground state of 210Po (j = 0*) is very weakly populated due to
a small value of 21° + 1, and it is shifted to lower energy by 1.39 MeV from the

centroid of the (1r( 1119/2), 1r(1h9/2)) multiplet. Comparing the spectrum with that of

 

83

the 20I3Pb("'Li,6He) reaction as a function of the reaction Q — values in fig. 5.8, no
significant difference is seen between the two spectra except that peak 7 of 210P0 is
slightly wider. Even the relative strengths of the peaks between the two spectra are
almost the same. Thus there is evidence that an extra proton in the lhg/g state does

not change the shape of the spectrum either at low excitation or at high excitation.

For the lowest 3 single particle states (1h9/2,2f7/2 and 1i13/2), the excitation en-
ergy for the centroid of each multiplet coupled with the target’s state (1719/2) were
calculated in chap. 3 using the shell model. The relative values for the excitation
energies of the centroid of the multiplets weighted by a cross section have very simi-
lar values to those of the single particle states before they are split even though the
multiplet states are spread over 3~4 MeV in excitation energy (see table 3.2 and
fig. 3.3). The comparison of the experimental values to the shell model calculations
shows that they agree within 0.3 MeV. As the interactions between the two states are
not very dependent on their excitation energies, these calculations for low excitation
states can be applied to high excitation states, and the shift of excitation energies in

high lying single particle states due to the 1129/2 proton state may be assumed to be

about 0.3 MeV.

In the 20"Pb("Li,6He)tmsBi reaction, the proton single particle states couple with
the target state (3111/2), and forming a doublet. For example, the single particle state,
lhg/g, couples with the 3p,” state to form 4+ and 5+ states, where the ground state
is 5*. The energy difference between the 4* and 5+ states is so small that they are
not separated in this spectrum. Not only the 1h9/2 state but also other single particle
states are split into two states with small gaps [Alfo 70]. The centroid excitation
energies of these multiplets at low excitation and the relative strengths between the

states are not changed much compared to the spectra of the 209Bi and 210Po nuclei.

Only the broad peak 7 (8.41 MeV) of the 2033i nucleus becomes slightly broader

84

compared to the same peak(7) in the 2”Hi nucleus, but has almost the same width

as peak 7 in the 210Po nucleus.

Overall, the spectrum of the 207'Pb(7Li,6He) reaction is almost the same as those
of the same reactions on targets of 208Pb and 209Bi, even at high excitation. The shell
model calculations, weighted by a cross section, for proton stripping on the 2("Pb
target are given in table 3.2, and the results show that the relative excitation energies
of the centroid of the multiplets are not changed much from the energies of the single

particle states.

Broad peaks are seen at excitation energies of 8.35, 9.66 and 8.41 MeV in the
spectra of the 208Pb, 209Bi and 20"'Pb(7Li,6He) reactions respectively. The peak from
the 209Bi target is shifted to higher excitation energy by about 1.3 MeV compared
to the other two peaks. But the reaction Q - values of the centroid for these broad
peaks are all within 0.3 MeV. The comparison shows that these broad peaks have the

characteristics of single particle states rather GR states.

Chapter 6

Analysis of Background

6.1 Introduction

In single particle stripping reactions there is a substantial background at high excita-
tion. In many cases, this background is so strong that the extraction of information at
high excitation is difficult. One major possible source of the background at high exci-
tation in single particle stripping reactions is breakup of the projectile. The projectile
breakup processes may be divided into sequential and direct processes according to
the time scale of the reaction. In sequential breakup, which has a relatively long life
time, the ejectile is produced in a particle unstable state which will subsequently de-
cay. In direct breakup on the other hand the projectile breaks up into a few fragments
due to the interaction with the target nucleus with a corresponding nuclear reaction
time. From now on, the discussion of the direct breakup will be limited to the process

of projectile breakup into two fragments.

In a direct breakup process the fragments are related to the projectile and hence
exhibit the properties of the projectile [Mei j 85]. In the past the background was often
estimated empirically and only occasionally was calculated theoretically. There are
several theories to calculate the background from a projectile breakup processes such

as the Serber Model 'ISerb 48], the Quasi Free Breakup Model, the Distorted Wave

85

86

Figure 6.1: Schematic diagram for the projectile direct breakup processes with 3 body
kinematics

Breakup Model [Meij 85] and a semi-classical theory to calculate the background
from a single particle transfer to continuum states developed by Bonaccorso and Brink
[Bona 85, Bona 87, Bona 88]. We chose two theories, the Serber Model which is based
on the geometrical structures of the nucleus to find a nucleon stripping cross section
and has been used commonly in the past, and a semi-classical theory developed by
Brink and Bonaccorso, which calculates a transition cross section of a single particle

from a bound state in the projectile to a continuum states of the target.

6.2 Projectile Breakup Background

6.2.1 3 - Body Kinematics of Projectile Direct Breakup
Process

In direct breakup processes in which the projectile breaks up into 2 fragments, there
are 3 fragments in the final state. The schematic representation for the 3 body motion

due to the projectile breakup

a+A——)1+2+3 (6.1)

87

is given in fig. (6.1), where A is the target and is represented as 3 in the final state. In
center of mass frame (CM), the projectile breakup cross section can be expressed as
functions of the parameters such as momenta, masses, and angles given in these two
motions. If a single fragment only is measured, the parameters of this cross section
can be changed into the single fragment’s parameters by averaging the contribution

from the other fragment’s parameters.

From Fermi’s golden rule, the transition probability per unit time from the initial

state I i) to the final state | f) may be written as
21r 2
Rfi = f | M1.- | MEI), (6-2)

where I M f,- I2 is a transition matrix element and p( E!) is the number of final states
with energy E f. Then the transition cross section per unit solid angle and per unit

energy is

dazfl
v.

_ 21E . 2
- h p. IMM MEI), (53)

where p,- and p.- are the reduced mass and momentum of the entrance channel in the

CM frame, respectively.

The three particles in the final state have 9 degrees of freedom, but 3 of them can
be eliminated due to momentum conservation. Then the cross section in the phase

space of 6 independent variables can be written as [Ohls 65, Meij 85]

 

d" - d" _
p(Ef) = p22fhi? 3(21rh)36(E¢o¢ - E1_23 - E2._3)

 

Pi—23P3-3dP1-23dP2_3dQ1-23d92-3 6

(27'5” (Etot - E1—23 - E2—3)

88

2 3
= W(Fl—23fl2-3)5IE1—23(E¢co¢ - E1-23)I%dE1—23dE2-3 °

dfll—23d92-36(Etot — E1-23 - E2—3)

= P1(E1—23)d91-23dE1—23d92—3dEfot, (6-4)

where E143 and Efo, are the kinetic energies in CM frame, and

E143 = Pi-za
211‘1-23’
Etcot = 19%;”- + £213— : 131-23 + E2—3- (6.5)
2/‘l-23 2I12—3

If eq. (6.4) is averaged over the solid angle (12.3 and integrated by E50,, then the

result is

 

2 m m m
P1(El-23)dE1-23dfll_23 ( l 2 3

i
2

dE1_23df21-23, (6.6)

where M is m1 + mg + m3. The relation of the phase space between the CM frame

and the laboratory frame is

l.
C 2
dEIdQI = (g) 63:40:, (6.7)

where c and I denote CM frame and laboratory frame respectively, Ef is E1..23(m2 +

m3)/M and E] is the kinetic energy of the fragment 1.

Now the phase space factor p1(E1_23) in the CM frame may be expressed as

the phase space factor for the single measurement in the laboratory frame, p1(EI)

[Ohls 65] ,

2 Mi(m m m )g
I I I I = 1 2 3 I .
p1(E,)dE,dQ,d92 (27"h)6 (mg + m3)? VE1

 

.1.

(mEfo, - EI + 2011/Ei cos OI — a?) 2 - dEIdflIdfl'z, (6.8)

M

89

2
where BI is scattering angle of fragment 1 in the laboratory system, and a1 is (EILEEN-fl

1

where VCM is the velocity of the center of mass.

If eq. (6.8) is substituted into eq. (6.3) and integrated about 0;, then the differen-
tial cross section for the single measurement of the projectile breakup fragment can
be expressed as functions of E] and GI ,

(I20 8w2ma

__ = — . 2 I .
daldEl 52k“ I M.“ I p(El)’ (6 9)

where a subscript “a” denotes projectile. For the measurement of the two fragments

1 and 2 in coincidence, the phase space factor and the cross section are

 

l mlmgmgplpg
p E1 = , 6.10
1( I) (2777”; m; + m3 — mgm-rfll' :- ( )
and
(Pa 22m,
= —— I 14,. I” MEI), (6.11)

dflldflngI hzka
where B is the incident particle’s momentum. The detailed derivation may be found

in previous reports [Ohls 65, Fuch 82].

Now the phase space factor is known explicitly, but the transition matrix still must
be formulated. To calculate the projectile breakup cross section for the (7Li,6Li) and
(7Li,6He) reactions, eq. (6.8) will be used as the phase space factor with the Serber
Model for the transition matrix. In the case of the coincidence measurement of
7Li ——4 6He + p, eqs. (6.10) and (6.11) will be used for the cross section with the

Serber Model transition matrix.

6.2.2 Projectile Breakup Cross Section Calculations Using
Serber Model

In calculating the projectile breakup cross sections of 7Li into 6He + p and 6Li + 11

using the Serber Model [Serb 48], it is assumed that one of the nucleons in the pro-

90

jectile is stripped off by the collision and the ejectile continues to move with its same
momentum 13} as at the moment of the breakup. The target is assumed to play no role
except to breakup the projectile at the collision, and is assumed to be transparent to
the breakup fragments. The coulomb and spin-spin interactions between the target
and the projectile are neglected. The residual nucleus and the ejectile are assumed to
remain in their ground states after the breakup processes. In this model the proba-
bility of observing a particle with momentum 13', is given by IM,,-I2= P(p,) ~ |¢(fi)|2,
where |¢(f)')I2 is the Fourier transform of the relative wave function between the two
constituents in the projectile and [7' is the ejectile’s internal momentum in the pro jec-

tile.

Using eq. (6.9) from the previous section, the differential cross section for observing

a fragment from the breakup process with energy E, can be written as

113—dim: ‘HN R'&¢—|¢(fll’p(5 21) (6.12)

 

35(5) = (21”,) )(%/¢r) )exp( --p 1")d3r, (6.13)
where N,, 3., R, and p(E,) are the normalization constant, target’s radius, projec-
tile’s radius and density of the final states respectively, rm, and E, are the mass and
kinetic energy of projectile, and 13' = 15', -— 13', where 13', is an observed final momentum
of the ejectile and 13', is its initial momentum in the projectile, corresponding to the

beam velocity and

I13]2 = Ifiolz 'l’ 2mrE1: ‘ 2IfioI V 277125.: ' 60301:, (6.14)

where m, and 0, are the ejectile’s mass and scattering angle.

A wave function of the Eckart form [Lim 73]

 

¢(r) = C (gr-Y 6:" (1 — e-fi')‘ (6.15)

91

is used for the relative wave function of the constituents in the projectile, where
a = fizz/h with p and 6 being the reduced mass and separation energy, and C is
a normalization constant. The constant ,6 is determined to give the best fit to the
experimental data. In this analysis 6 = 1.0 is used. By substituting eq. (6.15) into

eq. (6.13), and using the integral formula of

-3,-
_i-.F 6 _ 4W
/d3re q _r _ _,32 + q” (6.16)
the following result is obtained for 45(5) ,
1 4 6

 

 

 

 

602*) = C (8m)%(

(21r6)% 122+cr2 -pz+(a+fl)’+p’+(a+23)’

4 1
_p’ + (a + 36)2 + P2 + (a + 43?). (6°17)

 

 

Thus the differential cross section for the projectile breakup can be obtained by
substituting eq. 6.17 into eq. 6.12. The calculations were done for the kinetic energies
of ejectiles from 1 MeV in 1 MeV steps. The final results are expressed as a function
of the excitation energies of the residual nuclei for the comparison with the experi-
mental data, and are normalized to the experimental results. The excitation energies
corresponding to the ejectile’s incident energies assuming ejectiles velocities equal to

the beam velocity are marked with arrows.

6.2.3 Comparison of Serber Model Calculations with Ex-
perimental Data

The calculated projectile breakup cross sections for 7Li into 6Li + n, and 7Li into
6He + p on 9°Zr region and '2me region targets at Em = 30 MeV/n are given in
figs. (6.2) and (6.3) together with the experimental spectra from the (7Li,°Li) and

(7Li,6He) reactions. The calculations are normalized to the experimental data.

92

 

 

    

 

 

 

 

 

9 7 - 6 - 208 209 . 207 7 . 6 .
”Zr, ”Zr, 3 Y ( L1, L1) Pb, 131, Pb ( L1, L1)
r I l I r1 I I I I I I l I IfiII I TI II Iq :irt I I I] I I I I l I I I I I I I I I I I I
p " 20. a O :
15 f 9121.. “=60 10.0 r Pb' 9 8 ‘.
1 . 1
. 7.5 E- x ——
10 - C . I
C I 1 1
' I 5-0 :' 1
5 L E :
I 2.5 L- -:
9 I. " :
0 ’. ....1..L.1. . - 00.1. .. ....1HH .L. .9
2 OF I I I I I I I I h l I I I III I I I I I . J fl I I I I I I T I I I I l :
l ' ’8 o 'I - 1
Zr. O86 ._ - _.
:3 15 r I . . 10.0 _- 31°31. 9:9" I
\ : E
g - 7.6
v E
a: 5.0_
g :
v 2.5:
\ .
b
'6

0.0 I
10.0
7.5
5.0

2.5 I

 

 

 

 

 

 

0.0 “

 

O 10 20 30 40
Ex. (MeV)

Figure 6.2: Calculated breakup cross sections of 7Li (E = 30 MeV/n) into 6Li + n
using the Serber Model are compared with the experimental spectra. The solid lines
indicate the calculated breakup cross sections which are normalized to the experi-
mental results. The excitation energies which correspond to 6Li’s incident energies of
the beam velocity are marked with arrows.

93

90Zr, 91Zr, 89Y (7Li,°He)

 

(convict-roads
l

da/deE (mb/sr—MeV)

      
 
     

TTfiIIIIIIIIII’TI

t1 IV
I 4
—I

1
"Nb. o=6° ;

I

 

llllllllll

 

N G uh 00
III

IIIITIIIII

 

O
tvlvrv
O
I.—
p

”Zr. 0-6‘

_’
+— d-
l l 1111“].

 

 

 

1 A l A l l l l l

10 20 30 40
Ex. (MeV)

(a)

 

mm), ”“131, 2”Pb ("L1.°He)
2.5 :' ITr ' I l I ‘3
zoom. =9. “1+ .

2.0 _ .
1.5 I— -:

1.0 :-

 

 

 

 

 

Figure 6.3: Calculated breakup cross sections of 7Li (Em = 30 MeV/n) into 6He + p
using the Serber Model are compared with the experimental spectra. The solid lines
indicate the calculated breakup cross sections which are normalized to the experi-
mental data. The excitation energies which correspond to 6He’s incident energies of
the beam velocity are marked with arrows.

94

The experimental spectra for the (7Li,6Li) reactions are shown out to 40 MeV
of excitation energies and they are peaked at excitation energies ~ 25 MeV for 9"Zr
region targets, and at ~ 20,22 and 26 MeV for 2°8Pb, 20""Bi and 20"'Pb targets re-
spectively. However, the calculated breakup spectra are peaked close to the incident
energies of the beam velocity but smaller than them, by about 5 MeV, due to the
nucleon’s binding energy in the projectile. If the peaks of the experimental spectra
are caused by the direct breakup of the projectile, then they should appear always
at energies smaller than the energy of a 6Li particle which corresponds to the beam
velocity, and therefore higher in excitation energies as were seen in light ion breakup
experiments [Wu 78, Wu 79, Mats 78, Mats 80] such as (d, p), (a,t), (01,3He) and
(3He,p). But the experimental spectra observed are peaked at energies which are
higher than those consultant to the beam velocity by about several MeV for lead
region targets, and 3 ~ 5 MeV for zirconium region targets. These differences in the
peaks make it difficult to assume that the peaks of the experimental spectra are from

the direct breakup of the projectile.

In fig. (6.3) for (7Li,6He) reactions, the experimental spectra are given out to ~ 30
MeV of excitation energies. A very large fraction of the background is predicted as
projectile breakup by the calculations. The calculated spectra give somewhat better
agreement to the experimental spectra than the calculated spectra for the neutron
stripping reactions. Except in the 9°Zr target, the experimental spectra are not
observed up to high enough excitation energy to determine clearly where the spectrum

peaks.

The 9°Zr(7Li,6He) reaction was measured out to 50 MeV excitation with two dif-
ferent runs using the same conditions, except for the dipole magnetic field, and con-
necting the two spectra together. The extended breakup cross section on the 90Zr

target is given in fig. (6.4). The calculated cross section is normalized to the exper-

95

 

90 7 .6 _ o
Zr ( L1, He), (blah—6
I II I III II II I IIIII I

 

 

 

 

 

 

 

4 _ ' ‘ I I ' ' r 1‘
r; ’ I 7
m I “Nb
5. Sr -
L. I
Q “‘4“
.0 .
E 2 — _.
V .- ‘
5 : 1
C ’ ‘ ~
'0 1 — .
\ ..
b .
'o . II x

0 Li 1 1 1 1 I 1 1 1 1 I 1 1 1 1 l 1 1 1 1 I 1 1 1 1 l

0 10 20 30 40 50

Figure 6.4: Breakup cross section calculations of 7‘Li (Em. = 30 MeV/n) into 6He

+ p on 9"Zr target using Serber Model. The two spectra are connected at E3. ~ 26
MeV.

96

imental data. From excitation energies above 35 MeV, the calculated breakup cross
section agrees perfectly with the experimental spectrum. This good agreement per-
haps suggests that the high lying spectra (higher than 35 MeV) are mainly the results
of the projectile breakup processes rather than from the formation of the compound
states. In the (7Li,6He) reactions on targets of 91Zr and 89Y, since the excitation
energies are given only up to ~ 35 MeV, the comparison with the calculations is more
difficult. But, from the given spectra which are very similar to the spectrum from
the 9°Zr target, the similar spectra are expected at high excitation where Ex. 2 35
MeV from the 91 Zr and 89Y targets. One more or one less nucleon in a heavy nucleus
is not expected to be very important to the background at high excitation (Ex. 2
10 MeV). Even at low excitation the whole shape is not changed significantly by an

extra nucleon.

In the 208p}, region targets, the cross sections for the (7Li,6He) reactions increase
continuously up to Ex ~ 30 MeV. The calculated breakup cross sections normalized
to the experimental data explain most of the background in the given spectra. The
ratios of the contributions of the calculated breakup spectra to the experimental

spectra for the three 2”Pb region targets appears to be similar.

Since no spectra were measured at excitation energies higher than 30 MeV, it is
very difficult to know whether the normalization was done correctly or not. For further
investigations on this subject, it would be necessary to measure the higher excitation
energy region up to 50 MeV or so, about twice the beam energy per nucleon so that
the peak of the breakup processes can be seen clearly. Even though the coulomb
interaction, spin-spin couplings, and the quantum states of the transferred nucleon
are not considered, the simple Serber Model appears to provide reasonable agreement

with the shape of the continuum above about 35 MeV excitation energy.

97

6.3 Single Nucleon Transfer to Continuum States
Using a Semi-Classical Theory

6.3.1 Kinematics of Single Nucleon Transfer to Continuum
States

A semi-classical theory which was developed by Brink and Bonaccorso [Bona 85,
Bona 87, Bona 88] is used to explain the background for single nucleon stripping
reactions of (7Li, 6Li) and (7Li, 6He). In this theory, the colliding nuclei are assumed to
move along classical trajectories, but the transfer is calculated by quantum mechanics.
In this model, a nucleon makes a transition from an initial state $1 with orbital
angular momentum 11, m1, energy 61 and potential V1 in the projectile to a final state
$2 with angular momentum 12,m2, energy 62 and potential V,» in the target nucleus.
The amplitude for the transfer from the initial state 1 to the final state 2 becomes

using the time dependent perturbation formula

1 00

2"”: —oo
This perturbation integral can be transformed to a surface integral over a surface 2
drawn between the two nuclei perpendicular to the line joining their centers at the
point of closest approach (fig. 6.5). This surface lies between the two potentials V1
and V2 and which divides the space into regions R1 and R2, at a distance d; from the
center of the projectile and d2 from the target, with d1 + d2 = d. Then the matrix

element can be written

(ng | V; |¢1) = [m ¢;(r,t)V2(r,t)z/)1(r,t)d3r+A:¢;(r,t)Vl(r,t)1/21(r,t)d3r. (6.19)

The first term in eq. (6.19) can be reduced using the Schroedinger equation for 1121

/ w'Wzb1d3r: / $‘(ih2+flvz)¢1d3r (6.20)
m 2 Rx 2 at 2m

-
t

 

 

 

 

Figure 6.5: Coordinate system for transfer amplitude.

Applying Green’s theorem,

h?
[R . ¢EVI¢1J3T = 2—m- Ldfi-(wswl-wrwa

+/R (ih—¢2+—V21/)2)’ ¢1d3r+ih§tl 11);1/) t/Jldar(6. 21)

where (IS is a surface element normal to R]. If eq. (6.21) is integrated by the time
between t = —oo and co, the third term will vanish because of no overlap between
11)] and 11);. Then the matrix element (11); | V, | IA) can be reduced using Schrodinger

equation for 1,122

2
(dell/1W1) = thzdg (¢;V¢1-¢1V¢;)
+jR ¢,%¢1d3r+ [R zpmwrdar. (6.22)

In a peripheral collision where the two particles approach along the z-axis with
relative velocity v, the surface is parallel to the z-y plane, and the closest distance
between the two particles is d = (11 + d2, there is no overlap between the potentials

V1 and V2 and we can choose 2 so that V2(r,t) = 0 for all points in R1 on one side

 

 

99

of the surface, while V1(r, t) = 0 for all points in R2 on the other side. Then the last

two terms in eq. (6.22) vanish and the transfer amplitude becomes [Mona 85]

h co ~
A,, = .2_, .0. dt [2 d5 - (¢;V¢1 — 61%;). (6.23)

m:

By using the double Fourier transform, the coordinate space wave function with

respect to the coordinates y and 2 parallel to the surface is

~

66. k... k.) = f: f: dydz e-‘<v*~+'*')¢(z,y,z). (6.24)

The transfer amplitude was derived by Brink et. a1 [Mona 85, Bona 87] and after

considerable algebra, the result can be written

 

.h 00 ~ ~
‘ (116,072 + k3)%¢;(d2, kw k2)z/21(d1, k,, k1), (6.25)

A21 =
21rmv -oo

where 1121 and 1,122 are bound state wave functions and have single particle energies 61

 

and 62 where m is the nucleon mass, v = \/2(ECM — VCM)/u is the relative velocity
between the two nuclei at the closest approach where p, ECM and V0” are reduced

mass, relative kinetic energy and Coulomb energy at the closest approach, and

 

1127?
6) — — 2m , for l— 1,2, (6.26)
is the binding energy and 1) is defined by
17’ = k? + 71’ = k: + 73, (6.27)

where k; is the relative value of the transferred nucleon to the first nucleus and k2

relative to the second. Then

h(k2 — k1) = mv. (6.28)

The reaction Q-value is the nucleon’s binding energy difference between the two

nuclei

h2
Q = C1 - 62: 27:“: - kg) (6.29)

100
Eqs. (6.28) and (6.29) give

161 = —(Q + émvzflhv , and k2 = —-(Q — émvzvhv. (6.30)

The wave functions $1M}, Icy, In) and (52(d2, Icy, log) are amplitudes for finding the
nucleon with z-component of momentum k; in the first nucleus and kg in the second.
For a peripheral reaction, (11 and d: are large enough to use the Hankel function’s
asymptotic form for the bound initial state (b,- with l;,m,- and 6;, and the unbound

final state 16, with I f, m I and c, [Bona 88]
«6(1) 2 Ci‘hff’avrmmw, 6), (6.31)
and

Mr) 2 Cfélhif)(kfl') - W1h§;’(kfr>m,m,w, «6). (6.32)

where h)“ and hl') are Hankel functions and
k, = 2méf/h2. (6.33)

where e, is the kinetic energy of the transferred nucleon. The double Fourier transform

of 1b,(r) and ¢f(r) are

KZ‘.‘($, 16,, k2) = —Cg£e‘1’lxlyimi(icg), (6.34)
~ {51 . e-‘Ysll'l *
¢;(z,k,,,k,) = —Cfe I21rsm61,TYg,ml(k,), (6.35)

where 72 = 163+ k: + 72, 7 is related to the bound state energy 6 in eq. (6.26),
1;,- = E/Ikgl, k,- = —2mel/h2, 16, = k?/|k,| and 6;, is the phase shift for the If wave.

If eqs. (6.34) and (6.35) are substituted into to eq. (6.25) and integrated, then the
differential transfer probability becomes [Bona 88]

d d 1 ,
—P(I;,I.) - 33(533—1 Z MUM.” )

(.16, man,

= |1 - 5:,(61)|23(11: L“), (6-36)

 

101

where the probability amplitude was summed over the final angular momentum m f

and averaged over mg.

 

 

1 h m 2 12‘2””
3(lhli)=z a hzkflcll(211+1)PI.-(X6)P1,(X1)”R , (637)

P), and P), are Legendre polynomials of
k2 k2
X.- = 1+ 24,-, X, = 2—3- — 1, (6.38)
71 k}
and R = d1 + (1;, a strong absorption radius, and $1,051) = e-m‘! is a reflection

coefficient. This coefficient can be reduced to an optical model 5 matrix when the
coefficient is averaged over the energies of the final compound states. Then the energy
average < S), > is the 5' matrix for the elastic scattering of a nucleon with kinetic
energy Cf. Eq. (6.36) gives the probability of a transfer of a single nucleon in the orbit
I,- of the projectile to the continuum state of the target as a function of the nucleon’s

final energy, Cf.

6.3.2 Cross Section Calculations of Projectile Breakup and
Compound States

The transfer probability from the initial bound state (6.- < 0) to a final unbound state

(Cf > 0) can be rewritten as

dP(If? 13')

dc, = < |1— SUI2 > B(I,,l.-)

(|1— < S), > |2 + T1,) - B(I,,I.-), (6.39)

where 1.31] are the initial and final angular momenta respectively, T), = 1 — I < S), >
|2 , and EU 1,1,) is explained in the previous section. The first term in eq. (6.39)
Il- < S), > I2 is for the elastic scattering of the transferred nucleon by the target. The

second term T1, is due to the formation of the compound state in the target nucleus

by the transferred nucleon, and includes all of the residual nucleus’s excitation.

 

 

102

An approximate formula for the total transfer cross section can be obtained by

integrating over impact parameter [Bona 88]

 

 

d0 00 °° dP(R,If,I.') R, -ac 0° dP(R,,If,I.')
(16} ./R. ”2:5 ) d6! 1] ”Ego déf

(6.40)
where R, is a strong absorption radius and ac is a Coulomb length parameter. R,
can be obtained from the relation kR, = I + 1/2, where I: is the wave number of
the transferred nucleon and I is the angular momentum at IS I = 1/2. In the real

calculations, I I was truncated at 30 because 5' converges to one where I is much less

than 30.

In the eqs. 6.39 and 6.40, the contribution of the spin of the transferred nucleon is

not appeared. The dependence of the initial and final state spins can be introduced

as in refs. of [Bona 87, Hash 88]. Then the eq. 6.39 can be modified as

dP I ,I,- . .
((15,, ) = §(|1— < SI! >12 +1-|< 51', > |’)B(J;,J.-), (6.41)
where
. . 2' +1
301,11) = W“ + R)B(I,,I.-). (6.42)

The factor (21', + 1)/2(2I I + 1) is a statistical factor which is the probability of
reaching a final state j I if all angular momentum projections are equally probable.
R is a dynamical factor which depends on several variables of the transfer reaction
notably the reaction Q - value and the incident energy. In a single nucleon transfer
reaction, for the given channel specified (I,-,I,), there are four possible j —transfers
from 1'; = I.- i % to j j = :l:%. The detailed derivation for R is given in ref. [Hash 88].
The result is

R = D(J'r,je)F (E) (6~43)

 

103
Table 6.1: Coefficients 0051].!)

5\<: h-i h+§
u

1_l .L. -1

2 “I 110144)

 

 

1 -1 1
0+5 um“) wnwwn

 

 

 

 

 

where D(jjv, jg) is given in table 6.1 and

2km dP1.(X,') . 2kg!) (In, (Xf)

F(E)='vza.(x.-) am 1:36.06) dX;

 

(6.44)

where X is defined in section 6.3.1.

The S-matrix can be obtained from a DWBA calculation for the nucleon elastic
scattering reaction on the appropriate targets. They are dependent on the optical
potential parameters and the energy of the incident particle. The optical parameters
are also dependent on the incident particle’s energy. Thus it is important to have
good energy dependent parameters for the optical potentials. The real potentials such
as volume real and spin orbit potentials should be chosen to give the correct sequence
of the bound and resonance states of the target. Once they are chosen for a given
energy, they may be used in the vicinity of this energy because the real parts are
not so sensitive to the change of the incident energy. But the imaginary parts, such
as volume imaginary and surface potentials may give a big change to the absorption

probability with a small change in the potentials.

In this analysis, the real potentials are obtained by changing the input potentials
smoothly to give the best sequence of the known states of the target for the given
energy, and the imaginary parts are parameterized using the method of Mahaux and

Sartor [Maha 89] to reproduce the correct position of the given bound state of the

 

104

Table 6.2: The optical input parameters for the neutron elastic scattering reactions
on 9°Zr and 208Pb region targets. The units for the V3 and V30 are MeV, for r and
a are fm.

 

Targets V3 TR an r; a; V50 r50 ago

 

208Pb,2°9Bi,2°7Pb 45.8 1.25 0.5 1.25 0.3 9.0 1.25 0.5

9°Zr, 91Zr, 89Y 45.8 1.25 0.5 1.25 0.3 7.5 1.25 0.5

 

 

 

 

 

 

 

 

 

 

 

target for the given real potentials. The optical model potential used in this analysis

is

 

U(r, 6;) = V0 - VRf($R) + (mhcyvsoa - E%%f(zn)
- i[WV(EI) - 4aIWs(61);;]f($I) (645)

where V0 is the coulomb potential, V3 and WV are volume real and volume imaginary

potentials, V50 is the spin-orbit potential, W5 is the surface potential, f (to) = (l +

 

e"°)/aa where 2,, = (r - raAl/3), (mth = 2.0fm2, re, and A are radius parameter
and mass of the target, and 3 and I: are spin and orbital angular momentum of the
transferred nucleon respectively. In all cases C! denotes real(R) or imaginary(I) part

of the potentials.

The input parameters for the optical potentials to calculate the S-matrix elements
for the neutron elastic scattering reactions using DWBA program are given in table
6.2. For the imaginary potentials, Wv and W5, are used after they are obtained for

the corresponding neutron’s energy using eqs. (2.1), (2.3a) and (6.1a) of ref. Maha 89.

The S-matrix elements are obtained for the incident nucleon’s energy from 1 MeV

in 1 MeV steps for the orbital angular momentum from I = 0 to I = 30 in each step.

105

For the proton elastic scattering reactions, the same values are used. The calculations
for the neutron transfer cross sections are done by using the eqs. (6.39) and (6.40)
for the neutron’s final energy (Cf) from 1 MeV in 1 MeV steps. In each energy step,
the cross sections are summed from I f = 0 to 30 for the initial angular momentum
I,- = l in the projectile. For the proton transfer, the same procedures are used. But
the input values for the binding energies and reaction Q — values are used in their

effective values due to the Coulomb forces.

 

631! = 6,, _ 226 , a = 1,2 (6.46)

Qeu = 65” - 6}” (6.47)

where 21,; are the charge numbers of nucleus 1 and 2, and d1 and d; are determined

to satisfy the relations

d, A1”
a = A—éls, and d] ‘1' d2 = R. (6.48)

where are the mass numbers of nucleus 1 and 2. As a strong absorption radius R.,
11.2fm for me region targets, 8.47 fm for 9"Zr region targets and 2.29 fm for 7Li

are used.

6.3.3 Comparison of Semi-Classical Calculations with Ex-
perimental Data

The calculated cross sections for the reactions of (7Li,°Li) and (7Li,°He) at Em = 30
MeV/n on targets of 9”Zr, 9‘ Zr, 89Y and 2“st, 209Bi, 20"Pb are shown in figs. 6.6 and
6.7, and compared with the experimental results. Because the calculations are done
for continuum states where the final neutron is in an unbound state, the calculated
spectra are seen only where the excitation energies are higher than the threshold
energy for decay in the residual nucleus. The dashed curve is the absorption spectrum

which corresponds to the transfer to compound states and the dotted curve is the

 

do/deE (mb/sr-MeV)

GOZI‘, 9121,, 8

10

106

 

l5

IleI'l

I
D
p—
)-

 

IfrTlIII

III

91 Zr

I' I4

 

 

 

 

 

 

 

 

 

 

7.5 :
5.0 _
2.5
0.0 =-
10... g
7.5;
5.0

0.0 h

10.0
7.5
5.0
2.5
0.0

2.5 I

”Pb, ”“131, me ("Li,°1.i)

 

   

ITIITIIIIII'IIIII
D
D

—
p

10.0 ’

2""Pb

 

ITTIIII

 

bIIIIITIjIIIrTqI
p

 

I
0
11‘1144111L1 [1111

 

10 20 30 40
Ex. (MeV)

(b)

Figure 6.6: The calculated spectra of the reaction (7Li, 6Li) at Em = 30 MeV/n on
targets of 9°Zr, 91Zr, 89Y and 208Pb, 2”Bi, 2("Pb using the eqs. 6.36 and 6.37. The
dashed curve is the absorption, the dotted curve is the breakup and the solid curve
is the total spectrum. The spectra are normalized to the experimental results.

l’rrITlII

 

 

 

107

 

 

90Zr, 91Zr, ”Y (7Li,eHe) ”Pb, ”Bi. 2°7Pb (7Li,°He)
.l...¢....,..r.,....

'TIIIIIITTIIIIIIIIIII

All

2.5
II
Nb ' 2.0

     
   

lnLllll

5
4
3
2

l LllllllALllLl

1.5 E-
“ 1
1 1.0 :—

lllllulljlljl

...
‘ /

'11

0.5 I

 

0.0 _‘
2.5 _

as I
Nb ‘ 2.0 _

1111* All

1.5 I

reason
I

AJLLUJJIAA

1.0 ’

0.5 '

...

 

da/dfldE (mb/sr—MeV)

 

0.0 E
2.5 r

llllLLll

2.0 Z
1.5 I

1.0

N 03 ab (30
lllelLleillLljllA

AlllLAlJAA

 

0.5 F

' o

 

 

 

C
A ALLIL A

 

0.0 .L 1 1 1 ‘
40 0 10 20 30 40
Ex. (MeV) Ex. (MeV)

(a) (b)

 

Figure 6.7: The calculated spectra of the reaction (7Li, 6He) at Em = 30 MeV/n on
targets of 9"Zr, 91Zr, 89Y and 2me, 2""Bi, 2""Pb using the eqs. 6.36 and 6.37. The
dashed curve is the absorption, the dotted curve is the breakup and the solid curve
is the total spectrum. The spectra are normalized to the experimental results.

108

projectile’s elastic breakup spectrum. The solid curve is the sum of breakup plus
absorption and should correspond to the experimental data. In all cases the calculated

total cross sections are normalized to the experimental data.

In fig. 6.6.(a) for targets with masses near that of 90Zr, three peaks are predicted in
each spectrum. For the first peak of each spectrum, which is seen at Err. ~ 15 MeV,
about 50% of the strength is due to the I f = 6 contribution. The contributions to the
total cross sections for various I I components are shown in fig. 6.8. The centroids of
these peaks are very similar to those of the experimental results, whereas the widths
of 4 MeV are about one half of the experimental results. Even though only the
transfer to the single particle states is considered in the calculation, there is good
agreement with the experimental data in the centroids of the peaks. This suggests
that the peaks have the characteristics of single particle states rather than GR. The
contribution of I f = 2, which corresponds to the giant quadrupole resonance state, is

very small.

For the second peak at Ex. ~ 25 MeV, about 60% of the strength is due to I f = 7.
There is very good agreement with the experimental data in the position and width,
especially for the 91Zr and 9°Y spectra. It is interesting to note that in this region of
excitation energy there is little breakup predicted and it seems that the cross section

is mainly due to transfer to the resonance states.

For the third peak at Ex. ~ 32 MeV, about 60% of the strength is due to I f = 8

contribution to the sum, but the peak is not clearly seen in the experimental spectra.

The breakup predictions give smooth background curves which are peaked at
excitation energies corresponding to the incident beam velocity and similar to the
peaks predicted by the Serber Model. The contribution of the breakup to the sum

is about 20% at excitation energies lower than 40 MeV. The breakup contribution

 

0.10
0.08 :

0.06

 

0.04

 

0.02 '

 

 

0.00 ‘
0

 

0.125 :
0.100
0.075
0.050

0.025

 

 

0.000 ~'
0

 

Figure 6.8: The contributions for each angular momentum component (I f) to the
total cross sections in (7Li,6Li) reactions at Em = 30 Mev/n predicted by Brink-
Bonaccorso model. Unit is arbitrary.

110

becomes larger as the excitation energy increases, but still the resonance states are

predicted to be dominant up to Ex. ~ 45 MeV.

Fig. 6.6.(b) displays the (7Li,6Li) reactions on the 208Pb region targets. Only one
peak is predicted above the smooth transfer cross section curves in each spectrum.
This peak appears at E2. ~ 7 MeV for the 2°“"Pb and 210Bi nuclei, but it appeared
at E2. ~ 10 MeV in the 2“Pb nucleus. About 50% of the strengths of these peaks
are due to the I f = 5 contribution to the sum. In the experimental data the strong
peaks are not seen at the same positions, instead, very weak peaks are seen at a few
MeV higher excitation than the calculation predicted. The big differences, ~ 3 MeV,
between the excitation energies of each peak for different targets also suggest that
these peaks are from single particle states where I f is 5. Summing the contributions
for the various values of I f results in broad peaks at E2. ~ 22 MeV in 209Pb and
210Bi, and at E2. ~ 26 MeV in 20'3Pb in good agreement with the experimental data.
In the reactions using these heavy targets, the prediction of the breakup contribution

to the sum is even smaller than in the reactions using the 9°Zr region targets.

In fig. 6.7, the calculated cross sections for proton transfer to continuum states are
displayed with the experimental data. The calculated cross sections start from zero,
at the excitation energy corresponding the proton emission threshold, and increase
very smoothly at low excitation. This is due to the Coulomb barrier which the proton
must pass through to come out of the target nucleus. The cross section curve at low
excitation shows an exponential curve of exp a(Ea:. — Eu.) where 01, Ex. and E“, are
arbitrary constant, excitation energy and threshold energy for breakup. The shape
at low excitation is completely different from the neutron transfer cross section curve
where the Coulomb force does not apply. At high excitation, the curve is similar to

that of the neutron transfer cross section.

In fig. 6.7.(a), the cross sections of the (7Li,6He) reactions for the 9"Zr region

111

targets are displayed. Three weak peaks are predicted by the calculations. The
first one in each spectrum is dominated by I f = 6, the second one by I f = 7, and
the third one by I f = 8 contributions to the sum. The contributions to the total
cross sections for each I f component are shown in fig. 6.9. The predicted projectile
breakup contributions are also very small as in neutron stripping reactions on the
same targets. In fig. 6.10 where the spectrum is shown up to 50 MeV of excitation
energy, the cross section is dominated by the process of transfer to compound states

rather than the breakup process as in neutron transfer reactions.

In fig. 6.7.(b), no peak is predicted above the smooth curve. The main contribu-
tions to this curve are due to I f = 8, 9, 10 and 11. The predictions on the me region
targets do not fit to the experimental data well. One of the explanation is that this
model is very sensitive to the optical parameters and the input values may not be
good for this calculation. Another one is that angle dependence is not considered in

the calculations, whereas the experimental data are obtained at a particular angle.

One approach to solve the problem of the background is to obtain the pure transfer
cross sections using a coincidence measurement with the 9°Zr("Li,“He)mNb reaction,
where the 6He particles are detected at forward angles and the protons in an array
at backward and forward angles. Coincidence of the 6He with protons detected at
backward angles should select only the piece of the spectra corresponding to the
resonance states and should eliminate the breakup part of the spectrum, since the
protons arising from the breakup of 7L1 will be restricted to forward angles. By
measuring the 6He spectra while varying the angles, the angle dependence of the

absorption cross sections and the breakup cross sections can be measured.

112

 

0.150:....,....,.--.,....l...,rr?
0425:- 208Pb(7Li,6He) —f
0.100: 4
0.0755
0.050

0.025

 

 

0.000 ‘

 

 

0.150TI'UII't'Ir'IrIFII'IIrr'It..

1
L

I I

0.125 _
0.100
0.075
0.050

0.025 _

 

 

0.000 '
0

 

Figure 6.9: The contributions for each angular momentum component (I I) to the
total cross sections in (7Li,6He) reactions at Em = 30 MeV/n predicted by Brink-
Bonaccorso model. Units are arbitrary.

113

9021- (7Li,6He), 0m=6°

 

 

 

 

 

 

 

4 - T 1 I l I I I I I IfI I I I

9 I i
m _ 91Nb .
=1 3-

s. .

m .

\ .

'Q I.

E. 2 -
v )-

m b

'0 .

c 1-

'U 1 '-
\ .-

b

“U .

OF l-l.l°l..1.L1l1 l 1 1'1 1 l l I l L I l
O 10 20 30 40 50
Ex. (MeV)

Figure 6.10: Breakup cross section of 7Li (Em = 30 MeV/n) into “He + p on 9°Zr
target using Brink-Bonaccorso model. Two spectra are connected at Ex. ~ 26 MeV.
The dashed curve is the absorption, the dotted curve is the' breakup and the solid
curve is the total spectrum. The spectra are normalized to the experimental results.

114

6.4 Coincidence Measurement

A test run to examine the feasibility of the coincidence measurement of the products
from the projectile breakup processes, and from the transfer and decay processes, was
carried out. In the test run, the 9°Zr(7Li,“He) reaction with Em = 30 MeV/n was
used. “He was detected in the S320 spectrograph in coincidence with two arrays of

solid state detectors.

The forward array was used to set the coincidence timing using the projectile
breakup of 7Li -+ “He + p. Since the settings of the magnetic fields for “He and
triton were the same, the tritons from‘the projectile breakup of 7Li —1 4He + t were
also detected. The forward array consisted of 5, 1cm x 1cm Si pin diodes for AE
and 031 detectors for E (fig. 6.11). This AE — E arrangement allowed particle

identification such as p,d,t, 3He, and a (fig. 6.12).

The back angle array consisted of three, 3 x 3 cm2 Si pin diodes. This simple
detector array permitted the measurement of charged particles, mainly protons which
were emitted at back angle from the excited 91N b nucleus. Time and energy spectra
from the back angle detectors are shown in fig. 6.13. The back angle detector array
had a total solid angle of about 0.9 sr and covered angles from about 120° to 150°.
Good true to random ratios were obtained with a beam intensity of about 4 particle

nano amperes (pnA).

Unfortunately after setting up the coincidence electronics, only 8 hours was avail-
able in the test run and this allowed only poor statistics to be obtained for the true
coincidence spectrum. Only about 20% of the spectrum strength appeared to arise

from particle unbound states.

The problems which were found in the test run can be solved or improved by

changing the detecting method. Further suggestions for a future coincidence mea-

115

 

Backward Detector Array

/ Target 6 He

7L1 Beam _ l | 6°

To S320

  
  

Forward Detector Array

TARGET CHAMBER

Figure 6.11: Top view for the coincidence measurement of “He and p inside a target
chamber. Forward array was used to detect a proton from the breakup of 7Li into
“He + p, and the back array was used to detect a proton decayed from the 91N b' —v
9“Zr + p.

116

 

 

 

 

1 81%; p;-_' '

-¢» 7:"

   

 

 

 

 

 

 

Energy

Figure 6.12: Spectra from the forward array (from F1 to F5) as functions of energy
and time, and particle identification on the AE — E spectra from the reaction of
90Zr("Li,“He) at Em = 30 MeV/n.

117

 

 

 

 

 

 

 

 

 

 

I
B1 1
1
B2
B3
‘1

 

Energy Time

Figure 6.13: Spectra from the backward array (B1, B2 and B3) as functions of energy
and time for the reaction of 9°Zr(7Li,“He) at Em = 30 MeV/n.

118

surement of the reaction 90Zr(7Li, “He + p) are :

0 To carry out the coincidence measurement with better statistics, a longer run-

ning time is required, about 100 hours at 4 pnA.

o In each energy spectrum of the backward array, two peaks were observed (fig. 6.13).
The peak of the lower energy seems to be caused by detecting the low energy
electrons emitted from the target. These electrons can be blocked by placing a

thin film in front of the detectors.

0 Use the A1200 beam analysis device instead of the S320 spectrograph. The
advantages of the A1200 are its high acceptance (about 3 times larger than
the S320), enough space for the backward array, and a much higher resolving
power (up to 5 times better than the S320). Particle identification in the forward

direction can be done by using the two solid detectors (Si, 0.5mm, AB 1 —AE2).

o By placing six, 3cm x 3cm solid detectors (S i, 0.5mm) in the backward direction,
about 15% of the protons which are emitted isotropically by the decay process
from the excited 91N b nucleus, will be detected. The counting rate will be twice

than that of the test run.

0 Use AE -— E detectors for forward array to detect protons from the breakup

processes and identify the particle type.

Time has been approved for this experiment at the N SCL.

Chapter 7

Results of Single Nucleon Pickup
Reactions

7 .1 Introduction

In this chapter, the data from the one nucleon pickup reactions (12C,13C) and ("C,’“N)
at Em = 30 MeV/n on targets of 9"Zr, 91Zr, 89Y, 2“BPb, 209Bi and 2‘T’I’b are reported.
Data from the (7Li,“Li) reactions on the 90Zr region targets and 208Pb target are also
given and compared with those from the (”C,’3C) reactions. The ejectiles 13C, 13N
and “Li were measured at the respective grazing angles, namely 6° for the 9“Zr region
targets, and 9° for the 2O‘BPb region targets where the cross sections are large. In
the (”0,13C) reactions, the elastically scattered l"’C particles were blocked by using
a “finger” so as not to waste computing time by counting the unwanted elastically

scattered particles.

The purpose of the pickup reactions is to study deep lying hole states and to
explore the possibility of forming collective states. All the spectra are plotted as
functions of the reaction Q - values and excitation energies, and are compared with
each other. Overall, the spectra have much smaller backgrounds than those of the
stripping reactions, but the ejectile excitation in the 13C spectra and the poor energy

resolution were additional problems which were not seen in the stripping reactions,

119

120
(7Li,“Li) and (7Li,“He).

Theoretically calculated single particle energy levels for 9°Zr and 20“Pb nuclei are

given in fig. 7.1 to help understand the hole structures of 9"Zr and '2me region nuclei

[Gale 88].
7.2 90Zr, 91Zr, 89Y (12C,13C) Reactions

The energy spectra for the (12C,13C) reactions on the targets 9°Zr, 91Zr and 8.9Y at
Em = 30 MeV/n and 0,0,, = 6° are given in fig. 7.2. Since a “finger” was placed
in front of the focal plane detector to prevent the detection of the 12C particles, 13C
spectra corresponding to that position were not obtained. Excitation energies, Q —

values and widths of peaks observed in the 13C spectra are given in table 7.1.

In the 13C nucleus, the threshold energy for breakup into 1"’C + n is 4.946 MeV
and there are three bound excited states ( j1r = 1/2"' (3.09 MeV), 3/2' (3.68 MeV)
and 5/2+ (3.85 MeV)) below this energy. These three excited states are strongly

populated in the reactions on all 3 targets.

In the 9°Zr(”C, 13C)“9Zr reaction, peak 1 appears to be a composite of three low
lying single hole states of “9Zr, namely 199,2(ground state), 2p1/2(0.59 MeV), and
2p3/2(1.10 MeV). This peak is dominated by the 199,; state rather than the other two
p-shell states because the angular momentum of the 1g9/2(I = 4) state is close to the
favoured angular momentum transfer for this reaction (3 and 4h). The (2 j +1) factor
for the lgglg state also enhances its cross section. In peak 1, no ejectile excitation
contributions are observed because of the high excitation energy of the first excited

state of 13C.

Peak 2 (4.1 MeV) appears to be dominated by ejectile excitation. If the spectrum

is compared to those from the (7Li,“Li) or (2°Ne,2‘Ne) reactions [Fort 90], no peak is

121

902, 200pb

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MeV 1) Neutrons Protons () Neutrons Protons
ljisn *20~ —— ll1912
+20 —" 2'13/2
—_ 2h,”
—— 1 ,
—— 11‘5/2 *— 1le/2 J” 2
xlhm
-—-— . 11 flitmz
__.-11,3,2 —'" 19” “—vzhn/Z
+10 +10 ‘ =3: 3;;
2! \291/2
[109/2 7’2 3dS/2
‘11 ——-—-"1113/2 _’l|un
”’2 xlhmz ‘ll‘n/I —‘299’2
\ .

303/2 -Zhnn 1115/2
__ 2f,” _< 51/2 30 /3p1,z
0 197/2 0 .- /29:,’22 _—’393/2
"‘na ‘2‘35/2 —é"51;2 __\2'5/2
——__/2dm _‘3dsn 1i, .
\ ll.
“gn2 _ 1.16/2 \2f 7,;
=\a..,, —\1,nm \1h9/2

1 99/2
\stn 99/2 /391/2 /351/2
— 29"; _.—2f —-"2d311

2 _\ 5/2
_I 93/2 —\3pil2 ———o’lhn/2
-10 '19.” \1f5,2 :10 " I '13/2 ‘255/2
—\12f7/2 -1971:

—"12f91/2 h”:
—\2p::: "7/2 351/2 /ZP~/2
—.——1h“/2 —-1g,/2
\de ' \2p1/2

— 7’2
2’ 3n -1g,,2 —— "7x2

—’ 1/2 — 1d

\1d311 5’2 ———291/2 — 25”?
__ 155,2 —’1 5’2 -— 165/2

__/191/2 _- f?”
—_ 191/2

_30 \1 ~30” — 251/7 ——

Jpn; PM 1:11,; 191/2

—‘1P:m _ ldS/Z
—— 151/2

Figure 7.1: Single particle energy levels of 9°Zr and 2““Pb in a Woods-Saxon potential

well [Gale 88].

 

122

”2r,“zr,°°r(‘°c,“c), 91...=6° ”Zr.°‘Zr.°°Y(’zC.’3C). 91.6=6°

 

 

.1

p' I I I [I I I I I I I I I l I I III .I I IIIIIITI I r I III I I I I I

30 ' m 30 h —
1 P d

2 .

   

 

 

 

 

 

20- Zr 1 20_
E l
- 1
10- j
: fl 4
’>‘ . ~
0 '. .1.... . . .‘
2 38b IIIIIIIIII I I I —
I. - 2
s . :
“g 20;. 9021' —:
v F 1 :
1:1 .
v ._
c: .
'5 .
\ .
.8 .J.)“'*-'m.

 

 

 

 

 

 

 

 

0 10 20 30 40 0 10 20 30
— Q Value (MeV) Ex. (MeV)

(60 (b)

Figure 7.2: Experimental spectra of 9“Zr, 91Zr, “9Y ("Cf“C) reactions with E = 30
MeV/n. The valleys seen at excitation energies about 20 MeV are produced by the
“finger” used to block the elastically scattered 12C. Peak 0 in the 9°Zr spectrum is
from the pickup of an extra neutron, outside a closed shell, in a 2115/2 state. The
shaded area above the assumed background was used to obtain the cross sections for
peaks 1 and 2, and to compare the positions.

123

Table 7.1: Excitation energies for the peaks observed in the (12C,13C) reactions on
targets of 9"Zr, 91Zr and ”Y. F is the full width at half maximum, Q is the reaction Q
— value for the corresponding excitation energy and units are MeV. The uncertainty is

about 0.3 MeV. a is the cross section for the shaded area in mb/sr and the uncertainty
is about 20%

 

9OZI.(12(3913(3)89Zr 91 Zr(12C,l3C)9OZr 89Y(12C,13C)88Y

 

Peak Ex. I’ -Q 0 Ex. I‘ —Q 0 Ex. P -Q a

 

 

0.0 1.0 2.25 H
0.0 2 7.03 6 4.2 2.0 6.55 23 0.0 2.0 6.53 6
4.1 3.5 11.13 56 8.8 3.5 11.05 66 4.1 3.5 10.63 60
8.7 15.73 14.0 16.25 9.2 15.73
13.5 19.7 18.0 20.25 13.7 20.23

Atom—10:“:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

124

seen at about Ex. = 4.1 MeV in either of these latter two reactions on 9°Zr. Because
the excitation energy of the centroid of this peak (4.1 MeV) is higher than the ejectile’s
bound excited states (13C ; {(3.09 MeV), g-(3.68 MeV), and §+(3.85 MeV)) by 0.25
to 1 MeV, there must be a mutual excitation of the ejectile’s bound excited states and
the residual nuclei’s low lying single hole states at 0.59 and 1.10 MeV. The 1 MeV

energy resolution makes it difficult to give more detailed description of this peak.

Peaks 3 and 4 (8.7 and 13.5 MeV respectively), appear to arise from the deep hole
states. In the light ion transfer reaction, 9°Zr(13', d) [Kasa 83] at Egnc = 90 MeV, two
peaks were also observed at similar excitation energies to those of peaks 3 and 4. At
around 9.5 MeV excitation energy in the 9°Zr(2°Ne,2lNe) reaction, a very weak peak is
also seen at an excitation energy similar to that of peak 3. Comparing these excitation
energies with the theoretically calculated single particle energies (see fig. 7.1), peak
3 corresponds to the 199,2, 1f5/2 and 2173/2 hole states, and peak 4 corresponds to the

1f7/2 hole state.

In the 91Zr( 12C, 13C)9°Zr reaction, the spectrum is slightly different from the other
two spectra. Peak 0 arises from the pickup of the outmost neutron in the 2115/2 state
with no ejectile excitation. As both the first excited states in 13C (3.09 MeV) and in
the residual nucleus (1.76 MeV) are reasonably well separated from peak 0, no ejectile

excitation or excited state of the residual nucleus contributes to this peak.

Peak 1 is much more strongly populated compared to the reactions with the 9"Zr
and ”Y targets, and the ratio of peak 1 to peak 2 is much bigger than the other
two cases. This may be accounted for by the superposition of the two different peaks
resulting from the pickup of neutrons from the two different states. When the outmost
2115/2 neutron is transferred to the bound excited states in 13C, the centroid of the
ejectile excitation energy will be around 3.70 MeV. If a neutron in the 299/; state of

the 9°Zr target is transferred to the ejectile in its ground state, the excitation energy

125

will be 4.77 MeV which corresponds to the difference in neutron’s binding energy
between the 2115/2 and 2g9/2 states. Since the two peaks (3.70 MeV and 4.77 MeV)
are not resolved, they form a single peak at around 4.2 MeV. Compared with the

other two spectra, peak 1 is dominated by the ejectile excitation.

Peak 2 is very similar to that of the 90Zr(”C,’3C) reaction in the Q — value and
the cross section. This peak appears to arise from the mutual excitation resulting
when a neutron in the 299/2 shell is transferred to bound excited states in 13C as in
the reaction with the 90Zr target. The excitation energy difference between peak 1
(4.2 MeV) and peak 2 (8.8 MeV) is about 4.6 MeV, which is larger than in the other
two spectra by 0.6 MeV. This is because peak 1 is not a single peak but a combination
of two peaks at 3.7 MeV and 4.77 MeV which gives the centroid at 4.2 MeV, while
peak 1 from the reaction with the 9°Zr or ”Y target is a single peak arising from the

residual nucleus only.

Peaks 3 and 4 are very similar to those of the reaction with the 9°Zr target but
are very weak for all 3 targets. They appear at almost the same reaction Q - values.

The presence of one neutron in the 2115/2 state does not seem to affect these peaks.

In the reaction “9Y(”C,‘3C)““Y, the spectrum is very similar to that of the
9°Zr(”C,’3C) reaction. All four peaks occur at very similar reaction Q - values.
This suggests that the peaks are formed with the same components as in the reaction
with the 9“Zr target. The couplings of the proton hole of «(2121/2)‘1 to the neutron

holes in ““Y nucleus does not appear to change the spectrum significantly.

The broadening due to p - h or h - h interactions is not visible in these spec-
tra. Because of ejectile excitation, the exact strengths of single hole states or cou-

pling strengths between the hole and particle states are difficult to disentangle in the

(12C,’“C) reactions.

126

7 .3 90Zr, 91Zr, 89Y (7Li,“Li) Reactions

The energy spectra from the 9“Zr, 91Zr, ““Y (7Li,“Li) reactions at Em = 30 MeV/n
and 01..., = 6° are shown in fig. 7.3. The purpose of carrying out these reactions is
to compare the spectra with those from the (12C,’“C) reactions, and thus help to
determine which structures arise from excitation in the residual nucleus and which

from ejectile excitations. Since the threshold energy for breakup of “Li into 7Li + n

is 2.03 MeV, there is only one bound excited state, at E3. = 0.98 MeV.

In the 9°Zr(7Li, “Li)“QZr reaction, only two peaks are observed. Peak 1 (ground
state) arises from the pickup of a neutron in the 199,2 state. The second peak (1.14
MeV) appears to be a composite of an ejectile excitation (1*, 0.98 MeV) and the
residual nucleus excitation, mainly a 2113/2 (1.10 MeV), and 1f5/2 (1.45 MeV), which
are both single hole states. The 2111/; (0.59 MeV) state is likely to be weakly excited
because of the spin-flip process and the small value of 2j + 1. No other peaks are
observed at excitation energies higher than 3 MeV. In particular, the strong peak
seen in the 9°Zr(12C,13C) reaction at Ex. = 4.1 MeV is not seen in the “Li spectrum.
This suggests that the peak of Ex. = 4.1 MeV in the 13C spectrum arises from the

ejectile excitation.

In the 91Zr(7Li, “Li)9°Zr reaction, four peaks are observed. Peaks A and B arise
from the pickup of a single neutron in the 2115/2 state, leaving “Li in the ground state
for peak A, and in an excited state (1*, 0.981 MeV) for peak B. From the comparison
of peaks A and B, the ejectile excitation in “Li is less than-in 13C. In fig. 7.3.(a),
where the spectra are plotted as a function of reaction Q - values, peaks 1 and 2
of all three spectra appear at almost the same positions, while peaks A and B shift
to lower energy by 4.56 MeV. But in fig. 7.3.(b), where the spectra are plotted as a

function of excitation energies, peaks 1 and 2 are shifted to higher excitation energies

N

H
O

da/dfldE (mb/sr-MeV)

H
ONthOON-FGCD

127

 

IIIIIIIIIIIITIIII

III

p
b
p
p

IIIIIIIIIIIIII

l

IIII

 

 

 

 

 

 

 

11

11111

1111111111

111

111

111'

 

 

10,

1...
O

I'IIII I

II III

..a
ONIFGCDOON-FOO

 

IIIIIITIIIII

IIjIlI

 

 

 

 

 

    

 

 

 

 

0 5 10 15 20 25 30 -5
— Q Value (MeV)

(81)

 

Figure 7.3: Experimental spectra from the 9°Zr, 9‘ Zr, “9Y (7Li,“Li) reactions at E =
30 MeV/n. Peak A of the 9"Zr spectrum arises from the pickup of a neutron in the
2d5/2 state and peak B arises from the “Li’s excitation (1+).

128

compared to peak 1 from the same reaction on the 90Zr target by 4.56 MeV. Peak 1
(4.56 MeV) arises from the pickup of a neutron in the 199,2 state, as in the reaction
with the 90Zr target. Then the lg9/2 hole state couples to the single neutron particle
state, 2115/2, and forms many states, with j’T ranging from 2* to 7*. Peak 2 (5.70
MeV) is obtained by pickup of a neutron at the same state as in the 90Zr(7Li,“Li)
reaction, with some ejectile excitation. Then the neutron particle state 2d5/2 couples
to the hole state, and makes the hole state split into many states, which are not
separated clearly from peak 1. The existence of the neutron in the 2d5/g state outside
the closed shell does not change the shape of the spectrum substantially, but makes

the peaks a little wider, keeping the total strength the similar.

In the 89Y(7Li, “Li)““Y reaction, two strong peaks (at 0.2 and 1.32 MeV) and a
very weak peak (at about 5.5 MeV) are observed. The spectrum of ““Y is very similar
to that of “92L The only difference is that the ““Y nucleus has one less proton in
the 2101/; state than the 9°Zr nucleus. Peak 1 (0.20 MeV) arises from the pickup of a
single neutron in the 1g9/2 state. This neutron hole state 199,2 couples to the proton
hole state 2121/2 and forms 4‘ (ground state) and 5" (0.232 MeV) states which are
not resolved in this experiment. The centroid of these two states is at 0.2 MeV. Peak
2 appears at an excitation energy of 1.32 MeV. The energy difference between peak
1 and peak 2, and the ratio of their relative strengths are almost the same as in the
other two spectra. A very weak peak, seen at an excitation energy of about 5.5 MeV,
is not seen in the other two reactions at the corresponding reaction Q - values. It is

not clear whether this peak arises from the residual nucleus’s structure or not.

Overall, no deep lying hole state was excited in the (7Li,“Li) reaction. The cross
section for the 9°Zr(7Li,“Li) is smaller than the other two reactions by about 15%.
This probably can be accounted for by the uncertainties for the thicknesses of the

targets. The presence of one extra particle or hole outside a closed shell appears to

129

make little difference to the structures observed in the residual nucleus.

7.4 208Pb, 209Bi, 207Pb (12C,1“C) and 20“Pb(7Li,“Li)
Reactions

The energy spectra from the 20“Pb, 209Bi, 2(”Pb (”C,’“C) and 2““Pb("Li,“Li) reactions
at E,“ = 30 MeV/n are shown in figs. 7.4 and 7.5. The ejectiles, 13C and “Li were
measured at the grazing angles 0105 = 9°. The favoured angular momentum for the
(”C,‘“C) reaction is I = 6, and for the (7Li,“Li) reaction is I = 3 and 4. The spectra,
for all three targets, have very similar shapes. Excitation energies, Q - values and

widths of peaks observed in the 13C spectra are given in table 7.2.

In the 20“Pb(”’C,1“C)2°7Pb reaction, three broad peaks (at E3. = 1.14, 5.8 and
10.05 MeV respectively) are seen. In fig. 7.4.(a), plotted versus reaction Q - values,
peak 1 (E2. = 1.14 MeV) has almost the same Q — value (within 0.1 MeV) as peak 1
of the other two reactions. This suggests that these peaks are caused by the pickup of
neutrons from the same levels which are the single hole states (3p1/2(0.00), 2 f5/2(0.57
MeV), 3p3/2(0.90 MeV) and 2713/2( 1.63 MeV)). No ejectile excitation contributes to
peak 1 because 13C’s first excited state energy (3.09 MeV) is much higher than the
energy of peak 1. As the ground state of 1“C is p1 /2 (I = 1, j = I — 1/2) a high
spin state with no spin-flip process is preferable. From these conditions for preferable
transfer, 2f5/2(I = 3,j = I— 1/2) and 2i13/2(I = 6,j = I+ 1/2) states seem to
be equally dominant. The ground state (3171/2) of the 20"Pb nucleus is not strongly
populated due to the small factor of (2 j + 1) and small angular momentum transfer

(I = 1) compared to the favoured large angular momentum transfer (I = 6).

The excitation energy of peak 2 (Ex. = 5.80 MeV) is somewhat high to be as-

sumed as a pure ejectile excitation. It appears to be formed by mutually excited

130

an‘1>1>.""°131.“"’Pb("'c.”c). 0m=9°

 

-1""1""r""l'rfi«

60:- _‘
r 2 ‘

40"- “°"Pb _‘

20

O.

60

da/dOdE (mb/sr—MeV)

 

 

 

 

0 10 20 30
— Q Value (MeV)

(80

 

”pb.”ai.’°"1>b(“c.“c). 01.59"

 

pIIITIIII’IIfiIIIIIII
60? ‘1

40:

 

 

 

 

0 10 20 30
Ex. (MeV)

(b)

Figure 7.4: Experimental spectra of 20“Pb, 209Bi, 2“"Pb (”C,’“C) reactions with Em
= 30 MeV/n. The valleys seen at excitation energies 20 MeV are produced by the
“finger” to block the elastically scattered 12C. The shaded area above the assumed
background was used to obtain the cross sections for peaks 1 and 2, and to compare

the positions.

 

131

Table 7.2: Excitation energies for the peaks observed in the (12C,13C) reactions on
targets of 20“Pb, 209Bi and 2""Pb. I‘ is the full width at half maximum, Q is the
reaction Q - value for a corresponding excitation and the units are MeV. The uncer-
tainty is about 0.3 MeV. a is the cross section for the shaded area in mb/sr and the
uncertainty is about 20%.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

“08Pb(1“C,13C)207Pb “0931(12C,13C)20831 207Pb(12C,130)206Pb
Peak Ex. I‘ - Q 0 Ex. I’ - Q 0' Ex. I‘ - Q a'
#
1 1.14 1.7 3.56 16 1.12 1.7 3.63 12 2.16 1.7 3.95 12
2 5.80 3.5 8.22 160 5.70 3.5 8.21 115 6.80 3.5 8.59 160
3 10.05 2.0 12.47 10.12 2.0 12.63 11.00 2.0 12.79

 

 

 

132

 

15 IIIIIIIleIIIrIIIIlIIIIIIII

I j
1 1

10- A

 

 

 

da/dOdE (mb/sr—MeV)

      

I I I I I I I
p
L 1 1 1 l 1 1

 

11lLL11

 

 

 

1111111

-5 O 5 10 15 20 25
Ex. energy (MeV)

   

1 1 1

O

 

Figure 7.5: Experimental spectrum of 20“Pb("Li,“Li) reaction at E = 30 MeV/n.

133

states of 13C (la/£3.09 MeV), 1p3/2(3.68 MeV), and Ids/2(3.84 MeV)) and 207Pb
(1i13/20.63 MeV), 2f7/2(2.33 MeV), and 1h9/2(3.41 MeV)). Peaks 2 in all three re-
actions have almost the same reaction Q - values and they seem to be formed by
the pickup of neutrons in the same states in each target, and with some ejectile exci-
tation. Considering the maximum transfer matching conditions, the most dominant
transitions are likely to be from the 1i13/2 and 2 f7/2 states in 29813b, 11):”; and 1d5/2

states in 13C.

In the experiment done with the (2°Ne,21Ne) reaction at E,“ = 30,25 MeV/n
[Fort 90], two large peaks are observed at excitation energies of 2.5 and 6.5 MeV
where the threshold energy for breakup of 21Ne is 6.76 MeV. These two peaks are
very similar to peak 1 and peak 2 of the present experiment, except that they are
higher in excitation energies by about 1.4 and 0.8 MeV respectively. The differences
of the excitation energies of the peaks from the present experiment can be accounted

for by the different energy levels in the two ejectiles, 1:"C and 21 Ne.

While in the 208Pb(7Li,‘:"Li) reaction, low lying states are resolved clearly, which
correspond to peak 1 of the (12C,‘3C) reaction. A very weak bump is observed in the
spectrum at excitation energies between 5 and 8 MeV (fig. 7.5) which are likely to
be from the 2 f7/2, 1h9/2 and 1h" ,2 states (see fig. 7.1), where a strong peak 2 was
observed in the 208Pb(12C,13C) reaction. From the comparisons of the ‘30 spectrum
with the spectra of 8Li, 21Ne and the (120,130) reaction on the 9°Zr region targets,
peak 2 of 13C spectrum appears to be dominated by the ejectile excitation and little

is contributed by the real structure of 2”Pb.

Peaks 3 are seen weakly in all three reactions at almost the same reaction Q -
values, at about 12.5 MeV, and they have very similar strengths and shapes. They
seem to show some of the inner hole structure of 208Pb region nuclei. But, it is

not clear whether the strength of these peaks is due to the residual nucleus’s inner

 

 

 

134

hole states or mutual excitation. In the experiments of (2°Ne,19Ne) at Em = 25, 30
MeV/n [Fort 90], (7Li,8Li) (this experiment), and 208Pb(‘2C,13C) done at E,“ = 101
MeV [Oert 84], no peak was observed at corresponding excitation energies of about

10 MeV.

In the 209Bi(12C, 13C)2osBi reaction, the spectrum is very similar to that of the
208Pb(”C,13C) reaction. Three broad peaks are observed at almost the same exci-
tation energies and the reaction Q — values with those from the 2“Pb target, and
the difference of the reaction Q — values between the ground states, 0.09 MeV,is not
recognizable in the spectrum. 2093i has an extra proton in lhg/g state outside the
closed shell nucleus 2”Pb. The coupling of this proton to the neutron hole states

does not seem to change the shape of the spectrum or the centroid of the peaks.

In the 207Pb(”C,13C)2°6Pb reaction, the whole spectrum is shifted to higher exci-
tation energy compared to the spectra of the reactions from the 208Pb or 2098i targets,
by about 1 MeV. The 2(”Pb nucleus has a single neutron in the 3p1 ,2 state and the
reaction Q — value to pickup this neutron is higher by about 0.7 MeV than that to
pickup a neutron in a paired state of the 20‘l’Pb and 2”Bi nuclei. Except for this
unpaired 3121/2 neutron, all the processes of the pickup a neutron seemed to have the
similar reaction Q - values. The single neutron in 3111/; state couples to an inner neu-
tron hole state produced by a neutron pickup reaction, but the couplings appeared

not so strong enough as to observe any significant change in the spectrum.

For all (‘2C,13C) reactions on the 90Zr and 208Pb region targets examined here,
the predominance of ejectile excitation makes the investigation of deep lying single
hole states in the residual nuclei difficult. In the (7Li,8Li) reaction, ejectile excitation
is not so serious as in the 13C spectra, but the deep lying hole states are not excited

as much as in the 130 spectra.

 

135

7 .5 90Zr, 91Zr, 89Y (120,13N) Reactions

The energy spectra for the (12C,13N) reactions on targets 9°Zr, 91Zr and 89Y with
Em = 30 MeV/n at 0105 = 6" are shown in fig. 7.6. Because the threshold energy
for breakup into 12C + p (1.94 MeV) is lower than the excitation energy of the first
excited state (2.37 MeV), there is no bound excited state in 13N, and thus no ejectile
excitation contributes to the 13N spectra. The favoured angular momentum transfers
for this reaction are 2h and 311, and no spin-flip process is preferable. Excitation

energies, reaction Q - values and widths for the observed peaks are given in table 7.3.

In the 9°Zr(”C, 13N)89Y reaction, a strong peak is seen at low excitation (Ex. ~
1.58 MeV) and a broad weak peak is observed at medium excitation (Ex. ~ 6.56
MeV). The widths are about 3 MeV for both peaks. Since there is no ejectile ex-
citation, these peaks arise from the real structure of the residual nucleus. Peak
1 (1.58 MeV) arises from the excitation of the low lying hole states 2p1/2(ground
state), 199,2(0.91 MeV), 2p3/2(1.51 MeV) and 1f5/2(1.75 MeV) (see fig. 7.1) [Fort 90,
Gale 88]. The ground state is observed very weakly on the side of the large peak 1.
Considering the two transfer matching conditions (A1 = 2 and 3, and no spin-flip

process), the most dominant contribution very likely comes from the 1f5/2 state.

Peak 2 (6.56 MeV) appears to arise from the pickup of a lf-m proton. Since there
is only one proton hole state (If-m) near E3. = 6.56 MeV (see fig. 7.1), the 1f7/2
state accounts for most of the cross section between the excitation energies of 4 MeV
and 12 MeV. In the 9°Zr(cl,3He) reaction done with E4 = 52 MeV [Stui 80], two sharp
peaks were observed at E3. = 5 and 6.8 MeV above a broad large peak. But in the
present experiment, these peaks are not resolved. Similar peaks were also observed

in the reaction 9°Zr(2°Ne,21Na) with E = 25,30 MeV/n at Ex. ~ 7 MeV [Fort 90]

136

 

 

”2r."2r.°°v(“~’c.“N). e...=s° ”Zr.°‘2r.°°Y(“c.‘3N). e...=6°
12-..]. ..r...fi
2.0 :- .2
I 1 3
1.5 :— agY —:+
1.0 :— 1
: 2 3
0.5 — j

 

 

da/dOdE (mb/sr—MeV)

 

 

 

 

 

 

 

 

 

 

 

       

10 20
-— Q Value (MeV) Ex. (MeV)

(80 (b)

Figure 7.6: Experimental spectra of 9"Zr, 91Zr, 89Y (”C,”N) reactions with E = 30
MeV/n. The shaded area above the assumed background was used to obtain the
cross sections for peaks 2, and to compare the positions.

137

Table 7.3: Excitation energies for the observed peaks in the (12C,‘3N) reactions on
targets of 9°Zr, 9‘ Zr and 89Y. I‘ is the full width at half maximum, Q is the reaction Q
- value for the corresponding excitation energy and units are MeV. The uncertainty is

about 0.3 MeV. a is the cross section for the shaded area in mb/sr and the uncertainty
is about 20%.

 

9OZr(IZC,13N)89Y 91 ZI(12C,13N)90Y 89Y(120,13N)8881'

 

Peak Ex. P -Q 0' Ex. P -Q 0 Ex. I‘ -Q a

 

 

0.00 1.5 5.13
1.58 3.0 7.99 1.87 3.0 8.63 3.28 3.0 8.41
6.56 3.5 12.97 1.0 6.09 3.5 12.84 0.9 7.90 3.0 13.03 0.9

NHctflt

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

138

where the excitation energies are some higher than in the present experiment. The
differences might be caused by the low lying excitation (Ids/2, 0.33 MeV) of the ejectile
21N a, while there is no ejectile excitation in 13N. The high energy tail (Ex. 2 10 MeV)

can be explained by the pickup of a deep lying proton in the sd shell (see fig. 7.1).

The spectrum for the 91Zr(”C,‘3N)9°Y reaction is very similar to that of the
reaction with the 9°Zr target. When a proton in the 2p1/2 state is picked up, the
2d5/2 neutron state couples to the proton hole state (2p1/3) and forms a doublet. One
member of this doublet is the ground state (2’), which is shifted to lower energy by
1.87 MeV from peak 1, and the contribution of the ground state to peak 1 is not as
clear as in the 90(”CF’C) reaction. Peaks 1 and 2 appeared to be formed by the same
hole states as in the reaction with 9°Zr target. Significant change in the spectrum

due to the coupling between the 2d5/2 neutron and proton holes is not seen.

In the 89Y(”C, 13N)8‘3Sr reaction, the ground state (peak 0) is shifted to lower
energy from the centroid of peak 1 by 3.28 MeV, and it is separated from peak 1
enough to be recognizable as an independent peak. 89Y has one less proton in the
2p”; state compared to 9"Zr or 9‘Zr. The ground state is formed by pickup of a 2p1 ,2
proton as in the reactions on the 9°Zr and 91Zr targets. But the reaction Q — value for
the ground state in the 89Y target is much higher than in the other two targets, by
about 1.28 and 1.62 MeV respectively, because the 2p1 ,2 proton in 89Y is not paired.
This phenomenon is similar to the pickup of a neutron in the 3121 ,2 state seen in the
(”CPC) reactions on targets of 1“Pb, 209Bi and 20"'Pb. Thus the whole spectrum is
shifted to higher excitation energy. Peak 2 of this spectrum, which has an excitation
energy of 7.9 MeV, appears to be slightly narrower than those from the other two

targets, while the total cross section for peak 2 is about the same in all 3 reactions.

The mechanism of forming peak 2 is not understood clearly. This peak is seen

in a previous study which the authors designated as “giant resonance like structure”

139

[Stui 80]. But, from the comparison of the reaction Q - values and excitation energies,
the broad peaks 2 show the characteristics of single hole states rather than giant

resonance states.

7.6 208Pb, 209Bi, 207Pb (12C,13N) Reactions

The energy spectra for (12C,‘3N) reactions on the targets 208Pb, 2098i and 2°7Pb with
Em. = 30 MeV/ n at 9M, = 9" are shown in fig. 7.7. Excitation energies, reaction Q —-
values and widths for the observed peaks are given in table 7.4. The favoured angular
momentum transfers for this reaction are 2": and 3h. In each reaction, three peaks

are observed.

In the 208Pb(1"'C,‘3N)"’°7Tl reaction, one strong peak and two weak broad peaks
are observed. Peak 1 is observed at an excitation energy of 1.08 MeV with a width of
3 MeV. Similar peaks are also observed in the reactions on 2°9Bi and 20"Pb targets at
similar reaction Q - values. This peak appears to consist of the excitation of many
low lying states such as 3.91/2, 2d3/2, 1h" ,2 and 2d5/2 states at 0.0, 0.35, 1.35 and
1.67 MeV excitation energy respectively. Individual states are not resolved due to

the small energy gap between the states compared to the experimental resolution

(~ 1 MeV).

Peak 2, seen at about 5.4 MeV excitation with a width about 4 MeV, can be
accounted for by the hole states 2121/2, lgg/g, and 2p3/2. The main contribution seems
to be from the 199]) state due to the large factor of (2j + 1). A similar peak centered

at 5.4 MeV of excitation energy was also observed in the 208Pb(”0,18F) reaction at

Em = 376 MeV [Fern 87].

A very broad peak is seen at excitation energies ranging from 10 to 24 MeV. Peaks

at similar excitation are also observed in the reactions with 209Bi and me targets

140

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

da/dOdE (mb/sr-MeV)

 

 

 

 

 

 

    

 

 

 

 

 

 

an'Pb."°'Iai."""i=b("c.“to. om=9° “Pb.”Bi.‘°'Pb(“C.“N). e,..=9°
l I I I I I I I I I I I I I l I I I I I I I I I 7 I I I ll I I I I I I I I] I I T I l TI I I TI
: )-
o.a .- o.a E- 1
: : 207
0.6 :- O.6 _— T1
0.4 I- o.4 :—
o.2 :— o.2 :-
0.0 ”-4 0.0 ' '
0.6 :— 1 1 0.6 '_'- 1 1
: 2°°Pb : 1 mph 3
0-4 L— : 0.4 L" -:
0.2 ' ‘
0.0 3
t . : j
0'8 :- 1 “j 0.6 __ 1 -:
r- u L 4
: ZOOTI : C ZOOTI :
0-4 r' — 0.4 _— 7
,. ‘ C 2 1
0.2 0.2 :— .;
0.0“ 0.0"..J1....1....1.... .. .
o 10 20 so 40 50 o 10 20 so 40
- Q Value (MeV) Ex. (MeV)

(11) (b)

Figure 7.7: Energy spectra of 208Pb, 209Bi, 20"Pb (”C,‘3N) reactions with E = 30
MeV/n. The shaded area above the assumed background was used to obtain the
cross sections for peaks 3, and to compare the positions.

141

Table 7.4: Excitation energies of the peaks observed in the (”CPN) reactions on
targets of 208Pb, 2"‘*’Bi and 20"Pb. F is the full width at half maximum, Q is the
reaction Q - value for the corresponding excitation and units are MeV. The uncer-
tainty is about 0.3 MeV. a is the cross section for the shaded area in mb/sr and the
uncertainty is about 20%.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

208Pb(12C,13N)207T1 2mBi(12C,13N)208Pb ‘ 2°7Pb("C,‘3N)2°°Tl
Peak Ex. P - Q 0 Ex. I‘ - Q 0' Ex. F - Q a
#
0 0.00 1.0 1.86
l 1.08 3.0 7.15 5.00 3.0 6.86 1.41 3.0 6.95
2 5.40 4.0 11.41 8.30 4.0 10.17 5.70 4.0 11.24
3 I] 17.50 8.0 23.57 1.3 18.50 4.0 20.36 0.6 18.00 8.0 23.54 1.2

 

 

 

 

142

in this experiment, but were not observed in the experiments of 208Pb(""’Ne,21Na)
at Egnc = 25,30 MeV/n [Fort 90], 209Bi(2°Ne,21Na) at E,“ = 48 MeV/n, and
209Bi(36Ar,37K) at Em = 42 MeV/n [Fras 89]. This structure is not understood

at this point.

In the 2°QBi(12C,l3N )208Pb reaction, four peaks are observed. The ground state
(0*) is obtained by pickup of an lhg/g proton. This state is shifted to lower energy
by 5.0 MeV from the centroid of peak 1. Peak 1 is similar to those in the 206Tl and
207T1 spectra in Q - values and widths, but peaks 2 and 3 appear at lower energy
(Q - value) by about 1 and 3 MeV respectively compared to the other spectra. The
relative energy between peak 1 and peak 2 is about 3.3 MeV, which is smaller than
that of the values in the 2(”TI spectrum, namely 4.3 MeV. The shapes and the widths
of peaks 1 and 2 are very similar in all three spectra. But peaks 3 appear to be
slightly different. Peak 3 in the 208Pb spectrum is weaker than peaks 3 of the other
two spectra, and is only about half the width. The presence of a lhg/g proton outside
the closed shell not only shifted the position of peaks 2 and 3 but also changed the

relative energy between peaks 1 and 2, and the width and strength of peak 3.

In the 20"Pb(”C,‘3N)2""Tl reaction, the spectrum is very similar to that of 2°8Pb(”C,‘3N)
reaction. Peaks seen in this reaction can be explained in the same way as in the re-
action with the 2("’Pb target, with the exception of the extra coupling between the
neutron hole state (3121/2) and the inner proton hole states. One neutron hole in the
3113/2 state did not change the spectrum significantly from that of the 2°8Pb(”C,13N)

reaction, but only shifted the ground state to lower energy by about 0.5 MeV.

When peaks 1 and 2 of all three reactions are compared as functions of reaction Q
— values, they appear at similar positions (within 1.3 MeV). This suggests that peaks

1 and 2 of all three reactions are composed mainly of single hole states.

143

But the comparison for peaks 3 suggests a different result. In each reaction,
the width of peak 3 is very large. From the single particle energy levels given in
fig. 7.1, 1f5/2 and If”; states may account for this broad peak. This conclusion is
also supported by an (e, e’p) experiment [Gale 89]. If peak 3 is a broad single hole
state, the reaction Q — value of the peak should not change much from having an
extra particle or hole state outside the closed nucleus, while the excitation energy
may change due to the shift of ground state energy. On the other hand, if peak 3 is
the result of collective motion, the excitation energy should not change much, whereas

the reaction Q — value may change [see chap. 4].

The reaction Q — values of the centroid of the peaks of the (”CPN) reaction
are 23.57, 20.36 and 23.54 MeV on 208Pb, 2”Bi and 2°7Pb targets respectively. The
reaction Q - value for the 2093i target is lower than those for the other two targets
by about 3.2 MeV. While the corresponding excitation energies are 17.5, 18.5 and
18.0 MeV respectively. The excitation energy for the 2013Pb residual nucleus is higher
than those for the other two residual nuclei by 1.0 and 0.5 MeV, which are within
the resolution limit of this reaction, about 1 MeV. This comparison shows that some
of the characteristics of peaks 3 are closer to those of GR states than single particle

states.

 

Chapter 8

Summary

8.1 Summary

Experiments to investigate high lying single particle and hole states were performed
at Michigan State University using the K500 superconducting cyclotron. The purpose
of the experiments was to study heavy ion single nucleon transfer reactions including
the underlying background at high excitation, and to solve a particular question
viz. whether the broad peaks, observed in some recent neutron stripping reactions on
targets of 90Zr, 208Pb, 20"Pb, and 209Bi [Olme 78, Mass 86, Fras 87, Fort 90, Lhen 91],

are GR states or single particle states.

Projectiles and targets were chosen based on the requirements to distinguish the
nature of the broad peaks. For projectiles, 7Li and 12C were chosen, because the
resulting ejectiles such as 6Li, 6He, 8Li, 13N and 13C have very low threshold energies

for breakup or no bound excited states except 13C. For the targets, two even - even
nuclei '2me and 9°Zr, and their neighboring even - odd nuclei, 207Pb, 209Bi, 89Y and

91 Zr were chosen.
The reactions used were (7Li,6Li), (7Li,6He), (TLi,8Li), (”C,13C), and (‘2C,13N)

with Em = 30 MeV/n. For the (7Li,8Li) reactions, a limited number of targets were

used due to the limited beam time available. The reaction products were analyzed us-

144

 

145

ing the S320 broad range magnetic spectrograph and detected by the standard focal
plane detector system (two resistive wire position counters, two ionization cham-
bers, and a plastic scintillator). In the (12C,13C) reactions, elastically scattered 12C
particles were blocked by using a “finger”. Data obtained were analyzed using the

program SARA. Particles were cleanly identified using the two dimensional spectra

of AE.vs.E and TOF.vs.POS.

Shell model calculations were carried out on 208Pb region targets in order to es-
timate the coupling strengths of p — p, h — h, and p — h, and to observe how the
characteristics of the single particle states at high excitation, such as the centroid,
width, and strength of the single particle states, depend on these couplings. The re-
sults showed that the single particle states, split into multiplets by an extra particle
or hole in the target, were spread over several MeV. However, the centroid energies
of the multiplets were shifted by at most a few hundred keV from the values of the
single particle states. The calculations were compared with the experimental data in
chap. 3, and they agreed within a few hundred keV. The results provided evidence
that the presence of an extra particle or hole outside a closed shell nucleus does not

change the absolute energies significantly, but it may change the excitation energies.

The method used to distinguish GR states and single particle states was described
in chap. 4. In GR excitations, the motion is collective, many particles are involved,
and the excitation energies vary smoothly with the mass [Youn 76]. There should
be no significant change in the excitation energy for a change in mass (A) of 1
unit. In this experiment, giant quadrupole resonances were observed in the reac-
tions 9"Zr, 91Zr, 89Y (”C,”C) at Em = 30 MeV/n. No differences were found in
their characteristics, such as the excitation energies and widths. On the other hand,
in single particle states, only a few particles are involved, and the excitation energies

may vary drastically with the mass. The reaction Q - value is not expected to change

 

146

much, at most by a few hundred keV, due to p — p or p - h interactions, as was
shown in the shell model calculations. The comparison of the reaction Q - values and

excitation energies for certain states provides evidence for the nature of the states.

This method was applied to the broad peaks observed in single nucleon transfer
reactions on 9"Zr region targets, and 208Pb region targets separately, both for neutron

and proton transfer reactions in chapters 5 and 7.

One nucleon stripping reactions were discussed in chap. 5. The spectrum of each
reaction was plotted, for 9"Zr and 208Pb region targets separately, as a function of
both the reaction Q — values and excitation energies. A preference for the high spin

states with no spin-flip was observed.

In the (7Li,6Li) reactions with even—odd targets, the couplings between the single
particle states and the target’s ground state changed the shapes of the peaks of the
single particle states significantly at low excitation energies (Ex. 5 10 MeV) for both
9”Zr and 208Pb region nuclei. But they did not shift the centroid of the multiplet

significantly as indicated in the figures plotted versus reaction Q - values.

In each spectrum with 9"Zr region targets, a large broad peak at about Ex. = 14
MeV, was observed. The comparisons of the reaction Q - values and excitation
energies for these broad peaks showed that the broad peaks have the characteristics

of single particle states.

A similar phenomenon was observed in the same reaction on me region targets.
In each spectrum, a weak broad peak was observed at around Err. = 10 MeV. The
comparison of the Q - values and excitation energies suggested that the broad peaks
arise from the single particle states. The strengths for the broad peaks were much
weaker than in the reactions using 20Ne, a, and 36Ar projectiles at similar incident

energy per nucleon.

 

 

 

147

In the (7Li,6He) reactions with 9"Zr region targets, the spectra were very similar.
The presence of an extra proton particle or hole in the targets did not change the over-
all shape of the spectra, but some peaks at low excitation were changed significantly

in the widths.

In the (7Li,6He) reactions with '2me region targets, the broad peaks seen at
around 9 MeV of excitation energies appeared at almost the same reaction Q - values,
but differed in their excitation energies by about 1.3 MeV. This result again suggests

that these broad peaks have the characteristics of single particle states.

Substantial background appeared in all the stripping reactions studied and made it
difficult to observe structures at high excitation. An attempt was made to explain the
background by calculating the projectile breakup cross section using the theoretical
models in chap. 6. Among the many theoretical models, the Serber model, and a semi-
classical model developed by Brink and Bonaccorso were used. The Serber model
does not match the shape of the experimental spectra except at very high excitation
energy (> 35 MeV) in proton stripping reaction. The Brink-Bonaccorso model, does
match the shape of the experimental spectra for neutron stripping reactions very well

although it does not agree with the shape for the proton stripping case.

The Brink-Bonaccorso model predicted that only about 20% of the total contin-
uum arose from projectile breakup, and the rest of the continuum was predicted to
come from the formation of the compound states in the (7Li,6Li) reactions for both
9"Zr and 2“Pb region targets. The shape of the total cross sections agreed very well
with the experimental data for the neutron transfer reactions. But predictions for
the (7Li,6He) reactions did not agree well with the experimental data. One possible
explanation is that the optical parameters might not be very good for this calculation.
Another possibility is that the angle dependence was not considered in the calcula-

tion, whereas the experimental data were obtained at a particular angle. It would be

148

useful to have angle dependent predictions.

The results of the pickup reactions are presented in chap. 7. In the (12C,13C)
reactions, substantial ejectile excitation was observed both for 9°Zr and 208Pb region
targets. The presence of ejectile excitation made it difficult to explore the deep lying
hole states. The comparison of the reaction Q — values and excitation energies for

the peaks suggested that all the peaks had the characteristics of single hole states.

However, in proton pickup reactions of (12C,13N) on the 208Pb region targets, the
experiment suggested a different result. Broad peaks seen at the (‘20,‘3N) reac-
tions on the 1"’st, 2”Bi and 207Pb targets, have centroids at reaction Q — values of
23.57, 20.36 and 23.54 MeV, and excitation energies of 17.50, 18.50 and 18.00 MeV
respectively. From the comparison of the Q -— values and excitation energies, the char-
acteristics of these peaks appear to be closer to those of the GR states than the single
hole states. But, it is not very clear whether the GR states were really formed or not,
because the peaks are so broad that uncertainties are large. More investigation on

this subject is required for the clear understanding.

Bibliography

[Alfo 70]
[Baym 58]

[Becc 87]

[Bert 76]
[Bert 81]
[Bert81a]

[Bing 70]
[Bohr 69]
[Bona 85]
[Bona 87]
[Bona 88]
[Bona 91]
[Bfin7fl
[Chom 86]
[Chom 90]

[Craw 73]

[Duff 86]

W. P. Alford, J. P. Schiffer and J. J. Schwartz, Phys. Rev. C 3, 860(1970)

B. F. Bayman, A. S. Reiner and R. K. Sheline, Phys. Rev. Vol.115,
1627(1958)

F. D. Becchetti, D. A. Roberts, J. W. Janecke, A. Nadasen, C. A. Ogilvie
and J. S. Winfield, Annual Report of NSCL, 100(1987)

F. E. Bertrand, Ann. Rev. Nucl. Sci. 26, 457(1976)
F. E. Bertrand, Nucl. Phys. A 354, 129c(1981)

F. E. Bertrand, E. E. Gross, D. J. Horen, J. R. Wu, J. Tinsley, D. K.
McDaniels, L. W. Swenson and R. Liljestrand, Phys. Lett. Vol. 1033,
326(1981)

C. R. Bingham and M. L. Halbert, Phys. Rev. C 2, 2297(1970)

A. Bohr and B. R. Mottelson, ”Nuclear Structure”, Vol.1, 1969

A. Bonaccorso, G. Picolo and D. M. Brink Nucl. Phys. A 441, 555(1985)
A. Bonaccorso, D. M. Brink and L. Lo Monaco J. Phys. G 13, 1407(1987)
A. Bonaccorso and D. M. Brink, Phys. Rev. C 38, 1776(1988)

A. Bonaccorso and D. M. Brink, Phys. Rev. C 44, 1559(1991)

D. M. Brink, Phys. Lett. 403, 37(1972)

Ph. Chomaz, J. Phys. (Paris) Colloq. 47, C4-l55(1986)

Ph. Chomaz, N. Frascaria, S. Fortier, S. Gales, J .P. Garron, H. Laurent,
1. Lhenry, J. C. Roynette, J. A. Scarpaci, T. Suomijarvi, N. Alamanos,
A. Gillibert, G. Crawley, J. Finck, G. Yoo, A. Van der Woude, Annual
Report, IPN-Orsay 63(1990)

G. M. Crawley, E. Kashy, W. Lanford and H. G. Blosser, Phys. Rev. C
8, 2477(1973)

J. E. Duffy, Ph. D. Thesis, Michigan State University, unpublished,
(1986)

149

[Fern 87]

[Pine 82]
[Fink 73]
[Fort 90]
[Fox 85]
[Fox 89]

[Fras 87]
[Fra887a]

[Fras 89]
[Fuch 82]
[Gale 85]

[Gale 88]
[Gale 89]
[Gale 91]
[Goan 72]
[Hash 88]
[Herl 72]
[Hodg 80]

[Gerl 75]
[Kasa 83]

[Knop 70]
[Lanf 74]

150

M. A. G. Fernandes, F. E. Bertrand, R. L. Auble, R. O. Sayer, B. L.
Burks, D. J. Horen, E. E. Gross, J. L. Blankenship, D. Shapira, and M.
Beckerman, Phys. Rew. C 36, 108(1987)

J. E. Finck, Ph. D. Thesis, Michigan state University, unpublished,
(1982)

G. Finkel, D. Ashery, A. I. Yavin, G. Bruce and A. Chaumeaux, N ucl.
Phys. A 217, 197(1973)

S. Fortier, S. Gales, S. M. Austin, W. Benenson, G. M. Crawley, C.
Djalali, J. S. Winfield and G. Yoo, Phys. Rev. C 41, 2689(1990)

R. Fox, An. A. Vander Molen, B. Pollack and T. Glynn, IEEE Trans.
on Nucl. Sci., Vol. NS-32, 1286(1985)

R. Fox, An. A. Vander Molen IEEE Trans. on Nucl. Sci., Vol. NS-36,
1608(1989)

N. Frascaria et al., IPN - Orsay, Rapport Annuel, 41(1987)

N. frascaria, Y. Blumenfeld, Ph. Chomaz, J. Garron, J. Jacmart, J.
Roynette, T. Suomajarvi and W. Mittig, Nucl. Phys. A 474, 253(1987)

N. Frascaria et al., Pr0posal for CAN IL exp., (1989)
H. Fuchs, Nucl. Ins. and Meth. 200, 361(1981)

S. Gales, C. P. Massolo, S. Fortier and J. P. Shapira, Phys. Rev. C 31,
94(1985)

S. Gales, Ch. Stoyanov and A. I. Vdovin, Phys. Rep. 166, 125(1988)
S. Gales, IPNO-DRE—89-43, IPN Orsay (1989)

S.Gales, Private communications.

R. E. Goans and C. R. Bingham, Phys. Rev. C, 5, 914(1972)

H. Hashim and D. M. Brink, Nucl. Phys. A476, 107(1988)

G. H. Herling and T. T. S. Kuo, Nucl. Phys. A 181, 113(1972)

P. E. Hodgson, ”Groth Points in Nuclear Physics”, Pergamon Press,
(1980)

E. Gerlic, J .Kallne, H. Langevin-Joliot, J. Vande Viele and G. Duhamel,
Phys. Lett. 57B, 338(1975)

J. Kasagi, G. M. Crawley, E. Kashy, J. Duffy, S. Gales, E. Geric and D.
Friedsel, Phys. Rev. C 28, 1065(1983)

K. T. Knopfle and M. Rogge, Nucl. Phys. A 159, 642(1970)
W. A. Lanford and G. M. Crawley, Phys. Rev. C 9, 646(1974)

[Lhen 91]

[Ma 73]
[Maha 89]
[Mass 86]

[Mats 78]
[Moha 91]
[Mats 80]

[Mcgr 75]
[Mwsa

[Merm 88]

[Merm 87]

[Mona 85]
[Lim 73]
[Ohls 65]
[Olme 78]
[Oert 84]

[ostsa

[Ring 80]

151

I. Lhenry, T. Suomijarvi, Y. Blumenfeld, Pb. Chomaz, N. Frascaria, J.
P. Garron, J. C. Roynette, J. A. Scarpaci, D. Beaumel, S. Fortier, S.
Gales, H. Laurent, A. Gillibert, G. Crawley, J. Finck, G. Y00 and J.
Barreto. RIKEN-AF-los, 317(1991)

Chin W. Ma and William W. True Phys. Rev. 8, 2313(1973)
C. Mahaux and R. Sartor, Nucl. Phys. A 493, 157(1989)

C. P. Massolo, F. Azaiez, S. Gales, S. Fortier, E. Gerlic, J. Guillot, E.
Hourani, and J. M. Maison, Phys. Rev. C 34, 1256(1986)

N. Matsuoka, A. Shimizu, K. Hosono, T. Saito, M. Kondo, H. Sakaguchi,
Y. Toba, A. Goto and F. Ohatani and N. Nakanishi, Nucl. Phys. A 311,
187(1978)

M. Mohar, Ph. D. Thesis, Michigan State University, unplished, (1991)

N. Matsuoka, M. Kondo, A. Shimizu, T. Saito, H. Sakaguchi, A. Goto
and F. Ohtani Nucl. Phys. A 337, 269(1980)

J. B. Mcgrory and T. T. S. Kuo, Nucl. Phys. A 247, 283(1975)

R. J. de Meijer and R. Kamermans, Rev. od Mod. Phys. Vol. 57,
147(1985)

M. C. Mermaz, E. Tomasi-Gustafsson, B. Berthier, R. Lucas, J. Gaste-
bois, A. Gillibert, A. Boucenna, L. Kraus, I. Linck, B. Lott, R. Reb-
meister, N. Schulz, J. C. Sens, and C. Grunberg, Phys. C 37, 1942(1988)

M. C. Mermaz, B. Berthier, J. Barrette, J.Gastebois, A. Gillibert, R.
Lucas, J. Matuszek, A. Miczaika, E. Van Renterghem, T. Suomijarvi,
A. Boucenna, D. Disdier, P. Gorodetzky, L. Kraus, I. Linck, B. Lott, V.
Rauch, R. Rebmeister, F. Scheibling, N. Schulz, J. C. Sens, C. Grunberg
and W. Mittig, Z. Phys. A 326, 353(1987)

L. Lo Monaco and D. M. Brink, J. Phys. G 11, 935(1985)
T. K. Lim, Phys. Lett. 44 B, 341(1973)
G. G. Ohslen, Nucl. Ins. and Meth. 37, 240(1965)

C. Olmer, M. Mermaz, M. Buenerd, C. K. Gelbke, D. L. Hendrie, J.
Mahoney, D. K. Scott, M. H. Macfarlane and S. C. Pieper, Phys. Rev.
C 18, 205(1978)

W. von Oertzen, H. Lettau, H. G. Bohlen and D. Fick, Z. Phys. A 315,
81(1984)

B. A. Brown, A. Etchegoyen and W. D. M. Rae, MSU NSCL Report
Num. 524, (1988)

P. Ring and P. Schuk, ”The nuclear many body problem”, Springer-
Verlag, 1980

[5320 90]
[Sara 90]

[Serb 48]
[Sher 85]

[Stui 80]

[Suom 89]

[Suom 90]

[Ture 88]

[Vour 69]

[Warb 91]
[Winf 91]

[Woud 87]
[Wu 78]

[Wu 79]
[Yama 81]

[Youn 76]

[Zism 73]

152
H. Plicht and J. Winfield, ”THE 3320 SPECTROGRAPH MANUAL”,
(1990)

B. Sherrill and J. Winfield, ”THE SARA DATA ANALYSIS PRO-
GRAM”, (1990)

R. Serber, Phys. Rev. 72, 1008(1948)

B. M. Sherrill, Ph. D. Thesis, Michigan State University, Dept. of
Physics, unpublished, 1985

A. Stuibrink, G. J. Wagner, K. T. Knopfle, Liu Ken Pao, G. Mairle, H.
Riedesel, K. Schindler, V. Bechtold and L. Friedrich, Z. Phys. A 297,
307(1980)

T.Suomijarivi, D. Beaumel, Y. Blumenfeld, Ph. Chomaz, N. Frascaria,
J. Garron, J. Jacmart, J. Roynette, J. Barrette, J. Berthier, B. Fernan-
dez, J. Gastebois, P. Roussel Chomaz, W. Mittig, L. Kraus and 1. Link,
Nucl. Phys. A 491, 314(1989)

T.Suomijarivi, D. Beaumel, Y. Blumenfeld, Ph. Chomaz, N. Frascaria,
J. Garron, J. Roynette, J. Barrette, J. Scarpaci, B. Fernandez, J. Gaste-
bois, W. Mittig, Nucl. Phys. A 509, 369(1990)

P. Turek, A. Kiss, A. Djaloeis, C. Mayer-Boricke, M. Rage and S.
Wiktor, J. Phys. G : Nucl. Phys. 14, 771(1988)

G. Vourvopouros and J. D. Fox, Phys. Rev. Vol.177, 1558(1969)
E. K. Warbuton and B. A. Brown, Phys. Rev. C 43, 602(1991)

J. S. Winfield, private communication

Van Der Woude, Prog. in Part and Nucl. Phys. Vol.18, 217(1987)

J. R. Wu, C. C. Chang and H. D. Holmgren Phys. Rev. Lett. 40,
1013(1978)

J. R. Wu, C. C. Chang and H. D. Holmgren Phys. Rev. C 19, 370(1979)

T. Yamagata, S. Kishimoto, K. Yuasa, K.Iwamoto, B. Saeki, M. Tanaka,
T Fukuda, I. Miura, M. Inoue and H. Ogata, Phys. Rev. C 23, 937(1981)

D. H. Youngblood, J. M. Moss, C. M. Rozsa, J. D. Bronson, A. D.
Batcher and D. R. Brown, Phys. Rev. C 13, 994(1976)

M. S. Zisman, F. D. Becchetti, B. G. Harvey, D. G. Kovar, J. Mahoney
and J. D. Sherman, Phys. Rev. C 8, 1866(1973)

"11111111111111.1111]?