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. Them for (me, Degree «my.
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' 19:71

 

This is to certify that the

thesis entitled

The (p,t) Reaction On Rare Earth Nuclei

presented by

Ronald William Goles

has been accepted towards fulfillment
of the requirements for

__Ph.._D_.__degree in Minu—
Major professor
Date 7 I 26 I 71

 

0-7639

 

 
 
   
   

  

LIBRAR y ‘
Michigan Stan;
University

ABSTRACT

THE (p,t) REACTION 0N RARE EARTH NUCLEI

By
Ronald William Goles

The (p,t) reaction on 141Pr, 159Tb, 165Ho and 169Tm has been
carried out for the purpose of studying the general systematics of the
(p,t) reaction on rare earth nuclei. All experiments were conducted at
the bombarding energy of 30 MeV with the exception of the 141Pr(p,t)
experiment which was carried out at 40 MeV.

The (p,t) reaction on 141Pr was found to strongly populate
collective vibrational states in the more or less spherical 139Pr
nucleus. Angular distributions of states populated through this reaction
were collected between 15° and 65° at 5° intervals and have been
compared with distorted wave calculations.

In each of the remaining deformed nuclei studied, a strong
population of the ground state rotational band was observed with at
least six band members being excited in each case. Moreover, a B
vibrational band in 157Tb and y vibrational bands in 157Tb and 163Ho
were also found to be strongly excited through this reaction. Angular
distributions of states below 1.25 MeV of excitation populated through

159

the Tb(p,t) reaction were taken between 10° and 75° at 5° intervals

and have been compared with distorted wave predictions.

1 7
In addition, y ray experiments involving the £/B+ decay of 6 Yb

were conducted in order to complement the 169Tm(p,t) experiment. This

decay scheme study has established the existence of twelve new excited

Ronald William Goles

states and the probable placement of a thirteenth in the daughter

nucleus 167Tm. Moreover, these thirteen states together with the well

established low energy level structure of the 167Tm nucleus form a

consistant framework for the placement of 52 new Y rays associated

with the decay of 167Yb.

THE (p,t) REACTION ON RARE EARTH NUCLEI

By

Ronald William Goles

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1971

K, 7) 771

For my mother

711$

ACKNOWLEDGEMENTS

I wish to thank Dr. Wm. C. McHarris for suggesting this very
interesting area of study. His patience and help during the experimental
work and the preparation of this thesis are sincerely appreciated. I
would also like to thank Dr. W. H. Kelly, Dr. B. H. Wildenthal and
Dr. J. A. Nolen for their valuable advice concerning many aspects of
experimental work.

A very special thank you is extended to Dr. R. A. Warner for his
invaluable suggestions and experimental assistance.

Dr. B. Preedom, Mr. I. D. Proctor, Mr. J. A. Rice and Dr. G. F.
Trentelman are gratefully acknowledged for their help in data
acquisition and/or analysis.

I acknowledge the financial assistance of the National Science
Foundation, U. 8. Atomic Energy Commission and Michigan State
University.

Finally, I wish to thank my scientific assistant, Mary, who always

cheerfully found time to help her husband in his scientific endeavors.

iii

TABLE OF CONTENTS

DEDICATION . . . .
ACKNOWLEDGEMENTS . . .
LIST OF TABLES . . . . .
LIST OF FIGURES . .
Chapter
I. INTRODUCTION . .
II. NUCLEAR MODELS .
2.1. Shell Model

2.2. Liquid Drop Model

2.3. Unified Model . . . . . .
2.3.1. Rotational Spectra . . . . . . . . . . . . .
2.3.2. Vibrational States . . . . . . . . . .
III. DWBA SCATTERING THEORY . . .
3.1. Basic Theory . .
3.2. Differential Cross Section . .
3.3. Form Factor . .
3.3.1. Cluster Transfer and Zero Range Approximation
3.3.2. Two Nucleon Matrix Element . . . . . .
3.3.3. Finite Range Correction . . . . . .
IV. EXPERIMENTAL APPARATUS AND METHODS . .

4.1.

The (p,t) Reaction .

4.1.1..

4.1.2.

Cyclotron and Beam Transport .

Target Fabrication .

iv

ii
iii
viii
ix

Page

13
14
17
20
23
24
24
24

24

Chapter

4.2.

4.1.3.

4.1.4.

4.1.5.

167Yb

4.2.1.

4.2.2.

4.2.3.

6/8+

4.1.2.A. 1“Pr Target . . . . . . . . . . .
4.1.2.B. 159Tb Target .

4.1.2.C. 165Ho and 169Tm Targets . .

The Faraday Cup and Charge Collection . .
lulPr(p,t) Experiment . . . . . . . .
4.1.4.A. The Scattering Chamber . . . . . .

4.1.4.B. The Detector Telescope and Monitor
Counter . . . . . . . . . . . .

4.1.4.C. Electronics and Particle Identi-
fication . . . . . . . . . .

4.1.4.D. Dead Time Correction .

159Tb(p,t), 16SHo(p,t) and 169Tm(p,t)
Experiments . . . . . . . . . . . . .

4.1.5.A. The Magnetic Spectrograph

4.1.5.8. Monitor Counter . . . . . . . . .
4.1.5.C. Plate Reading . . . . . . .

167Tm Experiment . . . . . . . . .
Source Preparation . . . . . . . . . .

y-Ray Singles Experiments . . . . . .

y-Ray Coincidence Experiments . . . .

V. DATA REDUCTION . . . . . . . . . . . . . . . . . . .

5.1.

5.2.

Peak Areas and Centroids . . . . . . . . . . .

(p,t) Experiment . . . . . . . . . . . . . . . . .

5.2.1.

5.2.2.

Energies . . . . . . . . . . . . . . . .
5.2.1.A. 1°1Pr(p,t) Experiment . . . .
5.2.1.B. Spectrograph Experiments . .

Cross Sections . . . . . . . . . . . . . . .

Page
26
26
27
27
27

27

28

29

32

32
34
35
35
35
35
36
37
4O
4O
4O
4O
41
41

42

Chapter Page
5.3. y-Ray Experiments . . . . . . . . . . . . . . . . . 42
5.3.1. y-Ray Energies . . . . . . . . . . . . . . . 42

5.3.2. y-Ray Relative Intensities . . . . . . . . . 43
VI.”lPr(p,t)RESULTS.................... 45
6.1. Introduction . . . . . . . . . . . . . . . . . . . . 45

6.2. DWBA Analysis . . . . . . . . . . . . . . . . . . . 45

6.3. ll”Perfit) Spectra . . . . . . . . . . . . . . . . . 47

6.4. Angular Distributions . . . . . . . . . . . . . . . 49

6.5. Summary . . . . . . . . . . . . . . . . . . . . . . ' 54
VII.159Tb(p,t)RESULTS.................... 57
7.1. Introduction . . . . . . . . . . . . . . . . . . . . 57

7.2. Spectral Results . . . . . . . . . . . . ... . . . . 60

7.3. Angular Distributions . . . . . . . . . . . . . . . 63
7.3.1. DWBA Analysis . . . . . . . . . . . . . . . 63

7.3.2. Ground State Rotational Band . . . . . . . . 63

7.3.3. 7 Vibrational Band . . . . . . . . . . . . . 68

7.3.4. B Vibrational Band . . . . . . . . . . . . . 69

7.3.5. Other States . . . . . . . . . . . . . . . . 70

7.4. Summary . . . . . . . . . . . . . . . . . . . . . . 71

VIII. 165Ho(p,t)RESULTS.................... 73
8.1. Introduction . . . . . . . . . . . . . . . . . . . . 73

8.2. Spectral Results . . . . . . . . . . . . . . . . . . 73

8.3. Summary . . . . . . . . . . . . . . . . . . . . . . 76

Ix. STATES IN 157Tm . . . . . . . . . . . . . . . . . . . . . 80
9.1.159Tm(p,t)Results................. 80

9.2. y-Ray Studies of 167Yb Decay . . . . . . . . . . . . 82

vi

Chapter Page

9.2.1. Introduction . . . . . . . . . . . . . . . . 85
9.2.2. Experimental Results . . . . . . . . . . .'. 89
9.2.3. 167Yb Decay Scheme . . . . . . . . . . . . . 97

9.3. Summary . . . . . . . . . . . . . . . . . . . . . . 101

X. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . 104

LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 106
APPENDICES

A. 1L‘lPr(p,t) Spectra . . . . . . . . . . . . . . . . . . 110

B. Tabulation of lL*1Pr(p,i‘) Differential Cross Sections . 117

C. 159Tb(p,t) Spectra . . . . . . . . . . . . . . . . . . 121

D. Tabulation of 159Tb(p,t) Differential Cross Sections . 129

vii

LIST OF TABLES

Table Page

5.1. Y—Ray Calibration Standards. ......... . ................. 44

6.1. Optical Model and Bound-State Well Parameters used in
the Distorted-Wave Analysis of the 1H1Pr(p,t) Reactions 48 .

6.2. States Populated Through the ll‘lPr(p,t) Reaction....... 55

7.1. Multipolarities of y Rays Deexciting the Y Vibrational
Band in 157Tb .................... ....... .......... ..... 59

7.2. Multipolarities of Y Rays Deexciting the Vibrational
Bands in 157Tb... ...... ................. ..... .......... 59

7.3. States Populated Through the 159Tb(p,t) Reaction....... 62

7.4. Rotational Parameters Associated with Bands Populated
Through the 159Tb(p,t) Reaction........................ 64

7.5. Optical-Model and Bound-State Well Parameters used in
the Distorted-Wave Analysis of the 159Tb(p,t) Reaction. 66

8.1. States Populated Through the 165Ho(p,t) Reaction....... 77

8.2. Rotational Parameters Associated with Bands Populated

Through the 165Ho(D,t) Reaction... ..... . ............... 78
9.1. States Populated Through the 169Tm(p,t) Reaction ....... 83
9.2. y—Ray Transition Data for the 167Yb Decay .............. 92

9.3. Results of Integral Delayed Coincidence Study on 167Yb
Decay.... ................. .......... ................. .. 96

9.4. Relative Feeding Intensity Data to Members of the Ground
State Rotational Band..................................100

9.5. Theoretical vs. Experimental Reduced Transition Proba-

bilities. ..... .........................................102

viii

Figure

2.1.

4.1.

4.2.

4.3.

4.4.

4.5.

6.1.

6.2.

6.3.

6.4.

7.1.

7.2.

LIST OF FIGURES

Page
Coupling scheme for deformed nuclei .......... ...... ..... 6
Michigan State University Cyclotron, beam transport 25
system and experimental areas.... ................ . ......
Detector telescope summing circuit ..... ................. 30
Experimental Electronics associated with the E—AE
detector telescope .............. .. ................. ..... 31

TOOTSIE two dimensional E-AE display illustrating three

particle bands.......................................... 33

Experimental apparatus associated with y ray anti- and

delayed coincidence experiments.. ...... . ......... ....... 38
Decay schemes of 139”Nd and 139gNd. ..... ................ 46

lulPr(p,t) triton spectra taken with an E-AE detector

telescope........... ........ ...... ...... ................ 50

Angular distributions of states populated through the
lulPr(p,t) reaction. Theoretical two neutron pick-up
and cluster transfer calculations are represented by
continuous and broken curves respectively. Relative
cross sections have been normalized to reflect measured

absolute values......................................... 51

Angular distributions of peaks which might have a com-
posite nature. An i=6 angular shape has been included

for comparison sake only............... ...... ........... 53

Partial level structure of 157Tb. Arrows represent
deexciting y rays observed when various states are fed

by the s decay of 157Dy................................. 58

Log and linear displays of the 159Tb(p,t) spectrum taken
at the laboratory scattering angle of 20°........ ....... 61

ix

Figure

7.3.

7.4.

8.1.

8.2.

8.3.

9.1.

9.2.
9.3.

9.4.

9.5.

9.6.

9.7.

Page

States populated through the 159Tb(p,t) reaction........ 65

Angular distributions of states populated through the
159Tb(p,t) reaction. Theoretical two neutron pick—up
and cluster transfer calculations are represented by
continuous and broken curves respectively. Relative

cross sections have been normalized to reflect measured

absolute values..... ........... ..... ................... . 67
Partial collective level structure of 165Ho ............. 74
Log and linear displays of the 165Ho(p,t) spectrum taken

at the laboratory scattering angle of 20°.... ....... .... 75
States populated through the 165Ho(p,t) reaction........ 79
Log and linear displays of the 169Tm(p,t) spectrum taken

at the laboratory scattering angle of 20°............... 81
States populated through the 169Tm(p,t) reaction........ 84
Low energy rotational structure of 167Tm... ............. 86
167Yb singles y ray spectrum taken with a Ge(Li) detec—

tor using a graded lead absorber........................ 90
167Yb low energy y ray spectrum taken with a high
resolution Si(Li) x-ray detector ........ ....... ......... 91
Spectrum of 167Yb y rays involved in delayed coinci-
dences.................................................. 95
Decay scheme of 167Yb. All energies are given in keV,

and (total) transition intensities are given in terms of
+

percent per disintegration of the parent. The B Is

ratios are calculated values and the log ft values are

calculated on the basis of on 18 min half-life.... ...... 98

Chapter I

Introduction

The purpose of this thesis is to investigate the general
systematics of the (p,t) reaction on rare earth nuclei. Until quite
recently this area of study has been left literally unresearched,
although the (p,t) reaction work that has been done on intermediate
to heavy mass nuclei (Ba64, Ba68, Bj66, Re67, Ma66) has served to
establish the direct nature of this reaction at moderate bombarding
energies.

Direct reactions are particularly useful in the study of
nuclear properties since their associated mechanisms are simple and
are easily understood. Models of direct reaction mechanisms have
been developed and from these have come computer codes (B362, Ku65)
which are capable of predicting quite accurately observed experimental
phenomena such as angular scattering probabilities.

Pick-up reactions are a general type of direct nuclear
reaction which are characterized by the transfer of a nucleon or
group of nucleons from the target nucleus to an impinging, interacting
projectile. To be more specific, the (p.t) reaction is pictured as
proceeding through a one step transfer process in which the incident
proton plucks out an ordered pair of neutrons from the target nucleus
and scatters away in the form of a triton.

The particular target nuclei used in this study are: 11+1Pr,
159Tb, 165Ho and 169Tm. The 11‘1Pr(p,t) reaction was chosen to initiate

this study, because the spherical shape of the 1“Pr nucleus together

2
with the well known level structure of the residual nucleus, 139Pr,
allowed a straight forward analysis of the experimental data. The
results of this analysis then served to establish the basic character-
istics of the (p,t) reaction on rare earth nuclei.

Having completed the 1L‘lPr(p,7‘;) study and knowing a little
more of what to expect, the (p,t) reactions on the remaining strongly
deformed nuclei were conducted. In addition, Y-ray experiments involving
the €/B+ decay of 167Yb were carried out to complement the 169Tm(p,t)
reaction experiment.

The results of these studies have shown the (p,t) reaction
to be a very powerful tool for probing the collective properties of

nuclei, two neutrons removed from stability.

Chapter II. Nuclear Models

The interpretation of experimental results obtained for
the (p,t) reaction on rare-earth nuclei leans quite heavily upon the
use of several models of the nucleus. In this chapter, those nuclear
models which are to be used in the following chapters will be reviewed.

2.1. Shell Model

 

One of the most successful models of the nucleus is the
shell model with spin-orbit interaction (Ma55). In this model individ-
ual nucleons are considered to move in stationary orbits determined by
an effective spherically symmetric potential which is meant to approxi-
mate the nucleon-nucleon interactions occurring within the nucleus.
Moreover, within the nucleus these orbiting nucleons are pictured as
being paired off in such a way that values of many nuclear parameters
are determined solely by a single unpaired nucleon.

The great success of this model lies in its ability to predict
nuclear properties such as "magic numbers", nuclear isomerism, and ground
state spin systematics for even and odd mass nuclei.

However, because of the simplifications used, the simple shell
model cannot describe correlated or collective motion of nucleons within
the nucleus and is therefore incapable of describing the collective
properties exhibited by nuclei such as large quadrupole moments and low
lying collective excited states.

2.2. Liquid-Drop Model

 

The collective model of the nucleus (Pr63) separates the
nucleus into a core and extracore nucleons. The core is treated

macroscopically as a deformable drop of nuclear liquid in interaction

with the few extra-core nucleons that occupy unfilled shell model
orbitals. Such a system can undergo two types of collective motion -
surface vibrations in which the shape is distorted in an oscillatory
fashion with preservation of volume and volume vibrations with preserva-
tion of shape. Since the nuclear fluid is nearly incompressible, the
lowest excitations are associated with surface vibrations.

Clearly, this model of the nucleus is extremely useful in
describing vibrationally excited states of spherical nuclei. For
instance, in odd mass spherical nuclei, low lying vibrational states are
pictured as being constructed from the various possible couplings of
the vibrational angular momenta of the core A, called the multipole
order, with the spin, I, of the ground state. Thus, in the case of a
quadrupole vibration, A=2, one would expect to observe a multiplet of
vibrationally excited states with spins ranging from II-ZI to I+2.

To first order, this multiplet of core excited states are degenerate;
however, residual interactions between the odd nucleon and the core in
practice lifts their degeneracy.

In spite of the success of the liquid drop model in explaining
the low lying excited states associated with spherical nuclei, it is
inadequate to explain the level structure exhibited by permanently
deformed nuclei. Clearly the nuclear system is capable of motions not
envisaged by the simple liquid drop model.

2.3. Unified Model

Bohr (3052) and Bohr and Mottelson (B053) tried to fuse the

individual-particle and liquid—drop aspects of the nuclear system into

a single "unified" model. Briefly, the model consists of a deformed

rotating-vibrating nuclear core which provides a non-spherical field

in which individual nucleons move. The quantum state of the model is
—> ->

defined by the quantum numbers I, K, O, and.M, where I is the total

core plus odd nucleon(s) angular momentum of the state, K is the
_)

projection of I on the symmetry axis of the body-fixed frame, M is
.)

the projection of I in a fixed arbitrary direction (the laboratory

Z axis)and D is the component of the total angular momentum of the

..)
odd nucleon(s) j along the symmetry axis of the body-fixed frame. For

nuclei with cylindrical symmetry, which is true for low-lying rotational
+
states, the angular momentum of the core R will be perpendicular to the

symmetry axis and X will equal 9. A vector diagram relating the quan—

tities just described is illustrated in Fig. 2.1.

2.3.1. Rotational Spectra

 

The unified model of deformed odd mass nuclei predicts that
for each vibrational state of the even-even core and for each assignment
of the odd nucleon to a deformed single particle state, rotational energy
states characterized by quantum number K=Q will be produced by the
rotational motion of the core. The energies of these rotational states
are related to the total spin of the system through the following rela-
tionship,

I+1/2

EI = M2/21[I(I+1) + (-1) a(I+1/2)6 1 + E, (II—l)

I.1/2

with I taking on values K, K+l, K+2, . . .

2.3.2. Vibrational States

 

As in the previous model of the nucleus, the liquid drop picture

of the deformed vibrating nuclear core is assumed. However, the phonon

 

 

 

Fig. 2.1. Coupling scheme for deformed nuclei.

angular momentum Ais no longer a good quantum number, since in general
it is coupled to the rotational motion of the core. Nevertheless,
v, its projection along the body fixed symmetry axis may still be used.
A vibrationally excited state built upon the ground state is characterized
by a K quantum number which is related to the ground state projection
number K0 and projection number v by the following relationship,

K = Ixo +vl (II-2)

There are two exceptionally simple low energy vibrational
modes of excitation which are common to most deformed nuclei: 8 vibra-
tions whose angular momentum is perpendicular to the body fixed symmetry
axis of the nucleus and Y vibrations whose components along the symmetry
axis are :2. From above arguments, the unified model of the nucleus
would predict that a B vibration would give rise to a single excited
band characterized by the K quantum number K=K° while the Y vibrations

can give rise to two bands characterized by K quantum numbers IKoiZI.

Chapter III. DWBA Scattering Theory

The general formalism of DWBA scattering theory has been pre-
sented in detail in several excellent references (Ba62, Sa64, SaA65).
It is the purpose of this chapter to outline this theory briefly in order
to present the basic assumptions and approximations used in the analysis

of the present experimental results.

3.1. Basic Theory

 

Consider the general reaction, A(a,b)B, which is symbolic for

the following nuclear reaction expression:
A + a + B + b (III-l)

where A, a, B and b represent the target, impinging particle, residual
nucleus and scattered particle, respectively. Following Satchler (SaA65),
the total Hamiltonian for this system, H, can be expressed in terms of

either colliding pairs of particles, as is shown below.
H = B = H (III-2)

Furthermore, the prior and post forms of the total Hamiltonian HAa and

HBb’ respectively, can be expressed as

= + III-3
HM HA+Ha+TAa VAa ( )
and
H =H +H +T +V

Bb B b Bb Eb

where, if G and g are allowed to represent either A and a or B and b,

HF and Hg are the internal Hamiltonians of these particles, TGg is

their relative kinetic energy operator, and VCQ is the interaction
potential acting between the two particles.

The total wave function of the system V is thus defined by

09

the equation

(H

(i) + _ _
Gg - E) WGQ (E 6 r ) - 0 (III 4)

’0 9’ 09

where E represents the total energy of the system, gr and 59 are the
internal coordinates of G and g respectively, and the (+) and (-)
designate the usual outgoing or incoming wave boundary conditions. If
it is assumed that the internal coordinates of "g" are independent of

those for "G", the total wavefunction of the system may be factored and

written as follows,
_) +
ng = o (:G,gg) ¢<rGg> = ¢G<a0)¢g(5g>¢(rng) (III-5)

where ¢F and ¢g are eigenfunctions of the internal coordinates of G

and g, respectively, and satisfy the following eigenvalue equations

H0 $0 = E0 In
and (III-6)
H = E
g ¢9 9 ¢9

The total energy of the system may now be written as

E = E + u

2
09 KGg/ZUGQ

or (III—7)

7: 22
E E0 + E9 + H K Cg/ZUCg

10

where KFg is the wave number of the relative motion of the pair 0 and g

and p is their reduced mass.

09
Having the expression for the total eigenfunction of the sys-
tem, the transition amplitude for the reaction A(a,b)B can be represented

exactly by (T061, G064):

a: <+>
=<¢>Be B BIvBI‘Pa > (III-8a)
or
+ —+
_ (-) 1K 'r
t-<‘i’8 Ival‘i’ae a a> (III 8b)
where the abbreviations aEAa and BEBb has been used. The subscript a
on Va(+) signifies the solution with incoming waves in the a channel only

but outgoing waves in all open channels. Thus, asymptotically, the

wave function Va(+) will have the form
..)
‘i’(+) _> (be eiKa ra +ZYfO‘ ye?” r1) ‘i’ (III-9)
a a y

where the sum is over all Open channels 7 and

+ ->

. . (+)
fay °= (Wyeus I’Blvslwm > (III-10)

(i)

If the entire wave function ng

were known, then the problem
of calculating the transition amplitude and thus the scattering reaction
cross section would be solved. However, since the interaction potentials
vAa and va of Eq. III-5 are not known, approximations must now be made

in order to solve the transition amplitude equation.

At this point in the analysis a second potential US in the 8

channel together with its eigenfunction x8 are usually introduced, where

11

X8 satifies the time independent Schrodinger equation,
+ + -)'
[(E—E’B) - TB - U8] x’é (r8,KB) = O (III-ll)

The potential U which has been introduced is quite general in form

8
and is subject to only two basic restrictions: it is required that

U8 + O as r8 + w and that UB be diagonal in the 8 system. Using the

Gell-Mann-Goldberger relation (T061, G064, SaA65) for scattering by two

potentials, Eq. III-8a can be transformed as follows:

++

_ - _ + - iK °r _
t - (:oBXB Ive UBIWG:>> -+ <<:¢Bx8 lUsloae a €:> (III 128)

Similarly, the transformation of III-8b has the analogous form,

++

t - < (“)l -U| + + eiKsmslul +> (III-12b)
_ W8 va a ¢axa ;> <: $8 a ¢axa

Now, since the arbitrary potential U or Us is assumed to be diagonal in

8

the B or a system, the second term in these expressions for the transition
amplitude will be zero except for the case of elastic scattering.
Excluding this possibility, the exact expression for the post and prior

interaction forms of the transition amplitudes become

.. (r) _ (+)
tpost ' <:¢BX8 Ive ”alwo 3’ (III-13a)
and

= (wé‘) Iva-Ual °oX§+) > (III-13b)

prior
In order to evaluate the transition amplitudes in III-l3, one
has to choose a U or Ua which will make possible the replacement of

B
+
W(_) by some computable quantity. The distorted-wave Born approximation

12

(DWBA) follows from the observation that elastic scattering is

usually the dominant process occurring in any scattering situation. In
other words, this observation implies that the optical potential that
describes elastic scattering will be the dominant part of the interactions
vAa and va' Clearly then, if Ua and U8 are chosen as the optical
potentials for describing the scattering of a on A and b on B respec-

tively, the expressions va-Ua and v -U8 will become small perturbing

8
residual interactions responsible for the reaction, and the problem
can clearly be treated by perturbation techniques. Radial eigenfunc-

tions of optical model potentials satisfying Eq. III-ll can easily be

4.
calculated. The perturbation expression for Ta thus becomes

(+) e (+) "
Va ~ ¢oxa (rm) (III-l4)

while the distorted-wave approximation to the post interaction form of

the transition amplitude III—13a is

_ (—) (+)
tpost (DW) “<3thB [VB-UB|¢axa ;> (III-15)

The analogous prior interaction form of this amplitude can be written

as

(-) +
tprior(DW) = <:¢BXB [VB—Ueloaxi ):> (III—l6)

It is useful at this point to separate the integrand of the
transition amplitude into factors which are dependent upon internal and
relative coordinates. Letting v represent either the post or prior
interaction potentials, one can express the transition amplitude

corresponding to the reaction A(a,b)B as follows:

13

t = J I tips I drB xé'NKBmB) <B,b|v|A,a> x§+)(ta,pa) (III-l7)

+ —>
Here ra and r8 are vectors connecting the centers of mass of A and a

and B and b, respectively, while J is the Jacobian of the transformation
to these relative coordinates. The distorted waves X0 and x8 are
elastic scattering wave functions calculated from Eq. III-ll which de-
scribe the relative motion of the pair a, A(asymptotically with relative
momentum :a)before collision and the pair b, B (with :8) after colli-
sion, respectively.

The remaining factor in the amplitude III-l7 is the matrix

element of the interaction causing the inelastic event taken between

internal states of the colliding pairs

< B,b|v|4.a> = I ¢2¢Zv¢A¢adg (III-18)

where 5 represents all pertinent internal coordinates. This matrix
element or form factor contains all the information regarding nuclear
structure, angular momentum selection rules and even the type of reaction

being considered.

3.2. Differential Cross Section

 

Having obtained an expression for the transition amplitude,
t, connecting two non-identical nuclear states A and B via the A(a,b)B
reaction, one has the tools for calculating the differential cross
section for the scattering between these two states. For unpolarized
projectiles and target nuclei, the expression relating the differential
scattering cross section to the transition amplitude can be shown (Sa64)

to have the following form:

14

 

do‘ _ UGUB :_B_ thlz
do ‘ (2m)2 ta (2JA+1)(ZSa+l) and”

where JA and SA are the spin quantum numbers of the target and projec-
tile respectively and where the sum is taken over all spin projection
numbers of the impinging particle, target, residual nucleus and
scattered particle.

Thus, in order to obtain theoretical differential cross
sections for a scattering event, one has now only to evaluate the appro-

priate form factor < B,blle,a > .

3,3, Form Factors for Pick-up Reactions

Pick-up reactions are a general type of nuclear reaction which
are characterized by the transfer of a nucleon or a group of nucleons
from the target nucleus to an impinging particle with which the target
interacts. In order to adapt the previously developed DWBA formalism
to the particular case of pick-up reactions, one has to make the following

assignments to the components of the general reaction A(a,b)B:

b = a + x
and (III-20)

A = B + x

Here x denotes the nucleon or cluster of nucleons plucked out of nucleus
A by the incident interacting particle a.
As was shown in Section 1 of this chapter, the prior inter-

action form of the form factor is given by

f = (BvaAa-UAaIAa> (III-21)

15

In order to evaluate this matrix element, some explicit form for the
interaction potential responsible for the reaction must be derived.
Since the target nucleus A is pictured as being composed of a core "B"

and a bound particle or cluster "x", the interaction potential v

Aa

may conveniently be written as a sum of two terms

vAa = vxa + VBa (III-22)

The perturbing interaction responsible for the reaction may be written

as

= v + (v

VAa-UAa ma Bb-UAa) (111'23)

It is customary at this point to take vxa as the important interaction
responsible for pick-up, since from previous arguments one would expect

cancellation of VBa with UAa' Furthermore, it is generally assumed

+
that an is central, that is, scalar in Ema so that "a" and "x" are in

an S-state of relative motion within b. The nuclear matrix element

III-21 may now be written explicitly as:

+ —+
f = ”Lbs (e; B)¢;(aa F )v (5.5.1: )¢> (a Na A<£Bax.r3x)daadz;xd€b

mxaxxaxaaxaa

(III-24)

—>
where 5i represents the internal coordinates of particle i while rij is

the vector joining the centers of mass of particles i and j.

Since the interaction potential an is independent of EB,
the matrix element III-24 may be simplified by integrating over this
variable. The overlap of the target with the residual nucleus, <BIA>,

projects out the bound state wave function of the particle or cluster.

 

16

This overlap is usually evaluated by expanding ¢A in terms of ¢B and

¢x°

B A
=J‘E;(JB.jM MB. MA M>¢JBM (£3)flfl (Ex .rB x)

MB (III-25)

where J8 and Mb are the spin and projection numbers of B, j and u are
the angular momentum and projection numbers of x, ¢B(€B ) is the wave-
function of nucleus 8 with internal coordinates EB and quA is the

wave function of the bound particle or cluster x. Substituting this

expression of ¢A into the overlap integral, one has

4’3""? = Z (J8,j,B M ,fi.A MBIJA MA ”25; Axe; ”'3 x) (III-26)
j
The indexes B,A are carried as a reminder that 9 depends upon the
initial and final nuclear state.
The angular dependence of 935A may now be removed by expanding

in Spherical harmonics

34,2
“:9; mix” (eBxchxMS u_ Mo- 5 )(25M u- Mlju)
(III-27)

where S is the intrinsic spin of particle x. 3 need not be single

valued if x is a cluster.

Upon substitution of III-27 into III-24, one obtains the

following general expression for pick-up form factors:

 

l7

__ . . 2 .
f- 22 (JB’J’MB,MA-MB|JAMA)(1’) YZ(er)(lSM,U-MIJU)
j SM

2.
—> —> BA, J —>
If ¢b(gagx’rax)vxa(€a€x’rax) $5,ueM(€x’er)¢a(ga)d€adgx
(III-28)
The above equation marks the point of departure for two
different approaches which are commonly used in the evaluation of the
form factor III-28. A brief description of each method along with the

additional assumptions and approximations which characterize each will

now be discussed.

3.3.1. Cluster transfer and Zero Range Approximation. The
cluster model of two neutron pick-up reactions treats the two neutrons
as a structureless elementary particle of spin 0 and mass 2. In parti-
cular, the (p,t) reaction is pictured as proceeding through the transfer
of a "dineutron" from the target nucleus to the interacting incident
proton. Because the two neutrons are treated as being elementary, cal—
culation of the (p,t) form factor proceeds exactly as in single nucleon
transfer reactions such as (p,d) reactions.

Upon adopting this approach, one may immediately simplify
the matrix element III-28 by expanding ¢b in terms of ¢a and ¢x as
follows

(Db = Z (Saija’MxISbe)¢S M (Ean M (gxa’gx)
saijh a a x x

(III-29)

 

18

Substitution of III-29 into the matrix element contained in

Eq. III-28 one arrives at the following expression

< blvxalx,a>= Z (s j M ,M 'Sbe)

a x a x
SaJxMo
ABRj
x ¢ ¢- V ¢ ¢ _
[I SéMa JxM; xa S,u-M’ JaModgadgx (III 30)

Noting that the cluster assumption has eliminated the depen-
dence of Yxa on the internal coordinates and using the orthogonal

properties of the oa's, the integration over Ea yields the result

= BA lj +
< blvxalx’a> (SanMa’ MxISbe) x f ¢SxMxvxa ¢’S‘.:I-1M(1fi.7z.'cz, Eaway:

(III-31)

where the sum over jx has been reduced to a single term with Jx=3x,

since "a" and "x" are assumed to be in a relative S-state. Furthermore,

for the dineutron transfer Sx=0; however, Si will be carried along for

generality.

The remaining integral of Eq. III-31 can easily be carried
out by noting that since "x" is considered an elementary particle,
¢AB’£j (E F ) will be factorable into functions dependent upon

S,uwM x’ Bx

internal and relative coordinates as is shown in Eq. III-32.

BA, 94'

¢S,u-M = R2j(er)wS,ueM(gx)

(III-32)

19

Similarly,

¢>j M (éxmw) = 0(rawaM (ax) (111-33)
.2: (If x .2:

Substituting the above quantities into equation III-31, one obtains

the following result:

< blvxalxa> = (SanMa’MxleMmej (er)vax(rax)O(rax)

<3 6
X 536,8 MT, u-M (III-34)

Finally, using this result in Eq. III-28, one has the following

expression for the cluster transfer form factor:

f = Z (JBJMB,MA-MBIJAMA)(SanMa,Mb-MaleMb)
3‘9,

. 1 M .
x (7,) Y2 (er)vm(rax)e(rax)(RSxm,MxI,7MA—MB)

(III-35)

where m = M + m - M - M

In the above expression, the radial functions R1. are assumed
to be proportional to shell model eigenfunctions and are taken to be
the bound state wave functions of the dineutron in a Woods—Saxon well.
The form of this well in which the cluster is bound is given by

U(r) = V (——1———) ; a: = (r-1.25A1/3f)/0.65f (III-36)
o 1+ex

20

where A is the mass number of the residual nucleus and V6 is chosen to
reproduce the experimental two neutron separation energy.
The zero range approximation, which has been used with this

cluster transfer approach, consists of setting
a = -
V(rax) (ram) 006(rax) (III 37)

where Do is a constant characteristic of the reaction being consid-
ered.

This rather extreme approximation is imposed in order to
reduce the six-dimensional unseparable integral of Eq. III-17 to a
three-dimensional one which can be handled easily by present DWBA
computer codes. The effect of this approximation (SaA65) is to intro—
duce correlations between the various functions which are varying
rapidly in the nuclear interior. This phenomenon in turn tends to
overestimate the contributions to the scattering cross sections from
the interior of the nucleus.

Combining the zero range approximation, III-37, with equation
III-35, one obtains the general result that the form factor corresponding
to a particular RsJ cluster transfer will be proportional to the

bound state wave function of that cluster.

3.3.2. Two nucleon matrix element. As an alternative to the

gross approximations inherent in the cluster transfer formalism, one
can attempt to calculate the form factor corresponding to two neutron
pick-up through direct use of Eq. III-28. In this approach, one gives
up the idea of further simplifying the two neutron matrix element

expressions and instead attempts to approximate the functional quantities

21

present within it realistically.
Rewriting the two nucleon matrix elements contained in

Eq. III-28,

_ BA,2j _
< blVaxlx,a>— H‘bb(gb)vax¢s,p-M¢a (III 38)

the functional quantities which are used by the distorted-wave code
DWUCK (Ku71) in the finite range evaluation of this expression will

now be outlined.

For ¢b(€b), the internal wavefunction of the triton, a

Gaussian form is assumed (Ku71, Ch70)
¢ (g ) = Nexp(-n2[r2 + r2 + r2 ]) (III-39)
b b 12 1a 2a

where n is the size parameter of the triton, N a normalization constant,

+ + +
and r.. = r. — r..
tJ 1 J

Since two neutron pick-up is now being considered, the inter-

action potential, de, becomes the sum of two terms

= + -
de Val de (III 40)

where again a Gaussian form for these nucleon-nucleon interactions, Vdi,

is assumed and has the form,

V.. = U exp(-822". .2) (III-41)
13 0 LJ

where B is the reciprocal of the range of the nucleon-nucleon inter-
action, while ”0 determines the strength of this interaction.
. B,A£j
The two neutron wave function ¢S H’M determined from the over—
9

lap of the target and residual nucleus is usually expressed in terms of

22

single neutron wave functions as follows
2152.2 = Z
(PLA (r1,r2) A1A2(2122A1A2|LA)¢£1A1(r2)¢£2A2(r2)
(III-42)

The wave functions of the two initially bound neutrons ¢ and ¢£ A
2 2

21M

are then taken to be those of a particle bound in a Wood-Saxon well

of the form,

 

U(r) = —V01/(1+ex) + (“Z/mfloc)2V31/r %; (1+:x E°§ ]

(III-43)

where

x' = (r-roA1/3)/a (III—44)

In the above expression, E and E are the orbital and spin
angular momenta of the neutron, A is the massof the target nucleus
less one, PC is the real nuclear radius parameter, a is the diffusivity
parameter, V8 is the spin—orbit well depth and V6 is the real Woods-
Saxon well depth which is adjusted so that individual neutrons are
bound by one—half the two neutron separation energy.

Having made these substitutions in the two neutron matrix
elements, one has only to integrate this expression in order to obtain
an expression for the form factor III-28. The methods employed in
integrating Eq. III-38 are the subjects of several papers (Ku7l, Ch70,

B367) and will not be dealt With here.

23

3.3.3. Finite Range Correction. Once an expression for the two
neutron matrix elements and the resultant form factor III—28 is ob-
tained, one is faced with calculating a six—dimensional integral III-17
in order to evaluate the expression for the transition amplitude.

This procedure, if carried out, involves rather excessive computational
difficulties and is unsuitable for present DWBA computer programs.

The distorted wave code DWUCK employs an approximate correction factor
A to the usual zero range approximation in order to correct for the
effects due to the finite range of the nucleon-nucleon interactions.
This factor has the form

MbM R2
M.) = {1. 7L.

-1
2 WI) (r)-Ua (m‘Ux (r)—BEx]}
M M
a
(III-45)

where Ui is the optical model potential for particle i, M; is the mass
of particle i, BEx is the magnitude of the binding energy of the parti—
cle x and R is the range of the interaction.

It has been shown (Ku7l, Ch70) that with the correction factor

III-45, the zero range code approximates fairly well the correct finite

range calculations for two neutron transfer reactions.

CHAPTER IV

Experimental Apparatus and Methods

4.1. The (p,t) Reaction

 

The investigations of the (p,t) reaction on 1M1Pr, 159Tb,
165Ho and 169Tm have not all been carried out using the same methods
and apparatus. As a result, Sections 4.1.1. through 4.1.3. will deal
with matters common to all experiments, while Sections 4.1.4. and 4.1.5.

will deal with the details of specific experiments.

4.1.1. Cyclotron and Beam Transport

 

The experimental proton beams were provided by the Michigan
State variable-energy sector—focused cyclotron. Through use of quadru-
pole focusing magnets located at appropriate positions along the beam
line, the transport system illustrated in Figure 4.1. focused the ex—
tracted beam on slits SI and 53 whose apertures determined the beam
energy spread on the target. The proton beams were energy analyzed
and dispersed by bending magnets M3 and M4, each of which turns the
beam through 45°. The magnetic fields of these analyzingymagnets were
measured with NMR probes placed in the central fields of M3 and M4.
Bending magnet M5 was then used to deflect the beam into the desired
experimental area. Additional quadrupole focusing just prior to the
experimental areas allowed one to vary the beam dispersion on target.

4.1.2. Target Fabrication

 

In conjunction with experiments concerning the (p,t) reaction
on rare-earth isotopes, thin metallic targets of lulPr, 159Tb, 165Ho

and 169Tm have been prepared by vacuum evaporation at the Michigan State

24

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

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E \

f E
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r:
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beam trans

University cyclotron,

State

26

Cyclotron Laboratory. The details of the vacuum system used are de-
scribed elsewhere (6069).

The foils themselves were prepared by evaporating the 99.9%
pure metallic rare earth from a S-mil tantalum boat onto a ZO-ug/cm2
carbon backing. In order to insure a good uniformity of the foils, the
carbon backings were always placed 4-6 in. above the evaporation
crucible or boat.

The carbon backings used in the fabrication of targets had
no observable effects on the data taken since their thinness precluded
significant beam degradation, while their high (p,t) Q value disallowed
any possibility of interference.

Target thicknesses of fabricated targets were determined
through use of an 2“Am a gauge. This apparatus measures the energy
loss suffered by 35.5 MeV a-particles as they traverse a target. This
information can then be directly related to the target thickness through
use of range-energy tables (Wi66). A precision of i5% is assumed for
this method of measurement.

4.1.2.A. 1“1Pr Targets

 

1H1Pr targets readily oxidize when exposed to air. As a re-
sult, these targets were stored under vacuum. The target thickness of
the foil used in obtaining the triton angular distribution was 793-ug/cm2.

4.1.2.3. 159Tb Target

 

Studies of the (p,t) reaction on 159Tb were all conducted using
a 454pg/cm2 target. Although 159Tb does not oxidize readily, this
target was also stored under vacuum to minimize the effects of long term

exposure to air.

27

4.1.2.C. 165Ho and 169Tm Targets

 

Target thicknesses of 165Ho and 169Tm used in this experiment
were :3OO-ug/cm2. These targets showed no signs of long term deteriora-

tion from prolonged exposure to air and were not stored under vacuum.

4.1.3. The Faraday Cup and Charge Collection

 

The beam used in irradiating rare-earth targets was stopped
and collected by either an aluminum or a carbon Faraday cup. The
differential and integral charge collected during an experiment was
monitored with an Elcor model A3103 current digitizer and integrator.

An aluminum beam stop has the advantage of only producing
short-lived activities upon being bombarded by the beam. However, sig-
nificant y-ray backgrounds are produced during the periods of bombard-
ment which makes this beam stop unsuitable for experiments involving
photographic plates. During such runs, a carbon Faraday cup was used

which produced lower radiation levels during bombardment.

4.1.4. 1L'lPr(p,t) Experiment

 

In the study of the (p,t) reaction on 1“Pr, an Z800-pg/cm2
target of metallic 1“Pr was bombarded with SOO-nA beams of 40-MeV
protons accelerated by the Michigan State University sector-focused
cyclotron. An E,AE detector telescope was used to measure the energies
of the tritons produced while a monitor counter kept track of the number
of protons elastically scattered at right angles to the beam direction.

4.1.4.A. The Scattering Chamber

 

The 36" scattering chamber used in this experiment was equipped
with a central, remotely rotatable target ladder capable of holding a

scintillator and several targets, a remotely movable arm capable of

28

mounting a detector telescope at various radial positions, and an
unmotorized arm capable of mounting a stationary detector or monitor,
again, at several radial positions

The target and detector angle readout device was reproducible
well within a i0.15° limit.

A plexiglass window in the scattering chamber together with
a closed circuit television system allowed the beam spot to be observed
on a scintillator and finely adjusted with quadrupole focusing.

4.1.4.8. The Detector Telescope and Monitor Counter

The AE-E detector telescope used in this experiment was com-
posed of two cooled Si surface barrier detectors. The AE detector is a
thin diode incapable of stopping the least energetic particle of interest
and is always placed closest to the target. The E detector, which is
placed behind the AE counter, is a much thicker diode which is chosen
so that the total thickness of the two detectors, E+AE, is sufficient
to stop the most energetic particle of interest. The AE and E detector
thicknesses chosen for this experiment were 925 u and 2025 u, respectively.

The solid angle subtended by the detectors was determined by
a collimator slit placed directly in front of the detector package and
the radial position of the detector telescope. In this experiment a
llO~mil thick tantallum collimator with an oval aperture of 0.120"XO.260"
was used at a :10" radial distance from the target.

Cooling of the detectors was achieved by circulating ethanol
at dry ice temperature through a cooling plate in contact with the copper
detector mount in the telescope. This was done in order to reduce elec-

tronic noise within the detectors to a minimum.

29

A NaI(Tl) detector placed at right angles to the beam was used
to monitor elastically scattered protons. The number of elastic events
recorded for a given irradiation is proportional to the product of the
effective target thickness and the total charge collected during the
irradiation. As a result, relative cross-sections may be obtained which
are independent of the errors associated with target thickness measure-
ments, target nonuniformities,beam drift, and target deterioration. The
monitor output is also a very sensitive means of determining analyzer
dead times.

4.1.4.C. Electronics and Particle Identification

 

Having described the hardware associated with the detection
system, the electronic methods used to measure energies and identify
particles will now be discussed.

For each particle "seen" by the detection system, three signals
are received from the detector telescope: A pulse "AE" from the AE
detector proportional to the differential energy loss of the particle,

a pulse "E" from the E detector proportional to the energy of the parti—
cle emerging from AE detector, and a pulse, "2", proportional to the

total energy of the particle, obtained by summing the "E" and "AE"

pulses at the detector telescope. The summing circuit which produces

the 2 pulse appears in Fig. 4.2. The A5, E and Z pulses taken off the
detector telescope are then passed through charge sensitive preamplifiers
and sent on to the data acquisition area. Here they go through the
electronics setup illustrated in Fig. 4.3 which, in addition to amplifying
and shaping the pulses, requires the simultaneous presence of Z and AE
signals before these latter two pulses are sent on to a coupled pair

of 8192-channe1 digital to analog convertors (ADC's). The computer code

.uasoufio wcHEESm oncommamu nouomumn .~.c .mwm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.2205 ”TI madam”...
05m»
0 u
220...... ml mammal;
._<zo_m mdml, gammy...

 

 

 

ISSUE—0 02:23.3m

 

 

 

 

EXPERIMENTAL ELECTRONICS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I —-1 I s ’
j fl 7 T
08 as 06 'r'_' L G E _.
-- , I _-- . A I AE SIGNAL
I +DEt—IPREAMP "1 AMP s E H a
I
: as I___”"‘ C S
‘ ' ' ' A *r—— I _I,
I ,
: .h—J
: come.
I F—
. I I
I F-—T ‘F—-—-_1 »---1 s _-.k---J'
: I—q 2 G
:.-- E H E ..-- E .___.. A as SIGNAL
. oer mama 1 AMP ,L_I, g
I
: I—J I..___JI .L__4. L41
:
I
I
I
I
i
. , I
: F1 r—T
3.--..3.-- 2 _____.. 8
new no
L_____a. .L_____JI
as sneuAL—-—q “we 3
* N
8|92 CHANNEL c
ADC g 2-7
8 COMPUTER
8|92 CHANNEL 3
8 SIGNAL —-——u. ADC O
X-ADC E

Fig. 4.3.

 

 

 

 

 

 

 

Experimental electronics associated with the E-AE detector telescope.

32

TOOTSIE (Ba70) stores this digitized two-dimensional information and

is capable of displaying it on a storage scope. Just such a two—dimen-
sional display is illustrated in Fig. 4.4. Now, because particles
differing in mass and/or charge but having the same total kinetic energy
will exhibit different differential energy losses, different particles
"seen" by the detector telescope will fall into distinctly different
non-overlapping bands in this Z-AE two-dimensional space. The computer
code then allows gate lines to be drawn about the desired particle band
or bands in the form of polynomial fits to points designated in this
Z-AE plane. These gate lines are then used to route all total energy
pulses 2, falling within a given pair to any one of several 8192—channe1
memory blocks where the total energy spectrum is stored.

4.1.4.D. Dead Time Correction

 

In order to correct for pulses lost due to ADC dead time, the
elastic scattering portion of the monitor counter spectra was simul-
taneously scaled and sent to the channel zero associated with the pair
of ABC's used in the spectral analysis. The pulses sent to channel zero
are scaled only during time intervals when the ABC's are idle. Thus,
the ratio of these two numbers will be a measure of the fractional num-

ber of counts lost during the counting period.

4.1.5. 159T'b(p,t), 165Ho(p,t) and 169Tm(p,t) Experiments

 

In the investigation of the (p,t) reaction on 159Tb, 165H0 and
169Tm, ZBOO-ug/cm2 targets were bombarded with 30-MeV protons accelera—
ted by the Michigan State University sector-focused cyclotron. The
scattered tritons were analyzed by an Enge-split-pole magnetic spectro-

meter and collected on Kodak NTB nuclear emulsions.

... OOO

~ 0...... .0...

“:5. gm, ‘_ _- 0...... 0...

~ "fit, I . m ”coo-0....

.‘O' I‘ "' I, 9. .00. 000-0....
oak‘,g¢gpoco o. 0....

A ‘19:! In“ .
v I.. . ..-O--. -’-

v I

v-‘

.00....“ m”““-°'...~.... " O O. O... O

,W’ V 1 m! :3
I

Fig. 4.4. TOOTSIE two dimensional E—AE’ display illustrating three particle bands.

[“1” 'rmefififi’fi: ammo" . 0.33%?
D . O ‘

 

34

4.1.5.A. The Magnetic Spectrograph

 

An Enge split-pole, double focusing magnetic spectrograph was
used to momentum analyze thescattered tritons produced through the (p,t)
reaction on 159Tb, 165Ho, and 169Tm. This spectrograph is mounted on a
rail and is capable of being rotated about a stationary centrally located
14" scattering chamber' from -5° to 160°. The 14" scattering chamber
is equipped with a remotely rotatable central target post, a series of
removable ports located about its perimeter and a sliding seal which
forms the contact between the chamber and the spectrograph. A 0.372"x
0.387" slit located :10" from the central target post at the junction
of the chamber and spectrograph defined the solid angle of acceptance
for the spectrograph.

The spectrograph was chosen for this series of experiments
because of its high transmission and resolution capabilities. Kinematic
broadening effects were completely compensated for through a proper
positioning of the focal plane. This allowed for the use of large solid
angles without a corresponding kinematic loss in energy resolution.
Kinematic focal plane positions were computed with the computer code
SPECKINE (Tr70).

SPECKINE also allowed for calculations of dispersion matched
quadrupole settings which disperse the beam energy on target in such a
way that the spectrograph magnet will focus all rays producing a given
excitation. Perfect dispersion matching would make experimental resolu-
tion independent of the bombarding beam energy width. Clearly, disper-
sion matching allowed for much higher bombarding currents on target than
could normally be tolerated if the beam width was directly related to

resolution.

35

Particle identification was achieved solely through the momentum
analysis of the spectrograph magnet. A fortuitous combination of reac-
tion Q values always caused the tritons to be much more rigid than all
other observable reaction products.

4.1.5.8. Monitor Counter

 

A S-mm ¢ cooled Si(Li) solid state detector placed at right
angles to the beam was used to monitor the elastic scattering events
produced during the angular distribution experiment of 159Tb.

4.1.5.C. Plate Reading

 

The photographic plates which recorded scattering events were
scanned using a microscope whose plate platform could be continuously
moved both in a horizontal and vertical direction. A vernier associated
with horizontal motion (motion along the energy axis) allowed relative
plate positions to be read to within i0.005 mm.

Under normal scanning conditions plates were viewed under a
200 power magnification and read in 1/4 mm strips. However, in the cases
of high track densities and/or high resolution these conditions were

varied in order to suit the particular situation at hand.

+
68
4.2. 167Yb -——9>167Tm Experiment

 

The states of 167Tm have also been investigated through the
e,8+ decay of 167Yb. Gamma-ray singles and coincidence experiments

have been conducted in order to construct the 167Yb decay scheme.

4.2.1. Source Preparation

 

Samples of the 18.5-min 167Yb were produced by bombarding the
oxide of 100% abundant naturally occurring 169Tm with 23.5-MeV protons

accelerated Eur the Michigan State University sector-focused cyclotron.

36

Samples were bombarded for approximately 3 min with average beam currents
of Z-MA, and the resulting activities were counted for periods not
exceeding 3 half-lives

The 167Yb activity produced by the (p,3n) reaction is extremely
clean since the major competing reactions Qp,2n) and (p,n), lead to
stable and relatively long—lived isotopes respectively. Furthermore,
the relatively long-lived 167Tm activity decays almost entirely to a
single state in 167Er, giving rise to only 2 significant Y rays.

Y rays not associated with the decay of 167Yb were identified
through a crude half—life study and from the Y-ray spectra of residual
activities left after all 167Yb had decayed away. The only major con-
tamination identified in the 167Yb Y-ray spectra were the 207.9-keV

and 531.8—keV Y rays from the 167Tm decay.

4.2.2. Y-Ray Singles Experiments

The energies and relative intensities of Y rays associated
with the decay of 167Yb were determined by a series of Y-ray singles
experiments. The low energy portion (EY <200 keV) of the Y-ray spectrum
was taken with a Si(Li) x-ray detector. This detector easily resolved
several closely spaced low energy Y rays allowing accurate relative
intensity measurements to be made.

Spectra above 200 keV were taken using Ge(Li) detectors with
and without Pb absorbers. Graded lead absorbers placed between the
source and the detector were used to discriminate against low energy,
high intensity Y rays so that "hotter" sources could be counted in order
to bring out the high energy, low intensity y rays associated with the

167Yb decay. Spectra taken without Pb absorbers were used for relative

37

intensity and energy measurements of the stronger Y rays in the spec-
tra and also served to establish a correspondence between spectra taken
with and without Pb absorbers so that corrected relative intensities
of weaker Y—ray lines could be obtained.

Electronics components used with all Y-ray singles experiments
included an FET preamplifier and high voltage supply, a pulse shaping
linear amplifier with pole-zero compensation, an analog to digital con-

verter (ADC) and multichannel analyzer.

4.2.3. YfRay Coincidence Experiments

Y-ray cascade relationships were established through anti—
coincidence and delayed coincidence experiments. These studies were
conducted using a Ge(Li) detector in coincidence with an 8"X8" NaI(Tl)
split annulus and a 3"XB" NaI(Tl) scintillation counter. A complete
description of this coincidence system and its capabilities are dis-
cussed elsewhere (Au67). The electronics used in these coincidence
experiments is illustrated in Fig. 4.5.

In the anti-coincidence experiment, 167Yb sources were placed
at the center of the annulus tunnel which was then blocked by a 3"x3"
NaI(Tl) detector at one end and by the Ge(Li) detector at the other.
The source in effect was completely surrounded by detectors and repre-
sented a very efficient counting system. The single-channel analyzers
associated with the NaI(T1) detectors were set to accept all Y rays
above 70 keV. The coincidence resolving time used in this experiment
was 100 nsec.

With the exception of the operating mode of the linear gate

and the delay of 250 nsec added to the Ge(Li) side of the coincidence

38

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39

circuit, the delayed coincidence experiment was conducted exactly as

was the previously described anti—coincidence study.

CHAPTER V

DATA REDUCTION

5.1. Peak Areas and Centroids

 

The areas and centroids of spectral peaks were all determined
in the same manner, independent of the type of experiment. These com-
putations were achieved through the use of the computer code MOIRAE (Au68).

MOIRAE allows spectra in the form of computer card inputs to
be displayed on an oscilloscope. Having designated representative back—
ground points on both sides of a peak, the computer code will determine
the background under the peak through use of a polynomial fit to these
designated background points. The background fit or difference spectra
can then be displayed for visual inspection. Once an acceptable back-
ground is obtained and the positions of the high and low sides of the
peak are specified, MOIRAE calculates the net area of the peak, the
statistical error associated with this area and the peak centroid.

The areas and centroids of composite peaks were determined
using the computer code SAMPO (R069). SAMPO will strip a composite peak
by fitting Gaussian peaks with exponential tails to the data. The
characteristics of the fitting peaks were determined from singlet lines
appearing in the same spectra. A detailed discussion of this code is

given elsewhere (R069).

5.2. (p,t) Experiment

 

5.2.1. Energies

 

The methods used in obtaining excitation energies correspon—

ding to the various spectral triton peaks differed in the two types of

40

41

experiments conducted. As a result, these methods will be discussed

separately.

5.2.1.A. 141Pr(p,t) Experiment

The excitation energies of the various triton peaks occurring
in the 141Pr spectra were determined internally by making a correspond-
ence between some of the more obvious triton peaks and the well estab-
lished states of 139Pr (Be69). The centroids of these standard triton
peaks together with information concerning the proton bombarding energy,
scattering angle and particle masses were used in a FORTRAN kinematic
code to establish a calibration curve from which excitation energies of
unknown peaks were determined.

In addition, an independent energy measurement of some of the
more intense triton groups was conducted using a broad range magnetic
spectrometer and a 3-cm ¢ Si position sensitive detector. In this ex-
periment the ground state peak was placed at several different positions
along the detector in order to calibrate the detector's length. Excita-
tion measurements were then obtained using methods described in the

next section.

5.2.1.B. Spectrograph Experiments

 

The excitation energies measured with the spectrograph were
derived from the relative energy measurements of the various triton
lines based on a single peak of known excitation, usually the ground
state. Given the excitation energy and the centroid of the reference
peak together with the bombarding energy, the scattering angle, the
masses of particles involved, and the value of the spectrograph magnetic

field, the relativistic computer code SPECTRUM (Ri70) will calculate the

42

excitation energies of all other lines occurring in the spectrum based
on their relative focal plane positions. The uncertainties inherent
in this type of measurement have been determined to be :5 keV.

5.2.2. Cross-Sections

 

In the analysis of angular distribution data both absolute and
relative differential cross sections were calculated. Because of the
inherent errors involved in measuring absolute cross sections, only
relative values were used in the construction of angular distributions.
These curves were then renormalized to reflect the magnitudes of the
measured absolute curves. Error bars appearing in all angular distri—

butions reflect statistical uncertainties only.

5.3. Y-ray Experiments

 

The information extracted from Y-ray experiments are Y—ray
energies and/or relative intensities. These quantities, in turn, are
obtained from measured peak areas and centroids. The methods used in
extracting nuclear information from experimentally measured quantities

will now be discussed.

5.3.1. Y-Ray Enepgies

 

The energies of the stronger Y rays associated with the 167Yb
decay were determined internally by counting activities of 167Yb simul-
taneously with well known y-ray standards. The centroids of these
standard Y-ray peaks served to establish a correspondence between peak
position and energy from which energies of other spectral peaks could
be determined. The correspondence drawn between centroid and energy
took the form of a least-squared linear or quadratic calibration curve.

The energies of the lower intensity 167Yb y rays were then similarly

43

determined by using the stronger 167Yb Y rays as secondary standards.
Only those peaks falling within the range of the calibration points
were determined in this way.

The standard Y-ray sources used in the primary calibration of

the 167Yb spectrum appear in Table 5.1.

5.3.2. Y-Ray Relative Intensities

 

In order to relate relative peak areas to their relative
intensity values, the efficiency of the detection system as a function
of energy has to be determined. This can be done in an absolute or
relative sense but must be done empirically for each and every
detector used. The methods of determining a relative efficiency curve
are discussed elsewhere (D071).

The analytical forms of the relative efficiency curves for
the detectors used in this experiment are contained in the computer
code MOIRAE E(I) (Be69). Given the detector used, peak energies and
their corresponding areas, this code computes Y-ray relative intensi—
ties by correcting each peak area for its corresponding relative detec—
tor efficiency and normalizing this result to a single Y—ray intensity

defined as 100.

.-m -~-—.——---——— - N... .._...., ——_- q 0—» _--
...- _-- - ~- -- _,.,-_- __

44

Table 5.1. ,YéRay Calibration Standards

 

____. — .-fi—
, ~ -.H--._.m .. -.—__—.

 

Source Y-ray energy (keV) Reference
22Na 1274 53 +0 10
. 1 . Le68
”68c 889.18 +0.10 Le68
1120.41 10.10
6°Co 1173.22610.040 Le68
1132.48310.046
652m 1115.44 10.01 Le68
88y 897.96 10.10 Le68

1836.08 i0.07

Ag 657.71 10.03 Br69
706.68 10.04
763.88 10.04
884.67 10.04
1475.73 10.04
1504.90 10.08
1562.22 10.06
182Ta 1121.28 10.12 Le68
1221.42 10.10

20731 569.63 10.08 Le68
1063.58 10.06
1769.71 10.13

Chapter VI

ll+1Pr(p,t) Results

6.1. Introduction

 

The investigation of the general systematics of the (p,t)
reaction on rare-earth isotopes was begun with the 1“Pr nucleus. The
residual nucleus of this reaction, 139Pr, has been extensively studied
through the e/B+ decays of the ground and meta-stable states of 139Nd.
The latest level structure of 139Pr as determined through the decay
scheme studies of Beery, Kelly and McHarris (Be69) appears in Figure
6.1. As in other N=79 odd—mass isotones, the energy separation between
the 11/2- metastable and the 3/2+ ground states is rather small,
making the M4 transition connecting these two states quite slow. This
situation has the effect of allowing the two quite dissimilar isomers
to decay almost independently to two completely different sets of states
in the daughter nucleus 139Pr. Because of the large number of very
dissimilar states established by this decay scheme study, it was decided
to begin our investigation of the (p,t) reaction with lulPr even though
the main emphasis of our total study would involve only strongly

deformed nuclei.

6.2. DWBA Analysis

 

The distorted wave predictions for various i-value transfers
were calculated using a zero-range, cluster pick-up approach as well as
a more rigorous finite-range, two-nucleon transfer formalism.

The distorted wave code JULIE (Sa64) was used in the cluster

transfer analysis. The bound—state and optical potential parameters

45

46

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47

used in these calculations are listed in Table 6.1. The bound state
well depth was always chosen so as to reproduce the binding energy of
the two neutrons removed. This binding energy, Bx, was calculated

from the formula:
8x(cluster) = S-Ex (6.1.)

where S is the ground state separation energy of two neutrons and E;

is the excitation energy of the state being considered. Cluster trans-
fer predictions when compared with experimental results will always be
denoted by a broken curve.

The finite range, two nucleon transfer calculations were
performed using the distorted wave code DWUCK (Ku65). The bound state
and optical potentials used in this analysis appear in Table 6.1. The
real well depth of each of the two transferred bound neutrons was
chosen to reproduce one half their total binding energy. This single
neutron binding energy, Bx’ was calculated from the following relation-

ship:
Bx = (S - Ex) / 2 (6.2.)

Finite range two nucleon transfer calculations will in this and all
succeeding chapters be represented by a continuous curve when being com-

pared with experimental data.

6.3. 1{"1Pr(p,t) Spectra

 

Triton spectra obtained from the (p,t) reaction on ll+1Pr were
collected with an E—AE detector telescope and were with the exception

of 70° taken between 15° and 75° at 5° intervals. Typical spectra

48

 

 

 

m + H o a m + H xv m + H
:x up n m x . a o x o o to
PHTIIIIIVIII.’ Tlv+. H zsuzvullllsuHuHIu H.
.I 1 H .6 H N s H H. H v H v
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CV CV CV CL Ce 3. CC 9sz £65 92... 9sz 30.3.81
uo.H m o.H .m mu m o.H m> a: 03 o>

 

 

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.H.o manme

49

taken at 25° and 35° are illustrated in Figure 6.2. A complete compila-
tion of spectra taken in this experiment together with the pertinent

extracted data appears in Appendexes A and B respectively.

6.4. Angular Distributions

The experimental angular distributions together with their
distorted wave predictions are displayed in Figures 6.3-6.4. Figure 6.3.
exhibits those states populated through 2 value transfers from 0 to 3.
The angular distribution corresponding to the 5/2+‘+ 5/2+ ground state
transition clearly corresponds to an apparently pure £=0 transfer.

The finite range calculation of the transfer of two d3/2 neutrons fits
the lower angle data much better than does the cluster transfer analysis;
however, the latter calculation does a better job of predicting the
positions of therelative maxima occurring at 55° than does the finite
range approach. The overall agreement between theory and experiment

is good, and, since the angular shape of an i=0 transfer is sufficiently
different from all other R-values, the ground state of the residual
nucleus 139Pr appears to be populated by a pure i=0 wave.

The five angular distributions appearing below the £=2
designation in Figure 6.3 all exhibit a characteristic i=2 angular
shape. Again, at lower angles the finite range (d3/2):=2 calculations
fit the data much better than do the cluster predictions, although
beyond 25° both theoretical curves are remarkably similar. Moreover,
since the states populated through these i=2 waves have all been
previously (Be69) classified as being collective in nature, the purity

of these experimental £22 curves are assured (Pe63).

 

50

 

 

 

33

 

 

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51

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Fig. 6.3. Angular distributions of states populated through the 141Pr(p,t) reaction.
Theoretical two neutron pick-up and cluster transfer calculations are
represented by continuous and broken curves respectively. Relative cross
sections have been normalized to reflect measured absolute values.

52

The remaining angular distributions appearing in Figure 6.3
correspond to four states populated through i=1 and/or i=3 transfers.
The 1620-keV and ZOSO-keV states clearly exhibit an odd-2 character;
however, unique R assignments cannot be made on the basis of shape
alone, since both 2:1 and i=3 angular predictions fit the experimental
points equally well.

However, because these relatively low energy states are pOpu-
lated by odd 1 waves, their origins can only be explained in terms of an
octupole core excitation or in terms of a transferred hll/Z neutron. The
former explanation of course immediately eliminates the possibility of
any i=1 strength in the angular distributions of these states.

If, on the other hand, an h11/2 neutron participates in the
pick-up process leading to these excited odd parity states, then of
the possible even parity orbitals available, energetics alone makes
a d3/2 neutron the most probable candidate for the second neutron
transferred. Assuming this transfer configuration, one finds that of
the two possible 2 values associated with these two states only the
£=3 value is allowed by the conservation of angular momentum. This
pick-up mode, moreover, is consistent with the shell model configura.“
tions assigned to states of similar energy characterized by radioactive
studies (Be69, MC69) -

The remaining two states in Figure 6.3 appear to exhibit a
unique i=3 shape, although the limited number of experimental points
in these distributions make these assignments tentative at best.

Figure 6.4 exhibits two angular distributions which probably

represent more than one excited state each. An i=6 angular shape has

53

 

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54

been included for comparison sake only since both angular shapes are

believed to be a composite of several z values.

6.5. Summary

 

A comparison of the results of our (p,t) data with the pre-
viously described decay scheme studies appears in Table 6.2. The
first thing to be noted is that the g values assigned to the transitions
to the various states in 139Pr are in every way consistent with the
spin and parity assignments of the corresponding states established
through radioactivity studies.

Furthermore, the 2=2 assignments for the five states listed
further corroborate the collective vibrational character previously
ascribed to them. Since unique spin assignments have not been made
for most of these collective states, an attempt was made to clarify
this situation through use of the weak coupling model of collective
nuclear motion. Since these states are presumed to be members of a

multiplet constructed from the coupling of the d ground state with

5/2
the first excited 2+ state of the core, the weak coupling model would
predict the presence of five pure collective excited states with spins
ranging from 1/2 to 9/2 whose relative cross SECtiODS are in a ratio
of 1:2:3:4:5, respectively, and whose energy center of gravity corre-
sponds to the first 2+ excitation in the 138Ce nucleus. Although
several combinations of these six states would satisfy the latter
energy constraint, the former cross sectional relationship expected
for pure vibrationally excited states cannot be satisfied by any com—

bination of these states indicating that much mixing within and possi-

bly outside the multiplet must occur.

55

Table 6.2. States Populated Through the lulPr(p,t) Reaction

 

 

 

 

 

 

 

( This work ) ( Beery )
Energy 2 Energy Jn Classification
(KeV) value (KeV)
1
o 0 0. 5/2+ ("45/2)
2 —1
— — 113.8 7/2+ (“as/2) ("97/2)
1
405:10 2 405.0 3/2+,1/2+ (“d5/2) (2+)
1
590:10 2 589.2 5/2+ (nd5/2) (2+)
1
— — 821.8 11/2- (“hJI/z)
1
828.1 7/2+,9/2+ (:d5/2)1 (2+)
830:10 2 {
851.9 9/2+,7/2+ M/2)1(2+)
918:15 2 916.8 1/2+,3/2+ (n 025/2)1 (2+)
1010120 2 1024.0 7/2+,9/2+,11/2+ Collective
1311.8 1/2+,3/2+,5/2+
1330:20 ? 1328.2 5/2+
1369.6 9/2+,11/2+,13/2+
1501.2 1/2+,3/2+
1520120 2 %
1523.2 (+)
1623+20 1 3 1824 5 9/2— 11/2— (nd )1(vd )”1(vh )’1
_. ,. . 9 5/2 3/2 1.1/2
-1 «1
2050130 1,3 2048.8 9/2-,ll/2— (11d6/2):(\)d3/2) (thI/Z)
. . 1 .—z
2160:50 3 2174.5 9/2~,11/2— (nds/z) (vd3/2) (thl/z’
2240 3 — — —
2660 - - — -
2740 - - ~ —

2800 ~ - ~ -

56

Finally, in agreement with the model of direct nuclear
reactions, only those excited states corresponding to excited neutron
components or core excitations were populated by this reaction. Con—
spicuously absent are the 113—keV 7/2+ and the 821.8-keV 11/2- proton
states even though neutron and core excited states of similar spin
and parity were observed to be strongly populated by this reaction.
Additional 1L*1Pr(p,1b) experiments conducted at bombarding energies
of 35 MeV and 30 MeV further established the direct nature of this

reaction at these relatively high proton energies.

Chapter VII.

159Tb(p,t) Results

7.1. Introduction

 

0f the three deformed residual nuclei studied, 157Tb is
the best characterized. From radioactivity studies involving both
conversion electron and y—ray work (Pe62, B167), the partial level
scheme illustrated in Fig. 7.1. was developed. The main features of
this level structure are the identification of a rotational band built
upon a B vibrational excitation of the K=3l2I4ll] ground state and the
characterization of a K=l/2 band based at 598 keV.

Several investigators (Pe62, 3167) have differed as to their
interpretation of the rotational band based at 598 keV. There are two
possibilities for the origin of such a K=1/2 band. It can be explained
as a rotational band superimposed either on the 1/2+[411] single parti-
cle proton state expected from the Nilsson diagram in this region, or
on a y vibrational state based on the K=3l2 ground state. The vibra-
tional origin of these states is strongly suggested from both systematics
and the very small decoupling parameter associated with this band. The
empirical value of this decoupling parameter is ml/ZO of the theore-
tical value (3167) based on a nuclear deformation of ”=5 and is of
opposite sign. However, experimentally determined K conversion
coefficients imply significant Ml admixtures in transitions deexciting
this band to the ground band (see table 7.1 and 7.2); these should be
formally completely forbidden for states having a vibrational origin,
although band mixing could easily account for this phenomenon. In

light of the established directness of the CP,t) reaction at the

57

58

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59

Table 7.1

7
Multipolarities Of Y rays Deexciting the Y Vibrational Band in 15 Tb

 

 

 

Transitiona Bandb State Fed Grnd. Suggested
Energy Type Depopulated Member Multipolarities
554t2 Y 697 143.8 M1,E2
57712 Y 637 60.8 M1,E2
597t1 Y 597 Grnd. Ml,E2
637 Grnd.
636t1 Y { 698 { 60.8 M1,E2

 

a) Ref. Fe 62
b) Our assignment.

Table 7.2

Multipolarities OfY'rays Deexciting The Vibrational Bands In 157Tb

 

 

 

Transitiona Bandb State Fed Grnd. Suggested
Energy Type Depopulated Member Multipolarities
553.1t0.8 Y 697.4 143.8 M1
576.6i0.8 y 637.2 60.8 Ml
597.5t0.6 Y 597.5 Grnd. M1
931.7t0.8 B 992.6 60.8 E2
984.0t2 B 1044.5 60.8 E2+EO
992.812 8 992.6 Grnd. E2+E0

 

a) Ref. 8167
b) Our assignment.

6O

bombarding energies used in this study, the presence of these K=l/2
states in our triton spectra would be a sufficient condition for

establishing their collectivity.

7.2. Spectral Results

 

The 159Tb(p,t) triton spectrum taken at the laboratory
scattering angle of 20° appears in Fig. 7.2. The most striking feature
of this spectrum is the strong population of the ground state rotational
band, with members certainly up to 13/2+ and possibly as high as l7/2+
being excited. At 598 keV of excitation one finds three states which,
within experimental uncertainty, correspond to the first three members
of the previously discussed K=l/2+ rotational band. In addition, if
one generates the 7/2+ and 9/2+ members of this band by parameterizing
the simple rotational energy relationship, one finds two additional
states populated by this reaction which appear to be the next two higher
members of this (Y vibration) band.

The set of three states based at 994 keV of excitation pos-
sesses relative intensity characteristics which are remarkably similar
to those exhibited by the first three members of the ground state
rotational band. If the simple I(I+l) energy spacing is assumed for
these levels and one solves for I, one obtains a value remarkably close
to 3/2. Thus in addition to the two previously known members of the
B vibrational band, a third has been observed to be populated through
this reaction.

The results obtained from this spectrum are summarized in
Table 7.3. The theoretical values for the members of the various

rotational bands have been calculated using the rotational energy

TRRCKS PER l/BHH

IRRCKS PER l/BHH

61

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EXCITRTION ENERGY (HEV)
1.8 1.8 I.“ 1.2 1.0 0.0 0.0 0.9 0.2 0.0
500 9 t : : 1 a A. : 4 a
”a
“’18! P.1 l
30 no: ”’
400 . 20 use .
300» J
312“
an" 712
200 '- 4
112"
100 + m ‘
”[2
I112 . 312‘ .
012 712' 512' ”2 '3’:
o . Lil
930 l 130 1330 1530
DISTRNCE RLONG PLRTE (l/Bflfl)
EXCITRTION ENERGY ("EVI
1.8 1.8 I.“ 1.2 1.0 0.8 0.6 0.“ 0.2 0.0
10 ’ : a : 1 1 ¢ 1 a 4 1*
512312 I
"’18! PJ 1 3
”2:12 30 HEV n: q
.. 20 DEC
n:
a 4
1° 2 on 3
3 4
l “’2 4
: "I! 0’”. .4
l "2. $12 In“ J
n m: "
*- f 7”. 4
10 ' 1. l ..
I I
y- d
p- .4
r- 4
~ 4
10 ° L .
930 1130 1330 1530
DISTRNCE RLONG PLRTE (l/BHHI
Fig. 7.2. Log and linear displays of the 159Tb(p,t) spectrum taken at

the laboratory scattering angle of 20°.

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+..N\n qNHH In: QNHH +m\m In: m 0 m 0
en A>mxv A>mxv A>mxv sq A>mxv A>mxv A>mxv
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.COfiuummm Au.nvnhmmH mLu zwsouse wmumasaom mmumum .m.n manmh

63

formulas given by equation 2.1. The rotational parameters used in
these calculations are tabulated in Table 7.4. A level scheme of states

populated through 159Tb(p,t) reaction appears in Figure 7.3.

7.3. Angular Distributions

 

.Because the selection rules governing the (p,t) reaction on
odd-mass nuclei will usually allow states to be populated by several
a—value transfers, angular distributions of all the known states excited
by the 159Tb(p,t) reaction were obtained in order to determine whether
this type of experiment could be profitably used in the analysis of
odd-mass nuclear states. The spectra collected in this experiment were
taken between 10° and 75° at 5° intervals and appear in Appendix C.

The differential cross sections extracted from these spectra are tabu-
lated in Appendix D.

7.3.1. DWBA Analysis

 

The distorted wave predictions for the various SL—value trans-
fers were calculated as described in section 6.2. The optical potential
and bound state parameters used in this analysis appear in Table 7.5.
The h9/2 spherical shell model orbit was used in calculating the bound—
state wave functions of the transferred neutrons, since the least
bound pair of neutrons in the 159Tb nucleus occupies a Nilsson orbit
derived from this spherical state. Again, the finite range and cluster
transfer calculations are represented by continuous and broken curves
respectively when compared with experimental data.

7.3.2. Ground-State Rotational Band

 

The angular distributions of the ground state rotational band

members appear in Fig. 7.4.

64

Table 7.4

Rotational Parameters Associated With Bands

159

Populated Through The Tb(p,t) Reaction.

 

 

 

Band fig/2 J a E
(keV) (keg)
Grnd. 11.98 - -44.57
V 12.90 0.086 589.43

B 10.80 — 953.50

 

 

65

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mm
.so~_ .o H_~:_rw\m
.omw— ..u .mxm
.Qhw— .33— ..N\h
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a .mnn q~\__
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.sm:_
.uw:_ .uwm o~\m_
.omm .wx.
.mmm. .osu .wxm
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.mmu. «Na .s:m 1~\s~
.:ma 1wxn
.035. .o3c— owxm
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.ON—u 9N\h

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66

 

 

 

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oo o o o m a o o
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.m.n mHnme

dU/dn (mb/sr)

 

 

67

 

 

 

 

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Angular distributions of states populated through the

dU/dn (mb/sr)

da/dn (mb/sr)

 

 

 

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159

Theoretical two neutron pick-up and cluster transfer calculations are

represented by continuous and broken curves respectively. Relative cross

sections have been normalized to reflect measured absolute values.

Tb(p,t) reaction.

68

As in the previous case of the (p,t) reaction on the spherical
ll+1Pr nucleus, the 3/2+ + 3/2+ ground-state transition proceeds through
a strong dominant 2:0 transfer. The theoretical 2:0 curves predict
the positions of the relative maxima and minima quite well but clearly
underestimate the strength of the experimentally observed diffraction
pattern. This Phenomenon was also observed in the 11*1Pr(p,i:) experiment
and is in marked contrast to the i=0 ground state transition accompanying
the 176Yb(p,t) reaction (A571, Hi70), where the angular dependence on
cross section is not so pronounced. Again, the finite range, two-
neutron pickup calculation does a much better job of fitting the lower
angle data than does the cluster transfer prediction, although both
approaches do a respectable job of reproducing the experimental i=0
angular shape.

The 5/2 and 7/2 members of the ground state rotational band
have very similar angular shapes. The positions of the relative maxima
occurring in these curves are reminiscent of i=2 angular shapes; how-
ever, the deep minimum occurring at 30° along with the unusual strength
of the observed diffraction pattern makes the £=2 assignments for these
states extremely uncertain.

The remaining members of the ground state rotational band
populated through the (p,t) reaction on 159Tb exhibit angular distribu—
tions which cannot be explained in terms of any single dominant angular
momentum transfer.

7.3.3. YJVibrational Band

 

The angular distributions of the various members of the K=l/2

Y vibrational band are also illustrated in Fig. 7.4. The angular shapes

69

exhibited by the first three members of this vibrational band are,
within statistical uncertainty, identical, indicating a complete absence
of i=0 strength in the transition to the 3/2 member of this band. More—
over, the angular shapes exhibited by these three states, as well as

the remaining two members of this band indicate that these states are
populated by a complex mixture of several allowed l-values rather than
through a single dominant angular momentum transfer. Possibly this
phenomenon can be understood and explained in terms of band mixing which
from previous arguments certainly must be occurring in this Y vibrational
band. Qualitatively one wouldn't expect complex mixed states to be
populated through simple, pure angular momentum transfers, and perhaps
this is just the underlying reason behind the complex angular shapes
exhibited by these states.

7.3.4. B-Vibrational Band

 

The angular distributions of the members of the B-vibrational
band are illustrated in Fig. 7.4. Unlike the y-vibrational states, the
members of this collective band appear to be populated through a single
dominant angular momentum transfer. As in the ground state rotational
band, the 3/2+ band head appears to be populated by an 2=O wave; how-
ever, unlike the ground state transition, the agreement between the
experimental angular distribution and theoretical i=0 curves are some-
thing less than spectacular. The positions of the experimental maxima
and minima appear to be systematically shifted from their theoretically
predicted positions, indicating the possibility of small contributions
from higher allowed a values. Nevertheless, the overall shape and
underlying strength of this experimental curve undoubtedly express

its dominant i=0 character.

70

The angular distributions of the remaining two members of this
band exhibit a characteristic i=2 angular shape. The positions of the
relative maxima of these curves are predicted quite well by the theory
although their relative strengths are once again underestimated.

Recently' there has been considerable speculation as to the
reality of B vibrational shape oscillations. The very unsystematic
disappearance of these bands in some deformed even-even rare-earth
nuclei has cast some serious doubts upon the simplistic origin
associated with B vibrational bands in general. However, previous
y-ray and conversion electron work (3167) have shown that the first two
members of this band behave in a classic manner characteristic of pure
8 vibrationally excited states. Perhaps the simple manner in which
the (p,t) reaction populates these states is a measure or signature of
their collective purity. This statement although speculative is con-
sistent with previous arguments surrounding the complex nature of 2
transfers leading to the previously discussed Y vibrational states and
indirectly implies mixing in excited members of the ground state rota-
tional band.

7.3.5. Other States

 

Angular distributions of two additional states of unknown
origin were also determined in this study and appear in Fig. 7.4 under
the heading:"0ther States".

The 325 keV state appearing in 159Tb(p,t) spectra is a rela-
tively low intensity peak which exhibits no apparent relationship to
any other peaks in this energy region. Its angular distribution is

flat, unstructured and is in no way related to any single angular

71

momentum curve. Its angular shape, however, is much like those exhibited

by the members of the K=1/2 Y vibrational band. Perhaps this peak is

the K=5l2 Y vibrational state; however, this is only mere speculation.
The 1238 keV peak on the other hand is a highly intense,

strongly populated peak which might have a composite nature. The

angular distribution of this peak appears to have a dominating i=2

angular shape. However, since this peak occurs at or above the pairing

gap in this nucleus nothing really can be said about its origin based

onthese data alone.

7.4. Summary

 

As was expected from the previous 11+1Pr(p,t) results, the
(p,t) reaction on 159Tb was found to populate collective excited states
within the residual nucleus 157Tb strongly. With the exception of a
few extremely low intensity states, the entire triton spectrum below
the pairing gap was totally accounted for in terms of B- and y- vibra-
tional and ground—state rotational band members.

Angular distributions of the collective states populated by
this reaction showed absolutely no general simplifying tendencies. With
the exception of the ground state and the members of the 8 vibrational
band, states were observed to be populated by complex mixtures of angu-
lar momentum transfers. Why a very few states should be populated by
the lowest possible 2 value while all others are not is not immediately
clear.

Before concluding this chapter, something should be said
about the strange 20° differential cross section behavior exhibited by

many of the states studied. This strange behavior is manifested in

72

angular distributions by an apparent discontinuity at 20°. Both the
15° and 25° degree points are commonly much smaller than the 20° value,
which cannot be understood in terms of any single theoretical curve.
This effect, however, appears to be very real since three independent

sets of specta taken at 15°, 20° and 25° all reproduce this behavior.

Chapter VIII

165Ho(p,t) Results

8.1. Introduction

 

In the interpretation of the 165Ho(p,t) spectra, liberal use
has been made of the well established level structure of 165Ho (Le68)
since experimental facts concerning the residual nucleus of this
reaction, 163Ho, are all but nonexistent. A partial level structure
of 165Ho appears in Fig. 8.1 where only pertinent states of interest

have been included.

8.2. Spectral Results

 

The characteristics of the triton spectra obtained from
165Ho are very much like those exhibited by the previous 159Tb(p,t)
Spectra as is graphically shown in Fig. 8.2. In this spectrum, one
finds a strong population of the K=7/2-[523] ground state rotational
band with level spacings similar to those occurring in the same band
in the 165Ho nucleus.

From Coulomb excitation experiments conducted on 165Ho by
Seaman g£_al_(Se67) one would expect from systematics to observe the
K=3/2_ and 11/2- 7 vibrational bands at :500 keV and :900 keV, respec-
tively. And indeed one does observe a set of states originating at
562 keV of excitation which appear to have some intensity interrelation—
ships. If one assumes that the 562-keV and the 618~keV states are the
first two members of the K=3/2 y vibrational band and one generates
higher members by parameterizing the simple I(I+1) energy relationship,

one finds convincing evidence for the presence of additional members

73

74

 

 

 

 

 

 

 

 

 

 

11/2’ 507.0
17/2' 872.0
7/2'
5/2'
3/2'
15/2' “99.0
13/2' 305.0
11/2' 209.0
9/2' 99.7
7/2'1523] .0
185
87H098

Fig. 8.1. Partial collective level structure of Ho.

165

830.0

500.0

519.0

TRHCKS PER 1/8HH

TRHCKS PER [/8101

75

EXCITQTION ENERGY ( HEV 1
1.0 0.8 0.8 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 '4 1.2 .N 0.2 0.0
50° 1 ¢ 4 1 1 1 1 1
7/2
"’HOIPJ)
30 NEV
20 DEG
U00 1- H
u:
“[2
300 - rm 1
Ill2
200» 1
1”:
100 -'
1512' 13/2' J
o 1 an” 1 L
1080 1280 1'480 1880
DISTRNCE RLONG PLRTE (1/811111
EXCITRTION ENERGY (HEV)
S 1.“ 1.2 1.0 0.8 0.8 0.11 0.2 0.0
10 1 1 1 1 1 1 +1 m m :
“5HOIP.T 1 j
30 nev ”’1 .
20 DEC ‘
13/2 -‘
2 .
10 3/2 :1
5/2' 1:12 1
1512' . :
7/2
. 1112 d
0/2
I 1112‘ ‘
10 1 _ “I ma“ -<
.. 1 4
10 0 I ‘i. l ._J L

 

 

 

 

 

 

 

1050 1280 1950 1680
OISTRNCE RLONG PLRTE (1/811111
Fig. 8.2. Log and linear displays of the 165110 (p, t) spectrum taken at

the laboratory scattering angle of 20°.

76

up to a spin of 15/2. However, no evidence for the presence of a K=11/2
Y vibrational band could be found in our spectra. The results of the
165Ho(p,t) spectrum are summarized in table 8.1. Rotational parameters
used in the theoretical calculations of rotationally excited states

are listed in Table 8.2. A level scheme composed of all states popu-

lated through the 165Ho(p,t) reaction appears in Fig. 8.3.

8.3. Summary

 

As in the case of 159Tb, the Qp,t) reaction on 165H0 is found
to p0pulate rotational as well as vibrationally excited states in the
residual nucleus strongly. The present study has identified six
members of the K=7/2 ground state rotational band and seven members
of the K=3/2 Y vibrational band. Moreover, with the single exception
of the 791-KeV peak, these states completely exhaust the (p,t) reaction
strength occurring below the pairing gap in the 163Ho nucleus.

The origin of the strongly excited 791-KeV state cannot be
determined from our data since it doesn't appear to have any relation-
ship to any other states in our spectra. Being below the pairing gap,
this state certainly must be a collective excitation, but whether it

be a B, Y or octupole state is not clear from our data alone.

77

vamp HmCOHumunH>u> mnoxnx mo umnfima m .H ”vamp HchHumuou mumum mason» mo umnEmE n H

m

 

 

I.N\MH NwOH mmOH

III oooH

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In: mHmH III NH0
1:: nqu :11 wow
In: quH II: omm
1:: quH I.~\o «om mow
III mNMH 1:: Hon
1:: mQMH III mmn
III wOMH IN\~H man can
III omNH |.~\m moo moo
u.~\mH omNH mmNH I.~\m III mHo
In: quH I.N\m It: own
In: NmNH IN\mH mmn mmn
In: cmHH |~\MH mom mom
:1: mNHH IN\HH mum «mm
In: omHH Im\m nun ooH
nun NHHH Im\n cu: m 0

ea $8: 93: 1% 99: 38:

mucmacmem< xuomza amumcm mucmeomem< muomnH mwumcm

 

 

.coHuummm Aw.mvom,p mnu swsoune wmumHnaom moumum .H.m mHan
me

78

Table 8.2.

Rotational Parameters Associated With Bands

Populated Through the 165Ho(p,t) Reaction.

 

 

 

Band - H2/23 a E0
(REV) (keV)
Grnd. 11.11 - -175.00

y 11.60 - 516.50

 

 

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79

 

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Chapter IX

States in 167Tm

The level structure of the 167Tm nucleus has been studied
through the (p,t) reaction on 169Tm and through the e/B+ decay of 167Yb.
It was hoped that the collective characteristics of the (p,t) reaction
coupled to the single particle aspects associated with s/B+ decay would
lead to a more or less complete low energy characterization of the
167Tm nucleus. This chapter will discuss and compare the results ob-
tained from each of these independent but complementary means of inves-

tigation.

9.1. 169Tm.(p,t) Results

 

The triton spectrum obtained at 20° from the 169Tm(p,t)
reaction appears in Fig. 9.1. As in the previous results, the ground
state rotational band of 167Tm is found to be strongly excited by this
reaction; however, due to the rather large decoupling parameter asso-
ciated with this K+=ll2+[411], the first two members of this band have
not been resolved in this experiment. Nevertheless, at least six
members of this rotational band are found to be populated through the
(p ,t) reaction.

Coulomb excitation experiments conducted on 169Tm (Se67) have
identified a K+s3l2+ Y vibrational band at 571 Rev of excitation in
this nucleus. Based on this information and the previous results
obtained for 157Tb and 163Ho, the series of three-states originating
at 600 keV of excitation have all the appearances of being members of a

Y vibrational band. However, a consistent energy relationship cannot

80

TRRCKS PER J/BHfl

TRRCKS PER 1/8HH

81

EXCITRTION ENERGY (HEV)
1.2 1.0 0.8 0.8

 

 

 

 

 

 

 

 

 

 

 

1.8 1 u 0.9 0.2 0.0
200 1 1 1 1 ,1, 1 1 1 .
312.1/2
5/2
"‘1n1?.11
30 nev
150* 20 DEC ‘
III? III!
112
III! ‘
1180 1380 1580
DISTRNCE RLONG PLRTE (l/BHH)
EXCIIRTION ENERGY (HEV)
3 1.8 1 u 1.2 1.0 0.3 0.8 0.9 0.2 0.0
‘0 1 1 1 1 1 1 4. 1 1
t 2
1- H
p- !lZ.I/2 -4
p 4
C m j
"’1n1P.11
- 30 HEV W2 .
20 DEG
10 2 j
4
-4
4
11/2 ‘
10' .
1
.1
10 °. 4 l54l|| h} l

 

 

 

 

980138
DmlSTRNCE RLONG PLRTE (1/8HH1

 

 

 

 

 

 

 

 

 

1580

Fig. 9.1. Log and linear displays at the 169Tm(p,t) spectrum taken at

the laboratory scattering angle of 20°.

82

be established between these states for an assumed band head spin of
either 3/2 or 5/2. Because of their extremely low intensity, it is
entirely possible that only one or two of these states belong to the
K=3l2 y vibrational band expected in this region. If this is indeed
the case, the present data are insufficient to make a judgement one
way or the other since a minimum of three states is required in order
to make the spin assignment.

At 1000 keV of excitation, one finds a series of highly
excited, closely Spaced peaks whose doublet nature defies all attempts
at sorting these states into groups of common origin. Without higher
resolution, a meaningful interpretation of states in this region cannot
be made.

The series of three states originating at 1380 keV of excita-
tion appears to have some type of common origin. The energy spacings
between these peaks suggest, although not too strongly, a K=5l2
rotational band. Since these states appear to be above the pairing
gap in this nucleus, one can only speculate as to their K=5l2 Y vibra-
tional origin.

The results of the analysis of the 169Tm(p,t) spectrum are
summarized in Table 9.1. A level structure reflecting the states

populated through the 169Tm(p,t) reaction appears in Fig. 9.2.

9.2. y-Ray Studies of the 167Yb Decay

 

The states of 167Tm have been investigated through the y-ray
studies of the e/B+ decay of 167Yb. This study has firmly established
the existence of twelve new excited states and the probable placement

of a thirteenth in the daughter nucleus 167Tm. Moreover, these thirteen

83

Table 9.1. States Populated Through the 169Tm(p,t) Reaction.

 

 

Energy Energya Assignmentb
(keV) (keV) J"

 

c s 1/2+

10.4 3/2

117 116. 5/2+

142 142. 7/2+

329 326. 9/2+

374 371. 11/2+

470 --— ---

604 --- ---

624 --- ---

663 —-- ---

682 --- ---

706 -—- ---
1010 --- ---
1092 —-- ---
1154 --- _-_‘
1192 -—- ~--
1210 --- ---
1283 —-- ---
1320 --- ---
1380 ——- 5/2'“+
1404 --- 7/2"'+
1434 1435
1457 --— ———
1486 --- —--
1526 --- ---
1574 --- ---
1598 -—- ---
1625 --- -——
1655 --- ---

10 +

OU'I§O‘

D
O
\
N

+

 

 

a) Ref. Wi69
b) I and I"' are members of the ground and y vibrational bands respectively.
c) Energy calculated from the first two members of this band.

84

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85

states, together with the well established level structure below 300
keV of excitation in the 167Tm nucleus, form a consistent framework for
the placement of 52 new y-rays associated with the decay of 167Y1).

9.2.1. Introduction

 

In 1954 the 18.5 min. 167Yb activity was first produced
(Ha54). Since then a number of studies involving both conversion elec-
tron (Ha59, Gr65) and y ray work (Ha59, W160, Gr65, Ta65, P367) have
contributed to the now well known low energy level scheme of 167Tm which
is illustrated in Fig. 9.3. Significant new data have now been obtained
regarding this decay system through use of high resolution, high
efficiency Ge(Li) detectors.

The decay of 167Yb is characterized essentially by two distinct
groups of y rays. The first group is composed of a series of low-energy,
high-intensity and closely spaced cascade y rays associated with the
well-established low energy rotational states in 167Tm. The second
group, on the other hand, is composed of a series of high-energy, low-
intensity and closely spaced y rays originating from high—energy excited
states in 167Tm which feed the aforementioned low—energy rotational
states. Because of the low intensity characteristics of the high energy
y rays and the relatively short 18-min half-life of 167Yb, the only
practical coincidence experiments which could be conducted on this sys-
tem within a 24-h period would have to involve a high efficiency NaI(Tl)
detector coupled with a high resolution Ge(Li) detector, however because
of the high density of y rays characterizing this decay, gated experi-
ments involving a NaI(Tl) detector would be all but impossible to in-

terpret.

86

 

 

 

 

 

 

 

572-15321 321.7
772-15231* 292-7
7/2‘19091 179-"
7/2‘ 1Q2.3
5/2‘ 118.5
3/2‘ 10.“
172°[u111 .0
1137
89TH98

Fig. 9.3. Low energy rotational structure of 167Tm.

87

On the other hand,the shortcomings of the Ge(Li)-NaI(T1)
coincidence configuration could in theory be eliminated through the use
of a Ge(Li)-Ge(Li) two-dimensional megachannel experimental system
(D069). However, on the basis of a Ge(Li)-NaI(Tl) integral coincidence
experiment performed on the decay of 167Yb which is discussed later,
it was estimated that a minimum of 4-5 days of continual cyclotron use
would be required to perform this experiment. Moreover, because of
the high dead-time which would be necessary in conducting this experi-
ment, the number of y rays above the x-ray threshold which could be
cleanly gated would be small at best.

0n the brighter side of things, the 167Tm ground state
rotational band is based on the l/2+[4ll] Nilsson single particle state.
As a result, one might expect to find very characteristic reduced
transition probabilities associated with the y-ray transitions connecting
various excited states to the members of this ground-state rotational
band. This feature arises from the fact that the fully anti-symmeterized
wave functions of all odd-mass deformed nuclei for which vibrational
motion is neglected and a strong coupling model is valid have the

following form:

1/2 _
1’ (IKM) = 1%] “7131: (0) x: N) + (-nIi JerKm) x: (x')}

where x(x') describes the intrinsic motion of the odd "optical" nucleon
in the deformed field of the core, while 0(0) describes the rotational
motion of the deformed core. For a more thorough discussion of the

collective model, see Ref. (Pr63).

88

The energy-independent probability of a Y-ray transition
between an initial state i and final state.f via a multipolarity A,
(called the reduced transition probability), is obtained from the ma-
trix element of the field operator M(>.,11) between the wave functions of

the initial and final states which has the following form:
< wfaMK) |M(1,u) | Wi(I'K'M') >

This matrix element will, in general, be composed of a direct term as
well as a cross term contribution. However, only when (Ki+gf)il will

the cross term contribution be non-zero, in which case the expression

for the reduced transition probability will take on the following form:

I K
B().:Ii—>If) = A{C(IiAKi(Kf-Ki)|Ifo) + b(-1) f+ f C(IilKi-(Ki+Kf)lIf—Kf)}2

where A and b are constants characteristic of the initial and final
intrinsic states and are determined empirically from observed transition
data. It is the coherent sum of Clebsch-Gordon coefficients in the above
expression which is responsible for the very characteristic transition
probabilities most often associated with K=l/2 rotational bands.

Because of the technical difficulties involved in conducting
a prolonged two—dimensional Ge(Li)-Ge(Li) mega-channel coincidence ex-
periment and the doubtful value of such an experiment on the 167Yb
system, the approach taken in this study involved carefully measuring
energies and intensities of the y rays associated with the 167Yb decay,
conducting all pertinent Ge(Li)-NaI(Tl) coincidence experiments, and
using the unique properties of K=l/2 rotational bands as a handle along

with log ft values in determining the spins and parities of the states

89

proposed on the basis of the singles and coincidence experiments.
9.2.2. Experimental Results

Samples of the 18.5-min 167Yb were produced by bombarding the
oxide of naturally occurring 169Tm with 23.5-MeV protons. Samples
were irradiated for approximately 3 min with average beam currents of
2 0A, and the resulting activities were counted for periods not exceeding
3 half-lives.

The y-ray spectrum of 167Tm above 500 keV taken with a 2.5%
efficient Ge(Li) detector with resolution of 2.3 keV FWHM on the l332-keV
y-ray of 60Co is shown in Fig. 9.4. The low energy spectrum of 167Tm
was taken with a newly acquired "super-high" resolution Si(Li) x-ray
detector and appears in Fig. 9.5. A total of 110 y-ray transitions
have been observed to follow the decay of 167Yb and are listed in Table
9.2 along with their relative intensities. y—ray energies appearing
in brackets in Table 9.2 correspond to low-intensity Y rays which only
appear after long periods of counting and may very well not belong
to the 167Yb decay.

The results of an anti-coincidence and integral coincidence
experiment using an 8"X8" NaI(Tl) annulus with a 2.5% efficient Ge(Li)
detector confirmed the previously described decay characteristics of
167Yb but yielded no important additional information other than placing
a lower limit on the amount of time required to perform a two-dimensional
Ge(Li)-Ge(Li) mega-channel coincidence experiment.

Since the 179.4-kev 7/2+[404] and the 292.4-kev 7/2+[523]
states have been previously determined (Ta65) to be isomeric, a delayed
integral coincidence experiment was conducted utilizing an 8"X8" NaI(T1)

annulus and a 3"X3" NaI(Tl) scintillator together with a newly acquired

90

 

 

 

 

 

 

 

 

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Yb singles Y ray spectrum taken with a Ge(Li) detector using a graded lead absorber.

167

Fig. 9.4.

91

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92
Table 9.2.

Y—Ray Transition Data for the 167Yb Decay

 

 

 

Energy Photon Energy Photon
(keV) Intensity (keV) Intensity
25.90:0.10 --- 794. 2:0. 5 0.27
37.03:0.05 --- 815. 9:0. 3 0.94
x-rays 27200 829. 3:0. 3 1.69
62.88:0.05 524. 832. 9:0. 3 1.23
106.14:0.05 4770 846. 2:0. 2 2.50
113.3Q:0.05 10900 903. 3:0. 3 1.01
116.55:0.05 565. 905. 3:0. 3 0.49
l32.01:0.05 479. 920. 3+0. 2 18.01
l43.4l:0.05 337. 923. 5+0. 3 1.07
(150.5 :0.3) 4.65 933. 5:0. 3 1.27
(156.5 :0.5) 6.01 936. 5+0. 3 1.40
(162.6 :0.6) 25.12 970. 8:0. 4 0.76
(169.7 :0.5) 25 998. 4:0. 2 0.85
l76.31:0.10 2420. 1009. 0:0. 2 0.83
(184.0 :0.5) 1.75 1022. 8:0. 2 1.50
(198.3 :0.5) 1.68 1026. 2:0. 2 0.70
218.6 :0.3 11.54 1037. 0:0.1 3100.00
225.7 :0.4 14.48 1048. 7:0. 2 2.93
282.1 :0.2 12.88 1050. 3:0. 2 5.25
290.0 :0.5 14.43 1067. 6:0. 3 0.96
343.3 :0.2 3.11 1069. 5:0. 3 1.01
(351.8 :0.2) 2.15 1110. 4:0. 2 1.76
405.6 :0.2 2.02 1137.1:0. 5 0.59
441.2 :0.2 1.36 1139. 6:0. 2 7.47
447.1 :0.3 0.92 1165. 7:0. 4 -—-
457.0 :0.5 2.05 1213. 2:0. 2 1.32
460.4 :0.4 3.66 1217.1:0. 2 1.13
470.6 :0.2 2.29 1234. 6:0. 1 27.71
511.01 (7:) 431.05 1241. 9:0.1 2.98
541.5 :0.3 0.81 1288. 0:0. 3 6.81
547.6 :0.2 2.48 1304. 8:0. 2 5.94
(665.1 :0.5) 0.7 1320. 8:Q 2 2.34
(672.1 :0.3) 1.07 1332. 8:Q 2 0.95
(680.4 :0.3) 0.6 1336. 7:Q 5 0.21
687.1 :0.2 0.6 1339. 9:Q 4 0.33
(688.6 :0.4) 1.4 1342. 3:Q 4 0.78
(694.1 :0.4) 0.8 1355. 3:0. 3 0.35
695.6 :0.4 0.5 1358. 3:0. 4 0.13
697.3 :0.4 1.09 1361. 6:0. 2 2.96
707.7 :0.4 1.08 1365. 5:0. 5 0.48
719.7 :0.4 1.17 1369. 9:0. 2 1.97
733.1 :0.3 1.01 1385.1:Q 2 1.33
791.6 :0.2 1.84 1393.1:0. 2 1.05

 

93

Table 9.2. Continued

 

 

 

Energy Photon Energy Photon
(keV) Intensity (keV) Intensity
1401.910.3 0.55 1511.9:0.3 2.44
1410.4:0.3 0.57 1517.310.3 1.56
l427.7:0.2 0.65 1525.510.3 0.28
1433.5:0.4 0.29 1533.6:0.3 0.20
1438.4:0.1 4.00 1537.6:0.3 0.44
1455.1:0.1 4.11 1570.5:0.1 5.38
1460.7:0.4 0.31 1587.2:0.1 4.97
1464.7:0.3 0.91 1619.2:0.2 2.13
1481.0:0.3 0.42 1631.9:0.2 0.36
1486.5:0.3 0.83 1643.910.2 2.65
1487.6:0.2 1.26 1681.0:0.5 ---
1498.1:0.2 0.79 1694.9:0.5 ———
1509.0:0.5 0.32 1808.0:0.5 ---

 

 

94

3.6% efficient Ge(Li) detector. The coincidence timing resolution was
set at 100 nsec and a delay of 2200 nsec was added to the Ge(Li) leg of
the coincidence circuit. The resulting spectrum is shown in Fig. 9.6.
Several peaks were found to be enhanced up to two order of magnitude
relative to the 132.0-keV peak, which is not found to be involved in

any delayed coincidences. The results of this experiment are summarized
in Table 9.3. Based on these results and sum and difference relations,
states at 1216.4, 1229.9, 1318.9, 1527.6, 1534.7, 1580.8, 1597.5, and
1654.5 keV have been proposed.

The energy of the 9/2+ member of the 7/2+[404] rotational band
was established empirically by adjusting its calculated energy determined
from the moment of inertia of the same rotational band in neighboring
169Tm. Both the 1216.4-keV and 1318.9-keV states were found to feed the
7/2+ band head state strongly, and, in addition, y rays were found that
fit the calculated 9/2+ state within 0.6 keV. Moreover, both of these
y rays, when subtracted from the excited states from which they presum-
ably originated, gave results which were consistent within 0.03 keV.
This energy consistency, along with the expectation of an observable
feeding to the 9/2 member of this K:7/2 rotational band if the band head
member is strongly fed, led to the establishment of the 296.1-keV state.

A search for the 9/2 members of the K=1/2+ and K=7/2- bands
was made in a similar manner without any apparent success. However,
recently (W169) these levels were reported to have been populated through
the (a,2ny) reaction on 165Ho. The reported energies of these states
differed markedly from what one would predict from simple first—order
rotational model calculations. Since no really strong evidence exists

+
that these states are populated by the e/B decay of 167Yb, they have

95

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96

Table 9.3.

Results of Integral Delayed Coincidence Study on 167Yb Decay

 

 

 

 

 

y-ray Energies Relative Intensities
(keV) Singles Delayed Coin.
106.1 996.11 1607.
113.3 2277.66 28382.
132.0 5100.00 3100.00
142.4 70.46 159.
150.5 0.01 113.
162.4 0.05 3102.
169.7 0.05 602.
176.3 505.99 868.
218.6 0.02 275.
225.7 0.03 128.
447.1 0.001 47.
920.3 0.04
923.5 0.002 117°
1037.0 0.21 423.
1050.0 0.01 18.
1086.2 ----- 47.
1139.6 0.02 33.
1234.6 0.06 185.
1241.9 0.01 24.
1288.0 0.01 51.
1304.8 0.01 28.
1346.5 ----- 8.
1358.3 0.001 [ 20.
1361.6 0.01

 

 

97

been put into our decay scheme with dotted lines. This work also served
to confirm our placement of 9/2+ member of the 7/2+[404] rotational band.

The remaining high energy states were established mainly
through restrictive energy sums and feeding consistencies within the
various known low-energy rotational bands (Fig. 9.3) of 167Tm.

9.2.3. 167Yb Decay Scheme

 

The decay scheme developed from our work is illustrated in
Fig. 9.7. The resulting level structure forms a consistent framework for
accommodating 96% of the observed y-ray intensity associated with the
167Yb decay. A large portion of the unplaced intensity resides in a
single 143.4—keV y-ray transition. In a recent study of the (0,2ny)
reaction on 165Ho (W169) an undocumented decay scheme of 167Yb was in—
cluded for purposes of comparing the results of the two methods of
investigation. Besides confirming our placement of several excited states,
this decay scheme indicated that the 143.4-keV intensity arose from the
feeding of the 9/2- 285.9-keV member of a 1/2-[541] rotational band by
the 7/2_[523] Nilsson state via a 6.9-keV transition, which presumably
was measured with a B-ray spectrometer. However, the 285.9-keV state
plays no other definite role in this decay scheme other than providing
a source of the 143.4-keV radiation. One is also struck by the fact that
although much effort must have been expended in setting up an experiment
for measuring such a low-energy 18-min activity, the very intense 10.4-
keV transition conversion line was completely neglected.

If the 285.9-keV state is introduced into our decay scheme, one
finds no additional corroborating evidence to support its placement.

This fact coupled with the absence of explicit experimental information

98

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Fig. 9.7. Decay scheme of 167Yb. A11 energies are given in keV, and

(total) transition intensities are given in terms of
percent per disintegration of the parent. The B+le ratios
are calculated values, and the log ft values are calculated
on the basis of an 18 min half—life.

99

concerning the 6.9-keV conversion line led us to exclude the 143.4-keV
transition from our decay scheme temporarily.

Although the 25.8—keV and 37.1-keV Y rays have been seen in
spectra taken with our Si(Li) x-ray detector, reliable intensities for
these transitions are not available, since massless sources of 167Yb
were not used in our primary investigation. The intensities of the
25.8—keV and 37.1-keV Y rays used initially in determining the decay
scheme of 167Yb were theoretical ones based on the relative electron
intensities of Harmatz (Ha59), the multipolarities of Gromov (Gr65),
and the theoretical conversion coefficients of Sliv and Band (S165).
However, the results using these values led to inconsistent B+/e feeding
to the 5/2+ and 7/2+ members of the ground-state rotational band. As
a result the feedings to these states have been temporarily set equal to
zero until accurate intensity measurements of these y rays are made.

The preliminary assignments of spins and parities have been
based primarily on log ft values and reduced transition intensities where
they apply.

Five newly established excited states of 167Tm were observed
to feed the 1/2+[4ll] ground state rotational band with remarkably simi—
lar transition intensities. In each case oscillatory transition inten-
sities were observed in the feedings of the 3/2 through 7/2 members of
the ground state rotational band. These facts are summarized in Table
9.4. In order to explain this oscillatory feeding behavior exhibited by
these five states, calculations of the reduced transition probability
ratios corresponding to the feeding of the K=ll2+ rotational band were
made on the basis of all reasonable values of the K projection number

and spin of the depopulated state and on several assumed multipolarities.

100

Table 9.4.

Relative Feeding Intensity Data to Members
of the Ground State Rotational Band

 

 

 

 

State Spin of State Being Fed

(keV) 3/2 5/2 212
1527 1.5 0.6 1.3
1580 5.4 0.9 4.0
1597 4.9 0.4 4.1
1627 2.1 —-— 1.3

1654 2.6 0.4 2.6

 

 

101

A comparison between experimentally determined reduced transition
probability ratios and these calculations for the 1654-keV state
appears in Table 9.5. The results of these analyses appear, if one
neglects second order effects, to determine uniquely the spin of these
five states to be 5/2 and in addition strongly suggest a K=l/2 projection
number in each case. All other possibilities lead to absurd contradic-
tions between experimental results and theory. In addition, it is
found that the log ft values associated with these excited states of
spin 5/2 are all closely clustered about a value of 6.0. Since one
would expect much larger log ft values for first forbidden decays with
zulflm-forbiddenness associated with them,the a decay to these 5/2 states
appear to be allowed l-forbidden, which establishes negative parities
for these five states. Moreover, these negative parity assignments are
consistent with the strong observed feedings to the 7/2-[523] state
which is a common feature of each of these states.

The spin assignments of the remaining states are based pri-

marily on log fi values and feeding characteristics of these states.

9.3. Summary

 

A comparison between the states populated through radioactive
decay and (p,t) reaction processes reveals similarities only for lower
members of the ground state rotational band and for states occurring
above 1300 keV of excitation. Unfortunately, no evidence for direct
or indirect feeding of the states based at 600 keV of excitation is
found from this decay scheme study leaving unanswered the question of
whether a y—band exists in this region.

The series of three states based at 1380 keV of excitation

102

Table 9.5.

Theoretical vs Experimental Reduced Transition Probabilities

 

 

Members of the Ground State Rotational Band Being

Fed by the 1654 keV State.

 

 

 

 

 

 

A1) 2) 3) EXPerimental Theoretical

K J 3/2 5/2 7/2 1/2 3/2 5/2 7/2 9/2 11/2
2 1/2 3/2 1.00 0.23 1.40 1.94 1.00 1.17 1.40 --- --~
1 1/2 5/2 1.00 0.20 1.18 ---- 1.00 0.11 1.18 ---- ----
2 1/2 5/2 1.00 0.23 1.40 0.37 1.00 0.06 1.40 2.73 ----
2 1/2 7/2 1.00 0.23 1.40 ---- 1.00 0.02 1.40 0.003 3.77
2 3/2 3/2 1.00 0.23 1.40 17.2 1.00 24.5 1.40 ---- —---
1 3/2 5/2 1.00 0.20 1.18 ---- 1.00 1.14 0.36 ---— ——-—
2 3/2 5/2 1.00 0.23 1.40 0.58 1.00 0.99 1.40 0.04 -—--
2 3/2 7/2 1.00 0.23 1.40 ---- 1.00 1.05 1.40 1.01 1.28
2 5/2 5/2 1.00 0.23 1.40 0.88 1.00 0.56 0.17 0.02 ~--—
2 5/2 7/2 1.00 0.23 1.40 ---- 1.00 1.78 1.33 0.48 0.07
3 7/2 7/2 1.00 0.27 1.66 0.75 1.00 0.75 0.36 0.11 0.02
1)

A=y—ray multipolarity

2) K=K—projection number of 1654 keV state

3) J=spin of 1654 state

~_. _. _——.——___._

103

which exhibited some K=5/2 band characteristics are also found to be
unfed in this decay. This is a little surprising if the spin assignments
of these states are correct since the decaying state has spin and parity
of 5/2_. Again the combined results of these two studies are insuffi-

cient to resolve the questions regarding the spins and origins of these

three states.

Chapter X

Conclusion

The study of the general systematics of the Qp,t) reaction
on spherical and deformed rare earth nuclei has shown that this reac-
tion at the very least is a potent and powerful tool for probing the
collective characteristics of nuclei.

The lulPr(p,t) experiment illustrated how the Qp,t) reaction
on spherical nuclei might be used in selectively identifying states
having a vibrational origin. Moreover,(p,t) differential cross section
measurements can in theory be used to determine the spins of these
vibrationally excited states.

The (p,t) reaction on deformed rare earth nuclei clearly
established the collective strength associated with this reaction.

In each of the deformed nuclei studied, at least six members of the
ground state rotational band were found to be strongly excited through
this reaction. In two of three deformed nuclei studied, Y vibrational
bands were identified, with five members in 157Tb and possibly seven
members in 163Ho being populated. In addition, a B vibrational band
strongly populated through the l59Tb(p,t) reaction was also identified.
However, only three members of this band could be identified because
of high background problems.

The power of using this reaction to identify collective
states selectively in deformed nuclei is enourmous. This has clearly
been shown in the 159Tb(p,t) experiment where the disputed origin of

the K=1/2 band based at 598 keV in the 157Tb nucleus was resolved.

104

105

Our data unequivocally indicated that these states had large collective
amplitudes in their wave functions and were correspondingly identified
as members of a y-vibrational excitation of the K=3/2 ground state of
157Tb. This assignment has since been corroborated by the recent
identification of a rotational band based on the K"=l/2+[4ll] single
particle proton state located at 923 keV of excitation through 1560d
(3He,d) experiments (3071). It should be noted that the experimentally
determined decoupling parameter associated with this K=l/2 rotational
band is consistent with theoretical predictions (B071).

In conclusion, I believe that the results of this study have
clearly shown the (p,t) reaction to be as powerful a tool for probing
the collective characteristics of nuclei two neutrons removed from

stability as Coulomb excitation techniques are for stable nuclei.

LIST OF REFERENCES

[A571]

[Au67]

[Au68]

[Ba62]

[Ba64]

[Ba67]
[Ba68]

[Be69]

[33°66]

[B167]

[8052]

[3053]

[B071]

[Br69]

LIST OF REFERENCES

A

R. J. Ascuitto, M. K. Glendenning, B. Sdrensen, Phys. Lett.
34B, 17(1971).

R. L. Auble, D. B. Beery, G. Berzins, L. H. Beyer,
R. C. Etherton, W. H. Kelly, and Wm. C. McHarris, Nucl.
Inst. and Meth. 51, 61(1967).
R. Au, Michigan State University, private communication
(1968).

B

R. H. Bassel, R. M. Drisko, and G. R. Satchler, Oak Ridge
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G. Bassani, Norton M. Hintz, and C. D. Kavalaski, Phys.
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B. F. Bayman and A. Kallio, Phys. Rev. 156, 1121(1967).
B. F. Bayman and Norton M. Hintz, Phys. Rev. 172, 1113(1968).

D. B. Beery, W. H. Helly and Wm. C. McHarris, Phys. Rev.
188, 1851(1969).

J. H. Bjerregaard, Ole Hansen and 0. Nathan, Nucl. Phys.
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P. H. Blichert-Toft, E. G. Funk and J. W. Mihelich, Nucl.
Phys. A100, 369(1967).

A. Bohr, Dan. Mat. Fys. Medd. 26,nr.l4(1952).

A. Bohr and B. R. Mottelson, Dan. Mat. Fys. Medd. 22,nr.
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J. Boyno, Rodchester University, private communication.

3. M. Brahmovar, J. H. Hamilton, A. V. Ramayya, E. F. Zganger,
and C. E. Bemis, Nucl. Phys. A125, (1969)

106

[Ch70]

[D069]

[D071]

[Fr67]

[G064]

[Go69]

[Gr65]

[Ha54]

[Ha59]

[Hi70]

[1369]

107

C

N. S. Chant and N. F. Mangelson, Nucl. Phys. A140, 81(1970).

D

R. Doebler, 1969 Annual Report, Nuclear Chemistry Group,
Michigan State University (C00-l773-13).

R. Doebler, Ph.D. Thesis, Michigan State University (1971).

F
M. P. Fricke, E. B. Cross, B. J. Morton and A. Zucker,
Phys. Rev. 156, 1207(1967).

G

M. L. Goldberger and K. M. Watson, Collision Theory,
(John Wiley & Sons, 1964).

 

R. Goles, 1969 Annual Report, Nuclear Chemistry Group,
Michigan State University (COO-l773-l3).

K. Ya Gromov, A. S. Danagulyan, A. T. Strigachev and
V. S. Shpenel, U.S.S.R. Yad. Fiz., 1137(1965).
H
T. H. Handley and E. L. Olson, Phys. Rev. 243 968(1954).

B. Harmatz, T. H. Handley, and J. W. Mihelich, Phys. Rev.
114, 1082(1959).

M. 00thoudt, M. M. Hintz and P. Vedelsly, Phys. Lett.
32B, 270(1970).
I

G. J. Igo, P. D. Barnes, E. R. Flynn and P. D. Armstrong,
Phys. Rev. 177, 1831(1969).

 

108

K

[Ku65] The DWBA code DWUCK written by P. Kunz of the University
of Colorado, 1965 (unpublished).

[Ku7l] E. Rost and P. D. Kunz, Nucl. Phys. A162, 376(1971).

L
[Le68] C. M. Lederer, J. M. Hollander, and I. Perlman, Table of
Isotopes (John Wiley & Sons, New York 1966).
M
[Ma55] M. G. Mayer and J. H. D. Jensen, Elementary Theory of

Nuclear Shell Structure (John Wiley & Sons, Inc., New York,
1955).

 

 

[Ma66] J. R. Maxwell, Glenn M. Reynolds, and Norton M. Hintz,
Phys. Rev. 151, 1000(1966).

[Mc69] Wm. C. McHarris, D. B. Beery and W. H. Kelly, Phys. Rev.
Lett. 2_2_, 1191(1969) .
P
[Pa67] P. Paris, J. J. Phys. (Paris) 28, 388(1967).

[Pe62] Lars Persson, Hans Ryde and Karin 0elsner-Ryde, Ark.
Fys. 24, nr.34 (1962).

[Pe63] F. Perey. R. J. Silva, and G. R. Satchler, Phys. Lett. 4,
25(1963).

[Pr63] M. A. Preston, Physics of the Nucleus (Addison-Wesley, Inc.,
Reading, Massachusetts, 1963).

 

R

[Re67] G. M. Reynolds, J. R. Maxwell and Norton M. Hintz, Phys.
Rev. 153, 1283(1967).

[RiX)] J. Rice, Michigan State University, private communication
(1971).

[R069]

[Sa64]

[SaA65]

[8e67]

[8165]

[Ta65]

[T061]

[Tr70]

[W160]

[W166]

[W169]

109

J. T. Routti and S. G. Prussin, Nucl. Instr. and Meth. 22,
125(1969).
S
G. R. Satchler, Nucl. Phys. 52, 1(1964).
G. R. Satchler in Lectures in Theoretical Physics ,

Vol. VIIC (University of Colorado Press, Boulder, Colorado,
1965).

 

G. G. Seaman, E. M. Bernstein and J. M. Palms, Phys. Rev.
161, 1223(1967).

L. A. Sliv and I. M. Band, in Alpha, Beta and Gamma Ray,
Spectroscopy, ed. by K. Siegbahn, North Holland Pub. 00.,
Amsterdam (1965).

 

 

T
T. Tamura, Nucl. Phys. 62, 305 (1965).

W. Tobocman, Theory of Direct Nuclear Reactions (Oxford
University Press, 1961).

 

G. F. Trentelman, Michigan State University, private
communication.

W
R. G. Wilson and M. L. Pool, Phys. Rev. 120, 1296(1960).

C. F; Williamson, J. Boujot, and J. Picard, Centre d' Eludes
Nucleaire de Saclay, Report CEA-R3042(1966).

G. Winter, L. Funke, K. Hohmuth, K. H. Kaun, P. Kemnitz and
H. Sodan, Nucl. Phys. A151, 337(1969).

APPENDICES

APPENDIX A

11‘1Pr(p,t) Spectra

The following pages contain 1“‘1Pr(p,t)
angular distribution spectra taken with

an E-AE detector telescope.

110

COUNTS/CHRNNEL

COUNTS/CHRNNEL

100
80
80
90

20
0

125
100

00 Ln ‘0
Ln C3 Ln

0

111

EXCITRTION ENERGY (HEV)
L0 L8 L2 Q8 00 00

1 11

 

 

l l 1
fi I I I r

‘b

Lab.

 

] 1].]

 

k l l l

. l
3300 3900 3500 3800

CHRNNEL NUMBER

EXCITRTION ENERGY (MEV)
an 2J3 L8 1.2 Q8 0J4 00

 

 

L 1 1 1 1 1 L 1
I I I I f I W F

= 20°

0
Lab.
1

 

 

L I 1

 

J
3250 3350 3950 3550

CHRNNEL NUMBER

COUNTS/CHBNNEL

COUNTS/CHBNNEL

250
200
150
100

50

100

“Q J: 07 CO
C3 C3 C3 C3

0

112

 

 

 

 

 

 

 

 

 

 

 

 

 

EXCIIRTION ENERGY (MEV)
2.9 2.0 1.8 1.2 0.8 0.9 0.0
L- OLab.=25° fl .4
L J
L- J
M
i 1 L
3250 3350 3950 3550
CHRNNEL NUMBER
EXCITRTION ENERGY (MEV)
2.9 2.0 1.8 1.2 0.8 0.'-| 0.0
L OLab.= 300 J
t J
L 4
..J
L L 1 1 . .81- .. .l
3250 3350 3950 3550

CHQNNEL NUMBER

COUNTS/CHENNEL

COUNTS/CHBNNEL

113

EXCITRTION ENERGY [MEV)

 

 

 

 

 

 

2." 2.0 1.8 1.2 0.8 0.9 0.0

150 1 1 1 i + 1 ‘
120 L OLab.= 35° .1
90L J
Got 1
30* I 1
U L 1 L-A. . ,
3250 3350 3950 3550

CHRNNEL NUMBER

EXCITHTION ENERGY (MEV)
23 20 L8 1.2 011 0A 00

 

 

 

 

 

 

 

 

 

80 i 1‘ i 41 + 1 1L
OLab.= 40°
40 - l| ..
20 *- ‘ .1
0_ 1 1 j ' 1110' .LJ 1‘ - _ 1
3250 3350 3950 3550

GHRNNEL NUMBER

COUNTS/CHRNNEL

COUNTS/CHRNNEL

114

EXCITRTION ENERGY (REV)
21 20 L8 1.2 013 0A mo

 

 

 

 

 

 

 

80 1 1 1 1 1 1 1
so 1 OWE 45° 1 J
u01 . 1
201‘ 1 i w
.. . 11 1
3250 3350 3150 3550

CHRNNEL NUMBER

EXCITRTION ENERGY (MEV)
21 an L8 1.2 011 DA mo

 

 

 

 

 

 

 

60 1 1 1 1 1 1 1
)I.:1b.= 50°
110 1— -1
201 1
0 ,1 1 L1. .7 -1111“ . ,
3250 3350 31150L 3550

CHRNNEL NUMBER

COUNTS/CHRNNEL

COUNTS/CHRNNEL

100
80
80
H0

20
0

125
100

no L” ‘d
L“ CD UN

0

111

EXCITRTION ENERGY (MEV)

 

 

 

 

  

 

 

 

 

 

 

2.0 1.6 1.2 0.8 D.“ 0.0
‘ GLab.= 15 4
1-
1 '

__ J_ L L L L
3300 31100 3500 3600
CHRNNEL NUMBER
EXCITRTION ENERGY (MEV)

2.11 2.0 1.8 1.2 0.8 0.11 0.0
L- OLab.= 20° ..1
L 1
3250 3350 31150 3550

CHRNNEL NUMBER

COUNTS/CHRNNEL

COUNTS/CHRNNEL

100
80

.4: 07
C3 C3

“Q
CD CD

112

EXCITRTION ENERGY (MEVJ

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.11 2.0 1.8 1.2 0.8 0.11 0.0
p OLab.=25 fl 4
.1
J
W
L L
3250 3350 3950 3550
CHRNNEL NUMBER
EXCITRTION ENERGY (MEV)
2.11 2.0 1.8 1.2 0.8 0." 0.0
L OLab.= 30° 4
L 4
J
L 1 1 > 1.“-.. 1
3250 3350 3050 3550

CHRNNEL NUMBER

 

COUNTS/CHRNNEL

COUNTS/ CHRNNEL

113

EXCITRTION ENERGY (MEV1

 

 

 

 

 

 

 

2.11 2.0 1.8 1.2 0.8 0.11 0.0

150 1 1 +1 1 +1 1
120 1.. 011111.: 35° 1 .1
90 L 1 .1
601 J
301 ’ I 1
D L 1 ‘ L-A. . ,
3250 3350 31150 3550

CHRNNEL NUMBER

EXCITRTION ENERGY (MEVJ

 

 

 

 

 

 

2.11 2.0 1.8 1.2 0.8 0.11 0.0
80 1 fi1 1 1 1 41 1L
OLab.= 40°
l10 ~ l| —1
20L 1
_ 1
U 1 1 ' ‘111 .111 1.1 - . 1

 

3250 3350 3150 3550
CHRNNEL NUMBER

COUNTS/CHRNNEL

COUNTS,“ CHRNNEL

114

EXCITRTION ENERGY (MEVJ
2.11 2.0 1.8 1.2 0.8 0.11 0.0

 

 

 

 

 

 

 

 

80 1 1 1 1 1 1 1
BO __ C-)Lab.._- 45° 1 .1
L10 1 J
20 1— 1 I 1 1
0 L L111 ’ 1.1.
3250 3350 31150 3550

CHRNNEL NUMBER

EXCITRTION ENERGY (MEV1
2.11 2.0 1.8 1.2 0.8 0.11 0.0

 

 

 

 

 

 

80 1 1 1 1 1 1 1
”1.111).: 500
LID 1- 1 .1
20 1.. .1
0,1 i 7 L1- -111“ . ,
3250 3350 31150 3550

CHRNNEL NUMBER

COUNTS/CHRNNEL

COUNTS/CHRNNEL

H0

30

20

10

25
20
IS

10

s ,

0

115

EXCITRTION ENERGY (MEV)

 

 

 

 

 

 

 

 

 

 

 

CHRNNEL NUMBER

 

2.0 1.8 1.2 0.8 0.11 0.0
OLab.= 55°
1. .1
1.. .1
l 1 a 11.1.: ual .1511 1
3250 3350 3HSO 3550
CHRNNEL NUMBER
EXCITRTION ENERGY [MEV1
1.8 1.2 0.8 0.11 0.0
L GLab.= 60° 3
1- -1
1. 1 .1
1 1 L . . 4
_ 11'. 1.1. 1.1 1 1 1. 1 1
3250 3350 BHSO 3550

COUNTS/CHRNNEL

COUNTS/CHRNNEL

116

EXCITQTION ENERGY (MEV)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2 0.8 0.11 0.0
20 1 1 1 1 +
GLab.= 65°
15 1- ..
10 h ' 1
' 11
51‘ "‘
U 1 1 ‘111111 1; 1 i1 ,
3250 3350 31450 3550
CHRNNEL NUMBER
EXCITRTION ENERGY (MEV)
2.0 1.8 1.2 0.8 0.” 0.0
25 1 1 1 1 1
20 1' 11Lab.= 75° 1 ...1
IS 1— -1
10 1 .
5 1 "1
U 1 “11111 I“ 1‘ 2| 1 1
3250 3350 3950

CHRNNEL NUMBER

APPENDIX B

Tabulation of 1L’lPr(p,1:) Differential

Cross Sections

The following pages contain listings of the
center-of-mass differential cross sections
and scattering angles for the various states
populated through the 1111Pr(p,t) reaction.
A11 cross sections are relative and have
been normalized to reflect the magnitudes

of measured absolute values. The listed

errors are purely statistical.

117

118

P9141(PoT) P91“1(P:T)

Ex. .ooo Mgv fix- .405 MEv

ANG(CN) SIGNA1CM) ERRaR ANGCCN) SIGMA1CM) ERRfiR

(DEG) (MB/SR1 1x1 (DLG) (MB/591 1%)
15°21 1-3SE-c1 «.2 15.21 6-caE-ca 35-3
20°28 6072E'02 309 20028 903QE-03 12.7
25'35 9.a7E-03 8.2 25.35 1.486-02 603
300h1 3.38Eo02 «.3 30.41 3.07E-03 1705
35.47 1.87E.og 3.1 35.47 2.17E-03 17'9
#0053 1.«4E.og 6.3 40.53 3.62E.03 13'6
“5'58 1005E~02 808 “5058 “0515-03 1“.“
50063 1084E-02 507 50063 1037E-03 20‘9
55067 10h3E-02 6.9 55068 5.21E-cu 50'?
60071 2.66E-03 10.9 60.72 9.81E-04 1803
65.71 3.465-03 14.7 65.75 1.05E-03 26'7

PRI#1(P:T) PR1“1(P:T)

EX: .590 MEV EX! 0830 MEV

AmGtCN) SIGHA(CM) Enngn A~G1CN1 szGMA1CM) £5939

(DEG) (MB/SR) 1x) (DEG) (MB/SR) (x,
20028 10115-03 11.: 15022 4.36E-02 10'3
25035 2.165-02 5.1 20.25 5.47E-02 404
309kl 5.36E.o3 12.1 25.35 9.73E-02 2'3
35048 3.37Eoo3 14.3 30.“? 2.QSE-02 5'1
“0'53 5096E'03 1006 35048 IOSOE-OZ 5'3
«5059 5.64E-o3 12.5 no.54 2.34E-02 50a
50'6“ 10735'03 1806 #5059 30385-02 “'3
55068 1-PIE-03 30.5 50.64 6.96E-03 902
60072 1.115-03 16.9 55.65 6.25E-03 10's
65.75 9003E-04 2808 60.72 4.495-03 8'«

65.75 5.19E-03 12's

119

FR141(P.T1 PR1#1(P,T)

Ex. .910 mgv gx-1oolo MEv

ANGtCM) SIGNAccm) ganaa ANG(CN, SIGMA1CM1 ERRaQ

(DEG) (“B/SR) (21 (DEG) (MB/SR) (1)
20°29 1.24E-32 10.0 20.29 6.575-03 15'?
25035 2072E-02 #.u 25.35 1-OSE-02 7'4
30.43 5.95E-03 10.9 30.42 3.54E-03 15'»
350k8 3.18E-o3 13.5 35.48 1-06E-03 25'7
#0'54 4008E¢03 1208 #0054 2068E-O3 15.3
#5059 8.765-03 9.3 «5.59 4.98E-03 13'8
50'6“ 2062E-03 1501 60072 “0745-04 25.8
55068 1.50E-03 ?7.7

60072 8.22E-04 19.5

65076 2.41En03 17.7

PR1411P.T) P91“1‘P'T’

Ex.1.333 up. :x-1-bao HE»

AwG<CM) SIGMA(CM) ERRnR ANG1CM1 SIGHA1cM) ERRgn

(DEG) (”B/SR) 1%) (0(6) (”B/SR) (X)
25'35 20015-03 30.; 15.23 7.16E-03 2902
“0'5“ 1°615'o3 Fee“ 20.29 4.19E-03 18'8
«5'59 1-92E-03 P301 25.36 9.91E-03 9'5
5006“ 9.52E-0u 25.: 30.12 7.95E-03 9'8
350“8 6023E-O3 11.5
40.54 6.76E-03 1000
45.60 6.24E-03 1103
50.65 4.105-03 1106
55.69 2.5aE-03 1903
60.73 1.12E-03 1409
65.76 1.35E-o3 23-6

120

PR1a1(P,T) PR1411P1T)

Ex-1.620 MFV gx=2.oso MEV

ANG(CM) SIGMA1CM) ERRaR A\G(CN) SIGMA1CM) ERRaQ

(DEG)

(PB/SR) (x) (DEG) (MB/5R) 1%)
20'29 4019E-03 1908 85036 2.6uE-02 702
25036 3.0“E-03 73.1 3c.#2 9.51E-03 1307
30042 109“E-03 240M 350“9 ioISE-Ca 9‘5
350u8 1096E-03 23.3 45.60 5.84E-33 21'?
#0054 6069E-04 auo7 60.7“ 10935-03 16'?
«5060 1039E-03 29.0
60073 holle'Oh 2708
PR1u1(P:T) P91“1‘P'T’
EXa2.160 MFV 5x8202“0 HEV
ANG1CM1 SIGMA(CM) ERReQ ANG(CV) SIGMA1CH) ERRGQ
(DEG) (VB/SR) 1%) (DEG) (NB/5R) 1%)
20029 2.18E-02 10.7 20.29 1.65E-02 1&08
25.36 30235-02 6.1 25036 20845.02 6'9
30003 10135-02 10.9 30013 1.10E-08 12-2
35049 1.02E-cg 1006 35.19 1.19E-32 904
«0.55 7.29E-03 1601
45.60 9.82E-03 1303
60074 2.25E-03 1501

APPENDIX C

159Tb(p,t) Spectra

The following pages contain 159Tb(p,t)

angular distribution spectra taken with

a broad range magnetic spectrometer.

121

l/HMM

TRRCKS PER

i/HMH

TRRCKS PER

10

10

10

10

10

10

10

10

10

10

122

EXCITRTION ENERGY (MEVJ
L2 1.0 0J3 ms (LN 04? do

 

 

 

 

 

 

 

 

 

 

 

 

3 oLab = 10°
2

1
!;

560 880 780
DISTRNCE RLONC PLRTE (l/HMM)
EXCITRTION ENERGY (MEV)

u 1.0 0.8 0.8 O.” 0.2 0.0
3 ”Lab.= 15°

2

,

0 L 11‘ 1 L L

 

 

58.3

 

 

883 783

DISTRNCE RLONC PLRTE (l/HNM)

1/BNM

TRRCKS PER

TRRCKS PER l/HNM

123

EXCITRTION ENERGY (MEV1
3 LG.LH1.21.00J30J§0N 02 m
10 ,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 GLab.= 200 R 1
10
10 1 ‘. . ¢
100 L 1 f M
930 1130 1330 1530

DISTRNCE RLONG PLRTE (l/BMNJ

EXCITRTION ENERGY (NEVJ

 

 

 

 

 

 

 

10 q 1.0 0.8 0.8 0." 0.2 0.0
1 1 10m= :50 1— 1 11
10 3
10 2 f
10 1
10 °_ 1 H i L L
598 898 795

DISTRNCE RLONC PLRTE (l/HMNJ

l/HHM

TRRCKS PER

TRRCKS PER l/HMM

124

EXCITRTION ENERGY (NEV)

 

 

 

 

 

 

 

 

 

 

 

 

1.2 1.0 0.8 0.8 0.14 0.2 0.0
10 q 11 1 1 1 1 1 1
]U 3 C-)Lab.= 30°
10 3
10 1I
10 0_ 1 f L 14
580 680 780
DISTRNCE RLONG PLRTE (l/HNM)
EXCITRTION ENERGY (MEVJ
1.2 1.0 0.8 0.8 0.11 0.2 0.0
10 3 1 1 1 1 1 1
0Lab.= 35°
10 2
101 ‘ l
10 0 a 1 ‘J i 1‘ 1,

 

 

 

520 620 720
DISTQNCE RLONG PLRTE (l/HNNJ

..n,‘

 

TRRCKS PER l/HMH

l/HNH

TRRCKS PER

10

10

10

10

10

10

10

10

10

10

125

EXCITRTION ENERGY (MEV)
L0 me me an 02 mo

1 1 l
j 1* j

1.
qr

L L
I j

0 = 40°

3 Lab . fl

1 fl" 1
D 1 10
582 882 782

DISTRNCE RLONG PLRTE (l/HNN)

 

 

 

 

 

 

 

 

 

 

 

EXCITRTION ENERGY (HEV)
L0 me me mu 02 mo

#-

l _l L L l L
T I r T T —l

3 OLab.= 45

 

 

 

 

 

 

 

1'.
O L, 1'1

570 870 770
DISTRNCE RLONG PLRTE (l/umn)

11111

 

 

l/HMN

TRRCKS PER

l/HMM

TRRCKS PER

126

EXCITRTION ENERGY (MEV)
1.2 1.0 0.8 0.8 0." 0.2 0.0
10 " 1

 

 

 

 

 

 

 

3 OLab.= 50°

10

102

10‘

10 0‘ 4. 1-
580 680 780

DISTRNCE RLONG PLRTE (l/HNMJ

EXCITRTION ENERGY (MEV1
q 12 1.0 00 (LG 03 (L2 00
1 0 J l l

 

 

 

 

 

3 OLab.a 55°
10
102 I
10] fl ‘w ‘I
100 1 11 11' 1
530 830 730

DISTRNCE RLONG PLRTE (l/HNMJ

1/HNM

TRRCKS PER

l/HMM

TRRCKS PER

127

EXCITRTION ENERGY (MEVI
L0 me me on 02 do

10" 1 1 l %

 

 

 

 

 

 

10 3 OLab.=60°

10 2

101

10 °_ - 1“ 11111 L g
580 880 780

DISTRNCE RLONG PLRTE (l/HNNJ

EXCITRTION ENERGY (NEV1
L0 08 me on 02 do

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

103-1 1 1 1 1 1 1
OLab.= 65°
10?
101
100 11er I11
SS3 853 753

DISTRNCE RLONG PLRTE (l/HNM)

 

l/HMM

TRRCKS PER

PER l/HNM

TRRCKS

128

EXCITRTION ENERGY (MEVJ
L0 06 me an 02 mo

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 3 a1 1 1 1~ 1 1 1
0Lab.3 70°
10 2
10 ’1
10 07 ”L
550 850 750
DISTRNCE RLONG PLRTE (l/HNMJ
EXCITRTION ENERGY (NEV)
1.2 1.0 0.8 0.8 0.11 0.2 0.0
10 q 1 1 1 1 1 1 1
OLab = 75
10 3
10 2
10 1!
10 °_ 1 1111 ~ 1'
535 835 735

DISTRNCE RLONG PLRTE (l/HNM1

APPENDIX D

Tabulation of 159Tb(p,t) Differential

Cross Sections

The following pages contain listings of the
center-of-mass differential cross sections
and scattering angles for the various states
populated through the 159Tb(p,t) reaction.
All cross sections are relative and have
been normalized to reflect the magnitude

of measured absolute values. The listed

errors are purely statistical.

129

130

T8159(P,T, TB1S9(P,Y)

EX. .000 MEV EX: 0061 MEV

ANG(C”) SIGMA1CM) ERRPR ANGtCH) SIGMA1CM) ERRSR

(DEG) (MB/SR) (x) (DEG) (MB/SR) (X)
10013 1.666-01 .7 10.13 1.306-02 205
15119 2034E-oa .7 15.19 5.326003 10a
20025 8.44E-03 2.1 20.25 9.366-03 200
25031 1.75E-02 1.0 25.31 2.405-03 206
30036 “.61E-c2 06 30036 1076E903 3'3
35.n2 4.655.03 1.3 35.62 4.24E-03 4'3
“0'47 10685.02 1.2 “C0“7 “0955-03 2'3
45°51 90785-03 105 #5051 3022E-03 2'7
50'56 2062E-02 .9 50056 2.17E-03 3'3
55059 3'395'02 .9 55059 30‘35'03 2'7
60063 1.97E-02 1.1 60.63 1.78E-03 2'3
65°66 6038E-03 2.0 65066 3.63E-O3 2'7
70068 1008E~02 109 7C068 2077Ep03 3‘7
75070 1.66E-02 1.3 75.70 3.016-03 301
T81591P0T) TB159(P,T1
Ex. .141 MEV éx- 0251 MEV

ANG1CM1 SIGMA1CM) FRReR ANGKC?) SIGMA1CM) [RRBR

(DEG) (NB/5R) (X) (DEG) (MB/SR1 (X)
10'13 6'955'03 306 10.13 1069E'C3 701
15.19 2.9oE-oa 20c 15.19 50605'0“ “'6
20025 5000E-03 2.7 20.25 1.05E-03 600
25031 1050E-03 3.2 25.31 5.33E-04 5'5
30036 1011E-03 1.0 30.36 3.03E-01 .7'9
35042 2020E-03 5.9 35.43 3.19E-ok 1603
“0’37 20635.03 301 #00“? 40‘9E-O“ 7'5
#5051 10896003 3.5 45.52 5.86E-04 603
59056 10505-03 #00 50.56 5.93E-04 603
55'60 EOIOE'OB 30“ 55.60 60118-04 6'4
60°63 30085.03 209 60063 6058E-QH 6'2
65°66 2.03E-03 3.6 65.66 5.115-00 7.3
70068 2.?oE-03 4.2 70.69 8.2aE-ou 6'8
75070 10995-03 3.9 75.70 7.155-01 603

131

75159(p,1, T81S9(P.T)

Ex. .325 HEV EX0 .379 MEv

ANG(CM) SIGMA(CM) ERRDR ANG(CM1 516MA(cH) ERRSQ

 

 

(DEG) (MB/SR) (2) (0:6) (MB/5R) (X)
10013 10555000 2002 10.13 1.2.5003 8'6
15°19 3016E-DS 1906 15.19 5.02E-oa 409
20'25 8095E-05 200“ 20025 9051E-Q“ 6'3
25°31 90805005 11.6 25.31 5.07E-ou 5'6
30037 u-30E005 20.9 3c.37 3.96E004 609
#0947 50615.05 21.3 35062 6013E904 11.3
45052 2077E-05 28.8 40.67 “026E'O“ 7.7
50056 a001E-os 24.3 45052 3.735-04 703
60063 1.18E-ou 14.5 50.56 4.71E-94 701
65066 1.58E-05 4008 55.60 3.36E-04 8'6

'60063 30935-00 8'0

65066 30765-C# 8'#

70.69 5.21E-04 805

75071 5011EOOQ 7'6

(3159(p.r; TB1S9(P.T)

Ex. .527 Mgv gx. 0598 HEv

ANG(CV> SIGHA(CM) FRRQR ANG(CM1 SIGMAth) ERRaR

(DEG) (VB/SR) (x) (DEG) ("B/SR) (2)
10013 60o9E-00 12.2 10013 1078E-o3 7'1
15019 1.93E-oa 7.9 15019 5.356-oh “'8
20025 3069E-04 10.1 20025 6042E-04 7'6
25.31 30115-0“ 7.2 25031 30055-0“ 7'3
30037 2.62500. 8.. 30.37 2.99:.ou 709
35'“? 3051E‘0Q 1501 35042 4003E-O“ 13.3
#0007 2.04E-oa 11.3 #0047 2.76E-o4 906
“S058 1.91E-ou 11.5 45.52 2.67E-ou 903
50056 1.53E-04 12.6 50.56 3.68E-ok 8')
55060 1.29E-04 13.9 55.63 2.84500“ 9'3
6006“ 1.44E-Qu 13.2 60.60 2.00E-04 11'1
65066 6.30E-05 200“ 65.67 2.36E-ou 1005
70069 1.46E-04 16.2 70.69 2.7oE-04 1109
75071 1.07E-oa 16.7 75.71 2.34E-ok 1103

132

78159190T) T8159(F:T)

Ex. .660 HEV éXI 0699 MEV

ANG<CH) SIGHA(CM) ERRGR ANG(CM1 SIGMA(CM) ERRDP

 

(DEG) (PB/SR) (x) (DEG) (MB/SR) (X)
10013 10605-03 7.5 10.13 1.105003 9'1
15.19 “.61E004 5.1 15.19 3.65E-04 5°%
20025 6030E004 7.7 20.25 6.9.5.94 703
25031 3.07600. 6.2 25.31 4.37E-cu 601
30'37 30055-06 708 30.37 5.29E-04 5’?
35.42 3.105.04 15.8 35.62 4.735-04 12'5
40.47 2.37Ech 10.6 00.47 30275-04 8'8
#5052 2oa9E-04 ' 906 «5.52 3.64E-04 8‘;
50.56 3.04E.og 8.3 50.56 3.93E-ou 707
55060 30025-04 8.2 55.60 2.67E-ou 906
60'6“ 2.125006 10.9 60.6“ 2.52E-04 10'0
65°67 3010500. 9.2 65.67 3.63E-ou 1804
70069 2.32500“ 12.8 70.69 2.81590“ 11'6
75071 2.14E-ou 11.3 75.71 2.00E-04 1101
15159(p,r, TB159(P,T)

Ex. 0795 MEV :x- 0896 HEv

1N61C") SIGMA(CM) gunen ANG(CM) SIGHA(CM) [Rpaw

(DEG) (“B/Sn) (X) (DEG) (MS/59) (1)
10'13 2'“6E'04 19.3 10.13 9.73E-oh 907
15.19 8.02E-os 12.3 15.19 2.77E-ok 6'6
20025 zoeoE-oa 13.0 20.25 5.13E-0“ 8'5
25.31 1.566-04 9.7 25.31 3.05E-00 7'3
30037 1046E-04 11.3 30.37 2.65E.34 804
35042 2.09E-oa 19.3 35.42 2.9SE-oh 16°2
.0047 9.19E-05 16.7 40048 2.09E-0“ 11°J
45052 6.23E-05 1903 45.52 20375'0“ 9'9
50'57 5.#2E-05 20.9 50.57 2.97E-0“ 8'9
55060 7.uIE-os 18.3 55.61 2.17E-00 1007
60064 3.53E-05 26.7 60.64 1035570“ 13'7
65067 3.58E-05 26.7 65.67 1.07E-ou 13°.
70069 ..18E-05 30.2 70.69 1.82E-oa 1404
75071 2.37E005 35.4 75.71 1.69E-oh 1302

133

T5159(P.T1 TB1591PpT)

Ex. .927 HEV Ex- 099. MEV

ANG1CM) SIGMA(CM) ERReR A\G(CM, S1GMA(CM) E9939

(DEG) (MB/SP) (X) (DEG) (Ma/sq) (X)
10013 10385003 801 10013 2.63E-02 109
15019 n.6SE-ca 5.1 15.19 4.956-03 1'5
20025 5.97E-04 7.9 20.25 4.91E-33 206
25031 3.13E-oa 7.2 25.31 1.266-03 306
30'37 20505'0# 806 30.37 2.975-03 2'5
35'“? 2‘17E'O“ 18.9 35.42 6.7OE-03 3'“
40048 20225004 10.7 40.45 5.26E-03 202
45052 3018E-04 8.5 45.52 2.31E-03 302
50057 3009500. 8.7 50.57 2.20E-03 303
55061 20645004 9.7 55.61 3.276-03 207
60°64 2.12E-oq 10.9 60.6“ 3.78:003 2'6
65.67 2.07500“ 10.3 65.67 2.39E-O3 3'3
70070 2.47E-ou 12.. 70.70 1.886-03 405
75071 1063E-04 13.5 75.72 1.965-03 303
78159(P.11 TB159(P.T)

Ex-1.048 MEV :x-10123 MEv

ANG(CM) szGMA(cn1 ERRQR A~G(CM1 sxGMA(cM) ERRaR

(DEG) (MB/SR) (X) (DEG) (MB/SR) (X)
10013 9.99E-03 3.3 1c.13 6.25E-53 305
15019 3.4oE-03 1.9 15.19 2.01E.c3 205
20025 5010E-03 2.7 20.25 3.075-03 305
25031 10855-03 3.0 25.31 1.365-03 304
30037 1058E-03 3.. 30.37 1.165-03 400
35043 2.37E-03 5.7 35.43 1.60E.03 703
“0038 2058E'03 3.1 “O.“8 1.52E903 “'1
45052 2.21E-03 3.2 45.53 1.406-03 401
50057 1'23E'C3 6.“ 50.57 8.93E'0“ 5'1
55061 10005.03 5.0 55.61 6.576004 601
60064 1.925-03 3.6 60.64 9.855-04 5'1
65067 1.60E-c3 4.1 65.67 1.05E003 S03
70°70 10335.03 5.3 70.70 7.“9E'O“ 7'1
75072 60685-04 6.7 75.72 5.7oE-o4 702

134

T8159(P:T)

:X010235 MEv

A~G(CM1 SIGMA(CM) ERRfiQ
(DEG) (MB/GR) (x)
10013 1.98E-02 2'1
15019 5.775-03 1'5
20.25 8.93E-03 2'0
25.31 3.906-03 2'0
30037 3.“4E-o3 2'3
35.“3 3.535-03 “'7
40.48 2.87E-03 300
45.53 3.84E-03 2'4
50.57 3061E'03 2'6
55.61 2.71E-03 3'3
60065 2.238003 30.
65.68 2004E-03 3'6
70.70 2.63E003 303
75.72 2.025-03 3'3

  

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(I1((1)11(11111111111111)mumx

250