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HIGH-SPIN STRUCTURE OF 1168b AND 1188b

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Wayne Harold Bentley

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HIGH-SPIN STRUCTURE OF 1153b AND 1185b

BY

Wayne Harold Bentley

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Physics

1980

Ox 08\\5

ABSTRACT

HIGH-SPIN STRUCTURE OF 1155b AND 1185b

By
Wayne Harold Bentley

The high-spin structure of 116IllBSb has been studied
using the techniques of in-beam gamma—ray spectroscopy.
Experiments performed include gamma—ray angular distri-
butions, y-Y-t coincidence measurements, gamma-ray exci-
tation functions, and gamma-ray half-life measurements. The
reactions used to populate the high-spin levels were proton,
alpha, and lithium induced fusion evaporation reactions.
Level schemes for each of these nuclei have been constructed
from the results of these experiments.

The level schemes display behavior that can be ex-
plained only by assuming the existance of both deformed and
spherical states. Such coexistance of states has previously
been observed in neighboring nuclei. This investigation
extends these findings to the odd-odd Sb nuclei. A quali—
tative discussion of these various structures is made in
terms of the shell model and the particle—plus—deformed-

rotor model.

ACKNOWLEDGEMENTS

I wish to thank Dr. W. H. Kelly for his encouragement
and assistance during the experimental work and for his
never—ending patience during the preparation of this
thesis.

I would also like to thank Dr. R. A. Warner,

Dr. C. B. Morgan, Dr. S. R. Faber, Dr. R. B. Firestone,
Mr. K. Shafer, Mr. J. A. Carr and Mr. M. F. Slaughter for
their help during experiments and for teaching me much of
what I have learned.

I wish to thank Dr. F. Venezia, Dr. J. W. Mihelich
and Dr. E. G. Funk for assistance with those experiments
performed using the accelerator facilities of Notre Dame.

I wish to thank Dr. P. M. Walker, Dr. R. M. Ronningen
and Dr. W. C. McHarris for many valuable discussions
concerning the interpretation of the results, as well as
their suggestions during the preparation of this thesis.

Special thanks go to Dr. P. S. Miller, Dr. H. Laumer
and D. W.-S. Chien for their assistance in setting up and
running the M.S.U. cyclotron. Thanks also go to the
remainder of the cyclotron staff for their never-ending
assistance during all phases of this project.

Finally, I wish to thank Mrs. T. Awes for typing this

manuscript and the N.S.F. for financial support.

ii

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . .

LIST OF FIGURES . . . . . . . . . . . . . . . . . .

I.

II.

III.

IV.

INTRODUCTION . . . . . . . . . . . . . . . . .

THEORETICAL CONSIDERATIONS .. . . . . . . . . .
A. Nuclear Shell Model . . . . . . . . . . .
B. Vibrational Core Excitations . . . . . . .
C. Deformed States . . . . . . . . . . . . .
D. Rotational Model . . . . . . . . . . . . .
E. Extension of the Unified Model . . . . . .

EXPERIMENTAL CONSIDERATIONS . . . . . . . . . .

A.

B.

C.

D.

E.

Fusion Evaporation Reaction . . . . . . .
Gamma-ray Excitation Measurements . . . .
Gamma-ray Angular Distributions . . . . .
y—Y-t Coincidence Measurements . . . . . .

Gamma-ray Half-life Measurement . . . . .

1155b EXPERIMENTAL RESULTS . . . . . . . . . .

A.

B.

Experimental Arrangement . . . . . . . . .

Results of Gamma-ray Angular Distribution
Measurement . . . . . . . . . . . . . .

Results of y-Y-t Coincidence Experiment .
Results of Half—life Measurement . . . . .

Results of Excitation Function
Measurement . . . . . . . . . . . . . .

ll6Sb Level Scheme . . . . . . . . . . .
l. The I=7 Band at 1001 keV . . . . . .
2. The 21.6 keV Transition . . . . . .

3. The 3599 keV Level . . . . . . . . .

iii

Page

Vi

11
13
13 I
15
17
22
23
25

25

28
36

36

41
47
49
51

52

4. The 2560 keV Level . . . .
Spin and Parity Assignments . .
1. The 8‘ Metastable State .
2. High Spin Sequence . . . .
3. Medium Spin Levels . . . .
4. The I=7 Band . . . . . . .

5. The I=8 Band . . . . . . .

v. 1185b EXPERIMENTAL RESULTS . . . . .

A.

B.

C.

E.

F.

G.

Experimental Arrangement . .

Results of y-Y-t Coincidence Experiment

Results of Excitation Function
Measurement . . . . . . . . .

Results of Angular Distribution
Experiment . . . . . . . . .

Results of Half-life Experiment
1188b Level Scheme . . . . . .
Spin and Parity Assigments . .
l. The 8' Metastable State .

2. High Spin Sequence

3. Medium Spin States

0
I
o
o

4. The I=7 Band . . . . . . .

5. The I=8 Band . . . . . . .

VI. DISCUSSION AND SUMMARY . . . . . . .

A.

B.

C.

D.

REFERENCES

High Spin Sequence . . . . . .
Medium Spin Levels . . . . . .
Deformed States . . . . . . . .
Summary . . . . . . . . . . . .

iv

Page
52
53
53
54
56
57
58
59
59

65

65

65
70
77
79
79
80
81
82
82
84
84
87
88
101
103

Table

IV-1

IV-2

IV-3

LIST OF TABLES

Page
Energies (Ey), Relative intensities
(Io), angular distribution coefficients,
multipolarities and spin assignments
for transitions in 116Sb . . . . . . . 30

Results of y-Y-t coincidence experiment
for transitions in 1165b . . . . . . . 38
Half-lives determined for transitions
involved in the decay of metastable states
in ll6Sb . . . . . . . . . . . . . . . 43
Results of y-Y—t coincidence experiment

for transitions in 1185b . . . . . . . 67
Energies (Ev), relative intensities

(Io), angular distribution coefficients,
and spin assignments for transitions in

1188b.

I O O O O I I O O C I D O O I I 71

LIST OF FIGURES

Figure Page
III—l Cross sections for neutron evaporation

as a function of beam energy following

an a induced compound nuclear reaction. . l4
III-2 Schematic illustration of the decay

of a compound nucleus in a (HI, 3n)

reaction. . . . . . . . . . . . . . . . . 16
III-3 The spin alignment attenuation coefficient

mg as a function of spin for pure multi-

polarity transitions in 1168b.. . . . . . l9
III-4 The angular distribution coefficients

Az/Ao and A4/A0 for transitions to states

with spin If = 8 . . . . . . . . . . . . 20
IV-l Spectrum of 115In (a,3ny) obtained at

130° with respect to the beam . . . . . . 26
IV-2 Angular distributions for selected 1168b

transitions. The fits are normalized to l

at 90°. . . . . . . . . . . . . . . . . . 29
IV-3 Background subtracted gated coincidence

spectra for selected transitions in

116Sb

. . . . . . . . . . . . . . . . 37
IV—4 Delayed spectra from the 115In (a,3ny)
reaction. Delay time increases with each
spectrum from top to bottom . . . . . . . 42
IV-Sa Half—life data for transitions occurring
in the decay of the isomer at 1001 keV. 44

vi

Figure Page

IV-5b Half—life data for transitions occurring

in the decay of the isomer at 1624 keV . . 45
IV-Sc Half-life data for transitions occurring

in the decay of the isomer at 3599 keV . . 46
IV—6 Excitation functions for selected

transitions occurring in 1168b . . . . . . 48
IV-7 High-spin level scheme for ll65b . . 50
T—l Spectrum of 114Cd (7Li,3ny) obtained at

an angle of 125° with respect to the

beam . . . . . . . . . . . . . . . . . . . 60
V—2 Spectrum of 120Sn (p,3ny) obtained at an

angle of 125° with respect to the beam . . 63
V-3 Results of y-Y-t coincidence experiment

for transitions in 1185b . . . . . . . . . 66
V-4 Excitation functions for transitions in

118Sb. . . . . . . . . . . . . . . . . . . 69
v-s Angular distributions for selected 1185b

transitions. The fits are normalized to

l at 90° . . . . . . . . . . . . . . . . . 75
V—6 Half—life data for transitions occurring

in the decay of the isomer at 927 keV . . 76
V-7 High-spin level scheme for 1185b . . . . . 78
VI-l High—spin sequence of levels in 116'1188b

compared with similar levels from odd mass

Sb nuclei and doubly even Sn core nuclei . 85

Figure
VI-2
VI-3

VI-4

VI-5

VI-6

Page
Nilsson diagram for odd protons . . . . . 90
Nilsson diagram for odd neutrons . . . . 92
The rotational band spacing as a function

of 2I2 for the J=8 bands in l16'1185b . . 93

Levels for the J=8 bands in 116IllBSb

compared with levels for the KN=§I bands
in 115'117'1195b. . . . . . . . . . . . . 96

The rotational band spacing as a function
of 212 for the K=7 bands in 116,1185b
compared with the K=§ band in 1158b and

the K=§ band in 119Te . . . . . . . . . . 100

viii

I . INTRODUCTION

Until recently, nuclear structure physics, both ex-
perimental and theoretical, has concentrated primarily on
even—even and odd-mass nuclei. This is mainly because of
the complexities involved in studying odd-odd nuclei.
However, with increased understanding of odd—mass nuclei and
improvements in experimental techniques, much greater atten-
tion is now being given to understanding odd—odd nuclei.
Continuing in this direction, the present study of the high
spin structure of the two odd—odd nuclei 116I1185b was
undertaken. The goal of this work was experimentally to
determine high-spin level structures and attempt to gain an
understanding of these results in terms of existing theories.

There are many reasons for studying odd-odd nuclei,
the most fundamental of which is to obtain information on
the residual proton-neutron interaction. An understanding
of this interaction is a necessary part in forming a complete
description of nuclear structure. Such an understanding can
come only after the level scheme systematics from a large
number of odd-odd nuclei distributed over the entire mass
range has been collected. The results obtained in this
study will contribute to that collection of data. In
addition, recent interest has developed in high—spin rota-
tional structure in odd-odd transitional nuclei. Since
in odd—odd nuclei there are two unpaired particles that can
occupy high—spin single-particle levels, it is possible to
form high-spin states at relatively low excitation energy.

1

Such states are presently being studied theoretically (cf.
ref. 1). However, very little experimental information is
available to compare with this work. Since low-lying
deformed states were previously known to exist in the odd-
mass Sb nuclei,2 it was reasonable to expect similar low-
lying deformed states to exist in the neighboring odd-odd
nuclei. Such considerations indicated that interesting
phenomena should exist in the high—spin level structure of
116,1183b.

Much previous work has been done studying Sb nuclei
both at Michigan State University and elsewhere. The low-
spin states of 116,117,118,ll95b have been studied using the
3-6

(p,ny) reaction. In addition, the high-spin states of

113I115Ill7'll98b have been studied using the (6Li,3ny)

reaction.7

The results of these studies proved to be in-
valuable in sorting out and identifying the gamma-rays
belonging to 116IllBSb. In fact, in general a study of an
odd-odd nucleus would prove to be nearly impossible without
first having a partial knowledge of the structure of
neighboring nuclei.

In addition to these experimental studies, theoretical
attempts have also been made at describing Sb nuclei.
Except in the case of 1185b, various model calculationssl9
have been carried out and compared with all of the pre—
viously mentioned experimental results. In particular, much
effort has been expended in attempting to quantitatively

describe the rotational bands in the odd-mass Sb nuclei.10'l3

The next chapter of this thesis is a brief discussion
of some of the theoretical models used in describing nuclear
structure. Chapter III includes a general discussion of the
types of experiments performed in this study. In chapters
IV and V the experimental results are presented for ll65b
and 1188b, respectively, including a discussion of the
construction of the respective level schemes. The final
chapter contains a qualitative comparison of these results

to the models.

II. THEORETICAL CONSIDERATIONS
A. Nuclear Shell Model

The nuclear shell model was developed in 1949 inde-

14 15

pendently by M. G. Mayer and Haxel, Jensen, and Suess.
The assumptions behind this model are very similar to those
upon which the atomic shell model is based. Each particle
is assumed to move in an independent orbit. Therefore the
interaction between each particle and all of the other
particles can be replaced with an interaction involving the
particle and some average potential. In order to reproduce
the experimentally determined ordering of the shell model
states, a large spin-orbit coupling term was required as
part of this potential. One of the effects of this spin-
orbit term is the lowering of selected states into the next
lower major shell. These lowered states then have opposite
parity and higher spin values than the remaining states in
the shell. These states are referred to as unique-parity
states. Examples of states of this type include the 199/2,
lhll/Z and lil3/2 orbitals.

In real nuclei, however, the nucleons do not move in
completely independent orbits. There is a residual inter-
action between particles in each subshell. This interaction
is observable in the last subshell, if it is not completely
filled. A large part of the residual interaction is the
pairing energy which arises between two particles in the
same subshell with opposite mj-values. This is the result

of a large overlap in the wave functions of these particles.

4

5

Of particular interest in odd-odd nuclei is the re-
sidual interaction between the odd proton and the odd neutron.
When the odd proton and odd neutron are placed in given
single particle orbitals, a multiplet of states results from
the various ways of coupling the angular momenta of the two
particles. The p—n residual interaction is responsible for
the removal of the energy degeneracy of this multiplet.
Identification of the various members of these multiplets in
odd—odd nuclei gives direct information on the strength and
form of this interaction.

Shell model calculations for ll2'11‘1I116Sb have been
performed by VanGunsteren et. al.8 In these calculations
because Sb has only one proton above the Z=50 closed shell
the proton could be treated as a particle. However, in
order to include the pairing effects of the several valence
neutrons the odd neutron was treated as a quasiparticle.
These results were relatively successful in describing the
existing low-spin data. There were, however, no high-spin
results reported from these calculations.

B. Vibrational Core Excitations

In addition to the single-particle states described by
the spherical shell model, other modes of excitations are
available. These include collective vibrations of the core.
Theoretical treatments of the odd mass Sb nuclei involve
single—particle shell model orbitals as well as single-
particle states coupled to these phonon excitations of the

9

core. Similarly a complete theoretical description of the

6

odd-odd Sb nuclei would have to include the possibility of
vibrational coupling to the various two-particle shell model
states.

C. Deformed States

The Sb nuclei are only one proton away from the Z=50
closed shell. Because of this it would be reasonable to
expect that a spherical description of these nuclei should

be adequate. However, experiments have shown7

the singly odd
Sb nuclei exhibit evidence for coexistance of deformed

states with the spherical states. Band structure properties
in the odd mass nuclei have suggested2 rotational bands

built on a permanently deformed, prolate, proton hole state.
This interpretation is consistent with calculations of the
total potential energy surface,12 which show a well defined
minimum in the energy of the 9+/2 {404} proton orbital at a
positive deformation value. (620.15 for ll7Sb)

An alternative description based on a vibrational
model13 has also been employed in describing the observed
odd mass bands. However, the low-lying 9+/2 bandheads are
difficult to explain in such a model. Consequently, this
likelihood of deformed states in the odd mass Sb nuclei,
leaves the odd-odd Sb nuclei as interesting sources of
further information.

D. Rotational Model

The foundation for the nuclear rotational model was
developed in 1952 by Bohr and Mottelson. This model is

based on the average nuclear potential being non-spherical.

7
The axes determined by this deformed potential are then
allowed to rotate in space. This rotation is slow compared
to the motion of the individual nucleons, which collectively
produce the deformed potential. The Hamiltonian can then be
written as two terms, one of which describes the collective
rotation of the core, while the second term describes the
intrinsic states. These intrinsic states were described by
Nilsson and involve single-particle states in a deformed
potential. The resultant Hamiltonian is shown in equation(l)

and is referred to as the unified model.l6

H = He... + Hint = i a2 (1)
20
Here 0 represents the moment of inertia.
_)
In this model the total angular momentum I is shared
.+
between the particle angular momentum j and the core angular

momentum R, as can be seen in the following equation:
—> + +
I=R+j (2)

Quantum mechanics requires that R3, the component of
the rotation vector along the symmetry axis, be zero for an
axially symmetric core. Using this fact and writing the
Hamiltonian explicitly in terms of the particle and core
angular momenta results in the following expression:

+ ->
H = Hint + hi (3'2 - ii) + 23 <12 - 1%) - f1_2 (In—+14.) <3)
20 20 20

8
In this expression the 3-axis is taken to be in the direc-
tion of the deformation symmetry axis and the Ii,ji are
scalar operators very similar to the rotational raising and
lowering operators. (Ii = (IliiIZ), j._r = (jliij2)). The
first two terms in equation (3) refer to the particle motion.
The third term refers to the collective motion. The last
term, generally referred to as the Coriolis coupling term,
contains the interaction between the particle and rotational
motion. In the normal rotational model the first two terms
are combined to give the intrinsic energy, and the Coriolis
term is assumed to be small. This results in normal
rotational bands with energies given by the following
equation:

_ 2 _ 2
H — Eint + 11;?) {I(I+1) K } (4)

Here K is the component of the total angular momentum along
the symmetry axis and in this limit represents a good
quantum number. In well deformed nuclei this result works
quite well. Deviations from this result can often be
explained by treating the Coriolis term as a perturbation,
which results in the mixing of bands with different K
values. However, if the effect of the Coriolis term becomes
large a different approach is needed.

This can be seen by looking at the explicit form of the

intrinsic energy as determined in the Nilsson model.l7

2 . .
= _ 3n - (3+1) = , 2

In this equation 0 is the component of 3 along the
symmetry axis (Q=K for an axially symmetric core) and, K and
B are parameters that go into the Nilsson potential.
Explicitly, B is a measure of the quadrupole deformation.
The parameter C, which is defined by this equation, depends
on K, B and the particle angular momentum 3.

Substituting equation (5) into (3) and rearranging
terms results in the following expression for the total
Hamiltonian.

2 h

2
)9 - i5 (I+j-+I-j+) <6)

hZ

2+
H=ej+9_(j2+12)+(c—e—

20
For a given situation the first two terms of this Hamil—
tonian are diagonal and the problem resolves to diagonalizing
the last two terms. In well deformed nuclei the moment of
inertia O is large and consequently the Coriolis term is

2 and

small. In this case the solutions are eigenstates of Q
the normal strong coupling limit results.

As the total angular momentum I increases the importance
of the Coriolis term in the Hamiltonian increases also. At
sufficiently large I this term becomes much larger than the
92 term and the solutions become eigenstates of the Coriolis
term. In this limit 9 and K are no longer good quantum

numbers, nor is the strong coupling scheme applicable. It

has been shown that this situation corresponds to a rotation

10
aligned coupling scheme described by Stephens.18 In this
scheme the large Coriolis force decouples the particle from
the deformed core and aligns it in the direction of the
rotation. Now a, the projection of I on the rotation axis,
is a good quantum number rather than 0, the projection on
the symmetry axis. The particle now contributes to the
angular momentum without affecting the energy spacing of the
core rotational states.

In addition to the high angular momentum limit the
rotation alignment coupling scheme can be extended to low
spin states in some cases. This situation occurs when the
coefficient of the 02 term in the Hamiltonian is approxi-
mately zero. One of the requirements for this to occur is
that the Fermi energy level must be near the low Q orbitals
of the j shell. This corresponds to a particle state in
prolate nuclei and a hole state in oblate nuclei. An
additional requirement is that the value of the deformation
parameter be in the approximate range [B|=O.18i0.08. Larger
values of 8 result in strong coupling, while smaller values
lead to the weak coupling limit. The final condition is
that the spin j of the particle should be large. This
usually implies that the particle be in one of the high spin
unique-parity orbitals, such as the lil3/2 or lh11/2- For
the two nuclei under study here, the Fermi energy for the
neutron states is very near the low 0 components of the

lhll/2 orbital .

11

E. Extension of the Unified Model
A generalization of this model to include triaxially
deformed nuclei has been carried out by Meyer-ter-Vehn.19
In addition Toki and Faessler20 have included a variable
moment of inertia for the core, which accounts for centrifugal
stretching with increased angular momentum. This resulting
model has been quite successful in describing a large amount
of data on the odd mass transitional nuclei.

In addition work is currently being done by Toki and
Faessler to extend this particle—plus~gamma-deformed-rotor

model to odd-odd nuclei.1

In this case two particles must
be coupled to the core. They can both couple in the same
manner resulting in what Faessler has termed the "peaceful
case". Alternatively one of the particles can strongly
couple, while the second particle is rotationally aligned,
resulting in the "conflicting case."

The Hamiltonian for this model is given as the follow-

ing:

H = HRot + HShe11 + HDef + HPair + HRes

The first term represents the rotational motion of the
triaxially deformed core. The next two terms express the
single—particle energies of the two particles and their
coupling to the deformed core. The final two terms describe
the residual pairing interaction between the valance par-

ticles and the residual proton-neutron interaction of the

12

two odd particles. Calculationszo’21

using this model have
been carried out for 198T1 and 194Au. The results of these
calculations were quite successful in describing these
nuclei.

For completeness it should be noted that a similar
situation occurs for two quasi-particle states in doubly
even nuclei. Experimentally there is presently much interest
in the Coriolis effects on two quasi-particle sidebands in
these nuclei (cf. ref. 22). Theoretically treatments very
similar to those described above have been applied, espe-
cially with regards to the effect of the Coriolis inter-
action in producing backbending. (cf. ref. 23)

The doubly odd Sb nuclei are good candidates for a
consideration by this extended rotational model. The
neighboring nuclei, both odd-proton Sb and odd-neutron Te
nuclei, have demonstrated evidence for the coexistance of
deformed states. It is reasonable to expect that the doubly
odd Sb nuclei should exhibit similar behavior. In addition
the deformation parameter as determined in the odd mass Sb
nuclei is sufficiently small so as to allow for the possi-
bility of rotational alignment. This coupled with the
knowledge that the neutron Fermi level is located very near
the low-Q substates of the high angular momentum, unique-
parity 1h11/2 orbital, makes rotationally aligned neutron
states a very likely possibility. These observations will

be considered in detail in the final chapter.

III. EXPERIMENTAL CONSIDERATIONS

A. Fusion Evaporation Reaction

The study of high spin states first requires getting
the nucleus of interest into a high energy, high angular
momentum excited state. This can be done with a fusion-
evaporation reaction. An accelerated beam of heavy-ions,
alpha particles, or protons collides with a target of the
appropriate enriched isotope. The projectile and target
nuclei combine into a highly excited compound system which
loses most of its energy through the statistical evaporation
of energetic neutrons. Eventually a point is reached where
there is no longer sufficient energy to evaporate another
neutron. The resulting nucleus is still in a high energy,
high angular momentum state that now decays by emitting
gamma-rays.

The cross-section as a function of beam energy for
producing a given final nucleus is a peak about 10 MeV wide,
separated from neighboring peaks by about 15 MeV. An
example, showing cross sections for an (d,xn) reaction,
calculated using a standard compound nuclear reaction code,24
is shown in Figure III-l. Small cross—sections for com—
peting reactions which were not calculated include proton
and alpha evaporation, as well as direct reactions.

After the compound nucleus has cooled to where it is
stable against further particle evaporation, it is still at
a very high excitation (about 10 MeV). The density of
available states is extremely high at this energy. Because

13

14

10

 

p..-
O

(A)
I

l\)

10-

 

CROSS SECTION IN MILLIBARNS

100 +++ l

0 10

 

 

 

80

I I0 40 50
LASO ENERGY IN MEV

Figure III-l Cross sections for neutron evaporation as
a function of beam energy following an a
induced compound nuclear reaction

15

of the large number of states and the resulting myriad of
decay paths, only a statistical continuum of gamma-rays can
be detected from this portion of the decay process. This
continues until the nucleus has decayed down to the yrast
sequence, where yrast is defined as the lowest lying level
of a given spin value.25 At this point the decay proceeds
along or near the yrast line down to the ground state. The
limited number of available paths during this portion of the
decay results in discrete gamma—ray lines appearing in the
measured spectrum. A diagram demonstrating this sequence of
decay processes following a heavy-ion compound nuclear
reaction is shown in Figure III-2.26 Consequently, this
decay process selectively populates yrast and near—yrast
states, thus placing qualitative limits on the angular
momentum values of observed states.

B. Gamma-ray Excitation Measurements

Excitation measurements involve determining the inten-
sity of each gamma-ray as a function of incident beam energy.
These intensities should follow a very similar pattern to
that of the cross-sections shown in Figure III—l, thus
allowing identification of gamma—rays belonging to a given
final nucleus. In addition, the intensity curve for a given
gamma-ray also contains a dependence on the angular momentum
of the deexciting state. This is because a higher energy
incoming beam on the average leaves the residual nucleus
with more angular momentum, which results in the population

of higher-spin states.

 

16

 

 

 

COMPOUND NUCLEUS
HU’
\/
30>
a; NEUTRONS
2:
>_
LD
0: 20’
DJ
2:
LU
ENTRY LINE
STATISTICAL
10r GAMMA-RAYS
YRAST LINE
N0 LEVELS

 

 

 

5 10 15 2‘0 25
SPIN

Figure III-2 Schematic illustration of the decay of a
compound nucleus in a (HI,3n) reaction

17

Therefore, information on the relative spin values of dif-
ferent states can be obtained from this type of experiment.

C. Gamma-ray Angular Distributions

The large amount of orbital angular momentum brought
into the compound system by the projectile is oriented
in a plane perpendicular to the beam direction. Using this
beam direction as a quantization axis, it follows that the
high-spin states will have their angular momentum preferen-
tially aligned in low-m substates. This alignment is
greatest for high-lying states and slowly diminishes as the
nucleus decays down to lower-lying levels.

Because of the alignment, the probability for a decay-
ing gamma-ray to be emitted is not isotropic. When the
intensity of a gamma—ray is measured with respect to the
beam direction, it displays an angular dependence, the shape
of which is determined by the spins of the initial and final
states, the multipolarity mixing of the transition, and the
degree of alignment of the initial state. The angular
dependence can be expressed as an expansion of even Legendre

polynomials as shown in the following equation:

1(0) = A0 + A2 P2 (cos a) + A4 P4 (cos 0)

/
= IO {1 + azAE/AO P2 (cos 0) + a4A4/AO P4 (cos 0)}

The experimental intensities for each gamma—ray are fit to
. ’ / . .
this equation and the azAz/Ao and a4A4/AO coeffICIents are

extracted, as well as the integrated intensity Io- Once

18

the alignment attenuation coefficients c2 and d4 have been
determined, the resulting Ag/AO and AZ/Ao coefficients can
then be compared with calculated values to obtain informa-
tion on the allowable spin values of the levels involved.

Values for the attenuation coefficient a2 can be de-
termined experimentally if the nucleus exhibits several pure
multipolarity transitions. In deformed nuclei such tran-
sitions occur frequently as electric quadrupole I+I-2
transitions in rotational bands. In the case of 1168b,
using the (a,3nY) reaction, several such pure transitions
were excited. Figure III-3 shows a plot of the attenuation
parameter a2 determined from these transitions. It can be
seen from the figure that over the range of interest a2 is
quite insensitive with respect to the angular momentum of
the individual states. For this reason a2 was assumed to
have the same value, O.8i0.l, for all of the transitions
considered in this experiment.

An experimental determination of d4 is quite unre-
liable. However, making some simple assumptions about the
shape of the m—substate population allows S4 to be cal—

culated from «2.27

Using this method S4 for this experiment
was determined to be 0.510.l.

Once the attenuation coefficients are determined, com—
parisons with calculated results27 can be made. Figure
III—4 shows a plot of calculated angular distribution

coefficients. The alignment parameters discussed above have

already been folded in, so that this plot may be compared

l9

 

 

 

0.7-
0.8—
0.5-
0H—
0.3-

0.2-

0.1—

 

0.0

_.
i—.
>—.
.—

 

 

1 ll
78 910 1112131'+151S

Figure III-3 The spin alignment attenuation coefficient
012 as a function of spin for pure multi—
polarity transitions in 68b

 

I+3—+I __,
0.8— \ I+1 I

0.2— I'ZTI

— L I.-.

I-aI

 

 

 

-0.8-

-0.8-

 

l l I l l l

 

1 1 1 l 1
-0.‘-+ -0.2 0.0 0.2 0.'-+

Ami/A0

Figure III—4 The angular distribution coefficients A2/A0
and A4/A0 for transitions to states with
spin If = 8

 

21

directly with the experimentally determined coefficients.
Each ellipse corresponds to transitions with different Ii+If
values, while each point on an ellipse corresponds to a
different value for 6, the multipolarity mixing ratio.

Since mixed high multipolarity transitions are in general
quite rare, only single points corresponding to 6=O are
shown for the AI=2 and AI=3 transitions. The plots shown
here correspond to transitions with If = 8. Since these
curves change only slightly with different values of If,
they may be used to determined allowable spin values for any
of the high spin states. However, in order to get a
quantitatively correct value for the mixing ratio 6, the
theoretical curves corresponding to the correct final spin
must be used.

For the case of 1188b, a (p,3ny) reaction was used in
performing the angular distribution experiment. This
reaction does not leave the final nucleus with too much
angular momentum and consequently insufficient information
is available to determine accurately the attenuation co-
efficients. They should however, not be too different from
those determined in the (d,3ny) reaction. Because of this,
only a qualitative determination of the mixing ratios can be
made from this experiment.

In addition to determining possible spin values, angular
distribution results can also in some cases be used to
establish parity assignments. This is because the transition

probability varies widely for different multipolarity

22

transitions. Thus while M1 and E2 multipolarities mix quite
readily, El and M2 multipolarities have such differing
transition rates they do not mix. Consequently the observa-
tion of a large amount of mixing in a dipole-quadrupole
transition, will establish it as an Ml/EZ transition. A
similar argument can be applied to pure quadrupole transitions.
Because the transition probability for M2 transitions has
such a small value, they occur only with long half—lives.
Thus the observation of a pure quadrupole transition without
a significant half-life will establish it as an E2 transition.

D. y—Y-t Coincidence Measurements

Normally the lifetimes of most nuclear states are much
less than a nanosecond. Therefore, after a single compound
nuclear reaction, many gamma-rays will be emitted within a
very short time period. These gamma-rays then compose one
possible decay sequence of the excited final nucleus. By
detecting multiple gamma-rays resulting from a single
nuclear reaction event, it is possible to reconstruct the
decay sequence which produced them and thus determine the
excitation energies of the excited states.

Coincidence experiments were performed for both 116:1185b.
The energies of two gamma-rays from two detectors along with
the time interval between their detection were collected and
recorded event by event onto magnetic tape. Following each
experiment, gates were set on a specific gamma-ray energy
from one detector and a specific time interval. A projected

spectrum from the other detector is produced by collecting

23

all events with the first two parameters occuring within the
gated regions. The_gamma-ray peaks which occur in this
spectrum are then known to be in coincidence with the gated
gamma-ray.

E. Gamma-ray Half-life Measurement

Although most excited nuclear states decay very quickly,
occasionally there occurs a state which is unable to decay
by magnetic dipole or electric quadrupole transitions.

These states will probably have measurable half-lives. High
multipolarity transitions have intrinsically long half-
lives, while electric dipole transtions often involve
unique-parity single—particle orbitals which lead to £-
forbiddeness, thus slowing their decay.

The most straight forward method for measuring a nuclear
half-life requires a pulsed accelerator beam. The M.S.U.
cyclotron is ideal for this, because it delivers particles
in well defined pulses. In addition, to increase the
available time between pulses, a beam sweeper may be used to
select periodic cyclotron beam bursts. With this device
half—lives from about 1 nsec to approximately 1 nsec can be
measured.

A half—life experiment involves collecting gamma-ray
energies in coincidence with a time signal, which denotes
when the gamma—ray occured relative to a beam burst. The
gamma—ray is then placed in one of 10 spectra depending on
the value of the time parameter. Analysis of the data then

involves determining the intensity of the delayed gamma—ray

24

from each spectra. These intensities can then be plotted
against the corresponding time parameter, thus determining

the half-life.

IV. 1155b EXPERIMENTAL RESULTS

A. Experimental Arrangement

High—spin states of 116Sb were populated using the
115In(a,3ny)llssb reaction. The beams were supplied by the
M.S.U. Cyclotron. The target used was a natural, metallic
indium foil of about 1 mg-cm'2 thickness. This was ac-
ceptable because 115In has a natural isotopic abundance of
95.7%. The measurements were performed using Ge(Li) de-
tectors, standard electronics, and a Sigma-7 computer for
data acquisition. The same computer along with the peak
fitting code SAMPO28 was used for off-line analysis of the
spectra.

A singles spectrum of 1168b is shown in Figure IV-l.
This spectrum was obtained using a beam energy of 42 MeV
with a detector angle of 130°. As indicated in this figure,
in addition to the gamma-rays associated with the high—spin
states of 1168b, many gamma-rays appear which belong to
various neighboring nuclei. These result from the competi—
tion of the (a,2ny) and (a,4ny) reactions, which produce
1178b and 1158b respectively. These two nuclei, along with
ll68b, beta decay with half-lives ranging from 31 to 168
minutes, resulting in the appearance of gamma-rays belonging
to the daughter nuclei 115'116'117Sn. In addition, several
of the gamma-rays labeled 1168b are associated with the pre-
viously studied,3 low-lying, low-spin levels of this nucleus.
Since the present study contains no new or contradictory

information with respect to existing results concerning

25

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28

these other nuclei and low-spin levels in 1168b, no further
discussion or reference will be made with regard to these
transitions, except to indicate where they interfere with
transitions resulting from the decay of high-spin levels in
1168b.

An energy calibration was performed by simultaneously
collecting gamma-rays from a standard radioactive source,
152Eu. This was corroborated by the many known transitions
in the spectra which provided a very good internal calibra-
tion.

B. Results of Gamma—ray Angular Distribution
Measurement

An angular distribution experiment was performed using
a 42 MeV alpha beam. The detector used was an 8% efficient
coaxial Ge(Li) detector. An additional Si surface barrier
detector was included for normalization between the dif—
ferent angles. It was positioned at a fixed angle of -45°
and was used to detect elastically scattered alpha particles.

Gamma-ray spectra were collected at angles of 90°,
100°, 110°, 120°, 130°, 140°, 150°, and 155° chosen in a
random order to minimize the possibility of systematic
errors. At each angle data were accumulated for approxi-
mately two hours. Figure IV-2 shows some representative
examples of the angular distributions that were obtained.
A compilation of the results of the experiment is contained
in Table IV—l. Included in this table are the experi-
mentally determined angular distribution coefficients along

with the relative integrated intensities Io. These

29

 

III I 1r111 T T 1 1 1 I71 '1

17‘ 532.a keV ‘— 192.s keV ‘

 

775.7 keV

INTENSITY
C3
(D

P
00

 

 

 

0.7

 

 

1 l J l 1 l 1 l 1 1 l l 1 l 1 l 1
80 100 120 190 180 80 100 120 1510 180
ANGLE ANGLE

Figure IV-2 Angular distributions for selected ll68b
transitions. The fits are normalized to l
at 900 "

30

 

 

 

 

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31

 

 

 

 

H~.ovevaa.o Imsc+iesc ao.owmo.o H.e Awes.mee
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It.ueooc HueH wanes

32

 

 

 

 

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TS: oS DRESS
ms.oveveo.o m+HH eo.osmo.o- me.osae.o M.SH e.eee
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e NH+AH o<\e< e<\~a .Hmu A>mxv
AecoH Anise
It.ueooc H1>H wanes

33

 

 

 

 

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Amv+amv a.m AUVH.mom
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34

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36

intensities have been corrected for detector efficiency and
normalized such that the l399-keV transition, the most
intense transition appearing in the level scheme, has the
value 100. It should be noted that except for the 22—keV
transition which will be discussed later, no attempt was
made to correct for conversion intensities. For those
transitions which are part of unresolvable multiplets,
estimates of the intensity have been made from the coinci-
dence experiment, where possible. The table also includes
the proposed spin values of the initial and final states
associated with each transition, as well as the multipole
mixing ratio.

C. Results of y-Y-t Coincidence Experiment

The coincidence experiment was performed using a beam
energy of 38 MeV. Two coaxial Ge(Li) detectors, each with
an efficiency of approximately 9%, were placed at 1 90°
with respect to the beam direction. Approximately 30x106
coincidence events were collected. Figure IV—3 shows
several examples of the gated spectra. The results of this
experiment are given in Table IV-2.

D. Results of Half—life Measurement

A half-life experiment was performed using a beam
energy of 38 MeV. A high resolution intrinsic Ge detector
was positioned at 90° with respect to the beam direction.
Data were collected in 10 separate time spectra determined
with respect to the cyclotron r.f. signal. A portion of

these spectra showing the decay of the 426—, 753—, 647—,

N
O
O
O

1500

COUNTS PER CHANNEL

0.)
\l
U!

250

125 -

2000 1

1500 -

1000

500

Figure

37

 

2R1keV GATE

 

 

_lr_'r“¥|' . '3‘ :J .4 ‘ J

215 keV GATE

"

 

’ ' 193 keV GATE

 

 

100 keV GATE

1.” . l 1

 

 

 

1000 2000 3000
CHANNEL NUMBER

IV—3 Background subtracted gated coincidence
spectra for selected transitions in 1155b

R000

38

Table IV—2 Results of y- y— t coincidence experiment for
transitions in 1 Sb.

 

 

 

Gate Energy Coincident Gamma-Rays
(keV) (keV)
100(a) 136(a'e), 193, 215, (298), 317, 341,

352, 382, 389, 407<a 8), 410, 426,
(444), 542<a),776, 847,968, 973(a,e),
1021,1294(aee)

193 100, (142), 215, 317, 350, 352, 382,
410, 426, (444), 562(6), 776

215(b) 100, 193, 207(bre), 298, 317, 341, 352,
382, 389, 410, 426, 442(bre), 444, 542,
669, (735), 776, (792), 968, (1021)

226 241, 507, 753, 1184

241 226, (507), 598, 1184, 1399

298 (127), (215), 350, 670

317 100, (133)(e), 193, 215, 294(9), 320(6),

341, 352, 382, 407(9), 410, 426, 542
(735), (776), 968, (1021)

341 100, 215, 317, 389

350(C) 100, 193,197(Cre), 202(cre), 215, 317,
(352), (382), 411, 426, (527)(c,e),
(1000)(C e)

352(d) 100, 103(d'e), 157(dve), 193, 215, 317,
(341), (350), 382, 410, 426, 444, (532),
(542), 776, (792), 968, (1283), 1504

382 100, 193, 215, 298, 317, 352, 405(6),
410, 426, 444, 669, (839)(e), (854),
968, (1122)

405(3) 92(9), 100(are), 136(are>, 319(e),
381(e), 392(8), 411, 424, 426, 437(a,e),
(467)(e), 776, (859), 973(are),
1072(ale), 1294 are)

39

Table IV-2 (con't)

 

 

 

Gate Energy Coincident Gamma-Rays
(keV) (keV)
411(d) 92(dre), 100, 215, 224(dre), 317

338(dre), 352, 382, 392(e), 405(4),
(411)(e), 424, 426, 435, 776, (829),

(859), 968
424 (392)(e), 405, 411, 435, 529(e), (776)
426 100, 193, 215, 317, 341, 350, 352, 382,

(405), 410, 411, (424), 480, 542, (642),
684

444 100, 215, 317, (352), (382), 410, (792)
467 507, 598, (753), 1184, 1399

480 426

507 (226), (753)

532 100, (215)(e), (240)(e), (255)(e), 352,

382, (410), (933)(e)

542“" 100(9). 136<are), 215, (2940(8), 317,
(382), 426, (582)(e), 973(a,e),
1072(a,e), 1294(a,e)

598 (241), (407)(e), (467), (1184), (1399)
647 241, 753, 1184

670 100, 215, (298), (317), (352), (382)
753 (241), (317), (624), 647, 1021

776 (100), 215, 317, (352), (405), 411
968 100, 215, 317, 352, 382, 410
1015 215, (317), (352)

1184 (226), 241, 331(6), 467, 507, (598),

(753), (840)(e), (886)(e), 1399

40

Table IV-2 (con't)

 

 

 

 

Gate Energy Coincident Gamma-Rays
(keV) . (keV)
1399 241, (336) (e), (392) (e), 467, 495(9),
598, 1184
a) Algransition with this energy is known to occur in
Sn

b) as (a) but 1158b

c) as (a) but 117Sb

d) as (a) but the low spin level scheme of 1158b

e) These transitions have not been placed in the level

scheme

 

41

and 776- keV gamma-rays is shown in Figure IV—4. The
difference between each spectrum corresponds to a time
interval of 4.36:0.04 nsec. Half-lives were determined for
13 gamma-rays, involved in the decay of 6 long-lived levels.
The results of these measurements are tabulated in
Table IV-3.

A plot of intensity as a function of time for tran-
sitions depopulating three of the metastable states is shown
in Figure IV-S. It should be noted in this figure that the

753-keV transition displays evidence for a longer half-life

 

component along with the 4-nsec component associated with
the decay of the 1624-keV level. This, coupled with the
coincidence relationships between the 753-, 1021-, and 317-
keV transitions, indicate the 753-keV transition is a
doublet, with each component involved in the decay of
different states.

The two metastable states which display half-lives in
the l nsec region are at the lower limit of sensitivity for
this type of measurement. The difficulty is compounded in
the case of the 1293-keV level by doublets and feeding from
the higher lying 6-nsec states. Consequently, these two
half-life values are associated with relatively large
uncertainties.

E. Results of Excitation Function Measurement

In addition to the above experiments, which resulted in
the excitation of high-spin states, an excitation function

measurement was performed using a (p,4nY) reaction at 37.8,

42

 

I"

D.
m.

n

r4262
“-9387 S

’.——_————

-—— \
-.__————_.

-__—_

‘—

 

l

600

Figure IV—4

N
2 =1.
CU)“
U) =9
:’(n
321\'
N- OJCD
mm;
3"“)
| ID
|

I

I

"5In[o<,3n] 38 MeV

—6a6.7Sb"‘

300

—‘752.8 Sb’“
—775.7Sb"‘
—795.5 Sb'"

CHANNEL NUMBER

reams Sn“
\sass Sb

1200

Delayed spectra from the ll51n(01,3ny) reaction.

Delay time increases with each spectrum from
top to bottom

 

43

Table IV—3 Half-lives determined for transitions involved
in the decay of metastable states in 1158b

 

 

 

 

Metastable
Level Energy Transition Energy Half-Life
(keV) (keV) (nsec)
1001 12.6i0.2
776 12.77iO.21
426 12.33r0.22
1072 2.4:0.2
847 2.42:0.20
1624 4.09:0.06
1399 4.11:0.07
1377 4.02:0.17
753 4.30:0.10
647 4.02:0.23
1193 l.0i0.5
193 1.0i0.5
3049 l.3i0.4
1184 l.4iO.5
240 l.2:0.5
3599 7.1:0.2
1021 7.74:1.16
317 6.56i0.54

215 7.16:0.23

 

44

10“1

 

 

COUNTS
llle

l

 

 

 

h—

l

1 1
0 1 2 3 Li 5 S 7 8 8

l l l

 

TIME

L1.38 nsec/uni+

Figure IV-Sa Half-life data for transitions occurring in
the decay of the isomer at 1001 keV

45

 

 

 

 

 

L+
10 1 1 T T 1 I T 1 I _
- .1 T1/2Z9.08:i:0.08 nsec '7
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0 1377.8 keV
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A 696.7 keV
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TIME

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Figure IV-Sb Half-life data for transitions occurring in
the decay of the isomer at 1624 keV

46

1W

 

COUNTS

 

 

 

 

 

TIME

9.38 nsec/uni+

Figure IV-5c Half-life data for transitions occurring in
the decay of the isomer at 3599 keV

47

40.0 and 44.0 MeV. These reactions were able to excite
intermediate spin levels. The target used was an isotopi-
cally enriched 119Sn metallic foil. The exact isotopic
composition is unknown. However, from the results of the
experiment it is evident that the percentage of 119Sn is
less than 50%. The remainder of the target is predominantly
120Sn and 122Sn.

Levels with spin to approximately 11h were excited.
Because of the impurities in the target and the low in-
tensity of most of the gamma-rays of interest, results for
only 9 of the most intense gamma-rays were obtained from
this experiment. These are shown in Figure IV-6.

F. 1168b Level Scheme

Identification of those gamma-rays associated with the
decay of high-spin levels in 1165b first involves elmination
of those gamma-rays associated with other nuclei. The
remaining most intense gamma-rays can then be checked for
consistent excitation function behavior. This establishes
the lower-lying transitions in the level scheme. The
coincidence experiment then identifies the less intense and
higher-lying transitions, as well as those which form
doublets with transitions in neighboring nuclei.

Once the gamma-rays belonging to 1168b have been
identified, they may be arranged into a self—consistent
level scheme. This is done by requiring that energy sum
and coincidence relationships are satisfied and that the

total intensity leaving each level is greater than that

W
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RELATIVE INTENSITY

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48

 

 

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ENERGY [MEYJ

Figure IV-6 Excitation functions for selected transitions

occurring in 1155b

 

49
which is entering. Applying these considerations to the
gamma-rays associated with 1168b results in the level scheme
shown in Figure IV-7.

The placement of most of the transitions is well
established by the various experiments and consequently,
will not be discussed. There are, however, a few cases
where problems arise and these will now be discussed in
detail. In particular, this level scheme exhibits a large
number of gamma-rays which are part of multiplets. This can
easily be seen in Table IV-l where the multiple coincidence
relationships are evident. The large number of multiplets
lead to several difficulties in obtaining accurate energies,
intensities and angular distribution coefficients. The most
serious problem this caused was in the construction of the
band built on the 1001 keV level.

1. The I=7 Band at 1001 keV

For this band all of the transitions are relatively
weak components of multiplets. Explicitly, the 411-keV
transition is part of a triplet, the other components being
the 4lO-keV transition placed at 2970 keV and a 411-keV
transition placed in the low—spin states of 1168b.3 The
405-keV transition is part of a triplet with a very intense
407-keV transition in 1168n29 and a very weak 404-keV tran-
sition from the low-spin states of ll65b.3 The 424-keV
transition is part of a triplet with an intense 426-keV
transition placed at 6Sl-keV in the level scheme and a weak

424—keV transition from the low-spin states of 1168b.3

50

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51
The final transition with energy 435 keV is a doublet with

a very intense 437-keV transition in 116Sn.29 In addition,
the two Sn transitions at 437 and 407 keV have a very strong
coincidence relationship with each other, thus masking any
possibility of seeing the 435- and 405-kev transitions in
coincidence. Consequently, this makes the construction of
the band very difficult.

Because of these problems the 435-keV transition is
only tentatively placed as the highest transition in this
band. In addition, because of the relative uncertainties
in intensities, the ordering of the 424- and 405-keV tran-
sitions cannot be determined unambiguously. The order is
chosen as indicated in the figure to accommodate the place-
ment of the two crossover transitions, for which there is
some, although weak, coincidence evidence. The band con-
structed in this way displays problems with intensity
balances; however, these are probably the result of in-
adequacies in the peak fitting of the multiplets involved.

As the above discussion indicates, there is little
about this band that can be stated with experimental exact-
ness. However, the construction of the band as shown gives
results which are systematically consistent with those of
l:FBSb and consequently are quite likely correct.

2. The 21.6-keV Transition

The 21.6 keV transition depopulating the 1624—keV level
was not observed in any of the experiments. Its existence

was established by the occurrence of a 4-nsec delayed

52

component for the 1377-keV transition. Its intensity was
determined from the intensity ratio of the 1377-and 1399-
keV transitions in the delayed spectra. The intensity
contribution from conversion electrons was then subtracted,
assuming the transition to be a pure El.

3. The 3599-keV Level

The assignment of the 7-nsec half—life to the 3599-
keV level was based primarily on coincidence data. The
1021-, 317-, and 215-keV gamma-rays all displayed prompt
components in their decay, indicating they do not depopulate
this level directly. Consequently the metastable state
feeding them must lie somewhere above this cascade of
transitions. The 753-keV transition is established in the
coincidence experiment as the only transition lying above
and in cascade with these gamma-rays. Because it is a weak
component of a doublet with another delayed transition, it
is not possible to determine a half-life for this tran-
sition. However, because there appears to be evidence for a
longer component than the 4-nsec component resulting from
the decay of the 1624-keV state, the 7—nsec half-life is
assigned to the 3599-keV level, which the 753-keV transition
depopulates.

4. The 2560-keV Level

The 1122—keV transition brings too much intensity into
the 2560-keV level. This indicates that either this tran-
sition is a doublet or that there is an unassigned tran-

sition depopulating the 2560-keV level. There is no

53

conclusive evidence to indicate which of these alternatives
is correct. The placements of the remainder of the tran-
sitions are well established by coincidence and energy
relationships.

G. Spin and Parity Assignments

The spin and parity assignments were made primarily on
the basis of the angular distribution results. However, the
excitation function data and intensity information are used
in resolving some of the remaining ambiguities. It should
be noted that most of the suggested spin assignments are not
rigorously proven. They are based on many interdependent
arguments and assumptions concerning how high-spin states
decay.‘ These assumptions are well established and generally
give correct results. In this case they lead to a self—
consistent set of spin assignments which can be explained in
terms of the systematics of neighboring nuclei. The follow-
ing is a discussion of some of the specific spin and parity
assignments. For convenience of discussion the transitions
and levels will be divided into groups.

1. The 8' Metastable State

All of the spin and parity assignments depend upon the
spin and parity of the lowest level in the scheme. The spin
and parity for this level must be determined absolutely by
an alternative means. For the lowest level depicted in
Figure IV—7, there are two possibilities in 1165b, known
from previous studies. These are the l6-minute 3+ ground

state and the 60.4—minute 8' metastable state located at

54
225:60 keV. The latter of these two is the only reasonable
alternative. Several reasons for this may be given. The
most convincing of these is the appearance in the 115In
(a,3nY) reaction of Several very intense llGSn gamma—rays,
which result only from the beta decay of the 8' metastable
state. This implies that a very large percentage of the
intensity excited by this reaction must decay through this
state. Previous studies of this level have included a

30

determination of the spin by use of the atomic beam method

and a level energy determination31

32.

, using the results of a
beta decay study The values from these studies have been
adopted here.

2. High-Spin Sequence

This section will discuss those levels which depopulate
to the 8' metastable state through the 1399-, 1378- or
753-keV transitions. This sequence of transitions is
depicted on the left in Figure IV-7. The most precise
angular distributions were obtained for this sequence of
transitions. This is because they carry a very large per-
centage of the total intensity. This would tend to support
the association of these levels with members of the yrast
sequence. At the least, the large intensities imply in—
creasing spin values with energy. This is also supported by
the excitation function results which show the 753- and
1399—keV transitions displaying somewhat steeper slopes than
the other low—lying transitions. Consequently this sequence

will be referred to as the high-spin sequence.

55

The 753 keV transition which depopulates the 978-
keV level displays a large negative A2 coefficient indicative
of a AI=l dipole transition. This results in an assignment
of I=9 for the 978-keV level. In addition, the significant
non-zero mixing ratio displayed by this angular distri-
bution, requires this transition to have mixed Ml/E2
character. Thus, the 978-keV level is assigned I"=9'.

Similarly the 625-keV transition from the 1603-keV
level displays mixed Ml/EZ character. The 1378-keV tran-
sition depopulating the same level displays a characteristic
stretched E2 angular distribution. These results lead to
the assignment of I"=10’ for the 1603-keV level.

The 1624-keV level has two transitions which depopulate
it. One of these, the 1399-keV transition, has an angular
distribution which exhibits a very large positive A2 value.
It can be associated with either a Ml/EZ transition or
a AI=3 transition. Similarly, the 647-keV transition is
consistent with either a dipole or a slightly mixed M2/E3,
AI=2 transition. This results in two possible assignments
consistent with the angular distribution data. These are
Ifl=9' or 11+. The excitation function measurement results,
as well as the large intensities displayed by these tran—
sitions, support the higher spin assignment. In addition to
these considerations, the I"=ll+ assignment would require
the 1399-keV transition to have E3 multipolarity. Such a
high order multipolarity should result in an observable

half-life for the 1624-keV level. A 4-nsec half-life was

 

56
determined experimentally for this level. Consequently the
1624—keV level is assigned to have I"=ll+. With this
assignment there results a large enhancement factor over the
Weisskopf single-particle estimate for the half—life of the
1399-keV E3 transition. This is not unreasonable, however,
considering a similar E3 transition in the neighboring
nucleus 1158b is similarly enhanced,13 and the corresponding

10 in 1178b exhibits a larger enhancement.

transition

The 2808-keV level is assigned I"=l3+ on the basis of
the 1184-keV transition‘s stretched E2 angular distribution.
Similarly the 3049— and 3275-keV levels are assigned to have
IT=l4+ and 15+, respectively, on the basis of the stretched
E2 behavior of the 467-keV angular distribution and the
mixed Ml/EZ behavior of the 226- and 240-keV transitions.
Evidence concerning spin assignments for higher lying levels
in this sequence is rather inconclusive; consequently, no
assignments are made.

3. Medium Spin Levels

This section will discuss those levels located below
1300 keV, excluding the 978-keV level, which was discussed
in the previous section. These levels are shown on the
right in the level scheme. As can be seen in the figure,
several of these levels decay to the 8' metastable state.
Of these transitions, four clearly display the angular
distribution characteristics of AI=l dipole transitions.

These are the 54-, 426-, 776-, and 968—keV transitions. The

57
corresponding levels which they depopulate must then have
spin values of either I=7 or 9. The excitation measurements
and intensity considerations suggest the lower spin value
for these levels. This is also supported by the lack of any
measurable intensity into any of these levels from the
I"T=ll+ 1624—keV level. Consequently I=7 assignments are
made for these four levels. There is no evidence for parity
assignments.

The 523-keV level has a spin value of either 6'or 8
because of the AI=l dipole nature of the 127-keV transition.
The near isotropic angular distribution of the 298-keV
transition, which depopulates this level, eliminates the I=6
possibility. Therefore, the 523-keV level is assigned as
having I=8.

A tentative assignment of I=8 is made for the ll3l-keV
level based on the angular distribution data for the 480-keV
transition. Also the 1293-keV level is assigned as having
I=8 on the basis of three AI=l dipole transitions from it to
levels with I=7.

4. The I=7 Band

This band is built on the 1001-keV level, which has
spin value I=7, as discussed above. Because this band was
only weakly populated and most of the transitions are parts
of multiplets, the angular distribution results for these
transitions are subject to substantial systematic errors.
However, the two tentatively placed crossover transitions

display stretched E2 angular distribution characteristics

58

and the cascade transitions display consistent Ml/E2 be-
havior. Consequently, this band is tentatively assigned
spin values increasing by AI=l with each level.

5. The I=8 Band

This band is built on the 1293-keV level, which has
spin value I=8, as discussed previously. The second level
in this sequence, located at 1508 keV, decays to the Ifi=87
metastable state as well as to the 1293-keV bandhead. The
1283-keV transition, which populates the metastable state,
displays an angular distribution characteristic of a AI=l
dipole transition. This, together with the rather steep
slope, displayed by the 215-keV transition in the excitation
function data, result in an assignment of I=9 for the 1508-
keV level. The remainder of the spins in this band are de-
termined by the appearance of Ml/E2 cascade transitions
along with stretched E2 crossover transitions. A discussion
of the internal structures and configurations of the various

states is included in the final chapter.

v. 1188b EXPERIMENTAL RESULTS

A. Experimental Arrangement

High-spin states in 118Sb were populated using the
114Cd (7Li,3ny) 118Sb reaction. Two experiments were
performed. They were a y-Y-t coincidence experiment and an
excitation function measurement. The 7Li beams were sup-
plied by the Notre Dame tandem Van de Graaff accelerator.
The target used was a self-supporting, metallic foil with a
thickness of 1 mg cm’z, enriched to about 96% in 114Cd.

The measurements were performed with two coaxial Ge(Li)
detectors with efficiencies of about 9%. One of the de-
tectors was supplied by Notre Dame. Standard gamma-ray
electronics in conjunction with a PDP 9 computer were used
for the data acquisition. The data were recorded on mag-
netic tape and returned to M.S.U. for analysis.

A singles spectrum of 1188b recorded using this re-
action is shown in Figure V-l. This spectrum was taken
using a 7Li beam energy of 28 MeV and a detector angle of
125°. As indicated in the figure there are many gamma-rays
which result from competing reactions. Several gamma—rays
from both of the neighboring Sb isotopes appear in the
spectrum. These result from two and four neutron evapora-
tion. In addition, unlike the alpha reaction used to pro—
duce 116Sb, with the Li reaction charged particle evaporation
makes a non-negligible contribution to the total cross-
section. Consequently both lls'llGIn are populated re-

spectively by aZn and an evaporation. Gamma-rays associated

59

 

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62
with llst also appear in the spectrum. This is surprising
considering apn and ad evaporation should have a low cross—

section. A possible explanation is that 115

Cd was produced
by the direct reaction l14Cd (7Li, 6Li) 115Cd. This is
supported by the fact that only low-lying, low-spin states
were populated, which is not consistent with expectations of
a fusion-evaporation reaction at the beam energies used. It
is, however, surprising that a direct reaction would have
such a large cross-section. It must be that all of these
possibilities contribute. In addition to these transitions
several Sn gamma-rays appear, which result from the B-decay
of the Sb and In nuclei. As with the 1168b results, no
further reference will be made with regards to these tran-
sitions except to indicate where they interfere with tran-
sitions, resulting from the decay of high-spin levels in
1168b.

In addition to these experiments using heavy—ion
reactions, an angular distribution and a half-life measure—
ment were performed using a 1ZOSn (p,3nY) 1188b reaction.
For these experiments 30 MeV proton beams were provided by
the M.S.U. cyclotron. The target was a self-supporting
metal foil of 0.5 mg cm"2 thickness, isotopically enriched
to 98% 120Sn. A singles spectrum acquired using this
reaction at a detector angle of 125° is shown in Figure V-2.

The gamma—ray energies were determined by simulta-
neously collecting radiation from the standard long-lived

radioactive sources 1333a and 152Eu. This energy calibration

63

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65
was corroborated by the many gamma—rays of known energy

appearing in the spectrum.

B. Results of y-Y-t Coincidence Experiment

The coincidence experiment was performed using a 26 MeV
7Li beam. Two coaxial Ge(Li) detectors were placed at +900
and -1250 with respect to the beam direction. Approximately
2x107 coincidence events were collected. Figure V43 shows
several examples of the gated spectra. The results of this
experiment are given in Table V-l.

C. Results of Excitation Function Measurement

7L1 beams of 22, 24, 26, 28 and 30

For this experiment
MeV were used. A coaxial Ge(Li) detector was positioned at
125° with respect to the beam direction and recorded singles
spectra for approximately two hours at each energy. Table
V-2 includes the relative intensities determined from the 28
MeV run. They are corrected for detector efficiency and
normalized such that the 318 keV transition has the value
100. Figure V-4 shows plots of the intensity as a function
of energy obtained from this experiment for some of the more
intense transitions.

D. Results of the Angular Distribution Experiment

Two angular distribution experiments were performed for
118810. The first involved the use of a high resolution (.7
kev at 122 keV) small volume planar Ge(Li) detector. This
made possible the partial resolution of several low energy

multiplets. However, because the efficiency of this de-

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transitions in 1183b

 

67

Table V-l. Results of Y-y-t coincidence experiment for
transitions in 1185b.

 

 

 

Gate Energy Coincident Gamma-rays
(keV) (keV)
109 253, 318
152 1321
161 368(a), 378, 481, 490, 600(3), (641), 671,
1321
203(b'C) 96(b'a), 153(Cra), 223, (237)(Cva), 261,

297, 318, 326, 362, 387, 397, 415, 4651a),
507(c.a), (619), (677), (715), 937

 

223 203, 318, 326, 362, 397, 715, (749)(a)

253(9) 109, 318, 1051(dva), (1092)§d:a), 1230(d,a)

261(3) 203, 231(e.a), 326, 345(e.a), (362), 415,
490(a>, 677, 690(e.a)

297 (203)

306 1167

318 109, 203, 223, 253, 322, 326, 362, 371,

376, 387, 393, 397 (404)(a), 580(3), 619,
(836)<a), (1014)(a$

322 (203), 297, 318

326 203, 223, 297, 318, 362, 387, 397, (415),
937, 1177

362(f) 135<fra), 203, 223, 270(fra), 318, 326,

335(fia), 370(f,a), 382(f7a), 387, 397,
(415), 7oo(f.a), (937)

371(f) 135(f:a>, 270(f7a), 318, 335(fval, 362(fra),
376, 382(fra), 393, 397, (419), (444)(a),
(660)(a), 700(f.a), 715, 769

376(079) 115<cra), 254(a), 261, 318, 337(9.a),
366(9.a), 371, (393), 397, (419) (907)(a),
1160(9rC)

378 161, 671, 1321

Table V-l continued

68

 

 

Gate Energy

Coincident Gamma-rays

 

(keV) (keV)
387 203, (223), 253(3), 270<a), 326, 362,
397, 415
393 318, 371, 376, 397, (404)(a), 419, (715),
(907)(a)
397 203, 223, (254)(a), 261, 318, 326, (362),
371, 376, 393, 419, 747
415(C:h) 203, 209(Cra), 273(Cva), 304(cra), 326,
362, (387), 795(a), 819<hra), 1294(h,a)
481 161, (190)(a), 671, (1321)
490 (161), 190(a), (481), (671), 842(a), (1321)
619 318
671 (152), 161, (242)(a>, 378, (391)(a), 481,
(490), 1321
677 261
680 793, 941(a>
793 680
937(i) 183(a,i), 203, 326
1167 306
1177 326, 362
1321 152, 161, (378), (481), 671

 

a)

d)
e)
f)

9)
h)
i)

These transitions have not been placed in the level scheme.
b) A transition with this energy is known to occur in 116In.
c) A transition with this ener y is known to occur in the

low spin level scheme of 11 Sb.

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1195b
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69

 

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Figure V-4 Excitation functions for transitions in 118Sb

 

70
information on higher lying transitions could be obtained.

A second experiment using a coaxial Ge(Li) detector of
about 9% efficiency was performed to obtain angular dis-
tributions for the higher energy transitions. Normalization
between angles is achieved in the first experiment by using
x-rays. These are emitted isotropically and have sufficiently
high energy to be detected by the low energy planar de-
tector. In the second experiment a second Ge(Li) detector
was positioned at a fixed angle of -135° with respect to the
beam. Data were collected at each angle for about two
hours.

Table V-2 shows the angular distribution coefficients
determined in these experiments. For energies less than 300
keV the values are taken from the first experiment. Results
for energies above that are taken from the second experi-
ment. Examples of the angular distributions are plotted in
Figure V-5.

E. Results of Half—life Experiment

For this experiment the high resolution planar Ge(Li)
detector was positioned at 90° with respect to the beam
direction. Data were collected into 10 separate time
spectra each corresponding to a period of 7.65:0.05 nsec.
Half-lives were obtained for two delayed transitions asso-
ciated with the decay of the 927 keV level. A half-life of
21.7il.4 nsec. is assigned to this level. A plot of in-
tensity as a function of time for these transitions is shown

in Figure V-6.

 

71

mo.owmo.ou

 

R+ch eo.oflma.o1 m.m e.a~m
m+e eo.oneo.eu Ho.owao.o1 o.ooa M.SHm
a+xoac ~.oa loca.mom
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s.am onm.mm~
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87m oév ADVENON
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ea.osmo.o1 ao.oam~.o1 e.m m.moa
R.ma m.em
R+ch loca.sm
LH+HH o<\es o<\m< .Hwn x>0xv
Seen Assn

 

 

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a:

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72

 

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73

 

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a+AeHc m.HH H.mas
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m.e Aocm.eee
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74

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.mumHmHuHsE

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cmseausoo m1> manna

INTENSITY
H. r*
i» 00

H
o
O

P
(O

1.0
E:
’6‘»
§0.S
E,

P
00

P
\1

0.8

75

 

381.9 keV

 

 

 

 

719.8 keV

q—

 

 

 

111111114 1111411L1
111111111 IlarTlill
I
937.2keV

 

1 L 1 L 1 1 1 L 1
80 100 120 190 180
ANGLE

1 l 1 l J l 1 l
80 100 120 190 180
ANGLE

Figure V—5 Angular distributions for selected 118Sb

transitions.
1 at 90°

The fits are normalized to

 

 

76

 

 

10% I 1 I I I l I I H
— T1/2=21.7:1.9 nsec 7
_ T -
U)
*—
2Z1fii _
:1 _ _
C) : I
Q - 9

318.2 keV

388.8 keV

 

 

l l 1 I l l

0 1 2 3 a 5 G 7
TIME

7.85 nsec/mm

i—-

 

(DI.

Figure V-6 Half-life data for transitions occurring in
the decay of the isomer at 927 keV

77
F. ll88b Level Scheme

The 1188b level scheme was constructed in the same
manner as described for 1165b. It is depicted in Figure V-
7. This level scheme contains 38 transitions depopulating
26 levels. Except for the lowest lying level in the scheme
with energy 212 keV, all of the transitions and levels have
not been previously studied. Although as can be seen from
Table V-2 several of the transitions are parts of multiplets,
they can be placed unambiguously in the level scheme.

The only difficulty involved in the placement of

 

transitions in this level scheme occurs for the 37 keV
transition. This transition was not observed in any of the
experiments. Its existence is required by the placement of
the 1177 keV transition which depopulates the 1389 keV
level, along with coincidence relationships, which require
there be a sequence of gamma-rays which connect the 1389 and
1149 keV levels. This requires that the 203 and 37 keV
transitions be in cascade with each other, while connecting
the 1389 and 1149 keV levels. The order of the two tran-
sitions, however, cannot be determined unambiguously. It
was chosen in the manner displayed in the level scheme to be
consistent with the results for 1168b. Although this
selection is not experimentally rigorous, the extreme
similarity between the two nuclei with respect to this I=8
band (maximum energy difference between corresponding band
members in the two nuclei is 10 keV or about 3%) indicates
the 203 keV transitions should be placed as the lowest band

member.

78

NHN

nu:
HEW

won
Nmo

mmm

mm:

 

nmmHH Mom ofionom Ho>oH :HmmicmHm 51> onsmHm

fies

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

       

 

 

 

 

 

 

 

 

 

 

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r m. km: N. omw
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m. mm:

L

wmmm

79
This argument is also true in general for the two

nuclei. A comparison of the two level schemes for
ll6’118Sb reveals a striking amount of similarity in the
high-spin structure of these nuclei. This can be seen in
the transitions energies, intensities and angular distri-
bution coefficients. This is not unexpected, as there is
only a difference of two paired neutrons in the internal
composition of these two nuclei. Since the level structure
is determined predominantly by the unpaired odd particles,
the extremely similar level structure is merely the result
of having the same single particle orbitals available for
the odd particles to occupy. Because of this similarity in
the results for the most intense transitions, a systematic
correspondence is established between many of the levels.
These systematics lend support to the correctness of each
level scheme individually as well as provide supporting
evidence for the assignment of spins and parities based on
these systematics. This is especially helpful for 118Sb.

G. Spin and Parity Assignments

1. The 8' Metastable State

As in 118Sb the lowest level in the scheme can be
established to be the I"=8', 5.0 hr. metastable state of
ll6Sb. The spin was determined using the atomic-beam
magnetic resonance method.30 The level energy was deter-

33 These

mined to be 212:8 keV from beta-decay studies.
values have been adopted here.
For convenience of discussion the transitions and

levels will be divided into four groups. The first of

 

 

 

80
these is the sequence of ganmmrrays which depopulate through

the 680, 1167, and 1321 kefif transitions. These are displayed
on.the left in Figure V97. They will be referred to as the
high spin sequence. The second group includes those re-
maining transitions which depopulate levels lying below 1200
keV. These are drawn on the right in Figure V-7. They will
be referred to as the medium spin levels. The last two
groups will be the bands built.on the I=7 state at 927 keV
and the band built on the I=(8) state at 1186 keV.

2. High Spin Sequence

The first level in this sequence is at 892 keV and is
'depopulated by the 680 keV transition. This transition
displays a negative A2 angular distribution coefficient, in-
dicative of a AI=1 transition. The excitation function re-
sults for this transition display a rather steep slope,
indicating high spin. Therefore an assignment of I"=9(')
is made for this level. The parity is tentatively assigned
as being negative on the basis of systematics with 1168b.

The second level in this sequence is at 1379. This
level is assigned to have I=9. This assignment is determined
by the AI=l behavior of the angular distribution of the 1167
keV transition, along with its high spin excitation function
behavior.

The next level in this sequence is at 1533 keV and is
depopulated by the 1321 keV transition. This transition
displays a positive A2 and a negative.A4 angular distribution
coefficients, indicative of an E2 transition. This results

in an assignment of I"=10' to this level.

 

81
The next level is at 1685 keV. It is tentatively

assigned to have I=(10) on the basis of the excitation
function data of the 306 keV level.

The next level in this sequence is at 1695 keV and is
depopulated by the 161 keV transition. This level is
assigned to have Ifl=ll(+). The spin is determined by the
AI=l behavior of the angular distribution of the 161 keV
transition. The parity is tentatively assigned on the basis
of systematics with 116Sb.

No assignments are made for higher lying levels in this

sequence. This is because these levels were not populated

 

in the angular distribution experiment using the (p,3nY)
reaction. This fact, however, indicates they are high spin
states, which is again consistent with the reSUlts from
1168b.

3. Medium Spin States

The three transitions of energies 937, 715, and 318 all
decay to the 8' metastable state. In addition they all
display negative A2 coefficients in their angular distri-
butions, indicating they are AI=1 transitions. This results
in an I=7 or 9 assignment for the levels at 530, 927, and
1149 keV. The excitation functions for transitions de-
populating these levels indicate that the smaller of these
two values is the correct alternative in all three cases.
This is also consistent with the results for corresponding
levels in 1165b. Therefore spin assignments of I=7 are made

for the 530, 927, and 1149 keV levels. It should be noted

82
that these assignments are consistent with the angular

distribution results of the interconnecting transitions with
energies 222 and 397 keV.

The 852 keV level is tentatively assigned to have
I=(8). This assignment is made on the basis of the AI=1
character of the angular distribution for the 322 keV
transition, which dep0pulates this level. There is in-
sufficient information available to make further spin
assignments for levels in this group.

4. The I=7 Band

This band is built on the 927 keV level, with spin
value I=7 as discussed above. Angular distributions for
three of the transitions in this band were obtained. These
are the 371, 376, and 392 keV transitions. The angular
distributions are consistent with Ml/E2 multipolarities with
substantial positive mixing ratios (620.3). The cross—over
transitions are too weak to obtain any angular distribution
information. Spin values are assigned to this band con-
sistent with a AI=l increasing spin sequence. The tentative
spin assignment of I=(ll) for the highest member of this
band is made on the basis of these systematics.

5. The I=8 Band

The second band member located at 1389 keV depopulates
by means of the 1177 keV transition to the 8' metastable
state. The angular distribution for this transition
displays characteristic AI=1 behavior, thus requiring the

1389 keV level to have a spin of I=7 or 9. The excitation

 

83
function for this transiton indicates the higher spin value

is the correct alternative. This is again consistent with

results from 1168b.

Consequently an assignment of I=9 is
given to this level.

Angular distributions were obtained for the 203, 326,
and 362 keV transitions. Although it should be noted the
203 and 362 keV lines are known to contain contributions
from other gamma-rays. The angular distribution coeffi-
cients are consistent with AI=1, Ml/E2 transitions. The
mixing ratio (020.1) for these transitions is smaller than
those obtained for the I=7 band. Tentative spin assignments
are made for this band consistent with a AI=l increasing

spin sequence. A discussion of these structures is included

in the next chapter.

 

VI. DISCUSSION AND SUMMARY

A. High-Spin Sequence

The high-spin structure of odd—odd Sb nuclei is very
closely related to that of the neighboring odd mass Sb
nuclei. This is mainly due to the dominance of the high-
spin lhll/Z unique-parity single—particle orbital which is
readily available for occupancy by the additional odd neutron
in these nuclei. Excitation of the 1h11/2 orbital requires
only a few hundred keV of energy and provides at least two
additional units of available angular momentum over any
other easily accessible neutron single-particle state.
Consequenly it would be expected that the structure of the
yrast levels in ll6'118Sb should result from a coupling of
the yrast levels in the neighboring odd mass Sb nuclei to
the high spin lhll/Z neutron state.
Figure VI-l shows the high-spin sequence for 115'119Sb.
Also indicated in the figure are some pertinent yrast states
from the even Sn cores. The odd-odd Sb nuclei are normalized
to the I“=8' metastable states, while the odd mass Sb nuclei
are shown beginning from their I"=5+/2 ground states. The
similarity of the level energies and spacings is immediately
apparent from the figure. Qualitatively the situation may
be described as a systematic series of states. The first of
which begins in 1158b at 724 keV and steadily decreases in
energy to 270 keV in l19Sb. This is followed by a series of
two states at about 1300 keV that remain fairly constant

over the mass range shown. This is followed by a large gap

84

85

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86 .
in energy and then several closely spaced high lying states.

Each of these states will now be considered in more detail.

The structure of the I“=8' states in the odd-odd nuclei
is thought to consist predominantly of the 2d5/2 proton
coupled to maximum spin with the lhll/z neutron single-
particle states.34 This assignment agrees rather well with
the systematics established here. The 2d5/2 proton state is
the lowest lying single-particle proton state for these
nuclei and it is this state which is responsible for the
I"=5+/2 odd mass ground states. Other available proton
single-particle states are the 197/2 and lhll/Z' These
appear as the In=7+/2 and 117/2 states in the odd mass Sb
nuclei. Coupling these to maximum spin with a 1h11/2 neutron
results in I“=9' and 11+ states. From the figure it is
evident that these configurations correspond to the experi-
mentally observed yrast levels of the same spin in 116'1188b.

The I"=lO' states located at 1602 and 1512 keV re-
spectively in 1155b and 1185b, lie 1377 and 1322 keV above
their respective I"=8' metastable states. These energies
are approximately the same as the first 177:2+ phonon ex-
citation in the even Sn cores. Consequently these states
might be characterized as being predominantly a 2d5/2 proton
and lhll/Z neutron single-particle states coupled to the
first quadrupole phonon core excitation. This is consistent
with the systematics established by the neighboring odd mass
Sb nuclei and the Configuration assignments made for the

corresponding Ifl=9+/2 levels in these nuclei.

87
The higher lying levels in these sequences are most

likely four quasiparticle states made from three-neutron,
one-proton configurations. This is plausible because the
high-spin states in the Sn core nuclei have been found to be
relatively pure two-neutron states.35 For example there is
a I"=5' state at 2815 keV in 114Sn. This state coupled to
maximum spin with a 2d5/2 proton is the proposed7 configuration
for the 2517 keV, I“=lS‘/2 level in 1158b. Coupling this
state to maximum spin with another 1hll/2 neutron will
result in a I"=l3+ level in 116Sb. This is most likely the
configuration for the observed I"=l3+ level at 2808 keV.
This configuration may also be consistent for the 2366 keV
level in 1188b. The decrease in energy with respect to this
level in 1168b may be part of a systematic trend because the
I“=5' level in 116Sn is about 500 keV lower than the same
state in 114Sn. Similarly, the I"=15+ level in 1168b may
result from the Ifl=7' core excitation in 114Sn. Due to the
lack of definite experimental spin information for higher
lying levels, especially in 118Sb, a discussion of possible
configurations is unjustified. However, in general these
levels can be described as two neutron core excitation
states coupled to the odd proton in either the 2d5/2 or 197/2
state and the odd neutron in the lhll/z state.

B. Medium Spin Levels

Those leVels which lie below 1200 keV and are not members

of the two band structures can be characterized as having spin

values between I=6 and I=9. In addition since the first 1

 

88
phonon excitation requires more than 1300 keV and the first

two—particle Sn core excitations require more than 2 MeV,
these states must be described in terms of two coupled
single-particle excitations. These states are primarily
then alternative couplings of the same two-particle states
that made up the lower levels of the yrast sequence. The
lhll/Z neutron can be coupled to the 2d5/2, 197/2 and lhll/Z
proton levels resulting in several possible high-spin states.
Additional configurations that may contribute states to this
energy region are the {(“h11/2) (vd3/2)} and {(ng7/2)
(vg7/Z)'l}. A final possibility for forming high—spin
states at about this energy involves the g9/2 proton hole
state. It is this state which is principally responsible
for the band structure that is observed. However, it is not
possible to rule out this orbital as also contributing to
levels which are not directly associated with the band
structures. It is possible to make estimates of where each
of these configurations should lie based upon single-particle
energies determined from states in the neighboring nuclei.
However, because of the large number of possible states and
the complexity of the states, detailed shell model calculations
including the effects of the p—n residual interaction would
be necessary before specific configuration assignments could
be made.

C. Deformed States

In each of the nuclei under study two bands, one built

on a spin I=7 state the other built on a spin I=8 state,

89
were observed. These bands exhibit very characteristic

rotational behavior, in that they are composed of I+I-l
mixed Ml/E2 transitions, while additionally in some cases
displaying E2 crossover transitions. The energy spacings
between band members are also consistent with a rotational
interpretation. Consequently they will be discussed here in.
those terms.

As with the other states in this region because of
energy considerations the bandheads must be predominantly
two-particle states. In considering the structure of these

states it is once again helpful to look at the neighboring

 

odd mass Sb nuclei. The existence of bands built on a g9/2
proton hole state in those nuclei leads to the reasonable
assumption that the bands in the odd-odd nuclei also involve
a proton in this orbital. A few observations support this
assumption. First the excitation energies of the bandheads
in the odd—odd case are very similar to the excitation
energy of the I"=9+/2 bandhead in the neighboring odd mass
nuclei. In addition the high spin nature of the bandheads
would require a large angular momentum contribution from the
proton single-particle orbital. Figure VI-2 shows the
Nilsson levels for the odd proton. It is Clearly evident
that the only easily accessible high-spin orbital is the
9+/2{404}, which is derived from the 99/2 shell model orbital.
Finally this assignment is consistent with total potential

energy calculations12 which show the 9+/2{404} Nilsson level

displaying a minimum at a non-zero deformation for Z=51

E [MeV]

 

95

ds/Z /

 

90
pL/z

 

35 1

9.\
I
e\

'5/2*[a02)
7/2ttaoal

3/2‘1911] _

5/2*[a13]
//9/2*[aoa) q

-

1/2‘1920]
7/2*(a13)
3/2*(|+22) -

1/ 21301)

5/2‘1a22] '
1/2‘11131) J

3/2‘la31]

1,"2+[990]

 

 

0.0

Figure VI-2

Nilsson diagram for odd protons

 

91
nuclei. For the higher lying J=8, there is one additional

argument that can be made, which involves the band energy
spacing. This will be discussed later.

The Nilsson levels for the odd neutron are shown in
Figure VI-3. Available high-spin orbitals for the neutron
to occupy include the lhll/z and lg7/2 shell model orbitals.
Assuming a model in which the particles are strongly coupled
to the deformed core, K the projection of the total angular
momentum on the deformation axis is a good quantum number.
It is given by K = lKliKzl where Ki is the projection of the

angular momentum of the ith particle on this same axis.

 

Taking the proton to be in the Kl"=9+/2 {404} Nilsson orbital
and assuming a neutron Fermi energy of about 51 MeV, it is
evident from Figure VI-3 that in order to form a K=8 ro- '
tational band the neutron must be in the 7+/2 {404} Nilsson
orbital. Similarly for the K=7 band, the neutron must be in
either the 5+/2{404} or the 5'/2{532} orbitals. This strong
coupling description of the K=8 band will not be considered.

A plot of (BI—EI_l)/ZI as a function of 2I2

for the two
bands is shown in Figure VI-4. In a plot such as this the
intercept is the rotational constant'gij and perturbation
effects on the simple rotor model arezgmphasized. A ro-
tational band which has only the I(I+l) energy dependence
would appear on this type of plot as a horizontal line. It
is immediately obvious that the K=8 bands, except for the

first level, display this horizontal behavior to a remarkable

degree of accuracy. This is extremely compelling evidence

E [Nev]

 

j
11/2‘1505)

9/ 21519)

_ 3/2*(a02) _
1/2’1900)
55 1 7729909) -
F 5/2*(a02) _
h11/2
7/2'1523]

- ~ / +1 0)
‘Q 1:224:21) _

50 *- 7/ / 3/2W22) “
9 -

 

 

 

-\ "

‘

PdS/ 3/2'15911 H
3/2‘1911) _

" 1/2*(931]
1/2‘1550)

95 1 L 1 1 1 1 1 J V2190]
0.0 0.1 0.2 0.3 0.9

Figure VI-3 Nilsson diagram for odd neutrons

 

93

 

 

 

 

 

T 1 I T T T 1* T
: o 116 Sb J=8
_ O 118 Sb J=8
220-
; -
G) 1559-
': H
H I
(\J
U 10f
< _
ET-
0' 1 1 1 1 1 1 1 1
0 100 200 300 900

212

Figure VI-4 The rotational band spacin as a function of
212 for the J=8 bands-in l 5'113Sb

94
indicating that the strong coupling picture does indeed

apply in this case. However, there are several reasons for
arguing against this description.

The first consideration involves the moment of inertia.
From the figure it can be seen that the rotational constant
resulting from this K=8 band is about 16 keV. Comparing
this moment of inertia result to an empirical relation
determined from well deformed bands in the rare earth
region,36 the deformation is found to be extremely large
(B>O.5). The likelihood of such a large deformation occur-
ring so near the closed proton shell is rather remote.

The second reason involves the obvious anomaly in the
first band member. Such anomalies are quite common in well
deformed nuclei, and are explained by band mixing. In this
particular case the existence of a K=9 band is required.

The levels of such a band would mix with the levels of
corresponding spin from the K=8 band. This would lower the
energy of all levels except the K=8 bandhead for which there
is no mixing. This produces a compression in the band's
lowest transition. However, in this particular case using
the strong coupling scheme, both the neutron and proton are
already in the highest 0 components of their respective
orbitals, and there is no way of producing a higher spin K=9
band.

The final argument against strong coupling involves a
comparison with the bands in the neighboring odd mass nuclei.

These odd mass bands although being strongly coupled do not

 

95
have energy spacings that follow the simple I(I+l) pattern

of a single-particle coupled to an axially symmetric rotor.
Calculations have been performed describing these bands
using both the triaxial rotor model7 and the axially symmetric

12 In either of these cases it is

model with band mixing.
unlikely that such perturbations of the simple rotor model
would disappear upon adding an extra odd neutron. Consequently
the non-trivial structure of the odd mass bands should lead

to similar non-simple structure in the odd-odd bands. This
argument indicates that the simple appearance of the odd-odd
bands does not result from truly simple internal structure,

but is only a chance occurance caused by several interfering
effects. With this view there is good reason to consider
alternatives to the strong coupling scheme.

The opposite extreme to a strongly coupled neutron is a
rotationally aligned neutron. The data have features which
tend to support such an interpretation. This can be seen in
Figure VI-S, where the levels for the J=8 bands are plotted
along with the levels of the Kfl=9+/2 bands from the odd mass
Sb nuclei. The bands have all been normalized to the second
level. The figure clearly shows the striking similarities
in the energy spacing of the bands. .This is what would be
expected if the odd neutron was aligned. In this scheme the
nucleus rotates in exactly the same manner as without the
extra particle. The extra neutron is decoupled from the

motion of the core and contributes a component to the total

angular momentum, but has no effect on the rotational energies.

 

96

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97
With this interpretation it is-clear that the proton is

in the same 99/2 hole state as occurs in the neighboring odd
mass Sb bands. In addition the neutron must be in the
unique-parity lhll/Z orbital. This is consistant with the
Fermi level being near the low-0 components of this orbital.
In this picture the proton is a strongly coupled hole state
in the highest 0 component of the g9/2 orbital, indiCating
deformation alignment. The lhll/Z neutron is rotationally
aligned, which implies that its spin is generally perpen-
dicular to the direction of the proton's spin. The spin of
the bandhead should then be approximately given by 21
J2 (ll/2)2 + (9/2)2 = 7.1. This value is roughly consistent
with the experimentally determined value of J=8.

This coupling scheme also allows a J=9 band, which can
arise from a slightly different coupling of the neutron and
proton spin. Although there is no experimental evidence to
support the existance of such a band, it would be expected
to lie somewhat higher in energy and would mix with the J=8
band. This could explain the experimentally observed com-
pression of the lowest band transition.

The high moment of inertia is no longer a problem,
since a large portion of the angular momentum for this
band is coming from alignment of the neutron single particle
angular momentum, rather than an actual increase in the
rotational angular momentum. The observed moment of inertia

represents only an apparent moment of inertia. The actual

physical moment of inertia would be the same as determined

 

98
from the neighboring odd mass K"=9+/2 bands. Together these

observations, although quite qualitative in nature, do give
a consistent description of the J=8 bands.

Accepting this description for the J=8 bands, then
eliminates one of the possible neutron configurations for
the lower lying K=7 bands. The obvious differences in the
energy spacing, as well as the absence of any interband
connecting transitions, requires the K=7 and J=8 bands to
have rather different intrinsic structure. This implies the
K=7 bands do not involve the lhll/z neutron orbital.

The 5+/2{404} Nilsson level is the remaining alternative
for the neutron state, resulting in a band with both particles
strongly coupled to give KT=7+. This assignment may explain
the relatively long (21.7 and 12.6 nsec.) half-lives of the
bandheads. Since the 5+/2{404} Nilsson level at relatively
small deformations is predominantly made up of the 2d5/2
shell model state and the high-spin states lying below this
band are expected to involve the lhll/z neutron configuration,
the decay of these bands would be hindered by l-forbiddeness.

This configuration assignment is also consistent with
results obtained for the odd-neutron 117rll9r121Te nuclei.37
These bands are observed built on K"=5+/2 and 7+/2 states.
These are interpreted as rotational bands resulting from
the 5+/2{402} and 7+/2{404} Nilsson levels. The former of
these two is the same level as the proposed neutron configura-

tion for the J=7 odd-odd bands. It is interesting to note

that the K“=5+/2 band was excited to much higher spin and

99

with much greater intensity in 119Te than in 117

Te. This is

similar to the case in Sb where the proposed K71=7+ band in

118Sb is populated more strongly than it is in 116Sb. In

addition the Kn=7+/2 band was not excited in either 117'119Te,

121Te. This is also consistent with the lack of

116,1183b.

but was in
observation of any K'”=8+ strongly coupled bands in
Such a band however would be expected to appear in 120Sb.
Figure IV-6 shows a plot of AE/ZI as a function of 212
for the proposed K"=7+ bands in 116(1188b. Also included
are the odd-neutron K"=5+/2 band in 119Te and the odd-proton
K"=9+/2 band in 1158b. (The band was chosen from 119Te
because in 117Te it was only excited to the second band
member. The 1158b band was chosen to represent the odd mass
Sb bands because it has been excited to higher spin than in
the others. However, it should be noted that this Choice is
unimportant since all of the odd-mass Sb bands are essentially
identical.) From the figure it is Clear that all of the
bands have quite similar behavior. The moment of inertia
increases sharply with spin at low spin values and then
levels out at high spins. These similarities indicate that
core deformation is approximately the same for all of these
bands. This would be a surprising result if the Closed
shell Z=50 Sn nuclei were used for the Sb core. However, a
more suitable core to describe the Sb bands is the even Te
nuclei. This is because the proton configuration for the
Sb bands is a hole state. So even though the spherical Sb

states behave in a manner perscribed.by particles coupled

 

100

 

O 118 Sb K=7
<>118 Sb K=7 __
A 115 Sb K=9/2

CI 119 To K=5/2 _

50-

 

10- _.

 

 

 

1 1
200 300

212

1
0 100

Figure VI-6

The rotational band spacing as a function of 2I2 for the K=7
bands in 116(1188b compared with the K=2.band in 1155b and
the K=§ band in 119Te 2

2

101
to a Sn core, the deformed states in these nuclei are better

described as a hole state coupled to a Te core. Consequently
assuming the proton-hole configuration, the similar behavior
of the Sb and Te bands is expected to occur.

D. Summary

Experiments were performed studying the Y radiation
following the proton, alpha, and lithium induced reactions
which populated high-spin states in 116'llBSb. Level
energies, half-lives, spins, parities, and relative decay
intensities were measured and qualitatively discussed in
terms of the shell model and particle-plus-deformed-core
model.

The level schemes display behavior than can be explained
only by assuming the existance of both deformed and spherical
states. Such coexistance of states has been observed in
both the neighboring odd-proton Sb and odd-neutron Te nuclei.
This study extends these findings to odd-odd Sb nuclei.

The spherical states can be adequately described in
terms of either two-quasiparticle states, or two-quasiparticle
states coupled to either collective or single particle ex-
citations of the Sn core. The 1hll/2 neutron, unique-parity
orbital is found to play a role in most of these states.

In addition to these spherical states two rotational
bands are observed in each nuclei. These bands can be
described in terms of a 99/2 proton hole state strongly

coupled to a deformed Te core. In the rotational model this

state is described as the 9+/2 {404} Nilsson level. In

102
the case of the higher lying bands this proton state is

coupled to a lhll/z rotationally aligned neutron state
resulting in a Jfl=8' band, that looks very much like the
neighboring odd-mass Sb bands. This provides an example of
the "conflicting case" in which one of the odd particles is
aligned with the deformation while the other is aligned with
the rotation.

The lower-lying bands exhibit somewhat different
behavior and are best described as both particles being
strongly coupled. In this case the proton and neutron are
respectively in the 9+/2{404} and 5+/2{402} Nilsson levels,
resulting in a K"=7+ band. This represents an example of
the "peaceful case". .

In conclusion, this picture provides a qualitatively
good description of the odd-odd Sb nuclei, that is con-
sistent with the behavior of the neighboring nuclei in this

region.

 

103
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