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THESIE

LIBRA p 1!

Michigan Mata
University

 

This is to certify that the

thesis entitled

Conversi on—elec cron And Gamma. Ray Experiments
With The Decay Of Bromine-82 And Stron titan-83

presented by

Robert C. Etherton

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Physzics

Lil/{cal

Major professor

Date June 29. 1967

0-169

 

 

 

ABSTRACT

CONVERSION-ELECTRON AND y-RAY EXPERIMENTS
WITH THE DECAY 0F BRggINE-82 AND STRONTIUM—
By Robert C. Etherton

The energy levels of 82Kr populated by the beta decay
of 82Br have been studied. The internal conversion electron
spectra were recorded with permanent magnet electron spectro-
meters and the singles and coincidence spectra were recorded
using both NaI(T1) and Ge(Li) detectors. A total of 21
transitions have been identified. Excited states in 82Kr
have been placed at 772, 1H75, 1821, 209M, 2H29, 2560,
26M8, 2652, and 2832 keV. Angular correlation measurements
for eight of the prominent gamma-gamma cascades were made and
the results used to make unique spin assignments for the 777,
1&75, 1821, 2094, and 2648 keV states. Transitions from the
2832, 2652, and 2560 keV states and log ft values were used
to place limits on the possible spin assignments for these
states. The level structure of 82Kr was used to test some of
the predictions of the Davydov—Filippov asymmetric rotor model.

Similar experiments as those described for the investiga-
tion of 82Br were performed with the decay of 83Sr. An M2
isomeric transition was identified at 42.3 keV. Some sixty

transitions were identified enabling the placement of excited

states at 5.0, M2.3, 295.2, 389.2, u23.5, 736.8, 8ou.8, 99u.2,

 

Robert C. Etherton

1043.7, 1053.7, 1103.0, 1202.0, 1242.6, 1273.1, 1324.6,
1653.1, 1756.9, 1783.5, 1916.7, 1952.2, 2014.8, 2090.0,
2147.8, 2179.3 keV. Limits on the spins and parities of
these states were placed on the basis of gamma ray branching
and log ft values.

An attempt was made to correlate the level structure of
83Rb to that of 82Kr with the core-coupling model. No simple

relationship was found.

CONVERSION-ELECTRON AND y—RAY EXPERIMENTS WITH

THE DECAY OF BROMINE—82 AND STRONTIUM—83

By
\0

I

\e
Robert C. Etherton

We
l

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Physics
1967

ACKNOWLEDGMENTS

I wish to thank Dr. W. H. Kelly for the suggestion of
this thesis project. His guidance and helpful discussions
during the various phases of this investigation are deeply
appreciated.

Dr. R. L. Auble, Dr. L. M. Beyer, Dr. G. Berzins, Mr.

A. Bisson, and Mr. D. Beery were of great assistance with
the acquistion of the data.

I am grateful to Dr. M. L. Wiedenbeck and Dr. R. Woods
for making available the University of Michigan permanent
magnet electron spectrometers for the investigation of the
conversion—electron spectra of 82Br.

Dr. G. Berzins and Dr. L. Kull were of assistance in the
analysis of the data with the computer.

Dr. D. Horan contributed many valuable discussions.

Mr. N. Mercer and his staff were of assistance in the
fabrication of some of the apparatus used in this investigation.
I appreciate the financial support contributed by
Michigan State University and the National Science Foundation.

Finally, I wish to thank my wife Jean and my children
Michael, Kathy and Cindy for their encouragement and patience
and for the sacrifice of many vacations during the long
course of this study.

ii

TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . ii
LIST OF TABLES . . . . . . . . . . .
LIST OF FIGURES . . . . . . . . . . .
INTRODUCTION . . . . . . . . . . . . . . . 1
Chapter
I. NUCLEAR MODELS 6
1.1. The Shell Model . . . . . . . . 6
1.2. Residual Interactions . . . . . . . 8
1.3. The "Talmi- Unna Model” . . . . . . . 9
1.4. The Unified Model . . . . . . . . . 12
1.4.1. The Collective Model . . . . . 14
1.4.2. Axially Symmetric Nuclei . . . . 16
1.4.3. The Asymmetric Rotor Model . . . 19
1.4.4. The Core Coupling Model . . . . 23
1.4.4.A. Weak Coupling, Spherical
Nuclei . 2“
1.4.4.B. Strong Coupling, Deformed
Nuclei . . . . 26
1.5. The Experimental Determination of the
Properties of Nuclear States . . . . . 26
1.5.1. Beta Selection Rules . 27
1.5.2. Gamma Ray Transition Probabilities 29
1. 5. 3. Gamma-Gamma Angular Correlations . 29
1.5.4. Internal Conversion Coefficients . 32
II. APPARATUS AND EXPERIMENTAL PROCEDURE . . . . 33
2.1. The Gamma Ray Spectrometer . . . . . . 33
2.1.1. Singles Experiments . 33
2 l 2 Coincidence Experiments, NaI(T1)
detectors . . 34
2.1.3. Coincidence Experiments, NaI(T1)
and Ge(Li) detectors . . . 37
2.1.4. Anti— Coincidence Experiments . . 38

ill

Chapter

III.

IV.

82

TRANSITIONS IN Kr . . . . . . . . .

3.1.

3.
3.

4.
5.

Experimental Results . . . . .

3.1.1-

3.1.2.

The Internal Conversion Electron
and Gamma—ray Singles Spectra
Gamma—Gamma Coincidence . . . .

3.1.2.A. Gamma Coincidences with
the 1652 keV Gamma—Ray

3.1.2.B. Coincidences with the
650 to 1200 keV Region .

3.1.2.C. Coincidences with the 92
keV Gamma-ray . . . .

The Decay Scheme of 82Kr . .
Directional Correlation Measurements .

3.3.1.

3.3.2.

Analysis of Directional Correla-
tion Data . . . . . . .

3.3.1.A. The 1318— 777 keV
Correlation .

3.3.1.B. The 698— 777 keV and 828—
777 keV Correlations

3.3.1.0. The 828— 1044 keV and
1044— 777 keV Correla—
tions .

3.3.1.D. The 554— 1318 keV
Correlation

3.3.1.E. The 554— 1475 and the 619—
1475 keV Correlations

3.3.1.F. The Remaining Correla—
tion Functions .

Summary of Angular Correlation
Measurements and the Resulting
Spin Assignments . . .

Other Recently Reported Work .
Discussion of the Decay Scheme of 82Br

THE DECAY SCHEME OF 83116 . . . . . . . .

4.1
4.2

Source Preparation . . . . . .
Experimental Results .

4...21
4.2.2.
4. .3

The Gamma—ray Singles Spectrum .
Gamma—Gamma Coincidences Studies
The Internal Conversion Coefficient
of the 42.3 keV Transition

iv

Page
41
44
44
55
55
57
58
59
62
63

65
65

67
71
71
73

73

78
80

84

85
86

86
92

109

Chapter Page
4.2.4. Half—life Measurements for the
42.3 keV transition . . . . . . 113
4.3. The Proposed Decay Scheme for 83Sr . . . 117
4.3.1. Evidence for the 42.3 keV State . . 120
4.3.2 Evidence for the 423. 5, 804. 5 keV
and the 5.0 keV States . . . 120
4.3.3 Evidence for States at 295. 2 and
389. 2 keV . . . . 122
4.3.4. Evidence for States at 1202. 0,
1242. 6, and 1952. 2 keV . . . . . 123
4.3.5. The Remaining States . . . . 124
4.3.6. Spin and Parity Assignments . . . 124
4.4. Discussion of the Decay Scheme of 83Sr . . 125
V. SUMMARY AND CONCLUSIONS . . . . . . . . . 129
BIBLIOGRAPHY . . . . . . . . . . 132

10.

11.

12.

LIST OF TABLES

Page

Experimental and calculated energy differences . . l3
Gamma ray calibration energies . . . . . . . 35
Energy and intensity measurements of gamma rays
emitted in the decay of Br . . . . 46
Energy intervals used for the analyses of the two
parameter angular correlation data . . . . . . 64
Summary of 82Kr angular correlation data . . . . 74
Summary of 82Kr internal conversion coefficients,
mixing ratios, and multipole orders . . . . . 76
Eneggies and relative intensities of transitions

. . . . . . . . . . . . 89
Energies and relative intensities of gamma ray
in the decay of 3Sr observed in the anti—Compton
and "any gamma-gamma" coincidence experiments . . 93
Coincidence summary . . . . . . . . . . . 107
Summary of internal conversion coefficients and
multipole order of some of the transitions in
83Rb................114
Summary of gamma cascade energy sums . . . . . 119
Spin and Parity Assignments for states in 83Rb . . 125

vi

Figure

2a.

2b.

20.

3a.

3b.

3c.

6a.

6b.

60.

LIST OF FIGURES

Page
Presently accepted decay scheme of 82Br . . . 42
.Gamma singles spectrum of 82Br taken with a 3 cm2
x 4 mm Ge(Li) detector. Low energy region . . 47
Gamma singles spectrum of 82Br taken with the
Ge(Li) detector. Intermediate energies . . . 48
Gamma singles spectrum of 82Br taken with the
Ge(Li) detector. High energy region . . . . 49
Weak gamma transitions observed with the Ge(Li)
detector: 425-630 keV. Note the scale breaks
for both coordinate axes . . . . . . . . 50
Weak gamma transitions observed with the Ge(Li)
detector: 850-1100 keV . . . . . . . . 51
Weak gamma transitions observed with the Ge(Li)
detector: 1675-2050 keV . . . . . . . . 52
Gamma singles spectra of 82Br taken with 7.6 cm
by 7.6 cm NaI(Tl) detector . . . . . . . 53
Gamma spectrum in coincidence with the 1652 keV
gamma ray. Both detectors were 7.6 cm by 7.6 cm
NaI(T1) crystals . . . . . . . . . . 56

Gamma spectrum between 650-1200 keV in coincidence
with 1044 keV photopeak. Both detectors were
7.6 cm by 7.6 cm NaI(Tl) crystals . . . . . 58

Gamma spectrum between 800-1200 keV in coincidence
with 274 keV photopeak. Both detectors were
7.6_cm by 7.6 cm NaI(T1) crystals . . . . . 58

Gamma spectrum between 800-1200 keV in coincidence
with 221 keV photopeak. Both detectors were 7.6
cm by 7.6 cm NaI(T1) crystals . . . . . . 58

Gamma spectrum in coincidence with 92 keV photo-
peak. This spectrum is the difference between

the spectra obtained without and with a cOpper
absorber over the 92 keV detector. The detector
used to obtain this Spectrum was a 7.6 cm by 7.6

cm NaI(T1) crystal. The detector used for the 92

keV gamma was a 3.8 cm diam by 6 mm thick NaI(T1)
crystal . . . . . . . . . . . . . 60

vii

Figure

10a.

10b.

ll.

l2.

l3.

14.

15.

16.

Page

Proposed decay scheme for 82Br . . . . . . 61

Possible orders of 828-1044-777 keV transitions 69

Gamma singles spectrum of 83Sr taken with a 3
cm3 Ge(Li) detector. Low energy portion . . 87

Gamma singles spectrum of 83Sr taken with a 3
cm3 Ge(Li) detector. High energy portion . . 88

Anti-Compton gamma spectra of 83Sr obtained with

a 7 cm3 Ge(Li) counter and the NaI(T1) annulus
detector. Spectra A was recorded with the gamma

rays collimated into the Ge(Li) detector from

an external source. Spectra B was recorded with

the source in the tunnel of the annulus. The
energies of the weak transitions are listed in

Table 8 . . . . . . . . . . . . . 91

"Any gamma-gamma coincidence" spectrum of 83Sr
taken with the 7 cm3 Ge(Li) and NaI(T1) annulus
detectors . . . . . . . . . . . . . 95

Gamma spectrum in coincidence with the 94.2 keV
gamma taken with the 7 cm3 Ge(Li) counter. The
coincidence gate detector was a 3.8 cm by 2.5 cm
NaI(T1) crystal with a 0.013 cm beryllium window.

For comparison, spectrum B was recorded with the
NaI(Tl) detector gated on the region above the

94.2 gamma ray . . . . . . . . . . . 97

Gamma spectrum in coincidence with segments of
295—400 keV region taken with the 7 cm3 Ge(Li)
counter and a 7.6 cm by 7.6 cm NaI(T1) detector.
Spectrum A was recorded with the NaI(T1)

detector gated on 295-330 keV. Spectrum B was
recorded with the NaI(Tl) detector gated on the

low energy side of the 381, 418, 423 keV peaks 98

Gamma spectrum in coincidence with the 400—
450 keV region taken with the 7 cm5 Ge(Li)
counter and the NaI(Tl) split annulus detector . 99

Gamma spectra in coincidence with segments of

the 600-740 keV region taken with the same

detectors as for Figure 15. A singles spectrum

is given for reference. The spectra have been
arbitrarily displaced vertically for ease of
presentation. The energy scales have been

adjusted to be equal with the MSU CDC 3600

computer . . . . . . . . . . . . . 100

viii

Figure Page

17. Gamma spectrum in coincidence with the 762 keV
photopeak taken with the same detectors as in
Figure 14 . . . . . . . . . . . . . 101

18. Gamma spectrum in coincidence with various
segments of the 800-1100 keV region. Spectrum
A is a singles spectrum for reference. The
detectors were the same as Figure 15. The
scales have been adjusted the same as in
Figure 16 . . . . . . . . . . . . . 102

19. Gamma spectrum in coincidence with the 1147-
1160 keV doublet. The detectors were the
same as in Figure 14 . . . . . . . . . 103

20. Gamma spectrum in coincidence with the 1562.5
keV peak. The detectors were the same as in
Figure 14 . . . . . . . . . . . . . 104

21. Positron feeding spectra of 83Sr taken with the
7 cm3 Ge(Li) counter and the NaI(Tl) split
annulus detector. Spectrum A is a singles spec-
trum for reference. Spectrum B is the positron
feeding and double escape spectrum. Spectrum C
is the double—escape spectrum obtained with the
gamma ray collimated into the Ge(Li) detector
from an external source . . . . . . . . 105

22. Electron spectra obtained with an argon—
methane continuous flow proportional counter.
Spectrum A is the singles spectrum. Spectrum
B is the electron spectra in coincidence with

the x-ray . . . . . . . . . . . . . 111
23. Block diagram of the delayed coincidence

spectrometer . . . . . . . 115
24. Proposed decay scheme of 83Sr . . . . . . 118
25. Comparison of the energy levels of the odd—

mass strontium isotopes . . . . . . . . 127

ix

INTRODUCTION

A vast amount of experimental data have been
collected over the years in studies of the radioactive decay
of unstable isotopes by means ob beta and gamma ray
spectroscopy to provide information on the properties of a
large number of nuclei (1). Even so, large gaps in the
data still exist which hinder the nuclear theorist in the
construction of, and the testing of, consistent nuclear
models. This is partly the result of the fact that only
a few of the available states are populated in beta and
gamma decay because of the energy available and the selection
rules governing the decays (2). However, in a number of
cases, nuclear reaction experiments have complemented
these results, often giving information on the high energy
excited states not available to beta decay. But more
important, much of the data have been incomplete or
erroneously interpreted because the limited instrumentation
available to the experimentalist did not provide the
required energy resolution. This is particularly the case
for spherical nuclei (i.e., nuclei with small quadrupole
moments) in the medium mass region (70 i A i 150) where
the level structure has proved to be quite complex and

energy spacings very small (1).

In the deformed nucleus region of 150 i A :_190
and A > 220, it has been possible to formulate a nuclear
model which has had Spectacular success (3) in predicting
the level schemes for these nuclei. More accurate
experimentaldata hayetbeen available here, chiefly because
the highly converted nature of the transitions has enabled
their energy measurement with precision electron spectrometers.
Moreover, because of the success of the model, it has been
used as a guide in the construction of new decay schemes
for nuclei in this region.

For most of the isotopes, in the medium mass region,
the decay schemes GUT? unknown beyond the first one or two
excited states. This is especially true for those nuclei
whose half-lives were 5 1 day. Partly because of this,
very few model calculations have been performed for nuclei
in this region. Fortunately, the recent development of
the Ge(Li) detector and improved multi-channel analyzers
have wrought a great change in the situation for the beta
and gamma ray spectroscopist. Data can be recorded
relatively rapidly with energy resolutions that are nearly
an order of magnitude better than those previously
attainable. In addition, more particle accelerators
capable of accelerating a largerxmufirfimrof particles to higher
energies are becoming available. Hence, more complete and
more accurate systematic experimental studies can now be

made.

Davydov and Filippov have prOposed an asymmetric
rotor model of the nucleus to predict the level spacings
and transition probabilities of the excited states in
certain even—even nuclei (4). They have tested their
predictions with those medium and heavy mass nuclei for
which experimental data were available (4). In the regions
of deformed nuclei 150 i A :_190, and A i 222, their
calculations were found to be in good agreement with the
experimental data (4). In addition, good agreement with
experimental data was obtained for some nuclei in the
region 70 i A i 130, a region where nuclei are normally
considered to be spherical.

Marshalek, Person, and Sheline have shown theoretically
that this region has islands of deformed nuclei (5). The
regions are 74 i A :_80 (isotopes of arsenic and selenium)
and 120 :_A i 134 (isotopes of barium, cerium, and neodymium).
In addition, they suggest that the isotopes having 82 i A i 88
and 100 i.A :_112 are approaching regions of deformation.

In these mass regions, Davydov and Chaban have shown (6)
that the asymmetric rotor model predictions of energy and
gamma transition probabilities are in good agreement with

768e, 100Ru 106Pd 110 122

experimental data for , Cd, Te,

126Te, and 128X

3

e. It is possible then that the D-F model
may apply to other nuclei near these mass regions. In this
82

study, Kr, which is near one of the regions of possible

permanent deformation suggested by Marshalek et a1. (5)

was chosen to test the D-F model. The excited states of
this nucleus are strongly populated in the decay of
82Br.

0f further interest in this study is the examination
of the relationship between the level structures of the

82

nuclei Kr and 83RQ which differ by one proton. A simple
relationship should exist if the excited states arise from
the coupling of the single proton states to states of
excitation of the even-even 82Kr core. The excited states
in 83Rb are populated by the positron and electron capture
decay of 83Sr.

In addition, Talmi and Unna have made shell model
calculations (7) to predict the energy levels and spins of
the first few excited states of several Z = 38 or N = 50

83S

isotopes, including r. Since the experimental results
of the level structure of 83Rb should.imply, at least, the
ground state spin of 83Sr, it should be possible tijartially
test the calculations of Talmi and Unna for 838r.
The transitions from the decay of these two isotopes
have been studied with high resolution beta and gamma ray
spectrometers which are described briefly in Chapter 2.
The decay schemes constructed from these data are discussed
in Chapters 3 and 4.
Since comparisons of these decay schemes are made

with the predictions of the asymmetric rotor model of

Davydov and Filippov (4) and the shell model calculations

of Talmi and Unna (7), qualitative discussions of these
models and, for completeness, of the collective model (8)
are presented in Chapter 1. Also, the core—coupling model
is included as a guide in the comparison of the 82Kr and

83Rb level structures.

CHAPTER I

NUCLEAR MODELS

One of the primary goals in physics is to be able
to correlate theoretical formalisms with experimental
data. In the case of nuclear physics, the inadequate
knowledge of the nuclear force has rendered this a formidable
task. Nevertheless, a number of the properties of nuclei,
such as binding energy, level structures, magnetic moments
and quadrupole moments have been explained, at least
qualitatively, by some semi-phenomenological models (2).
Those models that are most pertinent to the present study

will be discussed very briefly here.

1.1. The Shell Model

 

Stimulated by the appearance of the so-called ”magic
nucleon numbers" (Z or N equal to 20, 8, 20, 28, (40), 50, 82,
and 126) where large discontinuities in nuclear binding
energy occurred, M. Goeppert-Mayer (9) and Haxel, Jensen,
and Suess (10) independently constructed a nuclear model
analogous to the atomic electron shell structure. In this
model, each nucleon is assumed to be moving independently
in an average potential due to all of the remaining nucleons.
This potential was picked to be intermediate between that of

an isotropic harmonis oscillator and a square well. In order

6

to generate the nuclear orbital energy spacings to give shell
closure at the "magic numbers" a strong spin-orbit coupling
term had to be added to the Hamiltonian. This had the effect
of splitting each harmonic oscillator level into two j = t +
1/2 and j = t - 1/2 levels which are (2j + l)— fold degenerate.
It was found empirically that the j = 2 + 1/2 levels lie
lower in energy than the j = t — 1/2. This then leads to
the required energy level spacings consistent with the "magic
numbers." The filling of the levels inside the shell must be
in accord with the Pauli principle for protons and neutrons
independently.

In the ground states, the nucleons are paired so
that the nuclear properties are determined by the last
unpaired nucleon. This has been found to be the case for
odd mass nuclei having one nucleon just outside a closed
shell. The model has failed to predict correctly the spins,
magnetic moments, and quadrupole moments for nuclei that
have several nucleons (holes) outside a closed shell,
i.e., those nuclei with only partially filled shells. This
is caused, in part, by the fact that the model cannot
predict the order of the level filling inside a closed
shell because the strengths of the spin-orbit coupling
and residual interactions cannot be determined accurately.
However, Mayer and Jensen have extended the application
of the model to include j—j coupling with some very simple

coupling rules (11). These rules require that: even—even

nuclei have zero spin and positive parity; in odd mass
nuclei, the ground state spin and parity are determined
by the odd numbered nucleons only; and these odd numbered
nucleons usually will couple their spins in such a way
that the total spin, J, of the nucleus is that of the
last partially filled orbit j.

It was found that most of the nuclei followed these
rules with a few exceptions in odd A nuclei where spins
of J = j - 1 have been observed. Exceptions have been

reported (1) for 776e, 793i, and 81Kr,all of which have

45 neutrons. It will be shown later that 838

r, one of
the nuclei studied in this thesis, is another exception

to the rule. 83Sr also has 45 neutrons.

1.2. Residual Interactions

 

The fact that Mayer and Jensen had to supplement
their independent particle model with coupling rules to
determine the ground state angular momentum for a given
nucleus indicates that nucleon interactions cannot be
completely specified by a potential well and spin—orbit
coupling. The energy degeneracy of the nucleons with
the same (nlj) quantum numbers can be partially removed
by extending the independent particle model to include
short range nucleon—nucleon residual interactions. When

this interaction is included, the Hamiltonian becomes

_ g _
o 3 £1. 1 +i§k Vik

where V1 is the residual interaction potential. All the

k
single particle configurations determined from the first

two terms in the Hamiltonian are couplied to give a set of
all the possible resultant angular momenta. The set of wave
functions so generated are, in general, too many to allow

an easy calculation to diagonalize the total Hamiltonian.

In lieu of this, the residual interaction has been
determined empirically for low mass nuclei.

The model has had some success in explaining the
features of the level structure of some light and medium
mass nuclei. For example, Kurath, using an interaction
potential determined from 6L1, has shown (12) that the model

is in good agreement with experiment for 10B. Also, Sweet,

92Nb using

Bhatt, and Ball have made calculations (13) for
a residual interaction determined from 92Zr and 93Nb which
are in excellent agreement with the experimental data.

However Elliot and Flowers, in extending the model to 19F
have shown (14) that the E2 lifetime of the 5/2+ state
calculated from the model is longer than that measured

experimentally by a factor of 4.

1.3. The "Talmi-Unna Model"

 

The residual interaction calculations have been
extended to other heavier nuclei which have a few nucleons
outside a closed shell. One such treatment has been
performed by Talmi and Unna (7) for nuclei having

N = 50 or Z = 38. Since one aim of this work is to test

10

some of their calculations, a summary of their treatment
of the shell model with residual interaction is presented
here.

In their analysis, a nuclear potential due only to
two-body effective interactions between nucleons is assumed.
The unknown matrix elements, including;those from
configuration interaction, which were taken to be the
same for all nuclei in the same subshell being filled, were
determined from experimental data.

Nine experimental energy differences which were used
were obtained from 89y, 87Sr, 86Sr, 853r, 91Nb, 93Te, and
9OZr to give nine equations involving six parameters to be
fit. These parameters were:

a = E — E
pl/2 g9/2

the difference between the single—proton energies in the
pl/2 and g9/2 orbits,

-1 —1

.. 61‘ 62>

which are the single neutron hole energy differences in the
pl/2 and g9/2 orbits. The other parameters arlse from the
effective two body mutual interaction and are taken to be
the same for the proton configurations and the neutron hole
configurations. These then are: the energy difference

_ _ 2 -2
between J - 2 and J - 0 states of gg/2 (or g9/2),

expressed by

11
y =V (gs/2, J = O) — V (ES/2: J = 2);

the interaction energy difference of the unperturbed

_ 2 2 . .
J -'0 states of g9/2 and pl/2 configurations given by
a = v (g2 J = 0) - v (p2 J = 0).
2 9/2’ 1/2’ ’

the non-diagonal matrix element of the effective mutual

interaction between the pi/2 and gS/2 states expressed by

2

V = <p1/2’

2
J = Olvlg9/2a J = O);

and finally the interaction energy difference in the three

I I 3 2
particle conflguratlon g9/2 or pl/2 gg/2 expressed by
6 = V (p g2 J = 1/2) — V (g3 J = 9/2 v = l)
3 1/2 9/2’ 9/2’ ’

where v is the seniority number.

The difference in the single particle energies taken
from 89Y and 87Sr were set equal to B and B' respectively.
The two and three particle configuration parameters, given
above, were determined from the diagonalization of two by
two matrices. For example, for 86Sr, the ground state

energy shift due to configuration interaction was obtained

from diagonalizing the matrix

1
28 + 62 V

V 0

12

The calculated energies thus determined from this analysis
were in good agreement with the experimental data. These
energies are listed in Table l which is taken from Talmi
and Unna's paper (7).

The experimental investigation of the states of
858r by Horen and Kelly (l5)indicates that the T—U level
predictions for this isotOpe are not in complete agreement
with the experimental data for those levels above the
first excited state. Experimentally, there appears to be
a preponderance of 7/2+ and 9/2+ levels. This discrepancy
could, in part, be due to insufficient experimental data
from which an insufficient number Of interaction parameters
were determined. These results may also indicate that the

nuclear states are due to different types of interactions.

1.4. The Unified Model

The experimental observation of large quadrupole
moments for some nuclei could not be explained by the shell
model. This is not surprising since the large quadrupole
moment could only arise from the collective motions of
several nucleons and departure from spherical symmetry, both
of which were ignored in the shell model. To account for
these motions and the possibility of nuclear deformation,
the "collective model" was proposed by Bohr (l6) and later
extended by Bohr and Mottelson (8).

In this model, the nucleus is considered in two

parts, the filled "core" and the nucleons in the unfilled

l3

 

mzoeom

 

33.0 mm.o I m\H + m\m mm
sm.o mmm.o + m\s + m\m mm a:
sm.o mmm.o I N\H + m\m smmm
HH.o mofi.o I m\H + mxm Haozmm
e:.o om:.o + m + o Aooeaoxo sonata on om
mo.m mma.m + m + o A.om ossosmv snow
H.H mso.fi + m + o wmsmw:

em

sm.o wwm.o u m\H + m\m mmammm
mo.o mam.o + m\m I m\H mmsmm

UopmHSono Hmpcoeflnooxm oonoofimcoo mao>oq mSoHosz

>oz CH monopoemfim mwposm no mcflom

 

 

 

 

 

 

 

neoconomefim mwnocm oopmHSOHmo ocm Hmpsoeflpooxm

H mgm<9

14

shell. The core is considered to be a deformable liquid
drop in interaction with the nucleons in the unfilled
shell. The motions of the nucleons can now be treated

in much the same way as the surface motion of a classical
liquid drop—-except, of course, the nucleon motion must
be quantized. A brief summary of the development is
presented here which follows the more detailed treatment

by Preston (2).

1.4.1. The Collective Model

 

The nuclear surface of any general shape may be
represented by
R=R[l+2 z 0!. Y“ (o,<1>)]
O A=o u=-A Au A
where e and c are polar angles with respect to arbitrary

axes. The collective motions are determined by letting

dMl vary with time. The kinetic energy is of the form

T=(1/2>Z B [a |2
A u A Au
9R:
where BA is BA = —;—, the mass parameter. The potential

energy, in terms of the dMl is

v =(l/2)ZI 0 lo I2
Au A Au

where CA is related to the surface tension by

1 2
C§)=SRO(A—l) (1+2).

15

If the liquid contains electric charge, the Coulomb

energy is reduced by the distortion so that

 

_ (l) (2)
CA ' CA - CA
where
c<2> = 3 22.2 1.1.1.
A 2 11 R0 2A + 1

The frequency of oscillation associated with the axu is

C, 1/2
U) = .——-o
A BA
The values of A = 0 or 1 are of no interest here since

w would be zero. The collective states will have the
excitation energies E n,~no,, where n, is the number of
phonons of order A. The state with nA = l is (2A + 1)
fold degenerate. Only low values of A need to be
considered since'nwA is a rapidily increasing function
of A. The first excited vibrational state would correspond
to one A = 2 phonon and therefore be a 2+ state. The 3—
state formed by one A = 3 phonon would have about the
same energy as the degenerate 0+, 2+, or 4+ state formed
by two A = 2 phononso

An easy test to see if nuclei exhibit collective
vibrational levels would be to compare the ratio of the
energies of the first and second 2+ states which should
be about 20 A large number of nuclei, particularly those

with 40 :.N i 80,do display vibrational characteristics (2).

16

Negative parity states can arise from the
combination of a A = 2 and A = 3 phonon which would give
five states from 1— to 5-. These states lie above the

3_ state formed by the A = 3 phonon.

1.4.2. Axially symmetric nuclei

 

For quadrupole shapes (A = 2) the expression for

the nuclear surface may be rewritten as

R = R0 [1 + z
u

P t v
a2u Y2 (0 o )]

where e' and ®' are the polar angles with respect to the
body axes.
Then

1.1 \)
2:212u Y (e', 6') = 2 Y (o,¢).

2 ..O‘2u 2

Since the products of the moments of inertia are zero,
a21 = a2_l= 0 and a22 = a2_2. Two distortion parameters,

8 and Y, are defined such that

8.20 = B COS Y

and

l 8 sin
t2 Y

a'22

The quantity 8 is the measure of the total nuclear

deformation since

2 I2_ 2 2

lug“

17
Hence the potential energy becomes
V = (1/2) C82.

The deviation, 6R from spherical symmetry in terms of

k,

B, and Y is

_ 5 2n
ORk-F-Tr-ROBCOS(Y-k-3-)

where RO is the undeformed nuclear radius and k equals

1, 2, or 3 and refers to the body axes. For fixed Y and

a time varying B (B-vibrations) the nucleus maintains its
symmetry axis; however, for a varying Y (y—vibration) the
nucleus loses its axial symmetry. The kinetic energy

can be put in terms of B and y, and becomes
'2 2 .2 3 g 2
T -(l/2>B (B + B y ) + 1/2kgl k wk

which is separated into vibrational and rotational parts.

The Hamiltonian is

2

k
._—i + 1/2 C 82
1 23k
where Lk is the component of angular momentum along the

k axis. There are three rotational constants of the

H = H + H +
B Y k

IIMUO
t—l

motion, J, M, and K determined by

2

L = J(J+1)
LZ = M
K

r‘
w
II

18

The motion separates into a vibrational part, f(8), g(Y)

and a rotational part and the energy correspondingly to

 

t t’ .
EVib + Erot° The ro a lonal part is
_ 2 2 2 2
Erot -‘n [J(J+l) — K] +‘n :
281 2 3

For axial symmetry, 9 = 0and hence k = 0 and

3

_ 2
El,0t — -h_(oJ(J+l)

2 5\

Only states of even J are possible for the axially
symmetrical case since the wave function 1JMK> = 0
vanishes for K = 0.

The model predicts spins of 0, 2, 4, 6, etc. of
even parity for the first few excited states with energies
proportional to J(J+l) for the rotational band. The
energy ratios are Eu/E2 = 3.33 and E6/E2 = 7. Many nuclei
in the region 150 i.A i 190 and A> 220, where large
nuclear deformations are known to exist as evidenced by
the large quadrupole moments, exhibit level structures in
agreement with these spin sequence and level spacings (1).

In this treatment of the collective motion, the
condition that K = 0 requires that the expectation value,
so, of B is large and that <(B—BO)>2 is small. Also the
expectation value of y is zero. This means that the
nucleus possesses a permanent axially symmetric deformation

and,as mentioned previously, excludes odd spin values in

19

the rotational band. Yet, the level structures of many
nuclei in these regions have been found (1) to have odd
spin states which may arise by a Y vibration to an

unsymmetrical excited state or by unsymmetrical ground

states.

1.4.3. The Asymmetric Rotor Model

 

The asymmetric rotor model proposed by Davydov and
Filippov (M differs from the collective model in the
following way. They use the general Hamiltonian with
three unequal moments of inertia. However, these moments
are considered to be constant for an intrinsic state through
the use of the adiabatic approximation. In this
approximation, the motion of the outer nucleons is assumed
to be much faster than the motion connected to the changes
in B and Y. Hence, these parameters are treated as fixed
with the values of Y restricted to 0°: y: 300° The
parameters B and Y are the same as defined in section
1.4.2.

The level structure predicted by this model now
includes odd spin states. The states predicted are 0+,
2+ (two states), 3+, 4+ (three states), 5+ (two states),
5+ (four states), etc.

The expressions for the level energies in units

of ‘n2 are, for J = 2

4B8z

 

20

 

2

 

9(1 — l - 8/9 sin 3 Y)

sin2 3Y

 

El<2>

 

9(1 + J1 - 8/9 sin2 3 Y)

Sin2 3Y

E2(2)

for which E2(2)

: 2 depending upon Y.
El(2>

For J = 3

2 = 18

E(3) = ._______
1 sin2(Y- %1 A) sin2 3v

A

 

ll MUO

2 to the energy for

Comparisons of the energies for J

J = 3 gives

31(2) + E2(2) E<3>

The three energy levels for spin 4 are determined by the

roots of the cubic equation

3 90 2 48 . 2 640
E — ———————-E + (27 + 26 Sln 3v) E — X
sin2 3y sinu 3y sinu 3v

(27 + 7 sin2 3v) = O

and for J = 5, the two energy levels are

 

2

 

(45 + 9‘\9 - 8 sin

Sin2 3Y

For'y equal to zero degrees, the energy levels are the
Seune as those for the permanently deformed axially

Ssnnmetric nuclei described in section 1.4.2.

21

A good test of this model is to compare the
reduced transition probabilities for the transitions
between the two spin 2+ states and the ground state.
Other models have assumed that these spin 2+ states are
one and two phonon oscillations of the nuclear surface
which make the transition between the 2nd spin 2+ to
the ground state hard to explain unless there is a
breakdown in the oscillator approximation. As was shown
in section 1.4.2., the matrix elements for d2p will be
non-zero for only those states that differ by one
phonon. Hence, the transition between the 2+, 2 phonon
state to the ground state would be forbidden. If,
however, the two states are assumed to be rotational
levels, the reduced transition probabilities can be
expressed in terms of the parameter, Y.

For the various transitions, these are given by,

2

 

 

 

 

 

 

 

 

13 (E2; 21 ——>0) =(l/2>(l + 3-2 sin 3y
9-8 sin2 3y
B (E23 22 $0) =(1/2)(1 .. 3'2 Sin2 3v
9-8 sin2 3y
. 2
B (E2; 22 921) =(10/7) Sll’l 3y
9-8 sin2 3Y
. 2
B (E2; 3 922)=(25/28)(1 + 3-2 Sin 3!
49-8 sin2 3y
- 2

49—8 sin2 3Y

 

22

expressed in units of e2 O: , where QO=3ZR28 is the

16 n 45 n

intrinsic quadrupole moment.

 

The ratios of the reduced transition probabilities
can be easily obtained from the experimental data.

The model has had mixed success when compared to
experimental data for those nuclei where it is expected
to be applicable. For example, the level spacings and
reduced transition ratios predicted (4) by the model are
in good agreement with those determined from experimental

data for llqu, 152Sm, 182W, 192Pt, and 238

76Se, 122Te, and 126Te the reduced

Pu. Yet, for
some nuclei, such as
transition ratios predicted (4) by the model are not in
agreement with experimental data. Davydov and Filippov
interpret these discrepancies as arising from a breakdown
of the adiabatic approximation for these nuclei (4).
Davydov amiChaban (6) have extended the model to
allow for violations of the adiabatic condition with the
introduction of a "nonradiabaticity” parameter, u. This

parameter is defined such that

u =.
,l l 2
CB 80

where C is the elasticity constant, B is the mass

 

parameter and Bo is the equilibrium value of B. As a

result, the parameters BKJ and CKJ contained in the

23

potential energy operator of the Hamiltonian are now
functions of u. The energies thus determined depend
only upon the ”non—axiality" parameter Y,and the "non-
adiabaticity" parameter,u. The reduced E2 transition

probabilities are

B(E2; JK ’9 J'K') = Ba(E2; JK ——> J'K') s

where Ba(E2; JK ——€5> J'K') are the reduced transition
probabilities computed in the adiabatic approximation

and S is the correction factor which accounts for coupling
between rotation and vibration of the nuclear surface.

This correction factor, S, is expressed by
-2 2
S = B ' '
. |<JKUIBIJ K.”

Davydov and Chabin show (6) that for u:0.5 the factor S is
approximately unity. Hence, the reduced E2 transition
probabilities are essentially the same as for those nuclei
which have u: 0.50

Klema, Mallmann and Day (17) have evaluated the
energy state predictions of this model for a number of
nuclei, including 82Kr. The predictions for those nuclei for
which u: 0.5 were found to be in good agreement with the

experimental energies.

1.4.4. The Core Coupling Model

 

The core coupling model may be thought of as an

extension of the collective model to odd A nuclei. In

24

this scheme, the motion of the odd particle is coupled to
the collective motion of the even-even core. As a result
of this coupling, it is expected that the resulting level
structure should exhibit characteristics similar to the
even—even core, but modified by the single particle
motion. In other words, one would expect the low lying
single particle states to have collective states built
upon them.

The core, for simplicity, is considered to be all
of the paired nucleons. The strength of the particle—
core interaction will certainly be a function of the
nuclear deformation, weak for small 8, Y deformations
near spherical nuclei, and strong for large nuclear

deformations.

1.4.4.A. -Weak Coupling, Spherical Nuclei.——For
nuclei near closed shells the interaction can be treated

by perturbation methods. The Hamiltonian is written as

H = H + H °+ H.
c p int

where HC is the collective Hamiltonian of the core, Hp
is the spherical single particle Hamiltonian. The

is

interaction term, Hint

_ _ u
Hint — k<r>Ai a,“ YA (so)

where dMJ are the distortion parameters described in
section 1.4.1. and k (r) is the coupling parameter.

25

The states of the uncoupled systems are formed by
the vector addition of the single particle state Ijm>
of angular momentum j with the collective state |NR>
of N phonons and angular momentum R. The Hamiltonian is
then diagonalized to determine the states as a result of
the coupling.

In order for the perturbation to be applicable it

is necessary that
5 1/2 k
16 n (th)l/2

<<1

 

where'nw is the phonon energy. If as in section 1.4.2.,
we restrict the nucleus to quadrupole shapes, the quadrupole

terms a restrict the coupling of the ground state to

2u
only those states with one 2+ phonon present. The matrix
elements involving the second order harmonics Y; will be
non-zero only if Aj i 2 and no parity change. Hence only
the single particle states of the same parity and Aj: 2
will mix. Lawson and Uretsky have shown (18) that the
center of gravity of a multiplet of core—particle states
in odd mass nuclei should occur at the same energy as
the corresponding collective state in the adjacent even-
even nucleus.

DeShalet has made calculations (19) for the core—
particle interactions for j=]/2 particle states coupled

to 2+ phonon level for nuclei in the medium and heavy

mass region. His calculationS,in general, are in good

26

agreement with the experimental data for those nuclei

used to test the model.

1.4.4.B° Strong Coupling, Deformed Nuclei.—-For
nuclei with large deformations, the perturbation method
described in section 1.4.4.A. can no longer be applied.
The procedure is to use the single—particle Schrodinger

equation,

A A A

Hp to = [T + V(8,Y; r, 2, S] w, = Ea (B,Y)¢a

where d represents the appropriate quantum numbers. The
Values of the parameters of 8 and Y are determined which
minimize the total particle energy. The calculations
may be simplified some what with certain assumptions.
These are: that the adiabatic approximation is
applicable; that the nucleus maintains axial symmetry;
and that there is only one nucleon outside the core.
Nilsson has made extensive calculation (20) for the
single particle states in deformed nuclei.

1.5. The Experimental Determination of the
Properties of Nuclear States

 

 

The nuclear models described in the previous sections
of this chapter predict the energies of nuclear levels
as well as their spins, parities, and transition
probabilities between states. Transition probabilities,
internal conversion coefficients, and gamma-gamma

directional correlation coefficients are all functions of

27

the change in angular momentum carried off by the

radiation and, in the case of transition probabilities

and internal conversion coefficients,also upon the

change in parity. Hence, the spins and parities of the

states producing the transition may be determined, though

not always uniquely, from these properties provided the

spins of one of the states is known from other experiments.
Since the transition probabilities, internal conversion

coefficient, and directional correlation coefficients have

such an important role, a brief description of the

selection rules and other properties governing them will

be presented here.

1.5.1. Beta Selection Rules

 

The transition probability for the beta decay from
an initial state, i, to a final state f, in the daughter

nucleus is given by

p

max
W(i > f) = g2/Tr3 g p2 q2 FO(:Z,A,P) x
o

 

s (—3-=.)2

1’1 dp

where g is a coupling constant, p is the electron

momentum, q is the neutrino momentum, F0 is the Fermi
function, A and Z are the mass and charge numbers of the
daughter nuclide, Sn is a shape factor, and n is the

order of forbiddeness. The plus sign is used for negatrons

and the negative sign for positrons. For most cases, the

28

shape factor may be set equal to one. A quantity
independent of the coupling constant is easy to determine
experimentally. This quantity is the reduced half-life,
ft where f is given by

p

f= $112chO dp

o
and t is the half life of the decay. The reduced half
life, ft, should be approximately the same for the
same degree of forbiddeness, independent of the decay
energy and of the nuclear charge.

Nomographs have been prepared (21) from which the
value of log ft can be determined from the beta decay
end-point energies and the half-life of the decay. The
degrees of forbiddeness associated with the log ft
values have been determined empirically. The accepted (22)
values are: for odd A, if log ft i 4.0 then AJ = 0,

An = 0; for Z < 80, if log ft i 5.8, the transition is
allowed (AJ = 0, 1 An = 0); if 5.8 i log ft i 10.6, the
transition is allowed or 1st forbidden (AJ = 0, or 1,

An = yes); if 10.6 i log ft 1 15 the transition is allowed,

first forbidden or second forbidden (AJ 2, or 3 An = no);

yes) if log ft

a beta transition is unique (AJ = 2, An

1 7.6 and if the Fermi plot has appreciable curvature

corresponding to a shape factor (p2 + q2)= Sl'

29

1.5.2. Gamma Ray Transition Probabilities

The transition of a nucleus in a state, i, to a
state, f, may occur through the emission of a photon
with an angular momentum, L (:1). This angular

momentum can be any of the values

Iii-ifliLiji

+if.
however, only those gamma rays with the lowest possible
L value are usually observed. In addition, gamma rays
with admixtures of angular momentum of L, and L + 1 have
also been observed. The character of the radiation will
be magnetic or electric 2L pole order depending upon
whether An is yes or no.

The transition probability for the gamma emission
is given by

2

L[(2L+ 1):: ‘H

W(c,L) =

 

 

where 0, represents the electric or'magnetic character of
the transition. The quantity, B(oL) is the reduced
transition probability, and is predicted by the various

nuclear models.

1.5.3. Gamma—Gamma Angular Correlations
The angulardistributionsof the emitted gamma rays
are functions of the multipole order characterizing the

transition. Unfortunately, the nuclei are randomly

30

oriented and, unless some means is available to align the
nuclei, the measured distribution will be isotropic.

When gamma rays are found to be in cascade, coincidence
counting techniques, which are described in Chapter 2, can
be used to measure only those gamma rays from similarly
aligned nuclei. The nuclei must be placed in an
environment which will not perturb the orientation of the
nuclei during the emission of the gamma rays. For life—
times of T i 10_12secs this condition is always fulfilled.
For life—times greater than lO-lBSecs the nuclei can be
placed in liquid solution to fulfill this requirement.

In this method, the angular distribution function
can be expressed (23) as

max

w<e) = 2 A P (e)
k=0 k k

where the coefficients Ak are functions of the spins of
the initial, intermediate, and final states and the
multipole order of both gamma rays. They can be

expressed as a product.

A = A (J. J, Ll, 61)Ak2 (j, Jf, L2, 82)

k kl 1’
Only even values of k occur kmax = min (2J, 2L1, 2L2) and
is usually never greater than 4. Akl is the coefficient for

the first gamma ray whereas A is the coefficient

k2

for the second. Since its not unusual to have

31

admixtures of L, and L + l multipole transitions, the
51 in the coefficient is the mixing ratio of the
admixture.

It is possible that there may be an unobserved
transition intermediate to the gamma rays of interest.

In this case, a correction (24) must be made for the

attenuation of the distribution in the form of

Ak = Ak (1) Uk (2) . . . . Uk (n—l) Ak (n)
for n gamma rays. The Uk'sare the coefficients for
the unobserved gamma rays. If the unobserved transition

is not pure then, in terms of the mixing ratio, 6, for

the unobserved transition,

Uk(L) + 62 Uk (L + l)
U' =
k

 

l + 62

The theoretical A coefficients can be calculated

k
from parameters that have been tabulated (21,23). In
some cases, the theoretical coefficients, Ak have been
tabulated (25) for various combinations of spin sequences
and mixing ratios. However, in comparisons of the ex-
perimentally determined coefficients with the theoretical
ones, it is not always possible to determine uniquely the
multipole order of the transition as there can be
considerable overlap depending upon the mixing ratio.

Some of the ambiguity can be removed if the mixing ratios

are independently determined.

32

1.5.4. Internal Conversion Coefficients

 

The internal conversion of an orbital electron is
in competition with the gamma emission for the transition
of the nucleus from state i, to state f. The branching
ratio between the two processes is defined as the internal
conversion coefficient. These coefficients are functions
of the change in angular momentum and parity in the
transition, the nuclear charge, and the energy available
for the transition. The theoretical coefficients for
given AJ and An as a function of Z and energy have been
tabulated (26) for K, L, and M shells. Here again it is
possible to determine AJ and 6 through the comparison of
experimental values with those of theory. These
determinations, used in conjunction with the angular
correlation data and transition probabilities, help to
remove some of the ambiguities introduced through a
single measurement.

The values of AJ and An determined in this way
are model independent. Hence they supply valuable
information with which to test the success of a particular

model.

CHAPTER II
APPARATUS AND EXPERIMENTAL PROCEDURES

2.1. The Gamma-Ray Spectrometer
2.1.1. Singles Experiments
In the early stages of this investigation, the gamma

ray spectra of both 82Br and 83

Sr were recorded with 7.6
cm by 7.6 cm NaI(Tl) scintillation detectors

mounted on EMI 95788 photomultiplier tubes. The pulses
from these tubes were electronically coupled through
Cosmic Model 901 linear amplifiers to a Nuclear Data
150FM 1024 channel multi-parameter pulse height analyser.
The energy resolutions of these detectors were each

= 9% for the 661 keV photon from 137Cs.

Later, the NaI(Tl) detectors were replaced by the
newly developed lithium drifted germanium detectors
[Ge(Li)] with sensitive volumes of l to 7 cm3. A Tennelec
Model 1000 preamplifier and this system gave resolutions
from 3 keV to 4.5 keV for the 661 keV photon from 1370s.
This greatly improved resolution facilitated gamma
ray energy measurement giving precisions which vary from
i 0.5 to i 1.0 keV. The energies were measured from
calibration curves determined from least squares fitting

the peak centroids of well known gamma ray transitions

33

3A

to a quadratic equation after the background had been
subtracted. The background was determined by making
a third order fit to counts in channels adjacent to
the high and low energy sides of the peaks. The MSU
CDC 3600 computer was used to make these calculations.
The calibration gamma ray energies (27) are listed
in Table 2.

The relative intensities of the gamma rays were
determined from experimentally determined efficiency
curves (28).

2.1.2. Coincidence Experiments--
NaI(Tl) Detectors

 

Knowledge of the gamma ray energies and relative
intensities alone is not sufficient information with
which to construct a decay scheme. Coincidence experiments
were used to determine those gamma rays that were in
cascade. For these studies, a conventional fast—slow
transistorized multiple coincidence unit, Cosmic Model
801, was used to provide the coincidence gate to the
multichannel analyser. The resolving times were variable,
but were usually set to 2T2 50 nsec.

Two 7.6 cm by 7.6 cm NaI(Tl) detectors, each
enclosed in a graded lead cylinder, were used as the
gamma detectors° Each crystal was usually placed 10 cm
from the source with the crystal axes at 90°. This

minimized coincidences due to crystal to crystal scattering.

35

Table 2.——Gamma ray calibration
energiesa.

— ;—
I

 

 

Source Energy, keV
1311 80.16u
l23mTe 159.000
1311 28u.307
1311 36u.u67
83Sr 511.006
1370s 661.595
6OCO 1173.226
60CO 1332.u83
ThC"(DE) 1592.u6
881 1836.2
ThC" 261u.u7

 

aReference 27.

bErrors in thegg energies are
0.1 keV except for Y which is i
0.3 keV.

<

36

The entire detection system was enclosed in a Styrofoam
box where the temperature was controlled to :_0.5° C.
This facilitated control of the gain stability to better
than i 0.25%.

The multi—parameter feature of the multi—channel
analyser was employed in a 32 x 32 channel mode to record
gamma—gamma coincidences and directional correlation
spectra. This enabled the correlations and coincidence
spectra of several gamma rays to be recorded simultaneously.

The equivalent chance spectra were simultaneously
subtracted by utilizing a second identical (except
delayed) coincidence circuit in parallel with the first (29).
The delayed coincidence output was coupled to the external
subtract input of the 102A channel analyser. The resolving
times for both coincidence circuits were monitored and
matched to within 1%.

For the directional correlation measurements on
the 82Br decay,an additional graded lead cone was placed
over the front of each NaI(T1) detector. The source,
in liquid fornn was contained in a thin wall Teflon
cup that was symmetrically located 11 cm from each
crystal. The dimensions of the Teflon cup were 0.3 cm
diameter by 1 CH1 with a wall thickness 0.08 cm. The
coincidence counting rates were measured in 45° increments
from 90° to 270° with 100 minute time intervals at each

angle. It has been shown by Reich et al;_(30) that this

37

method can give as accurate correlation functions as
those determined with smaller angle increments. The
singles counting rates in the moveable detector were
measured before and after the coincidence runs at each
angle. As a result of measuring the coincidence counting
rate in the symmetrical angular sequence, and the
division of the coincidence counting rate by the sum of
the singles counting rates, a first order correction is
obtained for source decay and geometrical asymmetries.
Comparisons of the singles counting rates at 90° with

the counting rates at 270°,and the counting rates at 135°

with the counting rates at 225° indicate that this

a
correction is good to within : 0.5%. Each directional
correlation measurement was repeated; and, in one case,
the measurement was repeated with 30° increments. The
correlation functions determined from the data taken at
A5° increments were in excellent agreement with those
determined from the data taken in 30° increments.

2.1.3. Coincidence Experiments——
NaI(Tl) and Ge(Li)

 

 

The energy spacings between many of the gamma rays

83

from the decay of Sr were very small. Because of this,

the coincidence data recorded for this isotope with the

NaI(T1) detectors were next to impossible to interpret.
83S

Therefore, all of the coincidence experiments for

3

I"

were repeated using the 7 cm Ge(Li) detector in place of

38

one of the NaI(Tl) detectors. This did not completely
solve the problem since the coincidence gate provided

by the NaI(T1) detector necessarily included two or

more gamma rays and many underlying Compton photons.
However, a consistent interpretation could be obtained
by quantitative comparisons of the different coincidence

spectra.

 

2.1.A. Anti—Coincidence Experiments

The small volume of the Ge(Li) detector and the low
Z of the germanium give rise to a relatively larger
Compton background in the gamma ray spectra recorded with
these detectors than in those spectra recorded with NaI(Tl)
detectors. Therefore, it is possible that low intensity,
low energy transitions are masked by the large number of
Compton photons from the more intense higher energy gamma
rays. In order to reduce this large Compton background
in the gamma ray singles spectra, an anti—Compton
spectrometer (31) was utilized. For this purpose, the

3 Ge(Li) detector was inserted into a large split

7 cm
annulus NaI(Tl) detector. The annulus was two and one
half inches thick and eight inches long with an outside
diameter of eight inches. Each half of the annulus was
optically isolated from the other half. Three RCA 8053
photo tubes were optically coupled to each half of the

annulus. The Compton scattered photons from the Ge(Li)

detector are very efficiently detected by the annular

39

NaI(T1) detector. The output pulses from this detector
are then used to provide an anti-coincidence gate to
the multichannel analyser. Therefore, those gamma ray
events detected in the Ge(Li) detector that are in
coincidence with those detected in the annular NaI(T1)
will not be stored by the analyser.

The Split annulus NaI(Tl) detector was also used
to provide some of the coincidence gates for coincidence

83S

experiments with r.

2.2. The Permanent Magnet Beta-ray Spectrometer

 

Three flat-field 180° permanent-magnet betarray
spectrometers were used to record the internal—
conversion electron spectrum for 828r. The magnetic
field strengths of these spectrometers provided energy
ranges 0 to 150 keV, 0 — 900 keV, and 0 to 2000 keV,
respectively (32).

The source was lined onto aluminized mylar film
with a standard drawing pen. The source strength of those
used in the high energy spectrometer were estimated to be
several millicuries. Photographic plates were exposed
to the sources in the spectrometer from four to eight
hours in the low—energy spectrometers, and for one to
two half-lives in the high—energy spectrometer. The

source in each spectrometer was followed for five half-

lives.

A0

The electron lines on the photographic plates were
measured with a low-power traveling microscope. The
least count of the vernier scale was 0.001 cm. Each plate
was read by three different persons. The energies of the
internal-conversion electrons were then determined from

the average scale reading made by the three individuals.

CHAPTER III

TRANSITIONS 1N 82Kr

The transitions in 82Kr following the beta decay

of 82Br have been studied by several investigators over

the past decade (33—38). Lu, Kelly, and Wiedenbeck (33),
using Nal(T1) detectors and single channel pulse height
analyzers,identified gamma rays of 555, 619, 698, 762, lOAO,
1320, and 1A75 keV as belonging to 82Kr. They constructed
a decay scheme for 82Br from the results of gamma ray
summing experiments. Later, Waddell and Jensen (3“)
reported gamma rays from the decay of 82Br essentially

in agreement with Lu et al.; however, their decay scheme
that was constructed from gamma—gamma coincidence
measurements was an inversion of the one proposed by Lu
gt_al. The decay scheme proposed (3A) by Waddell and
Jensen is shown in Figure l. The location of the first
excited state at 777 keV has since been substantiated (39)
by Coulomb excitation experiments by Heydenberg. The

spins and parities shown on the decay scheme were assigned
as a result of gamma-gamma angular correlation and internal
conversion electron measurements (3A). The electron data

were recorded (3A) with an intermediate image electron

spectrometer for which the resolution was nominally 3%.

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N. Benczer-Koller (35) later repeated the angular
correlation and internal conversion measurements. These
results are in agreement with those of Waddell and Jensen.
Hultberg and Hedgran (38),using an iron core n /72—
electron spectrometer, have reported the accurate
measurement of the transition energies. Dzhelepov, Eliseev
Prikhodtseva and Kholnov (37) made use of an external
converter to measure the high energy portion of the gamma
ray spectrum with an electron spectrometer. In addition
to all the previously reported transitions, they found
transitions at 16A8 and 1780 keV but were not able to
place them in the decay scheme.

The ordering of the 828—10AA keV cascade in this
decay scheme had been ambiguous with the only supporting
evidence for the placing of the state at 1821 keV being
the observation of weak coincidences of two gamma rays
at 250 and 350 keV with the 1A75 and 55A keV photons.
These results were reported by Duby, Mandeville, and
Rothman (36). More recently, Simons, Bergstrgm, and Anttila
have reported angular correlation coefficients (A0) for
832-104A, lOAA—777, and 832—777 keV gamma ray cascades
and conclude that the ordering of the 828-10AA keV gamma
ray cascade is such that the placement of a state at 1821
keV is correct.

In addition, Kennett, Webster andPrestwich have

reported (Al) finding coincidences between the 16A8-777

44

and 1648 -- 220 keV gamma rays and thereby place a state
at 2429 keV.

The present investigations were undertaken to test
the above energy level diagram and spin assignments and
to examine the characters of some of the excited states
prior to the reports of Simons et_al., (40), and Kennett
et al., (41). Of special interest was the 4- state at
2648 keV. No corresponding state has been observed in
adjacent even—even nuclei. The results of the present
investigation confirm many of the above described results.
Several additional weak transitions have been identified
which allow the placing of additional excited states in

82Kr.

3.1. Experimental Results

 

The 82Br sources for these investigations were

obtained from the Oak Ridge National Laboratory in the
form of KBr in water. The specific activities were
approximately 20,000 mc/gm at the start of the
experiments.

3Ll.l. The Internal Conversion
Electron and Gamma-ray Singles

Spectra

Examination of the internal conversion electron

 

spectra revealed several new, weak transitions in addition
to the previously reported strong transitions. The

energies of the corresponding gamma transitions that

45

were observed are summarized in Table 3. Also given
are the gamma-ray energies as determined from the
measurements using the Ge(Li) detector. These latter
measurements are discussed below. In addition to the K
internal conversion lines, L internal conversion lines
were observed for the 92.1, 554.1, 618.6, and 698.4 keV
transitions. The high energy transitions were observed
using a source of several millicuries that was exposed
in the spectrometer for approximately one half-life.

A typical gamma-ray singles spectrum measured with
the Ge(Li) detector is shown in Figure 2A, 2B, and 2C.
Portions of this spectrum are shown with linear scales
in Figures 3A, 3B, and 30. A stripped singles spectrum
taken with a 7.6 cm by 7.6 cm NaI(Tl) crystal is shown
in Figure 4 for comparison. The resolution of the NaI(Tl)

detector was approximately 8.8% for the 137

Cs photon.

All of the transitions that were observed in the internal
conversion electron spectrum, except that at 183.9 keV,
are resolved in the spectrum from the Ge(Li) detector.
This gamma—ray could have been easily masked by the high
back—scatter peaks from the strong transitions. The
singles spectra from the Ge(Li) detector also revealed
weak peaks at 274, 602, 952, 1085, and 1823 keV which were
not observed in the internal conversion electron spectra.

These weak transitions were observed to decay with the

same half-life as the strong transitions.

46

Table 3.--Energy and intensity measuremengg of gamma rays emitted in the decay of
Br.

 

 

 

Gamma Transition Relative Photon Previously Reported
Energies Intensities Resultsa
Internal
Conversion
Photon
Ge(Li) Electrons Photon Relative
E in keV E in keV Ge(Li) NaI(T1) Energy Intensity
96.3° 92.1 +_o.2 0.6
b 183.9 : 0.3 ?

222.9 221.4 1 0.3 2.8

274.2 + 1.0 "1.2

452.0 I 1.0 451.1 1 1.0 0.5

554.0 3 1.0 554.1 1 0.5 88.2 73 554.1 + 0.2 80
602.0 3 1.0 1.5 . I

618.9 1' 1.0 618.6 + 0.5 52.0 50 618.7 + 0.2 50
698.2 1 1.0 698.4 f 0.5 31.0 33 698.4 I 0.3 33
776.8 I 1.0 777.1 + 0.9 100.0 100 776.9 1' 0.2 100
827.7 f 1.0 828.0510 29.1 21 827.6 50.4 30
952.3 i 1.0 -
1010.2 i 1.0 1012.3 i 1.0 2.7
1044.1 + 1.0 1043.9 : 1.0 36.3 35.7 1044.0 i 0.2 35
1085.1 1 1.0 0.5
1318.4 I 1.0 1317.6 1 1.0 33.2 30 1317.1 i 0.2 32
1475.2 I 1.0 1475.1 + 1.0 19.9 22 1475.3 + 0.4 21
1651.6:1.0 1658 f 10 1.8 2.6 "
1782.6 r 1.0 1777 i 10 0.1
1822.6 I 1.0 0.03
1875.6 3 1.0 1872 1 10 0.07
1960.6 i 1.0 0.03

 

aEnergies and intensities were measured by the method of external conversion
with a double focusing B-spectrometer. Reference 36.

bThe low energy measurements with the Ge(Li) detector are not precise
because of non—linearity in low channels and the absence of well-known low energy
standards.

47

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1

l‘ l J 4% l l I

260 230 7/ 360 380
Channel Number

Figure 3a.——Weak gamma transitions observed with the Ge(Li)
detector: 425—630 keV. Note the scale breaks for both
coordinate axes.

 

51

 

 

 

 

 

 

 

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Figure 3b.-—Weak gamma transitions observed with the Ge(Li)
detector: 850-1100 keV.

l50

|00

Counts/Channel

50

52

 

 

 

 

 

 

 

 

 

 

 

 

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Channel Number

Figure 3c.-—Weak gamma transitions observed with the Ge(Li)

detector:

1675e2050 keV.

53

 

5250

200

 

 

 

.150
Number

 

 

 

 

 

 

 

 

IITIII I I TIIIIII I I TIIIIII
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10
Figure 4.—-Gamma singles spectra of 82Br taken with 7.6 cm by 7.6 cm NaI(Tl) detector.

54

The gamma-ray intensities, relative to the 777 keV
photon, were determined using photo-efficiency curves
measured by Auble for the Ge(Li) detector (28) and by
Heath for the NaI(Tl) detectors (42). The energies and
relative intensities are also summarized in Table 3.

Also listed in Table 3, for comparison, are the energies
and relative intensities of the transitions reported by
Hultberg and Hedgran (38). The results of the present
measurements are in excellent agreement with the

earlier data.

The gamma-ray energies determined from the Ge(Li)
detector are considered to be more accurate than the energies
determined from the internal conversion electron spectro—
meters. This is especially the case for the high energy
transitions since the electron spectrometer had not been
calibrated beyond 1500 keV and an extrapolation of the
calibration curve was used there. The energies of the
gammas that were determined with the Ge(Li) detector
were obtained from a calibration curve determined from the
well-known gamma-rays in 22Na, 137Cs, 60Co, and ThC"
in separate experiments. The calibration curve was
obtained by a least squares fit of a quadratic curve
to the positions of peak centroids as described in
Chapter 2. The energies determined in this way were
consistent to well within one keV for the strong

transitions for several different amplifier gain settings.

55

3.1.2. 'Gamma=gamma Coincidence

 

The gamma—gamma coincidence studies were made
with NaI(T1) detectors. It was not feasible to use
the Ge(Li) detector because of the poor efficiency of
the small volume Ge(Li) detector available at the time.
All of the previously reported coincidences
between the strong gamma-rays (34-35) were observed in
addition to coincidences for some of the weak transitions.
Only the coincidences between the previously unobserved

transitions will be discussed here.

3.1.2.A. Gamma Coincidences with the 1652 keV

 

Gamma-r_y.--The gamma spectrum in coincidence with the

 

1652 keV photopeak is shown in Figure 5. This spectrum
has been corrected for chance coincidences. The 1652

keV gamma-ray is seen to be in coincidence with the 221
keV photon and possibly with the 777 keV photon. The
peaks at 554, 619, and 1044 keV are the result of
coincidences with the sum of the 777 keV photon with
Compton scattered photons from the 1318, and 1475 keV
gamma-rays and with the 828 keV photopeak. Multi-parameter
coincidence Spectra of the 1500—1800 keV region with the
400-850, and 650—1200 keV regions verify these assertions.
In these measurements, the 554 and 1044 keV peaks were
enhanced relative to the 777 keV peak in the coincidence
spectra obtained when gating between 1550 and 1600 keV

while the 777 keV peak was enhanced relative to the 554

56

 

 

 

 

Counts (Channel

 

 

 

 

 

 

 

'04 I I I I I I I I I I I I I I
'- GAMMA‘ COINCIDENCES ‘
1” " WITH |652kev "
>
0
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0 50 . IOO I50

Channel Number

Figure 5.--Gamma spectrum in coincidence with the 1652 keV gamma
ray. Both detectors were 7.6 cm by 7.6 cm NaI(Tl) crystals.

57

and 1044 keV peaks in the coincidence spectrum obtained
when gating with the 1652 keV photopeak. It is therefore
concluded that the 1652 keV gamma-ray is in coincidence

with the 221 and 777 keV gamma-rays.

3.1.2.B. Coincidences with the 650 to 1200 keV
Region.——Coincidences in this energy region were also
studied in the two parameter mode of the 1024 channel
analyzer. The spectrum obtained with coincidences
between the 1044 keV photopeak and the 650-1200 keV
region is shown in Figure 6A. The 1044 keV gamma—ray
is seen to be in coincidence with the 1010 keV photons
in addition to being in coincidence with the previously
reported strong 777 and 828 keV transitions.

The coincidence spectrum measured between the 274
keV photopeak and the 800-1200 keV region is shown
in Figure 6B and, for comparison, the coincidence
spectrum between the 221 keV photopeak and the 800—1200
keV region is shown in Figure 6C. The 1044 keV gamma-
ray is seen to be in coincidence with the 274 keV gamma—

ray and the 221 keV gamma ray with that at 952 keV.

3.1.2.C. Coincidences with the 92 keV Gamma-ray.--
The gamma spectrum in coincidence with the 92 keV gamma-
ray is complicated because of the presence of interfering
coincidences with the underlying Compton background.

These interfering coincidences were minimized by subtracting

104 58

 

 

   

 

 

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0 IO 20 30 IO 20 30 40 IO 20 30 40

Channel Number
Figure 6a.-—Gamma spectrum between 650-1200 keV in coincidence

with 1044 keV photopeak. Both detectors were 7.6 cm by 7.6
cm NaI(Tl) crystals.

Figure 6b.--Gamma spectrum between 800-1200 keV in coincidence
with 274 keV photopeak. Both detectors were 7.6 cm by 7.6
cm NaI(T1) crystals.

Figure 6c.—-Gamma spectrum between 800-1200 keV in coincidence
with 221 keV photopeak. Both detectors were 7.6 cm by 7.6
cm NaI(Tl) crystals.

59

from the 92 keV coincidence spectrum a second coincidence
spectrum. This second spectrum was taken under identical
conditions except that 0.635 cm of copper was placed over
the face of the NaI(T1) crystal detecting the 92 keV
gamma. The difference spectrum is shown in Figure 7.

The 92 keV photon is thus seen to be in coincidence with
the 1783, 1475, 1085, 777, and 698 keV gamma—rays. The
excess of counts in the regions of 1318 keV is due to an
incomplete subtraction of a large 1318 keV peak that was
in coincidence with the underlying Compton background and

a small gain shift that occurred between the two runs.

3.2. The Decay Scheme of 8%h°

 

The proposed decay scheme for 82Br is presented in
Figure 8. The previously reported states (34—38) at
777, 1475, 1821, 2094, 2429, and 2648 keV are consistent
with the results of the present investigations. New
states have been placed at 2832, 2652, and 2560 keV.

The spin assignments shown in the figure are based on
angular correlation experiments that will be described
later.

Thecmfincidencasobserved between the 1010-1044 keV
gamma—rays are good evidence for the placing of a state
at 2832 keV. This placement is supported by the 184 keV
transition that was observed in the internal conversion

electron spectrum.

60

 

 

 

 

 

 

 

 

 

 

 

 

 

4
IO __ I I I
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WITH 92kev 7
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1
IOO . I50 200 250

Channel Number

Figure 7.--Gamma spectrum in coincidence with 92 keV photopeak.

This spectrum is the difference between the spectra obtained

.without and with a copper absorber over the 92 keV detector.

The detector used to obtain this spectrum was a 7.6 cm by 7.6

cm NaI(Tl) crystal. The detector used for the 92 keV gamma
was a 3.8 cm diam by 6 mm thick NaI(Tl) crystal.

61

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62

States are placed at 2652 and 2560 keV on the basis
of energy sums and the coincidence spectrum with the 92
keV transition shown in Figure 7. The intensities of the
photons in this coincidence spectrum support the proposed
level scheme. The energy difference of 4 keV between the
2652 and 2648 keV states is considered to be outside the
precision of the energy measurements of the gamma rays.

The state at 2429 keV, originally proposed by
Kennett et al., (41) is consistent with the coincidences
observed between the 221-1652 and 221-952 keV gamma rays.

The weak 452, 602, 1823, and 1961 keV gamma rays
that were observed in the Ge(Li) detector could not be
placed in the decay scheme with any consistency. It is
possible, however, that the 452 keV photon is a transition
between the 2648 keV state and one at 2196 keV that has
been observed (43) in the decay of 82Rb. The 1823 keV
gamma could conceivably arise from summing of the 1044.1

and 776.8 keV gamma rays in the detector as the source

was in contact with the Ge(Li) detector.

3.3. Directional Correlation Measurements

 

Directional correlations were measured for eight
of the prominent gamma—ray cascades. The experimental
procedures used forlflufiuemeasurements are described in
Chapter 2 .

Since most of the gamma rays were not resolved in

the sodium iodide detectors, the coincidence spectra were

63

taken in the two parameter mode of the 1024 channel
analyzer to facilitate the analysis of the data. The
32 x 32 channel mode enabled all eight correlation
combinations to be taken in a series of three successive
runs. The equivalent chance coincidence Spectra were taken
simultaneously as described in Chapter 2.

Table 4 lists the energy intervals to which the
32 x 32 channels were set for each run. The last column
is the energy interval used in the data analysis to
obtain the coincidence counting rate for each cascade.

3.3.1. Analyses of Directional
Correlation Data

 

 

All of the correlation functions were obtained by
fitting the data by least squares and were corrected for
the finite geometry of the crystal using the corrections
calculated by Yates (44).

In the analyses of the correlation functions to
obtain the Spin sequences and mixing ratios, the tables
of Taylor and McPherson were used whenever one of the
transitions was known to be pure (25). For the cases of
double mixtures the method of Arns and Wiedenbeck was
used (45). For the transitions of mixed multipole order
with unobserved intermediate transitions, the method
described by Fagg and Hanna was used (24).

The errors quoted include both statistical errors

and those resulting from corrections for interfering

64

Table 4.—-Energy intervals used for the analyses of the two
parameter angular correlation data.

32 x 32 channel

 

 

multiparameter
energy intervals Energy intervals
Cascade Detector 1 Detector 2 Detector 1 Detector 2
(in keV) (in keV) (in keV) (in keV) (in keV)
619-1475 1210—1510 425-715 1458—1491 618-636
554-1475 1458-1491 528—555
554-1318 1300-1333 528-575
828-1044 900-1410 650—950 1028-1060 827—845
1044-777 1028-1060 750-780
1318-777 1295-1337 750-780
698-777 625-930 675-950 760—780 670—690

828—777 760-780 830-850

 

65

coincidences. These errors were determined using a
pessimistic : 20% error in the relative intensities

listed in Table 1.

3.3.l.A. The 1318—777 keV Correlation.--The 1318—

 

777 keV gamma cascade is the only one for which there
are no interferences from Compton background or unresolved
photopeaks. The measured correlation function is

W(0) = 1 - (0.027 1 0.007) P
1318-777

2 (0) - (0.079 : 0.014) PM (0) (l)
The interpretation here is simplified because the first
excited state has been shown to be at 777 keV by Coulomb
excitation (39) and nuclear resonance fluorescence (46).

The Spins and parities of the ground and first excited

states of even nuclei are assumed to be 0+ and 2+,
respectively. The values for A2 and A4 in equation (1)

are consistent with the spin sequence* of 3(l,2)2(2)0

with a mixing ratio 6 = -4.40:0.9. This is the only

1318
reasonable spin sequence that agrees with the correlation

data.

3.3.1.8. The 698—777 keV and 828-777 keV
CorrelationS.--The photopeaks for the 698, 777, and 828

keV gamma rays are not resolved. However, according to

 

*The numbers in the parentheses are the multipole
orders, L, of the gamma transitions.

66

the decay scheme, the 698 keV gamma-ray is not in
coincidence with the 828 keV gamma—ray. For these reasons,
the two parameter spectrum was analyzed by dividing the
"gating channels" into three regions: (a) the low energy
side of the 698 keV photopeak, (b) the 777 keV photopeak,
and (c) the high energy side of the 828 keV photopeak.
The fraction of the 777 keV photons present in the Spectra
coincident with regions (a) and (c) can easily be subtracted
after normalizing the high energy side of the 828 keV
photopeak in the Spectrum coincident with the 777 keV
photopeak region, (b), to the high energy side of the
828 keV photopeak in the Spectra coincident with regions
(a) and (c). A small portion of the 828-777 and 698-777
keV coincidences are subtracted with this procedure.
However, these will be subtracted in the same ratio as
their respective correlation functions. The results will
then be the same as multiplying the correlation function
by a constant.

The resulting correlation function for the 698—777
keV cascade is

w<0) = 1 - (0.265 1 0.025) 22(0) + (0.249 1 0.038) PLI (0) (2)
698-777

The only Spin sequence that agrees with these data is

2(1,2)2(2)0 with a mixing ratio of 6698 = —3.0 i 0.7.

67
For the 828-777 keV cascade

W(0) = 1 + (0.149 + 0.029) 22(0) + (0.002 + 0.044) Pu(0) (3)
828-777 ' ‘

The analysis of this correlation function will be discussed
with those of the 1044—777 keV and 828—1044 keV correlation
functions (section 3.3.l.C.) since the ordering of these
transitions is uncertain. A number of spin sequences are

possible for the 828—777 cascade depending upon this order.

3;3.1.C. The 828-1044 keV and 1044-777 keV

 

Correlations.--A technique similar to that described in

 

section 3.3.1.B. can be used to obtain the 828—1044 keV
correlation function. Both the 828 and 777 keV transitions
are in coincidence with the 1044 keV gamma—ray. In
addition, the 777 keV gamma-ray is in coincidence with

the 1318 keV transition. The removal of interfering 777
keV coincidence in the 828 keV photopeak coincidence
spectrum can be achieved by normalizing the 1318 keV
photopeak in the 777 keV photopeak coincidence Spectrum to
the 1318 keV photopeak in the 828 keV photopeak coincidence
spectrum and subtracting. The resulting correlation
function for the 828—1044 keV cascade is

(0) 1 + (0.190 + 0.027) P2(0) - (0.028 + 0.047) Pu(0) (4)
828-1044 I "

68

The 1044-777 keV correlation function can now be
obtained from the Spectrum coincident with the 1044 keV
photopeak. The measured total angular correlation
function has the form

W(0) = aW(0) + bW(0) + cw(0) (5)
1044—777 828-1044 1318—777

where a, b, and c are constants which can be determined
from the decay scheme in terms of the relative

intensities given in Table 3. The correlation function
for the 1318-777 keV cascade is included Since the Compton
component under the 1044 keV photopeak will contribute to
the total 777 keV coincidences. The solution for the
1044—777 keV cascade is

W(0) = 1 + (0.095 1 0.018) P2(0) + (0.042 1 0.044) P4(e) (6)
1044-777

Since the order of the 828-1044 keV gamma rays are,
at this point, uncertain, the analyses of the correlation
functions given by equations (3), (4), and (6) were made
with the order of emission of the gamma rays arranged in
two successive orders: (a) 828-1044-777 keV and (b) 1044-
828—777 keV. The possible arrangements are Shown in
Figure 9. It is to be noted that in either case, one of
the three correlation functions will involve an unobserved

transition.

69

a

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70

For case (a), the correlation function for the
1044-777 keV cascade, equation (6), yields possible
spin sequences 4(2,3)2(2)0, with a mixing ratio 810““ =
0.02 i 0.03, and 5(3,4)2(2)0, with a mixing ratio of
510““ = 0.2 i 0.3.

The correlation function for the 828—777 keV
cascade, equation (3), is consistent with a Spin sequence
of 4(1,2)4[(2)]2(2)0 with a mixing ratio 6828 = -0.1 i 0.1.
The notation [(2)] indicates the multipole order of the
unobserved 1044 keV transition.

The spin sequence 5(3,4)2(2)0 for the 1044-777 keV
cascade was found to be inconsistent with the 828-777 keV
correlation function.

The correlation function for the 828-1044 keV

cascade, equation (4), yields a spin sequence of

. . . _ +0.09
4(l,2)4(2,3)2 With a mixing ratio 5828 — -0.02 —0.03 and
610““ = -0.1 i 0.1. This is the only spin sequence

consistent with the correlation function. This function
is independent of the order of emission of these
successive gamma rays.

Case (b) was found to give inconsistent results.
The 828-777 keV correlation coefficients satisfy spin
sequences of 2(1,2)2(2)0, with a mixing ratio 6828 =
—0.13 i 0.2, and 3(l,2)2(2)0, with a mixing ratio
6828 = -0.33 i 0.03; however, the 1044-777 keV and 828—

1044 keV correlation functions cannot be satisfied for

71

any possible combination of Spins based upon the 828-
777 keV cascade results. It is therefore concluded
that the ordering of the transitions is 828-1044-777

keV successively, namely case (a).

3.3.1.0. The 554-1318 keV Correlation.--The 554—

 

1318 keV correlation measurements contain coincidences
with the Compton background from the 777 and 1475 keV
photons. Corrections for these were made in the same
manner as in section 3.3.1.C. for the 1044-777 keV
correlation function. The correlation function for the

554-1318 keV cascade is found to be

W(0) = 1 — (0.065 1 0.012) P2(0) - (0.007 + 0.024) P4(O) (7)
554-1318 _

The correlation data are consistent with the spin sequence

+2.1

= 5.4 —1.4

of 4(1,2)3(1,2)2 with a = 0 i 0.1 and a

554 1318

or 61318 = 0.45 i 0.07. The Sign of 61318 is now changed
since the 1318 keV gamma-ray is now the second transition
in the cascade (47). The mixing ratio 51318 = 0.45 i 0.07

may be discarded Since it is not consistent with the
mixing ratio for the 1318 transition obtained from the
1318—777 keV cascade. This is the only possible spin
sequence that satisfies the correlation function.
3.3.1.B. The 554-1475 and the 619—1475 keV

Correlations.--The photopeaks of the 554 and 619 keV gamma—

 

rays are not resolved in the spectrum obtained in

72

coincidence with the 1475 keV photons. However, there
are no underlying Compton coincidences contributing.
Taking slices on the high energy side of the 619 keV and
the low energy side of the 554 keV photopeaks in the
multi-parameter spectrum, the coincidence data can be

expressed with the equations.

W(0) = all/1(0) + le(0)
554 Slice 554—1475 619-1475
and
W(0) = a2W(0) + b2W(0)
619 Slice 554—1475 619—1475
The coefficients a1, a2, b1, and b2 can be determined from

the relative intensities listed in Table 3. The coefficients

a and b are made relatively small by the choice of the

2 1
gating regions.

The results for the 619-1475 keV cascade is

W(0) = 1 + (0.138 : 0.031)P2(0) — (0.094 : 0'033)P4(O) (8)
619-1475

This correlation function is consistent with possible spin

sequences of 3(1,2)2(2)0 with a mixing ratio 6619 = -2.0
i 0.3 and 4(2,3)2(2)0, with the mixing ratio 6619 = -1.4
+ 0.1.

For the 554-1475 keV cascade, the result is

W(0) = 1 ~ (0.031 : 0.017)P2(0) + (0.028 : 0’029)P4(O) (9)
554-1475

73

If the mixing ratio is taken to be 6 = —2.0 i 0.03

619
for the unobserved 619 keV photons, then the spin
sequences consistent with the 554-1475 keV correlation
function is 4(1,2)3[(l,2)]2(2)0, with mixing ratio

655“ = 0.0 i 0.2. This spin sequence is in good agreement
with the results obtained in section 3.3.1.D.

3.3.1.F. The Remaining Correlation Functions.--A

 

brief attempt was made to measure the four angular
correlations of the 554-619, 554[619]698, 619-698,
619E698]777 keV cascades. The resolution of the detectors
and the presence of the underlying Compton backgrounds
from the higher energy cascades did not allow an accurate
determination of the correlation functions. Therefore,
these results are not reported here.

3.3.2. Summary of Angular Correlation

Measurements and the Resulting Spin
Assignments

 

 

 

The present results are summarized in Table 5 along
with the correlation functions reported by other
investigators for.some of the cascades (34, 35, 40). The
A2 and A4 coefficients are listed with the spin sequences
and mixing ratios. The sequences and ratios listed here
are only those that give a consistent decay scheme.

Comparisons of the correlation functions obtained
in this work with those reported by other investigators,

Show that agreement, in general, is good to within the

reported errors.

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75

Table 6 lists the internal conversion coefficients
that have been reported by other investigators (3H, 35, 37)
and the multipole orders determined from the correlation
functions and internal conversion data.

From these data, unique spin assignments for each
state can be made:

(a) The 777 keV State. The Spin of this state was
assumed to be 2+ because it is the first excited state of
an even-even nucleus. All of the correlation data are
consistent with this spin assignment. The internal
conversion coefficient for the 777 keV transition (3“, 35, 37)
is in agreement with the theoretical conversion coefficient
for an E2 transition.

(b) The 1u75 keV State. The angular correlation
functions obtained from the 619—1475, 554—1u75, and 698—
777 keV cascades are all consistent for a spin assignment
of 2 for this state. On the basis of the internal conversion
coefficients (3“, 35, 37) for the 1H75 keV and 698 keV
transitions, the assigned parity is positive.

(0) The 1821 keV State. The correlation functions
for the 828-10M4, lOuM-777, and 828-777 keV cascades are
consistent with a spin assignment of u for the 1821 keV
state. The possible spin sequence of 5(3,M)2(2)O,
determined from the lOMM—777 keV correlation that was
discussed in section 3.3.1.C. can be eliminated since it

does not lead to any possible Spin states that will

82

76

Table 6.-—Summary of Kr internal conversion coefficients, mixing ratios, and multipole

order.

 

“K x 103

 

Transition “K x 103 a Multipole
Energy Experimental Theoretical Order
551 keV 0.68 i luzb 0.676 0.0 0.1 El
0.70 i 0.10c
0.673d
619 keV 1.60 i 11%b 1.u0 2.0 0.3 0.2Ml + 0.8E2
1.3 i 0.20
1 23d
698 keV 1.1 i 15%b 1.0u6 3.0 0.7 0.1M1 + 0.9E2
0.81 i 0.11c . -
1 08d
777 keV 1.00 i 20%b 0.822 me E2
0.81 i 0.100
828 keV 0.32 : 30%b 0.282 0.0 0.1 El
0.29 i 0.011c
0.356d
1318 keV 0.18 i 11%b 0.2u5 u.u 0.9 0.05Ml + 0.95E2
0.21 i 0.03c
0.302d
1u75 keV 0.18b 0.188 02
0.21 i 0.30
0.137d

 

aThe theoretical conversion coefficients are those calculated using the multipole

order and mixing ratios listed for each transition.

ratios are from the angular correlation data.

bReference 3M.
cReference 35.
d

Reference 37.

eAssumed value.

The multipole orders and mixing

77

satisfy the 828-777 and 828-lOHH keV correlation
functions. In addition, the life—time for such a
transition would be much longer than the limit of 0.06
nsec reported by Flanger and Schneider (“8). The
internal conversion coefficient (3H, 35, 37) of the 1011
keV transition indicates that the parity is positive.

(d) The 209H keV State. On the basis of the
possible spin sequences determined from the SSH—1318,
1318-777, and 619-lu75 keV correlation functions, a spin
of 3 is assigned to the 209“ keV state. The possible
spin of H for the 2094 keV state determined from the 619-
1475 keV correlation function, discussed in section 3.3.l.E.,
can be eliminated since it is not consistent with the other
correlation functions. Also, the mixing ratio for the
619 keV transition for this case would give approximately
70% octupole radiation which would be inconsistent with
the lifetime and internal conversion coefficient (3“, 35, 37).
The internal conversion coefficients of the 1318 and 619
keV transitions indicate the parity of this state is
positive.

(e) The 26MB keV State. All of the correlation
functions for transitions from the 26M8 keV state are
consistent with a spin assignment of H. The internal
conversion coefficients of the 554 and 828 keV transitions

indicate that the 26MB keV state has negative parity (3M,

35, 37).

78

3.“. Other Recently Reported Works

 

Since the completion of the above experimental studies
of 82Br in 1965 and the publication of a report on the
results (49), a number of papers have appeared on the same
activity. These results are discussed briefly below.

Reidy and Wiedenbeck (50) used a 2m Ge curved—
crystal spectrometer to accurately measure a number of
the gamma ray energies. They report the energies: 92.19,
221.5, 273.5, 554.3, 619.2, 698.3, 776.6, 827.8, 10HH.3,
1317.5, and 1H7M.3. The agreement is seen to be excellent
except for that with the 1M7“ keV transition. In general,
Ge(Li) detectors are thought to be more accurate in this
energy region than are bent crystal spectrometers.

S. Raman (51), using a 0.22 cm3 Ge(Li) detector with
a 2.2 mm depletion depth, has studied the decay of 82Br.
He reports gamma rays at 9M : 2, 138 i u, 222 i 2,
27L: 1 2, 5511 i 0.6, 617.9 _+_ 0.8, 697.7 2“. 1, 775.6 i 0.8,
951 i 2, 1008 i 2, 10U3.3 : 0.8, 1317.8 i 0.7, 1173.1 : 0.9,
l6u9.5 i 2.5, 1778 i 3, 1868 i 2, 1953 i 2, and 2057 i 5.
Agreement is seen to be fair except for the high energy
gamma rays. Unfortunately, Raman does not report any
details as to how the energies were determined or that
he considered the existence of non-linearities in his
apparatus. Such non-linearities have since been found

to be common place (52). Raman proposes a decay scheme

with states at 0,776, 1474, 1820, 1953, 2093, 2026,

79

255A, 2697, and 2828 keV. Some of the differences
between this decay scheme and the one reported in this
thesis can be attributed to the discrepancies in the
reported energies.

Gfirtner, Reiser and Schneider have reported
some similar Ge(Li) measurements (53) on 82Br. The
scheme they report is similar to that of Raman.
However, they also do not give any details as to the
method of calibration which makes comparisons difficult.

Most recently, Hsu and Wu have reported their
work (59) with alcm3 Ge(Li) detector. They report
gammas at 93, 138, 222, 27“, 553, 606, 619, 698, 777,
827, 951, 1008, 104A, 1081, 1318, 1A75, 1650, 1778, and
1955 keV and place states at 0, 777, 1975, 1820, 1955,
2095, 2026, 2555, 2698, and 2828 keV. Again no details
are given as to the energy measurements and
calibrations.

In the present measurements, non-linearities were
carefully accounted for by calibrating the counting
system with sources of gamma rays with well-known
energies. The non—linearities were found to be large
enough to easily account for the discrepancies between
the measurements reported in this thesis and those
listed above. Non-linearities of this size are fairly

common in the field.

80

3.5. Discussion of the Decay Scheme of 82Br

 

It is interesting that the 2698 keV state has an
even spin and odd parity. The ground state spin of 82Br
has been reported (55) to be 5_ with the negative parity
assignment based upon the log ft value for the beta decay
and the negative parity of the 2698 keV state. The ground
state spin of 82Br can be described by a g9/2 neutron
coupling to a p3/2 proton hole state and is consistent
with the weak Nordheim rule. The even spin and odd
parity of the 2698 keV state can be accounted for:if,
in the beta decay, the g9/2 neutron is converted to a
gg/2 proton which then couples to the p3/2 proton hole.

A similar 9‘ state has recently been observed by Hendrie
and Farwell (56) and by Day, Blair, and Armstrong CS7) in
9OZr at 2.79 MeV. They interpret this state as arising
from coupling pl/2 and g9/2 proton states.

It has been observed that the beta decay of 82Br is
nearly 100% to the 2698 keV state in 82Kr. An upper
limit of 0.6% has been placed (35) upon the beta decay
to states lower than 2698 keV° However, on the basis of
a calculated log ft for a firstfbrbidden beta decay to
the 9+, 1821 keV state, the branching ratio to this state
should be approximately 90%. The branching ratio to the
3*, 2099 keV state is similarly estimated to be less than
0.5%. The fact that no branching has been observed to the
1821 keV state could indicate that this state is not a

simple shell model state.

81

The characters of the 2832, 2652, 2560, and 2929
keV states are uncertain since the spins and other
properties of these states are unknown. However, limits
may be placed upon their spins based upon the transitions
involving them. The spin and parity assignments of 9‘,
5_, or 6- for the 2832 keV state are based upon the log
ft = 5.7 for the beta decay to this state and on the fact
that this state gamma decays to the 9‘, 2698 keV and 9*,
1821 keV states. Similarly, a spin assignment of 9, for
the 2652 keV state is consistent with the log ft = 6.8
for the beta decay to this state. The spin assignments
of 2, 3, or 9 for the 2560 keV state are based upon the
gamma decays from this state to the 2+ states at 1975 keV
and 777 keV. The spin assignments of 2, 3, or 9 for the
2929 keV state are based upon the gamma decay of this
state to the 1975 keV and 777 keV states and upon the
fact that the spin 9', 2698 keV state gamma decays to
the 2929 keV state.

The ordering and spacings of the strongly excited
states in 82Kr are quite similar to those predicted by
the non-axial rotator model of Davydov and coworkers (9, 6).
It is interesting to compare some of the relative transition
probabilities that were determined in this and other
recent work (96) with the predictions of this model
(9, 6). This is done by comparing the "non-axiality"

parameter y calculated from the transition probabilities

82

with that calculated from the energies of the
states (18).

Davydov and Chaban have considered the interaction
of rotation and vibration in non—axial even-even nuclei
and have shown that when the "non-adiabaticity" parameter
u s 0.5 the reduced E2 transition probabilities are very
nearly equal to those predicted by Davydov and Filippov
who did not take this interaction into account (5). To
first order, the effect of the "non—adiabaticity" is to
cause a change in the "non—axiality" parameter y and
thereby change the reduced E2 transition probabilities,
B(E2). Klema, Mallmann and Day (17) have shown that
the energy of the 9+ state at 1821 keV can be described
in terms of the ratio of the energies of the spin 2' and
2 states and the parameters y = 27.70 : 0.2° and
u = 0.950 : 0.002 and that of the 3+ state at 2099 keV
by y = 29.00 : 0.1° and u = 0.38 i 0.02. Thus, the
Davydov-Filippov transition probabilities are expected to
be applicable.

The ratio of the B(E2) for the 698 keV and 1975

keV transitions from the second 2+ state is

B(E2; 2'+2)
B(E2; 2'+0)

 

=60:10

This corresponds to a y = 27.10 i 0.10 which is in fair

agreement with the values obtained by Klema et a1, (17)

83

for the 1821 and 2099 keV states that were quoted above.
Using the B(E2) that was recently measured for the 777 keV
first excited state in a nuclear resonance fluorescence
experiment by Beard (96) and the non—axiality parameter
y one can estimate (9) the intrinsic quadrupole moment
00, and, thereby, the deformation parameter 8. For
y = 27.1°, QO = 1.5 x 10-2ucm2 and B = 0.2. A nuclear
radius of R = 1.2 x 10-l3Al/3cm was used. These are in
reasonable agreement with the Qo and 8 values obtained for
other nuclei in this mass region (9, 58).

The results of Davydov and Filippov can also be
used to calculate the ratio of the reduced E2 transition
probabilities for the transitions from the 2099 keV 3+
state to the 1975 keV 2'+ and 777 keV 2+ states (9). The

transitions involved are the 619 and 1318 keV gammas.

The experimental ratio

B(E2; 3+2)
B(E2; 3+2')

 

= 0.017 i 0-005

which corresponds to y = 27.30 : 0.2°. This is somewhat
lower than 29.00 obtained for the 2099 keV state by

Klema et al., from energetics.

CHAPTER IV
8%;
THE DECAY SCHEME OF r

Talmi and Unna, using shell model configurations
with the assumption that the nuclear potential is due
to two-body effective interactions between nucleons,
have made calculations (7) to predict the characters of
the ground and first excited states of several strontium
isotopes. At the same time, these authors noted the
lack of experimental data for isotopes in this mass
region. The present work was motivated by a desire to
extend the data, as well as to test some of the results
of their calculations for 83Sr.

The first investigation reported only three
transitions of 90, 385, and 755 keV in addition to positrons
(59) as belonging to the decay of 838r. Preliminary
investigations by Maxia, Kelly, and Horen (60) have
indicated that the decay of 83Sr is somewhat more complex
with observed transitions at 90, 375, 908, 770, 1160, 1560,
and 1960 keV. Later, Reddy, Johnston, and Jha (61)
presented data in agreement with Maxia et al., and placed
levels at 90, 380, 980, 1160, 1560, 1960, and 2120 keV
for 83Rb. These data were all recorded with NaI(T1)

detectors.
89

85

It was soon evident from our early gamma-gamma
coincidence data taken with NaI(T1) detectors that the
decay scheme was much more complex. We have used high
resolution Ge(Li) detectors in singles and coincidence
configurations in order to perform a more complete
investigation. Some sixty transitions have been identified
as belonging to 83Sr decay and fitted into a complex

decay scheme.

9.1. Source Preparation

 

The strontium—83 activities were produced from
stable isotopes by means of two different nuclear
reactions. The early gamma ray measurements were made
using sources produced by bombarding arsenic metal with
10.9 MeV/nucleon 120 ions in the Lawrence Radiation
Laboratory HILAC. Later sources were produced by
bombarding rubidium chloride with 37 to 92 MeV protons
from the Michigan State University cyclotron.

In both cases the strontium activities were
separated chemically by precipitating the strontium with

SrCl carrier in chilled fuming nitric acid. Small

2
amounts of 82Sr and 85Sr were present in the sources from
the HILAC bombardment, whereas only the 858r contaminant

was present in the sources prepared with the cyclotron

bombardments.

86

The 83Sr gamma spectra obtained from the sources
produced from the two different nuclear reactions

appeared to be identical.

9.2. Experimental Results

 

9.2.1. The Gamma—Ray
Singles Spectrum

 

 

The gamma—ray singles spectrum taken with a Ge(Li)
3

detector of 3 cm sensitive volume and resolution of 3 keV
for the 662 keV l37CS photon is shown in Figure 10A and

10B. The low energy part of the Spectrum, taken with an
expanded gain, is shown in Figure 10A while the high

energy portion is shown in Figure 108.

The energies of the observed transitions are listed
in Table 7 along with their relative intensities. The
energies of the more intense transitions were determined
from spectra taken with 83Sr sources mixed with photon
emitters containing transitions of well known energies (21).
These energies are listed in Table 2, in Chapter 2.

The technique used to determine the energy calibration
curve was to least squares fit the peak centroids of the
well-known transitions to a quadratic equation after the
background had been subtracted from under the peaks as
described in Chapter 2. The deviations of the energies
of the calibration transitions from the quadratic fit

were never greater than 0.1 keV. The energies of the low

intensity gamma—rays were similarly determined using the

 

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89

Table 7.-—Energies and relative inten ities of transitions
from the decay of 3Sr.

 

Relative Photon

 

 

 

 

Intensitya
%fi:§§y Ge(Li) Na1(T1)
92.3 i 0.1b 5.2 1197.3 + 0.5 3.8 )7 8
99.2 i 0.5 1.0 1.0 1160.0 I 0.5 9.5 ) '
290.2 i 0.5 1.2_ 1.0 1202.0 I 0.5 0.9
381.5 i 0.50' 60 ) 53 1219.8 I 0.5 0.9
389.2 1 0.5 9.0 ) 1237.6 I 1.0 0.5
918.6 i 0.5 17.8 18 1292.6 I 1.0 0.3
923.5 i 0.7 9.6 1296.0 I 1.0 0.9
938.2 i 0.5 2.7 1329.6 I 1.0 0.5
511.0 163.2 1379.0 I 1.0 0.2
590.2 + 1.0d 0.1 1389.0 I 1.0e 0.5
652.8 I 1.0d 0.1 1528.8 I 1.0 0.2
658.6 I 1.0 0.9 1562.5 I 1.0 5.5 9.5
719.2 1 1.0 0.2 1596 I 2.08 0.1
732.0 1 1.0 0.2 1653.1 I 1.0 0.3
736.8 I_0.5 0.5 1666.0 I 1.0 0.1
753 i 2.0d 0.1 ) 1710 I’2.0e 0.3
762.5 1.0-5 5 100 ) E 100 1722 I 2.0e 0.2
778.9 + 0.5 5.5 1799 I2.0e 0.1
805 I 2.0e 0.1 1757 I 2.0e 0.1
818.6 I 0.5 2.9 1778 I 2.091 0.08
898.7 I 1.0 0.9 1796 I‘2.0e 0.19
853.8 I 1.0 0.9 1879 I 2.0e 0.1
889.2 i 0.5 0.9 1911.6 I 1.0 0.1
907.5 + 0.5 0.5 1997 1: 1.0e 0.1} 2 7
916.7 I 1.0 0.1 1952.2 + 0.5 2.6 °
999.2 1 1.0 0.1 2019.7 I 0.7 0.1
999.2 + 0.5 1.5 2097.9 I 0.7 0.3
1020.1 I 1.0d 0.1 2090.0 I 0.7 0.3
1036.6 + 1.0 0.2 2137.0 I 1.0 0.1
1093.7 I 1.0 0.5 2197.8 I 0.7 0.5
1053.7 I 0.7 0.6 ‘
1098.0 i 0.5 0.6
aA 10% error in relative intensities is estimated.
b

1 J2 beta-ray Spectrometer measurement.
CDoublet. dSeen in Coincidence only.

eSeen in anti—Compton spectrum only.

90

strong transitions in 838r as standards. The energies
thus obtained were consistent at various gain settings.
The RMS deviations from the average energies for the
strong transitions listed in Table 7 ranged from i 0.1
to :_0.2 keV. The errors quoted in Table 7 include an
estimate of i 0.3 keV to account for any systematic
errors that may have been present.

The relative intensities were obtained using
experimentally determined efficiency curves (28). For
comparison, the relative intensities of the strong
transitions measured with NaI(T1) detectors are also
listed in Table 7. In general, the agreement of the two
measurements was quite good.

Several very weak transitions were observed in
spectra obtained using the anti-Compton Spectrometer.
These spectra were obtained from two different source
geometries with respect to the Ge(Li) and NaI(Tl) split
annulus detectors, and are shown in Figure 11A and 11B.
In one case, the source was placed outside the annulus
and the gamma rays collimated into the Ge(Li) detector.
In the second case, the source was inserted into the
well of the annulus and a 5.1 cm by 5.1 NaI(Tl) detector
was mounted in the tunnel above the source to increase
the total solid angle subtended by the NaI(T1) detectors.
In this second case, more real coincidences due to gamma

cascades in the source were subtracted from the spectrum

91

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92

than in the first case. Therefore, in addition to
improving peak to Compton ratios, those transitions
involved in strong coincidence cascades can also be
determined easily. The energies and relative intensities
of the gamma rays observed in these anti—Compton Spectra
are listed in Table 8. These intensities are given
relative to the intensity of 1952.2 keV transition which,
as it will be seen later, is not in coincidence with

any gamma ray.

4.2.2. Gamma-Gamma Coincidence
Studies

 

Gamma—gamma coincidence experiments were made for
all of the strong transitions and many of the weak ones.
Initially, these were made using two 7.6 by 7.6 cm NaI(Tl)
gamma detectors. The energy resolutions of these
detectors were approximately 9 percent for the 662 keV

gamma of 1370s.

Later, the coincidence experiments were
repeated using either a 7.6 cm by 7.6 cm NaI(Tl) crystal
or the split annulus NaI(Tl) crystal as the gate detector
and a 7 cm3 Ge(Li) detector for display on the 102M
channel analyser. The energy resolution of the 7 cm3
Ge(Li) detector was 4.5 keV for the 662 keV gamma of 1370s.
The results of both studies were consistent, and only
those data taken with the germanium detector will be
discussed here.

In order to complement the anti-Compton data, a

coincidence spectrum with the NaI(Tl) annulus—Ge(Li)

93

gable 8.--Energies and relative intensities of gamma-rays in the decay of
3Sr observed in the anti-Compton and "Any Gamma-Gamma" Coincidence
Experiments.

 

‘Relative Intensity
Energy Anti-Compton '

 

(keV) Collimateda Uncollimatedb "Any Gamma—Gamma"
290.2 1.1
381.5 #8.0 2u.2 210
389.2 3.9 1.3 27.5
u18.6 13.7 6.8 50.3
“23.5 3.7 1.8 12.8
M38.0 2.3 0.3 7.5
511.0 256
658.6 0.33 5.8
71u.2 0.15 2.2
732.0 0.16 3.0
736.8 -0.u8 0.2 6.6
762.5 90.0 63.9 = 100
778.u u.5 1.2 31.8
805 0.1
818.6 1.8 0.67 15.5
8H8.7 0.3M 0.1 5.5
853.8 0.9a 0.2 2.6
889.2 0.38 3.5
907.5 0.57 0.29 11.u
916.7 0.2u 8.8
guu.2 0.55 0.1 6.8
99u.2 1.3 0.u3 12.5
1036.6 0.1u 0.06 2.7
10u3.7 0.86 0.37 6.8
1053.7 0.5 0.33 5.7
1098.0 0.63 0.22 u.0
11u7.3 3.3 1.2 3u.3

1160.0 309 309 3‘2
1202.0 0.56 o.u2

1214.8 0.7 0.2 6.8
1237.6 0.u6 0.u5

12u2.6 0.26 0.29

1296.0 0.3 0.u 3.5
132u.6 0.73 0.37 7.5
1374.0 0.20 0.0M

138u.0' 0.57 0.1M 5.u
1528.8 0.30 0.05 3.0
1562.5 5.0 1.7 39.3
1596 0.07

1653.1 0.21 0.22

1666.0 .16 0.05 2 3
1710 0.26

1722 0.18

17u9 0.10

1757 0.10

1778 0.08

1796 0.1M

187a 0.05 0.08

1911.6 0.1u 0.1M

19u7 0.1

1952.2 3 2.6C E 2.6c

201u.7 0.11 10.1u

20u7;9 0.3M 0.31

2090.0 o.u1 0.37

2137.0 0.11 0.09 .

21h7.8 0.57 0.55

 

aSource outside annulus tunnel.

bSource inside annulus tunnel, immediately adjacent to the Ge(Li).

cAdjusted to equal relative intensity of the 1952.2 photon in singles.

9M

system was recorded using an integral gate. This is
called the "any gamma-gamma coincidence experiment."

For this measurement, the source was sandwiched between
0.35 cm of copper to produce total annihilation and then
placed 2 cm above the Ge(Li) detector. A 2.2 cm thick
cylindrical iron shield was placed around the Ge(Li)
detector to reduce crystal to crystal scattering. The
coincidence spectrum recorded from this configuration is
shown in Figure 12. The energies and relative intensities
of the gamma rays observed in this coincidence spectrum
are also listed in Table 8. Almost all of the gamma rays
were noticeably enhanced relative to the 762.5 keV gamma
ray, indicating that this gamma-ray is not in so strong
coincidence as the others.

Additional coincidence spectra were recorded in
separate experiments with the gates set on the peaks with
energies of 9u.2, 381.5, 418.6, 762.5, 1147.3, 1160.0,
and 1562.5 keV. For comparison, coincidence spectra were
also recorded for coincidence gates set on the Compton
regions below and above these peaks. Also, the 600-735
keV and BOO-1100 keV regions of the spectra were divided
into six segments of 50 to 100 keV width and coincidence
gates set on each segment.

Three different NaI(Tl) detectors were used to
provide the coincidence gates. A 3.8 cm by 2.5 cm NaI(Tl)

detector with a 0.013 cm beryllium window was used for

 

 

 

 

 

 

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CHANNEL NUMBER

——"Any gamma-gamma coincidence" spectrum of 83Sr taken with the 7 cm3

Figure 12.

Ge(Li) and NaI(Tl) annulus detectors.

 

96

the coincidence gates set on the 94.2 keV peak and the
Compton region directly above it. A 7.6 cm by 7.6 cm NaI(Tl)
detector was used for the coincidence gates set on the
381.5, 762.5, and 1562.5 keV photopeaks. The split
annulus NaI(Tl) detector was used for all of the other
coincidence gates. The results of all these measurements
are shown in Figures 13—20, inclusive. Many of the spectra
have been gain shifted by the computer for ease of
comparison and presentation. These spectra have not
been corrected for chance coincidence; however, the gross
true to chance ratio was monitored and in every experiment
it was 25 to l or greater.

In order to identify the states p0pulated by
positron decay, a triple—coincidence experiment was performed
using the NaI(Tl) split—annulus and the 7 cm3 Ge(Li)
detectors. The source was placed into the well of the split
annulus and above the Ge(Li) detector. The pulses from
each half of the split annulus were used to provide a
coincidence gate on the 511 keV photo-peak. The
coincidence spectrum recorded from this configuration is
shown in Figure 21B. In order to distinguish those gamma
rays depopulating the states fed by the positron decay
from the double escape peaks of the high energy gamma
rays, the experiment was repeated with the source placed
external to the split annulus detector and the gamma rays

collimated into the Ge(Li) detector. This spectrum

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CHANNEL NUMBER

Figure lu.--Gamma spectrum in coincidence with segments of
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corded with the NaI(T1) detector gated on 295-330 keV.
Spectrum B was recorded with the NaI(Tl) detector gated

on the low energy side of the 381, U18, M23 keV peaks.

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I r ' I r I I T T I l I
A.SINGLES ”Sr _ a
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CHANNEL NUMBER

Figure l8.——Gamma spectrum in coincidence with various

segments of the BOO-1100 keV region. Spectrum A is a

singles spectrum for reference. The detectors were the

same as for Figure 15. The scales have been adjusted
the same as in Figure 16.

103

 

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250 500 - 750

CHANNEL NUMBER

Figure 21.—-Positron feeding spectra of 83Sr taken
with the 7 cm3 Ge(Li) counter and the NaI(Tl) split
annulus detector. Spectrum A is a singles spectrum
for reference. Spectrum B is the positron feeding
and double escape spectrum. Spectrum C is the
double-escape spectrum obtained with the gamma ray
collimated into the Ge(Li) detector from an external
Source.

106

which contains only the double escape peaks, is shown
in Figure 21C.

Note that the double escape peak of the 1562.5
keV gamma was greatly reduced in the spectrum obtained
with the source in the annulus (Figure 21B). This is
caused by the 511 keV annihilation quanta from the 1562.5
keV gamma ray summing with the coincident 94.2, 290.2,
and 389.2 keV gamma rays. These gammas were very
efficiently detected in the split annulus and the summing

produced pulses corresponding to energies appreciably

 

greater than 511 keV,and therefore the gate requirement
was no longer satisfied. The intensity of gamma rays in
cascade that are in coincidence with the positrons will
be reduced similarly in the coincidence spectrum.

In almost every case, the coincidence gates
necessarily included two or more gamma rays because of
their close energy spacings and, in addition, many
underlying Compton photons. This makes the interpretation
of most of the coincidence data difficult. However, a
consistent interpretation can be obtained by quantitative
comparison of the different coincidence spectra. A
summary of the coincidences seen in these experiments is
presented in Table 9. It is possible to establish by the
comparison of spectra recorded in the adjacent coincidence
gates that some of the peaks appearing in the coincidence
spectra are the result of coincidences with Compton photons

in the gate interval. These are listed in Table 9 under

10'?

 

 

 

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108

the heading Compton or Sum Coincidences. The appearance
of the 511 keV peak in all of the coincidence spectra of
the coincidence gates between 800-1200 keV can be
accounted for by sum coincidences. These arise from one
of the 511 keV annihilation quanta summing with any of
the coincident 381.5, ”18.6, M23.5 or 762.5 keV gamma
rays or their Compton photons in the NaI(Tl) annulus
detector.

Comparison of the coincidence spectra obtained from

gates at 680—7UO keV, 7uO—805 keV, 815-880 keV and 1100—

 

1200 keV (Figures 160, 17, 18B, and 19) reveals that the
762.5 keV transition is in coincidence with the 1147.3
keV gamma ray. Further, the peak at “38.2 keV is
concluded to be in coincidence with the 762.5 keV gamma
since the 762.5 keV peak is observed to grow as the
coincidence gate is moved from 330-MOO keV to 400-500 keV
(Figures 1MB and 15).

The ratio of intensity of the 381.5 keV gamma ray
to the combined intensities of the 418.6 and M23.5 keV
gammas recorded in the coincidence spectra obtained with
the coincidence gates at 3uO—MOO, MOO—M50, 7&0-805, and
1100—1200 keV (Figures 1MB, 15, 17, and 19) were very
informative and were crucial in the construction of the
decay scheme. These ratios were U.2, 5.2, 2.3, and n.0,
respectively,in comparison to 2.7 in the singles spectrum.

Furthermore, the 418.6 and “23.5 keV gamma rays always

109

appeared in the coincidence spectra together and in the

same intensity ratio as in singles. These ratios can be
explained only with the conclusion that the 381.5 keV

peak actually consists of two gamma rays very close in

energy with one of them in coincidence with the other as

well as with the “18.6 and “23.5 keV gamma rays. The
relative intensities of the two 381.5 keV gamma rays

have been calculated from the coincidence data to be 23.5 for
the one in coincidence with the “18.6 and “23.5 keV gamma
rays and 36.5 for the other. No noticeable broadening of

the 381.5 keV peak was observed. An upper limit of 0.2 keV

 

is placed for the energy difference of the doublet.

The “2.3 keV transition was not observed to be in
prompt coincidence with any of the gamma rays, X-rays or
positrons.

“.2.3. The Internal Conversion Coefficient
for the “2.3 keV Transition

 

 

An attempt was made to measure theI( internal
conversion coefficient for the “2.3 keV transition.
For this purpose, a continuous flow argon-methane
proportional counter was used. The source, which was
evaporated onto an aluminized Mylar film 3mg/cm2 thick,
was mounted internal to the proportional counter. The
recorded electron spectrum obtained is shown in Figure

22.

110

The K internal conversion coefficient was
calculated from electron coincidences with the X-ray
in the following manner. The number of K conversion
electrons, NKe’ in coincidence with the X—ray is given
by

NaK wK 9X 5X Q 5

N = 8 8(1 _ e-AATC)

K8 1 + 0T

 

where 0K is the K X-ray fluorescent yield, QXEX is the

solid angle and detector efficiency for the X-ray,

9858 is the solid angle and detector efficiency for the
electron, and ATC is the coincidence counting time.

The number of “2 keV gamma rays for an equivalent counting

time is given by

-At
S _
_ N 9142 Ell-,2 Pes (l _ e AAtS)

N _
“2
l+aT

where 9“2 €“2 is the solid angle and detector efficiency

for the “2 keV gamma ray, P is the X-ray escape ratio,

es

tS is the time of which the gamma ray singles spectrum
was taken after the start of the coincidence measurement,
and Ats is the singles counting time. Solving these two

equations for GK gives

= NKe ““2 842 Pes e“AtS (1 - e‘xAtS)

 

 

 

a

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CHANNEL NUMBER

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.o'o

SINGLES

A
B

 

 

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02 _,
OI

m
q.0 O

(81an AHVHJJBHV )' ‘81Nnoo

Figure 22.--E1ectron spectra obtained with an argon-

methane continuous flow proportional counter. Spectrum

A is the singles spectrum. Spectrum B is the electron
spectra in coincidence with the x-ray.

112

For these experiments a 6 mm NaI(Tl) detector with
a 0.012 cm beryllium window was used to detect the X—ray
and “2 keV gamma ray. The values of ”K and Pes were taken
from nuclear spectroscopy tables (21). The ratio of

erx

€“29142
was measured to be 0.85 in an absorption experiment using
858r and 137Cs x-y ray sources. The detector efficiency
solid angle product for the electrons is very difficult
to determine because of the geometry of the source mount
on the pr0portional counter. The source did not present a
full 2n steradians solid angle to the proportional counter.
This resulted from the relationship of the source diameter
to the diameter and wall thickness of the orfice of the
source mounting on the proportional counter. The source
diameter was 0.5 inch compared to 0.75 inch for the
orifice. In addition, the wall thickness was not
uniform but varied from 0.0“ to 0.16 inches. This made
the calculation of the effective solid angle difficult.
However, limits upon the solid angle were determined from
these dimensions. The solid angle subtended by the disk
source must be between the limits of the solid angle
subtended by two point sources, one located at the center
of the orifice and the other located outside the counter.

These estimates then give 0.25 :e:€ 0 i 0.5 assuming 100%

€

 

113

detection efficiency for the conversion electrons by
the proportional counter. The internal conversion
coefficient, 0K, was calculated to be 19 i 0K 1 38.
L. M. Beyer has since measured (62) the “K
conversion coefficient to be 29.3 i 3.5 using the
MSU "Orange" electron spectrometer. He has also shown
from energy differences of the K and L internal
conversion electrons of the “2.3 keV transition that this
transition is in 83Rb and not in 83Sr.
In addition to the “2.3 keV transition, Beyer has
measured (62) the internal conversion coefficients for
the 9“.2, 290.2, 381.5, “18.6, “23.5, “38.2, 762.5,
778.“, and 818.6 keV transitions. His data are summarized
in Table 10 since the multipolarities of the transitions
will be useful to determine the characters of the excited
states.

“.2.“. Half-life Measurements
of the “2.3 keV Transition

 

 

Since the “2.3 keV gamma ray was not found to be
in prompt coincidence with any of the radiations, a delayed
coincidence experiment was performed to measure its
half-life. A block diagram of the delayed coincidence
spectrometer is shown in Figure 23. The delay circuit used
here was the delayed-trigger circuit of a Tektronix 5“5
oscilloscope which provided a variable time delay from 2
to 500 microseconds. The delay circuit was adjusted to

provide a 20 microsecond delay. The linear gate circuit

 

11“

Table lO.--Summary of internal conversion coefficientsa
and multipole ordera of some of the transitions in 83Rb.

 

 

 

EY GK K/L + M Multipole Order
“2.3 29.3 i 3.5 M2

9“.2 2.2 i 0.2 (-1)b M1 1 10% E2
290.2 1.“ i 0.2 (—2) 10 i 2 35% M1, 65% E2
381.5 7.1 i 0.3 {-3) 7.“ E3, 3 10% M1
389.2 6.5 i 0.5 (-3) 8 :.2 E2, : 20% M1
“18.6 1.“ i 0.2 (—3) El
“23.5 1.6 i 0J4(-3) E1
“38.2 2.7 i 0.“ (—3) M1
762.5 9.5 i 0.5 (-“) E2
778.“ 9.6 i 2 (-“) Ml, E2
818.6 1.1 i 0.“ (—3) M1, E2

 

aReference 62 .

bThe number in the parenthesis is the appr0priate
power of 10, i.e., 2.2 i 0.2 (—1) means (2.2 i 0.2) x
10‘ .

 

115

 

 

 

 

 

 

 

I START
I 4’ TO ANALYZER

DELAY
J STOP INPUT

LATTEN} { AMP I

 

 

 

 

 

 

 

 

Figure 23.-—Block diagram of the delayed coincidence spectrometer.

116

in the analog to digital converter of a 256 channel vacuum
tube RIDL model 52 analyser was purposely disabled by
clipping the pins of the vacuum tube that controlled the
circuit so that the gate would not close. When a gamma
ray is detected in the first detector, a pulse from the
single channel analyser (SCA) starts the address scaler in
the 256 channel analyser which counts at 2 M Hertz.

When a gamma ray is detected in the second detector the
pulse from the SCA is delayed by approximately 20 usecs

and then amplified. After amplification it is also sent

 

into the input of the 256 channel analyser. This second
pulse has sufficient amplitude to cause the upper level
discriminator in the converter to act as the gate to stop
the conversion process and, hence, stop the address scaler
where it is at the instant of the second pulse. A count is
then stored in the appropriate channel. The resulting spectrum
gives the time decay curve of the transition. The spectro-
meter was tested by measuring the half-life of the 51“ keV
state in 85Sr. The half-life of this state was measured to
be (0.9 i 0.2) usecs, in excellent agreement with that
measured by Sunyar et al., (63).

The source strength must be very weak in order to
keep the chance coincidence rate low. This weak source
strength required long counting times in order to achieve

reasonable statistics. In addition, the spectrometer is

fixed by the frequency of the oscillator in the converter

 

117

(0.5 u sec/channel in this case). This limits the useful
range here to approximately 0.75 to 50 u secs.

To measure the life—time of the “2.3 keV state, the
single channel analyzers were set to the “2.3 keV photo-
peak and the X-ray, the 511, 381.5, and 762.5 keV photo—
peaks in separate experiments. The results were incon—
> 50 usecs. The latter

elusive either T < 0.5 usec,0r T

1/2 1/2
is consistent with the M2 character of the “2.3 keV
transition for which the life—time would be approximately

1 m sec, well beyond the range of this spectrometer.

“.3. The Proposed Decay Scheme for 83Sr

 

A decay scheme consistent with all the data has been
constructed from the results of the coincidence studies,
energy sums and relative intensities of the transitions
and is shown in Figure 2“. The log ft values listed on
the decay scheme were determined from the relative
intensities into and out of each state and from the X—ray
and positron intensities. The positron branching
ratios were determined from the Fermi plots (62) of the
positron spectrum and from the triple—coincidence
experiments between the gamma rays and two 511 keV
annihilation quanta.

A summary of the energies of the states in comparison
with the energy sums of the transitions in cascade depopu-
lating them are listed in Table 11. Those transitions that

were crossovers to the ground state were not included in

118

   
  
    

  
  

  
  

    
 

      
  

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Figure 2“.——Proposed decay scheme of 83Sr.

 

2119

Table ll.--Summary of gamma cascade energy sums.

 

State ' Cascade Sum Deviation Coin Spectrum

 

 

in Kev in keV in keV Figure No.
5.0
“2.3
295.2a 295.2 = 5.0 + 290.2
389.2 389.“ = 5.0 + 9“.2 + 290.2 +0.2 13A, l“A
“23.5 “23.6 = 5.0 + “18.6 +0.1
“23.8 = “2.3 + 381.5 +0.3
736.8 737.0 = 5.0 + 732.0 +0.2
8014.8b 80“.8 = “2.3 + 762.5
805.0 . -381.5 + “23.5 +0.2 l“B, 15
“ 805.3 = “2.3 + 381.5 + 381.5 +0.5 1“B
99 .2
10“3.7
1053.7
1103.0a 1103.0 = 5.0 + 1098.0 '
1202.0 1202.3 = “2.3 + 1160.0 +0.3
1201.9 = “23.5 + 778.“ -o.1 l“B, 15, 17
12“2.6 12“2.6 . 5.0 + 1237.6
12“3.0 = 389.2 + 853.8 +0.“ 18B
12“2.1 = “23.5 + 818.6 -0.5 1“B, 15, 17
. 12“3.0 = “2.3 + “38.2 + 762.5 +0.“ 15, 17
1273.1
132“.6
1653.1 1653.5 = 736.8 + 916.7 +0.“ 180
1652.8 = 658.6 + 99“.2 -0.3 .163, 18D
1756.9 1757.9 - 71“.2 + 10“3.7 +1.0 16c, 18E
1755.8 a 652.8 + 1098.0 + 5.0 -1.1 18E
1783.5a 1783.5 = 5.0 + 1778.5 .
1783.2 = 5“o.6 + 12“2;6 —0.3
1783.“ - 389.2 + 5“0.6 + 853.8 -0.1 18C
1916.7a 1916.6 . 5.0 + 1911.6 -o.1
1916.8 = “2.3 + 187“.5 +0.1
1916.6 = 67“.0 + 12“2.6 -0.1
1917.6 = 6““.5 + 1273.1 -1.1
1952.2 1952 .= 5.0 + 19u7
' 1951.9 = 5.0 + 9“.2 + 290.2 + 1562.5 -0.3 13A, l“A, 20
1951.7 = 389.2 + 1562.5 -o.5 '1“B, 20
1952.3 = “23.5 + 1528.8 +0.1 12
1951.6 . 736.8 + 121“.8 -o.6 16c, 19
1952.1 = “2.3 + 762.5 + 11“7.3 —0.1 17, 19
1951.2 = 907.5 + 10“3.7 -1.0 180, 18E
1951.7 = 5.0 + 1098.0 + 8“8.7 -0.5 180, 18E
1955 = 753 + 1202.0 —3 19
201“.8 201“.2 = 1020.0 + 99“.2 -0.6 180
2090.0 2090.2 = “2.3 + 20“7.9 +0.2
2089.5 - “23.5 + 1666.0 -0.5 12
2089.5 = “2.3 + 762.5 + 128“.6 -0.6
2090 3 = 1036.7 + 1053.7 +0.3 18E
2091.0 - 889.0 + 1202.0 +1.0
21“7.8 21“5.8 - “23.5 +.1722.3 ‘ —2.0
. 21“6.2 - 9““.2 + 1202.0 +1.6
2179.3a 2179.3 = “2.3 + 2137.0
- 2178.8 - “2.3 + 762.5 + 137“.0 -0.5
2178.6 - 85“.o + 132“.6 ' -0.6

 

aN0 gamma ray was seen at this energy.

bThe energy of this state was taken to be the sum of the “2.3 and 762.5 keV gammas.

120

the table because the energies and the state energies are
the same, except for the 80“.8 keV state. In Table 11 the
columnlabeled'Wkflnc Spectrum Fig. No." refers to the
coincidence spectra that support the placement of the
transition.

“.3.l. Evidence for the “2.3
keV state

 

 

The placement of a state at “2.3 keV was dictated by
the relative intensity of the “2.3 keV transition and its
long life-time. The total internal conversion coefficient, “T’

has been measured to be 33 which gives a total of 188

 

units for this transition (relative to 100 for the 762.5
keV gamma ray) making the “2.3 keV transition the strongest
in the decay scheme.
“.3.2. Evidence for the “23.5,keV,
80“28 keV and the 5.0 keV states
A state was placed at “23.5 keV as a result of the
relationships of the 381.5 and “23.5 keV gamma rays in the
coincidence spectrum. It is supported by several
observed coincidence cascades that are listed in Table 9.
It was not possible to account for the relative
intensity of the “2.3 keV transition without having the
762.5 keV gamma ray feeding the “2.3 keV state. Further—
more, a very low intensity gamma ray of about 805 keV
was observed in the anti—(kxmflxn1spectrum described in

section “.2.1. Therefore, a state was placed at 80“.8

 

121

keV, which is the energy sum of the “2.3 and 762.5 keV
transitions.

The 381.5 keV peak was shown in section “.2.2. to
consist of two gamma rays very close in energy in coincidence
with each other. The second 381.5 keV gamma ray is
therefore placed as depopulating the 80“.5 keV state to
the “23.5 keV state.

At this point, it was not possible to complete the
construction of the decay scheme,consistent with the

coincidence data without postulating a state at 5.0 keV.

 

The previously mentioned intensity ratios of the “18.6 and
“23.5 keV doublet imply that these transitions

originate from the same state. In addition, there were
several other doublets 5 keV apart, namely 732.0-736.8,
l237.6—l2“2.6, and l9“7-l952.2 keV pairs. The 732.0-736
keV doublet also always occured together and in the same
intensity ratio in both the single and the coincidence
spectra.

An effort was made to look for a gamma ray at 5 keV
with a proportional counter and with a thin window, high
resolution Si(Li) detector*;bug because of the highly
converted nature of low energy transitions, the results
were inconclusive.

A search was made in both the gamma ray andin.the in—

ternal conversion spectra by Beyer (62) for a transition

 

*We are grateful to Dr. George Beard, Wayne State
University,for the use of his detector.

122

of 37 keV which would fit between the “2.3 and 5.0 keV
states. The data limited the intensity for such a 37
keV transition to an upper limit of 1%, relative to
the intensity of the “2.3 keV gamma ray.

The triple coincidence spectra (Figure 21) support
the placement of these states. Only the 381.5, “18.6,.
“23.5, and 762.5 keV transitions are seen to be in prompt
coincidence with the positrons. The positron branching
ratios calculated from early triple coincidence data

obtained from NaI(Tl) detectors were, in units relative

 

to the 762.5 keV gamma ray, “.0 i 0.8 for the 80“.7 keV
state, and 7.2 i 1.5 for the “23.5 keV state and agree
within the experimental error with those obtained by Beyer
from Fermi plots (62) which were 5.2 i 1.0 for the 80“.7
keV state and 7.9 i 1.5 for the “23.5. These values are
consistent with those calculated using the proposed decay
scheme, relative intensities, and theoretical K/B+ and
eK/eL ratios (21, 6“).

“.3.3. Evidence for States at
295.2 and 389.2 keV

 

The coincidence spectra show that the 1562.5 keV
gamma ray is in coincidence with the 9“.2, 290.2, and
389.2 keV transitions and that the 9“.2 keV gamma ray is
in coincidence with the 290.2 keV gamma. The 389.2 keV
gamma ray was not observed to be in coincidence with

either the 9“.2 or 290.2 keV gamma rays. The energy

 

 

123

difference of “.8 keV between the 389.2 1 0.5 keV, and

the sum of the 9“.2 : 0.5 and the 290.2 i 0.5 keV gamma
rays is too large to be accounted for by experimental

error of the energy measurements of these three gamma rays;
therefore, the 389.2 keV gamma ray cannot be a crossover
transition for just the 9“.2 and 290.2 keV gamma rays
alone. These coincidence data can easily be explained
with the inclusion of the unobserved 5.0 keV transition in

cascade with the 9“.2 and 290.2 keV gammas. Hence,states

were placed at 295.2 and 389.2 keV.

 

The evidence for the placement of the state at 295.2 in-
stead of 99.2 keV is weak.It consists of the fact that
the 290.2 keV gamma ray is slightly more intense than the
9“.2 keV gamma. According to the energy sum, the very weak
1796 keV transition fits very nicely between the states at
2090.0 and 295.2 keV. However, the 1796 keV gamma ray
was seen only once and then in an anti-coincidence spectrum
that was taken over a long period of time. Therefore, this
transition was not placed in the decay scheme.

“.3.“. Evidence for States at
l202.0,l2“2.6and 1952.2 keV

 

 

The anti-Compton and the "any gamma-gamma" coincidence
spectra indicate that the 1160.0, 1202.0, 1237.6, l2“2.6,
l9“7 and 1952.2 keV transitions are not in prompt coincidence
with any of the other gammas. Therefore, they probably

populate the “2.3 keV, 5.0 keV, or the ground state.

 

12“

Numerous coincidence relationships and energy sums support
the placements of states at 1202.0, l2“2.6, and 1952.2

keV. These are listed in Table 11.

“.3.5. The Remaining States

 

The remaining states account for a very small
fraction of the decays of 838r and were placed on the
basis of the coincidence data and, in a few cases, upon
the existence of an energy sum alone. These are summarized
in Table 11. Those transitions not observed in coincidence
and not satisfying an energy sum were left out of the decay
scheme. These were the 1296.0, 138“.3, 1596.0, 1710,

l7“9, and 1796 keV gamma rays.

“.3.6. Spin and Parity Assignments

 

Hobson et al., (65) and Hubbs et_al., (66) have
measured the ground state spin and parity of 83Rb to be
5/2-by atomic beam methods. Beyer has determined (62)
the spins and parities of the 5.0, 99.“, 389.2, “23.5,
80“.8, 1202.0 and l2“2.3 keV states on the basis of his
internal conversion coefficients measurements. His
results are listed in Table 12. These assignments and the
log ft values for the decay of 83Sr to the excited states
in 83Rb,imply that the ground state spin of 83Sr is 7/2+.

The spins (and parities) of the higher excited states
are shown on the decay scheme and are assigned on the basis

of the log ft values and gamma—ray branching to the lower

excited states.

 

125

Table l2.—-Spin and parity assignments.

—7 __-— m *—“
~— 1 m—m—

 

 

 

State Energy, keV Spin and Paritya
0 5/2:b _C
5.0 3/2 , 5/2
“2.3 9/2+
295.2 1/2‘
389.2 3/2'
“23.5 5/2+
80“.8 7/2+
aReference 62. bReference 65 and 66.

03/2’ is preferred.

“.“. Discussion of the Decay Scheme of 838r

 

Talmi and Unna predict 83Sr to have a ground state
spin of 9/2+. Excited states of spin and parity 1/2‘
and 7/2+ are predicted at 170 keV and 320 keV,
respectively (7). Their proposed level structure is
similar to those proposed for other odd mass strontium
isotopes (1), namely 85Sr and 87Sr. The 7/2+ ground state
assignment from the present data disagrees with their
predictions. However, the predicted 7/2+ state does lie
relatively low in energy. The observation has been made
that the Talmi—Unna-calculations are the only ones in this
mass region in which the energy of the 7/2+ state is
depressed so low (67).

It is interesting to note that the other odd mass
nuclei with “5 neutrons, i.e., 77Ge, 7gse, 81K

and r, all

have 7/2+ ground state spins (1). Thus, the 7/2+ spin

126

and parity assignment for 83Sr are consistent with the
systematics in this region. This 7/2+ spin and parity

could be achieved from the shell model configuration

-3
Of (39/2)7/2'

The level diagram for odd mass rubidium isot0pes
is shown in Figure 25. It is apparent that the level
diagram for 83Rb is consistent with those of the other
odd mass rubidium isotopes. The ground state (5/2’), the
5.0 (3/2'), and the “2.3 (9/2+) keV states in 83Rb can

be explained qualitatively by shell model proton
)1

 

configurations of (f5/2)_l, (p3/2)‘l, and (gg/2
respectively. As can be seen from Figure 25, the (p3/2)‘l
and (f5/2)_l configuration are in competition for the
ground state of the rubidium isot0pes. Hence, it is not
unusual for 83Rb to have a low lying 3/2- state, though the
data do not rule out the possibility that the spin of the
5.0 keV state is 5/2‘.

The higher excited states cannot be explained so
easily as they probably arise from more complicated shell
model configurations as well as collective excitations.
Beyer has suggested that the “23.5 and 80“.6 keV states
may be vibrational states built upon the 9/2+ level or as
arising from the coupling of the 2+ core excitation with
the 9/2+ particle state (62). However, both of these
interpretations have difficulties associated with them.

In the first case, the crossover to cascade ratio is

too strong by about a factor of 7 when compared to the

ENERGY

IN keV

500

400

300

200

ICC

127

 

 

9/2‘

 

(5/2*.7/gf)

 

5/2'

 

(3/27

 

(l/2'I

 

(S/ZW

3/2'

 

 

9/ 2’

 

9/2’

(3/2: 5/2')
3/27 5/2'/ 5/27 3/27 3/27
87

0| 03 - 85 89

3'er44 37R b 37R b“ 31R bso 37R bsz

 

Figure 25.——Comparison of the energy levels of the
odd—mass strontium isotopes.

 

 

 

128

neighboring 2Kr even-even nucleus. In the second

interpretation, the 381.5 keV transition would be expected

(19) to be Ml, whereas Beyer has shown (62) that the
transition is probably E2.

 

CHAPTER V

SUMMARY AND CONCLUSIONS

The high resolution spectroscopic study of
the decay of 82Br has identified the location of several
weakly populated states as well as confirmed some of the
previous results for the strongly excited states. The

gamma-gamma angular correlation measurements have enabled

the unique assignments of the spins to the strongly excited

 

states and the multipolarities of the transitions from
them. Transitions from the new weakly populated states
and log ft values were used to place limits upon the spins
and parities for these states.

The level structure of 82Kr was used to test the
asymmetric rotor model of Davydov and coworkers (“, 6).
The distortion parameters computed from the relative
reduced transition probabilities obtained in this work and
from the lifetime measurements by Beard (“6) were in fair
agreement with those calculated from energetics (17) for
the strongly excited states. However, the D-F model is
unable to account for the new weakly excited states. Even
so, because of the fair agreement for the strong transitions
of this nucleus, and for other nuclei in this mass region

which were discussed in the Introduction, it may be possible

129

130

to use the D—F model as an indicator for nuclei approaching
permanent deformation. At least in these cases, it
corroborates the calculations of Marshalek et_al. (5).

A consistent decay scheme for 838r was constructed
from coincidence dataCrecorded with high resolution Ge(Li)
detectorsL energy sums and relative intensities. The level
structure of 83Rb was found to be very complex with many
closely spaced excited states. An isomeric M2 transition
was discovered at “2.3 keV. The level structure is
incomplete in that it is not possible to make unique Spin

assignments to most of the known states. This makes

 

comparisons of this decay scheme with any theoretical
model difficult.

Since 82Kr and 83Rb differ by the addition of a
single proton to an even—even core, it was originally
anticipated that the states in the two nuclei might be
simply related via the core—coupling model. However, no
simple relationship was found to exist between the level
schemes. For example, it was not possible reliably to
determine the center of gravity of the positive parity
core-particle multiplets which would be built upon the
9/2+, “2.3 keV state. This determination and others were
hampered by the uncertainties in the spin assignments,
particularly for the high energy states. Likewise, the

determination of the core-particle multiplets which would

be built upon the 5/2’ ground state is complicated because

131

of the very close 3/2-, 5.0 keV state. Since both of
these nuclei are several protons and neutrons from
closed shells, the coupling between core excitation and
particle states might be considerably stronger than that
normally considered as valid for the simple core—coupling
model.

The ground state of 838r has been inferred to be
7/2+ from the data presented in this thesis. This

assignment is consistent with other odd—mass nuclei with

 

“5 neutrons. Although this assignment did not agree
completely with the predictions of Talmi and Unna (7),
their calculations appear to explain in part some of the
properties of odd-mass nuclei in this region of the
periodic table. Their calculations are the only ones for

which the energy of the 7/2+ state is brought down so low.

11.

12.

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