THE MICHTGAN STATE umvmsm'
31x GAP 3-an SPECTROMETER mm ms APPLICATION
TO THE 3- AND MAY specmoscomc STUDIES
or 33 Sr AND‘31mTa

Thesis for the Degree of Ph. D.
MICHIGAN STATE UNWERSTTY
LOUIS M. BEYER
1967

 

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thesis entitled

Six Gap B-Ray Spectrometer and its Application

 

to the B- and y-Ray SpectrOSCOpic Studies
' of 83Sr and l3lmTe I

presented by
Louis M. Beyer

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in PhYSiCS

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Major professor

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ABSTRACT

THE MICHIGAN STATE UNIVERSITY SIX GAP B-RAY
SPECTROMETER AND ITS APPLICATION TO THE 8- AND y-RAY

SPECTROSCOPIC STUDIES or 83Sr AND 131mTe

by Louis M. Beyer

A six gap, iron core B-ray spectrometer has been con-
structed. The instrument, often called the "orange" spec-
trometer because of its geometric similarity to an orange,
is similar to the one described by Bisgard. The spectrom-
eter and its associated components are discussed in detail.
A semi-quantitative theory of the focusing properties of a
l/r field is included and the defocusing componentsof the
field that are characteristic of this type of instrument
are discussed.

The orange spectrometer and the MSU iron free «f? spec-
trometer have been used to investigate the internal conver-
sion electron and positron Spectra emitted in the decay of
83Sr. Information on the multipolarities of the strongest
transitions has been obtained. The M2 multipolarity assign-
ment of the “2.3 keV transition, in conjunction with exist-
ing coincidence and lifetime measurements, show that the
low energy features (5 80A.6 keV) of the decay scheme are
uniquely determined. These data, when combined with log ft
values obtained from a Fermi analysis of the positron spec-

tra, lead to spin-parity assignments (in parentheses) to the

Louis M. Beyer
ground state of 83Sr(7/2+) and to the 5.0 keV(3/2'),
42.3 keV(9/2+), 99.2 keV(1/2’), 389.2 kev(3/2'), M23.5 keV
(5/2+) and 804.6 keV(7/2+) states of 83Rb.

The 7/2+ assignment to the ground state of 83Sr does
not agree with the shell model calculations of Talmi and
Unna, although their calculations do predict a low-lying
7/2+ state at 320 keV. The level scheme of 83Rb is also
discussed with respect to expectations based on shell model
systematics.

131mTe has been thoroughly

The gamma-ray spectrum of
investigated with the high resolution Ge(Li) detectors, ac-
curately determining the energies and relative intensities
of AS transitions in the spectrum. The use of the NaI(Tl)-
Ge(Li) coincidence technique has resulted in the placement
of all but six very weak transitions into a consistent de-
cay scheme. The orange and n/F spectrometers have been used
to investigate the internal conversion electron spectrum.
Conversion coefficients were obtained for the 80.9, 102.3,
1A9.7, 200.7, 2h0.6, 33u.5, u52.7 and 773.7 keV transitions.
Further information on spin-parity assignments has been pro-
vided by the calculated log ft values which were obtained
using gamma-ray intensities. The combined data provide a
level scheme for 1311 with the following energies (in keV)
and spin-parity assignments: 0(7/2+), 1H9.7(5/2+), u93(3/2+),
603(3/2T. 5/2*), 773.7(9/2T, 11/2T), 852.1(9/2+, 11/2‘),
1059.7(7/2+), 1315(7/2+). 1556.u(7/2+, 9/2T). 1596.5(7/2+,
9/2+), 16u6(9/2, 11/2), 1797(9/2‘, 11/2'), 1888, 1899(9/2',

 

' 17—44—15;

 

 

11/2’).

R
n

he
have be
and Chc
able fc

the deI

system:
iodine
behavi.

5/2+ S'

Louis M. Beyer

11/2‘), 1980(9/2‘, 11/2'), 2001, 2168 and 2270.

131I

Recent theoretical calculations for the states of
have been performed by Kisslinger and Sorensen and by O'Dwyer
and Choudhury. Although there are insufficient data avail-
able for a quantitative analysis, a qualitative comparison of
the data has been made for both sets of calculations.

Finally, a survey has been made of the energy level
systematics of the low energy states of all the odd mass
iodine isotopes. Of special interest is the observed quadratic
behavior of the energies of separation of the l/2+. 3/2+ and
5/2+ states with respect to the 7/2+ state, as a function of

the neutron number.

THE MICHIGAN STATE UNIVERSITY
SIX GAP B-RAY SPECTROMETER AND ITS
APPLICATION TO THE 8- AND y-RAY SPECTROSCOPIC

STUDIES OF 83Sr AND l3lmTe
By

Louis MfrBeyer

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Physics

1967

 

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P ' ‘ ACKNOWLEDGEMENTS

I wish to thank Dr. W. H. Kelly for the suggestion of
this thesis project and for his guidance and continued en-
couragement throughout the construction phases of the spectrom-
eter as well as the period of data acquisition and analysis.

I am indebted to the members of the shops for their as-
sistance and advice in the construction of the spectrometer,
especially Mr. N. Mercer, Mr. R. Geyer and Mr. N. Bird of the
cyclotron machine shop, Mr. R. Hoskins and Mr. N. Rutter of
the physics machine shOp and Mr. E. Brandt of the physics
electronics shop.

Mr. G. Berzins, Dr. R. Auble, Mr. R. Ethertcn and Mr. w.
Johnston have aided in the acquisition and analysis of the
data. Discussions with Dr. S. K. Haynes concerning the data
recorded with the n/E spectrometer and his interest in this
investigation have also been very helpful. In addition, dis-
cussions with Dr. D. J. Horen of the U. S. Naval Radiological
Defense Laboratory have been informative.

I wish to express my appreciation to Drs. w. P. Johnson
and H. G. Blosser for their assistance with the cyclotron oper-
ation during the early irradiations.

I am grateful to Mr. R. Dickenson and Mr. A. Kaye for
efficiently handling many of the acquisition problems associated
with the spectrometer construction and radioactive source de-
livery, and to Miss Wilma Sanders for typing the thesis.

I wish to acknowledge the financial assistance of the

National Science Foundation which provided partial support for
ii

 

 

 

luring mu

supported

Fr)

ina
helping t

perience.

the experimental program and the spectrometer construction.
During much of the time this program was in progress, I was
supported by an NDEA Title IV Fellowship. .
Finally, I express my gratitude to my wife, Faye, for
helping to make this an enjoyable as well as profitable ex-

perience.

iii

TABLE OF CONTENTS

ACKAVOWLEDGEIQENTS O O I 0 O O O O O O O O O O O O O O O 0

LIST OF TABLES
LIST OF FIGURE
INTRODUCTION .
A. General
B. Specifi
C. Methods
CHAPTER 1. NU

l.A.

l.C'

l.D.

IOE.

'The Shell

S O O O O O O O O O O O I O O O O O O O O

ObJeCtj-ves O O O O O O O O 0 O O O O O O

c Objectives of this Study . . . . . . . .

of Constructing the Decay Schemes . . . .

CLEAR MODELS . . . . . . . . . .

The Shell Model: Spherical Nuclei . . . .

l.A.l. The Auxiliary Potential . . . . .

l.A.2. Residual Interactions . . .p. . .
a) Nucleon-Nucleon Coupling . . .
b) Pairing Plus Quadrupole Forces
Model: Deformed Nuclei . . . .
1.8.1. The Nilsson Single Particle Levels

1.8.2. Additional Levels Built on the

Deformed Single Particle Levels .

The Collective Model: Even-Even Nuclei .
1.0.1. The Various Collective Excitations
l.C.2. Quadrupole Vibrations of

Spherical Nuclei . . . . . . . . .
l.C.3. Excitations of Permanently

Deformed Spheroidal Nuclei . . . .
l.C.A. Ellipsoidal Nuclei . . . . . . . .
The Collective Model: Odd Mass Nuclei . .
Summary . . . . . . . . . . . . . . . . .

iv

Page
. ii
.viii
. ix
. l
. l
. 2
. 3

7
. 7
. 7
. 10
. 10
. l2
. 15
. 15
. l6
. 17-
. 17
. 18
. 20
. 21
. 22
. 25

CHAPTER 2.

CHAPTER 3.

30A.
3080
3.C.

30D.

The Theory of Toroidal Spectrometers

The Michigan State University
Multigap Spectrometer . . . . . .

2.8.1.

2.8.2.

2.8.3.
2.8.“.
2.8.5.

2.8.6.

2.8.7.

THE DECAY SCHEME OF
SYSTEMATIC TRENDS OF ODD MASS IODINE
ISOTOPES

The Vacuum System . . . .

The Magnet System and Coil
D631gn o c o o o o o o o o

The Power Supply . . . . .
The Detector System . . .
Earth Field Compensation .

The Performance of the
Spectrometer o o o o o o 0

Comparison with Other Types

of Spectrometers . . . . .

131m

30.5 hr Te:

Introduction . . . . . . . . . . .

Source Preparation . . . . . . . .

The Gamma-Ray Singles Spectrum . .

Gamma-Gamma Coincidence Studies and the

Construction of the Decay Scheme .

3.0.1.

3.D.2.

3.D.3.

30Douo

3.D.5.

The Present Coincidence Spectrom-

eter and its Advantages .

Evidences for Levels at 150,

603 and 1060 keV . . . . .

Evidences for States at 852

and 1315 Rev 0 o o o o o o

Evidences for the 16A6 and
1980 keV Levels . . . . .

Evidences for the 1556, 1596,

1797 and 1899 keV Levels .

THE TOROIDAL FIELD ELECTRON SPECTROMETER

O

Page
27

31

A1
A2

43
AA

50
51

52

54

58
58
60
61

65
65
68;,
7O
71

72

CHAPTER

30E.
3.F.

3.C.

“.

“0A.
“OB.
“.C.

“.D.

“.E.
“OF.

Page

3.D.6. Further Evidence for the 1556,

1596, 16“6, 1797. 1899 and

1980 keV States . . . . . . . . . 7“
3.D.7. Evidence for the Placement of

Other Gamma Transitions . . . . . 78
The Internal Conversion Spectrum . . . . . 80
The Proposed Decay Scheme and Discussion . 85

Systematics of Odd Mass Iodine Isotopes . 91

CONVERSION ELECTRON AND POSITRON
MEASUREMENTS OF 3“ HR 83Sr . . . . . . . . . 99

Introduction . . . . . . . . . . . . . . . 99

Source Preparation 0 o o o o o o o o o o o 100

Apparatus o o o o o 0'. o o o o o o o o o 10“

Conversion Coefficients and
Multipolarities . . . . . . . . . . . . . 108

“ODOl.

”ODOZO
“.D.3.
“CDC“.

4.0.5.
“ODO6.

The Positron Spectra of

The “2.3 keV Transition and
the Searc for an Isomeric
State in 3S? o o o o o o o o o c 108

The 762.5 keV Transition . . . . . 112
The 381.5 keV Transition . . . . . 116

The 389.2, “18.6, “23.5 and
“38.2 keV Transitions . . . . . . 118

The 9“.2 and 290.2 keV Transitions 119

The 778.“ and 818.6 keV
Tran31tion8 o o o o o c o o o o o 121

83Sr . . . . . . . 121

Spin-Parity Assignments for the Levels

of 83Rb
“OFOl.
“.F.2.

and the Ground State of 83Sr . . . 12“
The “2.3 keV State Of 83Rb o o o o 12“

The “23.5 and 5.0 keV States of
83R0 and the Ground State of 83Sr 125

vi

“.G.

CHAPTER 5. AN

5.A.

“.B.

BIBLIOGRAPHY

“.F.3. The 99.2 and 389.2 keV States. .
“.F.“. The 80“.6 keV State . . . . . .

Discu3310n o o o o o o o o o o o o c o 0

ANALYSIS OF THE EXPERIMENTAL RESULTS . .

The Necessity for Electron Measurements
and Magnetic Spectrometers . . . . . . .

Comparison of the Experimental Results
with Predictions Based on Nuclear Models

vii

Page
126

127

128

131

131

133
135

Table

l.

2.

3.

m,,..1

squa

31111
doc

itlt

Table
l.

3.

7.

LIST OF TABLES
Page
Typical results of linear vs. quadratic least

squares fit to calibration points. . . . . . . . 66

I31m

The Te gamma-ray energies and relative

1nten31ties o o o o o o o o o o o o o o o o o o o 67

131m

Results of the Te gamma-gamma coincidence

StUdieS O O O O O O O O O O O O O O O O O C C O O 81

Results of the internal conversion electron

131m

measurements of Te compared with theoretical

values for the various multipole orders . . . . . 86

The 83Sr gamma-ray energies and relative

intensities . . . . . . . . . . . . . . . . . . . 107

Results of conversion electron measurements of

the “2.3 keV transition in 83Rb . . . . . . . . . 110

Multipole order of the transitions from the
decay of 83Sr based on measured values of the

internal conversion coefficients . . . . . . . . 115

viii

:3 cu
. ob‘re

L

A typ:
which

direc

can I
to SI
aCtu;
ical

fiel

F i gure

1.

3.

LIST OF FIGURES

Page
A typical electron trajectory in a 1/r field,
which has infinite extent in the z and r
directions. The curve was calculated by a
numerical integration of equations (11), with
the parameters a . 1.0 and b = 0.6. The unit

of length for z and r is arbitrary . . . . . . . 35

Typical electron trajectories in a l/r field

as a function of the parameter a for b a 0.6.
This figure thus shows how portions of the field
can be used for focusing. The orbits are drawn
to scale for the present spectrometer, and the
actual pole boundaries are shown. The theoret-
ical boundary for focusing, neglecting fringing

field3,1salSOShown 0000000000000 37

The central region of the Spectrometer showing
two of the six gaps, as viewed from above and

along the axis of symmetry. A typical fringing
field line is also shown and is decomposed into

its various defocusing components . . . . . . . “0

The circuit diagram of the fine current

regulation system . . . . . . . . . . . . . . . “5

ix

26

.‘s-
IF.
C

(.1)
o

The not:

with co:

The re f1
is cont
potenti
by a pr

automat

A block

Compari

transni

Figure
5.

7.

10.

Page
The motor driven transformer power source
with coarse current regulation. The coarse
current regulator drives the fine current

reenlator o c o o o o o o o o o o o c o o o o o “6

The reference voltage source whose output

is controlled by a stepping motor driven
potentiometer. The stepping motor is actuated
by a programmable pulser unit coupled to the

automation system . . . . . . . . . . . . . . . “7
A block diagram of the automation system . . . . ”9

Comparison of the six gap resolution vs.

transmission curve of the MSU spectrometer

with the prototypell). The full curve is

from ref. 11, while the experimental points

have been obtained with this spectrometer . . . 53

The K and (L + M) internal conversion

137m

electron lines of Ba, recorded with

the MSU orange spectrometer . . . . . . . . . . 55

131m

The low energy part of the Te gamma-ray

2 x “ mm

singles spectrum taken with a 2 cm
deep (0.8 cm3) Ge(Li) detector and an FET

preamplifier O O O O C O O O O O O O O O O O O O 63

315m

11.

12.

13.

Tee hi

Figure
11.

12.

13.

Page

1 1m
3 Te gamma.

The high energy part of the
ray singles spectrum, recorded using a

0.8 cm3 GE<L1> deteCtor o o o o o o o o o o o o 0 6H

The 131m

Te coincidence Spectra recorded
with a Ge(Li) detector of 0.8 cm3 active
volume, gated by a 7.6 cm x 7.6 cm NaI(Tl)
detector on the peaks indicated below each
spectrum in the figure:
a) NaI(Tl) gate on the 150 keV photOpeak
b) NaI(Tl) gate on the 665 keV photopeak
c) NaI(Tl) gate on the 600 keV photopeak

d) NaI(Tl) gate on the “52-“62 keV photopeaks. 69

The 131m

Te coincidence spectra recorded with
a Ge(Li) detector of 0.8 cm3 active volume,
gated by a 7.6 cm x 7.6 cm NaI(Tl) detector
on the peaks indicated below each spectrum
in the figure:
a) NaI(Tl) gate on the 33“ keV photopeak
b) NaI(Tl) gate on the 81 keV photopeak
c) NaI(Tl) gate on the 102 keV photopeak

d) NaI(Tl) gate on the 1126 keV photopeak . . 73

xi

31pm

l“.

15.

16,

17,

gets
The
the
bein

the

The

396:

was

Figure
1“.

15.

l6.

17.

Page

The 131m

Te coincidence spectra recorded with
a Ge(Li) detector of 0.8 cm3 active volume,
gated by a 7.6 cm x 7.6 cm NaI(Tl) detector
on the peaks indicated below each spectrum
in the figure:
a) NaI(Tl) gate on the 200 keV photopeak.
b) NaI(Tl) gate on the 200-2“1 keV valley.

c) NaI(Tl) gate on the 2“1 keV photopeak . . . 75

The 131m

Te coincidence spectra recorded with
a Ge(Li) detector of 0.8 cm3 active volume,
gated by a 7.6 cm x 7.6 cm NaI(Tl) detector.
The gates are taken in small increments across
the 800 keV region, the major contrihution
being that indicated below each spectrum in

thefigur‘e...................77

The 131m

Te coincidence spectra recorded with
a 7.6 cm x 7.6 cm NaI(Tl detector and gated
by a Ge(Li) detector with 12 cm3 active volume.
The energy range included in the gate is indi-

cated below each spectrum in the figure . . . . . 79

The 131mTe internal conversion electron
spectrum measured from “5 to 2“0 keV. This

was recorded with the orange spectrometer . . . . 82

xii

22,

”he K C
photope

with t:

The K a
l“9.7 I

was re

13mm

A com;
deter:
1311.
*I

I)

Figure
18.

19.

20.

21.

22.

23.

2“.

Page
The K conversion line of the 33“.5 keV
photopeak of 131mTe. This was recorded

with the orange Spectrometer . . . . . . . . . . 83

The K and L conversion lines of the
1“9.7 keV transition of 131mTe. This

was recorded with the MSU n/2 spectrometer . . . 8“

The prOposed energy level scheme for

1311 as seen in the decay of 30.5 hour

l3lmTe O O O O O O O O O O 0 O O O O O O O O C O 88

A comparison of the experimentally

determined energy states in 1271, 1291 and

1311.

*) Populated by the decay of 1318;Te only
+) Populated by the decay of both 131gTe

and 131%e O O O O O O 0 O O 0 O O O O O O 92

131

The states of 1271, 1291 and I as cal-

culated by Kisslinger and Sorensen3) . . . . . . 93

131

‘I and I

as calculated by O'Dwyer and Choudhuryu) . . . . 9“

The energy states of 1271, 129

The systematic behavior of the energies
of separation of the low lying levels of
odd mass iodine isotOpes with the neutron

numbers. A quadratic curve has been fitted

xiii

Fgme

26.

2L

28,

The p
trans
lines
the 1

measu
m

Spect

detec

The 3
01‘ t1—
SPECt

a

Aree

Figure

25.

26.

27.

28.

Page

by means of the method of least squares

to the data points. All values marked "A",
except the 5/2-7/2 value for 1231 and the
3/2-7/2 value for 1331, have been included
in the least squares fit. The values marked
"F" are those obtained from the fitted

equation 0 o o o o o o o o o o o o o o o o c o o 97

The proposed decay scheme of 83Sr. The

transitions indicated by the more intense
lines in the drawing are those for which
the internal conversion coefficients were

measured 0 o o o o o c o o o o o o o o o o o o o 101

The low energy part of the gamma-ray singles
spectrum of 83Sr recorded with a 7 cm3 Ge(Li)

deteCtor o o o o o o o o o o o o c o o o o o o o 105

The high energy part of the gamma-ray
singles spectrum of 83Sr recorded with

a 7 cm3 GC(L1) deteCtor o o o o o o o o o o o o o 106

The K, L and M conversion electron lines
of the “2.3 keV transition in 83Rb. This
spectrum was recorded with the MSU iron

free "I? SpeCtrometer o o o o o o o o o o o o o o 109

xiv

g: The inte
of 8351‘

recorded

3. Tm inte
8

of 3Sr

This we

tronete

A. The int
and 29C
83Sr.
two 111

record-

32. p.

Figure

29.

30.

31.

32.

Page
The internal conversion electron spectrum
of 83Sr spanning the 7“0-830 keV region,

recorded with the orange spectrometer . . . . . . 11“

The internal conversion electron spectrum
of 83Sr spanning the 350-““0 keV region.
This was recorded with the orange spec—

trometer o o o o o o o o o o o o o o o o o o c o 117

The internal conversion lines of the 9“.2
and 290.2 keV transitions in the decay of
838r. Different sources were used for the
two lines. The 290.2 K conversion line was
recorded using a source thick enough to
cause line broadening. These were recorded

with the orange spectrometer . . . . . . . . . . 120

The Fermi analysis of the positrons emitted
in the decay of 83Sr. These data were re-

corded with the orange spectrometer . . . . . . . 123

XV

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INTRODUCTION

A. General Objectives

A large fraction of our knowledge concerning nuclear
structure and nuclear forces comes from the study of radio-
active decay and nuclear reactions. The low energy struc-
ture of nuclei is often more precisely determined by the
former. However, nuclear reactions have the advantage of
access to the higher excitation energies, as well as being
able to populate new lower states which are forbidden in
radioactive decay, due to the operation of selection rules.
The phenomena which ESE accessible for study through radio-
active decay are still of basic importance for the under-
standing of nuclear structure in general. The studies pre-
sented in this thesis are intended as an extension of such
attainable knowledge using the techniques of beta- and gamma-
ray spectroscopy.

Information on nuclear level structure is obtained from
beta- and gamma-ray spectrosc0py via the construction of de-
cay schemes. The decay scheme gives information on the en-
ergy level structure of the nucleus of interest, as well as
transitions between the levels, and the energy level spins
and parities. The experimental results thus obtained can
then often be compared with existing theoretical calcula-
tions, which serve as a test of the proposed models, as well
as providing more complete and accurate information for fu-

ture calculations.

B.

One of t
studied, bot?
Leaving odd A
particular, :
shell plus 01
presumably a
the single p
”3? states,
from couplir
excitations
fraction of
thesis is d,
the energy .
have three 1
The °bSErve

I".
"393 COMpar

B. Specific Objectives of this Study

One of the most interesting series of nuclei to be
studied, both experimentally and theoretically, are those

having odd A and spherical equilibrium shapesl’Z).

In
particular, systematic trends of isotopes having closed
shell plus one or closed shell plus three nucleons are
presumably amenable to calculation by known techniques.
The single particle states are expected as the lowest en-
ergy states, while the higher energy states should arise
from coupling of the single particle states to collective
excitations of the core. To test this hypothesis, a large
fraction of the experimental studies presented in this
thesis is devoted to a study of the systematic trends of
the energy levels in the odd mass iodine isotopes, which
have three protons outside a major shell closure of fifty.
The observed results, although limited in character, are
then compared with existing calculations by Kisslinger

3) and by O'Dwyer and Choudhuryu).

and Sorensen
A second set of experiments has been performed to study
the level structure of 83Rb populated by the decay of 838r.
Although no calculations have been performed for the levels
of the odd mass rubidium isotopes, the ground state spin and
parity of 83Sr can be inferred from such a study. Talmi

5) have performed shell model calculations for 83Sr,

and Unna
predicting the ground state to have spin and parity 9/2+.
Thus the experimental results serve as an initial test of

these calculations. The level scheme of 83Rb, hitherto un-

gown, sel‘VE
Little know:
is of intere
tween an eve
region
by a single
well known6
proven to b

If '
.eve I‘tn le 3

known, serves to extend the energy level systematics in this

little known region of the periodic table. In addition, it

is of interest to see if a simple relationship exists be-

tween an even-even nucleus and an adjacent odd nucleus in

this region of the periodic table. The 83Rb nucleus differs
82

by a single proton from the Kr nucleus, whose states are
well known6). The energy level diagram has, in this case,
proven to be so complex as to mask the effects sought after.

Nevertheless, considerable information has been obtained

for the low lying single particle states.

C. Methods of Constructing the Decay Schemes

The data analysis approach that is described herein has
been to first construct the proper energy level diagrams for
the nuclei of interest, and then perform experiments to de-
termine the spins and parities of the levels. The former
is accomplished by accurate measurement of the gamma-ray en-
ergies and relative intensities, and by coincidence counting
techniques. The methods employed are not new, but the equip-
ment now available is a vast improvement over that which was
in use only a few years ago. In the studies presented here,
advantage has been taken of the high resolution Ge(Li) radia-
tion detectors, both in singles and coincidence counting ex-
periments. Multichannel pulse height analyzers with split
memories and multiple coincidence circuits aided in the

faster accumulation of the data.

line ass
served enere
scaly used :1
germ angulz
:‘ne coincide
cf emission
iication of
version ele
an addition
tae paritie
decay scher:
“Telex to
tion result
ESSiglments
'v'EI'Sion COG

In bet

pol"ticmal
L
hr:

x eleme

fine
P8183

The assignment of spins and parities to the various ob-
served energy levels is not quite so straightforward. A com-
monly used method of spin parity assignment is via gamma-
gamma angular correlation eXperiments7). The anisotropy of
the coincidence counting rate, as a function of the angle
of emission between two cascading transitions, gives an in-
dication of the spin sequence of the levels involved. Con-
version electron-gamma angular correlation functions contain
an additional term in the matrix element which depends on
the parities of the levels of interest7). However, the two
decay schemes studied by the author were found to be too
complex to allow the obtaining of reliable angular correla-
tion results with present methods. Thus the spin and parity
assignments have been based on measurements of internal con-
version coefficients and log ft values.

In beta-decay, the quantity f is defined asa)

m 22
f - do 9 q Fo(p.Z)Sn
o
where p - the electron momentum, q - the neutrino momentum,

Fo(p,Z) the Coulomb correction factor. The shape factor,

Sn' is introduced to extend the validity of the calculation

to forbidden transitionsa). For allowed transition, S1 - l.

The quantity f times the half life of the transition is pro-

portional to 5'1

, where E is the square of the beta decay ma-
trix element. Since 5 is a quantity independent of the lepton

energies, the "comparative" or "reduced" half-life, ft, should

uA‘ ‘He very d

“V. U

T-‘wfi‘. 1!“ CE

buckle-o 5
in specif‘. :i
spin-parity

attained by

In“
:Gvficn Of S

'r1

matter of g;
~19 interna

5

not be very different for transitions with the same degree
of forbiddenness. The ft value is also independent of the
decay energy and nuclear charge.

Empirical results have shown that log ft values, with-
in specified limits, are indeed characteristic of certain

spin-parity changesg). The partial half-life t can be easily

obtained by experiment, while f is tabulated8). Thus beta
decay transition probabilities immediately give us an indi-
cation of spin limits.

The ratio of the number of conversion electrons to the
number of gamma-rays emitted in a nuclear de-excitation is

the internal conversion coefficientlo) a,

219.
NY '

a.

The internal conversion coefficients are sensitive functions
of multipolarity, eSpecially for low energy transitionslo).
A measurement of a often can be used to determine the multi-
polarity, L, of the transition between the initial and final
states, 1 and f. The spin change between the two states
is then limited by

f L i J + J

1‘71 " Jr' 1 r‘

The parity selection rule is

an - (-l)L if the transition is electric (EL)

L+l

An - (-l) if the transition is magnetic (ML).

test of the 5
this study he
salueS.

In order
spectra, a ma
instrument is
spectrometer
graven to be
array of tee

Chapter
PCP'dlar nucl
Wis quali
‘mierstandir
chapter 2 de
01‘ which ac,
Tne anJlioa:
fairs-pay C:
' 31' are de:

'38 restilts

Most of the spin-parity assignments in the decay schemes in
this study have been made by use of measured a's and log ft
values.

In order to measure the beta and conversion electron
spectra, a magnetic spectrometer has been constructed. The
instrument is similar to the six gap, iron core, toroidal
spectrometer described by Bisgordll). The instrument has
proven to be a valuable addition to the already impressive
array of techniques now at our disposal.

Chapter 1 contains a brief summary of some of the most
popular nuclear models in use today. The discussion is
mostly qualitative in description, designed to give a cursory
understanding of the types of calculations being performed.
Chapter 2 describes the orange spectrometer, the construction
of which accounts for a large fraction of this thesis project.
The applications of the spectrometer, in conjunction with a.
gamma-ray counting system, to the decay schemes of 131mTe and
83Sr are described in Chapters 3 and A. A short summary of

the results are presented in Chapter 5.

As in ms
retical devel
rate hases.
correlate ex
tions of the
is made to b
rencve conf}
fuse the va:
the other he
Plain the p]
Ituclear the:
SCIJe Other :
forces.
Since .

CCZpari 8 0n s

f»

CHAPTER 1
NUCLEAR MODELS

As in many other areas of scientific endeavor, the theo-
retical development of nuclear physics proceeds in two sepa-
rate phases. In the one case, people develop models which
correlate experimental results and provide simple descrip-
tions of the phenomena involved. Attempts are then constant-
ly made to broaden the range of applicability of each model,
remove conflicts between the different ones and ultimately
fuse the various models into a single unified picture. On
the other hand, theories are developed which attempt to ex-
plain the prOperties from the fundamental laws of nature.
Nuclear theory has not been able to develop as completely as
some other fields due to incomplete knowledge of nuclear
forces.

Since a major objective of experimental study is for
comparison with theoretical predictions, a brief survey of a

few of the more successful nuclear models will be presented.

l.A. The Shell Model: Spherical Nuclei
l.A.l. The Auxiliary Potential

It has been known for many years that nuclei of neutron
or proton numbers of 2, 8, 20, 28, 50 or 82 and neutron num-
bers of 126 exhibit exceptional properties of stability,

analogous to shell closures of atomic electronslz). The

7

. s.
s'*'e ..

II"

In
nu!
agvmab

.4..."

.105‘".

-h1

 

‘ c
.5 exp.

. 61 ‘
;:r'tel

q
”IVA ‘
|“U.e c‘

‘Hflgnvn
"Vile.

5‘]
3. "\r

A. ,,
Tah‘s

39"Ond

 

4"A‘{

 

above have often been referred to as the "magic numbers" of
atomic nuclei. Magic number nuclei have been found to have
higher than average binding energy, an abundance of isotopes
(magic Z) or isotones (magic N), very small quadrupole moments
(spherical), and the very small thermal neutron absorption
cross section a(n,y) for N - 50, 82 or 126. The "Shell Model"

or "Single Particle Model",pr0posed independently by Mayerl3)

and by Haxel, Jensen and Suesslu)

,has enjoyed great success
in explaining the magic numbers and predicting; other pro-
perties of low lying levels in many nuclei.

It had long been known that the assumption of individual
nucleons moving in an auxiliary central potential V(r) would
produce the magic numbers 2, 8 and 20 15). The requirements
of V(r) were that it be fairly constant inside the nuclear
radius and have a short range, i.e., it does not extend far
beyond the nuclear radius. It was then found that the intro-
duction of an additional term in the auxiliary potential gave
a unique explanation of the shell closures at all observed
magic numbers. It was postulated that there exists a strong
coupling between the spin and orbital angular momentum of
each individual nucleon. The sign of the term is opposite to
that found for atomic electrons, and its magnitude is approxi-
mately 30 times that predicted by relativistic Thomas coup-

ling13’lu),

In such a theory, which neglects tensor forces
between nucleons, conservation of the orbital angular momen-

tum l is still implied.

 

 

 

 

 

III

I"

.
II“

.p' .

u.

w.

.-

DU

'0

k!
In

Cl:

‘4‘

9

With inverted spin-orbit coupling, every level of given
1 splits into two levels with angular momentum j - 2 - 1/2
and j I L + l/2, the latter lying lower. The energy differ-
ence between these two levels is proportional to 2s + 1,
which means that splitting increases with increasing 2. Cal-
culations based on the model predict energy gaps after proton
or neutron numbers which correspond to the magic numbers, as
the shells are filled.

The shell model, as described above, also makes unique
predictions about the properties of nuclei which have only
one neutron or proton outside of, or missing from, a closed
shell. The angular momentum, parity and magnetic moment are
that of the extra nucleon or hole. For this reason, the model
is sometimes called the "extreme single particle model". For
such nuclei, shell model predictions are in substantial agree-
ment with experimental results. The same holds true in many
cases for single particles outside closed subshells. The
more general case, of course, is that of several particles

16) have augmented the

outside closed shells. Mayer and Jensen
shell model by the inclusion of j-j coupling together with

some very simple coupling rules. With such a scheme, the

ground state spin and orbital angular momentum can be predicted,
as well as more model sensitive properties like electric quad-
rupole and magnetic dipole moments, and transition matrix ele-
ments. The model has enjoyed considerable success, especially

for ground states and low excited states of some odd A spheri-

cal nuclei.

10

l.A.2. Residual Interactions
a) Nucleon-Nucleon Coupling

Except for low energy excitations in odd A nuclei, the

6)

model of Mayer and Jensen1 is not expected to give good re-
sults. The "extended" or "intermediate coupling" single
particle model has been introduced in an attempt to extend

the useful range of predictionsl7). The fact that coupling
rules were necessary in the original model demonstrated that
the effect of nuclear interactions cannot be completely re-
placed by a potential well plus spin-orbit coupling. One
expects a residual interaction potential arising from nucleon-
nucleon forces. Such a residual interaction is important in
determining properties of excited states.

Initial calculations based on the intermediate coupling

scheme consisted of solving

ifs - [Ho 4- Agni-31 + §>KV1KJw - En.

where H0 is the Hamiltonian for independent particles in a
harmonic oscillator welll7). The additional terms are the
single nucleon spin-orbit potential plus a residual two body
interaction. The procedure is to obtain the closely spaced
single particle levels determined by the first two terms in
1?. Nucleons are distributed in these levels in all possible
ways consistent with the Pauli principle. The single nucleon

angular momenta and isotopic Spins are then coupled to obtain

I ”A
‘0‘ ,5
I: “G
ou' ‘~
5. p «‘1
“..V"
o

I: 5’
an. H:
.,o‘l fi'
file...

 

.0. U ‘

 

'1.
L!
p

h‘

l_ rm
I

O

'1

S
in
'4 1

arr-1511.
..)
j

11

all possible resultant angular momenta and isotopic spins.
The resultant wave functions, which are many particle wave
functions, are then used to diagonalize the total Hamiltonian.
The calculation is feasible only if the number of nucleons in
unfilled levels is small. Results of this type of calculation

are exemplified by the calculation of Elliot and Flowersla)

for 19F.

The agreement between experimental and calculated
quantities is very good except for the electric quadrupole
(E2) transition rates. This discrepancy is typical for inter-
mediate coupling calculations. One solution to this problem
has been to use a potential which will enhance E2 transition
rates, i.e., a potential well with a quadrupole deformation
instead of a Spherical shape.

A somewhat different approach to shell model calcula-
tions with nucleon-nucleon interactions is that of Talmi and

5) who determine an effective nuclear interaction rather

Unna
than use a phenomenological potential. The method, applicable
to regions near closed subshells, determines the unknown diag-
onal matrix elements of two-body effective interactions be-
tween nucleons by comparisons with experimental data, and then
assumes the interaction to be the same for all nuclei in which
the same subshells are being filled. The non-diagonal ele-
ments, arising from configuration interaction, are determined
along with the diagonal elements by comparison with experi-
mental data. These terms are also assumed to have the same

values in all nuclei in which the same subshell is being

filled. The success of the approach depends on the considera-

t

01A;
"U‘. ‘
,, e};
..l i.ev
'n\
U
n.
b.
. a A‘-
.3: Ge

13:97.71

 

 

.e.‘,a"r:
2.2 V“:
(a ‘I'
V; H ‘
“a a
v era
:14 .
my. Y‘.
,1.

 

“kw—3m”
;' .
(D
0‘ J

12

tion of as many data points as possible. Predictions made

90

by the model in the Zr region do indeed seem to be realistic.

b) Pairing Plus Quadrupole Forces

3)"

The recent model proposed by Kisslinger and Sorensen
has at least partially removed objectionable features of the
intermediate coupling shell model. These authors have utilized
the pairing force introduced from the superconductivity theory

by Belyaevlg)

, plus a quadrupole force term. The inclusion

of such a pairing force tends to abstract the features of in-
teraction calculations into a more simplified form, which can
thus be applied over a wide range of more complicated nuclei.
The quadrupole term has the effect of introducing coherent
behavior amoung nucleons which is needed for enhancement of

E2 transition rates. The main assumption in the calculations
of K S is that the low lying states of spherical nuclei can

be treated in terms of two basic excitations, quasi-particles
and phonons. The pairing force gives rise to the former and
the quadrupole term accounts for the latter type of excita-
tion. For the most part, K S treat these as separate modes

of motion. The quasi-particle excitations, Ej' are calculated
in terms of the single particle energies e,, the average Fermi
energy A, and a quantity called A, which is approximately one-
half the gap in the even proton or neutron spectrum. 'The ex-

pression for E is:

J

_ _ 2 21/2
EJ {(.:J a) {A}

 

a
Hereafter referred to as K S.

‘-

.L'

 

 
    

I" .
vuvl

c ’ s
N‘u‘ua {M's-u". 30"!" ar-vm

14

Jet: a
.0!“ V
to} ’
00" o
. .L!
II.:V‘
rue: 1
its a

'A'EI‘E i
-‘ ‘ c.
3.3 v

umg“
1‘3“.
-'_:
n
.I.. s
t“
r
I
we I
‘A
a! I
f. '4
b.‘
"“5
..
:8
a..."

13

In order to treat a large group of nuclei, K S have
chosen ed for the various single particle levels and allowed
them to vary as a smooth function of A in order to agree
with experimental results. Different level spacings were
used for neutrons and protons. In the region of their cal-
culations, neutrons and protons are filling different shells,
and since the pairing force is most effective for shell model
pairs coupled to J - 0, two pairing force strength parameters

were used, G and Gn' The quadrupole force is effective for

P
all types of pairs, and thus has three strength parameters,
Xp, Xn and an.
Having chosen the parameter, K 8 approximately diagon-
alize the pairing Hamiltonian by use of the quasi-particle

transformationlg)

for neutrons and protons separately. The

quadrupole force is then described as an interaction between
the proton and neutron quasi-particles, which gives rise to

the phonon excitations.

The treatment of the quadrupole force is via the "quasi-
particle random phase approximation". The reason for using
this approximation instead of ordinary perturbation theory is
that only 2+ states among the many two quasi-particle states
are affected. This gives rise to a spectrum of energy levels
characteristic of energy levels in even-even nucleil), i.e.,

+, h+ triplet at

a 2+ first excited state followed by a 0+, 2
twice the energy‘hw of the first 2+ state. Thus, for even-
even nuclei, the essence of the QRPA is to neglect terms in

the quadrupole operator whose effects are spread over many

fi ’fi
J. H!

to. it.

 

5:»‘1
Shiv.

'Asu
“a,

  

.a J
L -
5n
( 2.

.cc- ”we‘rww—“a- .— “mm—'a—ri

4‘“
I.

1“

pair states of various angular momenta.

The model has been successfully applied3) to nuclei from
Ni to Pb,excluding the strongly deformed region (150 5 A 5 190).
Agreement with energy level systematics throughout the region
is qualitative, and E2 transition probabilities for the even-
even nuclei are within a factor of two of the experimental
values for the 2+ + 0+ gamma transitions.

More recently, Sorensen has performed calculations on
E2 transition rates in odd mass spherical nucleizo). His re-
sults agree with experimental values to within a factor of
two, while the actual values range over a factor of 1000.
Thus, even though the calculations based on pairing plus quad-
rupole forces are, relatively speaking, very simple, the suc-
cess is undeniable. The underlying reason is because this
particular combination of forces leads naturally to the two
most important residual effects, i.e., pairing effects and
quadrupole deformationzl).

Although the K S calculations have given good results
for spherical nuclei, they are not intended to be accurate
for deformed regions for the simple reason that K S have con-
sidered the quadrupole term weak in comparison with the pair-
ing effect. Investigations have now been undertaken to ex-
tend this type of calculation into the deformed regions by
considering the former to be slightly stronger22). Initial
calculations on the samarium isotopes indicate the model to

be very promising23).

.
.‘u‘

9

n
00“"

,s.g

d" O

4'! .I

A
A.

i

.1

‘.
n

s

b

_ t
f"
fly“

 

fi“
.1

4!
D»

15

1.8. The Shell Model: Deformed Nuclei
1.8.1. The Nilsson Single Particle Levels

For nuclei sufficiently far away from closed shell con-
figurations, nucleon coupling gives rise to non-spherical
nuclei. That such a phenomenon should exist can be pictorially
explained in a progressive manner. If there is a single nu-
cleon outside a closed shell moving in a shell model orbit-
al, the nucleon density distribution is already non-spherical
and concentrated in an equatorial plane. The addition of a
second nucleon will best correlate with the average field of
the first by moving as close to the plane of the first as pos-
sible. As can be seen,this is a compounding process. Thus,
far from closed shells, nuclei are expected to be ellipsoidal.
The amount of deformation is limited, of course, by the pairing
correlation which tends to couple pairs to total angular momen-
tum I.- 0 spherical distributions.

Two different models have been used for calculations in
the deformed region. The first, the collective model, sepa-
rates the nucleus into a core and extra-core nucleons. This
model is considered in the next section. The second, labeled

‘3)

as the Nilsson model2 , is in reality an extended single par-
ticle model. The auxiliary potential is considered nonspher-
ical, the energies of the single particle states are calculat-
ed as a function of a deformation parameter 6, and the dis-

tortion which gives the minimum energy is taken as the actual

distortion. 6 is, in general, different for each single par-

 

 

 

0:0.3

we...

“.50

4:..-

.53..

a;
'5

‘e

l6

ticle state. The actual potential used by Nilsson is

2

V1 - Vo{(l + 26/3)(x12 + 312) + (l - A6/3)z12 + C2 as + Dei

1 i
The above is, of course, an axially symmetric potential with
5x I 6y - 6/3, 62 - -26/3. The term in 12 serves to depress
higher angular momentum states, leading to better agreement
with the observed order. The constants C and D are chosen
to yield the shell model states for 6 - 0. Nilsson has pre-

24)

sented his results in now famous diagrams, depicting the

level spacing as a function of 6.

1.8.2. Additional Levels Built on the Deformed Single Par-

ticle Levels

Collective motions of the core nucleons are also known

to give rise to rotational levels, i.e., levels with spacing
,fi2
AE-fii(1+l), i‘K.K+1.K+2.eeo,

where K is the projection of j on the nuclear symmetry axis.

Thus, for odd A nuclei in the weak coupling limit, the spec-

trum of energy levels should be a few intrinsic states with

a superposition of bands of rotational levels built on each.
More recent calculations including additional force terms

due to pairing and Coulomb effects have been performedZS) to

obtain an expression for 6. Such calculations are two-fold.

First, they give a general contour of deformation over a much

1?

broader range of nuclei than have been experimentally observed.
Second, nuclear regions are searched where deformations might
be expected but have not yet been experimentally observed,
serving as a guide to future experiments to test the model.

The Nilsson model has enjoyed tremendous success in ex-
plaining the properties of odd-particle states in deformed
nucle126). It has also been successfully applied to nuclei
which were not previously thought to be deformed. A case in

point is the discovery by Pau127) 19F

that the spectrum of
can be described by the Nilsson model and that, in addition,
the quadrupole transition rates are in better agreement with
experiment than those derived from complicated shell model

calculationsla).

l.C. The Collective Model: Even-Even Nuclei
l.C.l. The Various Collective Excitations

As introduced in the previous section, the collective
model treats the nuclear core macroscopically as a deformable
liquid drop with perhaps a few extra nucleons in an unfilled
shell. For nuclear considerations, the core is considered as
an incompressible, irrotational fluid, and the system then

quantized12). Excited states of the nucleus can then arise

from collective motions of the core, either through rotation
of the body-fixed axes about the space-fixed axis, or by vi-

brations of the nuclear surface with respect to the body-fixed

av

 

 

The

18

The system has been treated in detail by A. Bohr28)

29).

axes. and

extended by Bohr and Mottelson

l.C.2. Qnadrnpple_y1brations of Spherical Nuclei

Let us consider the vibrational effect first. The surface

of the figure of general shape can be expressed as

m A
U
R(e,¢) - ROEI + 2 2 <1quA (6.c)]
A=o uI-A
where the T:(6,¢) are the Spherical harmonics.

Surface motions are expressed by allowing “Au to vary in

time. In the quadratic approximation, the kinetic and poten-

tial energies are of the form

T - 1/22 B In
A,u A Au

V ' l/ZX CAIGA I2.
A,u u

C and BA are related to the equilibrium radius, Ro,and to the

A

surface tension, S. Such estimates are useful for nuclei

provided appropriate values of R0 and S are used.

The frequency associated with the variable “Au is

1/2
“A ' (CA/BA)

80

E 3 nxfiwx.

19

The A I 0 term describes density oscillations of a spherical
nucleus whid1,if they occur, would be at much higher energies
than incompressible vibrations. The A I 1 terms simply describe
translations of the center of mass and are not internal degrees
of freedom. Thus,the first excited vibrational state corre-
sponds to the A I 2 quadrupole excitation and is therefore a

2+ state (the ground state of all even-even nuclei have J I 0+
andmost nuclei have a 2+ first excited state). Because of A
dependence of ml, w3 I 2w2 and mu I 3w2. Hence,no addition-

al terms are needed to describe low energy excitations.

Nuclei which can oscillate collectively about a spherical
shape should thus show characteristic spacing of energy levels.
The first excited state should have a 2+ state corresponding
to A I 2. A A I 3 phonon excitation has about the same energy
as two A I 2 phonons, so the second excited state should be a
3' state or a 0+, 2+, u‘ triplet. The latter is usually sepa-
rated by perturbations arising from the coupling of two A I 2
phonons to the 0+ ground state. The center of gravity of the
two phonon triplets should be about twice the energy of the
one phonon state. The hydrodynamic model predicts'hw2 should
be about 2 Mev for A near 100 and fall to 1 MeV for A near
200. In reality, E2./E2 does in fact cluster around a value
near 2, but‘hw2 is approximately half that predicted. This

simply means that the hydrodynamic calculations for C and BA

A
are not accurate enough. The crucial test of the theory is
the comparison of the E2 transition rates with experiment.

They are in substantial agreement, indicating that the low

' "I e!
-au
‘d

{pey-

,nvsl
I

up!“

IuV'

oIVI

EA‘:
HI”-

(I!
(l)
l’ 9‘

‘I .
Q ‘-
.U-nl
A

1‘-

v...
A

 

(ll

be!

HI
'0».

I.
D
9 O,

I
(.

 

20

lying states of even-even nuclei are probably one and two
phonon quadrupole vibrations. The regions of deviation are

those where nuclei are known to have permanent deformations.

I.C.3. Excitations of Permanently Deformed Spheroidal Nuclei

Nuclei with permanent, non-spherical shapes can also be
considered in the framework of this model, but a different
set of coordinates is more convenient. Considering only
spheroidal (A I 2) deformations, the orientation of the prin-
cipal axes of the nucleus with respect to the space fixed axes
is specified by the Euler angles. By well known transforma-
tion equations, the five variables 32“ are replaced by the
three Euler angles, and B and y. B is a measure of the total
deformation of the nucleus and y indicates its shape. The
equations defining B and 7 show that if 8 changes in time,
producing B vibrations, while 1 remains fixed, the nucleus
preserves its symmetry axis but alters the eccentricity of
its elliptical cross-section. The axial symmetry of the nu-
cleus is lost in y vibrations.

In the new coordinate system,

2
w

. .2 2.2 3 ‘J
{f0 - 1/2s(e + s y ) + 1/2Z K K

K81

where the w are the angular velocities of the principle axes

K
with respect to the space fixed axes andsJK correspondg to
the moments of inertia. Thus, terms corresponding to rota-

tional motion are automatically incorporated into the theory.

em
.0.

us

‘0

4....

 

 

;»....
osy‘"

 

.l 'n‘
I.
I. .

 

‘lv.l

‘
19‘

,‘
've

21

For axial symmetry, such a term predicts low lying states

EJ-g J(J+ 1), J-o,2,u,----,
Experimentally observed level spacings agree quite well with
this prediction. Small deviations may be ascribed to weak
coupling of the rotational modes of motion to other modes,
either vibrational or particle. The remarkable accuracy with
which experimentally observed energy levels in distorted

1'12) leaves little doubt

nuclei fit the rotational formula
about the collective nature of the excitations.

B and y vibrational levels are expected to be much higher
in energy than the rotational bands. Thus, distorted nuclei
will,in general, be expected to exhibit rotational bands built
on the vibrational levels. Due to weak coupling, the rotation-
al spectra of succeedingly higher bands are expected to show
more deviation from the predicted level spacing. Of course,

the possibility of particle excitations is also present, but is

not expected below 1 MeV for even-even nuclei.

l.C.“. Ellipsoidal Nuclei

Davydov and coworkers have considered the rotational
levels of permanently deformed non-symmetric nuclei in a series
of articles, beginning in 1958 3O). The model predicts slight
deviations from the J(J + 1) energy level separation of the
rotational states, but such an effect could be masked by coup-

ling to B or y vibrations. A very sensitive test of the model

.
«u
U)

nun. ‘

u!
I'- vb I

.3 ap-
.

.. Duel

we“

'II'.

old.

 

 

 

a
a“ o-
.

 

1"... I. 'POW m

 

22

lies in the fact that it predicts a 3+ state, whose energy is
the sum of the first two 2+ states. This prediction has been
confirmed in about a dozen cases. The model has also been

6,31)

tested in the spherical region and, for reasonable values

or the parameters, predicted E2 transition rates are in agree-

ment.

l.D. The Collective Model: Odd Mass Nuclei

Odd mass nuclei exist with both spherical and deformed
shapes, just as in the case of even-even nuclei. Those with
permanent deformations fall in the same regions of the periodic
table. The odd nucleon is expected to give rise to low energy
states and the ground state should be characterized by a
shell model configuration. For spherical nuclei, the single
particle model predicts the ground state, while the Nilsson
model is applicable in the (axially symmetric) deformed regions.
In addition, there should be states arising from the coupling
of states of the odd particle with collective excitations of
the core in both regions.

Let us first consider the near spherical nuclei, where

the Hamiltonian can be written as

x/ - Hc + Hsp + Hint'

H is a weak surface coupling term. It is only appreciable

int
in the tail where the nuclear density is changing, and can be

treated by perturbation methods. De Shalit has discussed pos-

 

  
   

S
s
g
i
F
F.

 

.J'.

a
use"

Ola!
volts

a
‘i

.l‘
.-

Uni

ID'II
’5‘!
n

.u
"

a s
(A)
(I)
-n

In}.

w.‘

.- -;
"In?

Cl)

 

23

sible experimental evidence for such a mode132)

. The expecta-
tions based on such a model are as follows: The lowest lying
states will be the single particle states. At higher energies
the core can give rise to quadrupole vibrations and, when
coupled to the single particle state j, can produce a multiplet
of states with spin J I j i'2, j i»l, or j. The "center of
gravity" of the multiplet should be hm, the first phonon en-
ergy of the core. The Splitting of the multiplet arises
from, and perhaps gives a measure of, the perturbing effects
of the interaction term.

A more complex problem arises when two A I 2 phonons or
a A I 3 phonon excitation of the core is considered. In such
cases both particle and collective states are expected to be
modified and considerable mixing of the states may occur.
Under these circumstances one can no longer expect to describe
a state as particle or collective, but as an admixture of both.
The situation is then described as "intermediate coupling".
Calculations based on such a scheme have been performed for

specific nuclei by Choudhury33) 3“)

35)

, Glendenning

1
, and O'Dwyer and Choudhury4). The calculations of

, Bannerjee and
Gupta
O'Dwyer and Choudhury are of particular interest here since
they have been performed for the odd mass iodine isotOpes.

They have considered the last odd proton of’these 53 proton
and 2d

nuclei to have the 2d single particle

5/2' lg7/2 3/2
states available. The proton state is then coupled to the
collective surface vibrations of the even-even core. The re-

sulting Hamiltonian of the coupled system, including one and

,..o

,n.

.
"4
Its.

DA

IV

6

1

«Ab
- -.

 

    

ICC,

‘-

 

. . .- 1" a“. .t.

 

:1. ‘

Viv

R:

2“

two phonon states associated with quadrupole vibrations, is
then diagonalized. The inclusion of the d3/2 state was found
to favorably influence the results, depressing the g7/2 state
sufficiently to make it the ground state for the higher mass
isotopes, in agreement with experimental results. The model
predictions are discussed further in Chapter 3. It should
also be pointed out that this type of calculation is expected
to improve as better experimental data for fitting of the
parameters become available.

Excited states of deformed nuclei have been discussed by

36)

Kerman and, from a different approach, by Pashkevich and

31)

Sardaryan . Kerman has obtained an expression for the energy
level spectrum for axially symmetric nuclei by considering
strong coupling of the Nilsson levels to rotational states of

the deformed core. The energies of the excited states EJ K are
t

given by

2 2 J+l/2

h [J(J+l) — 2x + 6K,l/2a(-l) (J+1/2)]

E

21

J,K" "K+

where EK I Nilsson single particle energy, J I total angular
momentum, K I projection of J on the nuclear symmetry axis,
.3. the moment of inertia, and a I the decoupling parameter.
The fact that only one moment of inertia,e£, enters into the
equation stems from the axial symmetry. of the motion of
the nucleons. There is no quasi-rigid rotation about the

symmetry axis, but collective oscillations of nucleons giving

rise to surface waves. Thus J3 I 0 andeo IJ, IJZ. The de-

 

 

 

4...
iv‘

aq‘
at.

5.9

9".

‘ll

3..

.“i
'0!

FW‘
VsI

I“

(V
f)

V.

(J

1""

(I.

25

coupling parameter expresses the strength of the particle-
rotational motion coupling. The energy level spectrum is
then a rotational band built on each single particle level.
All values J': K are permitted, and when K I l/2, the spec-
‘trum order is J - K, K + 1, K + 2, ..... If K - 1/2, the
ordering is determined by the value of a; viz. a I -2.5, the
order is 3/2, 1/2, 7/2, 5/2, ll/2, 9/2, .... Additional
correction terms arise from weak coupling of rotational-vi-
brational coupling. Kerman's calculations have been success-
fully applied to describe the levels of odd A deformed nu-
cle136).

The calculations of Pashkevich and Sardaryan3l) involve
asymmetric deformations. They are quite successful for nuclei
in the deformed regions. The authors have also performed cal-

1.. 119

culations for the "spherica Sb nucleus. Comparison of

the predictions with the most recent experimental data shows
some agreement with the low energy states, but cannot explain
the observed negative parity state nor the low spin states oc-

curring above 1 MeV37). However, the overall agreement is prob-

ably as good as that of Kisslinger and Sorensen's calculationsB)

l e E 0 Summer}!

To summarize, the model calculations of particular inter-

est to the experimental results reported here are those of

3) Ll)

Kisslinger and Sorensen and of O'Dwyer and Choudhury for

the iodine isotopes, and those of Talmi and UnnaS)

l6)

and Mayer

and Jensen for the strontium and rubidium level schemes.

 

{1’ >-
r .o
. . .

26

The results are presented in more detail in Chapters 3 and A

in connection with the decay scheme discussions.

’I

is

a.

in!

ps

“I

 

 

~16

h“

 

 

CHAPTER 2
THE TOROIDAL FIELD ELECTRON SPECTROMETER

One of the most valuable instruments in nuclear spec-

troscopy for the study of internal conversion electrons
still is the magnetic spectrograph, in spite of the recent
advances in high resolution semiconductor detectors. Con-
version electron spectra afford accurate determinations of
nuclear transition energies as well as allowing the separa-
tion of many peaks not resolved in the NaIKTl) gamma scintil-
lation detectors. Until recently, typical resolutions for
gamma-ray detectors were in the vicinity of 8% while electron
spectrometers operate in the range from A1 down to 0.01%, de-
pending on the type of instrument. The lithium-drifted ger-
manium detectors [Ge(Li)] have now removed the resolution
problem to a great extent for gamma rays. However, the elec-
tron spectrometer remains important because of the additional
information which it makes available.

The relative intensities of the internal conversion elec-
tron lines and photons from transitions between nuclear en-
ergy levels can give accurate information on the multipolari-

ties of the transitions. In particular, the internal conver-

sion coefficient a, defined aslo)
a _ Ne
N?

is a very sensitive function of multipolarity for a particular
27

28

energy. Thus, measurements of the electron line intensities

of a single nuclear transition, denoted by K, L L L

I’ II’ III
..., with respect to the number of gamma rays of that trans-

ition, determine the “K' “L , “L “L , .... When these

I II’ III 10)
numbers are compared with the accurate theoretical values
for the a's, the multipolarities are determined. The conver-
sion coefficients become quite large for low energy, high
multipolarity transitions. Thus, if such a transition exists,
conversion electron measurements become essential for a com-
plete decay scheme analysis since such transitions are often
almost totally converted.

Aside from conversion electron spectra, magnetic spectrom-
eters are well suited for detailed study of continuous beta
spectra, which also yields additional information to the ex-
perimenter.

The first beta-ray spectrometer that utilized the focusing
properties of a magnetic field was constructed by J. Danysz38)
in 1912 while an assistant in the laboratory of Marks Curie.
Following the success of this first simple instrument, empiri-
cal and theoretical studies on magnetic focusing have advanced
tremendously39). Spectrometer design and construction have
taken on many facets. However, the spectrometers can be cate-
gorized into two general types: a) the transverse field or
"plane focusing" and b) the longitudinal field or "space fo-
cusing" spectrometer. In the transverse field spectrometer,

the electron orbits are circular, lying in a plane, while a

longitudinal field produces helical particle paths. The lat-

29

ter is generally referred to as a "lens" spectrometer. The
type of spectrometer constructed is governed by the experi-
mental situation, e.g., the famous transverse field n/f'in-
strument gives the highest resolution yet attained while the
lens type has a higher transmission.

Prior to 1950, spectrometers had the inherent (and un-
desirable) feature that T/RSZ, where T is the transmission
of the instrument and R I Ap/p is the resolving power. Thus
a wfl? spectrometer operating at 0.10% resolution would have
a comparable transmission, while a lens spectrometer opera-
ting at 2.0% resolution may have a transmission as high as
“Z for the double lens system. At this point Nielsen and

Kofoed-Hansenuo)

turned their attention to investigating a
totally different design whereby, with modest resolution of
the order of 1%, transmissions as high as 10% could be at-
tained. The result of this work is the "orange" spectrometer,
so named because the magnet wedges and air gaps are a geomet-
ric facsimile of orange segments. The original machine and
the majority of those which followed are constructed of six
wedge shaped magnets, separated by six wedge shaped gaps
through which the electrons travel, Thus, it is actually six
spectrometers, symmetrically arranged around a circle. The
symmetry of the machine has led to additional advantages
other than the originally intended one of higher T/R ratio.
The orange spectrometer, as originally constructed by

Al)

Nielsen and Kofoed-Hansen and later enlarged by Bisgfirdll),

is a completely symmetric instrument. The source and detector

30

are placed on the symmetry axis equidistant above and below

the median symmetry plane of the spectrometer. The gaps and
magnet wedges are placed around the symmetry axis. In theory,
the entrance and exit profiles of the pole tips are identical.
Thus, the field is essentially a toroid, with the central
portion of the machine free of magnetic fields. This facili-
tates the placement of an alpha, beta or gamma detector direct-
ly above the source for experiments involving coincidences of
these radiations with the focused electrons.

The geometry is also amenable to the introduction of an
accelerator beam, using the target as a sourceuz). The high
transmission of the instrument should thus make electron studies
of very short-lived isotopes or states (5 1 sec) feasible. The
group at Chalk River has recently performed such experiments
with a 7 gap orange spectrometer and a Tandem Van de GraaffuZ).
It is also possible to use a separate detector for each gap and
with such an arrangement, directly accumulate information on
the angular distributions of the conversion electron spectrum
in coincidence with direct reaction particle groups. The MSU
instrument was originally conceived for such on-line cyclotron
experiments, independent of the above referenceu2). However,

the incomplete beam transport system has thus far limited our

studies to conventional radioactivity investigations.

 
 

31

2.A. Theory of Toroidal Spectrometers

The theory of the focusing of a % type magnetic field,
and its application to orange type spectrometers, has been
studied in detail by Jaffey and co-workersu3). For a complete
description, the reader is referred to their work. However,
the semi-quantitative features of the theory can be presented
with little difficulty if a few simplifying assumptions are
made.

It is convenient to apply cylindrical coordinates to this
situation where the z axis passes through the source and focus.
The magnet wedges and gaps are placed in a circle about the z
axis. The distance of the electron orbit from the z axis is
r and ¢(oS¢52n) is the angle of rotation about the axis. The
electron orbits thus lie in the z-r plane. The current in
the z-r plane closely approximates a closed curve, so the field
component in the r direction is zero. The magnetic field is
assumed to follow a closed curve, describing the toroidal
boundaries of the pole faces. Thus, neglecting fringing ef-

fects, the space outside the closed ring has zero magnetic

field while inside the ring

B . B . o,
I" Z

B¢ can be calculated by applying Amperés circuital law.

In Gaussian units

g
‘-

,3

pi it i
on 2. ...s ..
J. ..u u. A.
«\U I" .‘

‘lrwrlu “variant r! ,J.~J. V...” ...ulh. J. ... _. ..- no I»
e . . ..

   

 

32
HnNI
I-5--' gH-di (2)
where N is the total number of turns in the ring of coils

and c is the speed of light. Applying (2) to the different

regions of the field

UnNI , .
...c gee use + jhi as, (3)
gap iron
regions regions

Since B and H are exactly parallel in a vacuum and very

nearly parallel in the iron, assume

e-hn

where u I "o for vacuum and "i for iron.

NnNI l . l .
...c ...,; fee aways, as, (u)

gaps iron

Since (B)N, the normal component of B, is continuous across
the boundaries between the regions of different permeabil-
ities,

(B (I31)N =- B (5)

o)N . ¢

Upon integration, equation (A) becomes

 

  

3' b EVE-«Eilrly mused v,

.3 5.523,
a

 

B a
“WNI I A- [1 + .8- E]
c no a "i

where a is the total gap width and B is the total iron
width. For the present instrument, B/a I 2 while the ratio
of permeabilities of vacuum to iron is 2510'“. Thus, ne-

glecting the last term,

 

unNI . 82“
c no

With a I 6rd (six gaps each of angle d) the e component of

B can be written

1
B - --——-— g (6)

In order to arrive at an expression for electron orbits
in a l/r field, consider the general formula for the radius

of curvature, p, of a curve y I f(x) at any point P(x,y).
p - [1 + (dy/dx)2J3/2/<d2y/dx2)

- [l + (r'<x>>213/2/r"<x> <7)

The radius of curvature of electron orbits, p, is given

by the famous expression

9 . Cp/eB (8)

where p I the electron momentum and e I the electron charge.

'.e

,C.

I:P

l.A'I‘

u

“bl

 

34

Let
p I br.
Then, from (6)
b _ Booze
ggfirig (9)

The present instrument has a value b I 0.6. For an inhomo-
geneous field, eq. (8) is still true, except that B and p are
no longer constants.

Applying (7) to (8) and using the identities

fix) = NM. who I r'(z), f"(x) = m2) = __a_dr'<zz ,

2
equation (7) becomes, upon integration,

lo /2) dy
{b -[los(y/a)]

2}1/2 + 20 (10)
where a and 20 are two constants of integration.

Equation (10) gives rise to trajectories of the type
shown in fig. 1. These curves are more conveniently described
in terms of the parameter s which is defined as the angle be-
tween the z axis and the tangent to the curve. In the para-

metric representation,

r _ a-e'bc°8(e)

z - a0b°U(b,6) + z (11)

O

6
and U(b,e) - of cos(x)oe'b'c°s(x)dx
TI‘

35

nuwcea no news: one

.zheuuwnhc one u can N how
.o.o u A can o.H u a mueuoasuma on» nuws .Aaav ncowumsce

mo cowumhweucw HmowhoES: m up peasanoamo was oshso use .cowuoouwp N onu cw

acmuxm euwcwmcw no: Scans .pHuHm h\H s cw zhouoomouu conuooae asowomu 4 .H shaman

 

 

 

 

N T
~_ who who No 0.3 mm- so- me. N..-
_ _ 4 _ _ L a
_
ooh
_HO
1 . 1nd
DIQOuu DIGOuu
5mm
1 so
sfl
1mo
1 n.
I. m.—
s
_ _ _

 

 

 

 

n
.3!
.4!”

a
e.“
at.

\
ea I—

[n

 

[‘5
I]

I...
‘I'

53

Va

-
"p.
'OV

 

' EC."
. ~~.,

‘u...
, ,
'n

h-
«I
‘u

 

unit—2h

‘A

36
Then 2 I 20 for e I n and a corresponds to the value of_r

for e I n/2. Also,

I ae-b I‘ I aeb
rmin ’ max '
r
Thus, F£££>I e”2b I constant (12)
max

independent of a, the integration constant. a is simply a
scale factor describing the family of curves which are sim-
ilar with respect to z - 20 on the z axis.

Figure 2 shows how portions of a l/r field can be used
as a focusing spectrometer. Theoretically, the boundaries
of the pole faces can be determined from a numerical inte-
gration of eqs. (11) if no corrections are assumed necessary
for fringing field. As in fig. 2, a value of b is chosen as
well as the position of the source on the z axis. A family
of trajectories is then drawn by varying the parameter a.
From eqs. (11), r' I tans from which it follows that a tan-
gent can be drawn from the source position (zs, 0) to any

trajectory. Then the points (r 2,) should trace out the

JD
transition point from a B I 0 to the B I gia field, i.e. the
profile of the pole face. The theoretical boundaries shown
in fig. 2 have actually been calculated from closed expres-
sions. In practice, there are fringing fields which distort
the orbits near the entrance and exit slits. These aberra-
tions are empirically corrected by shaping the pole profile.

Finally, it should be clear that if zo is picked as the

point for the location of a symmetry plane, then the entrance

and exit profiles are identical. Then zf I 220 - 23' How-

37

.czonu ouas aw .epaowm wcwwcauu wcwuoeawec wcwmnoom hon huuvcaon

Asowusuoezu one .csono one weapopcnon each Amanda on» was .usuoEONuooae
unsound one you sauce on cause one muwnuo 0:9 .wcweaoom you poop on use
macaw us» no uncapped so: «305m menu ouswwm owns .o.o u A you s usuoasuan
any we cowuocsu a no macaw h\4 s aw muwuouoohmuu conuueae academy .N shaman

.N 0N .N
53 ON m. o. m o m- o_- 9- ON. .38-

 

who
seem
numm
9.510
.300.
uuoc
nuns

lion

AEov

‘F.

«W
I‘A

i] had

fish

at.

 

‘51

“*1

3».
a II

 

ya

‘0

e

 

38

ever, as Nielsen et a1. point out in their original articleQO),

an asymmetric machine would also produce focusing if the geo-
metrical situation (i.e. 215. I 220 - zs) warrants the addition-
al experimental difficulties of shaping both entrance and exit
profiles separately.

In a spectrometer with symmetrical entrance and exit
curves, there should be a first order focusing with a magni-
fication of unity. This should also hold true for particles
emitted from points lying at small distances from the 2-
plane, as discussed by Nielsen et al.u0).

The instrumental dispersion, defined as D I %% P. has
been evaluated both theoretically and empirically. In this
expression, Ax is the distance between foci of particles with
momentum between p and p + Ap. In both instances the dis-
persion has been shown to be a strong function of w, the
angle of electron emission measured with respect to the sym-
metry axis. The dispersion varies from about “00 mm in the
inner parts of the gap to 900 mm in the outer portions for
instruments of the size of the MSU spectrometer. For normal
gap openings the average dispersion is about 600 mm.

The major fraction of the resolution problems with this
type of spectrograph are those associated with the-fringing
fields. In the proper shaping of the pole profiles to give
the best resolution, the following effects were considered:
Axial defocusing, the lens effect, an effect due to a non-
uniform field, source size, and mechanical alignment. These

are discussed in this order.

39

Axial Defocusing. The fringing field will have a com-
ponent in the direction of the interior toroidal field.
Thus, there will be an additional deflection due to the ef-
fective boundaries being outside the real boundaries. Fur-
thermore, the fringing field has different effects for dif-
ferent s values. Thus, the theoretical profiles shown in
fig. 2 will no longer be quite correct. One would expect
to correct this effect by reducing the region enclosed by
the profile, and changing the profile somewhat. This is

11).

the procedure followed to some extent by Bisgcrd Un-

fortunately, B¢ in the fringing region also changes with ¢.
as can be seen from fig. 3. Thus,a correction for the axial
defocusing in the median plane does not work for all e values.
This is one of the reasons that the part of the gaps close
to the pole plates are not usually employed in the spectrom-
eter.

The Lens Effect. The fringing field at a given point

near the entrance can be decomposed into B and Brz’ as shown

¢

in fig. 3. B can be further decomposed into B

rz and B1,

t

where B is along the trajectory and B is perpendicular to

t
it. The net result of B

i

1 is to extend point sources into

line images. The axial defocusing problem discussed above
actually causes the line image to have considerable curvature.
Nonggniform Field Effect. An indirect effect of the

fringing field is to cause a variation of B¢ with e inside

the gap with B being stronger near the pole plates than in

e
the median plane. This is then another reason for not using

NO

 

 

 

 

 

 

YOKE
YOKE
PLATE
COIL
POLE
GAP / PLATE
as
J‘ ‘
Bu‘o‘
Q»
SOURCE
POSITION

Figure 3. The central region of the spectrometer showing two of the six gaps,
as viewed from above, along the symmetry axis. A typical fringing field line
is also shown, and is decomposed into its various defocusing components.

“1

those parts of the gap near the poles for the experiments re-
quiring the best resolution.

Source Size. The theory of focusing is for point sources.
However, sources of a 2 mm extent do not seriously affect the
resolution unless detector slit widths of smaller dimensions
are being employed.

Mechanical Alignment. In theory, the instrument should
be constructed as 6 identical Spectrometers working in unison
with no problems involved in the focusing properties by the
addition of the several gaps. In practice, this task is dif-
ficult to overcome.

As an example, the MSU spectrometer is a 1.0000 1 0.0001
meter diameter circle. The pole plates are vertical to within

10.10

and the radial alignment is better. Even a minor mis-
alignment problem has been found to deteriorate the resolu-

tion by a significant factor.

2.8. The Michigan State University Multigap Spectrometer

The orange spectrometer is essentially the same design
as that described by Bisgcrdll). However, enough innovations
have been used to warrant a description here for the purpose

of those who wish to use it in the future.

“2

2.8.1. The Vacuum System

The vacuum tank for the present instrument measures
approximately RS inches in diameter and 22 inches high. It
was constructed by rolling l-l/8 inch thick aluminum plate
into semicylinders and Joining the two halves by a heliarc
weld. An additional ribbon of aluminum l-l/8" x 2" was
welded around the outer upper and lower peripheries to pro-
vide larger vacuum gasket surfaces. The lid and base plate
are of the same material with grooves constructed to accom-
modate vacuum gaskets. Six brassrods around the central de-
tector ports maintain positive separation of the lid and base
plate. Although considerable difficulties were encountered
in welding such large volumes of aluminum, the tank shows no
leaks when tested with a mass spectrometer leak detector.

The pumping system consists of 2 mechanical pumps, one
of 15 cfm serving as a roughing pump and a second of 10 cfm
used as a combination forepump and roughing pump. In addi-
tion, a 5 inch diffusion pump is available for those appli-
cations requiring high vacuum. The mechanical pumps, oper-
ating in parallel, evacuate the system to 100 u in 13 minutes.
The diffusion pump can produce a vacuum of 5 x 10"5 mm Hg in
an additional 10 minutes, or S x 10'6 mm in an additional 30
minutes. The quoted pumpdown times are for the assembled
spectrometer, not Just the tank alone. No applications are
foreseen where better vacuums will be necessary. -

The pressure is measured by means of a thermocouple

gauge in the low vacuum range or a discharge gauge at high

 

r4

II

.1

 

i.e.l-roop r...,
.
.4

III, --n«-)....flw..
wl. u.- I

‘e

t
K.

“3

vacuum.

2.8.2. The Magnet System and Coil Design

The iron parts used in the Michigan State spectrometer
were made from prints provided by Bisgorduu). These parts
were made of low carbon Swedish steel by Dansk Insudstri
Syndikat, a Copenhagen firm. Thus, the magnet section is, in
principle, identical to Bisgord's design. However, the coil
design has been governed by two factors: 1) the maximum number
of ampere-turns which can be produced by an existing power
supply and 2) a shape reduction required in the dimension of
the coils to provide space to allow the cyclotron beam to pass
beside or over the coils, if desired. The latter problem was
solved by using pre-insulated square copper tubing. The insula-
tion is a double dacron-glass fiber tightly bonded with vitro-
tex resin+. The tube dimensions are 3/16" square outside with
1/8" diameter hole for internal water cooling. The material
was supplied in 1200 foot lengths. '

The final configuration of the coils is 12 layers of the
tubing with 10 turns per layer. The total length of wire on
each coil is about 250 feet. Each layer is electrically in-
sulated from the previous by 1/16" layer of laminated fiber-
glass. The core is simply a segment of brass pipe machined to
the desired dimension. After each coil was wound, it was

placed in a mold, saturated with a low vapor pressure epoxy

 

+Obtained from Anaconda Wire and Cable Company.

 

‘I I-A'W‘H-Cn'l

.‘. m

er

‘1

 

nu

.q‘
.
s‘dt

 

 

e
0"

r"

 

 

 

 

41
l-‘

v- 1

 

an

and evacuated. This evacuation insured good penetration of
the epoxy throughout the coil. They were then baked as pre-
scribed by the manufacturer, producing an extremely rigid and
durable package.

The procedure followed in winding the coils insured that
the number of turns varied by less than l/U turn out of the
120 turns total. Resistance measurements were also carefully
performed on each, and all were found to be within the variation
produced by slight temperature changes, insuring that they con-
tained no shorted turns. The cooling has been found to be very
effective also. With a parallel flow of l/M gallon per minute
per coil, there is a temperature rise of only 10° C at 50 amps.
Of course, such a system construction requires deionized water
which is readily available in the Cyclotron Laboratory. This
type of cooling is considered much more desirable than the ex-

ternal cooling of the coils of the previous instrumentsll'ul).

2.8.3. The Power Supply

The power supply is an all-transistorized constant current
unit capable of producing 50 amps at 50 volts. The power source
is a 208 V, 3 phase, motor driven auto-transformer whose output
is a slight modification of that reported by PatlachuS). The
circuit diagram is shown in figs. A and S. The reference vol-
tage is provided by a network of resistors across a mercury
cell as shown in fig. 6. The current has been found to be

stable to better than 5 parts in 105 for short term periods

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(5 min.) with extreme drifts of l/lOu over a period of a day.
Although the regulation of the magnetic field itself, instead
of the current, would give better regulation, the present sys-
tem is very satisfactory for this type spectrometer and the
achievable resolutions. It is felt that simply using better
resistors and stabilizing the temperature of the power supply
will give considerably better stabilities.

A very convenient feature of the power supply is the
ability to check base-collector voltage drops of all the power
transistors. Thus, in the event of a failure of one of the
transistors, it can be located immediately by a quick meter
check.

A simple, yet very effective automation system for step-
ping the power supply has been constructed. A block diagram
of the system is shown in fig. 7. The principal components are
a stepping motor driving a potentiometer, a programmed pulse
system to step the motor, mechanical timers, and a printing
scaler. The system is capable of counting times continuously
variable from 0 seconds to 20 minutes and read-out times rang-
ing from 2 sec. to 2 min. The current can be set at any value
between 0.5 and 50 amps and can be stepped in increments as
small as 5 ma over any 5 amp range and SO ma, or larger, over
the entire 50 amp (3.5 MeV) range. At the end of each counting
period, the scaler is printed out and reset, the currents ad-
vanced, and, after a pre-set time, the counting begins again.
Limit switches are provided on each limit of the 10 turn po-

tentiometer to prevent overdriving. The automation system,

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although partially constructed from outdated components, has

’proven both satisfactory and reliable.

2.8.h. The Detector System

The detector mechanism of this spectrometer incorporates
the general features of that designed for Bisgcrd's instrumentll),
but has been modified to incorporate a low noise system. The
field free region in the center of the spectrometer makes it
very convenient to use windowless scintillation detectors coup-
led to photomultiplier tubes. Anthracene and pilot 8 scintil-
lators have been used. Although anthracene has the undesirable
feature of slow decomposition in vacuo, its higher light output
has been used to good advantage in the detection of low energy
(.1 25 keV) electrons. Modifications in our detector mechanism
allow the light output from the crystal to split into two light
pipes which are coupled to two separate phototubes. A coinci-
dent signal is then required of both photomultiplier tube out-
puts in order that it be recorded as a true count. Since the
noise pulses in each tube are uncorrelated with time, this
technique enables one to efficiently detect low energy electrons
without the high noise count rates that are usually associated
with the required high voltage. With this system, 13 keV
Auger electrons have been detected. No sources have been made
thin enough to test the instrumentat lower energies. The power
supply is capable of regulating on currents corresponding to

focusing electrons of 2.5 keV energy.

‘A
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51

2.8.5. Earth Field Compensation

Following the final assembly of the Spectrometer, it was
found that the electrons from the various gaps still did not
focus at the same current. For the 62A keV conversion line
of 137C8, the deviation was found to be as much as 1.2% for
gaps located at 120° with respect to one another. A careful
search of the focusing current vs. angle was found to very
nearly follow a sine wave. Such a phenomenon arises from an
added horizontal field in a particular direction, i.e., the
horizontal component of the earth's magnetic field. Although
the earth's field is only 0.11 that of the spectrometer for
62“ keV electrons, the iron core concentrates it by a large
factor in the spectrometer. Therefore, a compensating field
is very necessary for even moderate resolution.

The problem has been circumvented satisfactorily by the
construction of Helmholtz type coils. These compensating coils
are 7 feet in diameter and 8 feet apart, thus deviating con-
siderably from the Helmholtz condition. However, with a field
produced by 75 amp-turns, the deviation in focusing currents
for the various gaps deviates by less than i 0.1%. East-west
coils have also been constructed, but have been found unnec-

137Cs. They may prove to be

essary for conversion electrons of
of use for fine adjustment of the field for very low energy
electrons. Coils to compensate the vertical component of the
earth's field are not necessary. The lateral deflection pro-
duced by this field in the upper half of the orbit is reversed

in the lower half.

 

 

 

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Measurements have shown that the spectrum taken with six
gaps,with the described external field, givesresolutions of
about 0.7%. Under the same conditions, a single gap has a
resolution of 0.6%. This is indeed a very satisfactory solu-
tion in view of the fact that without the external field, the

six gap resolution was 1.3%.

2.8.6. The Performance of the Spectrometer

The Michigan State University orange spectrometer has
been thoroughly checked in terms of transmission, resolution,
and linearity. The basis for Judgment of the performance has
been to compare the results with those obtained by Bisgord
with the prototypell). Figure 8 shows a comparison of the
resolution vs. transmission curve in the two instruments for
similar baffle openings. In this figure, the points are those
obtained with the MSU spectrometer and the curve is from the

work of Bisgordll). The source size in the present Spectrom-

eter, which is twice the width used by Bisgcrdll)

, may affect
the curve at the lower values. However, the ultimate single
gap resolution which has been obtained in this instrument with
a small source is 0.A5%, while Bisgcrd has operated his machine
at 0.3%. This may be some cause for concern that the machining
of the pole tips was not as good as it should be. There are
differences in the pole faces of the various plates that are

easily visible. However, such effects may not deteriorate the

focusing properties significantly when all 6 gaps are used to-

53

 

RESOLUTIO N , °/o

 

 

 

 

 

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4_ SLIT WIDTH:

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TRANSMISSION.°/.

Figure 8. Comparison of the six gap resolution vs. transmission
curve of the M.S.U. spectrometer with the prototype. The full
curve is from ref. 11, while the experimental points have been
obtained with this spectrometer.

5N

gether and operating at much higher transmissions. In any
event, the comparison of the two instruments is favorable.
The spectrometer has been found to be very linear when

operating above 250 keV. The calibration equation is
80 ' 270.2 I

where 89 is measured in gauss-cm and I in amperes. Unless

116)

meticulous premagnetization procedures are followed , the
8p vs. I relation is non-linear for the lower energies. For
example, the spectrometer constant is reduced from 270 to 2A5
when focusing 25 keV electrons. This effect is not considered
to be a serious limitation of the effectiveness of the machine
as long as the problem is known to exist. The energy measure-
ments of the transitions are usually performed on high resolu-
tion Ge(Li) detectors. Fermi analysis of continuous spectra
can be easily corrected for the non-linearity by the inclusion
of a quadratic term in the calibration equation.

A typical spectrum of the type recorded with the Spec-

trometer is shown in fig. 9. The source usedeas 137Cs.

2.8.7. Comparison with Other Types of Spectrometers

Direct comparisons of the Spectrometers of various types
anadifficult, if not impossible, because of the numerous fac-
tors involved. The spectrometer cannot compare with the res-
olution nor luminosity obtainable with the n/E'double focusing.

spectrometer. However, the transmission is much higher and the

COUNTS / (2 MIN)

28.8K

24.0 K

I9.2K

I4.4K

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CURRENT. AMPERES
Figure 9. The K and (L + M) internal conversion electron

lines of 137m8a, recorded with the MSU orange spectrometer.

 

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cost much less. The 100 gap iron-free version of the orange
spectrometeru7) is a superior instrument in resolution, lumi-
nosity, and transmission. However, the MSU instrument has
been constructed at less than 3% of the cost of iron-free
system. Other iron-free orange spectrometers have been con-
structed which actually have characteristics inferior to the

iron machineu7).

However, these are usually designed for
different purposes.

Probably the best comparison is with the lens spectrom-
eter which has been very widely used. Both spectrometers are
relatively easy to build and their costs are not excessive.
Both have relatively good figures of merit, but suffer tre-
mendously with source size. The theoretical limit for T vs.
8 in the lens spectrometer is T2 - 0.168, neglecting source

size effectsuu). The corresponding equation for the orange

spectrometer is - 1.258 - .0075. Thus, the lens spec-
trometer is capable of attaining better resolutions as long
as transmissionsof less than 2% are involved. However, the
.luminosity, L - AT, for the 6 gap orange spectrometer is
probably a factor of 10 better than for the lens type instru-
ment. In addition, the optimum angle of emission for the
lens spectrometer is A5°, which means that, in general, larger
counters must be used in this instrument. This has the effect
of increasing the background to true count ratio.

From these arguments, it may be concluded that the multi-

gap spectrometer is, in reality, a very versatile instrument.

It is capable of achieving both high resolution and high trans-

57

mission. It is ideal for e-y coincidence counting experiments,
and the single gap version is well suited for e-y angular cor-
relation studies. The geometrical arrangement is such that
charged particle beams can be introduced without any serious
instrumental modifications. Finally, the cost is small in
comparison with other tools of nuclear research in use today.
Once the instrument is constructed, the operating costs are
indeed nominal. These consist mainly of replacing the anthra-

cene detector which deteriorates in a vacuum.

CHAPTER 3

131m

THE DECAY SCHEME OF Te: SYSTEMATIC TRENDS

OF ODD MASS I ISOTOPES
3.A. Introduction

The study of the B and v decay of the odd-mass
(127 éIA £>l33) tellurium isotopes to iodine daughters
presents an excellent opportunity for the examination of the
systematic trends of the 53 proton levels as a function of
(even) neutron number. With the exception of 133Te, the
isotopes are easily produced by thermal neutron capture.
The half-lives of the isotopes are of sufficient duration to
allow a fairly detailed study. In addition, the B decay of
both 11/2' and 3/2+ isomers can be observed. Therefore, a
wide variety of spin-parity states are expected to be popu-
lated and not as many levels are missed as in many radioactive
decay studies. The systematic trends in this region should
thus be informative for comparisons with recent model calcula-

4)

tions, such as those reported by Kisslinger and Sorensen

and by O'Dwyer and ChoudhuryS).

The work reported here is primarily concerned with the

1311. The

u8-50)
51).

decay of 30.5 hr 131mTe, populating the states of
states of 127I and 129I have recently been re-examined
and the states of 1331 are under investigation elsewhere

52’53) of the internal and external

Early investigation
131mT
conversion electron spectra of e gave some indications

of the complexity of the gamma spectrum. The beta endpoint

58

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59

energy was measured to be 2.A5 MeV and the existence of an
isomeric transition of 182 keV energy between the 11/2' and
3/2+ parent isomers was found to account for 18% of the decay

131m

of the 11/2' state of the Te parent. Badescu, gg|gl.,

later published a series of paperssu'56

) over a period of
several years, in which scintillation techniques as well as
magnetic spectrometers were utilized. This group was able

to arrive at a decay scheme which would place the most promi-
nent transitions. Measured values for “K indicated the pres-
ence of El transitions, leading to the assignment of part of
the low energy states in the proposed decay scheme as negative
parity states. That such a situation should exist is somewhat
doubtful since all of the known low energy states of 1271 and
1291 have positive parityu8-SO). In addition, Badescu, E£.él'n
reported the strong 77“ and 852 keV transitions to be in

55) with a crossover transition of 16A5 1'1 keV. On

cascade
the basis of energy sums, such a situation cannot exist, of
course. These discrepancies, coupled with the fact that

the high resolution Ge(Li) detectors were now available, war-
ranted a reinvestigation of the decay scheme.

During the course of this investigation, Devare, Singru
and Devare published a more comprehensive study using scintil-
lation coincidence techniques, beta spectrometry, delayed co-
incidence techniques and some limited data recorded with a
Ge(Li) detector57). Even though some of their data were quite

informative, our technique of using a Ge(Li)-NaI(Tl) detector

combination for coincidence experiments made it obvious that

their propl
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60

their proposed decay scheme was in error. The investigation
was continued in order to establish a more complete disinte-
gration scheme of 131mTe, as well as to find and remove er-

rors which still existed.

I

3.8. Source Preparation

131m

The sources of Te were produced by the irradiation

for one week periods of 10 mg samples of tellurium metal, en-

130

riched to >99.5% Te, in the ORNL ORR reactor. The thermal

1A -1

neutron fluxes were approximately 2 x 10 n cm"2 sec . Sev-

eral sources were used during the course of the experiments.

C158>

All of the sources were chemically purifie to remove con-

1311 daughter. silver and antimony

taminants, eSpecially the
activities. The chemical procedure entailed dissolving the
metal target in aqua regia and transferring to a distillation

flask. The 131

I activity was then distilled into an ice
water bath or acetone, which dissolved the iodine gas. The
solution was then boiled to near dryness three times to re-
move all the nitrate ions. Tellurium metal was precipitated
from a 3N HCl solution with $02 gas and a trace of hydrOXy1_
amine hydrochloride, leaving any antimony in solution. The
tellurium metal was again put into solution with HNO3 and
AgNO3 carrier added. A drop of HCl then precipitated the
silver activities.

The sources thus purified were prepared for gamma count-

ing by drying the nitric acid solution that contained the

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sample onto a thin glass microscope slide or mylar film.
The samples were covered with mylar. Sources for singles
counting were typically about 30 no strength, while those
used for coincidence counting were 150 pc.

The sources for the electron spectrometers were pre-
pared by vacuum sublimation of the tellurium metal obtained
in the 802 precipitation. These sources contained trace

amounts of 110

Ag activity, but this did not interfere with
the measurements performed. '

The sources for the orange spectrometer were 2 mm diam-
eter while those for the n/2 iron free spectrometer were 1 mm
x 15 mm. The low specific activity made source thickness a

limiting factor in the resolutions obtained with both spectrom-

eters.

3.C. The Gamma-Ray Singles Spectrum

The singles Spectrum has been recorded and analyzed
with both NaI(Tl) and Ge(Li) detectors. The NaI(Tl) spectra
were taken with a 7.6 cm x 7.6 cm crystal having approximately
8% resolution for the 662 keV gamma-ray of 137Cs. The results
do not differ Significantly from the previous results of DSD57)
and are, therefore, not shown here. The high resolution data
were recorded with a Ge(Li) detector with a sensitive volume

A mm deep and 2 cm diameter which was made in our laboratory.

The associated electronics consisted of a low noise preampli-

fist" and a
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62

fier and a low noise RC pulse Shaping amplifier coupled to a
102“ channel analyrer. Near the completion of the study, a
room temperature field effect transistor preamplifier was
used. The low energy portion of the spectrum Shown in fig.
10 was recorded with this latter System..

The singles Spectrum, shown in figs. 10 and 11, consists
of A5 gamma-rays identified as belonging to the decay of
131mTe. These range in energy from 81 to 2270 keV. The 159
keV gamma-ray belows to 123mTe. Gamma-rays with energies

131

28A.3, 36A.5 and 638.4 keV belong to the decay of the I

1311 are

daughter. The 80.2 and 723.8 keV transitions in
masked by the strong 80.9 keV peak and the high Compton dis-
tributions respectively. '

The energies of the gamma-rays were determined by count-
ing the source of 131mTe, both simultaneously and consecutive-
ly, with a number of well-known standard sourcessg). The best
results were obtained by making separate runs with the low and
high energy portions of the spectrum, and recording the sin-
gles and calibration data simultaneously. The peak positions
were found by first subtracting a third order least squares
curve that had been fitted to several background channels
on both sides of the peak and then calculating the centroids
of the peaks, The centroids of the calibration peaks were
then fitted to a least squares quadratic curve, thus account-
ing for non-linearities in the electronics. These calcula-

tions were performed on the Michigan State University CDC3600

computer. The energies of the calibration points typically

J‘I

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Figure 10. The low energy part of the 131mTe gamma—ray singles spectrum taken

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Figure 11. The high energy part of the 131!“Te gamma-ray singles spectrum,
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65

reproduced to within i-O.15 keV or better, thus determining
the energies of even the weakest gamma-rays to within 1'--1 keV.
Typical results of a linear vs. quadratic fit are shown in
table 1. Gamma peak areas, in conjunction with the detector
efficiency curve, were used to determine the relative inten-
sities of the gamma-rays. A list of the 131mTe gamma-ray
energies and their relative intensities is given in table 2.

The errors quoted are RMS deviations from average values.

3.D. Gamma-Gamma Coincidence Studies and the Construction

of the Decal Scheme
3.D.1. The Present Coincidence Spectrometer and Its Advantages

One of the main difficulties in interpreting previous
coincidence data has been due to the multiplet of seven gamma-
rays in the region of 7UO-9lO keV. This region of the Spec-
trum accounts for a large fraction of the combined intensities
of all gamma-rays and six of the gamma-rays are in coincidence
with one or more of the remainder. The entire region is on
top of the Compton distribution of the strong 1126 and 1207
keV gamma-rays, which are also in coincidence with the stron-
gest gamma-ray in this region. A part of the difficulty in
analysis has been removed by using a NaI(Tl)-Ge(Li) coinci-
dence spectrometer. Although the pulse shaping requirements
from the Ge(Li) detector to the coincidence circuit prevent

optimum resolution, the coincidence spectra recorded with the

66

TABLE 1

Typical linear vs. quadratic least squares fit to calibration points

 

 

Linear ’EQuadratic
Source Energy, keV Linear deviation,Quadratic deviation,
fit, keV keV fit, keV keV
22Na 511.00610.0053) 508.313 2.690 510.938 0.065
137Cs 651,595:o,o76a) 650.329 1.266 661.730 -0.135
6OCO 1173.22610.ouoa) 117u.u72 -1.2u6 1173.1u3 0.003
22ua 127u.6 30.2b) 1276.157 -1.557 127u.5u6 0.05u
6°00 1332.u83i0.053) 133u.1uu -1.661 1332.u10 0.073
ThC"(D.E.) 1592.06 10.10a) 159u.56 -2.10 1592.62 -0.16
ThC" 261u.u7 10.10a) 2611.86 2.607 261u.u6 0.01

 

Linear equation
Energy (keV) - 7.187 + 2.582 (Channel)
Quadratic equation

Energy (keV) - 15.195 + 2.5U9 (Channel) + .000027 (Channel)2

a) Ref. 1u

b) Ref. 18

67

Table 2

131mTe gamma ray energies and relative intensities.

 

 

 

 

Present Work Devare, et a1.a)
Energyb) Rel.Int.c) Energy Rel.Int.
(keV) (Gamma) (keV) (Gamma)
80.9 i 0.11 148 81.1 23
102.3 1 0.14 107 102.1 56
115 3’- 1.5 2
135 3- 1.0 10
1119.7 3’- 0.2 280 1149.7 209
183 1 1.0 18
189 1 1.0 3
200.7 1'- 0.11 79 200.5 80
215 1’- 1.5 3
231 -+- 1.0 8
2140.6 3’- 0.u 91‘” 2141.5 82
2511 i 1.0 12
279.5 3'- 0.5 26‘” 278 37
310 i 1.0 3
3314.5 1- 0.11 100 335.8 1009)
3143 3'- 1.0 7‘”
3514 1 1.0 6
3814 3- 1.5 5
11314 1’- 1.5 7
1452.7 1 0.11 59 1152 66
1162.6 1 0.11 23
1493 i 0.8 11

 

 

 

 

67a

Table 2 (cont.)

131mTe gamma ray energies and relative intensities.

 

 

 

 

 

 

 

Present Work Devare, et al.a)
Energyb) Rel.Int.C) Energy Rel.Int.
(keV) (Gamma) (keV) (Gamma)
586 1 1.5 10
603 1 1.0 10 602 17
665 1 1.0 33 650-665 28
712 1 1.0 11
71111 1 1.0 114 7140 7
773.7 1 0.14 380 775 370
782.7 1 0.6 80 786 33
793.6 1'. 0.11 130 797 63
822.1 1 0.14 55 831 117
852.1 1 0.11 210 8514 190
870 1 1.0 0.1:. 869
910 1 1.0 35 915 146
922 1 2.0 5
980 1 1.0 0.1:.
995
1059.7 1 0.5 11 1050-1065 17
1125.5 1 0.14 120 1126 102
11118.5 1 0.5 38 11145 29
1206.5 1 0.5 95 1206 100 1 20
1238 1 1.0 5
112118 1 1.0 D.E.

 

67b

Table 2 (cont.)

13lmTe gamma ray energies and relative intensities.

 

 

 

 

 

 

 

 

Present Work Devare, et al.a)
Energyb) Rel.Int.C) Energy Rel.Int.
(keV) (Gamma) (keV) (Gamma)
1315 1 1.0 9 13110 11
1583
16146 i 1.0 111 1629 9
1888 1 1.0 15 1860 9
2001 t. 1.0 20 1965 19
2168 1 1.0 3 2130 is
2270 i 1.0 3 22140 5
2330 2
a) Ref. 120
b) Errors are based on rms deviations from the mean

0)

d)

value of several runs and include the quoted er-
rors of the standard energies.

Uncertainties in relative intensities are estimated

to be i 10% or less, except for peaks of intensity
less than 15 on the present scale. In these cases
the uncertainties are greater.

This peak is considered to be a possible doublet.
Normalization point for relative intensities. In

the original work, relative intensities were nor-
malized to I(774) + I(783) + I (793) - 100.

 

68

germanium detector are, in general, quite satisfactory.

In addition to the detectors previously mentioned, the
coincidence spectrometer consisted of conventional fast-slow
coincidence circuitry, resolving time 2110 nsec, and a 102A
channel analyzer. The analyzer was Operated in the automatic
chance-coincidence subtract mode described previously60).
Thus all spectra (with the exception of the 150 and 1126 keV
coincidence spectra) have been corrected for chance coinci-
dence contributions. In the cases where peaks were well
separated, coincidence spectra were recorded with separate
gates, set first on and then off the peak in order to correct
for underlying Compton distributions. Usually the NaI(Tl)
detector was used for the gate. Figures 12 through 15 show
the majority of these coincidence spectra. In some cases,
such as those shown in fig. 16, the Ge(Li) detector was used
as too gate in order to eliminate interference from photons
of comparable energy. The counting geometry was generally
90°, with some runs recorded at 180°. The spectra shown in

figs. 12 through 15 have been gain shifted by the computer

for the ease of comparison in this presentation.

3.D.2. Evidences for Levels at 150, 603 and 1060 keV

With the NaI(Tl) crystal gating the analyzer on— —the 150
keV';peak, gamma-rays of energies “53 and 910 keV are espe-
cialfily prominent, as shown in fig. 12. The peak areas have

been measured and compared to the peak areas of the photons

COUNTS (ARBITRARY UNITS)

69

 

 

 

 

 

 

T I
P -<
1 1 1
O
r- .n ~
'_ O
v No 3
p— QN _ N —<
C .3. a. 1
C JV\ r~ 3, N I
b -‘\A\N n 9 -1
» M ..
b d
V\IWA‘\~IM..
t .e . q "
Q ~ r~ n
n '\ N 0’ N
‘ - r~
L— ‘I‘.’-‘ N 8 9 1
F A I- 53A °’ ~
' o h 1
t I _ 3
O
» - N _ COINC WlTH 150 keV A L_---/\ s
P v . ' .-. -1
\_-_fl N ‘
. ~11 3) w .
‘-. r1 N N
’A. n 0‘0 :
_ ;I\ [L vv _2- n d
I o r" -. -. -MV-z EJ‘ '- 2
> 9 i: ‘ "’3' \‘-” I- . z '0 3 - \: ‘ ..
s. m - ' -
F A 3 '2 ~ ~ r~ 34 " ' 1‘
b . N _ -'\ - h m . - A
. v _,
I A ~ 2 .
, v
v- 7' .1 n 9 I b
_ 1 . .11 _
>- ‘-~__ . _‘
t 1' '\ ' ' 1 J ' 3
. -',. ( COINC WITH 665 keV - ._ q
r '_'_-'. _‘
b ‘ ~‘ ‘ - ‘ - -‘ “.o '1
h- " o .- * _’-'-" :A' - " '1
”AH: .-'-.~ ', . v n n
t O :- _ F cc as ..
9 -. b r~ I~
N - - __
-' NO - -
r 1' N” 9 1
: "'\! . Q a) -A
>- O o - ‘.-.A"‘-n \_ n 4
. 1 3 come WITH 600 keV -- «
N " v ..._. _
b I -‘ w v n 1
‘5" — N n . _
b ." 4
LN A A,
I . ‘5'v5 'xc- :
b J. . I“\”-' n v <
b i A" g n N ‘
?- _.. . _ N _‘
>- -&“_~.§'_. F g 4
1 ~ A A a. 1
1‘“ A"
.- ' ~ N .4
., *:' -~ N 0
‘ ._ (D N
r comc. WITH 452-462 keV .11 1 - 1
>- ' -4
t ' £0 ..
b ‘ o -1
b N .4
>- ‘ l - -I
t .1
’- ..- . f - - d
_l 1 1 2 ' 5:
I00 200 300

CHANNEL NUMBER

Figure 12. The 131mTe coincidence spectra recorded with a Ge(Li)
r‘etector of 0.8 cm active volume gated by a 7.6 cm x 7.6 cm
NaI(Tl) detector on the peaks indicated below each spectrum in
the figure:

a) NaI(Tl) gate
b) NaI(Tl) gate
c) NaI(Tl) gate
d) NaI(Tl) gate

on the 150 keV photopeak
on the 665 keV photopeak
on the 600 keV photopeak
on the ASZ and A62 keV photopeaks

70

recorded by gating on the high energy side of the 150 keV
peak. The A53 and 910 keV gamma-rays are enhanced by a fac-
tor of 2 more than the other gamma-rays that are present in
both runs. The A53 keV photons have been reported previous-
ly52-56’6l’62) as depopulating the 603 keV level in 131gTe
to the 150 keV level. The 603 keV level is also fed in

the decay of 131m

Te via the isomeric transition and, as shall
be shown in section 3.D.3, from the higher energy states.

The 910-150 keV coincidence is interpreted as evidence for
the placement of a level at 1060 keV and is complemented by

the existence of a 1060 keV photon seen in the singles spec-
trum. The remainder of the peaks in this spectrum, as well
as those not discussed explicitly in the following spectra,

are due to coincidences with underlying Compton distributions.

3.D.3. Evidences for States at 852 and 1312 keV

The results of runs taken with the analyzer gated on the
665 keV peak and the Compton distribution in the region of
600 keV are shown in figs. 12b and 12c, respectively. With
the 665 keV gate, gamma-rays of energies 150, “53, 462, 712
and 852 keV were observed. The remaining transitions were
found to be due to underlying Compton distributions by com-
paring relative peak areas with those in coincidence with
the 600 keV Compton region. Due to the low efficiencies of
the Ge(Li) detectors, higher energy photons are difficult to

observe. However, using NaI(T1)-NaI(T1) coincidence tech-

71

niques, DSD have observed a transition of about 1300 keV in
coincidence with the 665 keV gamma-ray57). This result is
consistent with our similar measurements. There is a level
at 1980 keV which can depopulate to a level at 1315 keV via

a 665 keV transition. (This level is discussed further in
section 3.0.u.) The 1315 keV level, in turn, depopulates

via the A62 and 712 keV transitions to levels at 852 and 603
keV, respectively, as well as by a crossover transition. As
a consistency check, a coincidence spectrum was recorded with
the “52-462 keV region in the gate. The results are shown in
fig. 12d. The 150 keV peak was greatly enhanced due to the
A52 keV photopeak, as expected. Also, the 852 keV gamma is
enhanced by a factor of 1 above that seen in coincidence with
the 600 keV gate, while the ratios of intensities of the 852
keV quanta are comparable with those obtained with the A62
and 665 keV coincident gates. The peak at 910 keV in fig.

120 is explained in section 3.0.7.

3.D.“. Evidences for the 16N6 and 1980 Levels

In previous works on the decay of 131m

Te, the intense
77M and 852 keV photons have been placed as a cascade de-
populating a level of approximately 1626 keV, along with a

55’57). In each in-

crossover transition of the same energy
stance, the 33“ keV gamma-ray has been shown to be in coin-
cidence with the crossover transition and has been substan-

tiated in this study. However, our energy measurement of

72

the photon is l6u6 1'ml keV which rules it out as a crossover
for an 852-77A keV cascade. Thus, a coincidence run was re-
corded, gating on the 33“ keV region of the spectrum. The
results, fig. 13a, show the 793 and 852 keV quanta to be en-
hanced. Evidence for such a cascade is supported by the en-
ergy sum 852.1 + 793.6 - 16A5.7 keV, which agrees with the
measured crossover energy to within experimental error.
Thus, the 33“ keV transition depopulates a level at 1980 keV
to one at 1686 keV, which, in turn, depopulates via a cross-
over transition and a 793 keV photon to a level at 852 keV.
The conclusion that the state must be at 852 keV rather than
at 793 keV is based on intensity considerations as well as
on the evidence for the 962-852 keV coincidence presented in

section 3.0.3.

3.D.5. Evidences for the 1556,1596J 1797 and 1900 keV Levels

The coincidence data recorded with the 81 and 102 keV
regions of the spectrum are shown in figs. 13b and 13c, re-
apectively. Peaks of energies 102, 200, 2N1, 77A, 793, 822,
852 and 1126 keV are found to be enhanced in the 81 keV co-
incidence run. With the exception of the 102 and 1126 keV
gammas, the same peaks show equal enhancement with the 102 keV
gate. The 81 keV transition does not show in this figure,
but another measurement, with a lower analyzer threshold set-
ting, also showed it to be in coincidence with the 102 keV

photon. The existence of the 102 and 1126 keV peaks in fig.

COUNTS (ARBFTRARY UNVTS)

73

 

 

 

 

 

p . T I I .1
: 1 a q o 3: E
l- I k/ j ' 0 O - _
_ 1, «_»~ - s _
_ . ~ 1. z 1 , _
1 .11 8' .,
. 7V ' . q 2 0!) 3‘\
D- . fly" \ N fl '1\ -1
4 -. 6. W1” Mail". ”"M‘vx.
e ”W ,0
IO 7 9 ~ \ 2 ~ 1
'- 1. g 3 ..
n 13“.... h -4
Z A o conwc.wnrw sssuov :- A j
1' . O 8 J I. 1 '4
o ' \
F U i 9 p ; 0 ~95," ..., ‘ I ‘ ‘
1 N J, l'f I .0. o
>- ' "1.5"!“ I “A ~‘ 3 _‘
I 3 ‘ I :1 ‘l'
I — 2 ff N
'03 r— ' f L c. .3 ~ ' fl -
C , I 2 'V N A 3 "s .v.'.. I
: o .- 8 \ V ' o' 7
"f . "I" ' u . . ' :4
L- h‘wfii" N ; ANN..‘*:..".~’,'V“'3‘...“'.'I....'|,‘, X‘. EE ‘1 : " ’1... ' . ' ' 1| _‘
>— ‘ 'f N 5’ I ' 1h.' :1 .. ..H
.M' i ' COINC. WITH Blkov “.4". a ‘0: ' .. . .H'..” .' "i
b- ? VI, N .' ', n n n' u
A; 3 ”'5- f g fiw ‘Eg: ' H
2 1 . "' - “I‘M". I .‘I I u '
'0 .7 . f‘ j1 ‘h F'l \%’~1r'~‘l"«'."'fi‘w '0. 'I.’ '~;'J fl. \ Pk :
: ."5 \ CO'NC WITH '02 HOV ~.~ "’ H A: J , lf'l.l. . g :
b n. , N ' _ -<
C . N .-
h— I “Lula ' ‘1'. I E Q g ‘..f . 1 -4
P " ' n ‘7. u . s A . ' n I ..
”N. i ' n 'II'. ' |‘ . .' ”I. 1" ' |
~ A '1‘ g. ,7 .
I . . . h. 5..I~|.'I.p.'~ .' '1. . a“ ‘ 'Ill 1) 1' . q . u . . i i
'0 '— I . :u'". . . ..l '3‘... ' . . I! ':
t ' 1,. ' n In. I 4
: " I, .’ '1: N . "1 “"7. . . :
r comc. mm uzsuw '«"' / 3 '.'I s
; I o. ' n ‘0’ ’1‘ ' . .1
F .1 . I. '.I I. i ‘3 'g ..‘I . 1"... . . . .4
' v ' ‘1 I ‘ '1 J ' ' if 'I ' .1
10° 1 1 ' ' ' " 1 " .
I O O 200 3 O 0 4 O 0
CHANNEL NUMBER
131mT . . .
Figure 13. The e coinc16enee spectra recorded with a Ge(Li) detector of
0.8 cm active volume, gated by a 7.6 cm x 7.6 cm NaI(Tl) detector on the peaks

indicated below each spectrum in the figure:

a) NaI(Tl) gate on the 33k keV photopeak
b) NaI(Tl) gate on the 81 keV photopeak
c) NaI(Tl) gate on the 102 keV photopeak
d) NaI(Tl) gate on the 1126 keV photopeak

 

7U

13c is atiributed to the incomplete resolution of the 81 and
102 keV peaks in the NaI(Tl) detector. The coincidence spec-
trum recorded with the 1126 and llh8 keV quanta in the gate,
is shown in fig.l3d. The 81 and 77H keV peaks are enhanced
by coincidences due to the 1126 keV photon, while the 852 keV
peak is attributed to a 852-llu8 keV coincidence. The con-
clusions based on these data are then as follows: The 81 keV
transition depopulates a level at 1980 keV to an 1899 keV
level. The 1899 keV level, in turn, depopulates via the 1126
keV transition to the 77“ keV level and the 102 keV gamma to
a level at 1797 keV. The latter level can feed levels of
energy 1596 and 1556 keV via the 200 and 2&1 keV quanta.

This ordering of the 81, 102, (ZOO-2&1) keV cascade is in
agreement with the delayed coincidence evidence of DSD57).
The levels at 1556 and 1596 keV are further supported by the
coincidence data and energy sums presented in the next sec-
tion. The weak peak at 253 keV and the possibility of a peak
at 3H3 keV in fig. 13b, taken with the gate set on the 81 keV

peak, is consistent with the proposed level scheme.

3.D.6. Further Evidence for the 1556,,1596,_l6h6,71197lgl&fla

and 1280 keV levels

The data shown in figs. lua and lUc are coincidence spec-
tra recorded with the 200 and 2&1 keV photons in the gate,

respectively, while fig. lub was recorded with the gate set

COUNTS (ARBITRARY UNITS)

 

 

102

O
U.
7
,‘_~_=

 

 

 

 

O
O
’— - -+
E on 3
t '2 o .
r- 0 — .‘
I I I :3" .2 ~ 4
” I . .’ A v
V m
- In
>- N ~‘1 J I .4
.. 9 n'\_ A“ p "\ "ft A‘. J; V n”
104 .. 2 :2 5'3: ..
I ’ 1 3 ~ :
I o COINC WITH 200 keV ' o g 1
" ‘IfiI 8 a31 I 3 j
'- ' ‘ .4
C I A is” 3 ”I I . ' .
. . N ‘ I." K L L ‘- ...,. -.
~ .. A I 2 ~ -
'03 h _ ./\ .V 3.x,- - 3 _
E 8 «ts-Ac; ~.“.‘,'.\.~ -__ f‘. E E E -1 Z 3
t A COINC WITH 200*241 keV Volleylu 4
0 '_ ‘- 4
t '1 O ".r .-_ ‘ — .. -4
II _ S _ . N g _ .
r 33 V g . . _ “.3 1
_ N .. .
’— fJ‘ 3‘ "_.‘__ _ fl I ‘ . .4
‘ ‘NA K “V «‘I ; ' —
2 l, __g ' s- «5 ‘ -:
' O E— .- 4 \_. L}... ,_ If, ‘ .‘ z n n ‘ ,‘ :
F g-...5;,_\,.r.,. _ x, K :52 - :2- , g _‘
>- h _ .4
. COINC WITH 24IkeV fl 3 .
O
>— ' .\ ~ . i x a -I
~-.‘,__ w I _
' ‘ IA. 1., .
IO 1' ., .- _ ,V_ 1
: ;S __ .. :
h 2‘ ‘
*- lx. -+
r 2.2:] :1 “
IO0 4 1 1
I00 200 300

CHANNEL NUMBER

Figure 1“ The 131mTe coincidence spectra recorded with a Ge(Li) detector

of 0.8 cm active volume, gated by a 7.6 cm x 7.6 cm NaI(Tl) detector on the

peaks indicated below each spectrum

a) NaI(Tl) gate
b) NaI(Tl) gate
c) NaI(Tl) gate

in

on
on
on

the figure:

the 200 keV photopeak
the ZOO—2&1 keV valley
the 241 keV photopeak

 

 

76

between the two peaks. Besides the (81 and) 102 keV transition,
the 7h“, 77“, 822 and 852 keV transitions are enhanced in the
200 keV coincidence Spectrum while the 783 keV transition is
more intense in the spectrum recorded with the 2H1 keV gate.
Again, there was considerable overlap in the peaks of the 200
and 2&1 keV photons in the NaI(Tl) gate as well as the under-
lying Compton distributions. However, by taking a third gate
between the two peaks and comparing photopeak areas in all
three runs, the results Just stated were clearly verified.
Thus the 1596 keV level depopulates via 7H“ and 822 keV tran-
sitions to the 852 and 77h keV levels, respectively. The
1556 keV state depopulates by a 783 keV transition to the 77h
keV level. The corresponding energy sums agree to within ex-
perimental error.

In order to complement the data presented above, a series
of NaI(T1)-Ge(Li) coincidence Spectra were taken gating on
small regions across the intense 7u0-850 keV region of the
Spectrum. The results are Shown in figs. 15a-15e. Due to
the poor resolution of the sodium iodide detector, one cannot
accurately determine the relative intensity of each transition
in the gate. However, a definite trend can be observed as
the gate is moved across the region in small increments. The
Principal contributions to the gates are those given on fig.

15. The results are seen to confirm the data presented above,
1.63. coincidences between 7HU-852, 783-77M, 793-852 and 822-
7718 keV.transitions.

COUNTS (ARBITRARY UNITS)

77

 

 

 

 

 

 

 

 

 

 

 

 

7
IO » , I T
I 3 o :
* i/ a 53 ‘7 3
” M A“ ‘
. Mu ‘ q
' ‘IJ! I I. V 2:
IO6 ? ."S w 2’ I El, ‘
I f 0 -.N ,3; 5
: A. 8 :.¢' ”(LU v d
*- L .23 v‘ 'f‘fa" 'Mw’fafafl" 3 :3 g :
P . J” I ”a.“ o n N .1
~ "LN" ' :. N. NE; A -
H i n ’vflsn/ ; . in.‘ a '. ‘9
'05_ .93 \I E I *f m‘ '7‘“ g 8
: . o —._"g \ comc WITH 744 774nm '.~. .. - . e 1
: . A 8 z. A \.~J . ...,.f" r :
I— ., 3 . '“\mfiwflwh 53 ~ ~ . . :
D- -8 '1 .s“ rs g 3 a n I ..
E I! v u. I . "‘
L- . “K \II o :2 A '."M. ,m' A \ I. I‘ "IN . . . .4
t ,~. k a, r :4 xv. I s," V h“ F H: . .
4 I z . 24 I , , ..II.I.H I :3 I
IO : _/ ' H 3 come mm 774-783-793kev .‘s'.-.-". ‘ : 8 j
t 3 VI, " - ‘3 «
r — l I / "
r- ,I” \ v-nmN N . ' p: d
_ .-. lbw/w we“ :22: g '. l i 2
p- “I 1 .' ' I "‘
b- N IV . . I. . . . ' ‘
. . (It I u I '
f Ii 33 I“ ; ' 'fl‘w” LA... 1‘32? o 'H‘h." "
E ' A :5 n to to 2‘
I ' «AL aw' I" comc WITH 793 szzuev "W3". 4 g 8 3
h : g *I l I. m l '. l / -<
t — z . ‘
P : 5 «U a : vnm 9N .\ ' d
u! 2 V2“. 2.." H... :th “5““ f‘
.c'.‘ I a.” “5".
I02: A}. :8 . Mm'w .f’. ,. A g . '5. ' :1
: «A ,I i. i '. f 3
.. flak" ' 2 I; I. fl i :
’- L A?!“ I .‘H H. 0" jhi u I" I J
t M! ”A I come WITH 822 852 keV «1.3. H ,' .' ".""-.. q
IV .I/ i m u '. . .H I I H
IO': "I. v‘.:v-.".\' ”F ' 35"...» ’ E935 ' ' H ' _.
.. V' "..o' w.“ “.l’ g :
C a . q
>- nll‘. m :
>- I' Ii". A .1
~ con~c WITH 852kev , I I c
>- ." '1' \ _‘
. I
“I,“ "t " I I
I00 1 J ' ,u g I, n I 1
ICC 200 300 400
CHANNEL NUMBER
Figure 15. The 131mTe coincidence spectra recorded with a Ge(Li)

detector of 0.8 cm3

NaI(Tl) detector.
the 800 keV region,

active volume, gated by a 7. 6 cm x 7. 6 cm
The gates are taken in small increments across

the major contributions being that indicated
below each spectrum in the figure.

78

3.D.7. Evidence for the Placement of the Other Gamma

Transitions

Further coincidence studies were performed on the 910
and 1060 keV photons, as shown in figs. l6a-l6d. The spec-
tra, in this case, were taken with a large volume germanium
detector. as the gating crystal, while recording the NaI(Tl)
spectrum in coincidence. The higher resolution facilitates
separating information of interest from underlying Compton .....
distributions by gating on the peak in one run and on the

neighboring Compton distribution in a second run. Thus, co-

incidence information was obtained on the weak 910 and 1060

 

keV photons without the interference of the strong gamma-
rays that were within 60 keV of each. However, due to the
low efficiency of the Ge(Li) detector, good statistics were
difficult to obtain. By comparing the spectrum with the gate
on the peak to the one with the gate on the Compton distribu-
tion, photons of energy 150, 586 and 920 keV are seen to be
in coincidence with the 910 keV gamma-ray. By the same
method, the 586 and 920 keV gamma-rays are seen to be in co-

incidence with the 1060 keV photono The 910-150 keV coinci-

T-Lin'p—T' ‘I (m: .-

dence is taken as evidence for a 1060 keV level, while the

 

‘ -—'Ir

920-910 and 920-1060 keV coincidences are interpreted as

arising from a 920 keV transition between the 1980 and 1060
keV' levels. The 586 keV gamma is then a transition between
the: 16U6 and 1060 keV levels. A summary of all the coinci-

h

I
A 12 cm3 Ge(Li) detector obtained from Nuclear Diodes, Inc.

79

 

T YTYYYY

T

IO‘5

1 T 1771‘

I

U IIIVVY]

COUNTS (ARBITRARY UNITS)
T TrTYTYI T T I TYIYYI I I

T

 

I T YTTTYI

0‘-

I

   
  

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~ .-

COINC- WITH 900'92010V

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COINC- WITH 10504070 IOV

COINC

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1

     

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1 1 111111

1

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1-1'1 11111

1

1 1 111111

L 1 1 111111

 

 

Figure 16.
7.6 cm x 73
with 12 cm

The

active volume.

131m

50

CHANNEL NUMBER

1
I00

|50

Te coincidence spectra recorded with a
6 cm NaI(Tl) detector and gated by a Ge(Li) detector
The energy range included in the

gate is indicated below each spectrum in the figure.

dence results

The inte
vestigated w:
:er2 and wit

6
spectrometer

with the oran

 

 

 

conversion 1'
39139. instrume
Lines of the
'a'it‘n the hig’:
19. Additim
of the 1452.5
SerVed in bo
versi‘m elec
ccnversion c
coefficient
has been cm
the N9"? k:
convergim .

I.
«~13 Can be

8O

dence results is presented in table 3.

3.E. The Internal Conversion Spectrum

The internal conversion electron spectrum has been in-
vestigated with the orange spectrOmeter described in chap-
ter 2 and with the Michigan State University iron-free n/E
spectrometer63). The spectrum from “5 to 2&0 keV recorded
with the orange spectrometer is shown in fig. 17. The K
conversion line of the 33M.5 keV transition, recorded on the
same instrument, is shown in fig. 18. The K and L conversion
lines of the 1&9.7 keV ground state transition, recorded

63) are shown in fig.

with the high precision u/E'spectrometer
19. Additional lines corresponding to the K conversion lines
of the “52.6 and 773.7 keV transitions have also been ob-
served in both instruments. The relative gamma-ray and con-
version electron intensities thus being known, the internal
conversion coefficients can be calculated if the conversion
coefficient is known for one of the transitions. This number
has been obtained by assuming that a correct value for “K of
the l§9.7 keV transition can be derived from the theoretical

10)

conversion coefficients and the experimental K/L ratio.

This can be done using the expression

A (K/L)oL(E2)-aK(E2)

aKTle-(K/LYQLTMl)

 

81

 

 

Table 3
Results of 131mTe gamma-gamma coincidences.
Gate
(keV) Photons in coincidence (keV)
81 102, 200, 2M1, 77a, 783, 822, 852, 1126
102 81, 200, 2H1, 77a, 783, 822, 852
150 u52, (665)a), (713)a), 910 (922)a)
200 81, 102, 7uu, 77a, 822, 852
2u1 81, 102, 77a, 783
33h 77a, 793. (l6U6)a)
152
“62} 150, 665, 713, 852
550-600 150, 33a, 910
665 150, u52, H62, 713, 852
77a 81, 102, 200, 2u1, 33a, 783, 822, 1126, (1206)a)
852 (81)a), (102)a), 200, 33u, I62, 7uu, 783, llu8b)
1060 586, 922
1126 81, 77M
>1500b'°) 81, 102, 189, 231, 279. 33a, 353

 

 

 

a) The peak may be too weak to be seen in this particular run
or is masked by coincidences with underlying Compton dis-
tributions, but evidence exists from other runs.

b) The data are not shown.

C) The gate includes sum peaks.

 

82

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.II lro.
I. 8
II 9 4 0 Ier.
6 6
l I x
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9
I x 11v?—
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N/ Bp, ARBITRARY UNITS

 

 

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II

.4 I
I III

 

 

4___L._J___.L
10‘
7.60 7.70 7.80 7.90

CURRENT, AMPERES

Figure 18. The K conversion line of the 33h keV photopeak of
131mTe. This was recorded with the orange spectrometer.

 

 

814

 

 

 

 

 

 

l r 1 N I 1 T l I

20 '-

|49.7 K

a) H

I: I

2 I5 - a
I)

>-

C!

<[

0:
I: I
3'50 / I

Q.
CI)
\
(I) I
F 1
g .

O 5 .—
0 .

o
o .0
I l L J( L 1 l l 1
I420 I440 I460 W I600 I620 I640 I660 |680
POT SETTING
Fig‘i‘re 19. The K and L conversion lines of the 119.7 keV transition
Of 31mite This was recorded with the TIT/'2' spectrometer.

 

85
where K/L is measured, 0's are taken from the tableslo), and

Al and A2 are the percentages of M1 and E2 multipole mixtures

in the transitions, respectively.

The results of the data analysis are summarized in table
14, as well as the theoretical values of the conversion coef-
ficients for the various possible multipole orders. The

data do not differ significantly from the results of Devare

et al.57 ). The most important aspect of the data is that they

confirm the El assignment for theZOl and 2111 keV transitions,
indicating the presence of negative parity states in 131I.
The results still do not indicate which of the levels have
negative parity. However, a measurement of the multipolarity
of the 822 keV transition, when coupled with the information
already determined, would allow the assignment of the parities
to the levels at 1556, 1596, 16146, 1797, 1899 and 1980 keV.
Unfortunately, it was not possible for us to measure the con-
version coefficient for the 822 keV transition. Because of
the very small energy difference between the.793.6 L and 822.1
K lines , such a measurement would require Operating a spec-
trometer at 0.05% resolution with mass separated sources. In
the discussion which follows, the 822.1 keV transition has

been assumed to be an E2 + Ml transition.

3°F° The Proposed Decay Scheme and Discussion

A proposed decay scheme, based on the extensive results

of the Coincidence measurements and energy sums, is presented

. .Hm pm .oam>oa mo mpHSmmp on» spa: pcmEoopwm voow CH ohm mucofioammooo coampo>coo 059

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mm.az ANIVH.H AmIvN.m AmIva.m AmIVm.H:.H Hm m.Hz.H x >.mmz
mm.az Amuvs.m AmIvm.m AmIve.o AmIvm.He.m em m.nm.z x m.smm
Hm Amlvw.m ANIVF.© Amlvm.a Amlv©.Hw.H mm o.HHo.m x m.o:m
an AmIve.m AHIca._ AmIve.m AmIv:.He.- as m.Hw m x 5.00m
m.Hm.mH 4
mm “OH .HE m.m m.w H.: :.m :.Hm.n AHIVH.N Aalvm.m Amlvw.m AHIvH.HH.m OOH +ooa x n.mzamm
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as ~.m 0.5 w.m a.m mHm Aalvm.m onH.H AHIVN.H Aalvm.Hm.m mm odeoa x m.moa
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afloafipasz >Hfim mmom Asaxmv H: mm Hm Assess a.awHHc 5.0sfixc «asap
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Ill

87

in fig. 20. The levels and transitions presented with dashed
lines are those for which no direct coincidence evidences
exist, but are indicated on the basis of energy sums. How-
ever, these photons are all very weak and the principal
features of the decay scheme are not dependent upon their
placement.

The spin-parity assignments are based on log ft values
calculated from the measured gamma-ray intensities and on the
measured internal conversion coefficients. The ground state

131

of I is known to be 7/2+ from microwave absorption and

magnetic moment measurementsl). The 150 keV state is assigned
a spin of 5/2+ on the basis of the M1 predominance of the 150
keV transition, and the allowed nature of the beta transition
from the d3/2 ground state of 131gTe6l). The assignment is
also consistent with the shell model systematics in this re-
gionl). The 3/2+ spin assignment to the II93 keV state is ob-
tained from the study6l) of 131gTe. The 603 keV state can
only be 3/2+ or 5/2+ since it de-excites to both the 7/2+ and
5/2+ states, and the beta transition from the 3/2+ parent
state 13 allowed6l), The conversion coefficient of the 452
keV transition indicates an Ml + E2 transition and confirms
the parity assignment. On the basis of the systematics of
the Other known odd mass iodine isotopes, the 5/2+ assignment

is fa"Cred.

The 7714 keV transition is predominately E2 on the basis

of the measured conversion coefficient. The 103 ft value or

9 indicates the beta transition to the 771% keV level is proba-

Rel
In! I0<3
(keV) ”0 "

I30 07 6 4 (9/2_

220 I4 6 3
280 I8 6 3»
3&5 I6 6 7

450 4 5 6 ‘7
470 BIO 6 I

(9
550 I65 6 (5

805 3 O E» 8

895 II 53 3

I390 25 85

I600 07 95 (’2

I680 2 5 9 O (2

r
5 2 (5’25
‘5 O
( ’2 I
F.‘ by
I
319T.
20 s 512'
\

 

2450 5 o 9 2 7/2’

Figure 20.
of 30.5 hour

2270
583
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I497

 

 

 

 

 

oposed energy level scheme for

I as seen in the decay

|059,7

7737

89

bly first forbidden. The spin of the level is then limited
to 9/2+ or ll/2+. Similar arguments apply to the same spin
parity assignment to the 852 keV state.

The log ft value of the beta transition to the 1060 keV
level is 8.6, so the parity is positive. The level depopu-
lates to both the 7/2+ ground and 5/2+ first excited state.
Assuming both transitions to be M1 4- E2 mixtures, the level
has 7/2+. The 1315 keV state is 7/2+ or 9/2+ when the assign-
ment is based on the same arguments as for the 1060 keV state.

The M1 character of the 81 and 102 keV transitions, the
El character of the 201 and 2141 keV transitions, and the
M1 + E2 mixture of the 3311 keV photon define a parity dif-
ference in the higher excited states. The 1556 and 1596 keV
levels must be of one parity, while the 16146, 1797, 1899 and
1980 levels are opposite. The log ft values of the higher
energy group range from 6.1 to 6.8, possibly indicating al-
lowed beta transitions and negative parity states. The log
ft values to the 1556 and 1596 states are high, but probably
“0‘3 high enough for second forbidden beta transitions. They
are Probably first forbidden transitions, leading to posi-
tive parity states. Furthermore, if the 1556 and 1595 keV
levels were not positive parity, the 71m, 783 and 822 keV
transitions would have to be of El character. This is in-
deed an unlikely situation. Finally, Singru and Devare“)
have measured the g factor of the 1797 level and found it to
be small and negative. They interpret their results as in-

(floating the level to be a three quasi-particle state, with

90

(gwgp , d3/2n’hll/2n) or (dS/Zp'd3/2n'hll/2n) configurations
possible. This measurement may not be conclusive, but it
at less t lends additional support to the evidence presented
above.

The positive parity assignment to the 1556 and 1596 keV
levels are indeed plausible with respect tothe core coupling
model: The 7714 keV state would correspond to a one phonon
excitation of the core, while the 1556 and 1596 keV levels
would arise from two phonon excitations. The average energy
of this pair, 1576 keV, is 2.0 times the 7714 keV one phonon
energy, as the model predicts. It should be noted, however,
that no weighting factors have been used in this simple
averaging procedure. The absence of crossover transitions
and the high log ft values may be another indication of the
collective nature of the states.

Another interesting feature of the decay scheme is the
852 keV level and the transitions to it. If the 77“ keV
level is a one phonon excitation of the core coupled to the
ground state, one would actually expect a multiplet of levels
in this vicinity which would arise from the coupling of the
2+ Phonon with the g7/2 quasi-particle state. The 852 keV
level is thus a very good candidate. However, upon examin-
ing the decay scheme, it is noted that those levels which
account for 95% of the gamma-ray feeding to the 852 keV level
also $1 Ve rise to ground state transitions. Such a situation
could a1"ise from phonon-quasi-particle admixtures in the wave

fImam-OHS of the excited states. One possibility would be

n

.1

91

that the 852 keV state is a one-phonon coupling with the
ground state, while the 1315, 1646 and 2001 keV states arise
from two phonons admixing with the same g7/2 single quasi-
particle state. The center of gravity of this multiplet
is 1.914 times the 852 keV energy. The large splitting of
the levels could arise from the stronger coupling between
the quas 1-particle and phonons involved.
In addition, one can conclude from such arguments that
the 771* keV state is probably 11/2+ and the 852 keV state
9/2+, since the 77M keV photon may be pure E2, and the 852

keV photon probably is an Ml + E2 admixture.

3-G- Systematics of Odd Mass Iodine Isotopes

An illustration of the presently known levels of the
odd A iodine isotOpes that are populated by the decay of
both the 3/2+ and 11/2' tellurium isomersliBmso'm'65 is
given in fig. 21. Figures 22 and 23 show the results of

3)

recent theoretical predictions of Kisslinger and Sorensen ,
and O'Dwyer and Choudhury“). Although there is insufficient
exPeri-mental information available concerning the properties
Of the states to allow a detailed quantitative comparison
With the predictions of transition rates and lifetimes, it
is interesting to make some qualitative comparisons and to
note systematic trends.

The calculations of Kisslinger and Sorensen, as dis-'4

cussed in chap. 1, are based on pairing plus quadrupole

92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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——————- Iuc'
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I27 I |29 I I3II

Figure 21. A comparison of the efnfrimentallv determined
energy states in 2 I, 1291, and ‘3 I.

131

‘fi) Ponulated by the decay of 5;Te only

1) Poou afed by the decay of both 131gTe
and 3 mTe

93

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 22. The states of I, ' I, I as calculated

by Visslinger and Sorensen.

 

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5/20 27
DIZO at 7/20 0 ,
IZTI I291 ISII

Figure 23. The energy stages of 1271, 1291, and 1311 as calculated
by O'Dwyer and Choudhury.

95

forces. The pairing interaction tends to couple like
nucleons to zero angular momentum, producing a spherical
shape, while the long range quadrupole force tends to cor-
relate the motion of the nucleons,giving rise to collective
features in the energy Spectrum. The application of this
model to the iodine isotopes is successful in predicting
the low lying single quasi-particle states of spin 5/2+
and 7/2+, corresponding to the dS/Z and g.”2 shell model
states. It also predicts 1/2+ and 3/2+ states below 500
keV, 7/2+, 9/2+ and 11/2+ states in the vicinity of 700 keV,
and a large energy gap between the first and second 5/2+
states. Although the actual energy values of the calculated
states differ considerably, the predicted systematic trends
are remarkably accurate. In addition, Kisslinger and
Sorensen explicitly state that the l/2+ state is mainly of
phonon character3). Experimentally, the 1/2+ state at 877
keV is very weakly populated by the negatron decay of the
tellurium parent having a spin and parity 3/2+. On the
basis of spin differences alone, this should be an allowed
transition. This may then be an experimental indication
that the l/2+ state is actually rf'lective in nature.

The calculations of O'Dwyer and Choudhury predict the
energy levels arising from phonons coupling to g7/2, d5/2
and d3/2 single particle states“). In these calculations,
the phonon energy hm, the single particle energies 6,, and

the coupling strengths 5 are used as adjustable parameters

to optimize the fit of the predicted states with the known

96

experimental levels. In the case of 1291, the M88 keV state,
rather than the 279 keV state was assumed to be the 3/2+
level in these preliminary calculations. The more recent
experimental results suggest that the “88 keV state in this
nucleus corresponds to the #17 keV 5/2+ state in 127I. The

position of the 3/2+ state in 131

I is as yet uncertain, but
the u93 keV state is more likely to be the 3/2+ state than
the 603 keV state used in the above calculations. As in the
case with many core coupling calculations33’35), a multitude
of states are predicted, all of which may not be populated
by radioactive decay. Reaction type experiments may be a
more sensitive test of this model. The correspondence of
the predicted 778 keV 9/2+ and 881 keV ll/2+ with the ex-
perimental 77M and 852 keV states is tempting, but may be
fortuitous.

Both models predict states of 9/2+ and ll/2+ in the 600-
800 keV region. These states probably lie at 6&9 and 715
keV in 1271, 696 and 730 keV in 1291, and 77a and 852 keV

in 131

I, although the ordering is not certain. Insufficient
information is known about the higher energy states to afford
even a qualitative comparison.

Perhaps the most interesting phenomenon observed in this
study of systematic trends is shown in fig. 24. The energy
level separation of the 1/2+, 3/2+ and 5/2+ states, with
respect to the 7/2+ states have been plotted as a function of

neutron number for the iodine isotopes. A least squares quad-

ratic fit has been performed on each curve for the known ex-

97

A

 

 

 

 

u I I ' ' fl FI254I
IOOO ,_ A 3 AC‘UO' Value 1 d
F = Value obtained from Least
_ Squares-Quad Fit
soo * 7 * _ . . o A877 ‘
s /2 5/2 Separatuon F875
soo _ - = 7/2‘ - 3/2’ Separation A788 -
o = 7/2’- I/2’ Separation ' F775
700 - q
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0
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F-l34.l
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7o 72 74 76 78 so 82

NEUTRON NUMBER OF IODINE ISOTOPE

Figure 2“. A comparison of the systematic energies of
separation of the low lying levels of odd mass odine
isotopes with the values obtained from a least squares
quadratic fit of the data points. All values marked

A except thSSS/Z ..7/2 value for 1231 and the 3/2 ..7/2
value for I have been included in the least squares
fit. The values marked F are those obtained from the
fitted equation.

98

perimental points. As can be noted from the figure, the fit
is exceptional. The curves have been extrapolated to the

neighboring isotopes (i.e. to 123I and 1331), effectively

predicting the energy levels expected. In the case of 1331,

the extrapolated curve gave very good agreement with some new

experimental investigations being performed at MIT66). This

same type of analysis technique has now been applied to low

energy levels of Sb isotopes, with equally good results67).

‘a

 

2
.E

99

CHAPTER H
CONVERSION ELECTRON AND POSITRON MEASUREMENTS OF 3H.5hr 83Sr

U.A. Introduction

83

The study of the decay scheme of Sr has been under-

taken for two reasons. First, using an effective configura-

tion interaction in shell model calculations, Talmi and

5)

Unna have predicted some of the energy levels of 83Sr.

The ground state spin and parity of the parent 838r can be
inferred from the experimental study, thus serving as an

initial test of the calculations. Second, the energy

83
37

tematic trends of the low lying levels of the Rb isotopes to

levels of Rb are obtained, extending the study of the sys-
the more neutron deficient side of the stable isotopes. This
is an interesting region of the periodic table in which to
obtain systematics, since there are subshell closures at
Z - 38 and “0. Hence, there should be low energy shell model
states available for particle-hole configurations on both
sides of the subshell closures. A wide variety of spin-
parity states are expected from such a situation.

Previous to the recent study by Etherton, Beyer, Kelly

and Horen69)

, very little was known about the decay scheme

of 83Sr. Previous investigations had determined the half-
life, the existence of the strong conversion lines of the
42.3 keV transition, and the positron end point energy70’71).

Sanka groups had reported studies of the gamma-ray spectrum

100

72'7“) but conclusions about

using scintillation techniques
the intense A2.3 keV transition remained in question. In
addition, the decay scheme was known to be incomplete and
thus no conclusions could be reached about the ground state
spin-parity assignment for the 83Sr parent. Internal con-
version electron studies were thus undertaken in order to
complement and extend the coincidence studies of Etherton

et al.69). A search has also been made for the presence of
the isomeric state in 83Sr that was predicted by Talmi and
UnnaS).

The decay scheme of Etherton, et al. is presented in
fig. 25. Although the coincidence arguments for the decay
scheme constitute an entirely independent study, the final
decay scheme depends very sensitively on the M2 multipolar-
ity assignment of the highly converted #2.3 keV transition.
Because of the requirements of intensity balance in the de-
cay scheme, the level structure below 805 keV would be quite

different if the u2.3 keV transition had another character,

8.8. E20

“.5. Source Preparation

The sources of 83Sr utilized in this study were produced
by a 85Rb(p,3n)83Sr reaction using natural RbCl targets. Pro-
ton energies from BA to AZ MeV from the Michigan State
Lhiiversity cyclotron were used with different targets. With

careful carrier-free chemical procedures, at least one source

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102

of sufficient specific activity was obtainable for the spec-
trometer studies from each bombardment.

Two entirely different chemical procedures were used
to separate the strontium fraction from the RbCl target.
The first involved the standard precipitation procedures of
strontium in fuming nitric acid75). The target was dissolved
in a minimum amount of distilled water and transferred to a
centrifuge tube immersed in an ice water bath. To this solu-
tion was added a few milligrams of BaCl2 in water solution.
Chilled fuming nitric acid was added in sufficient quantity
to bring the solution to at least 70% concentration. The
solution was allowed to digest for 30 minutes at ice water
temperature and then centrifuged. The Ba(N03)2 precipitates
under these conditions, carrying the strontium fraction with
it while the rubidium remains in solution. The barium-
strontium precipitate was dissolved in a few drops of 0.1N
HCl and the fuming nitric acid precipitation repeated to
remove the trace amounts of the rubidium remaining. The
final precipitate was dissolved in a few ml 0.1 NHCl and then
saturated with dry HCl gas in an ice bath. The BaCl2 will
precipitate under these conditions, leaving the strontium
fraction in solution. This solution was found to be radio-
chemically free from 83Rb, 8“Rb and 86Rb which were also pro-
duced in the bombardments. However, complete removal of the
barium was difficult to achieve.

The second procedure involved a slightly modified ver-

sion of the extraction technique that was originally reported

103

by Kiba and Mizukami76’77). The RbCl target was dissolved
in a few milliliters of a 0.5 M buffer solution composed of
acetic acid and ammonium hydroxide, adjusted to pH 8. This
solution was transferred to a separatory funnel, to which
was added an equal volume of an organic solution consisting
of 0.05M TTA (o-thenoyl triflouroacetone)in hexane (methyl
isobutyl ketone). After shaking the vessel for a few min-
utes, the phases were allowed to disengage. The aqueouS‘
phase was drained into a second separatory funnel and re-
extracted with the same organic solution. The two organic
phases were combined and again extracted with the buffer
solution to remove any rubidhmIcarried down in the first
operation. The resulting organic solution was found to con-
tain greater than 90% of the 83Sr produced in the activation,
and radiochemically free of rubidium contaminants.

This organic solution is very convenient for preparing
gamma sources, since it can be evaporated to dryness very
easily. However, for an electron source free of the large
TTA molecules, it was found very easy to back extract the
strontium activity into a very small amount of 0.2M HNO3
solution. When the resulting solution was evaporated to
dryness in a centrifuge tube, a small amount of mass still
remained. This residue was driven off by simply heating over
a flame. A few drops of water will then take up the stron-
tium activity, leaving one with the desired source of high
specific activity in a neutral solution. This extraction

procedure has been used exclusively from the time of its per-

10H

fection. It offers the obvious advantage of being very rapid
as well as avoiding the use of potentially hazardous fuming
nitric acid. In addition, electron sources are easier to
prepare because the solution is not corrosive to the thin
aluminum foils used in mounting. Furthermore, vacuum evapor-
ation is easier with Sr(N0

than with SrCl In one series

3)2 2.
of experiments designed to search for a short lived isomer

of 83Sr, the chemistry was performed and counting begun with-
in two minutes of the time the target was removed from the ‘

beam pipe.

“oC- W

The internal conversion electron spectrum of 83Sr was
measured with the "orange" spectrometer, described in Chap.
2. The baffles and detector slit were set for resolution of
0.8% and about 5% transmission. Some measurements on the
“2.3 keV transition were recorded with the Michigan State
University iron free w/Z spectrometer63). The baffles were
set for resolution of 5 0.2%, but, in actuality, the source
thickness determined the resolution of these low energy
lines.

Photon Spectra have been recorded with Ge(Li) crystals
ranging in size from 0.8 to 7 cc, as well as with NaI(Tl)
crystals. The low energy portion of the spectrum is shown

in fig. 26 and the remainder in fig. 27. Table 5 lists the

results of energy and relative intensity measurements.

105

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107

Table 5

The 83Sr gamma ray energies and relative intensities

 

 

I311€3nga) Relativeb) Energy iiiggéiiy Energy I:%:§:Ziy

( keV) Intensity (cont.) (cont.) (cont.) (cont.)
5.0 805.6 weak 1296.0 0.14
112.3 5.5 818.6 2.9 1329.6 0.5
5914.2 1.0 898.7 0.9 1339.5 weak
290.2 1.9 853.8 0.9 1379.0 0.2
381.5“ 23.5 889.2 0.9 1389.3 0.3
381.5") 36.5 907.5 0.5 1396.0 weak
389.2 9.0 916.7 0.1 1528.8 0.2
14:1. 8.6 17.8 999.2 0.1 1562.5 5.5
“2 3.5 9.6 999.2 1.5 1596.6 0.07
1+3 8.2 2.7 1020.1 weak 1653.1 0.3
511.0 163.2 1037.8 0.2 1666.0 0.1
5140.6“ weak 1093.7 0.5 1710.3 weak
559.9 weak 1053.7 0.6 1722.3 weak
565.2 weak 1069.9 weak 1799.1 0.08
6 14 14.5 weak 1087.2 weak 1756.5 0.09
652.8 weak 1098.0 0.6 1778.5 0.08
658.6 0.9 11147.3 3.8 1795.7 weak
ES'7'14.0 weak 1160.0 “.5 1878.5 weak
719.2 0.2 1202.0 0.9 1911.6 0.19
732.0 0.15 1219.8 0.9 1952.2 2.6
736.8 0.55 1237.6 0.5 2019.7 0.1
75 3.2 weak 1292.6 0.3 2097.9 0.3
762.5 100 1273.1 weak 2090.0 0.3
778.9 5.5 1289.6 weak 2137.0 0.1

'31II'7 Q

108

These gamma ray data are taken from a more complete discussion

which will be reported elsewhere69).

L; . D . Conversion Coefficients and Multuolarities

u . 13.1. The 92.} keV Transition and the Search for an

Isomer in 83Sr

It is well known that the isotopes 87Sr and 85Sr possess

is omeric states, arising from the large spin difference of the

1/2- excited state and the 9/2+ ground state. In addition,

Talmi and UnnaS) predict the same type structure for 83Sr, so

an isomeric state was expected in this latter isotope. The

ab 8 ence of transitions in prompt coincidence with the “2.3

keV photon initiated the question as to whether this might

be a transition in the parent. In order to answer this ques-

tion, as well as to determine the multipolarity and the ac-
curate energy of the transition, the conversion electron

ape ctrum was studied in the 17/2' spectrometer63). The K, L

and M electron spectra that were obtained are shown in fig.

2 8 . When compared to the x-ray binding energiess), the meas-

Lit-ed K-L and K-M energy differences were found, however, to
‘19 Viate by only 0.07 keV from the values for Rb, as shown in
tab le 6. Thus, the 92.3 keV transition occurs in 83Rb. Sev-

e Pal different experiments were then performed to specifi-

cally search for an isomeric state in 83Sr. No evidence has

been found to indicate its existence. The fast chemical pro-

.7

109

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cedures described in section 9.B. have been utilized to place
an upper limit of 2 minutes on the half-life of any existing
short-lived isomeric state. (If the half-life of an isomer
was long relative to the 35 hour ground state, it would have
been detected in the gamma-ray studies69). There is, of
course, the remote possibility of comparable lifetimes for
the two states in question. Final "evidence" for the ab-
sence of the 1/2' isomeric state stems from the fact that a
consistent decay scheme can be constructed without the pre-
sence of such a 1/2' state.)

In addition to the K-L and K-M energy differences, an

absolute value of 92.30 11.0.05 keV was obtained for the trans-

 

ition energy.

The measured K/L, LI/(LII + LIII) and K/M ratios for
the 92.3 keV transition are listed in table 6, along witfi“
the theoretical predictionle). An absolute value for the

K internal conversion coefficient a , has also been obtained

K
on the orange spectrometer by comparing electron and photon ””1
relative intensities. The technique is that that is ex-

plained in section 9.0.2. The measured value of “K is in

good agreement with the M2 multipolarity assignment based on

 

the above K/L and L subshell ratios. Thus the 92.3 keV
transition appears to proceed from an excited state of 9/2+
(or 1/2+) spin and parity to the ground state of 83Rb, which
has been measured78’79) as 5/2'. If the spin is 9/2+, such
a state would be analogous to the 519 keV state in 85Rb.

The values for the theoretical conversion coefficients

'7 ,. ' 441‘

112

must, of course, be interpolated between the energies listed.

As is pointed out by Roselo)

, a plot of log 0 versus log k
is very close to a straight line for a given Z. In order to
obtain better accuracy for the interpolated 0's, the computer

has been used to make a least squares fit of log 0 versus log

k. A first order equation will indeed give reasonable results

for the higher energy points, but screening effects tend to
pull down the values of a at lower energies. However, it has
been found that a fourth order equation will reproduce the
tabulated values to within 0.5% over the entire energy range
for all multipolarities. The theoretical internal conversion
coefficients listed for all the transitions have been calcu-
lated from the fourth order least squares routine.

The M conversion coefficient has not been compared with

the theoretical valueslo)

because Coulomb screening effects
have not been included in the calculations. It has been
shown that, as a result of neglecting this correction, the
tabulated values are not realistic82). An attempt was made
to apply the semi-empirical correction of Chu, and Perlman

to obtain a good value, but it was prevented by an interpola-

tion error in Rose's calculation383).

9.0.2. The 762.5 keV Transition

The absolute conversion coefficient measurements can
be performed very satisfactorily by making an absolute meas-

urement of a single transition, then comparing electron and

Tj
. ..._:.’

 

 

HR
5.

113

photon relative intensities of the remaining transitions.
The 762.5 keV transition conversion electron line, shown in
fig. 29, has been chosen as the standard line and its ab-
solute °K measured via the mixed source technique. The in-
ternal conversion line of the 661.6 keV transition in 137mBa
has been used in conjunction with relative gamma-ray inten-
sity measurements performed with a 7 cc Ge(Li) detector of

3.9 keV FWHM resolution. The relation

6 (66 6 19(762.5 I (661.6)
a.(7 2.5 - a. l. ) TIT762_5T with the measured
A K. T: 661.6)

80) Y

quantity ”(661.6) = 0.0899 yields the desired result di-

rectly.

 

As shown in table 7, the measured value of “K I

83Rb fits

(9.5‘: .5) X 10'3 for the 762.5 keV transition in
equally well for a pure E2 or an admixture of 70% El + 30%

M2. The K/L ratio, although not a very sensitive test of

the multipolarity in this case, was unattainable because of

the incomplete resolution of the 762.5 keV L and the 778.9 i*fi?
keV K lines of the internal conversion spectrum. In order .

to arrive at a consistent set ofresults, based on the log

ft values and spin assignments of the 92.3 keV state and the

 

83Sr ground state, the 762.5 keV transition must be an E2. g; A

In any event, the El + M2 mixture is very unlikely.

119

 

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m N m m a

COUNTS/8p, ARBITRARY UNITS

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CURRENT. AM PERES

Figure 29. The internal conversion electron spectrum 0
spanning the 790—830 keV region recorded with the orange
spectrometer.

f 838:.

 

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116

9.0.3. The 81. ‘keV Transitions

The conversion electron spectrum encompassing the region

from~350 to 990 keV is shown in fig. 30. The peak correspond-

ing to a 381.5 keV transition has been shown by Etherton,
33.31.69) to be a cascading doublet on the basis of coinci-
dence results, the upper member having about 60% of the in-
tensity of the lower one. The transitions are so nearly
equal in energy that no visible broadening of the peak has
occurred in either the gamma-ray or conversion electron spec-
tra. Thus, the “K obtained for this peak must be cohsidered
as a composite. However, since the transition cascades be-
tween the 809, 923 and 92 keV positive parity states, their
multipolarities are already limited to M1 or E2, or mixtures
thereof. The conversion coefficient of the composite peak
has been measured in an effort to determine whether either
of the transitions is predominantly M1.

The value of “K has been determined independently by
both the mixed source technique and by comparison with the
762.5 keV “K measurement. The former yields the result

+ —9

0K - (7.2 - 0.3) x 10‘3. Assigning eK - 9.5 x 10 for the

762.5 kev transition, the value a - (7.01 0.3) x 10"3 was

K
obtained for the 382 keV composite transition from their

gross relative electron and photon intensities. A simple
average of (7.1 i-O.3) x 10'"3 has been taken as the accepted
value. As is shown in table 7, this is in good agreement

10)

with the theoretical E2 value of 7.2 x 10'3. If the

v [7‘
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N/Bp, ARBITRARY UNITS

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I2 — S l —4
6 r— .-

 

 

 

I I I T f l T
8600 8.800 9.000 9.200 9.400 9.600 9.800

CURRENT.AMPERES

Figure 30. The internal conversion electron
spectrum of ‘3Sr spanning the 350—990 keV region.
This was recorded with the orange spectrometer.

 

 

118

lower limit of a is taken as 6.7 x 10'3, and all of the M1

K
admixture is attributed to the weaker of the pair, a maximum
value of 90% M1 is attainable. 0n the other hand, if the
weaker member is pure E2, and upper limit of 20% Ml admixture
is possible for the stronger transition.

The 381.5 keV L + M and 389.2 K lines are unresolved.

The measured K/(L+M) ratio of 7.9 :»0.5 for the 381.5 keV

transition has been obtained by the standard stripping pro- [_1

cess, whereby counts from the unresolved 389 keV K line were

removed. The theoretical K/L ratiolo) for an E2 transition

 

is 8.9. Application of the semi-empirical method of Chu . J

9

82) to the M shell yields a value 1.7 x 10' for

and Perlman
the total M conversion coefficient. Thus, the theoretical
K/(L+M) ratio - 7.9 for an E2 transition, in good agreement

with the experimental results.

9.0.9. The 389.2. 918.6..923.5 and 938.2 kev-Transitions

The K conversion lines corresponding to the 389.2, 918.6,

923.5 and 938.2 keV transitions have been analyzed using

 

standard stripping techniques, as shown in fig. 30. The 5 1

results of the analysis are given in table 7. The K conver-
sion line of the 381.5 keV transition was used for the stan-
dard line shape. The conversion coefficients have been cal-
culated by comparing the measured electron and gamma-ray
relative intensities with the 381.5 keV transition, and using

the measured value of aK(381.5). The resulting conversion

119

coefficients indicate the 389.2 transition to be predominate-
ly E2, while the 918.6 and 923.5 keV transitions are E1. The
938.2 keV K line is not completely resolved from the 918.6
and 923.5 L lines. However, the theoretical K/L ratio of 10
for these latter two transitions indicate that the majority
of the intensity of this composite line arises from the 938.2
K conversion line. The resulting comparisons with the theo-
retical coefficients indicate that the 938.2 keV transition

has an 91 multipole order.

9.0.5. The 99.2 and 290.2 keV Transitions

Figure 31 shows the K conversion line of the 99.2 keV
transition and the K and L lines of the 290.2 keV transition.
A summary of the results is given in table 7. The K conver-
sion coefficient for the 99.2 keV transition has been meas-
ured by comparing electron intensities with both the 92.3 and

+

381.5 keV K lines. A consistent result of a - (2.2 -»0.2)

1

K
is obtained which corresponds to an M1 transition.

x 10"
An admixture of 5 10% E2 is possible within the experimental
accuracy. The transition is not strong enough to allow a
reliable K/L measurement, but a lower limit of 8 could be
derived from the data. This is another indication that the
transition is not a pure E2, which would have K/L - 6.5.

The 290.2 keV transition is probably 65% E2 + 35% M1

on the basis of the measured “K' This value has again been

obtained by comparison with the 381.5 keV K conversion line.

 

 

COUNTS/ 3., ARBITRARY UNITS

120

 

 

290.2 K

 

 

IJLLJIILQ) l 1 l l l l l

 

 

1 1 ‘L i f v 1
3.400 3.520 3.640 C C 7.000 7.200 7.400 7.600 7.800

CURRENT. AMPER ES

Figure 31. The internal conversion lines of the 99.2 and 290.2 keV
transitions in the decay of “3Sr. Different sources were used for
the two lines. The 290.2 K conversion line was recorded using a
source thick enough to cause line broadening. These were recorded
with the orange spectrometer.

 

1T;

0_ r. J

 

fi" 'l. "_‘ r'. E...
-.

1“
P.

_ '3-
{my

121

The measured value of K/L - 10 i 2 lends little additional
information since the theoretical K/L ratio for M1 and E2

transition are very close for energies above 250 keV.

LI . 13.6. The [78.9 and 818.6 keV Transitions

The conversion electron spectrum from 790 to 870 keV
is shown in fig. 29. The intensity of the 778.9 keV K
electron line was obtained by subtracting from the total
counts in the 762.5 L and 778.9 K composite line, an amount
for the 762.5 keV L line based on the assumption that it is
a pure E2 transition. The resulting “K’ listed in table 7,
for the 778.9 keV transition indicates an M1 + E2 mixture.
However, nothing can be said about the mixing ratio within
the experimental accuracy of the measurement.
The K conversion line of the 818.6 keV transition is
Ve ry weak. The measured value for (1K is slightly high as

10) as is

compared to the theoretical M1 and E2 coefficients
Shown in table 7. However, they agree to within experimental

30. C uracy.

LI 0 E . The Positron Sgectra

The positron spectra have been measured on the orange
apeetrometer. The detector slit width was opened to produce

a higher positron count rate relative to counts registered

122

from the positrons annihilating in the material surrounding
the detector. Under these circumstances the resolution was
2% . The resulting Fermi plot is shown in fig. 32, which

indicates three principal groups. The high energy group is
assumed to be an unresolved composite, feeding the ground,

5 - O and 92.3 keV states. The second and third groups then

feed the 923.5 and 809.7 keV states, respectively. The strip-

ping procedure was accomplished by making successive first
order least squares fits to the high energy fraction of the
Fermi plots. The resulting analysis indicates 89.7% of the
positrons are contained in the high energy group. There is
9 - 2% and 6.1% feeding, respectively, to the 923.5 and 809.7
keV states, in good agreement with expectations based on
gamma intensities. These numbers, coupled with K/8+ and

E K/EL capture ratiosa’au)

have been used to fix the total
amount of feeding to each of the states indicated in the
de cay scheme, fig. 25. The division of the positron feeding
between the ground and 92.3 keV states has been fixed by the
requirements of intensity balance of the 92.3 keV state,

1 o e. the number of transitions to the state must balance
the number leaving the state. Kn: ring the number of gamma-
ray and conversion electron transitions into and out of the

8hate, the required amount of B feeding to the level was

then determined.

Li"

123

.uouosouuooam owcmho any nuwa vovpooou whoa sump sauna
.umno mo house 0:» ca pouuwao mcouuwmoa on» no manuamcd “show 059 .NM shaman

 

 

        

“>33 w
OOn. CON. 00: 000. 000 000 00B 000 00m. 00¢ OOn CON 00. 0
_ a — d _ . . o o o 0 fi — _ _ d _ _
o o . XXX
X
a ..
00 X
33.2: .. x
>3. mafia. ..
a o
o I.

         
 
 

3.N.$
>8. minnow

aremva
>3. 0N H 00¢

 

 

ON

0?

00.

ON.

0'.

129

9.F. Spin-Parity Assiggments faéthe Levels of 83Rb and the

Ground State of 83Sr

The transitions in 83Rb for which internal conversion
coefficients have been measured are shown as the more intense
lines in the proposed decay schemesg), fig. 25. The log ft
values shown in the decay scheme, fig. 25, have been cal-
culated on the basis of the Fermi plot analysis and gamma If“?

transition intensities. The spin-parity assignments pre-

sented here are based primarily on the internal conversion 7

 

coefficient measurements with the log ft values being con- j

sidered as confirming evidence.

83

quolo The “2.3 keV State Of Rb

The ground state spin and parity of 83Rb is known to
be 5/2' 78’79). The measured “K' K/L ratio and LI/(LII + _
LIII) ratio of the 92.3 keV transition indicate an M2 assign- : “a“
ment. Thus the 92.3 keV state must either be 9/2+ or 1/2+. I

Although the 1/2+ assignment would be difficult to under-

 

stand on the basis of shell model configurations available I 9
in this region of the periodic table, this alternative has

been considered. A consistent interpretation of all the

data was not possible with such an assignment. Hence, the

spin and parity of 9/2+ for the 92.3 keV state is considered

well established.

125

83

9.F.2. The 923.5 and 5.0 keV States of Rb and the Ground

State of 83Sr

The 923.5 keV state decays to the 5/2' ground state via

an E1 transition, and to the 9/2+ 92.3 keV state via a 381.5

keV transition which is predominantly E2. Thus, the 923.5
keV level must have spin and parity 5/2+ or 7/2+. Any Ml
admixture in the 381.5 keV transition would limit the spin
to 5/2+.

The El character of the 918.6 keV transition from the
5/2+ or 7/2+ 923.5 keV state to the 5.0 kev state limits
the latter to any value in the range from 3/2' to 9/2‘. If
the 5.0 keV state were 7/2' or 9/2', it would be expected
to be pOpulated by a 37.3 keV El transition from the 92.3
keV state. A search for the K conversion line of such a
transition was performed in the orange spectrometer, with
the result that, if such a line exists, its total intensity
is less then 1% of that of the 92.3 keV transition. Hence,
it would be retarded by a factor of 105 over the single

particle Weisskopf estimatea). Likewise, a 5/2' assignment

can be cast in doubt, since an M2 transition between the 92.3

and 5.0 keV states would be expected to compete favorably
with the 92.3 keV transition. It is therefore concluded
that the most probable spin-parity assignment for the 5.0
kev state is 3/2'. This assignment also fixes the spin-
parity of the 923.5 kev state to be 5/2+.

The ground state of the parent 838r is expected to be

1/2', 9/2+ or 7/2+ on the basis of the systematics and shell

I .II.
'11
P.
8

. _-_' ‘21. “.4.“-

 

“' .A"'A.‘.- -. I' ‘ -
but

 

126

model configurations available in this region of the periodic

1,16)

table The 1/2' possibility is ruled out immediately

because of the relatively large amount of positron feeding
to the 9/2+ 92.3 keV state. The allowed or first forbidden

nature of the log ft values of the beta transitions to the

9/2+, 5/2+ and 5/2' states in 83

7/2+ to the 83Sr ground state. Additional support for the

Rb favors an assignment of

7/2+ assignment ariSes from the negative results obtained
in the search for the presence of an isomer: The lifetime
of a 1/2' level in ggSrUS would be much less if the ground
state is 7/2+ rather than 9/2+. As an example, the 190 keV
1/2' state in Bg'Kru5 decays via an E3 transition to the 7/2+

3
ground state, with a half-life of 13 secondsl).

9.F.3. The_99.2 and 389.2 keV States

The M1 + 52 character of the 99.2 keV transition, in
conjunction with the 3/2' assignment of the 5.0 keV state,
limits the 99.2 keV state to 1/2', 3/2', or 5/2". The 5/2‘
possibility is ruled out on the basis of the high log ft
(:9) value for the decay to this level69). The 1/2‘ assign-
ment is considered to be the more probable of the remaining
possibilities because of the lack of transitions to this
level from the higher energy states whose spin-parity is
35/2*. ‘

The M1 + E2 character of the 290.2 and 389.2 keV transi-

tions, in conjunction with the above assignments, fixes the

127

389.2 keV state as 3/2'. This assignment is in agreement

with the log ft value of 38 for this state69).

9.F.9. The 809.6 keV State

The 762.5 kev £2 transition to the 92.3 keV 9/2+ state,
and the 381.5 keV E2 transition to the 5/2+ state, limit the
809 keV state to have spin-parity 5/2+, 7/2+,or 9/2+-all of
which are consistent with the allowed nature of the log ft
value of the level. The 5/2+ possibility is very doubtful
because of the absence of any transition from this level to
any of the lower energy 1/2' or 3/2' states. Etherton, 32.
69)

3;. have presented arguments based on the gamma feeding
to the 809 keV state from the higher energy states, which

favor the 7/2+ assignment.

9.F.5. The 1202 and 1293_keV States

The probable Ml + E2 character of the 778 kev transi-
tion, coupled with the log ft value of the 1202 keV state,
indicate a positive parity assignment, with spins 5/2 or
7/2 possible. The fact that this level decays to states of
spin-parity 5/2*, 9/2+, and 5/2‘ implies that the 1202 kev

state is 7/2+.

The 1292.6 keV state decays via the 938.2 keV Ml transi-

tion to a 7/2+ level and via the 818.6 keV Ml'+ E2 transition

 

 

128

to the 5/2+ 923.5 kev level. The state is thus limited to
a 5/2+ or 7/2+ assignment, in agreement with the log ft
value for the level. The weak 1237 keV transition to the

5.0 keV 3/2' state favors a 5/2+ assignment.

9.0. Discussion

The above results, based primarily on the transition
multipolarities obtained from conversion electron measure-

ments, are in good agreement with the spin-parity assign-

 

ments from log ft values if the ground state of ggSrus is
assigned as 7/2+. This assignment does not coincide with
the calculations of Talmi and UnnaS) which predict a 7/2+
state 320 kev and a 1/2‘ state 170 keV above a 9/2+ ground
state. However, the 7/2+ assignment is not surprising on
the basis of systematics. Even though ggSru7 and §88r99

have ground state spins of 9/2+, other 95 neutron even Z

F “"- .
77 79 81 + 85) 1
nuclei, 32Ge95' 398395’ and 36Kr95 have 7/2 ground states . ,_
These correspond to (g9/2);/2 shell model configurationsl6).

The 383r95 ground state probably has the same configuration.

 

In 83Rb, the ground state (5/2‘), the 5.0 (3/2'), the J

92.3 (9/2+) and 99.2 (1/2') keV states probably arise from
-1 ' -l 1

shell model proton configurations (f5/2) , (p3/2) , (g9/2)
and (pl/2)1, respectively. However, the extremely close
spacing of these levels may indicate an appreciable amount of
a more complex configuration mixing. The low lying 3/2' stave
)‘1

is expected since the (p3/2)-1 and (fS/Z configurations are

129

in competition for the ground state of rubidium isotopes, the

81Rb and 87Rb, the latter for 83Rb and

81 85

former prevailing for

85Rbl6). The 9/2+ states in Rb and Rb probably correspond
to the same type configuration assigned for 83Rb. The 9/2+ -
5/2' energy level separation is changing very rapidly in this
series of nuclei, the 9/2+ state actually being the lower
state in 81Rb. This trend may suggest that the 2970 keV state
in 87Rb is 9/2+, an assignment which is consistent with the
log ft value of the 8 transition to the levell). Very little
is known about the level schemes of these other odd mass
rubidium isotopes, suggesting the need for further investi-
gation in this region before established systematic trends

of the single particle levels are available.

The higher energy states in 83Rb probably arise from
more complicated shell model configurations, as well as
particle motion coupled to collective excitations of the
core. It is interesting to attribute the strongly excited
923.5 and 809.6 keV states to the latter phenomenon. This
can be done from two slightly different points of view, al-
though there are objectionable features to both interpreta-
tions. First, it is noted that the 809.6, 923.5 and 92.3
keV states are connected by relatively pure E2 transitions
of comparable energy, which suggests a vibrational structure
built on the 9/2+ single particle state. However, when com-

pared to the neighboring 82Kr even-even nucleus6)

, the cross-
over to cascade ratio appears to be a factor of 7 too strong

and the phonon energy (expected to be approximately 780 keV)

130

would have to be reduced by a factor of two, to 381 keV.
firhe other point of view, based on the core coupling model of
(is Shalit32), assumes the 809.6 (7/2+) and 923.5 (5/2+) keV
:states are part of a multiplet of states produced by coup-
ling of the 2+ core excitation with the 9/2+ particle state.
If this is the case, the crossover to cascade ratio, as well
as the phonon energy are more nearly what one would expect
them to be. However, transitions between members of the multi-
plet should be predominantly Ml, whereas an upper limit of
90% has been placed on the M1 contribution of the observed
transition. In either event, if the 809.6 keV state is
truly of collective nature, the E2 transition probability
of the 762.5 keV gamma ray should be greatly enhanced over
the Weisskopf single particle estimate8). A measurement of
the lifetime of the state might serve to test the hypothesis.
Finally, one would expect similar collective states
built on the ground and 5.0 keV state in much the same man-
ner as they seem to be built on the 9/2+ state. The 389 keV
level may indeed have such a composition. However, most of
the states so formed may be inaccessible to the B decay pro-
cess, since it requires a g9/2 neutron to be transformed into
an f5/2 or p3/2 proton, a process which is both J and 2 for-
bidden. On the other hand, one°might expect the 39/2 extra
core neutron in 83Sr to very effectively populate levels

built on the g9/2 proton states in the 83Rb daughter.

CHAPTER 5
AN ANALYSIS OF THE EXPERIMENTAL RESULTS

5.A. The Necessity for Electron Measurements and Magnetic

Spectrometers

It was mentioned in sect. C of the Introduction that there
are instances, such as have been encountered in the studies of
the two nuclei reported here, where spin-parity assignments
to the nuclear levels are extremely difficult to make on
the basis of gamma-ray studies only. In order to obtain more
information on the states of interest, a magnetic spectrom-
eter has been constructed for the purpose of measuring con-
version coefficients and analyzing continuous beta spectra.
In addition, it was known that energy level determinations
would indeed be very difficult on the basis of gamma ray
measurements alone if the spectrum contained low energy,
highly converted transitions. That such situations exist
has been very well exemplified by the study of the decay
scheme of 83Sr where the proposed level structure depends
very sensitively on the multipolarity of the 92.3 keV transi-
tion. The multipolarity, in turn, was accurately determined
by internal conversion electron measurements. Of course, a
very considerable amount of additional information on the

other levels of 83Rb and 131

I has also been obtained, which
would not have been possible without the ability to measure

internal conversion coefficients.

131

132

Subsequent to the time the orange spectrometer construc-
tion was begun, the quality and availability of solid state
gamma-ray and electron detectors have been greatly enhanced.
The solid state electron counters have proven to be such
versatile instruments that one is tempted to ask if there is
still a need for an intermediate resolution magnetic spectrom-
eter, such as the orange spectrometer. The experience gained
in the study of the 83Sr decay scheme has vividly demonstrated
that there is a strong need. The first objection to the solid
state detectors is that they have an appreciable Compton scat-
tering cross section, giving rise to a large background if
high energy gamma rays are present. Thus, internal conversion
lines from transitions in low Z nuclei (conversion coeffi-
cients are small for lowiz nuclei) or from weak transitions
may be masked by underlying Compton distribution in the re-
corded spectrum. Even more serious is the presence of an in—
tense B+ continuum, where it occurs. For example, the strong
high energy positron groups in 83Sr completely masked the

conversion lines of transitions in 83

Rb in a spectrum re-
corded with a solid state detector. Both problems are elimina-
ted in a transverse field magnetic spectrometer. The former
problem is eliminated because the detector is shielded from
gamma radiation, and the latter because positrons are bent

in a direction opposite to that of the electrons-—thus, only
electrons of one sign reach the detector. (The lens type

spectrometer has to be modified to discriminate between

positrons and electrons.) It can be concluded that solid

state
from

renal

5.8.

data
allo
tion
ture
poss

the

83m

staI
of .
Dar;

0P1

Cor
eve
171
K1.
is

the

133

state detectors are capable of removing much of the burden
from the slower magnetic spectrometers, but that the latter

remain an indispensable tool of nuclear spectroscopy.

5.0. Comparison of the Experimental Results with Predic-

tions Based on Nuclear Models

It has been pointed out in chapters 3 and 9 that the
data available for the nuclei studied are insufficient to
allow detailed comparisons with theoretical model predic-
tions. However, with the much improved energy level struc-
tures that are now available from these studies, it has been
possible to present some qualitative arguments correlating
the data with some of the predictions.

There are no specific calculations existing for the
83Rb nucleus, but the spins and parities of the low energy
states correspond well with what is expected on the basis
of the shell model. Without any basis for detailed com-
parisons, only speculations can be made concerning the
origins of the higher energy states of 83Rb.

The ground state assignment of 7/2+ for 838r does not
correspond with the predictions of Talmi and UnnaS). How-
ever, their calculations do indicate the presence of a low-
lying 7/2+ state at 320 keV. It has been pointed out by
Kisslinger and Sorensen3) that the Talmi-Unna calculation

is the only one that has been performed which can depress

the 7/2+ states enough to qualitatively agree with experi-

me

be
ne
wi
Ki
ca
an
ti
Sc
pc

CC

ac‘

bc

ti
CI
17
tk

ti

139

mental results in this region of the periodic table.

The low energy states of 131

I, as well as the systematic
behavior of these states with respect to the addition of
neutron pairs, can be said to be in qualitative agreement
with the pairing plus quadrupole force calculations of
Kisslinger and Sorensen3). However, neither this set of
calculations nor the core coupling calculations of O'Dwyer

and Choudhury“)

are able to explain the higher energy nega-
tive parity states that were observed in these studies.
Some evidence has been presented which indicates that the
positive parity states are due to quasi-particle-phonon
coupling.

In any event, the above results indicate the need for
additional experimental and theoretical investigations in
both of the regions of the periodic table studied here.

The results that have been presented can form a good founda-
tion for both types of examination. With respect to cal-
culations for the iodine isotopes, any future theoretical
investigations should, as one of the objectives, explain

the quadratic behavior of the single particle energy separa-

tions as a function of neutron number.

10)

NL'
N2

NI

P'I

LI

l)

2)

3)

9)

5)

6)
7)

8)

9)

10)

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