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ABSTRACT

NUCLEAR SPECTROSCOPIC STUDIES OF NEUTRON-DEFICIENT,
ODD—MASS RARE EARTHS NEAR THE N=82 CLOSED SHELL
By

Richard Earl Eppley

The decay schemes of Gdlug, Gd1“59+m and Smlu19+m have
been studied by y- and B—ray spectroscopy in an effort to elucidate
their nuclear prOperties. Also, a search for Dylu7g+m has been con—
ducted, although no decay scheme can be prOposed.

y-ray spectroscopic techniques including Ge(Li) singles,
Ge(Li)-NaI(T1) coincidence, and Ge(Li)—Ge(Li) megachannel, 2-dimen-
sional coincidence techniques have been employed. Where appropriate,
electron spectra have been obtained by use of Si(Li) surface barrier
detectors.

Twenty-five y rays have been attributed to the electron-
capture decay of 9.4-day Gd“+9 and incorporated in a decay scheme
having 13 levels with energies of 0, 149.6, 459.9, 496.2, 574.2,
666.0, 748.2, 794.8, 812.4, 875.8, 933.3, 939.1, and 1097.3 keV.

The isomeric decay of Gdlusm has been characterized as having a half-
life of 85:3 seconds and an M4 transition of 721.4i0.4 keV. A di—
rect c/B+ branch has also been determined as accounting for 4.7% of
the decay from this level. Gd1“59 is reported to have 38 y rays
associated with its decay, 26 of which (accounting for 197% of the

total y intensity) are incorporated into the decay scheme. This

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decay scheme has 19 levels placed at 0, 329.5, 808.5, 953.4, 1041.9,
1567.3, 1599.9, 1757.8, 1845.4, 1880.6, 2203.3, 2494.8, 2642.2, 2672.6,
3236.0, 3259.6, 3285.6, 3623.8, and 4411.3 keV. smlulg and Sml“1m
appear to have 9 and 32 associated y rays, respectively. Levels in
Sm1“19 have been placed at 0, 196.6, 403.9, 728.3, 858.5, 1292.7,
1495.6, and 2005.0 keV. Levels in 8m1“1m have been placed at 0,
196.6, 628.6, 804.5, 837.1, 974.0, 1108.1, 1167.2, 1313.2, 1414.8,
1834.0, 1983.1, 2063.5, 2091.6, 2119.2, and 2702.4 keV. The half—
lives of Sm1“19 and Smlhlm have been measured to be 11.3:0.3 and
22.1:0.3 minutes respectively.

Spin and parity assignments for the nuclear levels en-
countered in this investigation are based on log ft values, relative
Y intensities, and transition multipolarities (where internal-con-
version-electron intensities were available). Two intense tran—
sitions in Eulus, which account for ”722 of the B decay from Gdlusg,
are interpreted as being three-quasiparticle states. Also, there
are 6 states in Pmlul, lying between the energies of 1414.8 and 2702.4
keV, which appear to be three-quasiparticle states analogous to those
reported recently for Pr139. Mechanisms are suggested for these
three-quasiparticle types of decay in terms of simple shell-model
transitions and nucleon rearrangements.

Several families of nuclear isomers are compared with each
other in terms of their level energies and reduced M4 transition
probabilities. These include the Z=82, N=81, N=79, Z-SO, Z-49, and
”*49 families. High multipolarity electromagnetic transitions from

these isomers are considered to be quite ”pure" single—particle

 

 

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Richard Earl Eppley

transitions. The eXperimentally measured transition probabilities
are compared to these single particle predictions in an effort to
determine the degree to which this is true. Finally, levels in the
odd-mass N=82 and Z=63 nuclides are traced as far as possible in an

effort to understand nuclear behavior in this region better.

NUCLEAR SPECTROSCOPIC STUDIES OF NEUTRON—DEFICIENT,

ODD-MASS RARE EARTHS NEAR THE N=82 CLOSED SHELL

By

Richard Earl Eppley

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1970

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ACKNOWL Iil)( i [CM l'IN'l‘S

I wish to thank Dr. Wm. C. McHarris not only for suggesting
this region of study but also for guidance and help in all phases of
the ensuing investigation, including the preparation of this thesis.

I also wish to thank Dr. W. H. Kelly for his help and
advice. His suggestions on the performance of experiments and analysis
of data are greatly appreciated.

Dr. H. G. Blosser and Mr. H. Hilbert have assisted with
the operation of the Michigan State University sector—focused cyclotron.
As with any large, complicated machine, it had its temperamental
moments at which times their special touch was necessary for a
successful run.

The members of our research group have all contributed in
one way or another to the successful completion of this thesis research.
Dr. D. Beery, Mr. J. Black, Mr. w. Chaffee. Mr. J. Cross, Mr. R. Doebler,
Mr. R. Firestone, Mr. G. Giesler, Mr. R. Goles, Mr. K. Kosanke, Mr. R.
Todd, and Dr. R. Warner have all helped in this work. I particularly
wish to thank Dr. D. Beery for his help in the early stages of this
project. Mr. R. Todd and Dr. R. Warner have shared jointly in the
Sm]”] research. In addition they have provided me with many hours
of discussion on the research and other things philosophical.

Dr. P. Plauger, Mr. R. Au, Mr. and Mrs. w. Merritt and the
cyclotron computer staff have been helpful in the writing of programs

and with the operation of the computer.

11

Help has also 't
:32 :yclatron machine
ieztrmizs shop.

I also wish to
$1.: of this thesis as

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Finally, I the.
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Help has also been given by Mr. R. N. Mercer and his staff
in the cyclotron.machine shap, and by Mr. W. Harder in the cyclotron
electronics shap.

I also wish to thank Mrs. Ina Samra for her help with the
typing of this thesis as well as the typing of several reports for
publication.

The National Science Foundation, U. 5. Atomic Energy
Commission and Michigan State University have provided much of the
financial assistance for this research.

Finally, I thank my wife Sara for her help and encouragement
during these past few years. I also thank her for just plain putting

up with me during this hectic time.

111

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TABLE OF CONTENTS

Page
ACKNOWLEDGEMENTS ii
LIST OF TABLES
LIST OF FIGURES
Chapter
I. INTRODUCTION............... ................... . ...... 1
II. EXPERIMENTAL EQUIPMENT AND PROCEDURES... ...... ....... 6
2.1. y-Ray Spectrometers............... ............. 7
2.1.1. Ge(Li) Singles Spectrometer............ 7
2.1.2. Ge(Li)-NaI(T1) Coincidence Spectrometers 9
2.1.2.A. Coincidence Spectrometers
Using Ge(Li) vs 3X3-in. NaI(T1) 9
2.1.2.8. Ge(Li) vs 8X8-in. NaI(Tl)
Split Annulus................. 12
2.1.2.C. Ge(Li)-Ge(Li) Megachannel,
2-Dimensional Coincidence
Spectrometer.. ...... ..... ..... 15
2.2. Conversion-Electron Spectrometer................ 17
2.3. X-Ray Spectrometer........... ................... 18
2.4. Special Equipment for the Dy”7 Experiments..... 19
2.5. Chemical Separations...................... ..... . 20
2.5.1. Zn-HCl Reduction.... ....... ............. 21
2,5,2, HypophOSphorous Acid Reduction.......... 22
2.5.3. Ion—Exchange Separations ..... ... ........ 26
III. DATA REDUCTION............... ........ . ..... ........... 33

3.1. Gamma-Ray Energy and Intensity Determinations... 35
3.1.1. Program MOIRAE .......... . ....... ....

3.1.2. Program SAMPO............. .............. 43

iv

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4.1...
4.1.5

Chapter Page
3.2. PDP—9 Machine Operation for FORTRAN Programming. 51
3.3. Determination of the Decay Scheme Parameters
with Program SCHEME ............................. 54

3.3.1. Steps Necessary in the Determination
of Log ft values for B Decay ...... . ..... 54
3.3.2. A Short Look at the Log ft Equation ..... 56
3.3.3. Description of Program SCHEME ........... 57
IV. EXPERIMENTAL RESULTS .................................. 62
4.1. The Electron~C3pture Decay of Gdlqg.... ......... 62
4.1.1. Introduction ............................ 62
4.1.2. Source Preparation .......... . ........... 64
4.1.3. Gd“+9 Spectra ........................... 66
4.1.3.A. Singles Spectra ..... ... ....... 66
4.1.3.B. Prompt Coincidence Spectra.... 76
4.1.3.C. Delayed Coincidence Spectra... 88

4.1.3.B. Internal Conversion

Coefficients .................. 92
4.1.4. Electron-Capture Energy ............ ..... 98
4.1.5. PrOposed Decay Scheme ................... 101
4.1.6. Discussion .............................. 110
4.2. The Decay of Gdlqsm.. ........................... 118
4.2.1. Introduction ............................ 118
4.2.2. Experimental Results .................... 120
4.2.3. Gdlusm and N = 81 lsomers ............... 129
4.3. The Strange Case of Gdlhsg...................... 136
4.3.1. Preamble.. ............. . ..... . ...... .... 136

 

 

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Chapter

4.4.

4.3.2.

4.3.3.

4.3.4.

4.3.5.

The Decay of Sm

4.4.1.

4.4.2.

4.4.3.

4.4.4.

4.4.5.

4.4.6.

4.4.7.

Source Preparation ....................
Experimental Data .....................
4.3.3.A. Singles y—ray Spectra .......
4.3.3.B. Coincidence Spectra .........

4.3.3.C. Half-life Determination for
Gd1”59 ......................

Proposed Decay Scheme .................
Discussion ............................
4.3.5.A. Single—Particle States......
4.3.5.8. Three—Quasiparticle States..
4.3.5.C. The Remaining States.. ......

+
4.3.5.D. t/P Hatios .................

141m 1419 .

and Sm
Introduction ..........................
Source Preparation ....................

Half—life Determinations for Smlhlm

and Smlulg..
Smlul y—ray Spectra ...................
4.4.4.A. Singles Spectra ........... ..
4.4.4.8. Prompt Coincidence Spectra..
4.4.4.C. Delayed Coincidence Spectra.
Energy of the Sm“+1 Isomeric Level....
Smlulm

Decay Scheme ...................

4.4.6.A. The 196.6—keV and Related
Levels ......................

4.4.6.8. The 628.6—keV and Spin
Related Levels ..............

Spin and Parity Assignments for the

Decay of Smlglm ............ . ..........

vi

Page
139
140
140

142

154
155
163
163
165
169
170
172
172

175

180
180
183
196
196

199

201

202

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Chapter

V.

4.5.

5.1.

4.4.7.A. The ground, 196.6-, and
628.6—keV States in Pmlql....

4.4.7.8. The 804.5—, 837.1—, 974.0-,

1108.1—, 1834.0— and 1983.1—

keV Levels in Pm“1 ..........

4.4.7.C. The Levels Which Decay through

the Level at 628.6 keV .......

4.4.8. Sm1”19 y—ray Spectra ............. . .....

4.4.8.A. Singles Spectra ..............
4.4.8.8. Coincidence Spectra for

Sm1“19 .......................

4.4.9. Smi“19 Decay Scheme ....................

4.4.10. Spin and Parity Assignments for Sming.
4.4.11. Discussion ..... ........................

4.4.12. Remaining Peaks in the Smlh1m+9 Singles
Spectra.....OOIOOOOOOO......OOOOOOOOOO.

The Search for Dylu7........ ..... ..............
4.5.1. Introduction..... ...... ......... .......
4.5.2. Singles Experiments ....................

4.5.2.A. y-ray Singles Experiments....

4.5.2.8. Conversion—Electron
Experiments ........... . ......

4.5.2.C. x—ray Experiments ............

4.5.3. y-ray versus x—ray Coincidence
Experiments ............................

4.5.4. Discussion.... ....... . .............. ...

MULTIPOLE RADIATION AND THE SINGLE—PARTICLE MODEL....

Multipole Radiation
5.1.1. Mathematical Paraphernalia.............

5.1.1.A. Angular Momentum Operators...

vii

Page

205

209

211

211

218

221

226

229

233

234

234

235

235

244

244

245

246

250

252

252

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Chapter

VI.

Page
5.1.1.8. Spherical Harmonics .......... 253
5.1.l.C. Laplacian Operator ........... 254
5.1.1.D. Bessel Functions ............. 254
5.1.2. Maxwell's Equations... ................. 257
5.1.3. Multipole Expansion of the Radiation
Field. ............................ ..... 258
5.1.4. Sources of Multipole Radiation.... ..... 262
5.1.5. Transition Probabilities.., ........ ..... 265
5.2. Single-particle Transition Probabilities ....... 266
SYSTEMATICS OF THE 8:63 AND N=82 NUCLEI AND
DISCUSSION OF SOME M4 ISOMERS. ............. ..... ..... 271
6.1. Levels in Neutron-deficient, Odd-mass Eu
Isotopes...... ......................... ... ..... 271
6.2. Levels in Odd-mass, N=82 Nuclei...... ..... ..... 273

6.3. Survey of a Few M4 Isomeric Series............. 276

viii

 

 

 
 

 

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15.

16.

17.

18.

LIST OF TABLES

Oxidation Potentials ...... . ............................

y-ray energy standards used for Gd1H9 .............. ....

Energies and relative intensities of y rays from the
decay of Gdlhg. ......

Intensities of Gd“+9

Summary of coincidence data.... .............. . ....... ..

Intensities of Gd“+9 y rays in delayed and prompt

coincidence. .............. ... ..... . ....................

Experimental and theoretical internal conversion

coefficients for Gd“+9 transitions ..... . ...............

Experimental and theoretical K/h; [CC ratios for Gdlw3

.1.

transitions ............................ ..... ...........
Transition data for Gd“+9 ..............................

y-ray energy standards used for Gd1”5m. ................

Transition data summary for Gdlhsm.

Conversion coefficients for the isomeric transition in

GdIQSOOOOOOOIOOI .......... O ...... O 0000000000000000000 .0

Energies and relative intensities of y rays from the
decay 0f GdIQJg. ...... ....0.0.0.0.........OOOOOOOOOOOO

Relative intensities of Gd1”59 y rays in coincidence

experiments.. ..........................................

Summary of y-ray coincidences in GdeSg .............

. . . +
Comparison of experimental and theoretical a(tot)/B
145

ratios for decay to states in Eu ....................

published data for 3m1”1.... ...................... ....

Energies and relative intensities of y rays from the
decay of Smlulm.

ix

Y rays in coincidence eXperiments.

Page
23

67

71
8O

82

9O

93

96
103
121

125

128

144

148

152

171

174

184

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Table

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

191m

y—ray intensities for Sm coincidence experiments...

Summa of y-ray 2—dimensiona1 coincidence results

for Sln “ImOOOOOOOIOOOOOOOOIOO ..... .....IOOOOOOOOOIOOOOO

Com arison of log ft's assuming either the theoretical
e/B ratios or all e—decay.............................

Energies and relative intensities of y rays from the
decay of Smlqlg

.0... ..... ... OOOOOOOOOOOOOOOOOOOOOOOOOOO

Relative intensities of y rays assigned to Smlqlg as

measured in four consecutive 15 minute spectra.........

Coincidence transition intensity summary for Sm1”19..

Peaks in the singles spectra which have not been
assigned to the decay of Smlulg or Smlulm.. ..... .......

y—ray energies and peak areas for transitions observed
in a SmIL‘L+ target immediately after oombardment........

y—ray energies and peak areas for transitions observed
in a Sm1w target four days after the bombardment......

Coincidence results from the y-ray versus x-ray
experiment performed on a Smlm’r target.................

Expressions for single-proton transition probabilities.

Page

192

194

204

213

214

220

233

238

241

248

269

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10.

11.
12.
13.
14.

15.

16.

17.

18.

19.

LIST OF FIGURES
Page

Schematic illustration of the Ge(Li)—NaI(Tl)
coincidence apparatus..... ................. . .......... 10

Schematic illustration of the anticoincidence apparatus 13

Schematic diagram of the megachannel 2—dimensional
apparatus ............................................. 16

Ion—exchange apparatus ..... . .............. . ........... 28

Elution curve for Gdlb'g-Euw‘?”15L+ using Dowex 50X8

resin and c—hydroxyisobutyric acid as the eluant ...... 32

Oscilloscope and sense switches used for program
MOIR-AEOOOOOCOOOO ....... .0... ....... 00.0.0.0... ....... O 36

Oscilloscope displays generated by program MOIRAE..... 38

Sample of line—printer output from program MOIRAE ..... 41
Sample output from the computer program SAMPO ......... 46
Cd”9 singles y-ray spectrum from a Eu151 separated

isotope targetOOOO0.0.00.00.00.00. ...... O ......... O... 69
Cd”9 singles y-ray spectrum from a natural Eu target. 70
Gd“+9 x-ray Spectrum compared to a Ce139’1“1 spectrum. 73
Anticoincidence spectrum of Gdlqg........ ...... ....... 77
Integral-coincidence Spectrum of Gdlqg.... ..... ....... 78

Spectrum of y rays from Cdlug decay observed in
coincidence with the 149.6—keV transition ...... . ...... 83

Cd”9 coincidence spectrum taken with a prompt gate
on the 346.5-keV transition... ................... ..... 84

Coincidence spectrum of Cd“+9 with the gate on the
534.2-keV transition .................................. 85

Cd199 coincidence spectrum with the gate on the 600—
kev regiOUOIOOOOIOOOOOOO OOOOOOOOOOOOOOOOOOOO .... ..... O 86

Cd“9 coincidence spectrum with the gate set on the
goo-kev region.............OOOOOOOOOCO......OOOOCOOOOO 87

xi

 

 

 

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.... . . . . . n u u . .. .:~ u.“ .. . "J ...... ..J. ..u u .. ...... ..s ...... .. M ....

 

Figure
20.

21.

22.

23.
24.
25.

26.

27.

28.

29.
30.

31.

32.
33.
34.
35.

36.

37.
38.

39.

Gd1H9 delayed coincidence spectrum ....................

Experimental and theoretical conversion coefficients
for the transitions in Eu1H9 following the decay of
GdlL‘9......................O.. ........................

Graphical estimates for the electron—capture decay
energies for several odd-mass Gd isotopes, including
GdlL‘ ........ ....... . ...............................

Decay scheme for Gdlgg..... ...................... .....
Singles y-ray spectrum from 85~second Gdlgsm ..... .....
Half-life curve for Gd1“5m ........................... .

Electron Spectrum showing conversion lines from the

721. 4-keV‘M4 isomeric transition in Gdlqs. ...... ..... .
Decay scheme for Gdlu5m ........... .. . .. ..... .. ..
Plots of the h1+d3 y differences and of

the squares of lihe radiéfe matrix elements for the M4

isomeric transitions that connect these states in the
N = 81 Odd-111383 1801101188. 0 o o 0000000000000 o o o o o oooooooo
Singles y-ray spectrum for Gdlqsg .....................

Anticoincidence spectrum of Gdlqsg decay ..............

2-dimensional coincidence spectra for the decay of
Gdlksg

Additional gated spectra for the 2-dimensional run....
Gd1“59 coincidence spectrum gated on 511—511-keV......
Half-life curve for Gdlhsg.. ..... ...... ..... ..........
Decay scheme for Gdlusg..... .......... ................

Schematic re resentation for transitions between
states in Gd “5 and Eulgs... ................. . ....... .

Half-life curve for Sm1“1m ............................
Half-life curves for the 403.9- and 438.2-keV peaks...

y-ray singles spectrum for Sm1“1m+g (quad 1) ..... .....

xii

Page

89

95

99
102
122

124

127

130

132
143

147

150
151
153
156

157

168
178
179

181

, .. ...
... .... .
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... . 3.
S - .1
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Figure
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

Page
y—ray singles spectrum for Smlu19+m (Quad 4) .......... 182
2-dimensiona1 coincidence spectra for Smlulm .......... 186
511—51l-keV gated coincidence spectrum for Smlq19+m... 190

1419”?”

Anticoincidence spectrum for Sm ... .......... 191

Delayed-gate integral coincidence spectrum for Smlu19+m 197

Delayed "Spectrum" integral coincidence spectrum ...... 198
Decay scheme for Smlulm ............................... 200
Eulul y-ray spectrum .................................. 215

2—dimensiona1 gated coincidence spectra for SmIQIQ.... 219
Tentative decay scheme for Smlhlg .................. ... 222

Shell model sedematic representation of the reaction
mechanism for the formation cf three—quasiparticle
states in Pm”1 ....................................... 231

Spectrum resulting from a Smlb'L+ target immediately
after a 1 minute bombardment with a 120 MeV c12 beam.. 237

Spectrum resulting from a Sm1“” target 4 days after
being bombarded with a 120 MeV C12 beam ............... 239
y-ray versus x—ray coincidence spectrum from a Sm1w
target compared to a self—gated singles spectrum at
the same gain............. ............... . ..... . ...... 247

Levels in Eu nuclei which are populated by B decay.... 272

Levels in odd—mass, N=82 nuclei which are populated
by B decay................. ............... ...... ...... 274

Levels in odd-mass, N=82 nuclei which are pOpulated
in stripping (T,d) reactions ..... ... .................. 275

Upper: M4 transition energies for the N=79 and N=81
isotones.

Lower: Values of the squared matrix elements for the
single—neutron isomeric transitions in the same nuclei 277

Upper: Values for the squared matrix elements for the

M4 transitions in the Z=82 isotopes.

Lower: Isomeric transition energies for the above

nuclei ................................................ 279

xiii

a: o.
7. 3
s
In 0...
v.-
e 9
2.1~
...
.ru 93.

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’e:: V
isomenc

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ogh

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'-

Figure

59.

60.

61.

Page

Upper: Isomeric transition energies for odd-mass,

N=49 isotones.

Lower: Values of the squared matrix elements for the
isomeric transitions in the above nuclei.............. 281

Upper: Isomeric transition energies for odd—mass,

Z-49 isotopes.

Lower: Values of the squared matrix elements for the
isomeric transitions in the above nuclei.............. 282

Isomeric transition energies for the Sn isotopes...... 283

xiv

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CHAPTER I

INTRODUCTION

"...In the development of atomic physics the interaction
of atoms with electromagnetic radiation has been of paramount im-
portance for the understanding of atomic structure. In the case
of nuclei the interaction has not been so important a tool, since,
unlike the atomic case, the wavelengths of interest are so short
that they cannot be measured by the usual Optical devices. The
rather indirect methods which must be employed make the energy de-
termination quite inaccurate compared with spectroscopic standards,
and the available resolution is low. Furthermore, in most cases the
radiation process is only one of many competing processes (such as
particle emission or sometimes even beta—decay) and its probability
is correspondingly lower.

For these reasons the study of gamma-rays from nuclei has
remained on a rather rudimentary level..." (Blat52).

This was written in 1952, not so very long ago in terms of
years but a very long time ago in terms of technological development.
This thesis has been possible precisely because such a statement
about y-ray spectroscOpy is no longer valid.

In the early 1960's, when solid state detectors became
available, energy resolution was dramatically improved to the point

where, for the first time, individual transitions could be resolved

4;':.;'.e1 1"”? spec
:e::::s:c;y media:
restigatic. .

The present
:zzailezess of scier.‘
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filized at the outset

£15: suc

h a manner.

Fae original
aizient odd-mass rat
Iii: decay schemes in

M De of 83981: valu

 

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135 Possibly s

33:; '4.
3.3%: : . .

in complex y-ray spectra. Needless to say, a whole new dimension
was then Opened for the study of nuclear properties. y-ray
spectroscopy immediately became an important tool for these
investigations.

The present investigation is a good example of the unpre-
dictableness of scientific research. One begins a research project
.looking for answers to predetermined questions and, as in the present
case, finds a few answers and many more unanswered questions. Also,
one is apt to end up investigating certain phenomena which were un—
realized at the outset of the study. The topics of this thesis evolved
in just such a manner.

The original intent was to study a sequence of neutron—
deficient odd-mass rare earth isotOpes in an effort to elucidate
their decay schemes in as much detail as possible. This information
'would be of great value for the testing of existing nuclear models
as well as possibly suggesting a means of, at least semi-emperically,
being able to describe in a uniform fashion the change in the var—
ious levels as one goes from permanently deformed nuclei to spher-
ical nuclei near closed shells. Gadolinium was chosen as an element
satisfying this criterion, as well as possessing neutron-deficient
isotopes in the desired spherical region which would be obtainable
with our energy limitations (pmax = 45 MeV and Her:ax 8 70 MeV).

With this intent work was completed on the decay schemes of

Gdlug, Gdlusm, and Gdlusg. However, with our discovery of an 85-

7“ ‘sszer in C.‘

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second isomer in Gdlus, we became interested in studying other
N381 isotones (six of which were already known). Preliminary
calculations, based on the known.M4 N=81 isotones, indicated that
Dy1“7m should be of a half-life that we could handle by our count-
ing techniques. Thus, a series of experiments was initiated at
Yale University in an effort to identify this species.

At about this same time, states were observed in Nd139m
(McH69j,Bee69d) which were characterized as three—quasiparticle
states. These states are quite uncommon but where found to be
very useful for determining nuclear properties of relatively high-

lying states. Out of the Ndl39m work came predictions for similar

141m Nd137m.

states in Sm and
Consequently, the nuclear Species studied during the

course of this thesis work were Gdlug, Gdlusg, Gd1”5m, Sm1”19,

Smlulm 1u7.

, and Dy

Chapter II describes the many types of experimental set-
ups used during the course of this work. The latter part of the
chapter also describes three chemical techniques, used primarily for
Gdlug, for separating the Gd fraction of the target material from
contaminants of Eu and Sm.

Since we are fortunate in having two computers at our
disposal, an SDS Sigma-7 and a DEC PDP-9, data analysis could be
accomplished both in the quantity and in the quality needed for
this work. Three of the most useful data reduction codes used in

this laboratory are described in Chapter III.

The heart

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The heart of this thesis, the experimental results, com-
prise Chapter IV. During this work, certain "discoveries" proved
to be particularly interesting. As already mentioned, this invest-
igation began with Gdlug. The fairly complete study we made of
the Eu”9 levels populated by the decay of this Species will une
doubtedly prove valuable for any future theoretical considerations
of this region. Eull+9 is in the twilight zone. In 5 4.1. we re-
port the observation of more levels than can be incorporated in a
simple shell model picture, while, at the same time, the levels are
such that they cannot be fit into rotational structures as would be
expected of a permanently deformed nucleus. There is presently no
nuclear model which can adequately account for such a situation.

As apposed to higher mass Gd isotopes, Gdlusg decays pri-
marily to two states at 1757.8 and 1880.6 keV. These states, in turn,
decay predominantly directly to the ground state of Eu1”5. We report
over 30 7 transitions accompanying the decay of Gdlusg with the above
mentioned two transitions accounting for 3632 of the total 7 intensity.

This anomaly occurs, most likely, because the 8 state drops down

1/2
to become the ground state (replacing the d3/2 state). Another in-
teresting facet of this work was the observation of an e/8+ branch
from the isomeric decay of Gdl“5. 0f the Nb81 isomers which have been
studied previously, only Sm1“3 appears to have a B-decay branch.

From such branchings one can directly arrive at occupation probabil-
ities for the state involved.

In apparent confirmation of the three-quasiparticle pre—

dictions discussed above, Sm1“1m does exhibit 6 B-allowed states lying

tests: 1414.3 Re?
1:: those in 55
:=::i:’.e states in '
531:2; :hese State
2:71;; transition-
:‘.;aL'.y to an 111,2- 1
2:12:er bypasses t
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fe;::;r:sed for this
The c'e:av o:
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ifiife of 10.0 mim-

.. dese transitions b1

“i=7 of Sci“;

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898:5
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The identifi

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““8 prOblm

 

We
5) after Out ex

. The only 6
58‘s
M on either .

between 1414.8 keV and 2702.4 keV. These states have properties sim—
ilar to those in Nd139m with one notable exception. The three-quasi—
particle states in Nd139m have a plethora of interconnecting tran—

sitions; these states in Sm1”1m

have not a single observed intercon-
necting transition. Five of these six states in Pm”1 decay prin-
cipally to an 11/2' state at 628.6 keV. The sixth state, however,
completely bypasses the 11/2- state, preferring to decay to the
ground and let excited state instead. In 5 4.4.11. a mechanism will
be proposed for this three-quasiparticle type of decay.

The decay of Sm1”19 still remains as a partly unsolved pro-
blem. There are two intense transitions, at 403.9 keV and 438.2 keV,
neither of which can be ruled out as belonging to this ground state
decay. The puzzle is that one of them, the 403.9-keV state, exhibits
a half-life of 11.3 minutes, while the other level has a measured
half-life of 10.0 minutes. We have evidence both for and against both
of these transitions being from levels in Pmlul. Other than this the
decay of Smlulg seems to be straightforward, decaying largely to the
Pm”1 ground state.

The identification of Dy1“7g and Dy1”7m still remains a
challenging problem. We began a search (primarily for the Dylu7m
species) after our experimental determination of the decay properties
of Gdlhsm. The only feasible means of producing this species is with
a C12 beam on either a Nd”2 or a Sm1”“ target. Because of the beam
requirement we repaired to Yale University where their heavy ion linear

accelerator was made available for our use. 54.5. will describe our

results to date. We have evidence from several types of experiments

:1: indicates that we
Lmeendence that t]
:1: stable half- if‘
2513- This COUId "
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Chapter V site:
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Sa

which indicates that we do produce Dy1”7. We do have seemingly con-
clusive evidence that there is no Dy1“7m.M4 transition (at least not
in our useable half-life range) with a measurable internal-conversion
intensity. This could well mean that Dylu7m de-excites predominantly
via an e/B+ branch.

Chapter V sketches the derivation of the single-particle
transition probability expressions for various multipole transitions,
beginning with the Maxwell equations. These expressions, first ex-
pressed by Weisskopf, are by far the most frequently used estimates
against which to compare experimentally measured transition half-
lives. The purpose of the chapter is not to present a mathematically
rigorous derivation but rather to give a beginner a feeling for
‘what is invloved in such a derivation.

The final chapter, Chapter V1, is primarily concerned with
the trends in families of nuclear isomers, both neutron and proton,
around the 50 and 82 closed shells. For example, the N-79 and N581
isotones show marked energy dependence on Z while the isomers of the
lead isotopes (Z-82) are quite similar in energy and consequently
show a constancy in their reduced transition probabilities. The
trends of other isomeric families will be compared to these.two
seemingly different types of behavior.

Inasmuch as possible the energy levels of nuclei in the
Gd-Eu—Sm region will be traced as functions of energy. The avail-
able information on much of this region is quite sketchy and few

conclusions can be drawn.

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CHAPTER II
EXPERIMENTAL EQUIPMENT AND PROCEDURES

All of the nuclear species studied in the present in-
vestigation decay by positron emission and/or electron capture. A
variety of techniques, discussed in this chapter, were used to
construct decay schemes based on the study of these decay char-
acteristics.

This chapter is divided into three main parts. The
first, consisting of § 2.1. through 5 2.3, describes the electronics
set-ups for the y-ray and conversion—electron data taken at Michigan
State University. The apparatus used at Yale University, in con—
junction with the Dy”7 experiments, is briefly described in 5 2.4.
§ 2.5 describes the chemical separation techniques used principally

for the isolation of the 0d”9 activity.

:t::;:a:e-y 3: yea:

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2.1. y—Ray Spectrometers

 

AS mentioned in Chapter I, the Ge(Li) y-ray detector

has been principally responsible for the resurgence of the study of
complex nuclear structures by measurements of the y-ray de-excitations.
Hand in hand with the development of these solid state detectors has
been the develOpment of vastly improved electronics. In just the ap-
proximately 3% years since the beginning of this study, we have gone
from a y-ray spectrometer system having a resolution of 25.6 keV FWHM
for the l333—keV y of C050, a detector efficiency of <<1%, and an
analyzer having 1024 channels of memory to our present System: a
detector resolution of 1.9 keV FWHM for C060, a detector efficiency
of 3.62 (relative to a 3X3-in. NaI(T1) detector 25 cm. from a Co60
source), and the capability of obtaining Spectra up to 8192 channels

in length.

2.1.1. Ge(Li) Singles Spectrometer

 

Our y-ray spectrometer is really a "system" that includes,
besides the Ge(Li) detector and bias supply, a charge sensitive FET
preamplifier, a spectrosc0py amplifer, an analog to digital converter
(ADC), and some type of memory or storage unit and associated spectrum
readout. The majority of the electronic equipment is modular so that
equipment from various manufacturers can be used together for a par-
ticular experiment.

A typical Spectroscopy charge-sensitive preamplifer in—
tegrates and Shapes the charge output from the detector and presents
a tail pulse (rise time :25 nsec, decay time :50 psec) to the main

amplifier.

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The spectroscopy amplifiers which we use have considerable versatility.
Shaped unipolar or bipolar output pulses with 0.25-us widths are avail-
able for timing purposes or for input to an ADC. These amplifiers have
highly linear amplification responses and include such features as ad—
justable pole—zero cancellation and base-line restoration.

The pole-zero feature permits precise elimination of under—
shoots on the amplifier pulse after the first differentiation. This
becomes important at high counting rates, Since if the undershoot
saturates,the amplifier will be blocked not only for the time of the
primary pulse, but also for the duration of the undershoot. Also, suc—
ceeding pulses which may fall into the undershoot will have an ap—
parent area smaller than the actual area, thus causing a loss in
resolution.

Base—line restoration also improves resolution at high
count rates by restoring the undershoot of the amplifier signals to
a DC baseline after all other shaping has been accomplished. The
improved resolution is accomplished by the reduction of pile—up dis—
tortion caused by undershoot. I

In this laboratory Spectra can be collected in a variety
of analyzers. 0f principle use for the present research has been a
Nuclear Data ND-2200 4096-channe1 analyzer, a PDP-9 computer inter-
faced to a Northern Scientific NS-625 dual 4096-channe1 ADC, and our
Sigma 7 computer interfaced to four Northern Scientific 8096—channel
ADC's. The NS-625 has a 40—MHz digitizing rate and the NS-629 has

a 50—MHz digitizing rate.

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2.1.2. Ge(Li)-NaI(Tl) Coincidence Spectrometers

 

Coincidence Spectra have played an important role in the
present research. Since the vast majority of nuclear excited states
have very Short half—lives as compared with our ability to measure
them, coincidence units with resolving times on the order of nano—
seconds can be used to study those transitions which are in fast or
"prompt" coincidence with one another. In this manner, coincidence
Spectra are a useful tool for determining the relationships of the
observed y-transitions and their interconnections with the deduced
nuclear energy levels.

Several types of Single parameter coincidence spectra have
proved to be useful. Both prompt and delayed coincidence spectra
have been used, utilizing a Ge(Li) detector for one leg of the timing
circuit. In addition, anti—coincidence spectra and Sll-Sll-keV (pair)
coincidence spectra have been obtained by use of a Ge(Li) detector in
conjunction with an 8XS-in. split annulus. Each of these will be de-

scribed in the following sections.

2.1.2.A. Coincidence Spectrometer using Ge(Li) vs 3X3-in. NaI(Tl)

 

Before the advent of Ge(Li)-Ge(Li) coincidence techniques,
which will be described in § 2.1.2.C, NaI(T1) scintillators coupled to
photomultiplier tubes provided the principle means of obtaining timing
pulses for coincidence spectra. Such a set-up is shown in Figure 1.
In addition to the equipment needed for the collection of a singles
spectrum, equipment is needed to provide timing information. As

shown in this figure, a 3X3—in. NaI(Tl) detector was used for this

purpose. The pulses from the photomultiplier were fed to a Spectrosc0py

  

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amplifer through a cathode follower, which is used simply as a buffer
for impedancemismatch between the photomultiplier and amplifier. The
NaI(Tl) signals are then presented to a timing Single channel analyzer
(TSCA). The TSCA, in turn, is used first to determine the energy gate
and then to output a logic pulse to a fast coincidence unit. In this
manner timing pulses are output only for pulses which fall in the volt-
age range selected by the TSCA.

Similarly, a timing signal must be derived from the Ge(Li)
linear signal. This is accomplished by the use of a second TSCA which
outputs a logic signal to the coincidence unit. The function of the
fast coincidence unit is to output a logic signal only when a Ge(Li)
and NaI pulse arrive within a Specified time interval of one another.
For most of our coincidence work this resolving time (2T) was set at
100 nsec.

The majority of coincidence runs utilized an external lin—
ear gate. A logic pulse from the fast coincidence unit opens the gate
for a pre—determined length of time, allowing any linear signal present
at the input during that time to pass through the open gate and on to
the ADC. In this manner, only pulses from y-ray transitions occurring
‘within the specified resolving time are allowed to pass through the
linear gate and be digitized by the ADC. The delay amplifier shown
in Figure l is solely for the purpose of delaying the linear signal
to compensate for the delay incurred by the timing signals while they
ennzproceedingthrough the coincidence circuits. The delay can be
adjusted to insure that the linear singnals and coincidence timing

signals arrive simultaneously at the gate.

Several I
stasizg the SP1“
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12

2.1.2.B. Ge(Li) vs 8XS-in. NaI(Tl) Split Annulus

 

Several types of coincidence experiments can be carried
out using the split annulus for one of the detectors. One-half of
the annulus can be used as a simple NaI(T1) detector. In addition
to the usual prompt and delayed coincidence and anti-coincidence
experiments that can be accomplished with the annulus are Compton
suppression experiments. The annulus can also be used as a pair
spectrometer for obtaining 8+ feedings and double escape spectra.

For the present research, the annulus was used primarily for anti-
coincidence experiments and as a pair spectrometer.

While coincidence Spectra show the relationship of y-rays
which are related to each other, anti-coincidence spectra enhance
those transitions which are either transitions to the ground state
from levels populated primarily by electron capture with little or
no y-ray feeding from above, or transitions from a level with a
half-life considerably longer than the resolving time of the apparatus,
i.e., transitions from isomeric levels. The electronics set-up using
the annulus in an anti-coincidence experiment is shown in Figure 2.

A 3X3-in. NaI(Tl) detector is positioned in the tap of the annular
tunnel in order to increase the solid angle subtended by the detec—
tors. The Ge(Li) detector is positioned in the bottom of the annular
tunnel, facing the 3XB-in. NaI(Tl) detector at the top. The source
is placed between these two detectors, approximately in the middle of
the tunnel. The electronics used is very similar to that used in the
coincidence experiments which have been described in § 2.1.2.A. above

The main difference is that now there are three timing signals

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14

necessary instead of just one. These timing signals must be combined
in some way so that the fast coincidence unit is presented with a
single logic pulse (no matter whether a signal is present in only one
leg or a combination of the legs). For this purpose we have used an
ORTEC universal coincidence module, shown in Figure 2 as an AND/OR
gate. The number of coincidence requirements is set to l on this
module to effect the desired single, well shaped output pulse. In
this mode, resolving time for the unit has no meaning and does not
have to be set. The only relevant resolving time consideration is
that associated with the fast coincidence module, which was commonly
set to 100 nsec for these experiments.

Another use for the annulus was as a pair spectrometer for
determining the 8+ feeding of levels. In this mode of Operation the
resulting Spectra show enhancement of those y—rays involved in prompt
coincidence with levels which are fed by 8+ emission. Of course,
double-escape peaks are also greatly enhanced in these spectra. The
apparatus shown in Figure 2 can be employed,with the exception that
the 3XB-in. NaI(T1) detector and associated electronics are not used.
Since we are now interested in a triple coincidence requirement, i.e.,
a coincidence output pulse only when a timing signal from the Ge(Li)
detector and both halves of the annulus occur within the resolving
time of the fast coincidence module, the AND/OR gate is not needed.
Signals from each half of the annulus, as well as the Ge(Li) timing
signals, are routed directly to the fast coincidence unit, which is
set for the triple-coincidence requirement. With these exceptions
and different settings of the linear gate, the experimental set—up

remains the same as for the anticoincidence experiment.

4.: .-‘Y. '—-
...;...:;. USdaII} In

Q

1
J.

 

nge 3. This '
-A.:'.'.. v.3...al to be
‘35: y” c V
.-..CICEUCE URI
~ .. €121] detectr
4:5 -
cw: effzcier‘c’
Ccincidenr
asik ““ ‘
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15

2.1.2.C. .Ge(Li)-Ge(Li) Megachannel, 2—Dimensional

 

Coincidence Spectrometer

 

With the availability of larger volume Ge(Li) detectors
came the technique of 2—dimensional coincidence experiments. The
ultimate aim of such experiments is to obtain coincidence data for
any and all peaks or regions with a single run. (In practice the data
obtained usually fall somewhat short of this goal.)

Even though Ge(Li) detectors are still quite inefficient
with respect to available NaI(Tl) detectors, they compensate for this
in other waysl Due to the Ge(Li) resolution, peak to Compton ratio,
etc., good coincidence data can be obtained with fewer counts per
channel than necessary with NaI(Tl). The electronics used in this
laboratory for the 2-dimensional coincidence experiments is diagrammed
in Figure 3. This is a double coincidence set-up where we want the
linear signal to be recorded from each of the detectors, hence the
fast coincidence unit transmits a logic pulse to two linear gates,
one for each detector. The two detectors presently used for these
runs have efficiencies of 2.5% and 3.6%.

Coincidence events are collected on magnetic tape by use of
a task called EVENT which runs under the JANUS monitor system of our
Sigma-7 computer. The data obtained under this system are a 2-dimen-
sional integral coincidence array.

Each linear gate transmits a linear signal when Opened by a
coincidence event. These two linear signals are input to separate
ADC's, operated in a synchronous mode, which are interfaced to the

computer. The encoded coincidence pair is then stored on magnetic

 

 

 

 

 

 

 

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TIMNG * e TIMING LINEAR
ANPLIFER AMPLIFIER ANPLII-‘ER
l FAST
8“ ' COINC. 50“
— +
SCALAR~—----J
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LINEAR ’
GATE

 

 

 

 

 

 

 

Ix-SIDE sIscoIANNEL 8l92 CHANNEL Y-SIDE
'l o-sv ADC ADC o-sv
F , Webs

 

 

 

 

 

 

INTERFACE TO SIGMA 7

’ CHANNEL No. CHANNEL No. ’
or EVENT or EVENT
FROM SIDE x EROHSIDE v

I

BUFFER IN SIGMA 7
mpg "JANUS“
CHANNEL No. I CHANNEL No.

 

 

 

 

 

 

 

 

 

 

 

 

ONE WORD

 

 

 

 

 

MAGNETIC TAPE

CHANEL M). CM NO.

OF EVENT OF EVENT
IIZ WORD 0/2 WORD

 

 

 

 

 

 

Figure 3. Schematic diagram of the megachannel 2-dimensional

apparatus.

 

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tape as one word, the first half of the word being the address from
detector 1 and the second half of the word being the address associ-
ated with detector 2. The lead absorber shown in the diagram between
the detectors is used to reduce y-ray scattering between the two de-
tectors. Without the absorber Spurious peaks appear in the coinci—
dence spectra. These scattering phenomena are discussed in (Gie70)
The data thus stored on the magnetic tape represent infor-
mation on all peaks in coincidence with all other peaks. All that
remains is to strip these 2-dimensional data by taking the appro—
priate slice representing a particular peak on energy region. These
gated specta are recovered off-line on the Sigma—7 computer through
use of the program EVENT RECOVERY (event). This code allows us to
search the tape for a miximum of 10 gates per single pass of the
tape. Background subtraction can be effected for any or all of the

gates on the same pass.

All coincidence runs used in the present work utilize a
4096x4096 array. The system Operates satisfactorily at counting rates

up to ”2000 coincidence events per second.

2.2. Conversion-Electron Spectrometer

 

For the conversion electron spectra of Gdlhsm we utilized
a 100-u thick Si(Li) detector. This detector was mounted in the usual
y—ray cryostat and cooled to methanol-dry ice temperature (277°C) for
Operation. A 1/4-mil Havar window was used for this detector. A ZOO-V
bias was used for Operation of the detector. A typical resolution of

25 keV on the C3137 K—conversion peak was Obtained, thus allowing

gratin of {me _.

I ..a- vr-l“.red \: “

.-t .Cu—xn "“‘

::s::;::ents recuir

I '-
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exhaust: barre.
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18

separation Of the K— and L— conversion electron peaks. In addition

to the required bias supply, an ORTEC 109A preamplifier and 451 spec-
troscopy amplifier were used in conjunction with an analyzer. To
utilize this detector for the determination of internal conversion
coefficients required the simultaneous counting Of the source with
both the conversion—electron detector and Ge(Li) y—ray detector.
Normalization between the detectors (efficiency corrections) was Ob-
tained through the counting of standards having known (and measurable)
conversion coefficients, 03137 and B1203 being the most suitable.

dlusm

Conversion electron spectra of G are shown in the experimental

section.

2.3. X-Ray Spectrometer

 

X-ray spectra also provide a powerful method of studying
nuclear decay. With the resolution presently available it is possible
to determine unambiguously which elements are present in particular
sources. Coincidence experiments using an x-ray detector will be dis-
cussed in § 2.4. The x-ray detector in use at Michigan State is a
Si(Li) detector with a 150 X gold surface barrier contact. This ORTEC
detector has a warranted resolution of 275 eV at 6.4 keV, counting
through a 5 mil Be window The detector active diameter is 6mm, with a
sensitive depth of 3mm. This detector is Operated at a bias of 1500 V
at liquid N2 temperature. An integral part of the detector is an ORTEC
model 117 preamplifier with a cooled FET first stage. The preamp is
directly attached to the cryostat to reduce capacitance.

The useful efficiency range of the x—ray detector is from

about 5 keV to <100 keV. This type of detector is also quite sensitive

n ’4
_ sane: par-4

r4299: ge and 8

‘§~5‘

ztizles cause

:sx-rai' Wises
7,355 are 1:3le
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1“
e: if“

..¥ Lot.

 

19

to charged particles such as electrons and positrons. This is both an
advantage and a disadvantage when obtaining spectra with high positron
fluxes, such as the spectra obtained in this research. These charged
particles cause detector output pulses of a much higher voltage than
the x—ray pulses under consideration. As a consequence, the positron
pulses are badly clipped by the amplifier, which cause a great deal

of ringing on the pulses, and present a complex problem for the ADC.
The ill effect of this situation shows up as a high noise background
below approximately 10 keV. This problem can be partly alleviated by
running the experiment in a self—gated coincidence mode. This allows
the single channel analyzer to stOp all pulses above the window level.
This produces a cleaner spectrum but is not completely satisfactory
since the problem is still present in the detector and can still have
the adverse effect of lowering the system resolution.

.A few attempts have been made at using various sized magnets
for deflecting the positrons before they reach the detector. Unfor-
turnately, no improvement has been realized. In addition, using a
magnet requires removing the source to a greater distance from the
detector. Due to the already extremely low efficiency of the detector,

this becomes impractical.

2.4. Special Equipment for the Dy1"7 Experiments
The Dy”7 experiments, described in Chapter 4, were carried
out at Yale University using their Heavy Ion Linear Accelerator. While
the detectors and electronics used for these experiments were standard
items, most of the equipment was not the same as used for the other ex-

periments reported in this thesis.

Fcur

I V
-~ s;:g-es , Y

"“Liience ex:
The s!
Lie: Locking- 1

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20

Four types of experiments were accomplished at Yale: elec-
tron singles, y-ray singles, x-ray singles,and y—ray versus x—ray
coincidence experiments.

The search for the predicted M4 transition in Dy“+7 in-
cluded looking for the expected conversion electrons. This was
accomplished with the electron detector described in § 2.2. A 400-
channel RIDL analyzer and an ORTEC 410 amplifier were used in con-
junction with this detector.

For the y-ray and x-ray experiments, the data were taken
with a PDP-8/I cOmputer interfaced to a dual Northern Scientific ADC.

y-ray spectra were obtained with a Princeton Gamma-Tech
Ge(Li) detector having a 2.3-keV resolution on the 1.33 MeV peak of
CO60 and an efficiency of 6.5%. The detector was coupled to a Ten-
nelec TC-137 preamplifier, ORTEC 451 amplifier, and the PDP-8/I.

The x—ray spectra were obtained with a Nuclear Equipment
Corporation x—ray detector and preamplifier. The remainder of the
system was the same as for the y-ray detector.

X—ray versus y-ray coincidence spectra were obtained using
the x—ray and y-ray detectors described above in conjunction.with a
standard fast coincidence circuit. Representative spectra collected

at Yale are shown in § 4.5.

2.5. Chemical Separations
The rare earth group of elements (Z-57 through Z-7l), in
general, pose a real challenge for separation. These elements differ

from one another mainly in the filling of inner 4f shell of electrons,

-; 221:6? eleC :1

fibers of this
52:65 and 011313
.‘1 rare earth e
:1; cerium has 4
23:3, thuliUT
states.

For the
ire: sazaritzn and
raiizactive specie
l‘ie long enough t
E: the separation

35;: _ .
9!: success full

 

21

the outer electronic configuration being very similar for all of the
members of this group. Consequently, they exhibit similar oxidation
states and oxidation potentials - hence, the separation difficulty.
All rare earth elements exhibit the characteristic +3 oxidation state.
Only cerium has a relatively stable +4 oxidation state, with samarium,
europium, thulium, and ytterbium exhibiting semi—stable +2 oxidation
states.

For the present research, we needed separations of gadolinium
from samarium and from gross amounts of eurOpium. Gdll+9 was the only
radioactive species involved in the present investigation with a half—
1ife long enough to make some sort of chemical separation feasible.
For the separation Of Gd1H9 three different techniques were tried, two
of them successfully. Two of these techniques utilized the fact that
europium and samarium have 2+ oxidation states, while gadolinium ex-
hibits only the 3+ state under the same conditions.

The first technique was that Of HCl-Zn reduction. The
second was an attempt at forming the 2+ europium species by use of
hypophosphorous acid as the reducing agent. The third was that of

ionrexchange. These are described in more detail below.

2.5.1. Zn~HCl Reduction

 

This procedure is similar to the one reported by R. N.
Keller (Kel61). Targets usually consisted Of about 100 mg of Eu215103.
.After bombardment, these samples were dissolved in 3M HCl, keeping the
volume to about 10-15 ml. This dissolution takes anywhere from a few
minutes to an hour. Heating helps to speed up the process. The dis-

solved sample was then heated to boiling in a water bath and powdered

_-._. added. aims“
:tire period to We
25:15 manner for C
At this :3
also: for pIECiP’i
aliec‘ to cool. 'u':
fies-elation. Ynez:
Listed, and reduce
71' fer counting.
I: satin ccatzzi
3 separation proce
iteration was not 0
“in and Cd to the

henna. The first

 

22

zinc added, nitrogen being bubbled through the solution during this
entire period to prevent oxidation. The mixture was allowed to react
in this manner for one hour.

At this point a few drOps of H280“ was introduced to the
solution for precipitation of SmSOn and EuSOu, and the solution was
allowed to cool. While cooling, the N2 gas was still bubbled through
the solution. When cool the mixture was centrifuged, the supernate
decanted, and reduced in volume to allow transfer to a small glass
vial for counting. This resulting solution should be free of eurOpium
and samarium contaminants. This solution could be used to run through
the separation procedure a second time if itwes.found that a complete
separation was not Obtained. We have found that one pass does separ-
ate Eu and Gd to the extent necessary to obtain a "clean" Gd y—ray
spectrum. The first separtion takes 2-3 hours, with each succeeding

cycle requiring an additional 1 1/2 hours.

2.5.2. Hypophosphorous Acid Reduction

The HCl-Zn reduction technique discussed in the last sec-
tion takes a minimum of two to three hours to perform, as does the
ionrexchange method discussed in §2.5.3. A method was sought which
would allow separation of species with shorter half-lives. Again, a
reduction technique was sought which would allow the formation of
Eu++ and Sm++ in the presence of Gd+++. The relevant oxidation
potentials are given in Table l.

Hypophosphorous acid was tried as the reducing agent. Since

H3P02 is hygroscopic as well as being unstable, it must be prepared as

needed. The method chosen for the production and purification of

P}
Lu
I

2* ..
.. HOEQEI

... \-
’ "b5 '
.

"*"I 593' York. 1

 

 

23

Table l. Oxidation Potentials*

 

Gd(s) + + Gd+3(aq) + 3e' +2.40
Eu(s) + + Eu+3(aq) + 3e” +2.41
Sm(s) + + 5m+3(aq) + 3e“ +2.41
Eu+2(aq) + + Eu+3(aq) + le’ +0.43
sm+2(aq) + + Sm+3(aq) + le' +1.55
H3P02+ H204- -> H3PO3 + 2H+ + 2e’ +0.59

 

* T. Moeller, The Chemistry of the Lanthamldes, Reinhold Publishing
Corp., New York, 1963.

333. is that of K1

.
I
m
,1 1
’13
C)

v

TETQEQQ; was pas:
5e! 55%). The I
3521:: on a water 1

z; sect tnere unti.

 

 

 

24

113P02 is that of Klement (K1e49). This method employs the reaction,
NaH2P02 + HC1—+H3P02 + NaCl.

The NaH2P02 was passed through the H+ form of a cation exchange column
(Dowex 50x4). The resulting solution of H3P02 was dehydrated by evap—
oration on a water bath and then placed in a vacuum chamber over P205
and kept there until all of the waterwas removed. The acid was then
recrystallized. This method yields a product with a purity of approx-
:MMtely 98%. It was found that the H3P02 could be kept for a long
period of time by keeping it in a closed container at dry ice tem-
perature.

We were primarily interested in separating Gd from the
eurOpium target material. That is, we attemped to reduce Eu+++ to

'H-
Eu , the appropriate reaction being
2EU + H3P02+ H202 2EU++ + H3P03 + 2H+

The addition of H2801, to this reaction mixture would precipitate
EMSOH, thus effecting the desired separation.
The half reactions for the reduction step are

2Eu"' + 2e- + —> 21m4+

and
+ _
H3P03 + 2H + 29 + + H3P02 + H20
therefore,
0 O 0
cell = Ered — Box = 0'16V'

3:: esrspzun,

It,
I

Eu

11‘ ft: 6390;,

h,

Acid

 

"‘

25

For europium,

2
0 RT 1n aEu+3
E = E +-—— -—-——— .
Eu Eu nF 2
a +2
Eu
and for H3P02,
E - E0 +51,- ln —-—3-—-au P03 '61?
Acid ‘ Acid nF a H+
aH3P03
O _
= EA id + 5;. ln a 0.0591 (pH).
C nF H3P02

Consequently, the cell reaction can be written as

 

E0 E0
Ecell = Eu %A d) + O. 0591 (pH)
aEu +3 °aH3P02
+ RT 1n -
a2 Eu+2 aH3PO3
Finally, 2
- aEu+3 ' aH3P02
Ecell = 0.16 + 0.0591 (pH) + 0.0591 1n

 

aEu+2 ' aH3PO3
As a result of this analysis, it is seen that as the pH increases,
there is a better chance for the reaction to take place, all else
being constant.

A reduction attempt was first carried out at a low pH (=1),
with a solution containing equal parts of Eu and Cd. H280“ was
added in order to precipitate any Eu++ that might be formed. How-
ever, no precipitate was visible, indicating that the reduction had
not taken place. Reductions were attempted by raising the pH in

small increments. Up to a pH of about 4, no precipitation occurred.

Vq ‘
:ETEI, a COIPL‘La
—.~-xi:'e 919C331”

:13: 1:93am to pre

A: th 5 F3
.i. jean. :urtrlé

O
t: ‘ o
J. ”“3"" “
._., ....c.. ;....'
. ‘
ion-eanaI‘J

.==.:' '
, .e.n_..que for

,:.a.;:n technique

1: mere are

~c~ OI Stevenson a“

 

'1 Cit least in
:.”_ "‘1‘? I
«a. separatic
.‘f :5“? e
.' eaklon of p‘
“‘0“. Maud;
52ng A
fCrOSS 11
T .3?er
and t
“”3 the r-
‘ ‘1'“ I
“REYES t'lfie

 

26

However, a complicating factor was that as the pH was raised above 4,
hydroxide precipitation of the rare earths began to occur. Both Cd
and Eu began to precipitate at the same pH and at that point the re—
duction process could no longer be checked.

At this point attempts of Eu reduction by this method were
terminated. Further study is needed to determine whether the hy-
droxide formation can be repressed or whether the apparent activation
energy can be reduced in a manner to allow the reaction to proceed at

a lower pH.

2.5.3. Ion-Exchange Separations

 

Ion—exchange is probably the single most powerful, and most
used, technique for the separation of the rare earth elements. Even
a casual inspection of the literature reveals literally hundreds of
separation techniques, each tailored to specific separations and con-
ditions. There are numerous review articles, one of the best being
that of Stevenson and Nervik (Stev60). The abundance of articles
proves, at least in part, that a technique must be developed for the
particular separation of interest. There is no one single method for
the separation of all rare earth mixtures. Many factors influence the
separation, including the column size, the resin particle size and
degree of cross—linkage, the flow rate through the column, the column
temperature, and the mass of the sample.

Cation-exchange techniques all involve two steps. The first
is to adsorb the rare-earth mixture onto the resin. The second step

then involves the desorbtion Of Specific elements by the appropriate

I
4v

272 :zssen n-njv...
:. o "n J ‘ ‘ ‘
..TE.‘ Eu .Or tn:
e. 1. ..-._ F... - '
L. 5.1-:53Ln (balk—'3

2:2: elements by

:v-.
..P:‘! ..' E
233‘; ..
*~~ finer? 0‘ I
' n L
- v a
A ‘Lb a
c-
:7:
W :e::
*4.

 

 

27

eluting agent. For the separation of Cd and Eu target material, we
have chosen o-hydroxyisobutyric acid as the eluant. This eluant was
first used for the separation of actinide elements by Choppin, Harvey,
and Thompson (Ch056a) and later adapted to the separation of the rare
earth elements by Choppin and Silva (Ch056b).

The column bed was composed of Dowex 50x8 (200—400 mesh), 3
cation—exhange resin. Dowe 50 is a sulfonated styrene—divinylbezene
compound. The x "n" designation indicates the degree of divinylbenzene
cross-linking. The lower the cross—linking, the more porous the struc-
ture. All else being constant, very little cross linking is desirable,
inasmudh as this produces a greater surface area per volume. However,
a resin with a small amount of cross linking, say x1, has the unfor-
tunate property of greatly changing volume as the solution acidity
changes. Thus, a compromise must be reached,and in our case we chose
a x8 resin.

Our apparatus, shown in Figure 4, is similar to that de-
scribed by Thompson, Harvey, ChOppin, and Seaborg (Thom54). The
column dimensions are 5cm x 2mm, with the column being surrounded by
a liquid jacket used to maintain a constant temperature throughout
the procedure. For our purpose, boiling trichloroethylene allowed us
to maintain the column at 87°C.

The resin bed was composed of Dowex 50x8 (200-400 mesh),
which has been described earlier. 8N HCl was used to wash the resin.
After thoroughly mixing the resin in the acid, only the resin still
suSpended after about 30 seconds was used to pack the column. This

allowed a very densely packed column having a high resin surface area.

Flare 4. Ion-excha:

se;aratio:
resin. I:

jacket su:
stant tea;
sate then
turns to I
is a water
escape of
necessary
bed to re

 

 

28

Figure 4. Ion—exchange apparatus. This was used principally for the
separation of Gd1”9. The side arm contains the ion-exchange
resin. Trichloroethylene vapor (87°C) passes through the
jacket surrounding the resin bed to keep it at this con-
stant temperature. The Trichloroethylene vapor and conden-
sate then passes out the top of the heating jacket and re-
turns to the boiling flask. At the top of the apparatus
is a water cooled condenser to insure that there is no
escape of the "heatant" to the atmOSphere. It was generally
necessary to use a pressure head at the inlet of the resin
bed to regulate the flow rate through the bed.

29

 

 

 

 

 

The eluant
aria z-hydrozn'is
r‘setc adjust the ;
:::.;ar rare-earth e
:E :f the eluent. C
1: 5:: lutetiuzr-ytt
311:: for neodjcrzi:

.
1:.

“:2: tan lower t'."

“5:8 ($1860) 51:3,

‘In 5")“

...e the GLETi

“G.

3: team 0T1 the co]

.
.5 ..
W‘:=

i=Pfactica1,

Flow rate

 

 

 

30

The eluant is prepared by first making a 0.2.M solution of
ammonium a—hydroxyisobutrate solution, to which HCl is added drOp-
wise to adjust the pH to 4.00. The time necessary to remove a par—
ticular rare-earth element from the column is highly dependent on the
pH of the eluent. ChOppin and Silva found that a pH of 4.0 was Opti—
mum for lutetium-ytterbium-thulium separations and a pH of 4.6 was
Optimum for neodymiumrpraseodymium—cerium—lanthanum separations.
Rather than lower the pH below 4.2, they found it more desirable to
increase the o—hyroxyisobutrate concentration to 0.3 M or 0.4 M. Ref-
erence (Stev60) shows the time versus pH relationship for Am, Cm, and
Cf. Since the elements are eluted in reverse order, lowering the pH
. to a value less than 4.0 can cause the lower mass elements of a series
to remain on the column for such a long time that the separation be—
comes impractical.

Flow rate has a great effect on the degree of separation,
also. An optimum flow rate was found to be 0.5 drop/min.

The target material was dissolved in 1—2 M HCl and diluted
to obtain a final solution 0.05 M'in HCl. Eluant was allowed to
flow through the column, at 87°C, until bubbles no longer formed in
the resin bed. At this point the flow of eluant was stopped and the
space above the resin bed was cleared of any remaining solution.

This space was theanashed with hot water to insure removal of all
traces of eluant. Two drops of the water was allowed to flow through
the bed. This procedure was then repeated using hot 0.05 M HCl. The

top cavity (above the bed) was then cleared of all remaining HCl.

fitirrs of the s

"—' ‘arget was the

uh h

: flew through th

is :3; cavity. 7
1.12:2 solution a:
:-.‘ :5 I b. 'h . -
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3315 Cf 0.5 drop 7-

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353:1
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fit , ‘
Sreati, Enhaqc

 

31'

TWO drops of the solution, (adjusted to 0.05 M Hcl), prepared from

the target was then introduced to the top of the resin bed and allowed
to flow through the bed. Two drOps of H20 was then used to wash down
the top cavity. This cavity was then filled with the hot a-hydroxyiso—
butrate solution and a pressure head connected. The pressure was then
adjusted, by the height of the water bulb, to obtain an eluant flow
rate of 0.5 drop/min.

Draps were collected on small aluminum planchets, two drops
each and dried. They were then counted and a graph prepared of counts'
per channel versus drop number. An elution curve is shown in Figure 5
for a separation of Cd and Eu, using the above method. The target
material (Eu%5103 + Gdlug) was dOped with Eulsz:151+ so that the Eu
peak could be identified. The separation is not complete for various
reasons, one of the most important being the necessity of having to
separate minute quantities of Gd from a gross amount of target mate-
rial. Running the Gd fraction through a second exchange procedure

would greatly enhance the separation.

m on 5 R5

COUNTS PER MINUTE (xlO'a)
A

32

 

 

IO

I...]...

l T I l I

Gd I49 + Eul52,l54

 

|

|
|l
II
‘I

7
g

 

 

‘I
H
H
H
1|
1|
'n
|

k

. SM

 

 

20 so 40 so 60

DROP NUMBER

Figure 5.

Elution curve for Gd1“9-Eu152’15“ using Dowex
SOXB resin and a-hydroxyisobutyric acid as the
eluant.

 

At Micn‘gaf
:er prsgraa to
rat; free relative
a: efficiency curves
.23.; scan a given 5
issues and relative
Ifezargies and ince:
iérticalar nuclear s;

u 1
-~...,,

3 to arrive at
In addition

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J‘veriufi‘ntal Cr

 

CHAPTER III

DATA REDUCTION

At Michigan State University we have a wealth of
computer programs to assist us with the analysis of spectra,
ranging from relatively simple programs for determining energy
and efficiency curves to quite complex programs which automat-
ically scan a given spectrum, pick out peaks, and determine their
energies and relative intensities. Once the fundamental parameters
of energies and intensities are determined for the decay of a
particular nuclear species, they must fit together in a coherent
fashion to arrive at a decay scheme.

In addition to the various coincidence and anticoincidence
techniques used to place nuclear levels and y transitions in a
decay scheme, we have programs which look systematically at sums
of 7 transitions to determine whether certain energy sums equal
other energies or energy sums. For example, a sum of two energies
could be compared in turn to each single y-ray energy. If these
agree to within a predetermined limit, the computer prints the
results. In like manner, three can be compared to one, etc.

The results of such a program cannot be used alone with any degree
of confidence, but prove to be helpful when used in conjunction
with experimental coincidence data.

One of the more tedious jobs necessary for the con-

struction of a decay scheme is that of determining the B feeding

33

 

teat; of the daug'z;
refine: transition p
calves a considera
as; schemes poss ‘5

:5 cazputer opera:

 

 

34

to each of the daughter levels, and ultimately to arrive at a
reduced transition probability, or log‘ft, to each level. This
involves a considerable amount of arithmetic, particularly with
decay schemes possessing many levels, and is easily adaptable

to a computer operation.

This chapter singles out three quite useful computer
programs, MOIRAE, SAMPO, and SCHEME and gives a brief description
of each one. Also included in § 3.3.3. is a step by step description

of the operation of our PDP-9 computer and its usefulness for FORTRAN

programming.

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'35

3.1. Gamma Ray Energy and Intensity Determinations

3.1.1. Program MOIRAE

 

MOIRAE (Moir) could be described as a computerized
"graphical" method of spectral analysis. This program, as
with all programs currently in use in this laboratory, is based
on the analysis of photopeaks only. This method of analysis is
desirable for several reasons. For example, while total response
functions are known for NaI(Tl) crystals and are quite reproducible
for all detectors of a given size, they do not reproduce well
in going from one Ge(Li) detector to another. Also, using total
response functions to strip a y-ray spectrum results in an error
accumulation that is proportional to the complexity of the spectrum
being analyzed. Using only photOpeaks for the analysis limits
any errors from one part of the spectrum from having any effect
on the analysis of other parts of the spectrum.

All analysis by means of MOIRAE is performed by instruc-
tions to the computer via interfaced sense switches arranged
below the display oscilloscope. This equipment is shown in Figure
6. The oscilloscope provides a live display of the spectrum as
well as a diaplay of the fitted background curve, channel marker,
centroid position of analyzed peak, and provision for displaying
the net spectrum that results after subtraction of all events
below the background curve. Output is provided by the line

printer and/or punched cards, all controlled by the sense switches.

 

 

 

 

 

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'.: a. O N

‘9

’9
‘o
a

"‘l h
.

... rv‘f..

...." unorr

 

 

Figure 6. Oscilloscope and sense switches used for program MOIRAE.

37

MOIRAE is used predominantly for the calculation of cen—
troids and net peak areas of y-ray spectra. No provision is cur—
rently available for y-ray energy and y—ray intensity calibrations
within the program. These conversions must be made with one of
several available auxiliary programs.

Another disadvantage of MOIRAE is its inability to strip
individual peaks in a multiplet. These must either be done by
hand or by SAMPO (to be described in the next section). Also,
MOIRAE requires the constant attention of the user, since all Opera-
tions are manually controlled by visual reference. A complete y-
ray analysis by use of MOIRAE can take 2—3 hours for complex Spectra.
Figure 7 shows photographs of a segment of the Gdlugg y-ray spectrum
in various stages of analysis. These will be referred to in the
following description.

Generally, the first order of business when using MOIRAE
is to expand the spectrum horizontally to display only a segment
that can be conveniently displayed on the scOpe. Figure 7a shows
an expanded segment of the Gd1”59 singles y-ray spectrum, includ-
ing the 808.5—keV transition (middle peak). The and peaks are the
double escape peaks from the 1757.8-keV and 1880.6—keV transitions.
The same horizontal expansion is usually kept throughout the entire
analysis, the spectrum being "walked" across the sc0pe by use of a
sense switch. The vertical display is adjusted for a good view of

the background level and is readjusted as necessary.

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39

Background can then be fit over all or any portion of
the displayed spectral segment. Channels are selected which are
to be included in a polynomial least-squares fit, lst through 10th
order being available at the discretion of the Operator. Figure
7b shows the background fit to a 5th order polynomial. The large
vertical line at the left of the diSplay is the marker used for
choosing channels to be used in the analysis. The shortest vertical
lines along the bottom of the display are markers showing those
channels used in the least-squares background determination.

The background curve can then be modified as seems appropriate
after inspection.

Once the background under a given peak is properly fitted
(in the operator's judgment), the vertical marker is used to
designate the upper and lower channels to be considered as end
points for the peak. A center of gravity calculation is then
performed over the channels which fall beetween the markers to
determine the centroid for that peak. This feature is shown in
Figure 7b. The two tallest vertical lines under the 808.5-keV
peak (middle peak) mark the beginning and ending channels used
in the centroid calculation. Notice that the centroid is also
marked on the display.

Figure 7c is a display of the same region after
subtraction of all counts falling under the background curve
shown in Figure 7b, and can be used as another means of checking

the "goodness" of fit for the background curve.

 

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40

In this manner all resolvable peaks in the Spectrum are
analyzed. The results for each peak are stored on a computer disk
and are output together at the end of the analysis. At that
point all results are output on the line printer and/or punched
cards. Figure 8 shows a sample of the line-printer output from
MOIRAE. Beginning at the top of the figure, the raw data are
presented for the spectral segment which was diSplayed on the
scope. The center portion of the figure shows the counts per
channel for the segment actually used in the background determination.

' of this curve. This gives a visual

Notice the "smoothness'
indication of any unexpected fluctuations in the background curve.
The bottom portion of Figure 8 shows the counts in the spectral
segment after subtraction of the background. Also included is

the listing of the analyzed parameters. In particular, the
"difference between raw data and background" is the net peak area
used in the determination of the y-intensity, the "centroid" is
later used for the energy determination, the "sum of raw data and
background" is the raw data count of the peak, the "square root
of above" is the square root of the raw data, and the "end points

used" are the beginning and ending channels used for the centroid
and net area determinations.

The results obtained from MOIRAE are only as good (or had)
as the user's judgment of the analysis as based on the observation
of the scope display. Net peak areas can change drastically for

peaks situated on Compton edges or other bad—background regions.

 

 

 

 

 

 

 

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Sample of line-printer output from program MOIRAE.

Figure 8.

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42

The results depend on ones judgement as to the shape of the back—
ground underlying the peak itself. Since a polynomial background fit
can be performed for any size spectral segment, questions arise as
to the "best" way to perform this fit. In particular: How large a
segment should be fit at one time and what polynomial approximation
should be used? Unfortunately, there is no single answer. There is
always the unanswerable question of the shape of the Compton back—
ground under a peak. For an ideal peak of high intensity situated
on a smooth, horizontal background, a straight—line approximation
for the background would seem appropriate. For peaks situated on
Compton edges, etc., the answer is not so clear cut and must be left
to individual judgement. However, if any rule of thumb is valid, it
could be said that when the actual Compton shape is not known, a
straight-line approximation is as suitable as any other approx—
imation. With this in mind, it seems reasonable that any size inter—
val can be fit to a single polynomial curve as long as the back—
ground is fit smoothly and appromixmates the desired background shape
under each of the peaks included in the interval. Background fitting
over a region is easily accomplished with MOIRAE since the operator
is always in visual control. The great advantage of fitting a whole
region at one time rather than just over individual peaks is the time
saved in the analysis.

It is fortunate that even in the midst of a somewhat un—
certain placement of the underlying background, the peak centroid
changes only slightly with the different background choices that

might be made.

 

One other
:izec. This is the
:resition through :1:
mwuld have to re
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43

One other very useful feature of MOIRAE should be men-
tioned. This is the ability to study easily the changes of a single
transition through many Spectra in a convenient manner. Ordinarily
one would have to read in a spectrum, adjust the vertical and hori-
zontal gains by means of the sense switches, and move through the
Spectrum to the peak of interest. MOIRAE alleviates this bottle-
neck in that any particular peak or spectral region, once displayed
on the scope, can be followed through as many as 20 spectra for such

purposes as determining transition half—lives.

3.1.2. Prggram SAMPC

This computer program was first described by Routti and
Prussin (Rou69). It utilizes the photopeak method of analysis, with '
each experimental peak being fit to a Gaussian function having ex-
ponential tails. The program used at Michigan State University is
an abbreviated version of this program. At present we have no
scope display or light pen capability with this program.

SAMPO performs several analysis tasks including:

1. Fitting of photOpeaks to an analytical function

and determining the precise centroid for each peak.

2. Fitting and subtraction of background.

3. Calculation of energy and statistical error of
the energy for each peak from an internally pre-

pared calibration curve.

 

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44

4. Calculation of net area and statistical error of
the area for each peak and converting this net
area to a relative intensity by way of an in—
ternally prepared detector efficiency cali—

bration curve.

5. Stripping of multiplets and determining the
parameters of steps 1—4 for each of the

peaks in the multiplet.

The results of SAMPO analysis are output on the line
printer, including plots of the raw data and accompanying fitted
background and peak curves. Figure 9 shows a portion of SAMPO out-
put for a Gdthg spectrum. This figure will be referred to in the
following description.

Peak centroids are determined by fitting the experimental
peak with the Gaussian—eXponential function whose parameters must
be determined from "standard" peaks. The standard peaks should be
chosen from single, well-shaped 7 peaks spaced at regular intervals
over the whole spectrum under consideration.

Shape parameters for fitting the experimental "standard"
peaks with the mathematical function are determined by minimizing

the function,

km 2
X = l (n.-f.) /n. ,
i=k—2 1 1 1

i= channel
11, = counts
1

it = approx:

A

f, = +
for i

2 here the minini

Tile-D" The . ar
1 P1

p1= C0119...

P2 = SlOpe

 

 

where

and

and where

to the pi.

45

i = channel number
ni = counts in channel i ,
k = approximate channel of peak ,

£,m = channels limiting the fitting interval ,

. , 2 2
f. = p1 + p2 (1—p4) + p3 exp [-l/2(1—p4) /P5]

2 . 2
forpA-p6_<_1_<_P4+P7,

_ ._ 2 ._ 2 2
f1 - D1 + P2 (1 pa) + p3 exp [1/2 p6 (21 2p4+p6)/p5]

2
o < -
for 1 p4 p6

U

. 2 . 2 2
f. - pl + p2 (1-p4) + p3 exp [1/2 p7 (2p4—21 + p7)/P5]
f i > + 2
or P4 P7 9

the minimization process is carried out with respect
The pi are defined as follows:

p1 = constant in the continuum approximation

p2 = slope of the continuum approximation

p3 = height of Gaussian

= centroid of a Gaussian

p5 = width of the Gaussian

p6 = distance in channels to lower Gaussian-exponential

juncture.
p7 = distance in channels to upper Gaussian-exponential

juncture.

 

 

 

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Figure 9. Sample output from the computer program SAMPO.

 

These shape
trigia: and can be 1151
.1. :ier the same 1
35;: sazizg in c0293

The rec-taint
: 1e Gaussian-expo."
2:221:26 by a linea
s:=;:a:~:' peaks.

An energy c
staid-s determine:
5.7%: for these peaks
23:71:: a Piecewise 1

‘;:Em-.;” ‘ 0 ‘5
Che hely’ Illgnle

.: castration curw

.
r,“ .

\1515.

The line
322‘; :.
”3‘48 at the to;

..-\:a :01. the fit:

9: 1% 9.
“4‘31 C011nt.c

gets at the 'D‘

51:11. .
1e fitted back

at e
.311

 

,1.
‘dta1 the

.‘n I
m I. ,
' the .P-'

311‘s
5 Used fOr t' l

C1313;E -
DI the

47

These shape parameters are part of the output from the
program and can be used in subsequent analysis of y-ray spectra
taken under the same experimental conditions, thus affording a
great saving in computer time.

The remainder of the peaks in the Spectrum are fitted
to the Gaussian-exponential function using shape parameters
determined by a linear interpolation between values obtained for
standard peaks.

An energy calibration curve is prepared from the
centroids determined for the standard peaks and the energies
given for these peaks. The usual calibration method is to
perform a piecewise linear fit between succeeding Standard points.
Alternatively, higher order polynomials can be used to prepare
the calibration curve. Figure 9 shows the results of such an
analysis. The line printer plot alone shows a wealth of information.
Beginning at the top of the figure,"YFIT" shows the counts per
channel for the fitted peak and background curves, while "YDATA"
is the actual counts per channel for the raw data. The three rows
of numbers at the bottom of the plot Show the counts per channel
for the fitted background curve, the channel deviation between
the raw data, the total calculated counts for each channel,
and the channel numbers for each channel in the plot. The
symbols used for the plot itself are given vertically on the right

hand side of the plot. Further to the right are the results

 

recalvsis tor t~

spear is determine
32:23 for a given 1
:::2: fraction for t‘:
iiL-‘ifi'id counts uni.

’1‘-

_:a..as which are 0:

i-...‘,..:

1...-.. and not are.‘
125522: peak areas 1
:zersities by means

5:: intensity data 5

. :3 1::ezsity data

I-‘..
h ' A.
"Q :AE

as are output

The statis:

553E“: ‘
- “5‘ as a percer

....erence be tween ti

 

 

48

of the analysis for the plotted segment. The background under
each peak is determined by fitting it to a polynomial curve. The
net area for a given peak is then determined as the area of the
fitted function for the peak minus the area of the fitted
background counts under the peak. Therefore, with SAMPO the

net areas which are output are areas determined by the fitted
functions and not areas determined directly from the raw data.
These net peak areas can be transformed into relative transition
intensities by means of a detector calibration curve prepared
from intensity data supplied for the designated standard peaks.
If no intensity data are input, only net peak areas and relative
peak areas are output by the program.

The statistical error in an area determination is
expressed as a percentage error. Such an error reflects the
difference between the fitted analytical function and the raw
experimental points for a given peak; therefore, such an error
value partially reflects how well the peak shape matches the
shapes of the bracketing standard peak shapes.

At this point a comment is in order on the use of
higher order curves used for energy calibration. While such a
curve may seem to fit the selected data points with a smaller
standard deviation, when there is a significant nonlinearity in
the system, oscillations can occur in the fitted curve which
may cause significant errors in the peak energies determined
between the fitting points. Consequently, in a system of

unknown or marginal linearity the piecewise linear fit can be

222::er approximati'
:sceiure chosen for

Another p0
stic' energies he s.
1:: créer when the
:fstaziard centroids
:tiizg on the degree
ital? be off by 56
All of the

:50".-
..fi J} No E‘J‘

\.\.{J S ’ -

‘33:“ 15 u88d for -‘

"‘“°‘¢5~ SA‘fPO is

$.39”
”‘ucally searcn
E
tide:

 

 

“£17515 I
The manna
ESE 3 v
I
Jfifi
‘ its for we]
".5! i.
" 1Q! ..
Jqll re
‘r
a. 1
.::t

 

 

49

a better approximation for the calibration curve. This is the
procedure chosen for SAMPO.

Another point to be made is that under no circumstances
should energies be sought from a calibration curve of higher than
first order when the centroid to be converted is outside the range
of standard centroids used in the preparation of the curve. De—
pending on the degree of curvature, energy values so obtained can
actually be off by several keV.

All of the above described tasks can be performed by
SAMPO in two modes, automatic or manual. Generally, a combination
of both is used for the complete analysis of a y-ray spectrum.
First, peaks are picked which are to be used for energy and shape
standards. SAMPO is then allowed to determine and shape parameters
and energy calibration curve from this information. Next, SAMPO
automatically searches the spectrum for all suspected peaks. Each
candidate is screened for statistical significance as well as for
possessing the proper shape before receiving SAMPO's seal of approval.
Each.peak passing the required tests is then fully analyzed as al-
ready described. In complex spectra there are always weak peaks
which fall below the minimum statistical limit set for automatic
analysis. The manual mode of Operation is then used for the analysis
of these peaks. In the manual mode, analysis is performed only on
those peaks for which approximate centroids are input on FITS cards.
Thus, it usually requires two passes of SAMPO through the computer

to effect a complete analysis of a y-ray spectrum, the second pass

w; recuired for {3

s.-

.';-: :ct recognized

223317515 results.
:4: i: sumary for:
:27 the results 1

mar.
One of the

fire-salve, or strip.

cards, severe
«.::. the centroids

each card along s

‘1’ «f.
- wahm’ that ana

“‘5 reaard sacs-a

energies and it‘

v- .'

51a:

‘r
\_:

one Pass t
:Iteu anas
iyses are

‘.-
_ v
V“‘

‘e

50

being required for the manual analysis of the weak peaks and multi-
plets not recognized in the automatic analysis mode on the first pass.
The analysis results, like the sample shown in Figure 9, are given
again in summary form at the end of the lineprinter output. In this
summary the results for all peaks are given in ascending centroid
order.

One of the more powerful features of SAMPO is its ability
to resolve, or strip, peaks belonging to multiplets. Using SAMPO in
its manual mode is the most satisfactory procedure for this purpose.
The approximate centroids for each peak in the multiplet are input
on FITS cards, several cards generally being input at one time on
which the centroids are varied slightly. SAMPO outputs the results
for each card along with the chi-square calculation for each one.
Most often, that analysis is chosen which has the lowest chi-square.

In this regard SAMPO has proven itself able to determine accurately

both energies and intensities for each peak in the multiplet. When

more than one pass through the computer must be made for an analysis,
or when analyses are to be performed on several y-ray Spectra taken
under the same experimental conditions, the originally determined
shape parameters can be input at the start of the program rather than
requiring SAMPO to recalculate them. This results in less computer
time being used for the analyses. A general rule of thumb is that
the Sigma-7 computer can analyze a complex Spectrum (say 50 peaks)

in a period of about 15 minutes. This compares to the 2—3 hours

necessary, under favorable conditions, for the same analysis by use

of MOIRAE.

51

On a few occasions MOIRAE and SAMPO have been used for the
analysis of the same spectrum. For the intense peaks the centroids
agree to less than 0.1 channel, with an overall average of about 0.2
channel for all peaks in the analysis. As might be expected, the peak
area determinations show a greater variation between the two methods
of analysis. The variation is particularly pronounced on badly
shaped, weak peaks. The better method for these "bad" cases must be
determined on an individual basis. Area determinations for the ma—

jority of peaks, however, show agreement to usually better than £102.

3.2. PDP—9 Machine Operation for FORTRAN Programming

 

 

Being able to use the PUP—S computer for running computer
programs, as well as for Spectra acquisition, is a great benefit.
This is particularly true when, for one reason or another, the Sigma—7
is not available. The use of DECtape greatly Simplifies the operation
of the PDP—9 for this programming. To facilitate the use of the POP—9
by future personnel in the laboratory, the following descriptions are

offered.

Keyboard Monitor System

 

This is the monitor system furnished by DEC for use with the
DECtape Option. This allows all of the FORTRAN math library, editor,
FORTRAN compiler, Macro assembler and loader, as well as the Monitor
to be stored on a single DECtape. In addition, several other utility
programs are stored on this same tape.

It is most useful to create and modify FORTRAN programs by

use of the editor supplied by DEC. The description of this program

 

<tndin the [tilj

375:2: {TEX}. The e.

;::'2 cute punched pa;
:tarmder the cont}

:;s abinary CDC!
terxrational may
.1 gum and calle

Several use
lite next section,

. , .
n l e n
‘. “.3

A 3e(men: 1.

L333 15 the follOVi

H

Mona
the
loca
MOur

the

 

10C;
3. MI
I

4, Pia

 

 

52

is found in the Utility Programs Manual for the Advanced Software
System (UPM). The editor outputs the created FORTRAN program in ASCII
code onto punched paper tape. This tape is then read into the com-
puter under the control of the FORTRAN compiler program, which in turn
outputs a binary coded paper tape in machine language to be used as
the operational program. These binary object programs can be stored
<x1 DECtape and called through the Keyboard Monitor.

Several user programs, including SCHEME which is described
in the next section, are available and are further described in (Ann69).
All input and output communication with these programs is via the tel-
etype.

A sequential guide for loading and using these FORTRAN pro-

grams is the following:

1. Mount SYSTEM TAPE on one of the transports. Set
the tranSport address to 8. Set the remote-off—
local switch to remote.

2. Mount the user tape on the other transport. Set
the transport address to 2. Set the remote-off—
local Switch to remote.

3. Turn on the TTY.

4. Place the Advanced Monitor Bootstrap paper tape
in the reader. Set the address switches to 17637.

Press I/O Reset on the computer, then press Readin.

At this point the Bootstrap will be read, which in turn initiates the

loading of the keyboard Monitor System into core. When the system is

53

ready, "Monitor V43" will be typed on the TTY.

5. Type in load, then hit the carriage return. This
will cause the Linking Loader to be brought into
core. When accomplished, "Loader V3A" will be
typed out.

6. Type the name of the program, followed by the
name(s) of any user subroutines which the main
program calls for. Each name is to be separated
by a comma. Press Alternate Mode (225 the

carriage return).

The user program and subroutines will be loaded first, followed by all
subroutines, functions, etc., from the system tape which are neceSsary
for the operation of the user program. AS each is loaded, the name
and loading address will be output on the TTY. Any loading error en-
countered is noted by number of the TTY and can be looked up in one of
the manuals (e.g. UPM). When the program is successfully loaded, a

"control S" (+8) is output on the TTY.

7. To initiate program operation, +8 is typed on

the TTY.

At this point control is turned over to the program. Pro-
gram input parameters and formats are obtained from the appropriate
program listing.

A program can be reinitialized at any time by simply typing
+8. Also, control can be returned to the Monitor at any time by typ-

ing +C.

54

3.3. Determination of the Decay Scheme

 

Parameters with Program Scheme

 

Program SCHEME is one of the available FORTRAN programs for
use with the PDP-9 computer. This program relieves the user of some
of the drudgery encountered on the way to obtaining log ft values for
B decay. Utilizing the level energies and 8 feeding for the daughter
States as the input information, it calculates EC(K)/EC(tot), EC(K)/
8+, and EC(tot)/B+ decay to each level. The resulting electron— cap—
ture percentages are then used in the log ft calculations. To use

this program one should have an understanding of the steps necessary

for arriving at the log fr values.

3.3.1. Steps Necessary in the Determination of ngufr values

for B Decay.

 

The following is a summary of the steps necessary for log
ft determinations. These steps will vary to a degree depending on

the nucleus under discussion.

1. Obtain total transition intensities for all
electromagnetic transitions involved in the
decay schema. This must include corrections
to the y-ray intensities for the internal-
conversion process.

2. Total 8 decay to each daughter level is determined
by subtracting the electromagnetic intensity to
a level from the total intensity out of a level.

8 decay to the ground state presents a special

 

 

 

5, From
for

6. Pro
inte
7, Cal:

on

The log ;

.311 log -‘- 1
night side «I
3167) or ($5732

'. he above

\ .sareric leve

{1:3‘.
sgnetic an

. ‘fu '
\sQ‘.eq.

55

problem and can be arrived at by a variety of
means, including determination by use of the
annihilation peak, x—ray peaks, or through

the positron intensity to the ground state

as determined from a positron spectrum.

Obtain EC(K)/EC(tot) for each level, where EC(K)=
K—electron capture intensity and EC(tot) = total
electron capture intensity.

Obtain EC/B+ for each level, where 8+ = positron

intensity.

The parameters of steps 3 and 4 are obtained from graphs in the

Table of Isotopes (T167).

5.

From steps 3 and 4 the ratio EC(tot)/8+ is obtained
for each level.

From steps 2 and 5 the total electron capture
intensity to each level is obtained.

Calculate the log ft value for each level, based

on the EC(total) decay to each level.

The log fr values are usually determined through the

equation log ft = log fat + log C + Alog ft. .All three terms

on the right side of the equation can be read from graphs given

in (T167) or (NST59).

The above steps assume decay from a Single parent level.

If an isomeric level is present in the parent, which can decay by

electromagnetic and 8 transitions, the procedure becomes more

Complicated.

56

3.3.2. A Short Look at the Loggft Equation

 

Retreating one step, to a paper by Moszkowski (Mosle),
we can take a look at the origin of the parameters involved in
' +
the above equation for arriving at log ft values. For B decay,

f; is given by

fb ‘ W(W2-l) (w -W)2dW +
1 0

[wg/30)-3/20)w§-(2/15)][wg-1)] + (2.302/4)wb log[W§-l) ],

where W0 is the transition energy in units of mcz. This rather

complex expression reduces to f6 = (W0 + EK)2, in units of mcz,

for electron-capture. In this equation E is the k-binding energy

k
for the parent species. From this expression, log fbt is easily
obtained. Note that t, the half-life, is the total half-life
for the parent species. Log C is a factor arising as a Coulomb
correction term. For EC decay this is a constant for a given
Z and is most easily obtained from available graphs. A log ft is
a correction term for a branch that consists of less than 100% of
the total decay. It is simply A log ft = - log (p/lOO), where
p is the percent electron—capture decay to the particular level.
Note that to obtain this percentage, the electron—capture intensity
to the level is normalized to the total intensity (both EC and 8+)
to all levels, including the ground state.

To go through the procedure described in $3.3.1. once

would be bad enough, but if it should happen that some number

has to be changed along the way, say a change in a y—ray intensity,

57

the whole procedure must be repeated since all parameters are related,
and a change in one means a change in all of them. At this point one
appreciates the convenience of letting the computer do all this busy

work.

3.3.3. Description of Program SCHEME

The following is the computer listing of the program
SCHEME and the required subroutine BRATE. The program requires the
input of the 52531 B intensity to each daughter level, including the
ground state. The program assumes B decay from a single parent level.
The following program listing for SCHEME contains comment statements
as an aid in the use of the program. The parameters A, B, and C are
the coefficients resulting from a least squares fit of EC(K)/B+ values,
over the appropriate energy range, from the graph in (TI67). This

could not be incorporated into SCHEME because of memory limitations.

OOOOOOOOOOOOOOOOOO

GOO

000

3P

106

220

200

210

390

PROGRAM SCHEME

THIS PROGRAM IS FOR THE DETERMINATION OF EC/B+ RATIOS:

TOTAL EC INTENSITIES TO EACH LEVEL: PERCENT DECAY TO EACH

LEVEL AND THE LOG FT'S TO EACH LEVEL.

EC = ELECTRON CAPTURE ENERGY TO THE GROUND STATE.

AK! 3 TO BE READ FROM THE GRAPHS<TABLE OF ISOTOPESaP.S76)

BK = K BINDING ENERGY

BLI = Ll BINDING ENERGY

S = L2 TO Ll RATIO

V = TOTAL(M+N+...) TO TOTAL L RATIO

EN(I) = LEVEL ENERGIESCINCLUDING 0.0)

ANTN(I) = TOTAL INTENSITY TO LEVELS(EC + 8+).

CIN(I) = K-CAPTHRE INTENSITIES TO LEVELS

A:BaC = COEFFICIENTS FROM LEAST SOUARED FIT OF EC(K)/B+
DATA FROM GRAPH IN THE TABLE OF ISOTOPESo

Z = LOG(C) FROM GRAPH FOR EC IN THE TABLE OF ISOTOPES-

HF = TOTAL HALF-LIFE IN SECONDS-

DIMENSION OE(5@)3RC5O):CAP(5@):ANTN(43)
DIMENSION CINIAO):FN(AO):DELT(AO)
COMMON/CI/EN(40):RESULT(40)
WRITE<IJIOO)

FORMAT(27H PROGRAM SCHEME: ENTER DATA/I)
READ(2:220)N

FORMAT‘IQ)

READIZJZOO)EC:AKI:BK:BLI:SIV
FORMATCEIS-S)

WRITECIaldO)

READIZ:2|O)(EN(I):I=19N)

FORMATCFIO-Z)

WRITE(I:I40)

REAO(ZJZIO)(ANTN(I)JI=I3N)

WRITEII:IAO)

REAOIZaZOO)AaB:CoHF:Z

FOR OBTAINING EC DECAY ENERGIES FOR EACH LEVEL.

DO 300 I=IaN

DE(I) 3 EC'ENCI)

CONTINUE

R = LI TO K RATIO FOR ALLOWED AND IST. FORBIDDEN TRANS.

DO BIO I=IJN

ANUM = (DECI)-BL1)**200
ADEN = (DE(I)-BK)**2.0
R(I) = AK1*(ANUM/ADEN)

310 CONTINUE

CO

GOO

000

59

CALCULATION OF PERCENT DECAY BY K-CAPTURE

SUM = I000*S
DO 320 I=IsN
CAPII) = Io0/(Io00*R(I)*SUM*(IO00+V))
320 CONTINUE
WRITEIIJIIO)
IIO FORMATIIHO/Il)
CALL BRATEINJAJB:C:EC)
WRITEII9I20)
I20 FORMATI8X37H ENERGYJBX18HECLI/ECKl6XJI3HEC(K)/EC(TOT))8XJ
I8HEC(K)/B*/)
DO 330 I3I3N
WRITE‘IJI30)EN(I):R(I):CAP(I):RESULT(I)
I30 FORMAT(5X:FIO.2:(3(5X:E12o6)))
330 CONTINUE
WRITE(I:I40)
I40 FORMAT(IHO)

SECTION FOR DETERMINING EC(TOT)/B+ RATIOS

DO 50 I=IDN
S0 RESULT(I) = (RESULTII)/CAP(I))

FOR DETERMINING TOTAL EC TO EACH LEVEL.

DO SI I=ION
IF(ANTN(I)¢GT.0.0) GO TO 49
CIN(I) = 000
GO TO SI
49 CINCI) 8 (RESULT(I)*ANTN(I))/(Io00*RESULT(I))
SI CONTINUE
ADD 3 0000
DO 52 I=ION
ADD 3 ADD’ANTN(I)
52 CONTINUE
DO 53 I=I9N
ANTN(I) = (ANTNII)/ADD)*I00-0
CIN(I) = (CINCI)/ADD)*I00.0
53 ANTN(I).= (ANTNCI)’CIN(I))

5. l4

...!

0000

60

SECTION FOR THE CALCULATION OF LOG FT VALUES

DO 800 I=I:N
F0 8 ((DE(I)+BK)/SII.O)**2.0
FN(I) = ALOGIO<FO*HF)
IF(CIN(I).EQ.0.00) DELT(I) = 20.00
IF(CIN(I).E0.0.00) GO TO 800
DELT(I) 8 -ALOGIO(CIN(I)/IOOoOO)
800 CONTINUE
WRITE(Io365)
365 FORMAT(SXo7H ENERGY:SX:9HZEC DECAY:SX:9HZB+ DECAY:2X:6HLOG FTI)
DO 810 I=IaN
VALU = FNCI)+Z+DELT(I)
WRITE<I:370)EN(I):CIN(I)aANTN(I):VALU
370 FORMAT<2XaFI0.2:(2(2X:E12oS))a2X:F602)
8I0 CONTINUE
WRITE(I:140)
WRITE<IaISO)
I50 FORMAT(I9H END OF CALCULATION)

MM USED FOR HALTING THE PROGRAM
PRESS CARRIAGE RETURN TO REINITIALIZE THE PROGRAM.

READC2s230)MM
230 FORMAT¢II)

GO TO I

STOP

END

flu l.li Isle RIU ‘11- C All A...‘ Ali

61

The following subroutine, necessary for the determination

of the EC(K)/B+ ratios, must be used with program SCHEME. These

ratios are determined from a quadratic equation whose coefficients

must be determined separately (due to memory limitations) from

data given in (T167).

000000000

235

IS

SUBROUTINE BRATE

TO BE USED WITH PROGRAM SCHEME.

FOR THE DETERMINATION OF EC(K1/B+ RATIOS BASES ON THE

GRAPH IN THE TABLE OF ISOTOPES (P.S7S).

AoBaC 3 COEFFICIENTS FROM LEAST SOUARED RESULTS (LOG VALUES).
EC = ELECTRON CAPTURE DECAY ENERGY TO THE GROUND STATE.

N 3 NUMBER OF ENERGY LEVELS TO BE CONSIDERED.

EN = LEVEL ENERGIES.

SUBROUTINE BRATE (NsAsBaCJEC J
COMMON/CIIEN(40)aRESULT(40)

CONST 3 EC'I022-0

WRITE(2:235)CONST

FORMAT(2X:25H TOTAL 3* DECAY ENERGY = :F8o2/l)
DO I0 ItIaN

ANUM 3 CONST'ENCI)

IFCANUMoGToDoD) GO TO 2

WRITE(2:230)I

FORMAT(IX:7H LEVEL :I2033H IS GREATER THAN THE DECAY ENERGY/I
RESULTCI) 3 100E20

GO TO 10

RESULTCI) = ALOGIO(ANUM)

CONTINUE

DO I5 I=IsN

ANSW = A*B*(RESULT(I))+C*(RESULT(I)*RESULT(I))
RESULTCI) 3 I000**ANSW

CONTINUE

RETURN

END

..1

P: l
l- no.

 
 
 
 
 
 

Chapter IV
EXPERIMENTAL RESULTS
4.1. The Electron-Capture Decay of Gd1ng
4.1.1. Introduction
Neutron-deficient Gd isotopes lie in a region of Special
interest for the testing of nuclear models. They and their Eu
daughters range from nuclei that have large quadrupole moments,
suggesting permanently deformed nuclei, through closed-shell
nuclei that can be described by an extreme single—particle shell
model. The heavier isotopes (N390) are permanently deformed and
exhibit well-developed rotational bands and other features that
have been described successfully by the Bohr-Mottelson unified
model. Spherical nuclei appear as one approaches the closed neutron
shell at N582. It would be of considerable interest to be able
to correlate the nuclear levels, especially in the odd-mass
nuclei where single-particle states are most easily observed,
as one moves from the Spheriodal region into the spherical region,
and we have embarked on a program to do this, primarily through
the study of the radioactive decay of neutron-deficient GD isotopes.
As Gdlsz, Gd15“through Gd158, and Gd16° are Stable (Gd152 is
slightly a active), Cd153 is the isotope nearest stability which
permits the study of Eu states. And, because the decay schemes
of Gd153 and Gdls1 (refs. Alex 64 and Shir 63) are fairly well
characterized, the logical place to begin the experimental

investigation was with Gdlug.

62

i»

 
 

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63

9.4-d Gd1ng was first discovered by Hoff, Rasmussen,
and Thompson (Hoff 51) in 1951, who produced the isotope by

the reactions, Eu151(p,3n)Gd1“9 and Smlk7

(a,2n)Gd1“9. Since

that beginning, several papers have been published on its partial
decay scheme. Because of the complexity of the y-ray Spectrum,
however, the earlier investigations (Hoff 51, Shir 57, Pras 62)
that used NaI(Tl) detectors did not observe a number of the
weaker and/or more closely Spaced lines because of the inherently
poor resolution of these detectors.

However, even in more recent investigations, in which
Ge(Li) detectors (Jak 66, Adam 68) and conversion-electron
detectors (Ante 58, Adam 58, Dah 59, Harm 66) were employed,
discrepancies remain as to many of the Eu”9 energy levels and
also even with respect to which transitions properly follow Gd”9
decay. In particular, there has been disagreement in the placement
of transitions appearing at 993, 1013, and 1082 keV in the y-ray
spectrum. we undertook the present investigation to try to
eliminate some of these uncertainties.

Gd”9 decays almost exclusively by electron capture,
although a small a branch of 4.6:1.5><1O-6 and an energy of
3.01:0.02‘Mev has been reported (Siiv 65). We have been able to
put an upper limit of 10-3(B+/K) on the positron branch (cf.§ 1.4).
This means that the electromagnetic transitions become the exclusive
tool for its study. Very good conversion electron data already
existed, so we made use of these and have concentrated on the photon

spectra and coincidence and anticoincidence experiments.

64

4.1.2. Source Preparation

 

Gd1“9was prepared by the reaction, Eu151Q9,3n)Gd1”9.
Both natural europium oxide (47.82% Eu151, 52.18% Eu153) and
separated isotope (96.83% Eu151, 3.17% Eu153) obtained from
Isotopes Division, Oak Ridge National Lab., were used in the
proton bombardments. The proton beam was furnished by the MSU
Sector-Focused Cyclotron, using a beam energy of 28 MeV with
a typical current of 2 uA. Typically, 100 mg targets were bombarded
for periods of 1-2 h.

For the first few hours after the bombardments, several
Short-lived peaks were evident in the Spectra. However, after
these disappeared, essentially pure Gd”9 remained. This happy
circumstance results because other (p,xn) reactions that should be
possible have product nuclei of long half-lives. Activity
resulting from the decay of the daughter, EuM9 (t = 106 d), did
not Show up for several days. However, some spectra (particularly
for the anti-coincidence runs and for the study of the 993—,

1013—, and 1082-keV peaks) were obtained after chemical separation
of Gd from the target material. Two different methods of chemical
separation were employed.

The first method was the utilization of Zn-HCl reduction,
described in §II.5.1. Owing to a semi-stable Eu++ state, Eu can
be separated from the reduction mixture by precipitation with H280”.
This technique, carried out two successive times on the target

material, yields quite pure (as to the radioactive components) Gdlug.

Far y-ray analys:
scarce must be e:
:he Zn” must be
sf the Zn++ with

The sec
described in g2.
resin (200-400 :r.
iimter- A tri
Elm t(”—l'G-wratu
agent Was 0. 4 M

‘0 approximatel.

 

 

65

For y-ray analysis, this was the only step necessary. When the
source must be essentially "mass free", as for an electron source,
the Zn++ must be removed. This can be accomplished by extraction
of the za++ with methyl-isobutyl ketone (hexane).

The second method of separation used was cation-exchange,
described in 52.5.3. The resin beds were composed of Dowex 50X8
resin (200—400 mesh) and were 4-5 cm in length and 2 mm in
diameter. A trichloroethylene bath was used to maintain the
column temperature at 87°C during the separation. The eluting
agent was 0.4.M a-hydroxy-isobutyric acid with the pH adjusted

to approximately 3.8-4.0 by the addition of NH3 solution.

vl

Al.

.
d

cl.

66

4.1.3. Gd”9 Spectra

4.1.3.A. Singles Spectra

 

Two Ge(Li) detectors, both of which were manufactured
in this laboratory, were used for all spectra. One was a 7-cm3
S-Sided coaxial detector, the other a 3-cm3 planar detector.
Both were mounted in dip-stick cryostats having aluminum housings
0.16-cm thick. The detectors were used with low-noise room-
temperature FET preamplifiers, RC linear amplifiers having pole-zero
compensation, and 1024— and 4096-channel analyzers.

The Gd“+9 sources were usually counted after having aged
several days, but spectra were obtained at times varying from
immediately after bombardment to several weeks after bombardment.
This technique, together with the chemical separations, enabled
us to identify impurity y rays.

The y-ray energies were determined by comparison with
the standards listed in Table 2. The larger peaks were first
determined by counting the Gd1H9 sources Simultaneously with
these standards. The weaker peaks, which would be obscured by
the standards, were later determined by using the then well-

determined stronger Gd1H9

peaks as internal standards. The centroids
of the standard peaks were determined by using a computer program
(Meir), described in §III.l.l. that first subtracts the background
by performing a cubic least-squares fit to several channels on

each side of the peak. The channels included in the peak are fit

to a quadratic curve to determine the centIOid. and the centroids

of the peaks are fit to a least-Squares nth degree curve, which

 

__._ .43-.

(’3

67

Table 2. y-ray Energy Standards used for Gdlug.

 

 

Nuclide y-Ray energies Reference
(keV)

Am2“1 50.54520.031 a
c.1“1 145.43 20.02 b
om2“3 209.85 20.06 c
228.28 20.08 c
277.64 20.02 c
c.137 661.59520.076 d
Mus“ 834.85 20.10 e
C060 1173.22620.040 f
1332.48320.046 f
c656 846.4 20.5 8
1038.9 21.0 8
1238.2 20.5 g
1771.2 11.0 g
02598.5 20.5 g

 

8J. L. WOlfson, Can. J. Phys. 43, 1387 (1964).

bJ. s. Geiger, R. L. Graham, I. Bergstrbm, and F. Brown, Nucl. Phys.
§§, 352 (1965). '

cR. E. Eppley, unpublished results (1969).

dD. H. White and D. J. Groves, Nucl. Phys. 521, 453 (1967).

ew. w. Black and R. L. Heath, Nucl. Phys. 529, 650 (1967).

fG.‘Murray, R. L. Graham, and J. S. Geiger, Nucl. Phys. 63, 353 (1965).

3%.9L.)Auble, wm. C. McHarris, and W. H. Kelly, Nucl. Phys. A91, 225
1 67 .

68

becomes the calibration curve. This calibration curve, in turn,
is used to determine the energies of the unknown peaks by a
similar process.

The relative peak intensities were determined from the
peak areas with the use of relative photopeak efficiency curves
for both Ge(Li) detectors. The curves were obtained by the use
of a set of standard y-ray sources whose relative intensities
have been carefully measured repeatedly with a NaI(Tl) detector.

We have identified 25 Y rays as resulting from the c decay
of Gd1”9. Singles Spectra are shown in Figure 10 (separated
Eu151 target) and Figure 11 (natural Eu target). A list of
the y-ray energies and intensities is given in Table 3. These
energies and intensities are average values from many runs in
which various counting geometries, both detectors, and different
combinations of associated electronics were used. The listed
errors are the overall experimental errors determined as 1/2
of the range of the values obtained for all the runs included for
each average value.

The K x-ray intensity was obtained by a direct comparison
with Celul, of which 70% decays to the 145.4-keV state of Prlkl.
The Gd”9 x-ray spectrum is shown in Figure 12 along with x-ray
spectrum of Ce139’lul. The gain of these Spectra is such that
the 149.6-keV y-ray for Cd”9 is included as are the 145.4-keV

and 165.8-keV transitions for Celul and Ce139, respectively.

69

 

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CHANNEL NUMBER

Gd”9 singles y-ray Spectrum from a Eu151 separated isotOpe target.

Figure 10.

7O

 

de- SINGLES

 

91”?

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SEM- .

 

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250

NUMBER

Gd“+9 singles y-ray spectrum from a natural Eu target.

CHANNEL

Figure 11.

71

 

 

Table 3. Energies and relative intensities of y rays
from the decay of Gd1“9.
This work Jaklevic, Funk, Adam, Toth,
and Mihelicha and Meyer
Energy Intensity Energy Intensity Energy IntensityC
(keV) (keV) (keV)
[(x-rays 468 :100 K x-rays 487 :35 - -
149.6:0.2 233.4 :10 150.0:0.5 197 :20 149.8 258.9 9.20.0
- - - - 184.8 0.23 3 0.12
H4Jfi0.6 0.81: 0.10 216.0:0.5 1.6: 0 8 216 0.91 : 0.40
- — — - 230.4 0.65 : 0.31
- - - — 235.1 0.14 : 0.07
252.3t0.7 1.08: 0.25 - - 252.5 0.54 : 0.15
2MLS:0.3 5.80: 0.4 262.0:0.5 7.0: 0.7 260.9 4.70 : 0.80
- _ - - 264.6
- — — — 267.8 0.061: 0.015
- — - - 268.6
N2Jh0.2 14.6 : 0.6 272.0:0.5 16.1:2 272.6 11.6 : 1.0
2%L5:0.2 126.7 : 10 298.5:0.5 106 :10 298.7 114.8 : 4.9
346.5:0.3 5100 347.0:0.5 100 :10 346.8 100.0 : 4.9
405.5107 ‘ 3.7 2 1.5 - - 404.0 0.70 2 0.30
430 21d 0.332 0.05 - - - —
459.9:0.3 2.4 : 0.2 461 :1 2.3: 0.3 460.3 1.81 : 0.30
478.7:0.3 0.95: 0.10 480 :1 0.4: 0.1 478.3 1.80 : 0.51
496.4:0.3 7.2 : 0.4 497.0:0.5 7.2: 0.7 496.6 6.61 : 1.00
516.4:0.3 11.1 : 1.5 517.0:0.5 10.7: 1 516.8 10.30 : 1.00
534.2:0.3 13.2 : 0.6 534.0:0.5 12.5: 1.3 534.4 13.50 : 1.00
645.2:0.3 5.9 : 0.5 646.5:0.5 7.0: 0.7 645.2 6.20 : 0.59
6EL3:0.7 1.1 : 0.2 - - 663.4 4.51 1 0.49
666.2:0.7 3.9 : 0.6 666.5:0.5 6.0: 0 6 666.6
748.2103 34.6 : 4.0 749.5:0.5 37.0: 749.1 34.1 1
788.6103 29.6 : 3.0 790.5:0.5 34.8: 789.3 31.2 :

 

 

72

Table 3 continued

 

 

 

 

812.420.5 0.552 0.13 813 21 0.721 813.0 0.642: 0.149
863 21 2 0.322 0.10 865 21 0.320.05 '- -
875.8:0.4 0.902 0.11 878 21 0.720.1 876.2 0.980: 0.201
933.320.5 2.22 0.5 934 21 2.8:0.3 934 2.4120.30
939.120.4 9.0 2 1.4 ' 939.0205 12.122 939.0 11.2 2 2.0
947.7205 3.7 2 0.6 949.020.5 4.820.5 948.0 3.70 2 0.70

- - 993 21 1.52o.2 - -

- - 1013 21 1.3.20.1 - -

- - 1082 21 0.820.1 - —
a(Jak66)
b(Adam68)

cThese intensities were obtained by normalizing the intensity (891:44) for the
346.5-keV y as given in (Adam68) to 100, always retaining the original number
of significant figures.

(1
This transition was not seen in the singles spectra but only in the 600-keV region
gated spectrum. (Figure 18) .

PER CHANNEL

COUNTS

73

 

 

KJEul

KAEN

I496 (50”)

 

 

K a( PR+ LO)

KB(PR+LOl

AL...-

c—dn—
I454(Pwml

I658 (1069)

1 l

l

 

 

Figure 12.

500

Gdlhg

IOOO I500

CHANNEL NUMBER

x-ray Spectrum compared to a Ce

1399191

2000

spectrum.

 

74

Due to the presence of the contaminant Ce139, the
total Ce x-ray intensity had to be corrected apprOpriately in
order to arrive at the experimental Ce”1 K -x—ray intensity.

This correction was accomplished by use of the K-shell fluorescent
yield and Iy/IK;X (IC + EC) values reported by Donnelly and
Wiedenbeck (Don 68). The total relative Ce139 K x-ray contribution,
both electron capture and internal conversion, could then be
calculated from knowing the intensity of the 165.8—keV y ray
accompanying the de-excitation of the Ce139. The ratio of K
x-rays to 145.6—keV 7's in Cell+1 has been measured (Nam 61) to

be 0.34l:0.010. The area ratio [K x-ray/149.6-keV y] for Gd1H9
was measured to be 2.45. When corrected for efficiency by the
Celhl ratio, this becomes 2.01. The errors involved Should be
quite small even though the efficiency curves are changing rapidly
in this region, because the energies of the Gd”9 and Ce”l x—rays
and y-rays are so Similar.

As can be seen from the singles Spectrum resulting from
the bombardment of separated Eu151 (Figure 10), peaks are present
at 963, 993, and 1013 keV in addition to those at lower energies.
These three "high-energy" peaks were also seen in many of the
bombardments using natural Eu, and they have been reported
previously (Jak 66) as belonging to the decay of Gdlug. We
questioned this because, as can be seen in Figure 11, a Spectrum
taken from an older source (in this case using natural Eu target)

no longer cOntains these transitions. An excitation function

75

was run using a natural europium oxide target with proton beams
from 10 MeV to 35 MeV at 5 MeV intervals. The characteristic

Gd”9 peaks first appeared in the 20 MeV spectrum as expected

(Q = -l6.9 MeV) and had all but vanished by 35 MeV, thus exhibiting
an excitation function with a width typical of a compound nuclear
reaction. 0f the three peaks (961, 993, and 1013 keV) only the

961 keV peak was in evidence in any of these runs. However, it
first appeared in the lO-MeV Spectrum and continued to be present
in all of the higher energy spectra. It was accompanied by

peaks at 121 keV and 841 keV, these three transitions being
characteristic of the decay of the 9.3—h isomeric level of Eu152.
This activity could easily be made by the Eu151(n,y)Eu152m reaction.
The peaks at 993 keV and 1013 keV did not appear in any of the
excitation function Spectra; however, the statistics were such

that very weak peaks at these energies would not be observed.

When observed in other singles spectra these two peaks do appear

to decay with a half-life Similar to, but less than, that of Gd1“9,
although no specific half-life determination has been made. It
should be noted that, when present, these peaks do remain with

the Gd fraction after separation in an ion-exchange process.

76

4.1.3.B. Prompt Coincidence Spectra

 

Both prompt and delayed Spectra were obtained by a
variety of methods. The 7-cm3 Ge(Li) detector was normally used
for recording spectra, with a 3X3-in. NaI(Tl) detector setting
the gates. For some of the Spectra, however, the Ge(Li) detector
was placed at one end inside the tunnel of an 8X8—in. NaI(Tl)
split annulus (Aubl67). The source was placed on top of the
Ge(Li) detector inside the annulus. For an anticoincidence
Spectrum a 3X3-in. NaI(Tl) detector was placed at the other end
of the annulus tunnel in order to subtend a greater solid angle
from the source, thereby further reducing the Compton background,
in particular the Compton edges resulting from backseattering
from the Ge(Li) detector. For all of the coincidence experiments
a standard fast-slow coincidence circuit was used and the lower
discriminators of the single-channel analyzers were adjusted to
accept only pulses with energies greater than those of the K x—rays.
For the coincidence runs the resolving time (21) of the fast
coincidence unit was =100 nsec, while for the anticoincidence
run it was =200 nsec. These experimental set-ups are described
in more detail in §II.1.2.

The anticoincidence and integral or "any” coincidence
Spectra are shown in Figures 13 and 14. These Spectra complement
each other in helping to elucidate the decay scheme. The enhancement

of a peak in the anticoincidence spectrum implies a ground-state

77

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79

transition either from a level fed primarily by direct a decay
or from a level with a half-life long compared with the resolving
time; examples are the 748.2— and 496.4-keV y's. In the integral
coincidence spectrum such transitions should be either absent or reduced
in intensity. The integral coincidence spectrum also confirms much
of the information gained from the individually-gated Spectra
below. The relative intensities of peaks in the coincidence runs
are given in Table 4 and a summary of our inferences from them is
given in Table 5.

Other useful coincidence Spectra were obtained by
gating on the 149.6-, 346.5-, and 534.2—keV peaks and on the 600-
and 900-keV regions. These are shown in order in Figures 15-19.
Tables 4 and 5 again summarize the relevant information from these
spectra, but we defer any detailed discussion until §1.5,
where points essential to our construction of the decay scheme

will be covered.

80

 

 

 

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82

 

 

Gate energy Peaks in coincidence Figure no.
(keV) (keV)
Integral gate 149.6, 214.5, 260.5, 14
272.0, 346.5, 405.5,
459.9, 478.7, 516.4,
534.2, 645.2, 663.3,
666.2, 788.6, 947.7
149.6 272.0, 346.5, 516.4, 15
645.2, 663.3, 788.6,
947.7
346.5 149.6 16
534.2 214.5, 260.5, 405.5 17
600 region 149.6, 272.0, 430.3 18
900 region 149.6 19
149.6 delayed coincidence 252.3, 298.5 20

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87

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88

4.1.3.C Delayed Coincidence Studies

 

Many nuclei in this region have an hll/Zisomeric state,
and Eu1“9 is no exception. The 496.4-keV state was first suggested
to be isomeric by Shirley, Smith, and Rasmussen (Shir 57), who
assigned the 346.7-keV transition as M2 on the basis of its
conversion ratios. The half-life of the state was later measured
by Berlovich, et a1. (Berl 61), to be 2.48:0.05x10-6 sec. In
several previOus studies (Pras 62, Jak 66) delayed-coincidence
experiments were performed to determine the feeding of the 346.7-keV
state from above, but we obtain somewhat different results from
these.

We used a 3X3-in NaI(Tl) detector to gate on the
346.5-keV y and on the 149.6-keV y that is in coincidence with it
(cf. the decay scheme in Figure 23 below). The 7-cm3 Ge(Li)
detector signal was delayed relative to these gates by inserting
passive delays ranging from 0.25 to 0.50 nsec, depending on the
particular run. The fast resolving time (21) again was set at
=100 nsec. The spectrum resulting from the 149.6-keV delayed gate
is shown in Figure 20 and the intensities of peaks in this Spectrum
are compared with their intensities in the correSponding prompt
spectrum in Table 6. A summary of the conclusions is also included
in Table 5. The spectrum resulting from the 346.5—keV gate
produced essentially the same results so is not shown.

In all the delayed spectra the 298.5—keV y was enhanced,

indicating that it does indeed feed the 496.4—keV level. There was

89

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90

Table 6.1ntensities of Gd”9 y rays in delayed

and prompt coincidence.

 

 

 

E} (keV) Relative Intensity (normalized to singles intensity)

149.6-keV 149.6—keV

delayed prompt
149.6:0.2 4.78 -
252.3iO.7 0.85 ‘
260.5i0.3 0.86 2.88
272.0i0.2 2.08 33.3
298.510.2 3126.7 15.7
346.5t0.3 18.2 272.5
496.410.3 1.17 -
516.4iO.3 1.51 511.1
534.210.3 2.73 2.36
645.2i0.3 - 6.22
663.310.7

{ - 1.11

666.2iO.7
748.2i0.3 15.37 -
788.610.3 5.68 16.3

 

91

also some evidence for enhancement of the 252.3-keV y. However,
the 459.9-keV 7, which had previously been reported (Pras 62,

Jak 66) as feeding the 496.4-keV level, is completely missing
from Figure 20. This, and other evidence which will be discussed
in §4.1.5., leads us to the conclusion that the 459.9-keV y does
not proceed to the 496.4-keV level but instead depopulates a

newly proposed 459.9-keV level.

92

4.1.3.D. Internal Conversion Coefficients

 

For the determination of internal conversion coefficients
we used the electron intensities reported by Harmatz and Handley,
(Harm 66) who reported extensive values for K electrons along with
some values for LI andMI electrons. These values were obtained
with flat-field permanent magnet Spectrographs using photographic
plates and have reported uncertainties of =15% for the most
prominent lines. For purposes of normalization we assumed the
346.5-keV transition to be pure M2 and used the theoretical value
of GK from Hager and Seltzer (Hag 68).

Multipolarities or possible multipolarities were
assigned for all transitions where K—electron intensities were
'3 of Hager and

available. The experimental 's, theoretical a

“K K
Seltzer (Hag68), and assigned multipolarities are listed in

Table 7. Where necessary, (logarithmic) quadratic interpolation

was made between the tabular theoretical values. As our lowest
energy was 149.6 keV, this method yielded satisfactory results.

These theoretical values were used to construct the smooth curves

in Figure 21, upon which we have superimposed the experimental points

along with their estimated errors (ranging between 15 and 30%).

and K/M

Usually K/L ratios can be used as

(tot) (tot)

indicators of transition multipolarities. For the present case
only a few LI and MI values are reported (Harm66). Where possible
the LI conversion values were used with the experimental K-conversion

values to determine experimental values for K/LI ratios. These

values are compared in Table 8 with theoretical values based on

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94

8018368)

No precise error estimates could be assigned to these conversion
coefficients. Harmatz and Handley (Harm66) assigned intensity
errors as being £151 for their most prominent lines. Our y-ray
intensity errors are given in Tables 3 and 9.

cThese transitions are probably Ml's; the closeness of the M1 and E3
conversion coefficients makes a decision based on these alone

difficult, but.Ml assignments are consistent with the remainder of
the decay scheme.

95

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96

Table 8. Experimental and Theoretical K/LI ICC Ratios for

Cd”9 Transitions.

 

 

 

 

 

 

 

 

 

 

 

 

Energy Exp. Theoretical K/LI Ratiosa Indicated
(keV) K/LIb E1 E2 E3 M1 M2 M3 Multipolarityc
149.6 8.5 9.3 9.9 9.5 7.6 5.7 -- E1,M1
272.0 8.7 8.2 8.0 7.7 7.3 5.9 4.9 El

298.5 8.5 8.3 8.0 7.5 7.4 6.1 5.1 El

346.5 7.3 8.9 9.3 8.9 8.0 7.2 6.2 M2

496.4 6.5 8.5 8.1 7.5 7.8 6.9 6.1 M2 or M3
516.4 7.2 8.7 9.1 9.0 7.9 7.6 7.2 M3

534.2 9.0 8.8 9.5 9.7 8.0 7.9 7.7 El

939.1 8.4 8.6 8.9 8.9 8.0 8.0 8.0 El

3(Hag 68)

bBased on values given in (Harm 66L

cThese multipolarities are indicated by the theoretical ratios given here.
They are not necessarily the adopted values determined from other experimental
evidence.

97

the tables of Hager and Seltzer (Hag 68). As is easily seen,
the ratios are so similar and vary so slowly they are only of
marginal use for multipolarity assignments. The indicated
multipolarities, based on comparison of the experimental and
theoretical ratios, are also shown in Table 8. These values
were not used as the primary factor in assigning transition

multipolarities.

98

4.1.4. Electron-Capture Energy

 

Because there is no measureable 8+ emission from the
decay of Gdlkg, a direct measurement of its decay energy is not
possible. Various estimates of€2€ range all the way from 1.220
MeV (Avot 7) to 2.275 MeV (Harm 11). As an alternative to an
arbitrary adoption of one of the several published values, we
made a graphical estimate of€2€, using a method similar to that
suggested by Way and WOod (Way 54) and previously used by
Grover (Grov 59).

A plot (Figure 22) was made of all experimentally known
decay energies vs Z for pairs of nuclei having the same neutron
numbers as the pair for which the decay energy is to be determined.
Both electron—capture and B_ decay pairs were plotted, and for
our particular graph, as Qe is chosen to be positive and Q8- negative,

the abscissa for the former is Z and for the latter
parent

149

For example, in estimating Q6 for Cd , the experi-

Zhaughter'
mental decay energies of all pairs with RE85486 or ”986285 were
plotted. As can be seen from Figure 22, these points all fall

d179 can be read from the same line.

on a straight line, and as for C
Using this method we estimate¢%:as 1.320 MeV. The plots for

Gd1‘*5, Gd “‘7, and Cd 151 have also been included for reference.
As read from the graph, Cizfor these isotopes is 4.9, 2.2, and
0.56 MeV, respectively. These compare with previous estimates

of 5, 1.8 and 0.4 MeV (refs. Grov 59, Mat 65 and Alex 64,

respectively).

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54 56 58 6O 62 64 66
PROTON NUMBER

Figure 22. Graphical estimates for the electron-capture decay energies
for several odd-mass Gd isotopes, including Gd1“9.

100

In essence, this method involves taking the difference
between two parabolas cutting across the mass surface and assumes
that there are no appreciable bumps or ridges to distort the
surface in the region involved. Had we chosen to make a similar
plot based on proton pairs rather than neutron pairs, it is easy
to see that the N=82 shell would have introduced a serious distortion.
Although there is no formal justification for the plot we did
make, the fact that no major proton shells or subshells are likely
to be encountered means that such estimates for Q6 should be

reasonably reliable.

101

4.1.5. Proposed Decay Scheme

 

0n the basis of the foregoing coincidence, delayed

coincidence, and anti—coincidence spectra, aided by energy
sums and intensity balances, we have placed excited states in
Eulu9 as indicated by our decay scheme, presented in Figure 23.
The results of our y-ray energy and intensity measurements,
conversion coefficients, and assigned transition multipolarities
are summarized in Table 9. Unfortunately, as we have intimated
earlier, the preparation of clean Gd”9 sources, free from
subtle contaminants, is not a trivial task, and many incorrect
transitions and states have accrued in the literature. Thus,
we have included in our decay scheme only those states that
were actually indicated by experiments in our laboratory. To
ameliorate this inflexible position somewhat, we have included
in Figure 23, to the side of our decay scheme, some placements
that we could neither confirm nor deny and which appear to be
reasonable. For the most part these originate from the conversion—
electron work of Harmatz and Handley (Harm 66), who observed
a number of transitions too weak to be detectable in y-ray
Spectra.

I Specific evidence for our placing of each level and

its associated transitions follows:

a; 1320 keV

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Figure 23.

Table 9.

103

Transition data for G

 

——

.
---

.. *v-‘.n~
—. — --_._

(1199.

 

Energy Photon K—Conversio Total Exp 01K Multipole
Intensity Intensitya’ ’C Intensity Order

K X-rays 468 1:100 - - - -
149.6i0.2 233 210.0 124.9 377 0.54 M1
216.5:o.6 0.81: 0.1 - 0.84 - -
252.3207 1.1 i 0.2 0.14 1.23 0.13 M1
260.5603 5.8 1 0.4 0.15 5.92 2.6 10'2 El
272.0602 14.6 t 0.6 1.75 16.3 1.2 10'1 M1
298.5:0.2 127 t 10 10.75 138 8.5 M1
346.5:0.3 2100 20.0 123 0.20 M2
605.5:0.7 3.7 t 1.5 0.033 3.7 9.0 10'3 5'1
430 0.33: 0.05 — 0.33 - —
459.9103 2.4 t 0.19 0.073 2.49 3.0 10’2 Ml
l'78-7t0.3 1.0 t 0.1 0.011 0.96 1.2 10-2 E'2
l1966:0.3 7.2 t 0.35 0.238 7.49 3.3 10"7- E3
516.6203 11.1 t 1.5 0.213 11.3 1.9 10-2 M1
534-2193 13.2 r 0.55 0.256 13.5 1.9 10"2 Ml
645.2203 5.9 t 0.5. 0.018 .9 3.0 10"3 El
563-30.? 1.1 t 0.2 0.016 1.10 1.5 10'2 Ml
566.210.7 3.9 t 0.6 0.026 .0 6.6 10"3 22
748.2103 34.6 i 4.0 0.071 34.7 2.0 10-3 151
'88-510-3 29.6 t 3.0 0.15 29.8 5.1 10‘3 M1+E2
”2'4“” 0.55: 0.1 - 0.55 - —
3639' " 0.32: 0.1 weak - - —
”5'810-4 0.90: 0.1 0.0041 0.91 4.6 10-3 M1
133.310, 2.2 t 0 5 - 2 2 - —
’39-110. . . -3

9.0 - 1.4 0.044 9.0 6.9 10 M1
947.71().5 -3 .

3.7 t 0.6 0.0062 3.7 1.7 10 (kl)

‘3‘: -_':—'.:2::;:3:;:=::.; 7.: ..'.-

...-... -—
—. --- :2..-

---
--

104

aIntensities from (Harm66).
bIntensities renormalized such that the aK (346.5 keV) E 0.20.

cErrors in the relative intensities are reported as being 15%
for the most intense peaks and increasing for the weaker ones.

dFor the purpose of arriving at total intensity values, theoretical
L and.M conversion coefficients were used for the indicated
multipolarities. Interpolated values from Hager and Seltzer

(Hag68).

eNot included in the decay scheme.

105

149.6-keV level. The 149.6-keV peak is by far the
most intense transition in the y-ray Spectrum. If this were
not a ground-state transition, we should see other transitions
of comparable intensity that would de-excite the level fed by
the strong 149.6-keV transition. Therefore, in agreement with
all previous workers, we place the first excited state near 150
keV, specifically, at 149.6 keV. This is also consistent with
an overwhelming mass of systematics showing that odd-proton
nuclei with 5152303 have 5/2+ or 7/2+ ground states or first-
excited states separated by an energy rarely greater than 150 keV.
The coincidence experiment having its gate on the 149.6-keV
peak (Figure 15) showed enhanced peaks at 272.0, 346.5, 516.4,
645.2, 663.3, 788.6, and 947.7 keV. These results agree with
those of Jaklevic, Funk, and Mihelich (Jak 66), with the exception
of the 663.3-keV peak, which they did not see in a coincidence
spectrum. All of these transitions can thus be considered as
feeding the 149.6-keV level, and it will be shown later that, with
the exception of the 272.0-keV y, all feed it directly.
The 149.6-keV coincidence spectrum, in conjunction with
the singles spectra, made it possible to determine the energies
of the peaks in the 663.3- 666.2-keV doublet more precisely than
before. As only the 663.3-keV 7 was in coincidence with the 149.6-
keV 7, its energy and intensity could be determined directly from
the coincidence spectrum. These values were then used to subtract
the 663.3-keV peak from the singles doublet, leaving the 666.2-keV

peak quite well determined by the difference.

106

459.9-keV level. Owing to the results of the delayed
coincidence spectra (Figure 20), the 459.9-keV y can no longer
be considered to be feeding the 496.4—keV level, as had been
concluded by previous workers. (Pras 62, Jak 66, Adam 68).

Also, as seen in Figure 13 and Table 4, this y ray is enhanced
in the anti-coincidence spectrum but is absent from most of
the prompt coincidence spectra. From this evidence, we place
the 459.9-keV y as emanating from a level of this same energy.

On the basis of energy sums, the 478.7-keV y could be
placed connecting the 459.9-keV level with the well—established
939.1-keV level (see below). Other evidence for this placement
comes from the 534-keV gated spectrum (Figure 17). While the
459.9-keV peak is less intense than in the singles Spectra, it
is still present -- most likely due to some of the 478.7—keV y
in the relatively wide NaI(Tl) gate. The fact that it is present
to more than a very small extent implies that it does not feed the
496.4-keV level, which has a half-life of 2.48 usec. In Figure 7
the 459.9- and 478.7-keV y's have the same intensity relative to
each other as they do in the singles spectra, suggesting again
that they are related as above.

496.2-keV level. This is the relatively well-known
11/2- isomeric state, again a characteristic of odd-Z nuclei
in this region. Its half-life has been measured (Ber 161) to be

2.48:0.05 usec. As a result of this half-life, the transitions

107

to and from this level must be studied by means of delayed
coincidence techniques. From the results of such experiments
(§4.l.3.d., Figure 20 and Table 6), only the 252.3— and 298.5-keV
y's are placed as proceeding to the 496.2—keV level. It is depop-
ulated by the 496.4-keV y to the ground state (cf. Figure 13)
and by the 346.5-keV y to the 149.6-keV level (Figure 15 and §4.l.3.D.).
The adopted energy, as for all of the excited states to be discussed,
is a weighted average of these y rays.

534.2-keV level. In the 534-keV gated coincidence
spectrum (Figure 17) the 214.5- and 260.5-keV peaks are most.
obviously enhanced. Other relatively intense peaks are those at
272.0, 405.5, 459.9, and 478.7 keV, all of which are more intense
than can be ascribed to chance coincidences. We have already
dealt with the 459.9- and 478.7-keV peaks, and the 272.0—keV peak
can be explained from the 516.4-keV y falling within the gate.
This leaves the 405.5-keV y as feeding the 534.2-keV level, although
its coincidence intensity is somewhat less than expected. This
coincidence spectrum does not rule out its feeding the 748.2-keV
level, which in turn feeds the 534.2-keV level. From energy sums
and differences, however, it is one of 5 y rays that depopulate
the 939.1-keV state, and this is the only placement consistent
with our proposed decay scheme.

666.0-keV level. The three primary peaks included in
the gate for the "600-keV region" coincidence Spectrum (Figure 18)

lie at 645.2, 663.3, and 666.2 keV. We have already discussed

108

how the 666.2-keV y appears to be a ground-state transition
(above, in the section on the 149.6-keV level), implying the
existence of a level at this energy. The peaks in Figure 18 are
those at 149.6, 272.0, 430.3, and perhaps 516.4 keV (crossover
timing jitter cut down on the intensity of the latter). That
these transitions are involved in cascades is corroborated by

the integral-coincidence spectrum. The 149.6ekeV coincidence
spectrum shows the 516.4—keV y to feed the 149.6-keV level; if we
try to place it as feeding this level indirectly through some.
higher level, we obtain no consistency whatever with the remainder
of the decay scheme and very quickly exceed the available decay
energy. Thus, it depopulates the 666.0-keV level.

The 272.0- and 430.3-keV y's feed into the 666.0-keV
level from the 933.3- and 1097.3-keV levels, respectively. These
placements are the only ones supported by energy sums.

748.2- and 8l2.4-keV levels. The 748.2- and 812.4-keV
y's were indicated to be ground state transitions by the anti-
coincidence spectrum. In addition, the 534.2-keV coincidence
(Figure 17) and the delayed coincidence (Figure 20) spectra
indicated our placement of the 214.5- and 252.3—keV y's, making
the level at 748.2 keV reasonably certain. Similarly, the
enhancement of the 663.3-keV y in the 149.6-keV gated spectrum
adds confidence to the placement of a level at 812.4 keV, which
had not been adduced by previous workers (the 812.4-keV Y had

been variously assigned).

109

794.8-keV level. There are no transitions to the
ground state from this level, probably because of the preposed
high spin of the state. However, each of the transitions leading
from it was enhanced in the appropriate coincidence spectrum --

260 keV in Figures 14 and 17, 298.5 keV in Figure 20, and 645.2 keV
in Figures 14 and 15.

875.8-keV level. Perhaps the least certain level in our
decay scheme, this placement rests solely on the enhancement of
the 875.8-keV y in the anti-coincidence spectrum and its suppression
in all of the coincidence experiments. Also, there is no other
position consistent with the remainder of the decay scheme in
which to put it.

933.3-, 939.l-, and l097.3—keV levels. In the "900-keV
region" gated coincidence spectrum (Figure 19), the only peak
present is the one at 149.6 keV. From the integral, 149.6-keV
gated, and anti-coincidence spectra, it is evident that the 947.7—keV
y is the only one in coincidence. It indicates a level at 1097.3
keV, which is corroborated by the enhancement of the 430.3-keV
Y to the 666.0-keV level, as discussed above. The 933.3-keV
level is placed on the basis of its sole transition to the ground
state. The 939.1-keV level, on the other hand, depopulates by
5 y rays, all of which are confirmed by coincidence spectra, as
discussed above under the sections concerning the levels to

which each feeds.

110

4.1.6. Discussion

 

63Eugg9, with four neutrons above the N=82 closed shell,
must have its structure interpreted cautiously. Although the
closed shell is only four neutrons away in one direction, well-
defined rotational structure makes its appearance (Alex 64) at
Eu153, only four neutrons in the other direction. This means
that when discussing states in Eu”9 one must be careful not to
draw arbitrary conclusions from the spherical shell model and must
be prepared to accept collective effects and the fractionation
of single-particle strengths over many states.

That Eu1H9 should be very soft toward vibrational

deformations is borne out by the fact that Smlua, its even-even
core, has a 2+ one-phonon vibrational state (Baba 63) at only

551 keV, a 3— (octupole?) state at 1162 keV, and a 4+ (from the
two-phonon vibrational triplet?) at 1181 keV.

The simple shell model predicts that above Z=50 the available
proton orbits are 97,2 and d5/2 lying close together, then, after
a gap of a few hundred keV, h11/2’ 31/2, and d3/2. The parent,

Gd1“9, should have eight 97/2 and six d protons (or some

5/2
distribution of proton pairs in these nearly degenerate orbits)
outside the z=50 closed shell. Its last three neutrons should

lie in h9/2 and/or'f7/2 orbits, the unpaired neutron being in

the f7/2 orbit, similar to many other 10:7/2— nuclei above N=82.
[This neutron assignment involves somewhat circular logic connected

with the Gd”9 a decay properties, but no other assignment gives

any sort of consistent picture.]

111

Similarly, the ground state ofEulL‘9 can be characterized
as (97/2)8(d5/2)S protons above Z=50 and (129/2)1+ or (f7/2)“
(or some combination) neutrons above N=82. This 5/2+ configuration
is well established from its edecay (Harm 61) and again is consistent
with many odd-Z nuclei in this region. The first-excited state
undoubtedly has a g7/2 proton hole as a major component in its
configuration, i.e., (g7/z)7(d5/2)6, again in agreement with many
other odd-Z nuclei in the region. These assignments are consistent
with the 0.32-nsec half-life (Berl 62) of the 149.6-keV state,
a half-life quite in line with R-forbidden Ml transitions between
97/2 and dS/z states.

The a decay to the ground and 149.6-keV states demonstrates
quite clearly that they are separate single—particle states and
not members of a K=5/2 rotational band. From our above assignments
the a decay can be pictured as ads/2+ f7/2 for the ground state
and ng7lz+vf7lzfor the 149.6-keV state. The observed branchings
(and log ff's), 17.1% (7.7) and 36.3% (7.3) are perfectly consistent
with such transitions. On the other hand, if the 149.6-keV
state were the 7/2+ member of a K=5/2 rotational band, the relative
a population should be predictable by the ratio of the squares of

the following vector-coupling coefficients,

(IiKiMKf-Ki)lIiQWZexcited ___ <7/2 7/2 1 —1L7/2 1 7/2 5/2)’
- r 2 _ 7
(IiKiHKf Ki)|Ii£IfJ(f) ground <7/2 7/2 1 1|7/2 1 5/2 5/2)

 

= 1/3 .

112

This is clearly in the wrong direction even before the energy
dependence has been included.

The only other simple single—particle state that can
be clearly identified is the hll/ZState at 496.2 keV. The
measured M2 and E3 multipolarities of the 346.5- and 496.4-keV
transitions indicate the 11/2- assignment, as does the 2.48:0.05-usec
half-life of the state. Single-particle estimates (MOSZ 53) for
the half-lives of the M2 and E3 are 3.8><10‘8 and 8.2x10-S sec,
respectively, to be compared with the measured partial half-lives
of 2.7><10"6 and 3.6><10'5 sec. The M2 is retarded by a factor of
approximately 70, but, then,.M2's are commonly retarded by such
factors. More surprising, the E3 is enhanced by a factor of about
2.3 over its single-particle estimate, and most E3's are also
retarded. However, there are three other known enhanced E3
transitions (Bee 69, Hise 67) in La137, Pr139, and Eu1”7, all
nuclei just above or below N=82 and all involving an 7111/2 state.
A cursory attempt (Hise 67) has been made to explain the enhance-
ments on the basis of octupole—coupled admixtures of the ground
states in the hll/Z states, but at this point meaningful
quantitative calculations cannot be made. However, the assignment

of the 496.2-keV state as an.h state is warranged, and its

11/2
receiving no direct a population from Gdluq is consistent with
this assignment.

A number of spin and parity assignments can be made for

the other states, but deciding much about their internal structures

113

is quite difficult. Many of the states are undoubtedly core-
coupled, e.g., the 459.9- and 534.2-keV states, but most conclusions
at this point would be somewhat arbitrary. Unfortunately,
theoretical studies of this region are all but nonexistent,
and even useful experimental systematics are scarce. We are
currently studying other nearby Gd isotopes and hope to be able
to say more about the structures of states in the various nuclei
in this region at the conclusion of these studies. Meanwhile, in
this paper we confine ourselves to a more or less straightforward
discussion of the spins and parities per se, as they can be deduced
from the Y transitions. The e decay itself yields little information,
for most of the log ft'values lie in the range which indicates
either first-forbidden or allowed transitions, and it will be
necessary to know more about the internal structures of the states
before drawing serious conclusions from these values.

The 459.9-keV state can be assigned 3/2+, 5/2+, or
7/2+ because of the M1 character of its ground-state y-ray
transition. The log ff value of 9.1 seems to imply a first-
forbidden unique transition. However, if one considers this state
to arise from core-coupling to the one-phonon 551-keV state in
Smlue, the loglft value would be expected to be larger than normal.
With this in mind, the a decay could in fact be a normal first-
forbidden transition. Consequently, the spin assignment for the
459.9-keV state cannot be narrowed down from the above. And if

the d ground state were the single—particle component of

5/2

114

the core-coupled state, this could easily explain the absence of
a transition to the 149.6—keV state.
The 534.2—keV state can also be assigned 3/2+, 5/2+, or
7/2+ because of the M1 character of its ground-state transition.
It is also tempting to think of this state as the dS/2 ground
state coupled to the 2+ quadrupole vibrational state. We shall
see below that the assignment for the 534.2-keV state can be
narrowed down to 7/2+.
The 666.0—keV state is limited to 5/2+, 7/2+, or 9/2+
by the M1 transition to the 149.6—keV state. If, as it appears,
the 666.2-keV transition to the ground state does have appreciable
Mfl admixing in its E2 character, the 9/2+ possibility is eliminated.
Assignments for the next two states, at 748.2 and
794.8 keV, can be much more specific because of the many y-ray
branches proceeding from them. The 748.2-keV E1 y implies a spin
of 3/2-, 5/2-, or 7/2- for the 748.2-keV state. The 252.3—keV y
to the ll/2- state appears to be an M1, which is inconsistent with
the 748.2-keV 7 being an E1. However, assuming the 252.3—keV y
to be really an E2 narrows the choice for the 748.2-keV state to
7/2-. The log ft of 7.4 is somewhat high for an allowed transition,
but, remembering that the 748.2-keV state undoubtedly has a complex
structure, one would expect a 8 transition to it to be hindered.
With a 7/2— assignment, the 214.5—kev y to the 534.2—kev state
allows the narrowing of assignments for the latter down to

5/2+ or 7/2+.

115

The strong 298.5-keV M1 transition from the 794.8—keV
state to the 496.4-keV state suggests the possibilities 9/2~,
11/2-, or 13/2- for the upper state. The 645.2-keV El transition
to the 149.6-keV state limits the choice to 9/2-. The log ft for
a decay to this state is the lowest for decay to any state,
implying that this transition, if any, is allowed, again consistent
only with the 9/2- assignment. The 260.5-keV El Y then allows
the assignment for the 534.2-keV state to be narrowed further
to 7/2+.

If we may be forgiven a little speculation at this
point, a word about one component of the wave function of the
.794.8-keV state might perhaps be in order. Consider the two facts:
1) a relatively simple mechanism must exist for populating the
state so readily from Gdlug, and 2) the abnormally large intensity
of the transition to the 496.4-keV state indicates a similarity
to that state. Now, there is ample indication (Fel 70, Wild 70a)

that,below N=82 at least, there is appreciable h character

11/2
in the proton pairs of the Gd isotopes, and this should also be

true here. Any 5 transitions from Gd149

1nvolv1ng 97/2 or d5/2
protons would not be expected to proceed at all rapidly to the
available final neutron states, nor would they lead to 9/2-
overall final states. On the other hand, a "hll/Eth/Z transition

not only would proceed relatively quickly, but also it would lead

t .
o the final configuration, (11h11 l2)(vh9 /2)(vf3 /2)’ which could

116

furnish a 9/2- state among its couplings. Similar cases,
resulting in three-particle final states are known (Bee 69d and
McH 69a) in the N=82 region, although the three-particle states
lie considerably higher than 794.8 keV. Thus, although we do not
suggest this as the primary component of the 794.8-keV state,
such an admixture would account satisfactorily for the a decay.

The state at 812.4 keV is assigned 5/2+, 7/2+, or
9/2+ on the basis of its ground-state y transition and the 663.3-
keV Ml transition to the 149.6-keV state. A.possible 3/2+ assign-
ment for this state is ruled out on the argument that the large
log ft is probably a result of internal complexities in the state
necessitating multi—particle rearrangement during the a decay
rather than the e decay being first-forbidden unique.

The single 7 transition of 875.8 keV emanating from
the state of this energy is assigned an M1 multipolarity. This
limits the state spin to 3/2+, 5/2+, or 7/2+, assignments that
are compatible with the a decay to this state.

Harmatz and Handley (Harm 66) do not report conversion-
electron intensity values for the 933.3—keV transition. Therefore,
we cannot make a definite spin assignment to the 933.3-keV state
on the basis of this transition. From the log ft value of 8.3,
assuming this again to be a hindered first-forbidden transition,

the spin could be 5/2+, 7/2+, or 9/2+.

117

The 939.1—keV.Ml ground-state transition suggests 3/2+,
5/2+, or 7/2+ for the 939.1-keV state. The 788.6-keV transition
(if it really contains an appreciable M1 admixture) eliminates
the 3/2+ possibility, as does the relatively low log fr value of
6.8. Neither the 478.7- nor the 272.0-keV y's allow this to be
narrowed further. It should be noted that an El multipolarity
for the 405.5-keV transition, while eXperimentally indicated is
incompatible with the other assignments. A three—particle final
state component can also be invoked here to explain the e decay,
this time a ng7/2 + vhglz transition resulting in (flg7/2)-1
( vh9/2)( va/Z) as a component of the final state.

The 947.7-keV El transition implies 5/2-, 7/2-, or
9/2- for the 1097.3-keV state. The log ft is compatible with

any of these possibilities, but other than this, little can be

deduced about the state.

4.2. The Decay of Gdlusm

 

4.2.1. Introduction

 

Gadolinium isotopes cover a wide range of nuclear types, ex-
tending from permanently deformed nuclei to spherical single closed—
shell nuclei at N = 82. As a result, systematic studies of their de-
cay properties and structures should prove quite rewarding, for here
is one of the few regions in the nuclidic chart where one can follow
trends in nuclear states when moving from one extreme nuclear type to
another. Gd145m was our second invesigation of the Gd isotOpes; an
isotOpe on the neutron—deficient side of the N = 82 closed shell. In
this region the Gd isotopes have not been very well characterized un—
til quite recently, although their decays present some interesting
anomalies, such as the peculiar ground—state decay of Gd“+5 into what
appear to be three-quasiparticle states in its Eu”5 daughter, the
subject of which forms § 4.3. On the neutron—deficient side of N =
82, a systematic study of the odd—mass isotones also appears well
worthwhile because of the appearance of long series of nuclear isomers
having quite different and distinct decay prOperties. The longest
series of these isomers, in the N = 81 nuclei, extended from Te133
to Smlu3, and it seemed reasonable that Gd1”5, as the next nucleus in
line, should also exhibit isomeric states.

We subsequently observed the metastable state in 0d”5 and
its isomeric transition. The energy of the transition was found to
be 721:0.4 keV and the half—life of the state, 8513 see. These values
were consistent with our predictions based on the systematics of the

other N = 81 isotones, and they were first reported in November 1968

118

119

(Epp7OB). Since that time, Jansen, Morinaga, and Signorini (Jan69)
have published results in very good agreement with our y—ray energy
and half-live values. Since our first preliminary report we have
also observed the conversion electrons from the isomeric transition,
clearly identifying it to be of M% multipolarity, and we have ob-
served a B+le branch from Gdlusm directly to states in Eu1”5.
Even by 1951 some 77 nuclear isomers had been classified by
Goldhaber and Sunyar (GoldSl). Since then, of course, isomers have
been one of the prominent nuclear properties used to test the validity
of nuclear models. In particular, M4 transitions are of interest for
testing the extreme single—particle model. If such a thing as a "pure"
single-particle transition exists, these transitions are good candi—
dates for that distinction. The M4 transitions observed in the N =
81 nuclei are thought to proceed from h11/2 to 613/2 states, and the
h11/2 state should be particularly pure owing to its being the only

odd-parity, high-spin state at low excitations. We discuss the pro-

perties of these M4 transitions in § 4.2.3.

120

4.2.2. Experimental Results

We produced Gdlusm in this laboratory by both the Sm1““(r,2n)
Gdlusm and the Sm1”“(u,3n)Gd1”5m reactions. The calculated Q—values
for these reactions were —10.4 and —30.9 MeV, reSpectively (Myer65).
For all of these experiments separated isotOpe Sm1M (95.10%, obtained
from Oak Ridge National Laboratory) in the form of Sm203 was used as
the target material. The T and a beams, typically 20 MeV and 40 MeV,
respectively, were furnished by the Michigan State University Sectorr
Focused Cyclotron. Excitation functions were run to determine the
energy for maximum Gd1“5m yield in each case. Most of our experiments
were performed with the T beam, and typically a lO—mg or smaller tar-
get would be bombarded with a 0.5-uA beam for l min. Because of the
short half—life of Gd1“5m, no chemical separations could be carried
out. Fortunately, they proved to be unnecessary, owing to the clean—
ness of the reactions. After most bombardments it took less than 2 min
to retrieve the target and transport it to the counting area.

We also produced Gd1“5m in a set of confirming experiments
performed at the Yale University Heavy—Ion Accelerator. C12 beams
ranging between 70 and 120 MeV were used, and the reactions of inter-
est were Nd1”2(C12,aSn)Gd1”5m and Sm1”“(C12,203n)Gd1”5m. The latter
twas discovered quite by accident and has an unexpectedly large cross
section. It must proceed by a combination of cluster stripping and
cxnmpound nucleus formation.

The y-ray energies were determined by simultaneous counting
‘Jith the standards listed in Table 10. A y-ray singles spectrum is

sflaown in Figure 24. The peaks appearing in this Spectrum without

121

Table 10. y-ray energy.standards used for Gd1”gn.

 

Nuclide y-ray energies Reference
(keV)
Ce1“1 145.43:0.02 a
0m2“3 209.85:0.06 b
228.28:0.08 b
277.64:0.0Z b
C056 846.4 i0.5 c
1038.9 $1.0 c
1238.2 :0.5 c

 

8J. S. Geiger, R. L. Grahrn. T. Bergstrbm, and F.Brown,
Nucl. Phys. 68, 352 (1965).

R. E. Eppley, unpublished results (1969).

cR. L. Auble, Wm. C. McHarris, and W. H. Kelly, Nucl.
Phys. A91, 225 (1967).

b

122

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123

energy assignments listed come from the decay of the ground state of
Gdll+5 (see § 4.3). The detector used was a five-sided trapezoidal
Ge(Li) detector fabricated in this laboratory. It had an active
volume of z7—cm3 and a resolution of 2.9 keV FWHM for the 0060
1.333-MeV y. The y rays associated with the decay of Gdlusm had
energies of 721.4i0.4, 386.6:0.3, and 329.510.3 keV, as determined
from the averages of a number of experiments.

The Gd1”5m half-life was determined with the help of a com-
puter code called GEORGE (Geor). This code allows us to accumulate
data through an 8192-channel ADC interfaced to the MSU Cyclotron Lab-
oratory Sigma-7 computer. We can dump segments of the spectrum in
successive time intervals: counting can be stopped, the spectrum seg-
ment dumped onto a Rapid Access Disc (for punching on cards at a later
time), the memory erased, and the counting resumed, all in consider-
ably less than one second of elapsed time. In the present case the
spectra were dumped at lS-sec intervals. A pulser peak was included in
each spectrum for later determination of the proper dead-time corrections.
The net peak areas, corrected for dead time, then yielded the half—life
information in the usual manner. A plot of a Gdlhsm decay curve, cor—
rected for dead time, is Shown in Figure 25. The reported half-life
is an average of three such least-squared decay curves.

A listing of our EY and half—life values is given in Table 11,
‘where they are compared with those of Jansen, Morinaga, and Signorini.

The electron spectra were obtained by use of a lOOO-u thick
Si(Li) surface barrier detector, cooled to methanol—dry ice tempera-

ture and Operating with a bias of +200 V. The resolution of this

124

 

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125

Table 11. Transition data summary for 061W"

 

 

 

This work Jansen, Morinaga, and
Signorinia
37014) 721.4:0.4 keV 721.3307 keV
Evan)b 386.6103 keV ......
3,091)" 329.5:0.3 keV ---
ti 8513 see 85:7 sec
a(Jan69).

bThese transitions occur in f 165 and result from the direct

feeding of the h11 2 state in that nucleus by Gdlusm. The
multipolarities aré assumed from the properties of the states
as determined from Gdlusg decay and scattering. Cf. refs.
54.3. and (New70).

126

detector was typically 5 keV FWHM in the 600—keV region, the electrons
having passed through a 0.25—mil HAVAR window. A resulting electron
Spectrum is shown in Figure 26.

In order to arrive at a value for the conversion coefficient
of the isomeric transition, the y-ray and electron spectra were mea—
sured simultaneously from the same source, which was placed in a fixed,
reproducible geometry. Again, owing to the short half-life, "mass-
free" sources could not be made. However, as can be seen from the
electron Spectrum, our "thick" sources led to a minimum of straggling.
For calibrating the detector efficiencies and the geometry corrections,
a C3137 source was used as a standard. A value of 0.094 was used for
the 0K of its 661.6—keV transition; this is an average of the values
given in (Dan62 and Hult 61).

Two separate experiments, made at widely differeng times,
were performed to determine the Gd1”5m K— and L—internal—conversion
coefficients. The results, compared with theoretical values for var—
ious multipolarities, are shown in Table 12. The logarithms of the
theoretical values were interpolated from a quadratic least-squares
fit to the tabulated values of Hager and Seltzer (Hag68). The experi—
mental uK value definitely Shows the isomeric transition to be M4 in
character. The measured K/L ratio places it as being either M3 or M4.
The former is a more sensitive test, however, and an M4 assignment fits
in quite well with the systematics of transition probabilities in the
N = 81 isotones, as we Shall see in the next section.

We shall see later that the 386.6— and 329.5-keV y's fit be-

tween known (5 4.3 and New70) States and imply that 4.7% of the decay

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128

Table 12. Conversion coefficients for the isomeric transition

 

 

 

in Gd1”5.
Experimental Theoreticala
E3 E4 M3 M4
0K 0.12:0.2 0.011 0.024 0.054 0.118
aK/uL 5.410.? 3.50 3.53 5.77 4.88

 

U
11

 

a(Hag68).

 

129

“+5
9

of Gdlusm goes via a direct 8+le branch to an h state in Eu

11/2
the other 95.3% going via the isomeric transition. The 4.7% branch
was determined by correcting the 386.6-/721.4—keV photon ratio (found
to be 0.048) for conversion, again using the conversion coefficients
of Hager and Seltzer and assuming the 386.6—keV transition to be a
pure M2 transition. The 329.5-keV y results also from the decay of

the ground state of GdluS, so no quantitative information about its

intensity could be obtained from these experiments.

6.2.3. 061“?” and IV = 81 Isomers

 

Figure 27 shows our decay scheme for Gdlusm. While the other

known N = 81 odd-mass isotones have been assigned d ground-state

3/2
configurations, there is some evidence (see § 4.3) that in Gdll”5 the
31/2 state has replaced the d3/2 state as the ground state, which may
account partly for the peculiar ground-state decay of Cdlhs. Newman,
et al., (New70) also came to this conclusion when interpreting their
scattering data from the Sm1L*l*(r,d)Eull’5 reaction in conjunction with

their Gdl”59 decay data. If the s assignment is correct, the M4

1/2
isomeric transition in Gd”S does not proceed directly to the ground
state but to a state AE in energy above the ground state. This ex-
cited d3/2 state would then decay to the ground state via a predom-
inatly Ml transition.

In search for a low—energy M1 transition, we have utilized
a Si(Li) x-ray detector, which is useful in the 5-100-keV energy re-
gion for y rays and is also sensitive to charged particles. No peaks
that are in evidence in any of our Spectra in the lO-lOO—keV range can

'be attributed to the decay of Cd1“5m. The high positron flux, primarily

from Gd1”59 decay, contributed to a high background problem below 10

 

 

 

 

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eaeusz

. . _ [1.771
Figure 27. Decay scheme for Gdlti .

131

keV and ruled out observing a transition in that region. Assuming

such a low-energy transition to be present, most likely M1 in char-
acter, it would be converted primarily in the LI shell, with uLI hav-
ing a value of 4.5 at 46 keV and increasing to 246 at 9.38 keV (Hag68).
Consequently, assuming the transition to be low in energy, say, 20

keV or less, would preclude observing the photons. However, we should

have been able to see the L conversion line if the energy were above

I
10 keV. The radial matrix elements for the M4 transitions in the N =
81 odd-mass isotones were calculated using Moszkowski's (M03253)

approximations for a Single neutron hole,

 

2L 2
SP 2(L+1) (El 2. 2 . .
T(ML) = “3.3 __0_ __L (“ND IMI S<Ji.L.Jf).
L[(2L+l)!!]2 he 0 meRo

where L is the multipolarity of the transition, R0 is the effective
nuclear radius, 5(ji,L,ij is a statistical factor (i.e., angular
momentum portion of the matrix element), which for ll/2—+3/2 tran-

sitions has the value 15/11, and u is the dipole moment of the neutron.

N
Symbolically, |M|2 has the form,

M2 = E {r
1

 

(Dur results are plotted in Figure 28, where we also Show the differences
:in energy between the hll/Z and d3/2 states.
The resulting transition probabilities are consistently

:smaller than the approximation of a constant wave function,

|M|?— = [—3—2(6NL)2= 16.6,

113”

 

132

 

 

'64

 

 

55' 1. -‘P- (3 "
ll

.2,

(0". 49— O '4
201

03

“'13

t'. --r-- 0 ‘J
(O

33‘

E5. fit- 0 -1
O

0:

Lil O -- O -
8

;; g. -h- (3 "
2

. ‘F' . -
i l 1 ll 1 I [J
0 CO V N
o‘ o’ o' o’ “ '° “‘ ‘

 

(Aawt ASHBNB leI

Figure 28.

Plots of the hll/ + d3 energy differences and of the
squares of the radial méfrix elements for the M4
isomeric transitions that connect these states in the

N a 81 odd-mass isotones.

62

60

56 58
ATOMIC NUMBER

54

52

Fig. 4

133

but this fact Should not concern us particularly, for M4 transitions
are customarily retarded over such estimates and one needs much more
detailed information about the nuclear wave functions in order to
make detailed comparisons meaningful. What is of more importance is
the fact that the values of IMI2 are not constant but show a definite
trend in this series of isotones. [It is unusual for IM’I2 not to be
constant over such a series. For example, in the odd-mass neutron—
deficient lead isotOpes, IM’I2 was constant to the point that an ap-
parent 15% discrepancy at Pb203 suggested that an unobserved tran—
sition was competing with the M4 isomeric transition, and this com—
peting transition was subsequently discovered (Doeb68)]. Other isomeric
series will be discussed in Chapter VI.

The complete answer as to why the discrepancy in magnitude
and in trend exists between the experimental and theoretical values
is still not forthcoming. Kotajima (Kot63) summarizes several effects
that could contribute to these deviations: l) cancellation of the
magnetic moments because of the mesonic effect, 2) configuration
mixing or Spin polarization, or 3) the use of too crude an approxi-
mation for the radial wave functions. In the same paper he explores
the usefullness of applying a more realistic function for these radial
wave functions, but the matrix elements were remarkably insensitive
to changes in these wave functions. This effect, then, by itself
could not explain even the deviations in magnitude, much less the
"bowing" of the curve as seen in Figure 28.

More recently, Jansen, Morinaga, and Signorini (Jan69) have

also sought to better the experimental-theoretical agreements. In a

134

calculation Similar to that used by Kotajima, they recalculated the
radial matrix elements using a potential function consisting of a
Woods-Saxon part and a Spin-orbit part. In this manner they recal—
culated the radial part of the Schrbdinger equation for theSe nuclei.
In addition to this refinement, they took account of configuration
mixing by utilizing the results of Horie and Oda (Hor64). In this
manner, much of the Z dependence was removed. However, the experi~
mental values are still lower than the theoretical ones for all rea-
sonable values of R6. For an R0 of 1.22 f, the experimental -to—
theoretical ratio hovers around 0.5.

An alternate attack on this problem might prove to be useful.
Recasting the problem in a quasi—particle framework would allow a
simplified picture, the transition probabilities depending only on
the particle-hole character of the states involved. Stripping and
pick-up reactions are just now beginning to be carried out on nuclei
in this region, so occupation numbers may very well become available
from these before long. As soon as such information is available,
this type of formulation can be explored more fully.

Finally, it should be noted that as Z increases there is an
increase in the direct B+/e decay to the h11/2 states in the daughter
nuclei. On the neutron-deficient side of the N = 81 odd-mass isotones,

Cellgm does not have sufficient decay energy to populate such a state

in La139, but the decay is energetically possible for Nd1”]m, Smlu3m,
and Gdlusm. We have made a careful search for direct population of

the h11/2 state in Prll”1 by Nd 1”1m decay (Bee68) and have been able

to set an upper limit of 0.01% on any such population. This results

135

in a log ft greater than 7. From Sm1”3m decay, however, Feldsteiner
and Rosner (Feld70) were able to detect a direct branch of 0.2% to
the state in Pmlu3, implying a log ft of 6.7. And we find a direct
branch of 4.7% from Gdlusm decay, resulting in a log ft of only 6.2.
We consider this to be an indication of the increased occupation of
the 7211/2 orbit by proton pairs as one moves up the series. This is
an aSpect of the decay of the N = 81 series that is still under

investigation.

136

4.3. The Strange Case of GdeSg

4.3.1. Preamble

 

This investigation continues our overall studies of the
neutron-deficient Gd isotopes, the decay of Gd“*9 (5 4.1.) and the
characterization of the isomer, Gdlhsm (54.2), having been reported
previously.

Although several earlier papers speculated on Gdlus,
Grover (Grov59) 1959 seems to have been the first to characterize
this nuclide to any degree of clarity. It was also reported at about
the same time by Olkowsky, et a1. (Olk59). Both sets of results,
having been obtained with NaI(Tl) detectors, were incomplete. A
good example is the fact that the two intense transitions at 1757.8
and 1880.6 keV were previously unresolved. The NaI(Tl) data Showed
these as a composite peak reported to be 1.75 MeV (Olk59), although
with considerable insight Grover (Grov59) decided that there were
two transitions in the peak but did not elucidate further.

As far as we have been able to determine, no conversion
electron studies have ever been made on Gd1“59 decay, and, indeed
its short half-life (21.8 m, cf. § 4.3.3.C. below) and the high en—
ergies of its stronger transitions make such experiments impracti—
cable. And until the recent paper of Newman, et a1. (New70) no high
resolution, e.e., Ge(Li), y-ray studies had been reported. The lack
now and in the forseeable future of electron data cripples one in
trying to assemble a complete decay scheme, for he has to work with-
out direct information on the multipolarities of the transitions.

However, the spins and parities of a number of the lower states in

137

the daughter Eulub were determined by Newman, et al., through an
analysis of the Sm1""*(r,d)Eull*5 reaction. This reaction tends to
discriminate against complex states, though, and, as will be seen
later in this paper, we have reason to believe that the primary states
populated by the decay of Gdlusg are complex. Our work has proceeded
in parallel with the work of Newman, et al., and, indeed, there has
been exchange of information between the groups (Toth69). They con-
centrated on the (T,d) studies, however, taking only single y-ray
Spectra, whereas we have concentrated on y-ray studies, using various
coincidence and anticoincidence techniques. Their experiments thus
excite and explain many of the more straightforward lower-lying
states that we see only weakly or not at all. We, on the other hand,
see evidence of a number of higher—lying states populated or depop-
ulated by weaker y-rays, and we think we can explain what we call
"the strange case" of Gdthg decaying overwhelmingly to the two
states at 1757.8 and 1880.6 keV. Here, then, is an excellent case
where B-Y Spectrosc0py from one laboratory and the reactions spec—
trosc0py from another laboratory supplement and complement each other.
By "the strange case" we mean the abrupt break in the de-
cay properties of the odd-mass N=81 isomer pairs (0 4.2.), that occurs
at Gdlhsg. By now there is a known series of seven N=81 isomer pairs,

the ground state in each case presumably being a single (1,3 neutron

/?

hole in the N=82 shell and the metastable state being an h11/7

neutron hole. The metastable state decays exlusively to the ground
State via an M4 transition in the lighter mass isotones, although

recently some direct branching has been observed from Sm1"3m decay

138

and from Gd”5m decay. More germane, on the netron—deficient side
of the N-81 series, the (\2623/2)”1 ground states of 58Ce139, 60Nd11+1
and 6281111“3 (Geig65,Bee68 and DeF68, respectively) all decay in a
very straightforward fashion to the "dB/2 states in their daughter
nuclei. A priori there was no reason to expect the decay of Gquégsg
to behave otherwise, yet it was soon discovered that there is essen-

tially no decay to the nd 2 ground state of Eu“+5 - its unhindered

5/
decay pepulates the two aforementioned high-lying states. We now
think we have a reasonable explanation for this, involving: 1) a

crossing of the vd3 and val/2 orbits so that the ground state of

/2
Gd”5 is really (val/2)'1, coupled with 2) a shift downward in
energy of the "hll/Z orbits, allowing an appreciable (nhll/z) comr
ponent in the deS wave function- There is now indirect evidence
(§ 4.2. and New70) for both of these, and if they be true, the Gd”5
can be described as a "straightforward" decay into high-lying three—

quasiparticle states, somewhat analogous to the decay (Bee69d) of

Nd139m. This will be discussed in 5 4.3.5. below.

139

4.3.2. Source Preparation

Gd1“59 sources were prepared primarily by the Sm1”“(r,2n)
Gdl“5 reaction, which has a Q value of -10.6 MeV (Myer65). 20—MeV r
beams (the threShold for Gdluu production), furnished by the Michigan
State University sector-focused cyclotron, were used to bombard en-
riched targets of Sméwo3 (95.10% Smluu, obtained from the Isotopes
Division, Oak Ridge National Laboratory). Typically, 25—mg targets
were bombarded for 1—2 minutes with 0.5—uA of beam current. We also
used the Sm1“”(u,3n)Gd1l+5 reaction (Q = —30.9 MeV) to prepare a few
sources, bombarding similar targets with 40—MeV 0's.

It is interesting to note the competing reactions that can
accompany (T,xn) reactions. After a bombardment at MSU to produce
Gdlua by the Sm1““(r,4n)Gd1l+3 reaction (Q = -3l.2 MeV) using 40-MeV
T's, we found that we had produced quite a pure source of Sm1“1m+9
(see § 4.4), most likely by a Sm1””(r,02n)8m1”l reaction (Q = -9.8
MeV). Also, on attempting to produce Dy1”7 by the Nd“*2(C12,7n)Dy1‘"7
reaction (Q = -74.9 MeV) using 70-120-MeV C12 beams from the Yale
University Heavy-Ion Accelerator, we found a sizable amount of Gd”5
to be present, presumably through the competing Nd1”2(C17,05n)Gd1”5
reaction (Q = ~56.2 MeV). And, as a climax we found we were also
able to produce Gd1H5 by the Smll”*(012,201372)Gd1'*5 reaction (Q - —38.4
MeV) which has an unexpectedly large cross section. It must proceed
by a combination of cluster stripping and compound nucleus formation.
The low binding energies of 0's in these neutron-deficient nuclei be-
low N=82 makes for large cross sections for evaporating u's as well

as n's. Not only does this cause a large number of different nuclides

140

to be made in most bombardments, thus complicating the task of
analysis, but also it may set a practical limit to the production of
nuclei farther from stability in this region by standard bombarding
techniques. Our bombardments by the 20—MeV T beam did, however, pro-
duce quite pure sources of Gdlusg. Here, apparently, the bombarding
energy was too low for any competing (T,axn) reaction. The next
higher mass nuclide, Gdlhe, which Should still have an appreciable
formation cross-section at this energy has a half-life of 48 d and
thus posed no problem. In addition, Eu“+5 has a half-life of 5.9 d
and a well worked-out decay scheme (Adam68a), so we did not have to
worry about contamination of the spectra by daughter transitions.
Each source was counted within 2—3 minutes of the end of
the bombardment and counted for varying intervals of time up to a
maximum of 80 minutes, approximately 4 half-lives. The y rays
attributed to Gdlusg decay all retained their constant relative in-

tensities over this period.

4.3.3. Experimental Data

 

4.3.3.A. Singles y-Ray Spectra. Two separate Gd(Li)

 

detectors were used to obtain the Gdlusg y-ray Spectra. One was a
7-cm3 active volume 5—sided coaxial detector (2o.5% efficient for
the Co60 l333-keV 7, compared with a 3X3-in. NaI(Tl) detector at
25 cm) manufactured in this laboratory, the other a 2.6% efficient
detector manufactured by Nuclear Diodes, Inc. The best

resolution we obtained was 2.3 keV FWHM for the Cor‘0 l333-keV

141

peak. Both detectors were used with roomrtemperature FET preampli—
fiers, linear amplifiers having near-Gaussian pulse shaping and
4096-channel analyzers or ADC'S interfaced to computers.

The y—ray energies were determined by counting the spectra
simultaneously with the standards listed in Table 2. The larger
peaks in the Spectrum were first calibrated by use of the standards.
These calibrated peaks, in turn, were used to determine the energies
of the weaker peaks in Spectra taken without the standards. The
centroids and net peak areas were determined with the aid of the com-
puter code SAMPO, as described in § 3.1.2. The backgrounds were first
subtracted and the centroids then determined by fitting the peaks
to Gaussian functions having exponential tails on both the upper and
lower sides of the peaks. The specific peak shapes were determined
by comparisons with reference peaks Specified at intervals through-
out the Spectrum. The energies were then determined by fitting the
centroids to a quadratic calibration equation. Peak areas are then
converted to y—ray intensities through curves previously determined
in this laboratory for each detector. These curves were obtained
by using a set of standard y-ray sources whose relative intensities
had been carefully measured with a 3X3-in. NaI(Tl) detector.

A word about the energies of the higher-energy y—rays
(EY > 1880.6 keV): Because of the weakness of these peaks it was
not possible to observe them in spectra when standards were counted
simultaneously. Thus, we had to resort to an extrapolation of our
calibration curves up into this region. Various polynomial extra—

polations were tried and discarded, for we found that a linear

142

extrapolation gave the best agreement between the energies of the
photopeak and those determined from double-escape peaks falling within
our well-calibrated energy range. One should be somewhat wary, how-
ever, of systematic errors in the energies of these y rays.

After taking Spectra from and following the decay of at
least 15 different Gdlusg sources prepared at widely differing times,
we have identified 38 Y rays as resulting from the B+/e decay of
Gdlqsg. A singles Spectrum taken with the 7—cm3 detector is shown
in Figure 29. A list of these y rays and their relative intensities
is given in Table 13, where they are compared with the results of
Newman, et a1. (New70). All values from our work are the averages
from many determinations, with the quoted errors reflecting the

statistical fluctuations found among the different runs.

4.3.3.B. Coincidence Spectra

l. Anticoincidence Spectra. One of the most convenient

 

”first steps" in elucidating a complex decay scheme such as that of
Gdlusg is to determine which transitions are ground-state transitions,
especially the primarily e-fed ground-state transitions. To obtain
such information.we performed an anticoincidence experiment between
the 7-cm3 Ge(Li) detector and an 8X8-in. NaI(Tl) split annulus.

This setup has been described in § 2.1.2.B., but in brief it works

as follows: The Ge(Li) detector is operated in an anticoincidence
tmode (resolving time, 21 2200 nsec) with either (optically isolated)
half of the annulus or the 3X3—in. detector. Thus, the system serves

both as a Compton-suppression and, more important, as a cascade-

143

 

- 5ND

 

I
(54205

GAMMA SPECTRUM OF 06"“

 

 

 

 

 

CHANNEL NUMBER

Figure 29.

Singles y—ray spectrum from Gd]””g.

 

144

 

 

Table 13. Energies and Relative Intensities
of y rays from the decay of Gdllfl’g

This work E. Newman, et 31.61
Energy(keV) Intensity Energy(keV) Intensity
329.5102 30.8:2.0 330.1 31
808.5:0.2 5100 808.4 —:—100
949.6+_0.3 8.6:0.3 949.4 5.9
953.4103 lS.8_+_0.3 953.7 11.8
1041.910. 11214.0 1041.9 107
1072.010. 31.1.0 1072.2 17.6
1567.4¢0. 10.410.2 1307 10.2
1599.930. 2030.4 1599.9 19.6
l7l9.4¢0. 13.3:0.1 1719.5 11.8
1757.810. 380110 1757.9 392
1784.410. 4.810.2
1806.935. 2.7:0.3
1845.410. 6.3:0.l 1844.7 4.7
1880.610. 364310 1880.6 384
1891.610. 4,910.2
2203.310. 2.2+,0.l 2202.8 7.1
2451.710. 3.6:0.2
2494.810. l4.5:0.5 2494.3 15.3
2581.810. 3.0:0.2
2642.220. 21.610.12 2642.9 25.9
2662.8;10. 6.7:0.7 2663.2 3.5

145
Table 13, continued

 

 

Our Work E. Newman, et a1.CZ
b c
Energy(keV) Intensity Energy» Intensity
2666.1¥0.4 7.2iO.1
2672.6:0.9 1.8i0.2 2674.0 2.4
2765.2il.5 1.9iO.l
2837.4:0.3 4.6iO.4 2837.7 9.8
2868.1:0.7 1.3:0.1
2907.0:0.4 l.2:0.l
2956.4¥O.2 1.5a
3236.0:0.5 1 6:0.2
3259.6iO.6 2.2:0.2
3285.6:0.5 l.7iO.1
d
3294.1:0.5 1.63
d
3369.8:0.5 0.88
3544.6¥0.5 1.69
d e
3602.8:0.5 1.0
3623.85.105 2.f
3666.61105 0.?
3685.9cii1.6 1.48 J,
781.3 3.1
914.6f 2.7
1070.2f 9.8
1781.9f 7.1
a(New70). bThe errors given on the intensities reflect only the statis—

tical scatter about the average over many runs.

The absolute uncer-

tainties will be larger, perhaps 110% for the more ingense peaks and
(narrespondingly greater for the less intense peaks. The intensities
:tven.in (New70) were renormalized so that the 808.5 keV yEIOO.
Tfliese y rays Show up only weakly (but consistently) in the spectra,
so we place them only tentatively as originating from Gdl 1‘59 decay.
eThese intensities may well be off by as much as a factor of 2.
f’I‘ransitions reported in (New70) for which we found no corresponding
truansitions. See the text for a discussion of these transitions.

146

suppression spectrometer. An anticoincidence Spectrum is shown in
Figure 30 and the relative intensities of the y rays.in this Spec-
trum are compared with those in the singles Spectra in Table 14.

2. Megachannel coincidence spectra. Our two-dimensional
"megachannel" coincidence experiment utilized two Ge(Li) detectors,
the Nuclear Diodes 2.5% detector and an ORTEC 3.6% detector. A block
diagram of the electronics is shwon in Figure 3. The experiment was
much like a standard fast-slow coincidence experiment, except that
both the x and y events were processed each time a fast coincident
event was detected. The x and y addresses were stored in the two
halves of a Single (32—bit) word in a dedicated buffer in the MSU
Cyclotron Laboratory Sigma-7 computer. When the buffer was filled,
events were collected in a second, similar buffer while the contents
of the first were written on magnetic tape. The spectra were re-
covered later off—line by a program that allowed one to obtain gated

"slices" with or without a linearly interpolated background sub-

traction.

The short half-life of col”59, coupled with the fact that
tflaere just are not too many coincidences associated with its decay,
Inakes it difficult to obatin "pretty" coincidence spectra. In order
tc> record as many coincidence events as possible during a limited
ccnxnting time, we used a 180° geometry for the detectors, although
ttuis can cause serious complications because of Compton scattering
between the detectors (Gie70). With repeated bombardments during a

l—ci period we were able to collect l.8><106 coincidence events, which

 

 

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148

Table 14. Relative Intensities of Gd”59 y rays in Coincidence

 

 

 

 

Experiments.
a Relative Intensities
Energy
(keV) Integral 511-511 Anti-
Singles Coinc. Coinc. Coinc.
329.5 30.8 60 24
803-5 .3100 2100 5100 86
949.6 8.6 18.4 5.5
153.4 15.8 19.3 11
1041.9 112 85.6 28.0 112
1072.0 31 35.6 21
1567.4 10.4 11
1599.9 20 0.64 21
1719.4 13.3 13.5 6.6
1757.8 380 216 100 507
1784.4 4.8
1806.9 2.7
1845.4 6.3 7.9
1880.6 364 171 86.8 497
1891.6 4,9
2203.3 4.4 5.6
2451.7 3.5
2494.8 14.5 1.5 20
2581.8 3.0 1.1
2642.2 21.6 30

 

 

“The errors for these y-ray energies are given in Table I.

bNo coincidence information was obtained above this energy.

149

were then analyzed. The integral coincidence spectra for the x
(2.5%) and y (3.6%) detectors, and six gated spectra (gates on x,
display from y), including background subtraction, are shown in
Figures 31 and 32. Of the slices taken, these were the only ones
that contained substantially useful information. Relative inten-
sities from the integral coincidence spectra are included in Table
14, and the results of the megachannel coincidence experiment
are summarized in Table 15.

An important gate that is missing from Figure 31 and
32 are the ones on the 329.5-keV y, which depOpulateS the first—
excited state in Eulus. Because of its position atop the intense
y: Compton edge, coincidence spectra gated on it, with or without
intricate or nonintricate background subtraction, could not be
"unconfused" from Spectra indicating 6+ feeding. Unfortunately,
this has ramifications on the construction of the decay scheme, as

will be Shown in 54.3.4.

3. Pair Spectra. The two halves of the 8XB-in. NaI(Tl)

 

Split annulus were used in conjunction with the 7-cm3 Ge(Li)
detector to determine the relative amounts of 8+ feeding to the
various levels in Bull‘s. Each half of the annulus was gated on
the Sill-keV 7: peak and a triple coincidence (resolving time,
21 2.100 nsec) was required among these and the Ge(Li) detector.
A resulting spectrum is shown in Figure 33. Note that double-

escape peaks are also enhanced in this spectrum. A discussion

150

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Table 15.

152

Summary of y-ray Coincidences in Gd1“59.

 

Gate Energy (keV)

y's Enhanced (keV)

 

Integral

808.5
949.6
953.4
1041.9
1072.0
1757.8
1880.6

511-511

Anti

329.5, 808.5, 949.6, 953.4,
(1041.9)“, 1072.0, 1719.4

949.6, 1072.0

808.5

(329.5)b, (893.2)c

(329.5)b, 808.5

1*.

Y

i

Y

808.5, 1041.9, 1757.8, 1880.6
2494.8d, 2642.2d
1041.9, 1567.4, 1599.9, 1757.8,

1845.4, 1880.6, 2203.3, 2494.8,

M

 

QAs seen in Table II, the intensity for this transition is less than

in singles. This is reasonable since it is only weakly fed by two

Y transitions and 3+.

bThis transition appears weakly in the gated spectrum.

c?rom.EuJ“5 decay.

dThis peak is very weak in the Sll—Sll—keV spectrum.

153

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154

of the 6+ feedings extracted from this experiment is deferred until
§4.3.5., where they are presented in Table 16.

4.3.3.C. Half-Life Determination for Gdlusg. The half-
life of Gdthg was determined by following the net peak areas
of the 1757.8- and 1880.6-keV peaks as a function of time. We
used a 50—MHz ADC interfaced to the MSU Cyclotron Laboratory Sigma-7
computer for this experiment. A code called GEORGE (GEOR) allowed
us to take data, have a live display on an ll—in. scope, and dump
the displayed data onto the computed disc at precise intervals that
were determined at the beginning of the run. The sequence of events:
count for the predetermined length of time, stop the counting, dump
the spectrum onto the disc, erase the memory and begin counting
again. The entire dumping process takes significantly less than 1
sec. The spectra can be punched on cards later as they are re-
moved from the disc, thereby making the start and stop times of
data acquistion independent of the card punching time. A pulser
peak was included in each spectrum so that dead—time corrections
could be properly applied to the data. In this manner the half—
life can be measured independently for any or all of the peaks in
the entire spectrum.

Forty consecutive spectra were obtained for each of the
two peaks at 1757.8 and 1880.6 keV, each one representing a 2-minute
time span. After background subtraction and dead-time corrections

the points were least-squared to straight lines (semilog). From an

155

average of these calculations we determined the half—life of Gd1”59
to be 21.8:0.6 minutes, to be compared with the less precise value
of 25 minutes obtained by Grover (GR059). Figure 34 shows the half-
life curve obtained by observing the decay of the 1757.8-keV peak in,

one series of Spectra.

4.3.4. Proposed Decay Scheme

 

Our prOposed decay scheme for Gd1“59 is shown in Figure 35.
It is larely in agreement with the level scheme proposed by Newman,
et a1 (New70), the main differences being our omission of their
proposed levels at 2112.0, 2662.5, and 3167.2 keV and our addition
of nine new levels at 953.4, 1567.3, 2203.3, 2642.2, 3236.0, 3259.6,
3285.6, 3623.8, and 4411.3 keV. 0f the 38 y rays listed in Table
13, 26 have been placed in the decay scheme accounting for over 97%
of the total y-ray intensity. It is entirely possible that many of
the remaining y rays proceed from levels that decay via single
transition. These y rays were all too weak to have been seen in any
of our coincidence work, so, with no further evidence for their
placement, we have omitted them entirely.

The assigned spins and parities, discussed in §4.3.5.,
represent a combination of deductions from our work and also the
conclusions of Newman, et al., for the states observed via the
Sm11'1('r,d)Eu“‘5 reaction. The results of the two studies are in
good agreement for most states. We calculated (see §4.l.4.) the

total e-decay to be 2 5 MeV. The B+/e ratios displayed on Figure 35

156

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158

are calculated values using the methods of Zweifel (Zwe157).

We shall see later (cf. Table 16) that our experimentally deduced
ratios for some of the more hindered transitions do not agree with
these values. However, we do not have experimental values for
many of the states, and to be consistent we have used the cal—
culated values. This does not alter any significant conclusions

presented on the decay scheme.

The relative y-ray intensities listed in Tabele 13 were
based on a value of 100 for the 808.5-keV y. The relative x-ray
intensity was not measured. Thus, the intensities given on the
decay scheme are based on the assumption that there is no direct
B decay to the Eu1”5(d5/2) ground state. This seems to be a good
assumption in several respects. First, in light of good evidence
(§4.2 and New70) for the ground state of Gdll“5 being predominantly
an sl/Zstate, a direct transition to the Eu1”5 ground state would
‘be a second-forbidden transition. Also, Newman, et al., determined
that the =25-minute component of the 7: could be accounted for by
.assuming no 8+ decay to the ground state, based on the B+YK x—ray
'value of 0.6 obtained by Grover.

Specific evidence for the placement of levels and
transitions in the decay scheme is given as follows:
(lround, 329.5-, 716.0—, 808.5-, and 1041.9—keV States. These states
were all pOpulated strongly by the Sm“"‘(r,d)(‘;d1 [*5 reaction and
appear to be essentially single-particle states, viz., the

cis/Q, 97,2, h11/2,81/2, and d3/2 in that order. We also see

159

specific evidence for the 329.5-, 808.5-, and 1041.9—keV levels.
The 716.0—keV state is the "hll/Z isomeric state, which is not
papulated by the decay of Gdlhsm but is populated by the decay
(54.2) of Gdlhsg.

As seen in the integral coincidence spectra of Figure 31,
the vi Compton background peaks near the 329.5-keV y, so no
reliable information can be obtained from a gate on this Y ray.
That it is indeed involved in cascades is indicated by the
anticoincidence spectrum (Figure 30), where its intensity is
diminished. The four transitions into the 329.5-keV state were
placed strictly on the basis of energy differences. From the
intensity balances, we deduce that the 329.5—keV state receives
0.552 e and 1.5% 8+ feeding. Also, the vi coincidence spectrum
(Figure 33) shows the 329.5-keV y. However, this much B+le feeding
implies a log ft of 7.5, which is much lower than reasonable
considering that the transition to this state would most likely
be a 1/2+ + 7/2+, i.e., second forbidden, transition. And, although
the 329.5 lies in a particularily bad place for a precise intensity
determination, we do not think that our intensity value (or that
of Newman, et a1.) can be wrong enough to give us this low log ft
value artificially. In addition, although we could have missed
placing several y rays that feed into the 329.5—keV level from
above, the overall intensity of the unplaced y rays is rather
small, so it would be difficult to alter the intensity balance

by placing them. We are left with a B+/€ feeding that we do not

160

believe but cannot explain away easily.

The placement of the 808.5-keV y as proceeding from a
level of the same energy is consistent with our coinciden.3 and
anticoincidence data. The 949.6— and 1072.0—keV y's can be seen
to be in coincidence with the 808.5-keV y in Figure 31. The 2451.7-
and 3602.8—keV y's are too weak to be picked up in our coincidence
spectra and were placed purely by energy differences. As we
shall see in §4.3.5, the 808.5-keV state is a 1/2+ state, which is
consistent with its depopulating only to the ground state. The
log ft of 6.9 is somewhat high for an allowed transition, but it
falls within a reasonable range, and we shall see that the trans-
ition involved a multi-particle rearrangement, so it would be
expected to be slow.

The 1041.9-keV y can also be seen to be a ground-state
transition, as it is enhanced in the anticoincidence spectrum.
There are no strong coincidences in the 1041.9-keV gated spectrum
(Figure 31), again suggesting direct decay to the ground state.
The 2581.8— and 3369.8-keV y's, too weak to be seen in our
coincidence spectra, were placed solely on the basis of energy
differences. The log ft for B+le population of the 1041.9-keV
state is quite in line with an allowed transition, consistent
'with the assignment of this state as 3/2+ by Newman, et a1.

1757.8- and 1880.6-keV States. The two intense Y rays at

 

1757.8 and 1880.6 keV dominate the entire Gdlusg y-ray Spectrum.

They are enhanced in the anticoincidence spectrum and depressed in

161

the integral coincidence spectra, and the spectra gated on them
(Figures 31 and 32) show nothing other than yi. Thus, they are well
established as ground-state transitions from levels having the same
energies. Further, the 808.5—keV gated spectrum showed that each

of these two states decays additionally through the 808.5-keV

level. Together, these two states receive 71.9% of the total

B+le population from Gdlusg. The low log ft (5.6 for each) values
certainly suggest allowed transitions, and, assuming the 1/2+ ground
state assignment for Gdlksg, this means that the states are 1/2+

or 3/2+. This is consistent both with their decaying directly to
the ground state and through the 1/2+ 808.5—keV state. The 1757.8-
keV state appears to be excited only slightly in the Sm1””(1,d)Gdlusg
reaction (New70) and it is not clear whether the 1880.6-keV state

is excited or not (it falls too close to the peak from the 1843—
keV state). Needless to say, neither state appears to be simple in
structure, and we shall explain both of them as three-quasiparticle
states in the next section.

953.4- and 2672.6-keV Levels. These levels were placed on the

 

basis of moderately convincing, although by no means airtight,
coincidence results. Both the 953.4- and the 1719.4-keV y's were
enhanced in the integral coincidence Spectra, neither was enhanced
in the anticoincidence spectrum, and neither could be detected

in the pair spectrum, implying that 8+ feeding could not account
for their appearance in the coincidence spectra. Unfortunately,

'both are weak enough that the gated spectrum on the 949.6-953.4-

162

keV region proved inconclusive. Additionally, the sum, 953.4 +
1719.4 = 2672.8 keV, so we place levels at 953.4 and 2672.6 keV,
the order of the two transitions being chosen because of their
relative intensities.

1567.3—, 1599.91, 1845.4-, 2203.3—, 2494.8— and 2642.2—keV Levels.
These levels were placed on the basis of their respective ground-
state transitions being enhanced in the anticoincidence spectrum.
Newman, et al., also observed states at 1843 and 2480 (doublet)
keV excited by the (T,d) reaction.

The Remaining Levels: 3236.0, 3259.6, 3285.6, 3623.8, and

 

4411.3 keV. Because of the weakness of the y rays, no coincidence
data of any significance could be obtained above the line at 2642.2
keV. Thus, these four levels had to be placed solely on the basis
of sums and must be considered as tentative. Under "normal"
circumstances we would not venture to suggest levels on just this
basis, but here there are mitigating circumstances. First, the
precision of the sums is quite good, considering the energies and
intensities involved: 0.5, 0.6, 0.3, 0.2 and 0.5 keV for the

five levels, respectively. Second, the states are spaced rather
widely apart in the nucleus with the y rays having reasonably
disparate energies. In addition, each level does account for at
least two y transitions to lower, well founded levels. Such would
tend to make accidental agreements less probable than under normal
circumstances; yet it must be remembered that these are by no means
random numbers, and there may be some subtle, insidious relations

not recognized. Thus, bear in mind: Tentative.

163

4.3.5. Discussion.

 

Some twenty states have now been placed, with varying
degrees of confidence, in Eulus. In some respects, then, this
nucleus finds itself among the better known members of the N = 82
series. All five major proton orbits between Z = 50 and 82 lie
reasonably close together, resulting in relatively low-lying
single-particle states that are not so fragmented as in the lighter
N = 82 isotones. Also, the peculiar decay properties of Gdlhsg
give us some information about what appear to be three-quasiparticle

states.

4.3.5.A. Single-Particle States. The five states at 0,

 

329.5, 716.0, 808.5 and 1041.9 keV comprize the major components
of all of the single-proton orbits between Z a 50 and 82, viz.,

h and d3/2’ respectively. This was amply

075/2, 97/2, 11/2,81/2

demonstrated by Newman, et a1. (New70), in their (T,d) scattering
reaction, where their spectroscopic factors indicated precisely
the occupations expected for adding a proton to a Z a 62 nucleus.
The 5/2+ nature of the ground state is also corroborated
by the decay properties (Adam68a) of Eu”5 itself. The primary
component of its wave function appears to be just what one might
expect from a simple shell-model picture, (ng7/2)8(fld5/2)5 above the
closed Z = 50 shell. Note, now, that there is little or no B+/c

decay (log ft 3 7) from the Gdlhsg to this nd ground state. Herein

5/2

lies the first half of the Gd1”33 "strange case", for both Nd‘”13

and Smlhag decay (Bee68) quite readily (logfi =5.3) to the wd3/2

164

ground states of their respective daughters, in simple shell model
terms this decay being (ng7/2)8 (nd5/2)2(vd3/2)-1—+(1rg7/2)8 (1! 5/2)

for Ndlulg and (flg7/z)8(wdslz)”(ud3/2)"1-+(wg7/2)8(wd5/2)3 for
Sm173g. There are many ways in which one could explain away a
milder retardation of the Gd1”59 decay to the Eu1”5 ground state,

but the only reasonable explanation that we find for the experimental
fact (hindered by at least a factor of 100 and probably much more)

is that the ground state of Gdlus is not a (vd3/2)'1 state but in-
stead a (val/2).1 state. Newman, et al., also came to this conclu-
sion. Some reasonable indirect evidence for this is available, viz.,
the (V81/2)-1 state does progress to lower energies with increasing

Z in the N-81 nuclei: it lies at 281 keV (Bir63) in Ba137, at 250 keV
(Bir63 and Yap70) in Cel39, and at 195 keV (Wild70) in the Nd1“1.

Thus, it might be expected to have replaced the (vd )-1 state by

3/2
Gdlhs. However, in our study (5 4.2.) of Gdlhsm we were neither
able to confirm nor to deny this. Thus, it must be admitted that

there is only indirect for this 8 assignment, but more will be

1/2
said about it in the next section.
The 0197/2)"1 state (actually a (ng7/2)7(d5/2)2n...state -
‘more about the dots and the pairing force in the next section) at
329.5 keV is well-established, but, quite surprisingly, it may re-
ceive a small amount of B+/e population, with the log ft being =7.5.
.Actually, we do not believe this, and, considering the uncertainty
in the intensity of the 329.5-keV y because of its position in the
spectrum, perhaps most of the feedings can be attributed to experi-

tnental difficulties. The results, however, are duly recorded on Fig-

ure 35.

165

As expected the h state at 716.0 keV is not populated

11/2
by Gd1“5g decay, although we noted (§4.2.) its being populated di-

rectly by 4.7% the Gdlugfl decays. The log ft was found to be 6.2.

The fact that such a direct decay takes place implies some population

of the h11/2 orbit by proton pairs in Gdlqs. This, as we shall see p
in the next section, is the second clue toward explaining the
"strange case" of Gdlusg.

The B+le decay to the s 808.5— and d3/2 1041.9-keV

1/2

 

states, with respective log ft's of 6.9 and 6.5, appear to be a1-

."n' J

lowed transitions. However, note that these are somwhat high log ft
values for allowed transitions eSpecially, when compared with the log
ft's for decay to the 1757.8— and 1880.6-keV states. The implication
could be that they are not altogether straightforward transitions.
Also, as can be seen in Table 16, the e(tot)/B+ ratios for decay to
these states are large compared with the predicted (Zwe157) ratios
for straightforward allowed transitions. Often such squelching of
the 8+ branch is also indicative of complexities in the decay process.

This, then, is the third clue.

4.3.5.3. Three-Quasiparticle States

 

The fourth and most obvious clue, of course, is the strong
decay of Gd“+59 to the states at 1757.8 and 1880.6 keV. These two
states account for 722 of the Cdthg decay, and the low log ft's,
both 5.6, clearly indicate non-hindered allowed transitions. Now,
the state at :1757 keV p0pulated by an i=2 transfer (transfer (im—

plying I"= 3/2+) in the (T,d) experiment of Newman, et al., may

166

or may not be the same as the 1757.8—keV state populated by GdlkSg
decay. In any event, the extracted Spectrosc0pic factor (028) was
only 0.02, indicating the structure of that state to be more com-
plicated (or at least different) that what could be attained by a

simple drOpping of a proton into a vacant or semi-vacant Smlun orbit.

"a

The 1880.6-keV state may or may not have been p0pulated (Wild70) (cf.

Fig. 3 of New70) in the (T,d) experiment, but if p0pu1ated at all it

V_.__.__—_.-.-——
. . - .

-u~‘ "' ‘, ’fi. .

was only to the slightest extent. Also, in their shell—model cal-
culations using a very truncated basis set (proton states above con-
sidered, g7/2 and dS/Z orbits deginerate and occupied by pairs, and
the only allowed states resulting from the single odd proton moving
from orbit to orbit with or without the breaking of a single addi-
tional pair, but never more than one proton to be promoted into the
h11/2’ 31/2, or d3/2 orbit region), Newman, et al., were unable to
construct states corresponding to the 1757.8- and 1880.6-keV states.
Our inference here is that perhaps these states involve the promotion
of more than one proton into the hll/Z’ 81/2, and d3/2 region or,
considering that they lie well above the pairing gap, they involve
broken neutron pairs.

We have arrived at a simple shell—model picture that,
qualitatively at least, explains all four clues, or effects, quite
‘well: 1) no B+/e population ot the Eu“‘5 ground state, 2) some
direct population of the 716.0-keV state by Gdlusm, 3) hindered
transitions to the s and d states, and 4) fast transitions

1/2 3/2

to the 1757.8- and 1880.6-keV states - meaning that these last go by

167

major components of the wave functions and not minor admixtures. Our
model is outlined in stylized form in Figure 36 and involves two as-
sumptions: l) the ground state of Gd“‘5 is indeed a (V81/2)—1 state

and 2) there is appreciable population of the h orbit by proton

11/2
pairs in both Gdthg and Gdlksm. Both have already been implicitly

discussed and 2) has been directly proven by the population of the

716.0-keV h state by Gdluan (cf. the appropriate transition in

11/2
Figure 36). [A150, compare the rapid drop in positon of the h11/2
state from 1.1 MeV in PrlL‘1 to 716.0 keV in Eulus. It should lie

le5

even lower in G , and the pairing force should insure its partial

occupation simply by virtue of its large degeneracy.]

145 ground state

Lack of appreciable p0pu1ation to the Eu
comes about naturally if Gdlusg is (val/2)'1. Protons in the oc-
cupied orbits, 97,2, dS/z’ and to some extent hll/z’ should have
little tendency to transform into an 81/2 neutron. Even the most
favorable case, nd5/2—évs1/2, should be slow.

Now, there are well—documented cases of B+/e decay into
high-lying three-quasiparticle states from the nearly nuclei Nd139m
(Bee68 and McH69a) and Smth" (54.5), both of which follow quite
straightforwardly from simple shell-model considerations. Looking
about for analogous transitions in the present case, one is immedi-
ately struck by the availability of the vh9/2 orbit — by a crude
extrapolation from the lead—bismuth region we would predict it to
orbits. Thus, the

lie some 1.5-2.5 MeV higher than the s or d

1/2 3/2

primary decay of Gdlusg can be represented as "hll/Z-évh9/2’ or more

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169
completely, (1th]1,2)2n(\)s1/2)u1 + (nh11/2)2n_1(vh9/2)(v31/2)-1 .
This would make the 1757.8- and 1880.6-keV states three-quasiparticle

states having the primary configuration, (nh )(vh9/2)(vs )—1.

11/2 1/2

This model also explains the hindrance of the B+le decay
to the 808.5- (81,2) and 1041.9-keV (d3/2) states in Eu175. Each
would require, in addition to the unfavorable transformation of a
proton into an 81/2 neutron, a promotion of the remaining proton in-
to a higher orbit. Thus, these transitions probably proceed primarily
through admixtures.

Appealing though it be, this explanation must at this time
remain a hypothesis, for we have no direct proof of l) the (val/2)-l
nature of Gd1“59 and 2) the fact that it is specifically the “ha/2
orbit that participates in the three—quasiparticle states. Informa-
tion would be useful concerning Dy1”7M+g, the next member of the series,
but it is far enough from stability to present formidable preparation
difficulties (§4.5.). The same is true for Tblus, which could popu-
late states in Gdlus. Perhaps more promising would be the study of
Gd”5 states via the Sm1”“(r,2ny) reaction.

4.3.5.0. The Remaining States.

Relatively little can be deduced about the remaining states
at this time. The 953.4-keV state is anybodys guess. Although placed
by reasonably convincing coincidence data, we have no clues as to its
structure. The remaining states are all populated by transitions
having log ft's in the range of allowed or fast first-forbidden tran-
sitions. Thus, they are all probably 1/2 or 3/2 states, with the

majority having even parity. One word about the 1599.9-keV state:

170
We observe its being populated by Gdlhsg decay, which implies a 1/2
or 3/2 assignment. This is incompatible with the 7/2+ assignment
made by Newman, et al., but they consider the statistics in their
angular distribution for this state to be poor enough to make that
assignment somewhat questionable.
4.3.5.D. a 8+ Ratios.

From our yi gated spectrum (Figure 33) we obtained rela-
tive 8+ feedings to seven of the Eu“+5 states. The deduced e/B+
ratios for the transitions to these states are listed in Table 16,
where they are compared with the theoretical ratios calculated by
Zweifel's methods (ZweiS7). We normalized the experimental values
on the transition to the 1757.8-keV state, which we think is one
of the two most straightforward transitions in the entire decay
scheme. (If one normalizes to, say, the 808.5-keV state, then the
8+ feeding to the other states quickly exceeds 100%.) It can be
seen that the s/B+ ratio appears to be a fairly sensitive test of
the degree of hindrance of a transition, for it does not take much
to depress the 8+ feeding per se. Unfortunately, the entire theoret-
ical consideration of e/B+ ratios vs forbiddeness needs serious
overhauling, so little can be said in a quantitative sense at this

time.

171

Table 16. Comparison of Experimental and Theoretical e(tot)/B+
Ratios for Decay to States in Eulus.

 

 

 

Energya e(tot)/B+
(keV)
Experimental Theoreticalb

808.5 11 0.36
1041.9 1.6 0.65
1599.9 19 1.2
1757.8 51.4c 1.4
1880.6 1.7 1.7
2494.8 5.0 5.0
2642.2 12 7.1

 

8These are the only states in Eu“5 that are measurably fed by
8+, as determined from the yi gated coincidence spectrum.

bThese values are anly as precise as can be read from the graphs
in Ref. (T167).

cThe experimental ratios were normalized to the theoretical ratios
by assuming that the transition to the 1757.8-keV states is al-
lowed and unhindered, presumably yielding the expected ratio.

172

4.4. The Decay of Smlulm and Smlulg.
4.4.1. Introduction

Our interest in the decay of Smlhl was stimulated by
the investigation of the decay of Nd139m (Bee69d) which was carried
out here at MSU. Six levels in Pr139 at relatively high energies
are selectively populated by the isomeric decay of Nd139. These
levels have been characterized as three-quasiparticle excitations
which decay predominantly to the h11/2 state in Pr139. Work
on this nucleus led to the prediction (McH69j) that other N = 77
or 79 nuclei (specifically Sm1“‘m and Nd137m ) might possess
similar states. Quite specific and stringent requirements must
be met for the population of this type of state. The parent nust
contain a high spin, low energy isomeric level which decays.
predominantly via an e/B+ branch. In addition, the decay energy
mmst be sufficient for the p0pu1ation of levels above the pairing
energy gap of the daughter nucleus.

Prior to the present investigation very little work
had been done on Sm1”1. In fact, prior to 1967 it is doubtful
vdJether it had been observed at all. In 1957 an activity, reported
as Sminl, was assigned a half-life of 17.5 to 22 days (Pav57) and
then in 1966 there was a report (Lad66) concluding that 8111“"1 must
lmave a much shorter half-life and, in fact, was probably less
than 3 days. Correct identification of the Smlul species seems
to have first been made correctly at about the same time by a

German group and a Russian group (Bley67 and Ar167). Their results

173

are summarized in Table 17. The principle disagreement between
our data and theirs is the half—life for Sml ”19. As will be
discussed in 54.4.8, this half-life is still somewhat uncertain
(being a choice between 10.0 and 11.3 minutes). Our half-life
value of 22.1 minutes for the Sm171m decay is consistent with these
other recently reported values. Hesse, in a more recent and more
complete article(Hess69) on Smlulm, has reported 32 y rays as
belonging to the decay of this species. These results are
compared with ours in §4.4.4.

We have indeed found the decay of Smlhlm to exhibit
similar characteristics to Nd139m. Sm1”1m seems also to have 6
states which have log ft values ( average a 6.1) consistent with
their being fed by allowed 8 transitions. Also, these states decay
predominantly through the 628.6-keV state which has been identified
as the h These states will be discussed in §4.4.11 in the

11/2'
light of what is known about three-quasiparticle states.

174

 

 

 

Table 17. Published Data for Sm“+1
Authors Half-life Half-life 2M4“ E'Y for
for Sm1”1m for Sm1“19 Transition M4
(Arl67) 21.5 min. <10 min. - 215 keV
(Bley67) 23.5 min = 2 min. <12 3 200 keV

 

 

a
Estimated Values

175

4.4.2. Source Preparation
The principle means of producing Sm“+1 has been by the

Nd1‘*2(He3,4n)Sm1"'1 reaction (Q= —27.3 MeV), although Smll+1 has also
been produced indirectly by the Smlb'1(p,4n)Eull+1 reaction (Q= -31.2
MeV). This second reaction was used primarily for the purpose of
enhancing the Sm1“19 species and also as an additional verification
that the 438.2—kev transition is not associated with the Smlulg de—
5 4.4.9.

cay. The results via this reaciton will be discussed in

For the He3 runs 25 mg targets of separated isotope Nd;”20,

(>902 Nd192) were bombarded with a beam energy of 35 MeV and a

current of 0.1—1.0 pa. Targets were bombarded for periods of 1-5

minutes. For the proton runs, 40 MeV beams of 0.5 us were used in

one minute bombardments.

Due to the short half—life of both Smlulg and Smlulm (11,3
:minutas and 22.1 minutes, respectively) no attempt was made to
chanically separate these species from unwanted contaminants.

The primary means of determining which y rays are associated
with the decay of each of the 311,141 species was by comparison of
relative intensities of the Y rays in four consecutive spectra, each
of which represented a 15 minute counting interval with the first
spectrxun starting two minutes after the and of each bombardment.
These 4096-channal spectra were obtained by use of a routing circuit.
This method allowed us to keep the four quadrants in the Sigma-7
memory simultaneously with no necessity of dumping the data between
This also allowed us to accumulate data from several

spectra.

targets in each of the quadrants. In general, it was relatively

176

easy to pick out the Smluhn transitions by this method. However,
the Sml‘hlg transitions, with the exception of the 403.9-keV trans-
ition, are quite weak and considerably more difficult to ascertain.
These determinations were complicated by several factors. Due to
to both activities having short half-lives, it was necessary to
begin counting the target material quite soon after bombardment.
Thus, other short-lived activities could not be kept out of the
spectra. Also, Sml‘fll77 and Smlhky have half-lives which are so
comparable it is difficult to obtain a spectrum of SmluD" (having
the longer half-life) by waiting for the Smlklg to decay. It is
difficult to obtain meaningful statistics for some of the weakest
observable transitions - a particularly acute problem for any
short half-life species studied by off-line techniques. Many
cyclotron bombardments must be made to complete a given experiment,
and a compromise must be reached between using unlimited cyclotron
time and minimum acceptable statistics for the experiment. This
meant, for example, that the Sm”l 2-dimension coincidence data
show quite low statistics for the gated spectra. Another problem
is that as solid state detectors become more efficient and exhibit
ever improving resolution, many very weak peaks become noticeable
in the spectra. Many are too weak to obtain a measure of their
half-lives and cannot easily be assigned to a specific activity.
Still another problem with short half-life studies in general is
the problem of competing activities. As the desired reaction

takes one farther and farther from beta stability, reactions com-

peting with (p,xn) and (He3,xn) become a problem. Reactions such

177

£6 (p.0xn) and (He3gixn) begin to contribute measurably to the pro—

duct activities.
All of the above mentioned problems were encountered in the

Sm171m+9 investigations.

4.4.3. Half—Life Determinations for Smlulm and Smlulg

The half-lives for both Smlulm and Sm1”19 were determined
with the help of a computer code called GEORGE (GEOR). This code
has been described previously in §4.2.2. A pulser peak was in-
cluded in each spectrum for determination of the proper dead-time
correction. The net peak areas, corrected for dead—time, result-
ing from the analysis of the spectra, were used in the usual
manner for the half-life determinations. The Sm1”V" half-life was
determined independently from the 196.6-kaV, 43.9-keV and the 538.5-
keV peaks. Series of spectra were obtained at two minute time inter-
vals. The results of one analysis, using the 196.6-keV peak, are
shown in Figure 37. The data points obtained were least-square
fitted to a straight line (on a semi-log plot) to obtain the half-
life value. The results for each of the above mentioned peaks were
averaged to arrive at the value of 22.1:0.3 minutes for the half-
life of SmIW". The s...”19 half-life was determined from the 403.9-
keV peak only, since this is the only intense peak in the ground
state spectrum. The results of one of the analyses is shown in
Figure 38. These data points were obtained from spectra taken at
one minute intervals. An average of the least-squared results

yields a value of 11.3:0.3 minutes for the half-life of Smlulg,

178

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Figure 38. Half-life curves for the 403.9— and 438.2-keV peaks.

180

4.4.4. Smlul Y—ray Spectra

4.4.4.A. Singles Spectra

141m

The Y rays associated with the decay of Sm were ascer-

tained by their relative intensities in four 4096 channel spectra as
described in § 4.4.2. These singles Spectra were obtained with the
2.5% Ge(Li) detector as described in § 2.2.1. Figures 39 and 40
show the first and fourth of these spectra, respectively. Only the
Y rays assigned to either Smlulm or Smlulg have energies shown on the
figures. From their erratic intensity behavior many of the other
peaks can be ruled out as belonging to Smlul. These unclaimed Y rays
are listed separately in 5 4.4.12.

All of the data analysis was accomplished by use of either
MOIRAE orSAMPO, both of which are described in § 3.1. Y—ray energies
were determined from spectra taken by simultaneously counting with
Y-ray standards which have been listed previously in Table 2. Various
combinations of these standards were used in Sm1”1 spectra at dif-
ferent times and with different experimental setups. The centroids
determined for the standard peaks were used to prepare energy cali—
bration curves (generally quadratic) whereby energy determinations
for the intense Smlul peaks could be made. These intense peaks were
then used as internal standards for the energy determinations for
the remainder of the peaks in other spectra obtained in the absence
of y-ray standards.

Transition intensities were determined by correcting the
net peak areas by use of detector efficiency curves which have been

constructed for each detector.

181

 

     

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183

By this technique we have assigned 32 Y rays as belonging to
the decay of Smlulm. The energies and relative intensities of these
transitions are presented in Table 18 along with the recently pub-
lished results by Hesse (Hess 69). These two sets of data are seen
to be in substantial agreement with each other. We have included Y
rays with energies of 247.9 keV, 577.8 keV, 607.9 keV, 955.4 keV,
974.1 keV, 1029.6 keV and 1108.4 keV which have not been reported by
Hesse. Conversely, Hesse has reported Y rays with energies of 1136.6
keV, 1530.7 keV, 1879.9 keV, 1966.6 keV, 2281.1 keV, 2302.6 keV and
2582.3 keV which we do not include with the decay of SmluD". The
1136.6-keV, 1530.7-keV, 1966.6-keV, 2281.1-keV, 2302.6-keV and
2582.3-keV peaks do not show up in our spectra within the limits of
our statistics. Therefore, we can say nothing about them. There is

some question as to whether the reported 1879.0-keV peak is due to

the daughter Pm”1 activity.

4.4.4.8. Prompt Coincidence Spectra

 

Several types of prompt coincidence experiments have been
carried out. These included 2-dimensiona1 coincidence experiments, 511
keV coincidence experiments and anticoincidence experiments. More da-
tail on the setup of these experiments is given in Chapter II.

The 2-dimansional coincidence experiments actually yield a
2-D (5 2.1.D) array (4096X4096) of prompt coincidence events (21 -
100 as). For the Sm“l investigation, regions of the resulting x-
axis integral spectrum were gated. All events in prompt coincidence
(on the y-axis) with the events falling in the gate were assembled
and output as a gated coincidence spectrum. Thus, the plots of the

2-dimensional coincidence data in Figure 41 show gated spectra

184

Table 18. Energies and Relative Intensities of~yRays from the Decay

 

 

 

 

of &m“1m.

This Work Hessea
Energy Intensity Energy Intensity
(keV) (keV)
196.6i0.3 184 :18 196.5 0.5 260.i30
247.9i0.2 1.91iO-35
431.8:0.1 100 :5 431.7»0.5 100:10
538.5t0.3 20.9 11.4 538.0'0.5 1815
577.810.3 2,2440,60
607.9+0.2 25410.30
628.7iO.l 6.6210.20 628.3.0.3 6.8+1.0
684.6:O.2 19.6 i1.5 684.2i0.5 21.8:2.6
725.710.5 3.59i0-60 726.3i0.7 9.9il.7
750.3:0.3 3.94i0.60 749.5i0.8 4.611.0
777.4:O.3 50.3 i2.0 777.110.5 58.2+7.0
785.9i0.1 16.9 $1.0 785.8+0.5 20.712.5
805.9i0.1 8.80f1.6 806.OIO.6 10.8+1.6
837.1:0.2 8.87t0.30 836.7+0.7 11.5+3.0
875.0i0.l 3.0910.10 874.6r0.7 4.6+1.0
896.5i0.1 3.5910.40 896.2*O.7 S.6+1.5
911.3+0.3 22.8 10.60 911.1.o.s 26.5'3.5
924.7i0.l 5.6710.80 924.4»O.7 6.9Il.3
955.4i0.5 1.67t0.10
974.110.5 0.50i0.10

983.3i0.3 18.0 i0.80 982.9*0.5 21.613.5

185

Table 18, Continued.

 

 

 

This Work Hesse‘:Z
Energy Intensity Energy Intensity
(keV) (keV)
1009.1i0.4 7.23t0.60 1008.3:0.5 10.512.0
1029.6i0.6 1.25:0.30
1108.4:0.2 3.07:0.25
1117.6i0.2 8.04i0.60 1117.2;O.6 11.1t1.8
1145.1i0.2 . 21.6 i0.80 1144.9i0.5 27.5i4.0
1463.4f0.6 4.47i0,80 l462.1:0.8 5.4:2.0
1490.3i0.l 22.9 :1.5 1490.2:O.5 27.4r3.5
1786.4i0.4 27.1 :1.10 l785.9:0.6 33.6i4.0
1898.0f1.0 0.94:0.15 1898.5 1 2 2.5t1 O
1979.6‘50-2 0.99i0.12 1979.210.8 l.6i0.7
2073.710.2 3.53il.2 2072.9*0.6 11.812.0
b
1136.6:O.8 5.2+1.5
b
1530.7il.0 2&1
b
1879.9i0.8 6.3il.5
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1966.9:0 8 2.511 0
b
2281.1:l.0 1.5+0.5
b
2302.6:1.0 1.110.4
b
2582.311.0 2.9iO.8

 

 

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These transitions could not be identified in the present investigation.

 

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

    

  
 

 

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resulting as subsets of the y—axis integral spectrum. .In this figure
the x-axis and y-axis integral spectra are shown in addition to 21
gated spectra. In spite of the low statistics exhibited by some of
the gated spectra, much useful information has been gleaned from them.
The implications of these spectra will be explored fully in §4.4.6.

The 511 keV-511 keV coincidence spectrum shown in Figure 42 was
obtained with the NaI(Tl) split annulus and the 2.5% Ge(Li) detector
in an arrangement described in 2.1.2.C. For this run, the single
channel analyzers associated with the annulus had their windows ad-
justed to accept only the 511-keV peaks. Coincidence pulses (21 =
lOOns) were required between each half of the annulus in order for
the fast coincidence module to generate a gate signal. Thus, Figure
42 shows only those transitions aesociated with levels being fed by
3+ emission and those peaks due to the double escape process. The
511-keV annihilation peak in the spectrum is a measure of the chance
contributions to the spectrum.

The anticoincidence set-up described in § 2.1.2.B. was used to
obtain the spectrum in Figure 43. Anticoincidence spectra show en-
hanced those transitions which are not in prompt coincidence with
other rays or with 3+ emission. This technique is particularly use-
ful for placing single transitions to delayed states or to the ground
state (when those states are not appreciably fed by 3+ emission).

The Sm1“1m coincidence results for the anticoincidence, integral
coincidence and 196.6—keV gated coincidence spectra are listed in
Table 19. The 2-dimensiona1 coincidence results for Smlhrm are
summarized in Table 20. This information will be used further in the

construction of the Smlulm decay scheme (54.4.6).

190

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192

 

 

 

 

Table 19. 'Y-Ray Intensities for SmU+hn Coincidence Experiments.
Energy Relative Intensities
(keVfl

Singlesa Anti— Integral 196.6-keV Delayed Integral

Coinc. Coinc. Gate Coinc.

196.6 100 77.1 60.4 5.74
247.9 1.04 1.67 0.98 1.67
431.8 54.6 2.32 22.3 53.0 2.32
538.5 11.3 11.3 8.81 11.3
577.8 1.22 1.30
607.9 1.38 1.79 1.90
628.7 3.60
684.6 10.6 8.32 7.30 8.32
725.7 1.95
750.3 2.14 1.55 1.70 1.55
777.4 27.4 27.4 27.4
785.9 9.20 10.2 4.99 10.2
805.9 4.78 4.50 3.45 4.50
837.1 4.82 3.99
875.0 1.68 1.64 1.97
896.5 1.95 1.33
911.3 12.4 12.6 12.3
924.7 3.08 1.67 2.06 1.67
955.4 0.91
974.1 0.27
983.3 9.80 8.03 7.96

Table 19., Continued

193

 

 

Energy

 

 

 

 

Relative Intensities
(keV)a
Singlesa Anti- Integral 196.6-keV Delayed Integral
Coinc. Coinc. Gate Coinc.
1009.1 3.93 4.04 4.46
1029.6 0.68
1108.4 1.67 1.64
1117.6 4.37 3.99 3.97
1145.1 11.8 12.3 14.1
1463.4 2.43
1490.3 12.5 17.9 3.30 17.9
1786.4 14.6 9.78 17.0
1898.0 0.51
1979.6 0.54
2073.7 1.92
aThe errors placed on these values are given in Table 18.

194

Table 20. Summary of Y-ray 2—dimensional coincidence

results for Smlhlm.

 

 

Gate energy y's enhanced
(keV) (keV)
Integral 196.6, 247.9, 538.5, 577.8, 607.9,

684.6, 750.3, 777.4, 805.9, 837.1,
875.0, 896.5, 911.3, 924.7, 983.3

196.6 431.8, 607.9, 777.4, 875.0, 911.3,
983.3, 1009.1, 1117.6, 1145.1,

1490.3, 1786.4

247.9 538.5
431.8 196.6, (1490.3)8
538.5 247.9, 896.5, 924.7
577.8 837.1 (weak)
607.9 196.6
676.7+684.6 (196.6)a, 750.3, 805.9
750.3 (196.6)8, 684.6, 858.5b
777.4 196.6, 1117.6, 1145.1
785.9 No coincidence in evidence
805.9 684.6
837.1 No coincidence in evidence
875.0 196.6, 911.3
911.3 196.6, 875.0, 983.3
924.7 (196.6)8, 538.5, (777.4)8
893.3 196.6, 911.3
1009.1 196.6, 777.4

Table 20., continued

___

1117.6 196.6, 777.4
1145.1 196.6, 777.4
1490.3 (196.6)8
1786.4 196.6

—k

aThese intensities are less than expected for these transitions
to t>e in coincidence. They are considered to be due to chance.

bThis; is not a Smlulm transition.

196

4.4.4.C. Delayed Coincidence Spectra

Owing to the presence of the h state at 628.6 keV in Pm1“1,

11/2
running delayed integral coincidence experiments proved to be very useful.
AS will be discussed in § 4.4.6., this state has an estimated half—life
of 400 nsec, long enough-to obtain useful information using a coincidence
resolving time of 100 nsec.

Two types of Spectra were obtained. In one case the gate sig-
nals were delayed 0.25 psec with respect to the linear spectrum sig-
nals. The resulting spectrum should enhance those transitions pro-
ceeding from the delayed state. Such a spectrum is shown in Figure
44. The other case was that of delaying in the opposite direction.

That is, the gate signal preceeded the linear spectrum signals by
0.25 psec. This arrangement should enhance those transitions pro-
ceeding to the delayed state. This spectrum is Shown in Figure 45.

4.4.5. Energy of the Sm171 Isomeric Level

As Shown in Table 17, the isomeric transition energy for Sm”1

has only been estimated. Based on a least-squares fit of experiment—
ally measured,M4 levels in other N = 79 nuclei we arrive at an energy

of 171.6 keV for the expected h level. A level of this energy

11/2
would be expected to have a lownM4 transition intensity (previously
estimated to be <12 by (Bley 67)). The vicinity of 171 keV is a
particularly unfortunate region for the observation of a weak y ray
since the annihilation quanta back-scatter peak is also 170 keV. We

have looked for this transition both in Y—ray spectra and In clovtron

Spectra without success. An M4 transition of this energy should be

197

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199

prominent in an electron spectrum due to the large conversion co-
efficient; however, there is no evidence of any transition peaks
above the continuum. These results demonstrate that such a transi-
tion is indeed very weak if not totally absent. Based on the statis-
tics of our Y spectra, we place an upper limit of 0.22 of the total
isomeric decay for this M4 process. The absence of an observable M4
trasition is interesting in the light of much experimental evidence

which definitely shows the existence of an 7111/2 level in Sm121.

4.4.6. Smlulm Decay Scheme

121m has been constructed from a combina-

A decay scheme for Sm
tion of the above described prompt and delayed coincidence spectra
and to a lesser extent from energy sums. This decay scheme is shown
in Figure 46. Thirty-one of the thirty-two y rays listed in Table 18
have been placed in the decay scheme, the 1979.6-keV transition being
the only exception. The calculated ground state decay energy for
Sm1“1(Qe) is 5.015 MeV (Myer 65). The y-ray transition intensities
are given in units of percent disintegration of the parent Sm1“1m.
The 3+ and a intensities to each state are also calculated values
(TI 67 and Zwei 57). The energy assigned to each level is a weight-

ed average based on transitions out of that level.

The discussion of this decay scheme will be broken into two
parts: a discussion of those levels which decay in a manner that by-
passes the 628.6-keV level and those levels which decay primarily

through the 628.6-keV level.

  

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Figure 46. Decay scheme for Sm1 41m_

  
  
    
  

201

4.4.6.A. The 196.6-keV and Related Levels

The 196.6-keV transition has been placed as proceeding from
the first excited state of Pm”1 0n the basis of its being the most
intense transition in the singles spectrum (Figure 39). This also
seems reasonable from the systematics of the region. The levels at
804.5—keV, 837.1-keV, 974.0-keV, 1108.1-keV, 1834.0-keV, 1983.1-keV
and 2702.4-keV bypass completely the 628.6-keV level, having da-
excitations either through the 196.6-keV level or directly to ground.
The 628.6-keV level has no choice but to decay to ground either dir-
ectly or via a 431.9-keV transition to the first excited state. Both
of these branches are observed. The level at 804.5-keV has been
placed on the basis of at 196.6-keV and 607.9-keV coincidence as shown
in the 2-dimensional spectra (Figure 41). Purely on the basis of sums,
Y rays of 1029.6-keV and 1898.0-keV are placed as feeding this level.
These are weak transitions and would not show up in the 607.9—keV gated
coincidence spectrum due to the low statistics involved. Notice that
there is an 805.9-keV Y ray. This transition is clearly in coinci-
dence with the 684.6-keV transition (which feeds the 628.7-keV
isomeric level) and is not to be confused with the 804.5-keV level.
The 805.9-keV peak is clearly not a doublet (see Figure 39) and we
must conclude that there is no appreciable ground state decay for
the 804.5-keV level.

The level placed at 837.1 keV is somewhat of a puzzle. It is
enhanced in the integral coincidence spectrum and attenuated in the
anticoincidence spectrum. There is weak evidence for coincidence

with the 196.6-keV transition on inspection of the 837.1-keV gated

202

spectrum. However, there is no enhancement of the 837.1-keV peak in
the 196.6-keV gated spectrum. Possibly Compton events from other
peaks (e.g. 875.0—keV) could account for the 196.6-keV peak appear-
ing in the 837.1-keV gated spectrum. With this somewhat conflicting
evidence the 837.1-keV transition has been placed as originating from
a level of the same energy. The levels at 1834.0 keV and 2702.4 keV
have been placed solely on the basis of sums. The 577.8-keV and
955.4-keV transitions have also been placed by energy sums. The
placement of these two transitions does have the distinction of being
accomplished without the introduction of any new levels. The remain-
ing levels of this group, at 974.0-keV, 1108.1-keV, and 1983.1-keV

are placed by the prompt coincidence data (Figure 41), energy sums,

(and relative intensities of the interconnecting Y rays.

4.4.6.8. The 628.6-keV and SpineRelated Peaks

The remaining levels can be divided into two sub-groups:
those that decay exclusively through the 628.6-keV level and those
that decay through both the 628.6—keV level and the 196.6-keV level.
The levels at 1167.2-keV, 1313.2-keV and 1414.6-kaV belong to the
former sub-group while the levels at 2063.5-keV, 2091.6-keV and
2119.2-kaV decay at least partly via the 196.6-keV level and thus
belong to the latter group.

The 628.6-keV level is almost certainly an h level.

11/2
That this is, in fact, the high spin level is demonstrated by the re-
sults of the delayed coincidence spectra. In the delayed gated spec-
trum (Figure 45), only peaks at 196.6-keV and 431.9-keV are present.

For this Spectrum the gate was delayed for 0.25 us. That these two

203

transitions are in coincidence is substantiated by spectra gated on
these energies (Figure 41). This uniquely fixes an isomeric level
at 628.6—keV. Further support for this conclusion is given from the
enhancement of the 628.7—keV Y ray in the anticoincidence spectrum
(Figure 43). This would be expected for a transition proceeding from
an isomeric level. The Y rays which interconnect this group of
levels can be placed using the delayed integral spectrum (Figure 45)
as the basis. In this spectrum only those transitions feeding the
628.6-keV level should be enhanced. Additional placements and con—
firmations are obtained from the gated coincidence spectra (Figure
41) and the anticoincidence spectrum (Figure 43). The log ft values
shown on the decay scheme have been computed using the electron-
capture percentages to each level.

The 6/8+ ratios calculated by the method of Zweifel (ZweiS?)
are not in good agreement with the results of the 511-keV-511-kev
coincidence spectrum shown in Figure 42. This figure shows that the
196.6-keV, 403.9-kev and 438.2-keV transitions are the only transi-
tions to receive significant 8+ decay. These results, than, are in
disagreement with the theoretical values shown on the decay scheme.
Table 21 compares the "normal" log.ft values (obtained from calcula-
ted e/B+ ratios) versus the log ft values obtained on the assumption
that all B-decay is via the e-mode. The levels at lower energies are
seen to be the most affected, although all of the values change less
than one log ft unit. Either set can be used without significantly
changing the conclusions drawn from them.

The only unplaced transition is the one of 1979.6-keV. This

is a very weak transition and in no way affects the following discussion.

204

Table 21. Comparison of log ft's assuming either the

theoretical s/B+ ratios or all e-decay.

 

 

Level energy Normal e-decay only
(keV)
196.6 7.2 6.5
628.6 6.7 6.1
804.5 8.5 8.0
837.1 7.3 6.7
974.0 6.9 6.4
1167.2 6.9 6.5
1313.2 7.0 6.6
1414.8 6.5 6.1
1834.0 6.9 6.6
1983.1 5.9 5.7
2063.5 6.5 6.3
2091.6 5.9 5.7
2119.0 5.7 5.5
2702.4 6.5 6.4

 

205

4.4.7. Spin and Parity Assignments for the Decay of Sm“+lm

Since no conversion-electron data are available for the
transitions following the decay of Smikl, multipolarity assignments
cannot be made definite for these transitions. Because of this
state of affairs no multipolarities are shown on the decay scheme

(Figure 46)

4.4.7.A. The ggound, 196.61,iand 628.6-keV States in Pmlul
The shell model predictions by Kisslinger and Sorensan
(Kis 60) and systematics of this region suggest 5/2+ and 7/2+ con-
figurations for the two lowest levels of Pmlul. As previously
pointed out (Bee 69t), sixteen nuclei in this region have ground
and first excited states which are well characterized (TI 67). For
each of these nuclei, assignments of 7/2+ and 5/2+ are made for

these two states. In the Pm isotopes there is a change of ground

Pull” Pmlh7

state spin between PmlHS-and . and higher mass isotopes
exhibit ground and first excited states of 7/2+ and 5/2... , respec-
tively. Pm“5 and Pm”3 exhibit ground state and first excited

states of 5/2+ and 7/2+, respectively. Similarly, looking at other

N - 79 isotones shows a reversal in these spins in going from La137

to Prl39.

Pr139 is assigned ground and first excited state spins
of 5/2+ and 7/2+, respectively. The lower mass N - 79 isotones
exhibit ground and first excited state spins of 7/2+ and 5/2+.
From these trends it seems reasonable to assign the value of 5/2+

for the ground state of Pml21 and to make the assignment of 7/2..-

for the first excited state at 196.6 keV. Since the isomeric level

206

in SmMl is undoubtedly the 7111/2 level, this would mean that a
transition between this level and the ground state of Pm?“1 would
have to be at least 2nd forbidden. Thus, it is assumed that this
branch is negligibly small and is not considered in any calculation
involving intensities. The B-branch to the 196.6-keV level, using
7/2+ as thecf" value for this level, must be at least lst forbidden
unique and very little B-feeding to this level would be expected.
However, from Y-ray intensity balance for this state, it appears
that 5.32 of the B-decay does go to this state, resulting in a log
‘ft of 7.2. This compares with 32 decay to the first excited state
of Pr139 (Bee 69d) with a log.ft of 7.6. At first glance, it would
seem reasonable to attribute at least a fraction of this decay to
errors in‘Y-ray intensity determinations. However, the 511-511 keV
coincidence spectrum (Figure 42), after correction for chance, shows
that there is, in fact, 8+ decay to this level. Figure 37 shows

the plot of the half-life curve for the 196.6-keV peak. In this
plot there is no evidence of an 11.3 minute component, which

means that any B+la decay to this state must be from.Sm}““". In
spite of this small B-branch to the 196.6-keV state, the bulk of
evidence still suggests that it is the 7/2+ level.

That the 628.6-keV level is 11/2- has already been
discussed in 54.4.6. The log.ft of 6.7 is on the high side for an
allowed transition but still possible. As will be discussed in
54.4.12, this is an entirely reasonable value because of the particle
rearrangement necessary for this 11/2‘+1l/2- transition. The half-

life of the 628.6-keV state has been estimated from the 431.8-keV

207

,M2 transition and the 628.7-keV E3 transition, resulting in values
of 470 nsec and 323 nsec, respectively. These values are based on
the measured value of 40 nsec for Pr139 (Bee 69d) and relating the

two nuclides by the appropriate single-particle-transition equations

(see Chapter 5).

4.4.7.3. The 804.5-, 837.1-,4974.0—, 1108.l-, 1834.0—,_and
1983.1-keV Levels in Pm1”1.
The Y transitions from these levels completely bypass

the h level at 628.6-keV. They exhibit log ft's ranging from

11/2
5.9 to >8.
The 804.5—keV state (log ft = 8.5) appears to be fed by
a let forbidden or lst forbidden unique transition. Thus, positive
parity states are possible with spins ranging from 15/2 to 7/2.
Since there is only one transition, 607.9-keV, from this level,
it is somewhat difficult to draw conclusions. From one point of
view, the absence of a transition to the ground state would tend to
rule out the 7/2+ assignment since that assignment should make an
.M1 ground state transition more favorable. A 9/2+ assignment would
favor the transition to the 7/2+ level, as is observed. However,
assuming the 804.5-keV level to be a vibrational level based on
coupling the 2... level in Nd”0 with the 196.6-keV state would ex-
plain the single Y da-excitation to this level. From this point of
view, a 7/2... assignment for the 804.5-keV level would also be
reasonable. Hence, we feel that 9/2+ and 7/2+ must both be left as

possible assignments for the 804.5-keV level, higher spins being

ruled out by the single transition to the 7/2+ level at 196.6 keV.

208

The state at 837.1 keV, having a log,ft of 7.2, is most
likely fed by a let forbidden B branch, resulting in 13/2+, ll/2+,
and 9/2+ as possibilities for theIJ1T assignment. An assignment of
13/2+ or ll/2+ should rule out the transition to ground. 9/2+
must remain as a possibility by the same arguments as for the 804.5-
keV level. This level may also arise from vibrational coupling to
the ground state.

The 974.0-keV level decays to both the ground state and
the lat excited state with Y intensities in the right ratio to be
M2 and E1 transitions, respectively. The log ft of 6.9 for this level
suggests a let forbidden nonunique B branch to this level, result-
ing in assignment possibilities of 13/2+, ll/2+, or 9/2+. The Y-
ray intensities, coupled with the absence of any transition to the
11/2' level at 628.6 keV, tend to rule out 13/2+ and ll/2+. Thus
the assignment of'Jw - 9/2+ is made for this level.

Within the limits of our Y—ray statistics there is no
feeding to the 1108.1-keV level. This leaves several possibilities
for the J" of this level. Spins higher than 9/2 can most likely be

ruled out by the absence of a transition to the h state at

11/2
628.6 keV and the presence of transitions to 7/2+ and 5/2+ states.
This leaves 9/2 and 7/2 as possible candidates. The assignment of
9/2' can be ruled out since this would mean aanZ 1108.4-keV trans-
ition and an El 911.3-keV transition, a very unlikely combination.
Thus, we limit the assignment to 7/2t'being the most likely, with
9/2+ assignment being a possibility.

The 1834.0-keV level has a log ft (6.9) that puts it in

that grey region between allowed and first forbidden transitions.

209

We feel that a 13/21t assignment is improbable because of the fact
that the only two transitions from.this level are to levels with
9/2 and 7/2, 9/2 assignments. However, there is no way to limit
the assignment beyond 11/21 or 9/2t.

The low'log.ft value of 5.9 for the 1983.1-keV level
suggests that it is one of the B-preferred three-quasiparticle
levels. This. is persued further in§4.4.12. From the B decay, J1T
values of 13/2-, 11/2-, and 9/2- are the candidates. Here again,
this level shuns the 11/2' level at 628.6 keV, choosing instead to
decay to levels having 7/2+ and 9/2+ assignments, with the 1786.4-keV
‘Y ray (to the 196.6-keV level) being by far the most prominent. The
only J1r assignment consistent with this information in 9/2_. This
would mean that the three'Y transitions from this level would
probably all be El '8, a conclusion which is qualitatively in agree-

ment with the observed relative intensities of these Y rays.

4.4.7.C. The Levels which Decay through.the Level at 628.6
32!.

The remaining seven levels decay at least partially through
the 628.6-keV level. Five of these levels, at 1414.8, 2063.5, 2091.6
2119.2, and 2702.4 keV, are proposed as being members of a three-
quasiparticle multiplet (5 4.4.12). The remaining levels, at 1167.2
and 1313.2 keV, have log ft values (6.9 and 7.0, respectively) too
‘high to make them.likely candidates for this preferred type of decay.

Considering these last two levels first, we see that they

exhibit quite similar properties; the log ft's of 6.9 and 7.0

210

are almost identical and each one de—excites by a single transition
to the 628.6—keV level. Again, these logift values are of a magni-
tude which could mean the 8 branches are allowed or let forbidden
nonunique. The possibletf1r assignments would then be 13/21, ll/Zi,
or 9/2*. Going on the assumption that there would be decay to
several other states if the assignment were 9/21, this value is ruled
out. The J1T values of 13/2t and ll/Zi are left as real possibilities
with the ll/Zt assignment being the more likely. Without further in-
formation the choices for this level can not be narrowed any further.

The level at 1414.8 keV, having a log'ft of 6.5, is
most likely an allowed transition. Since this level has an appre-
ciable de—excitation mode via the 577.8-keV transition to a 9/2+
level, a spin assignment of 13/2- would mean that the multipolarity
of the 577.8-keV transition would have to baIUZ. Such a transition
should not compete favorably witthl and/or El transitions. In
addition, considering this to be a threa-quasiparticle level would
also make improbable anIUZ transition, basing this statement on the
fact that the threa-quasiparticle levels in Pr139 de-excited ex-
clusively via El, E2, and M1 electromagnetic transitions, and that
all transitions out of such a multiplet appear to be hindered.
This means that anhMZ should be very slow. Hence, we limit the
assignments for this level to 11/2- or 9/2'.

The remaining levels, at 2063.5, 2091.6, 2119.2, and
2702.4 keV, have log ft's ranging from 5.7 to 6.5. Each is assumed
to be fed by an allowed 8 branch, resulting inJJr choices of 13/2',

11/2-, or 9/2-. Using the same arguments as for the 1414.8-keV

211

level discussed above, the 13/2' can be ruled out as being very
likely. Neither the 11/2‘ nor the 9/2' assignments can be ruled out

without more information.

4.4.8. Sml“191hraySpectra

Determining which y rays constituted transitions result-
ing from the decay of Sm}“19 has been a most difficult task, one that
is still not completely settled. Originally, Sm1“1g transitions were
sought as ones maintaining a constant intensity relative to the
403.9-keV peak intensity, as measured in the four singles spectra
described in §4.4.4.A. The 403.9-keV peak was picked as definitely
belonging to the decay of Sml“1g both.from.its half-life and from.the
fact that it exhibits the same excitation threshold as do the peaks
identified as coming from Sm1“h" decay. The almost equally intense
438.2-keV peak still presents us with problems, as will be discussed

in 54.4.9, but is tentatively placed as a level in Pm1“1.
4.4.8.A.. Singles Spectra

Obviously, because of Sm1“H? having the shorter half-
life, this species could never be viewed in the absence of SmJHN".
The Smllolg peaks are therefore maximized relative to the Sum” peaks
in spectra obtained immediately after bombardment. Such a spectrum
is the one shown in Figure 39, which represents 15 minutes of count-
ing beginning 2 minutes after the end of the bombardment.

It turned out that many of the observed transitions,

aside from the ones assigned to the decay of SmihV", had aratically

IQ
h.
IQ

behaving intensities. There are transitions present in the singles
spectra having apparent half-lives ranging from less than 10
minutes to greater than 20 minutes. In the final analysis, only 2
or 3 peaks can definitely be said to have the same half—life as the
403.9—keV peak. in spite of the difficu]ties, 10 transitions were
observed having decay properties near enough to the 403.9—keV peak
to be placed tentatively as belonging to the decay of SmluKy. These
energies and relative intensities are listed in Table 22. Unfortun-
ately, Table 23 shows why these transitions are only tentatively
placed. In this figure the intensities, relative to the 403.9-keV
trnsition intensity, are given as determined from the 4 spectra
taken in four consecutive 15 minute periods. Only 2 or 3 of the
peaks can be said really to follow the 403.9—keV half—life.

The SmI"'°(p,4n)Eu'"l (M: —36.8 MeV) ’ Sm"IIH reaction
was also used in an effort to enhance the SmIHHI/Smlflnn ratio, a
result depending on the absence of a B—emitting isomeric level in
Eulul. This indeed turned out to be the case as evidenced by the
greatly increased 403.9/43l.9-keV intensity ratio. Figure 47 shows the
results from such a bombardment for the production of Eul”j. Each 01 the
three spectra represents 5 minutes of counting time with the count—
ing begun on the first spectrum 2 minutes after the end of a 30
second bombardment. The very intense peaks seen in the first spec—
trum have a common half—life of roughly 2.0:0.5 minutes and have not
yet been positively identified as to their origin. This is still
under investigation at MSU. Unfortunately the presence of all the

short half-life activities precluded the attainment of better in-

213

lkfiflte 22. Energies and Relative Intensities of y rays from the

 

 

Decay of Smlklg.

 

___. —-—_.-_---_ —-.--.—.--_—._.__—A_
___—..— .— .....-

 

 

Energy Intensity
196.6:O.3 (0.64)a
324.5i0-2 2.29
403.9:1.1 23.4
661.9i0-1 0.64
858.5i0.2 1.66
1292.7iO.1 3.67
1495.6?0.l 1.29
1600.9i0.3 2.07
2005.010.5 0.21

___.-.____ -.__ -.-..-_-..__- ___- ... e- . - -. _ _~ . _ - . . _ _ _ _ _. - -...- ___ -~_ --- .... . _ . --.. _ - _ . - - - . .—
—.—__~_- ...-.— _._____..___.._..._ ...._....r, - -7-_. _ .- _— - - - _ - - ._- —-* -.. _ - -..- V - -..- ,V._ - . _ -__ _ - - _ . '

aThis is a common energy level with the SmIle

activity. Therefore,
the intensity due only to the Sm1419 decay alone cannot be accurately

determined and is assumed to be totally from feeding of this level

by the 661.9-keV transition.

Table 23

214

Relative intensities of Y rays assigned to Smlhlg as

measured in four consecutive 15 minute spectra.

 

 

 

 

Energy Intensity

(keV) Quad 1 Quad 2 Quad 3 Quad 4
196.6 - a - - -
324.5 9.8b 13 16 21
403.9 100 100 100 100
661.9 2.7 5.7 7.2 8.3
728.8 .77 - — -
858.5 7.1 16 16 28
1292.7 9.4 ~16 23 25
1495.6 5.5 11 8.9 14
1600.9 8.8 7.7 11 -
2005.0 0.90 - - -

 

a The 196.6-keV transition intensity cannot be measured directly be-

cause of the Sm4“lm decay through this level.

b The intensity values from this first quadrant are used in the de-

cay scheme construction.

 

 

215

 

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500
Figure 47.

 

tensity data for the Smiklg decay. If anything, it was more diffi-
cult, via this reaction, to determine which transitions were due to
the Smdulg decay. An intriguing question, presently unanswered, per-
tains to the origin of the intense peak at 438.2-keV. In the early
stages of this investigation it was supposed that this transition
also came from the decay of Smdulg. On closer examination, however,
this assignment came into question on several counts. First, the
438.2—keV transition has a similar but different half-life. This
'was carefully measured by the computer program GEORGE (described in
§ 2.2), resulting in a value of 10.0:O.4 minutes. This was measured
several times with quite good precision. Another interesting bit of
information on the 438.2-keV transition is that there is no clear-
cut evidence for transitions which are in coincidence with it. The
consequence of this is that there is no way of relating the 438.2-
keV transition with any other y ray in the spectrum. This would
indicate that if this transition is due to the decay of Still“1 it
‘must be a ground state transition in Pmlul from a level of the same
energy.

The Sm1‘*'*(p,4n)1§u1"1 reaction was again called upon for
the purpose of determining whether or not the 438.2-kev peak was
produced in this manner and for the purpose of determining its rela-
tive intensity if it was produced. It is obvious from Figure 47
that this peak is indeed present with approximately the same in-
tensity relative to the 403.9-keV peak as it has in Figure 39. An
excitation function was run on the Smlu“ target by changing the

proton beam energy in increments of 5 MeV. The 403.9- and 438.2-keV

217

peaks, as well as the 196.6-keV, 431.9-keV and other Smlulm peaks,
first appear at the bombarding energy of 35 MeV. However, the
403.9 keV/438.2 keV intensity ratio is larger here than at higher
energies. This could mean that the 438.2—keV transition originates

from a species having a 2-3 MeV higher excitation threshold.

1 An excitation function run on the Ndl.“2 target (He3 beam) shows sim-
ilar behavior; that is, the 438.2-keV peak seems to have a slightly
higher excitation threshold.

The above arguments could well be used to show that the
438.2-keV transition does not belong as a level in ngul. Our most
recent experiment, however, can be used as a counter argument. This
experiment was a 2-dimensional coincidence run using a Y-ray detector
versus an x-ray detector. The Y-ray spectrum was subsequently used
for setting gates on various y-rsy peaks. The resulting gated y—ray
spectra should show those x-rays which were in coincidence with the
gated~yrays. In this manner y-ray gates were set on the 196.6-,
403.9-, 431.8-, and 438.2-keV peaks. The results for each gated run
‘were the same: all of the above y rays were in coincidence with Pm
x-rays. This makes certain that the 438.2-keV transition is from a
level in a Pm isotope. That this level is in fact in PmM1 is
suggested by the fact that no matter what reaction has been used for
production, the 403.9- and 438.2-keV peaks always appear together -
and in about the same ratio.

The bulk of the experimental evidence seems to be
telling us that both the 403.9-keV and the 438.2-keV transitions

141

must be from levels in Pm which are fed predominantly from the

218

ground state of Smlul. Bear in mind that we must still explain why
the 403.9-keV and the 438.2-keV transitions have measurably different
half-lives (10.0 and 11.3 minutes, respectively). A number of pro-
posals have been offered in explanation of this puzzle, almost all of
which seem to have serious defects. Two alternate proposals will be
made for the Smdglg decay in 54.4.9.
Also notice, just in passing, that there is an intense

538-kev peak (same energy as in Sm1“”" decay) which exhibits the

same 2 minute half-life as do the other intense peaks found in the

4.1
first Eu1 spectrum.

4.4.8.13. Coincidence Spectra for Smll'lg.

As with the singles spectra, the Smll'lg coincidence

luv" peaks and other short-

peaks can only be observed amidst the Sm
lived activity. Four relevant 2-dimensional coincidence spectra,
gated on Smll’lg peaks, are shown in Figure 48. The original x-

and y-axis integral coincidence spectra are shown in Figure 41. These
gated spectra point up a difficulty in constructing the Smluk? decay

scheme. The ground state decay of Sml‘+1

really seems to be lacking
in coincidence transitions.

The 511-511-keV coincidence spectrum and the anticoinci-
14194-112

dence spectrum, both for Sm are shown in Figures 42 and 43,
respectively. Table 25 summarizes the principle coincidence intens-

ity data obtained from these various spectra.

r'lzrt pl‘ll—ANNCL

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Figure 48.

2—dimensional gated coincidence spectra for Smlulg.

220

Table 24. Coincidence Transition Intensity Summary for Smdllg.

 

Relative Intensity

 

 

Energy

(keV) Singles Integral-gate Anti
324.5 2.29 4.60

403.9 23.4 19.1 21.7
661.9 0.64

858.5 1.66 3.10

1292.7 3.67 3.36
1495.6 1.29 2.03

1600.9 2.07 1.88

2005.0 0.21

9

 

221

4.4.9. Smll’lg Decay Scheme

The Sm1”M7 decay scheme, presented in Figure 49, has

been constructed without consideration of the 438.2-keV transition,

which cannot be placed definitely. This decay scheme is to be con-

sidered purely hypothetical atthis time; the final word must await
further investigation, particularily into the origin of the

intense 438.2-keV peak. After a discussion of the decay scheme as
presently envisioned, mention will be made of a possibility which
may exist for the inclusion of the 438.2-keV peak in the Sml“k?decay
scheme. The decay scheme in Figure 49 has been constructed from the
available coincidence data, intensity balances and energy sums.

As shown in Table 22, the 403.9-keV transition is by far the most
intense transition resulting from the Smdulg decay, accounting for
672 of the Y—ray intensity. From the 403.9-keV gated spectrum shown
in Figure 48, one can see evidence for coincidences with the 324.4-
keV and 1600.9-keV peaks, which suggests levels at 728.3 keV and
2005.0 keV. 7 transitions have been observed at both of these
energies. These 5 transitions, at 403.9, 324.4, 1600.9, 728.3

and 2005.0 keV, form the heart of the decay scheme. Weak evidence
for a common level with that of Smlunn can be found for the 196.6-
keV level. Placing a level at 858.5 keV allows the placement of an
858.5-keV transition to ground and a 661.9-keV transition feeding
the 196.6-keV level. These transitions are too weak to be seen in
the coincidence spectra and can only be tentatively placed by energy

sums. The remaining levels at 1292.7 keV and 1495.6 keV are placed

12m

222

 

2005.0 0.38%c. 020748159)

 

  

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 49.

Tentative decay scheme for Sml“lg.

223

on the basis of single transitions at those energies. The 1292.7-keV
peak is enhanced in the anticoincidence spectrum (see Table 24) and
is thus placed as a ground state transition. This would be in keep-
ing with the 1292—keV gated coincidence spectrum (Figure 48) which
shows that only the 511.0-keV annihilation peak is in weak coincidence. F3
The 1495.6—keV level is placed on a more tenuous basis. First

of all, it has been kept as belonging to Smlulg on the basis of having

relatively similar decay characteristics. It was placed in the decay

 

“‘3‘.— A

scheme even though no other peaks can be found that are in
coincidence. The integral coincidence spectrum does indicate an
enhancement of this transition. However, it cannot be gated due to
the close lying 1490.3-keV peak. The integral coincidence enhance-
ment could be due to 8+ feeding to this level, but at present the
inclusion of this level is a very borderline situation.

The log.ft values shown on the decay scheme have built-
in assumptions on the percent 8 feeding to the ground state and the
196.6-keV state. In the proposed decay scheme only the 661.9-keV
transition feeds this state. That the 196.6-keV state is only
weakly fed by the Smlqk? decay (both y- and B-decay) is supported
by the visually absent 11.3 min component in the 196.6—keV half-life
curve shown in Figure 37. We therefore make the assumption that
there is no direct B feeding from Smlhu7 . An upper limit on the

amount of direct B feeding to the Pmlul

ground state was set by
reference to the 511-Sll-keV spectrum displayed in Figure 42. The
levels fed by 8+ decay, other than any ground state feedings, are

the 196.6-, 403.9-, and 438.2-keV levels. The intensities of these

224

peaks, after correction for chance, were normalized to the singles
spectrum on the assumption that the 403.9-keV transition was allowed
(or at most lst forbidden nonunique). The resulting normalized in-
tensities were subtracted from half of the annihilation peak intens-
ity to arrive at this upper limit. This is an upper limit since we
cannot determine the amount of 511.0-keV intensity arising from
other ground state transitions (assumed to be low). This limit
turns out to be 91.8%. That is, 91.81 of all s/B+ transitions

from the decay of Sml“lg proceed directly to the ground state of

Pmlkl.

Total electromagnetic transition intensities are taken to
be the same as the y—ray intensities; conversion coefficients for the
energies involved would be negligibly small. At this point only
speculation can be made as to the placement of the 438.2-keV trans-
ition. If it must indeed be placed as a Pmdkl level this would
probably mean that the true 8min“? half—life is 10.0 minutes (as
opposed to the 11.3 minutes states in 54.4.3), the half-life measured
for the 438.2-keV peak. To account for the longer half-life of the
403.9-keV peak would require a small amount of Y decay to this level
from another Pmiul level which is populated by the 22.1 min Smluhn
decay. Folding in a 20% 22.1 min component could raise the 10 min
half-life curve to one of over 11 minutes. This small amount of

Smlkhn admixture would not be noticeable as a break in the 438.2-keV

curve (Figure 38 ).

 

225

If this is in fact the real situation, the 728.3-keV
level would have to be fed by a 8 branch from Smluv". The strongest
transition from this level is the one at 324.4 keV which is situated
on the 511.0-keV Compton knee. This makes an accurate determination
of its intensity impossible. From the intensity data we do have it
is conceivable that it does have a 22.1 minute half—life. It is only
about 10% as strong a transition as the 403.9-keV transition and it
is still questionable whether this is enough to account for the 11.3
Ininute half—life of the 403.9-keV transition. This would mean, of

course, that the 728.3-keV level should rightly be included in the

Smllllm decay scheme.

226

4.4.10. Spin and Parity Assignments for Smlklg

 

The spin and parity assignments for the Pm1M1 levels p0p-
ulated by the decay of Smlulg are based on the log fr values and rel-
ative y-transition intensities shown on the decay scheme presented
in Figure 49..

In § 4.4.7 we have already discussed the evidence for
assigning the ground and let excited states the J“ values of 5/2+
and 7/2+, respectively. This is seen to be consistent with a log f%
of 5.7 for the ground state and a lack of feeding to the lat excited
state.

The 403.9-keV level exhibits a log ft of 6.8, which most
likely means that it 13 an allowed transition. Since we have not
observed transitions from this level to the 7/2+ level at 196.6 keV,
it seems reasonable to eliminate the 5/2+ assignment from further
consideration, although there is the possibility that 403.9-keV
level is core coupled to the 5/2+ ground state. This could account
for the single ground-state transition. Thus, we tentatively assign
the values of 3/2... or 1/2+.

The log ft of 7.6 for the 728.3-keV level is high for an
allowed transition, although this remains a possibility. The spin
of 5/2 can be ruled out on the absense of any transition to the 7/2
level at 196.6 keV. A spin of 3/2 (with even or odd parity) cannot
easily be ruled out, although an assignment of 1/2+ seems more rea-
sonable. This assignment would indicate an E2 multipolarity for the
de-exciting 728.8—keV transition and an M1 multipolarity for the

324.4—keV transition (an assignment of 1/2' would mean M2 and El

227

multipolarities for these transitions, clearly improbable). Thus, we
assign a spin of 1/2+ for this level with 3/2‘zbeing less likely but
still possible choices.

For the 1292.7-keV level (log f%-7.3) we have a similar
argument. The log ft value is ambiguous enough to allow us the
liberty of assuming either an allowed or a first forbidden nonunique
8 transition. Here we have a 661.9-keV transition to the 7/2+ level
and an 858.5-keV transition to the 5/2+ ground state (no transition to
the low spin state at_403.9 keV). This situation most likely rules
out a 1/2 assignment. 3/2- can also be ruled out since this would
mean competing M2 and El transitions. This leaves the assignments of
5/2i and 3/2+ as possibilities that cannot be easily ruled out with-
out more information.

The two levels at 1292.7 keV and 1495.6 keV have log f%'s
of 7.3 and 7.5, respectively. Again, either allowed or lst for-
bidden nonunique transitions. Since each of these levels has only
a single transition to the ground state, not many conclusions can be
drawn. Absence of transitions to the 7/2+ state at 196.6 keV is
taken as weak evidence for the elimination of 5/2+ as possible
assignments (the emphasis here is on weak).

The 2005.0-keV level prefers to decay to the ground and
403.9-keV levels rather than to the 7/2+ level at 196.6. This,
coupled with the assumption tht the 2005.0—keV level is a B-allowed

level (log f%-6.9), allows us to limit the assignments to 3/2+ or

1/2+.

228

At this point it should be re-emphasized that the Sml“lg
decay scheme, including the spin and parity assignments for the pro-
posed levels, is tentative. Further work is presently underway with
a special emphasis on the characterization of the intense 438.2-keV
transition. Properly placing this transition will help greatly in

clearing up the uncertainties in this decay scheme.

229

4.4.11. Discussion

As mentioned in 54.1, the impetus for carrying out the in-
vestigation of SmMl was the prediction (Bee 69d) that the isomeric
level in this nucleus should p0pu1ate three-quasiparticle states in
Pmlgl similar to those found in the decay of Nd139n. The require-
ments for populating these levels are a parent nucleus containing a
relatively low energy, high spin isomeric level and an electron—cap-
ture decay energy large enough to be able to populate levels above
the pairing-energy gap in the daughter nucleus. The isomeric level
in the parent should be low enough in energy such that the probabil-
ity for the high multipolarity electromagnetic transition to ground
is sufficiently low, thus allowing significant decay by the 8 process.

Since this nucleus has been predicted to be similar to
Nd139 in its decay properties, it might be interesting to compare
first the overall features of the isomeric decay in the two nuclei.
The ground state decay for both Smll+1 and Nd139 is principally via
an allowed transition to the ground states of the daughter nuclei.
Both are to a large degree straightforward decays. The B feeding in
both Sml“vn and Nd139" show remarkable similarities: very little
feeding to the ground and lst excited states, a somewhat more hind-
ered decay to the lowest 11/2-level than expected, and several
states of relatively high energy which exhibit abnormally low 10g
ft values. These two decays are, on the other hand, completely dis-
similar in one basic feature. One of the quite remarkable character-
istics of the Nd139m decay is the large number of interconnecting
transitions between the high-lying, three—quasiparticle levels.

All of them seem to prefer decay to other members of the multiplet,

230

in spite of the low energies involved, rather than to other lower
lying levels. Now, a look at the Smlhlm decay scheme (Figure 46)
shows that none of the high lying levels have any interconnecting
transitions. They are still levels preferred by Smlulm for B
feeding, as indicated by the low log ff values, but for some reason
they remain independent of each other. In both nuclei, the conclu-
sion is reached that there is no direct 3 population of the daughter
ground state. There is some evidence, however, that there is some
8 feeding to the lst excited state in each daughter (Pr139 and Pmlkl).
Beery (Bee 69d) places an upper limit of 3% on the s decay from
Nd139m to the 7/2+ state at 113.8 keV in Pr139. This would lead to
la log ft value of 7.6. In the present case, there seems to be =5%
8 branch to the lst excited state (7/2+) in Pmlhl . This yields a
log‘ft of 7.2. In both cases, the log;fi€s are too low for what
should be a lst forbidden unique 3 transition. There is no satis-
factory explanation for this state of affairs.

Both the Pr139 and Nd1“1 nuclei have 11/2- levels
fed by 3 branches having abnormally high log ft's (7.0 and 6.7,
respectively) for what is presumably an allowed ll/2’+11/2- trans-
ition. As will be seen in the following discussion, this is explain-
ed by the particle rearrangement which must take place for this trans-
ition.

In each case, the proposed three—quasiparticle levels
have similar 10g.fL values. For the multiplet of 6 three-quasiparl-
icle levels in Pr139 the average log ft is 6.0, while in Pm1“1 the 6
levels have an average log.ft of 6.1.

Figure 50 shows a shell model representation for the

 

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232

141
formation of the three-quasiparticle states in Pm . The ground
state of Smlkl has 4 protons outside the 097/2)8 subshell. A major
component of its wave function could be represented as being

(ads/2)-2(vd3/2)1. B+ls decay from this state can be considered sim-

ply to be the transformation of a ds/2 proton into a d3/2 neutron.

This results in a PmMl ground state configuration of (nd5/2)-3

141

(w33/2)% The isomeric state of Sm is formed by promoting an.h11/2

141m

proton to theci orbital, resulting in the Sm configuration

3/2

being (ndS/2)-2(vd3/2)2(vhll/z)‘1. Now, the PmlLfl three-quasipar‘

ticle states are formed by converting a d proton into a d

5/2 3/2

neutron, resulting in the quasiparticle configuration ("ds/zl—3

(vd )"1 (vh

)‘1. Since it is assumed that paired nucleons

3/2 11/2

do not contribute to the spin of a state, we could just as easily
’1
)

rewrite the "effective" part of this configuration as (ndS/2

(“d )-1(vh )-l, the same configuration as given for the three-

3/2 11/2

quasiparticle states in Prlkl.

Now we can consider why the allowed 8 transition
(ll/25+ll/2-) between Smluvn and Prll+l is hindered. From the diagram
in Figure 50 it is seen that the transition requires not only the
promotion of 8‘15/2 proton to the hll/z state, but also the conver-

sion of anotherci proton to anlz neutron. This "double move"

5/2 11/2
‘would certainly be expected to hinder the transition and is indeed

141

the case for both Nd139 and Sm , as previously discussed.

The remaining states in the Pm11+1 nucleus, as seen both

141m and Sm14lg decay, are less easy to deal with. Viewing

from Sm
all of the Pm”1 states as quasiparticle states would allow one to

discuss these remaining states as probably best described as single-

232a

quasiparticle states. They could be formed from fragmented single
particle states or they could be described as vibrational states
formed from core-coupling the lowest 2+ state in Pm“+0 to a single-
quasiparticle state. That this is possible at low energies is born

out by noticing that the 2+ level in Pm1”0 lies between 0.77 and 1.0

MeV (TI 67).

4.4.12. RemaininggPeaks in the Smlh1m+g Singles Spectra
As already mentioned several times, many peaks in the
Smlklm+g Spectra cannot be positively identified as originating

1”1m 0r Sm1“19. Some of these peaks are due to

from the decay of Sm
contaminant activities produced during the bombardments or to the
daughter activities that build up. These peaks are listed in Table
25: those with half—lives under 20 minutes, those with half-lives
over 20 minutes and those which occur only in quadrant l of the 4
quadrants mentioned in 5 4.4.2. The intensities in each case are
normalized to the Sm]”1m 196.6—keV intensity. Those peaks recognized

as belonging to contaminatnts have been labeled as such. The in—

clusion of this table is purely for future reference.

233

 

 

 

 

Table 25. Peaks in the singles spectra which have not been
assigned to the decay of Smlulg or Smlklm
ti <20 min t% >21 min In Quad 1 only
Energy Intensity Energy Intensity Energy Intensity
(keV (keV) (keV)
114.4 (Nd'3”m)? 1.37
189.8 3.59
438.2 9.8 208.9 (84139”) 0.29 648.6 0.13
549.2 0.39 424.9 (Nd'3Um)? 1.02 717.7 0.19
677.0 2.39 622.3 (Pmlql) 1.33 753.4 0.81
693.8 0.87 641.6 1.44 756.6 (Pm‘“1) 1.03
843.7 (Mg’V) 5.10 768.1 (Ndllqmi? 0.64 854.3 0.77
1014.6 (Mg27) 1.84 738.1 (Nd139m) 0.52 891.7 0.42
1057.1 1.47 764.1 0.30 958.4 0.26
1091.8 1.15 820.8 0.34 978.0 0.33
1482.4 0.40 886.4 (pm1”1) 4.53 1046.9 0.42
1901.7 0.46 952.2 0.76 1094.9 0.27
2037.7 1.64 1037.7 0.24
1223.3 (Pm'“1) 7.79
1345.7 (Pm1“1) 2.76 1460.9 0.97
1369.1 (Na?“) 1.82 1479.8 0.23
1403.5 (Pm1“1) 1.23 1482.4 0.40
1564.9 (Pm1“1) 0.80 1768.2 0.63
1576.0 6.28 1967.5 0.19
1597.3 (Pml‘+1 1.70 2312.6 0.50
1627.9 (Pmlul) 0.40
1732.2 1.47
1765.5 0.99
2244.9 0.55

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234
4.5. The Search for DyM7

4.5.1. Introduction

 

Our first observation of Gd195n (§4.2.) along with the
previously discoveredlv = 81 isomers led us to speculate on the exis—
tence of (and possibilities for producing) Dy1“”n. It was felt that
there would be a better chance for observing Dy1“7n than there would
be for observing Dylhfl7 since this latter species should g/B+ decay
to Tb197 with quite a short half—life 0%: = 7.3 MeV, (Myer 65)).
Also, it should be easier to identify thefid4 decay of the isomeric
species by the internal conversion electron peaks, similar to the
technique we used for Gdlhgn.

The energy of the Dy197 isomeric level was estimated to be
604:16 keV, based on a quadratic—least-squares extrapolation using
the 7.M4 energies which were available for the other N = 81 isotones.
The reducedlv4 transition probability was estimated in the same
fashion, and resulted in a value of 3.04 for the Dy1“W" species.
These values for the energy and the transition probability were then
used to obtain an estimate for the M4 half—life of this state by re-
lating them through the.M4 single particle equation (see Chapter V).
This procedure resulted in a value of SUEHUEHS for the M4 half-life
of the Dy1“7 isomeric species.

These results were of such a nature that it seemed worthwhile to
attempt a search for this species. This resulted in the performance
of several experiments at Yale University using their Heavy Ion Linear

Accelerator to furnish the required C12 beam.

235

During the course of these experiments we have obtained singles
spectra for Y rays, x-rays, and positron decay. In addition, a Y-
ray versus x-ray coincidence run was carried out by gating on the Tb
‘KB x-rays and observing coincidence Y rays.

The point at which we presently find ourselves does not allow us
to make a positive statement on the nature of Dy197. As will be
brought out in the following sections, there is indirect evidence

that we do, in fact, produce Dy157. However, we cannot specifically

identify those Y rays resulting from its decay.

4.5.2. Singles Experiments

 

All of the equipment used at Yale University is des—
cribed in 52.2.4. In all cases it took a minimum of 2 - 3 minutes
to retrieve the target at the end of the bombardment, transfer it to
some suitable container for counting, and transport it to the count-
ing area. Because of the short half-lives involved, no chemical sep-
arations of the target material were attempted.

4.5.2.A. :X-ray Singles Experiments

 

The logical reaction for the production of Dy1“7(the one
we started with, of course) is the Nd1'+2(C12,7n)Dyll+7 reaction (Q =
—78.9 MeV). Several spectra were obtained from Ndé‘V/O3 targets
which had been bombarded with C12 beams ranging in energy from 80
to 120 MeV. In all of these spectra, we paid particular attention
to the peaks in the 500—700 keV region, peaks which might be due to
the predicted‘M4 transition. As it turned out, we were never lack-

ing for possible candidates in this or in any other energy region.

236

During these runs we observed the two intense peaks at energies of
1757.8 and 1880.6 keV which belong to G01“ (54.3). We postulate
that this activity was produced by the Nd”2 (C12 ,aSn)Gd1"’5 reaction
(¢2= -56.2 MeV). From this observation we reasoned that this might
also be a preferred type of reaction using 56““+ as the target. Thus,
a set of runs was made over the same GL2 energies with the expecta-
tion that the S11:‘”‘“(C12 ,aSn)Dy1“7 reaction (Q= —65.2 MeV) would
constitute a major reaction path. Figure 51 shows a typical-y—ray
spectrum. This was obtained by counting a Smll+l+ target for 13 minutes
beginning 2-3 minutes after the end of the bombardment. The bombard-
Inent was for 1 minute with the full energy (120-MeV) C12 beam. The
energies shown on Figure 51, as well as on the other figures and
tables in this section, were obtained from an energy calibration
curve constructed from a separate Co56 standard spectrum at the same
.amplifkr gain and same source position. Because of this the reported
energies are only good to approximately:il.0 keV.

Table 26 is a list of the y-ray energies and net peak areas for
the spectrum of Figure 51. Net peak areas must be reported (as
Topposed to relative transition intensities) because of the unavaila-
‘bility of detector efficiency curves for the detectors used at Yale.

Figure 52 is a spectrum from a Sm1”“ target obtained 4 days
after a 1 hour bombardment at full beam energy (120 MeV). Energies
.are shown only for some of the more prominent peaks to save clutter
:3n the spectrum. A listing of energies and net peak areas for most
of the peaks on this spectrum will be found in Table 21 Notice on
Figure 52 that peaks have been identified which prove the presence

of Gdlu9, Gd1“7, and Eu1“7. This is taken to be evidence of the

 

 

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238

Table 26.. y-ray energies and peak areas for transitions observed
in a Smlku target immediately after bombardment.

 

 

 

Energy Energy

(keV) Peak Area (keV) Peak Area

50.995 0.20 (5) 546.596 0.20 (4)
100.727 0.94 (4) 620.313 0.53 (4)
106.201 0.52 (4) 631.738 0.26 (4)
139.697 0.69 (3) 638.024 0.13 (4)
165.034 0.25 (4) 653.473 0.72 (3) '
176.518 0.73 (4) 721.487 0.30 (3)
196.995 0.53 (3) 775.071 0.29 (3)
253.708 0.20 (4) 784.410 0.33 (4)
257.019 0.14 (4) 789.361 0.75 (3)
334.618 0.92 (3) 795.875 0.45 (4)
379.847 0.40 (3) 808.700 0.16 (3)
386.197 0.39 (4) 882.269 0.14 (4)
397.030 0.26 (5) 1010.372 0.30 (3)
412.295 0.37 (3) 1152.783 0.24 (3)
432.459 0.71 (3) 1397.440 0.11 (4)
437.941 0.55 (3) 1702.252 0.15 (3)
463.404 0.47 (3) 1758.145 0.23 (3)
476.839 0.16 (4) 1778.766 0.49 (3)
488.953 0.88 (3) 1880.932 0.19 (3)

510.959 0.12 (5)

239

 

 

 

  
  
    

 

 

 

 

 

 

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Table 27. y-ray energies and peak areas for transitions observed
in a Sm1”“ target four days after the bombardment.

 

 

 

Energy Energy '
(keV) Peak Area (keV) Peak Area
138.052 0.17 (4) 337.758 0.59 (4)
148.829 0.37 (6) 244.737 0.13 (6)
154.141 0.28 (6) 350.037 0.66 (4)
169.806 0.53 (4) 367.983 0.53 (5)
173.913 0.91 (4) 386.001 0.31 (4)
179.154 0.13 (5) 394.075 0.98 (5)
189.890 0.21 (5) 409.015 0.19 (4)
196.057 0.29 (6) 420.083 0.96 (3)
210.665 0.40 (5) 428.642 0.64 (4)
215.580 0.11 (5) 434.439 0.16 (4)
227.782 0.46 (6) 442.036 0.15 (4)
236.752 0.10 (5) 458.174 0.21 (4)
241.176 0.96 (4) 477.166 0.26 (4)
250.255 0.82 (4) 483.250 0.78 (4)
259.233 0.23 (5) 494.858 0.12 (5)
269.937 0.28 (5) 509.501 0.17 (5)
277.202 0.65 (4) 515.115 0.67 (4)
285.404 0.64 (4) 532.910 0.11 (5)
296.746 0.20 (6) 541.234 0.80 (4)
307.910 0.15 (5) 557.723 0.11 (5)
316.582 0.72 (4) 581.941 0.29 (4)

325.821 0.31 (4) 586.213 0.17 (4)

242

 

 

Table 27. (Continued)

600.299 .13 (5) 929.507 .19 (5)
608.517 .71 (4) 933.776 .80 (4)
617.978 .46 (4) 939.333 .54 (4)
624.2.6 .98 (4) 938.604 .15 (4)
632.694 .67 (5) 956.628 .48 (4)
644.447 .43 (4) 969.928 .13 (4)
652.685 .25 (5) 975.647 .59 (3)
660.736 .23 (4) 989.451 .38 (3)
664.793 .74 (4) 996.274 .16 (4)
676.830 .18 (5) 1007.357 .11 (4)
692.274 .12 (4) 1059.535 .25 (4)
702.463 .59 (4) 1070.312 .59 (4)
726.527 .57 (3) 1078.163 .79 (4)
741.713 .24 (4) 1116.643 .53 (3)
747.034 .83 (5) 1121.741 .13 (4)
754.787 .16 (4) 1131.624 .47 (4)
765.397 .15 (5) 1151.083 .81 (3)
776.826 .84 (4) 1160.404 .31 (3)
788.677 .15 (5) 1173.832 .78 (3)
798.587 .95 (4) 1177.014 .67 (3)
835.001 .40 (4) 1237.704 .11 (4)
846.691 .81 (3) 1256.340 .81 (3)
857.173 .40 (4) 1274.970 .13 (4)
861.709 .23 (4) 1297.552 .18 (4)
880.552 .41 (3) 1325.341 .72 (3)
894.136 .82 (5) 1332.755 .96 (3)
911.326 .20 (4) 1360.289 .19 (3)

243

 

 

Table 27. (Continued)

1407.963 0.88 (3) 1804.775 .55 (3)
1423.464 0.25 (3) 1858.433 .19 (3)
1461.246 0.88 (4) 1877.228 .60 (3)
1533.335 0.27 (3) 1931.645 .26 (3)
1534.024 0.19 (4) 1997.581 .31 (4)
1587.674 0.40 (3) 2053.078 .20 (3)
1593.272 0.70 (3) 2081.450 .41 (3)
1659.010 0.78 (4) 2103.933 .17 (3)
1756.281 0.19 (3) 2204.446 .34 (3)
1765.016 0.15 (4) 2437.360 .17 (3)
1785.094 0.19 (3) 2448.057 .10 (3)
1796.490 0.36 (3) 2614.826 .13 (4)

244
original production of Dy1”7 at the time of bombardment. One could

argue that the 147 mass chain was originally populated by a (formal)
fhfl9“(C12,3p6n)Tb197 reaction and this certainly cannot be ruled out.
However, as will be discussed in §4.4.2.C., there is other evidence
that Dy197 is produced.

An interesting sidelight is that when using the Sm194 targets we
were still able to observe Gdlkfiy in the resulting spectra. This
suggests a reaction which could be written as Sm1““(012,2a3xDGd1“5.
Whether this product is produced via a compound nucleus (or possibly

a stripping reaction) is uncertain.

4.5.2.B. Conversion:E1ectron Experiments

 

 

Anfid4 transition of 171 keV should have a}(-conversion
coefficient of :50. Both the BMW2 and the Sm191+ targets were used
to obtain 8+ spectra with the Si(Li) surface barrier detector des-
cribed in §2.2.2. At no bombarding energy (70-120 MeV) were we able
to identify any conversion peak rising above the 3+ continuum. Thus,
if we are indeed producing Dylkfin, as we believe, it either has a
half-life shorter than we are able to cope with or it decays pre—

dominently via an E/B+ branch.

445.2.0. X—ray Experiments.

 

\

An x-ray detector (described in §2.2.4) became available for use
during the experiments with Smlgq. Spectra were taken for Sm19“
targets, bombarded at various energies, both immediately after the

bombardments and at later periods. While x-ray peaks cannot show

245
the specific isotopes which are making contributions, they are very

useful for confirmation of the elements being produced. In our

case, we could verify that immediately after bombardment the Tb x-
rays were the most intense ones present. This is what would be ex-
pected for the ground state decay of Dy. By following a given target
versus time it was possible to watch the Tb dying away and the
daughter x-rays (mostly Gd and Eu) increasing in intensity. The fact
that there was no recognizable Dy peak is added evidence that we are
not able to ”see” the isomeric transition in DyUV7. We are un-
doubtedly also producing higher mass Dy species such as DylHB, Dylhg,

etc., but we cannot pin down the relative abundances from these ex-

periments.

4.5.3. '1-ray versus x-ray Coincidence Experiments.

 

Since the x-ray detector had quite high resolution (275
eV @ 6.0 keV), it was practical to set up a y—ray versus x-ray co-
incidence experiment with a coincidence gate set on theKB x-ray
of Dy. In this manner we could identify those Y rays which were in
coincidence with the Dy x-rays.

Possibly a few comments are in order on some of the difficulties
encountered with this type of experiment. First and foremost is the
inherent differences in the timing characteristics of the x-ray and
the y-ray detectors. In this case the x-ray detector had a much
greater "walk" problem than did the y—ray detector. Therefore the
dynamic range of the coincidence experiment for a given resolving
time was much less than for other types of coincidence experiments

which we have performed. Another problem is that of finding a

246

source having coincidence-Y and.x~rays which can be used for timing
purposes. Since positron sources cause saturation and ringing prob—
lems in the x-ray detector, it is best to use a source decaying solely
by electron capture. Since this "ideal" source was not available at
Yale, we set up the electronics using the same source as for the
experiment. Still another difficulty is detector geometry. Because
of the large size difference between these two detectors it is diffi-
cult to obtain similar counting rates in each. The source must be
placed by trial and error to maximize the count rate.

Our coincidence Spectrum is shown in Figure 53 along with a
self-gated singles spectrum taken at the same gain. The net relative
peak areas for the coincidence spectrum are compared with their
singles values in Table 28. From the analysis it is found that the
peaks at 100.7, 176.5, 397.0 and 620.3 keV are clearly in coincidence
with the Dy x—rays. As in the previous types of experiments, we are
still not able to identify explicitly those peaks due to the decay of

Dy1'47,

4.5.4. Discussion

 

It has become obvious that more research will have to be
done on this region in order to elucidate further the structure of
Dy197. In particular, more complete and detailed information for
such species as Dy198, Dy199, Tb197, Tb198, Tb199, etc., is needed.
What little work has been reported on this region has been carried
out with scintillation methods and lacks the detail which we need.

In summary, the research which we have conducted to date allows

us to say that if Dy197m exists for a period of time long enough for

r1111 CHANNEL

VVUIV 1 O

247

 

A.Coincidence Spectrum

3920

'0
16
N
10

 
 

 

 

 

 

 

 

11111 1 "' "l'
250 500

750 IOOO

3910

B.Self—Goted Singles

5&0

 

 

 

 

 

 

1 1 1 1
O 500 IOOO l500 2000

CHANNEL NUMBER

Figure S3. y-ray versus x-ray coincidence spectrum from a Sm”1+
target compared to a self-gated singles spectrum at
the same gain.

 

248

Table 28. Coincidence results from the y—ray versus x—ray experiment

gggggggg g; g ggl'“ tggget.

 

 

 

 

 

Energy a Peak Areab
(keV)

Singles Coincidence
100.7 39.8 41.3
106.2 20.5 29.6
176.5 13.1 15.8
253.8 10.8 17.4
386.6 8.42 14.2
397.0 5100 2100
477.1 ? 3.6
511.0 108 13.0
547.1 3.09 4.45
620.3 26.5 26.7
652.5 4.75 7.69
a

These energies were obtained by using an external Co56 standard
spectrum. Hence, they should not be depended on to be closer than
$1.0 keV.

b

No efficiency curve was available for the detector used in this

experiment.

249

us to count it must decay predominantly via e/B+. .xeray spectra
show us that the mass 147 chain is populated. The x—ray gated spec-
trum identifies the more prominent peaks in coincidence with Tb
x-rays. Hopefully these results will be useful for further investi-

gations in this region of nuclides.

250

CHAPTER V

MULTIPOLE RADIATION AND THE SINGLE PARTICLE MODEL

Nuclear reactions which are initiated by accelerated ions
generally occur via a compound nucleus which, in turn, emits one
or more neutrons (and frequently 0 particles 0 protons). This
leaves the product nucleus on the neutron—deficient side of B sta-
bility. Consequently, the nuclei studied in this investigation, which
were produced by cyclotron bombardments, are e/B+ emitters. To account
theoretically for these processes of nuclear decay requires the ad0p-
tion of a model of the nucleus with explicit mathematical relationships

for the interactions among nucleons.

Almost all nuclear excited states decay at least occasionally
by spontaneous emission of electromagnetic quanta, emission which can
be characterized inafashion analogous to the multipole description of
atomic transitions. The intent of this chapter is to give the main
steps on the way to obtaining numerically tractable equations express-
ing the matrix elements and transition probabilities arising when a
single, unpaired nucleon changes its angular momentum state, i.e., by
using a simple shell model picture of the nucleus. Since this type
of model is particularly applicable to nuclei near closed shells, it
will be of interest to compare these theoretical predictions with the
experimental information available for the M4 transitions of the odd-

mass nuclei near closed shells. These calculations have been used in

§ 4.2. and will be used in Chapter 6.

251

5.1. Multipole Radiation

 

y rays were recognized to be electromagnetic in nature by
von Laue in 1923. The description of this y-ray process essentially
uses the theory already developed for atomic transitions, that is,
using the theory of multipoles. Several books (Jac62,Roy67,Mosz65,
Blat52) describe this theory in varying detail. The notation used
in this chapter is pretty much common to these texts.

The job at hand is to describe in some way the electro—
magnetic field that causes the emission of an energy quantum from a
de—excitingnucleus. The source of the emitted quantum is then to be
described in terms of a charge-current distribution confined to a
small region of nuclear dimensions. The field and the source must
then be connected and finally transformed into the equivalent quantum
mechanical expressions.

This overall derivation is most eloquently expressed by the
use of quantum electrodynamics; however, this requires more math-
ematical SOphistication. It is therefore desirable to carry
the derivation as far as possible in classical terms and then trans—
form the result to the equivalent quantum mechanical expressions.

It will be seen that electromagnetic transition probabilities
can be derived without invoking a specific nuclear model. The so-

called "long-wavelength" approximation is used, the wave length of the

252

electromagnetic radiation being large relative to the nuclear dimen—

sions. Finally, after the expressions are derived in general terms,

a model must be introduced in order to obtain numerical results.
Before beginning the derivation, several mathematical re—

sults, which will be used along the way, must be considered.

5.1.1. Mathematical Paraphernalia
The theory of multipole radiation draws on a diverse set
of mathematical techniques. A few definitions and results that will

be needed later are given in this section.

5.1.1.A. Angular Momentum Operators

 

The orbital angular momentum operator is defined as

+ l->->
L = I(rxv) ,

or in cartesian coordinates,
it '1'I.+'> +KL
x 32y 2’

These components can be regrouped as follows:

... 3 W L - 3— (1)
L+ - Lx + iLy e (30 + 1cotea¢
= _ = ”W _ L §_
L_ Lx iLy e ( 30 + 1C0t08¢ (2)
3
L2 — i—a'a (3)

Angular momentum identities which will be useful later on are:

253

 

 

 

 

LZZ = LL (4)
LXL = if (5)
Ljv2 a VZLj (6)
where V2 = :::2(r) — %;-- (7)
5.1.1.8. Spherical Harmonics
Spherical harmonics are solutions to the differential
equation
Lngm = -[sifll0 a—g— (sine 8%) + sir1120 32:]Yim = £(£+1)Y£m, (8)

where L is the total angular momentum, 6,0 are the spherical co-
ordinate angles, and Y2m are the spherical harmonics. These solutions

are usually written as

(22+1)(2- )1‘ 1
Y2m(0,¢) = ‘J m P2m(cose)e m0, (9)

 

4n(£+m)!
where the first factor on the right side of the equation is for nor-
malization. These functions form an orthonormal set with the orthog-

onality condition:

2‘" TI’ *

I do Isine de Y£,m,(6,¢)Y£m(6,¢) = 6£,£ 6m,m (10)
0 0
The "P" functions in the expressions are called associated Lengendre

functions and can be expressed as

m/2 dm

m ___—___—
P1m(c°89) = (‘1) (1-c0820) (d(cose))m

P£(coso). (11)

Retreating one more step, we have the Legendre functions defined by

the recursion relationship

254

 

7.
1 (1 7 2.
’ \ ‘ = - . l _-
IK(CObU) 212! l (d(cosu))y I (COS , 1) ' (12)

For our purposes, the vector Spherical harmonics can be

defined as

+ 1 +
X = ___—- L ° Y (6,¢) 0 (13)
m I: 2(2+1) 5““

The first factor on the right arises from normalization. Operating
on the spherical harmonics with the angular momentum operators of

Equations 1, 2, 3 yields the results:

 

 

L+Y£m = /(£-m)(2-+-m+l)Y£’m+1 (11.)
L_Y£m = f(2,41n)(9.-m+1)Y1,m_1 (15)
LzYim = inm (16)

5.1.1.0. Laplacian Operator
The Laplacian operator (V2) can be written in terms of

spherical coordinates (r,0,¢) as

 

 

 

 

2.1.2.. 2.3... T1.....__'a__ 8_ 1 8’
V 7 r‘ 3r(r 3r ) '+ r sine 80(Sin0 80) + r7g1576 302 (17)
5.1.1.D. Bessel Functions
The differential equation
d2R 1 dR v2
dx2 + 32'3"- + (l-Si—E)R - 0 (18)
is called the Bessel equation. The two solutions are
J (X) 3 (§)\) 2 £-l)j §)23
v 2 j!1‘(j+v+l) 2 (19a)
1’0
j .
J = .E ‘V ::E (‘1) .fi 23 1
_v(X) (2) j,r(j_v+1) 2) ( 9b)

1'0

These are Bessel functions of the first kind of order iv. These two
solutions are linearly dependent when v is an integer. A second sol-
ution which is always linearly independent with Jv has been found to

be

Jv(x)cos VW - J_V(X)

Nv(x) = sin VW (20)

 

This is known as the Newmann function or Bessel function of the
second kind.

It is generally useful to combine Bessel and Neumann func-
tions to form Bessel functions of the_£hi£d kind. These are known as

Hankel functions and are written as

HV(1)(x) Jv(x) + iNv(x) (21a)

HV(2)(x) Jv(x) - iNv(X) (21b)

Hankel functions are still valid solutions to Bessel's equation and
are frequently the form of the solutions that are used in problems.
Now that the Bessel functions have been defined in their most general
form, we need to consider specific cases which will be of use in

the present derivation. If we redefine the equations as Spherical

Bessel functions and let v = E + %3 the following formulas result:

..t
J,<x) - [§;} J,+% (x) (22a)

nz(x) = (g;) Ni+% (x) (22b)

h2(132)(x) = [E]*[J2+1/2(X) + 1N2+1/2(X)]. (22C)

256

It is often difficult to evaluate expressions numerically containing
these functions. Under certain circumstances asymptotic values can
be used. In particular, it is useful to look at the expressions which

result when x<<l and for when x>>l.
Asymptotic limit for x<<l

This would be an appropriate approximation for working atomic

and nuclear problems. In these cases the wavelengths of the emitted

quanta are large compared to the size of the source (nucleus). In

this limit the results are:

 

n
A X
12(x) ’ (22+1)11 (23a)
- 22+1 11
“2(x1-+-£;E;il——' (23b)

Asymptotic limit for x>>l

 

A useful application for this asymptotic limit (wave-zone
approximation) would be in describing fields far from the source such

as problems dealing with angular distributions. The appropriate ex-

pressions are:

j£(x)-+'%-sin (x- £g)

(23c)

n£(X)-+ —- i- cos (x- 1%) (23d)
, ix

h§1)(x)—+(—i)2+1'g;— (23c)

257

5.1.2. Maxwell'squuations

All of electromagnetism is contained in the Maxwell equations.
It has been said about electrostatics (a subset of these equations)
that "°°'there is nothing to the subject; it is just a case of doing
complicated integrals over three dimensions'°°" (Feyn64). This is
just as true for the full set of Maxwell equations. The catch is
knowing how to solve the integrals.

In a source-free region, Maxwell's equations can be written

 

as + + 1315 13?:
—> —>
V =— =_._._
x E cat V x B c at
(24)
++ —>—>
V°E = 0 V-B = O
In the quantized case, the frequency is proportional to the energy,
and thus has a definite value. In this manner, by assuming a
sinusoidal time dependence of the fields, the fields may be written
as
3 + _ + + —iwt
.E(r,t) - Re[E(r)e ] (25a)
2 + ‘+ + —i t
B(r.t) = Re[B(r)e w ] (25b)
where m is the angular frequency, related to the pr0pagation vector
+
k by w = kc, where k = 2n/A.
This assumption allows the rewriting of the equations thus:
-> —> + —> + —>
V x E = ikB , V X B = -ikE (26)
This set of equations can be reduced in number by solving for E or
B in terms of the other. Thus, on elimination of E
(v2 + k2)§ = o
(27)

+ +
V x B

+
E =

x4e:

+ +
V°B=O

258

_)
On elimination of B, an equivalent set of equations can be

written as

<Nr
Bil
ll
0

(E72 + kzfi = 0
(28)
17 x E

_).
B=-

xflhl

In each of these sets the first equation is seen to be a vector
Helmoholtz equation. It is now necessary to determine the multipole

solutions of the functions E and B.

5.1.3. Multipole Expansion of the Radiation Field

 

For a time varying EM field we need an expansion in terms of
vector spherical waves. It is easiest to consider first the scalar
wave function, which can be written as W(;,t) and which satisfies the
wave equation,

2
2 _1i_‘k=
v11; Fat2 0

A Fourier analysis in time yields:
W(?,t) = fim9(f,w)e-iwt dw (29)

where w = kc and k is the propagation vector. Each component of the

above transform satisfies the Helmholtz wave equation
2 2 ‘*
(V + k )w(r,w) = 0.

V2 is the Laplacian operator as given in equation 17. Assuming the
nucleus to be symmetrical about its orgin, solutions can be found to
the Helmholtz equation in terms of Spherical harmonics. Therefore,

solutions are sought of the form

1115,10) = Zf£(r)Y£m(6,¢) (3o)
£,m

259

in terms of the Spherical harmonics as defined in equation 9. The

functions fe(r) are related to the Bessel functions of equation 19 by

’b ..
f£(r) % l:- J£+%(x) _ l;(2%)j£(x), where x Ekr. (31)
r2

Equation 30 can be written because of the assumptions made in arriv-
ing at equation 25. This is just the familiar separation of var-
iables technique, separating the radial and angular parts of the
function. Utilizing the Hankel function (22c), a more general

statement (30) is

1.62) = Z [zigmdékm + .42“ 18,40] Y,m(e.¢) (32)
2 m

The X's must be determined from the imposed boundary conditions.
Since each component of 8 satisfies the Helmholtz equation

(27), it can be written in an analogous fashion to (30) as

B = 2[ 11‘3“ h‘ikkr) + Mandi) (kr)] Y£m(6,¢) (33)
2,m

+
The condition V-B=0 must now be considered. This condition must

hold separately for each term in (33); for example, the A's must

satisfy the requirement

v - 22,11“ 112(k) Am Ym(0,¢) = 0. (34)

Using the spherical coordinate expression for the gradient

+
V a

nlu+

3 1 + +
"a—E-p-I'XL (35)

260

yields
ah ih 2 :1
—+ 2, —> 2, -«> —> _
r . Z [ r 2 Aim Yim - r L x Aim Yfim - O (36)
2 m

The recursion formula for the spherical Bessel functions dictates

the requirement
. 3 = (37)
r Z Aim Yim O

in order for the A's to be uncoupled. Equation 34 also requires the

condition

2m 2m

2 - (f x :2: X Y ) = 0 (33)

m
to hold. These two conditions (37 and 38) are all that are necessary
to determine a unique set of functions.

It turns out that a solution fulfilling all requirements is

K Y i Y
Z l’m’ 25m’ 2 aim 2m (39)

’

m m

(37) is satisfied since :-L = 0

(38) is satisfied since

++ + ~+

- + +
r°(L x Aiinm) = r°(L X a2m L Yim) = a},m r°(iLY2m) 0 (40)

—> -~>
again since r-L = 0.

By assumption (37) we now have a Special set of functions, fulfilling

the Schradinger equation, and forming a set of electromagnetic fields.

261

Elm - f£(kr) L ng ( )
_ _1 T

Eim - k V x Bim

f2(r) = A(:)h(:)(kr) + A(:)h(:)(kr).

Any linear combination of this Special set of functions will satisfy
the Maxwell equations. They also exhibit the pr0perty that the

radius vector is perpendicular to the magnetic field,

The reduced set of Maxwell equations (28) could have been used equally

well to arrive at the eXpansion

E - f (k ) Z Y

m ' 2 r 2m (42)
+ i ->
82m ‘ "E'V x Ezm

.+
The expressions L-Y in equations (41) and (42) are the vector

lm’
spherical harmonics which were defined in (13). Using this expres-
sion, together with the most general combination of equations (41)

and (42), a solution to the Maxwell equations can be written as:

E = Efl— ka aE(£ m)V x f £(kr) Xfim + aM(2,m)g£(kr) X2;] (43)

B =- % [ aE(IL,m) f£(kr) le - i. aM(Q,m)-V X 851 (kt) 329m] (44)
£,m

The coefficients aE(£,m) and aM(Q,m) are the magnitudes of

each field component. These are to be determined later.

5.1.4. Sources of Multipole Radiation

Once the description is obtained for the multipole radiation
field, it remains to describe similarly the source of these fields.
The usual procedure is to assume that these fields arise from three
localized distributions in the nucleus: The charge density (p(¥,t)
current density 3(;,t), and the intrinsic magnetization M(f,t).
Assuming harmonically varying quantities, these distributions can be
written as

_ 9 _. + + _.
p(?)e iwt’ J(?)e 1wt, and M(r)e 1wt, respectively.

In the presence of these sources, Maxwell's equations in

vacuum can be written as

:.§=.a,:a=o (w)
-> -> —> 4 -> +
VxH+1kE=—J, V-B=4flo

along with the continuity equation

.)

+
V'J -' 1400 00

It is desirable to have the solutions in the same form as for the
source-free case. Consequently, to obtain a vanishing divergence

for the E field it is rewritten as

+

E' = E + 4ni

w

 

.+
J C
With this substitution, reduced sets of Maxwell's equations can be

written similar to (27) and (28).

For E—radiation

 

. .
w2+em =-glhx3+c:.$.fl (a)

263

For M-radiation

 

+ -> + -> ->
(V2 + k2)E’ = - é??- [CV x M+ -1]—;-2—V x V x J] (47)
—> + + -‘1 -> -> 41Ti + +
v-E’=o, B-T(VXE’-—w—Vx J)

Outside the source these equations reduce to (27) and (28). Inside
the source 8 and E still have vanishing diverguences and thus can be
solved for with the preservation of the general form (44) which has
already been derived. The sole difference arises in the form of the
radial functions, f£m(kr) and ng(kr)° For example, the magnetic

induction is written as:

+ -> 1 + +
B 3 E [ fun“) Xim ' '12 V X 3m“) Kim] (48)
i m

We need to determine the equations satisfied by the elec-
tric multipole function f£m(r) and the magnetic multipole function
g£m(r). To do this, the above expression for 8 is substituted into
the first equation of (46), the scalar product of both sides with
some 21m is taken, and the result integrated over all angles. In this
fashion an inhomogeneous differential equation results. By substitut—
ing an equivalent expression for E’ into the first equation of (47),
and following an analogous procedure, the same type of differential
equation results. Both of these equations can then be solved by means
of a Green's function technique. More details on this procedure are
given in several texts, for example (Jac62) and (Ray67). The solution

of the equations for f2m(r) and g£m(r) allow the identification of the

multipole coefficients. Since, as has already been mentioned, the

264

long-wavelength approximation is used (krmax<<l), the asymptotic
limit (equations 23) can be used for the Bessel functions that arise.
On keeping only the lowest order terms involving kr, the approximate

solutions are

E—Coefficients

 

2+2
4 k 2+1 ’4. ,
aEUL’M) 3 12224-1)” ( 2 ) mm + 2m) (493)

where the Q's are multipole moments defined as

92‘“ 3' I rZY’Em “‘13" (4%)
I _ -+ ~> +
le = E§§~Jr2 ng V°(r x M) d3x (49c)

M—Coefficients

 

2+2

_ 4nik 2+1 ,

anm’m) ‘ (22+1 I! 2 (M2111 + M2111) (508)
where,
M = -—-1— if ;- (£15432. (50b)
2m 2+1 1' 2m c
—>

M9; 3 - JrP'YZn V o“ d3x (50C)

\

In equation (49c), the expression for Q’Rm is usually much
smaller in magnitude and can be dropped from further consideration.
In equations (50b) and (50c), both the momentMEm and the intrinsic
moment M"2m are of similar magnitudes and must be retained in further

calculations.

265

5.1.5. Transition Probabilities

The total power radiated by a pure multipole over all angles

is given by
c (51)

811k2

 

ll

2
P(2-.m) |a(i.m)l
where P is the total power radiated and the a's are the multipole co—
efficients. In quantum mechanical terms, the transition probability

is given as

. = .1. = .13_ (52>
T hm
where T is the transition probability and 1 is the mean life of the

Species. This allows transition probabilities to be written as

 

 

2'11C 9+1 2‘1,+2 ' -”
9, = -- : ___- ! 53
TM( ,m) lim[(22+l)!!]/ V, le’m + M2111! ( a)
T (2 m) = 2“ a (“1) 18“? l2. + Q, l7 (53b)
E ’ fiw[(29.+l)!!]’~ 2 2m 2m _
The expressions for the multipole moments must be changed from the
classical expressions for charge and current densities, as given by
equations (49) and (50), to their quantum mechanical equivalent.
That is,
> * , ->
p(r) ..__+ 2 e ¢f(r) wi(r) (54)
and
t. > - E * " + " _jl'h7*'41 , (55)
m) ——> 2m 1, (F)p‘l'i(r) - m L i - 1.1511]

where wi and wf are the initial and final states of the transforming

266

nucleon. The results of these transformations are

2.
Qim = e <f|r ngli>

--> ->

’ - 1212;. -* +.-* 1* 2* 2.2 .

Qim - - 2(2+1)M7‘f|un O x r V(r Yim) +12r Yfim 5 l1
_ 811 + 2* +

M2111 ' (2+1)M < flu" Y2m L)“ >

’ - 1 ED. +o+ Q * '

Mm — éunM <f|o V(r ng)l1>

This is about as far as the equations for the electric and
magnetic multipole transition probabilities can be carried without

first introducing a specific nuclear model.

5.2. Single Particle Transition Probabilities

Numerical evaluation of these multipole expressions can
be obtained most easily by resorting to the shell model (humorously
called "simple"). This model provides expressions for the wave
functions and subsequently the radial matrix elements. It assumes
that the structure of the nuclear excited states is due entirely
to the last single, unpaired nucleon in the nucleus, either a proton
or a neutron. The nuclear spin is determined solely by the angular
momentum of this unpaired nucleon. 7 transitions from the excited
nuclear states are viewed as changes in the state of the odd nucleon
under the influence of spherically symmetric potential created by

the remainder of the nucleons in the nucleus.

(56a)

(56b)

(56c)

(56d)

267

The usual procedure for formulating the single-particle
transition probabilities is to assume the odd particle to be a proton.
Neutron transitions can then be expressed by slightly modifying these
expressions. The expressions for the proton transition probabilities
are derived in (M08265).

Considering transitions of a pr6ton in a central velocity

independent well, equations (53) and (56) can be simplified and ex—

pressed as

 

 

m 2
(EL) 2(2+1) e2 ma 22. £_2
Ti+f " 2[(22+1)11]2 “(1:5) (‘5 (JOKES) nil-2.11) “31”“? (573)
(ML)_ 2(lifl) _§g_g§_22.ih_ 2, 2 2 m £_2-1 2 2
T1+f ' 2[(22+1)!!]?‘”hc c ) (Inca) (“pl ’ m)( 0Rf(a) R1 r dr (57b)

“5(310293f)

In these equations, 2 is the angular momentum carried away by the
emitted quantum.
R1, Rf = Radial wave functions of the initial and final
states, respectively.
w = (Bi-Ef)/H
c = velocity of light
a - nuclear radius
u - proton magnetic moment
S - statistical factor

The statistical factor, 8, represents the angular dependance of the

transition probability and can be derived as

268

S<ii.fi.jf) = (2jf + 1)[<ji%jf%|jijf20>] (58)

where the bracketed term is a Clebsch-Gord 1 coefficient. For the
Special case where [ji—jfl = 2, the results are comparatively simple.
For example, the statistical factor for the M4 transitions considered
in this thesis is

3(11/2,4,3/2) = 15/11.

The radial integrals can be evaluated only after substitution of ex-
plicit forms for the nuclear wave functions.

On the basis of a constant density model, where the wave
function is constant over nuclear dimensions and zero outSide the

nucleus, the radial integral can be evaluated as

3
(2+3)

 

L Rf(§)2Ri r2dr2 - (59)
Using this assumption, along with a = l.2><10-13 cm and up = 2.79,
we can simplify the transition probabilities to a point where they can
be evaluated numerically. Several of them are listed in Table 29 for
reference. Again, it must be remembered that these equations apply
to a very specific case, that of a single proton in a spherical well,
considering the wavefunctions to be constants, and for particular
fixed values for a and u .

As explained in (M03265), magnetic transition probabilities
in odd-neutron nuclei are expected to be smaller than odd-proton

nuclei by the factor

269

Table 29. Expressions for single-proton transition
probabilities.

 

E1 1.0x101“° A2/3' E3 5
E2 - 7.4x107 - A“/3- E5 5
E3 = 3.4x101 . A2 - E; 5
E4 = 1.1x10“5- A8/3- E9 3
E5 = 2.5x10“12 AID/3 Ell 3
M1 = 2.9x1013- A0 -. E3 3

M2 = 8.4x107 - A2/3- E5 5

M3 = 8.7x101 - A“/,- E7 s

Y
M4 = 4.8x10’5o A2 .- E3 5
M5 =

1.7x10-11 A8/3' EL1 3

These equations are approximations for proton transitions,
assuming constant nuclear wave functions, up = 2.79 and a =

1.2x1o-13cm

270

 

11,, 2
up-(£+1)'T J (60)

The M4 transition probabilities calculated for the present invest-
igation have included this factor. Particular use has been made of
the resulting M4 expression in § 4.2 and will be used further in
Chapter VI.

These single particle estimates are the ones most generally
used when estimates are sought for transition probabilities. Hence
it is important to have a feeling for the method used in deriving
these equations and the approximations used along the way. Hopefully

this chapter contributes to that understanding.

CHAPTER VI

SYSTEMATICS OF THE Z=63 AND N=82 NUCLEI

AND DISCUSSION OF SOME.M4 ISOMERS

As mentioned in Chapter I, this thesis project began as a
study of the decay properties of the neutron—deficient, odd-mass Gd
isotopes. In this vein we studied Gd”9 and Gd155m+9 (§ 4.1, § 4.2,
and § 4.3, respectively). The first part of this chapter is a brief
look at these results along with previously published data on the
decay of Cd”7 and Gd151. The levels in Eu1“5 will then be cone
sidered in relationship to levels in other N-82, odd-mass nuclei.

The second part of this chapter compares the trends in several series
of.M4 isomers. The energies and reduced transition probabilities are

plotted.

6.1. Levels in Neutron-deficient, Odd-

mass Eu Isotopes

 

The neutron-deficient Eu levels can be traced only over
four Eu isotopes with any certainty: Eulus, Eu157, Eu159, and EulSI.
Eu1“3 has not as yet been studied in enough detail for levels to be
placed, however, it is reported (Ma166 and Kot65) to have a half-
life of 2.3-2.6 minutes, with no strong y rays having been observed.
Atthe other end of the scale, Euls3 exhibits rotational structure
and thus is of limited use for our purpose. Figure 54 is a plot of

those Eu levels which have been assigned spins and parities. The

271

ENERGY (MeV)

2.0

LB

0)

in

ix)

5

0.8

0.6

04

0.2

 

:21..—
145

Eu

Figure 54.

 

272

5',7',9'

9',II" + §
5*7‘9-4—5 7
..L.L./EFfi§7fiFF‘
5+ 7013+
21f];—
ll' ___—5‘ 7.

7+

Il‘
_
3*.5’g7+

7+

5 0 5+ §4-
|47 I49 ISI

Eu Eu Eu

Levels in Eu nuclei which are populated by B decay.
Spins are shown in units of 2J. Only three levels

 

‘ are shwon for which spin assignments have been

made.

273

Hull”S levels are taken from § 4.3. and (New70), the Eu1|+9 levels

from 5 4.1, and the Eu11+7 and Eu151 levels from (T167). In all cases
the ground state is 5/2+ and the first excited state is 7/2+, as would
be expected from a simple shell model picture. The only other states
that can be followed with any regularity are an 11/2— and a 9/2- state.
In all cases these states drop in enrgy as one moves from the closed

shell at Eu”5 toward the rotational systems.

6.2. Levels in Odd—mass, N=82 Nuclei

The odd—mass, N=82 nuclei are much better characterized than
are the odd-mass, Z=63 nuclei. For the N=82 series, extending from
1135, experimental information is known both from B-decay studies and
from stripping reactions. Some of this information is summarized in
Figures 55 and 56. The levels having assigned spin and parities as
determined from B decay are shown in Figure 55 and the levels known
from stripping reactions are shown in Figure 56. This latter figure
is complements of Wildenthal, et al., and, in addition to showing the
energies of the levels which are excited by the stripping reactions,
it shows the magnitudes of the spectroscopic factors by the width of
the lines marking each level. The lines connecting the various levels
trace the energy centroids of the single particle orbits in the

"961,13" 8118].]. (lg7/2,2d3/2,2d5/2,381/2, and 1h ). From these

11/2

stripping reactions the 5 single-particle states can be traced in
137 145

all of the species from Cs to Eu . The d3/2, 81,2, and h11/2

states decrease in energy with increasing proton number over the

series. Notice that the g7,2 and 675/2 states cross each other in

ENERGY (MeV)

|.2

LO

0.8

0.6

0.4

0.2

 

I35

Figure 55.

274

 

1’ 3‘
—.'—.-—
.14.}.—
I. 3. 50
'0 :0 :0
(5')
(3’)
30
I.
H-
7+
5‘ 7*
7O 7* 5+ 5+ 50
I37 l39 l4l I43 I45

Cs Lo Pr Pm Eu

Levels in odd-mass, N=82 nuclei which are populated
by B decay. Spins are shown in units of 2J. Only
those levels are Shown for which spin assignments
have been made.

275

Q'. ..
M v

N AA‘IIRNk _
u 9%

 

 

X3
MOW) A983N3 NOI1V1I3

276

going from La139 to Prlgl. As mentioned in §4.2, this makes the
7/2+ assignment for the 329.5-keV level in EulLis quite certain even
though there appears to be a small 8 branch to this level from the

+
B decay of GdlkSg (1/2 ).

6.3. Survey of a Few M4 Isomeric Series

Study of M4 electromagnetic transitions continues to hold
a special interest for the testing of nuclear theories. In particular,
the high multipolarity electromagnetic transitions from such excited
states are considered the best candidates for being relatively "pure"
single particle transitions. A considerable effort has been expen-
ded on the study of these isomers, particularly the.M4 isomers found
in the odd-mass, N=81 nuclei. This series was discussed at some
length in § 4.2. in conjunction.with the decay of Gd125m and its
associated 721.4—keV M4 transition. Figure 57 shows the experi-
mentally measured isomeric transition energies for this N=81
(1112’—+3/2+) series and also for the N=79 series for comparison.
The experimental reduced transition probabilities, IMIZ, are also
shown on the figure. These probabilities were calculated by using

experimental energies and half-lives in equation (57b) of § 5.2. and

solving for the factor

00 g, 2
_ 2
L 5’ng Rir dr
0

which is defined in the same section. Partial half-lives for the M4
branches were determined from the experimental half—life values and
dividing by the percent decay via the.M4 branch. y-ray half-lives

were then computed by multiplying the M4 half-lives by the factor

7 ENERGY (keV)

I12!2

800

600

400

200

277

 

 

 

 

 

I I I I I I I I
I.— _—
739 .141 ' 0
. Ce Nd 3mm 0 d145
— BOB? ""
0
)Q;35
133
Te 24
I35 x x
— x X9133 BO CeI37 Nd '39 11x11l4| .—
Te131 Sm
l I I I I I I I
I I I I T I I I
—- ‘3' x:h¢:7¥) _—
Te 0: N=8l
h- )«933 .2
86'35 "139
_ T6133 Cexll’a? Nd ...
o
__ 2&935 __
I37 .59
I30 (Se . . 1.
L— Ndl4l Sm'43 Gdl45 _L
I I I I I I I I
A= |3I I33 I35 I37 I39 I4| I43 I45
Figure 57. Upper: M4 transition energies for the N=79 and N=81

isotones.The Sm11+1 point is predicted (see §4.4.5).
Lower: Values of the squared matrix elements for the
single-neutron isomeric transitions in the same nuclei.

278

(1+atot), where a is the total theoretica p conversion coefficient

tot
as determined from the tables of Hager and Seltzer (Hag68). As can

be seen in this figure, there is a pronounced "bow" to the probability
curve. On assuming constant density wave functions in the above ex-
pression, [Mglz for neutrons comes out to be 14.6 (see 5 4.2.3.).

Not only does this yield a constant probability for the series, but
also is substantially larger in magnitude than are the experimental
values. Much better experimental—theoretical agreement has been ob-
tained by Jansen, Morinaga, and Signorini (Jan69). They recalculated
the N-8l radial matrix elements using a "realistic" potential con-
sisting of a Woods-Saxon part and a ant: orbit part. In addition,

the calculation included a configuration mixing term as calculated by
Harie and Oda (Hor64). In this manner much of the Z dependence was
removed, although the theoretical values still remain the layer for
all reasonable values of Ho.

The reduced transition probabilities for the Z=82 isomers,
which are shown in Figure 58, are remarkably constant over the whole
range from Pb197m to Pb207m. This is so in spite of the large range
of energies envolved. The [MEIZ values are ones reported by Doebler,
McHarris, and Gruhn (Doeb68). The value for szosm’ reported as
18:2, has been omitted from the figure. This value is probably in-
accurate because of an unresolved doublet in the spectrum.

This notable difference in the probability trends between
the N=81 and Z=82 series of nuclei piqued our curiosity as whether

other.M4 isomers followed one or the other of these two types of

TRANSITION ENERGY (MW)

279

 

 

|.6 -

L4-

|.2 '-

O.8 -

O.4 -

 

 

. C . . . -
I I .... I I I I
I I I I I I
_I
.'
.'
. —
.1
. —
.1
I I I I I I

 

I97 I99 ZOI 203 205 207

MASS NUMBER FOR Z = 82 ISOTOPES

Figure 58.

Upper: Values for the squared matrix elements for the
M4 transitions in the Z=82 isotopes. The value for
szoshas been omitted because of an inaccuracy in

in the intensity measurement caused by an unresolved
doublet.

Lower: Isomeric transition energies for the above
nu11vi.

280

trends. Consequently, we plotted the energies and experimentally
determined reduced transition probabilities for the N=49 (Figure 59)
series of isomeric transitions, the Z=49 (Figure 60) series of isomers
and the Z=50 (Figure 61) series. These are 1/2'—+9/2+, 1/2”—+9/2’,
and 11/2"—->3/2+ transitions, reSpectively. All data for these tran—
sitions have been taken from the Table of Isotopes (T167). As it
turns out, little can be said about the Z=50 series since only two
isotopes, Sn117m and Snllgm, have reported electromagnetic branches
from the isomeric level. We calculate that these reduced transition
probabilities are 3.5 and 5.3 f0; Sm117m and Smllgm, respectively,
although they have not been plotted to F'gure 61. The N=49 isomers,
whose energies and reduced transition probabilities are plotted in
Figure 59, show a "bow" in the series of probabilities, but one that
is less pronounced than found for the N=81 series. There is no

83m since this species decays exclusively by 8. emission.

value for Se
As a contrast, the series of Z=49 isomers (Figure 60), Show a marked
curvature in the plot of their y—emission probabilities. The value
for In117m is noticeably out of line, possibly due to an inaccurate
value for the percentage of decay via the y branch.

It undoubtedly would be useful to carry out "realistic"
calculations for these series analogous to the N=81 calculations.
At this point about the only conclusion that can be drawn is that
even for these high multipolarity transitions, in nuclei adjoining
closed shell, there are residual interactions contributing with
significant strength. Because of the deviations from the ideal shell

model picture, the M4 isomers seem assured of providing a source

of continued interest and study.

 

 

ISOMER ENERGY (MeV)

0.8

0.6

0.4

0.2

281

 

 

 

 

 

«- 1+
N= 49 ISOTONES (I/Z ——-> 9/2 I
...I
.1
9|
0 I950 '1
2.89
99 ED?’ "
(s .22;
. ER is?
. .- Kr .1
SagJ
I I I I L
I I I I
.1
K785 0 p a 39
Sir”? Zr . '-
M09"
I I I I I
83 85 8'?” 89 9|
MASS NUMBER
Figure 59. Upper: Isomeric transition energies for odd-mass, N=49
isotones.
Lower: Values of the squared matrix elements for the

isomeric transitions in the above nuclei.

V)

(5:)

IV.

(

TRANSITION ENERGY

[ r]2proton

0.8

O. 6

0.4

0.2

6.0

4.0

2.0

282

 

 

 

 

 

L— Z = ~33 inUI..\: DATii'ia
'Iry" '0 u
(Is/L ’ 9/2 )
a
” —
— . -‘
C . .
— -
I l I l I I
l l I I l l
p. -1
G
O
_ -
O . o
b d
I I I I I
l09 III II3 I55 II? "9
MASS NUMBER
Figure 60. Upper: Isomeric transition energies for odd—mass, Z=49

isotopes. No isomer is reported for Inlll.
Lower: Values of the squared matrix elements for the
isomeric transitions in the above nuclei.

283

.meOuomw am ecu pow mmfiwumcm cowufimamuu owumEomH .Ho onswflw

mum—232 mmflz

mm. MN. _N_ m: N:

 

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BIBLIOGRAPHY

(Adam58)

(Adam68)

(Adam68a)

(Alex64a)

(Alex64b)

(Ann69)

(Ant058)

(Arl67)

0A6b167)

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(Siiv65)

(Stev60)

(Thom54)

(T167)

(Toth69)

(UPM)

(way54)
(Wild70)

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K. Way and M. Wood, Phys. Rev._94, 119 (1954).

B. H. Wildenthal, MSU, private communication (1970).

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