ABSTRACT
Title of Disertation:INVESTIGATION OF SHEL MODEL STATES IN
EXOTIC OD-A ANTIMONY ISOTOPES
Jason Michael Shergur, Doctor of Philosophy, 2005
Disertation Directed by:Profesor Wiliam B. Walters
Department of Chemistry and Biochemistry
The level structures of 
134
Sb and 
135
Sb were studied in the ?
-
 decays of the very-
neutron-rich 
134,135
Sn isotopes. Tin isotopes were produced by proton- or neutron-induced
fision at CERN/ISOLDE and ionized using a resonance ionization laser ion source.
Following mas separation of the Sn nuclei, it was possible to collect ?-ray singles and ?-
? coincidence data as a function of time for the decays of 
134
Sn and 
135
Sn. From these
data, the position of the 7
-
 ?-decaying isomer in 
134
Sb has been established at 279 keV,
and the 5
-
 and 6
-
 members of the f
7/2
?g
7/2 
multiplet in 
134
Sb have also been identified,
along with thre new 1
-
 levels at higher energy.
New structure information was also obtained for 
135
Sb. New important levels in
135
Sb were established at 282, 440, and 798 keV, which are given tentative spin and
parity asignments of 5/2
+
, 3/2
+
 and 9/2
+
, respectively. The level structures of both 
134
Sb
and 
135
Sb were compared with shel model calculations.
Following ?-delayed neutron decay of the parents, half-lives (T
1/2
) for 
135,136,137
Sn
were measured to be 530(10) ms, 300(15) ms, and 250(30) ms, respectively. The
corresponding ?-delayed neutron probabilities (P
n
) for these nuclides were measured to
be 20(2)%, 27(4)%, and 33(12)%, for 
135,136,137
Sn decay. Limited data indicated an upper
limit of 150 ms for the T
1/2
 of 
138
Sn.
Low-spin levels in 
111
Sb and 
113
Sb were identified at Argonne National
Laboratory following the ?
+
/EC decay of 
111
Te and 
113
Te, respectively. 
111
Te and 
113
Te
were produced and separated by the Fragment Mas Analyzer via the
56
Fe(
58,60
Ni,2pn)
111,113
Te reactions. Analysis of the ?-singles, ?-? coincidence, and ?-time
data resulted in the identification of new levels in 
111
Sb, including levels at 487 and 881
keV that have been tentatively asigned spins and parities of 1/2
+
 and 3/2
+
, respectively.
In addition, a more precise T
1/2 
for 
111
Te decay was measured from the decay of the two
most intense ? transitions to be 26.2(6) s. The positions of these new levels were
compared with shel model calculations for the odd-A Sb isotopes from A = 105 to A =
111.
Several new ? rays and levels in 
113
Sb were identified, with data supporting a 3/2
+
and 7/2
+ 
asignment for the previously ambiguous 1019- and 1181-keV levels,
respectively. Identification of the spins and parities of these states suggest a 5/2
+
asignment for the ground state of 
113
Te.
INVESTIGATION OF SHEL MODEL STATES IN
EXOTIC OD-A ANTIMONY ISOTOPES
By
Jason Michael Shergur
Disertation submited to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfilment
of the requirements for the degre of
Doctor of Philosophy
2005
Advisory Commite:
Profesor Wiliam B. Walters, Chair/Advisor
Profesor Michael Coplan
Profesor Alice Mignerey
Profesor John Ondov
Profesor Robert Walker
? Copyright by
Jason Shergur
2005
i
Dedicated with love to
My wife, Veronica, and thre children; Acacia, Kylie, and Ayden
ii
ACKNOWLEDGEMENTS
First and foremost, I would like to thank my advisor, Bil Walters. I atribute my
desire to gain knowledge of experimental and theoretical nuclear structure physics to his
endles enthusiasm and dedication for a continued deeper understanding of the
fundamental properties that describe the nucleus. Throughout my graduate carer, Bil
has provided me with an abundance of opportunities, resources, and most importantly,
the support that alowed me to pursue my own interests and develop my carer as a
scientist.  In addition to being instrumental to my development as a scientist, Bil?s
dedication to my succes went beyond what could be expected from any advisor. For the
numerous discussions, about a myriad of diferent topics, that were not always thesis
related, he has my appreciation.
For the technical aspects of my graduate work, I cannot extend enough gratitude
to Darek Seweryniak and Andreas W?hr. They both spent countles hours teaching me
about detector electronics, data sorting, and the physics that govern how al of these
proceses work. Both of them were heavily involved in al of my thesis experiments, and
took the time to make sure that al aspects of the experiments went smoothly. For their
time, patience, and wilingnes to teach me, I wil always be grateful.
For the theoretical calculations that provided insight into the observed structures
of the heavy odd-A Sb isotopes, I would like to thank Profesor Alex Brown from
Michigan State University (funding from the National Science Foundation). In addition, I
would like to thank David Dean from Oak Ridge National Laboratory (Department of
Energy funding) who was responsible for the calculations that involved the light odd-A
iv
Sb isotopes. Another theoretician I would like to thank is Victor Zamfir at Yale
University who took the time to teach me about the Interacting Boson Fermion Model.
From the Universit?t Mainz, I would like to thank Profesor Karl-Ludwig Kratz
(supported by various German funding agencies), Dr. Pfeifer, Oliver Arndt, and Iris
Dilmann for their help with the experiments at ISOLDE. Profesor Kratz and Bernd
brought their many years of experience to ISOLDE, which was useful for making
important technical decisions. Oliver and Iris were also important participants in the runs
at ISOLDE. Without their help seting-up and siting shifts, it would have been very
dificult performing these experiments. At ISOLDE, I am also thankful for the help of the
in-house support staf. The most important members of this staf include Uli K?ster,
Richard Catheral, and Valentin Fedoseyev for their help with beam tuning, ion source
preparation, and laser optics, respectively.
For aranging my appointment at Argonne, I would like to thank Alen Bernstein,
as being part of this Physics Division has contributed greatly to my education. The staf
at Argonne provided me with the technical support needed for the Te decay experiments;
and the scientists took the time to teach me the practical aspects of proposal writing and
running a large-scale experiment. More specificaly, I would like to thank Robert
Janssens, my on-site advisor, for his guidance and open-door policy. He took the
initiative and a lot of time lecturing me about nuclear physics. In addition, I would like to
thank Cary Davids, who was always wiling to answer my questions and alowed me to
participate in al of his experiments involving proton emiters. Finaly, from Argonne, I
would like to thank John Schifer, for both his time and the portion of data from his
transfer reaction experiment at Yale.
v
Another person of note from the academic realm that deserves thanks is Jo
Resler. She participated in the first Sn experiment at ISOLDE, helped me make the
transition from Maryland to Argonne, and was always wiling to lend advice and support
regarding the many questions I had about how to survive the pangs and toils of graduate
school. I would also like to thank everyone else who was not mentioned, but participated
in the Sn and Te decay experiments, as the succes of these experiments was dependent
on the collective eforts of everyone involved.
I should mention that al of the above experiments and travel would not have been
possible without funding from the Department of Energy. Not only did they provide me
with the resources to perform the experiments contained in this thesis, but also the
support to present my research around the world at various conferences.
Finaly, and most importantly, I owe most of my thanks to my family. My mother,
grandmother, and father have provided me with love and support my entire life; and it has
helped me to overcome adversity, achieve goals, and be succesful at whatever it is I
have atempted. I would also like to thank my wife for having faith and confidence in my
ability to finish my thesis, and for enduring the extended time that I have spent on travel
in eforts to present research, perform experiments, or improve my understanding of
nuclear physics.
vi
TABLE OF CONTENTS
List of Figures x
List of Tables xiv
Introduction???????..???????????????????1
1 Radioactive Decay and the Shel Model??.??????.????5
1.1 Overview???????????????..?????????5
1.2 Theory of Beta and Beta-Delayed Neutron Decay?????..???6
1.3 Theory of Gama Decay??????????????????.10
1.4 Nuclear Structure and the Shel Model????????..????..14
1.5 r-Proces Nucleosynthesis??????????????????23
1.6 Implications of the Nuclear Physics and Astrophysics Concepts???27
2 The Structure of 
134
Sb??.????????????..??.????29
2.1 Overview???????????????..?????????29
2.2 Scientific Motivation?????...??????????????29
2.3 Experimental Details??????..?????????????..33
2.4 Identification of ? Rays which Depopulate Levels in 
134
Sb???...?..35
2.4.1 ?
-
 Decay of 
134
Sn????.?????????????..35
2.4.2 ?dn-Decay of 
135
Sn?????..???????????.41
2.5 Shel Model Calculations??????????????????.48
2.6 Summary and Outlook???????????????.????53
3 ?
-
 and ?dn-Decay Studies of 
135-137
Sn???.????..??.????54
3.1 Overview???????????????..?????????54
vii
3.2 Scientific Motivation?????...??????????????54
3.3 Experimental Details??????..?????????????..57
3.4 Measurement of the T
1/2 
and P
n
 Values for 
135-137
Sn?????......?..59
3.4.1 
135
Sn?????.???????...?????????..59
3.4.2 
136
Sn???????????.???????????.60
3.4.3 
137
Sn???????????.???????????.61
3.4.4 
138
Sn???????????.???????????.62
3.5 Identification of the ? Rays Asociated with the Decay of 
135
Sn???.63
3.6 Analysis of the ? Coincidence Matrices????????.????66
3.7 The 
135
Sb Level Scheme?????????????..?????71
3.8 Astrophysical Implications of Measured Decay Properties?.????74
3.9 Anomalous Behavior of the 282-keV Level?.?????.?..???76
3.10 Shel-Model Calculations for 
135
Sb?.?????.????..???80
3.11 Summary and Outlook???????....?.??????..???86
4 The Structure of 
111
Sb??????????.????..??.????88
4.1 Overview???????????????..?????????88
4.2 Scientific Motivation?????...??????????????88
4.3 Experimental Details??????..?????????????..90
4.4 Identification of the ? Rays Asociated with the ?
+
/EC Decay of 
111
Te..91
4.5 The 
111
Sb Level Scheme?????????????????.?.95
4.6 Discussion and Interpretation????????..????????100
4.7 Summary and Outlook???????...??????..?????105
5 The Structure of 
111
Sb??????????.????..??.????106
vii
5.1 Overview???????????????..?????????106
5.2 Scientific Motivation?????...??????????????106
5.3 Experimental Details??????..?????????????..108
5.4 Identification of the ? Rays Asociated with the ?
+
/EC Decay of 
113
Te..109
5.5 The 
113
Sb Level Scheme?????????????????.?.114
5.6 Transfer Reaction Data??????????..???????.?.124
5.7 Level Systematics of the Odd-A Isotopes Near the N=64 Subshel Gap.127
5.8 Summary and Outlook??????...???????????.?.129
Conclusions??????????.????..??.??????...???131
Apendix A: ISOLDE, CERN??????????.?..??.????133
A.1 ISOLDE, CERN Facility?????????.?????????133
A.2 Proton Synchrotron Booster??...???????.???????133
A.3 Target and Ion Source??..???????????.?????..135
A.3.1 Target and Neutron Converter????????.????135
A.3.2 Laser Ionization System?????????...?.????136
A.4 Mas Separators?????????????????????..138
A.5 Ion Implantation and Data Acquisition????????.???.?.138
A.5.1 Tape Station and Timing Module???????.????139
A.5.2 ??? and Neutron Detector Arays?????...?.????139
A.6 Data Acquisition????.??????????????..?.?.142
A.6.1 ?dn-Decay Data?????????..????.????144
A.6.2 Data Collection in the ?-? Detector Aray??????..?.145
Apendix B: Argonne National Laboratory???????.????150
ix
B.1 Argonne National Laboratory Facility?????????????150
B.2 ECR Ion Source??...???????.??????...?????150
B.3 ATLAS??..????????????..???.??????...151
B.4 Fragment Mas Analyzer (FMA)??????????...????.152
B.5 Focal Plane Detectors and Moving Tape Collector?...?..,?.???.153
Apendix C: Radioactive Decay and Statistical Eror?????.?157
C.1 Radioactive Decay Proces?????????????.????157
C.1.1 The Radioactive Decay Law?????????????157
C.1.1 Radioactive Decay Chains??????????...???158
C.2 Counting Statistics and Eror Propagation??...????...????159
C.3 Curve Fiting by Least Squares Analysis????????????161
Apendix D: List of Thesis Experiments??????????..?.?162
D.1 
135-137
Sn Decay Studies [IS378] at ISOLDE, CERN, Summer 2000..?162
D.1.1 Participants????????????????......??162
D.1.2 Representative Publications??????????.???162
D.2 
135-137
Sn Decay Studies [IS378] at ISOLDE, CERN, Summer 2002..?163
D.2.1 Participants????????????????......??163
D.2.2 Representative Publications??????????.???163
D.3 111,113Te Decay Studies at ATLAS/ANL, Fal 2002?????...?164
D.3.1 Participants????????????????......??164
D.3.2 Representative Publications??????????.???164
Bibliography?????????????????????????.?165
x
LIST OF  FIGURES
1.1Various Approximations for the Nuclear Potential at A=10????.??17
1.2 Predicted Nuclear Energy Levels Using Harmonic Oscilator,
Square Wel, and Woods-Saxon Potentials??????????...??21
1.3Representation of Solar-System Abundances as a Function of A??.??24
1.4Paths of s- and r-Proceses as a Function of Increasing Z and A????..26
2.1 States in 
134
Sb Populated via ?
?
 Decay of 
134
Sn and ?dn-Decay
of 
135
Sn??.???.?????????????????????.33
2.2 Time-Gated ? Diference Spectrum Obtained for the ?- and
?dn-Decays of 
134
Sn??????????????????...???36
2.3 Coincidence Spectra Gated on the 922-, 872-, 965-, and
1015-keV ? Rays in 
134
Sb???????????????????...37
2.4 Coincidence Spectra Gated on the 318- and 707-keV keV
? Rays Following ?
-
 Decay of 
134
Sn???????????????...38
2.5?
-
Decay Scheme for 
134
Sn???????????????????39
2.6Laser-Of Subtracted ?-Spectrum Obtained for A = 135?.??..??..?..43
2.7 Coincidence Spectra Gated on the 53-, 162-, 171-, and 338-keV
? Rays in 
134
Sb following ?dn-Decay of 
135
Sn??..?????????.44
2.8Level Scheme for 
134
Sb Following ?dn-Decay of 
135
Sn.???.????..45
2.8 Time-Gated ? Diference Spectrum Obtained for the ?-
and ?dn-Decays of 
135
Sn????????????????????45
2.9 Coincidence Spectra Gated on the 282-, 440-, and 798-keV
? Rays in 
135
Sb Following ?-decay of 
135
Sn????.????????..47
2.10 Origin of Excited States for 
134
Sb and Comparison of
Corresponding Experimental 
134
Sb Levels with Shel Model
Predictions??????????????..???????????49
3.1? Spectra Obtained with and without Use of the Neutron Converter???.57
xi
3.2 Least Squares Fits for the ?dn-Decay of 
135
Sn and Decay
of 282-keV Transition in 
135
Sb????????????..?????59
3.3 Least Squares Fit of the ?dn-Decay of 
136
Sn???????.????... 60
3.4Least Squares Fit of the ?dn-Decay of 
137
Sn????????????.61
3.5?dn Spectrum Taken at A = 138?????????????????62
3.6Laser-Of Subtracted ? Spectrum Taken at A = 135???.??????.64
3.7 Time-Gated ? Diference Spectrum Obtained for the ?- and
?dn-Decays of 
135
Sn??????????.???????????..64
3.8 Coincidence Spectrum Gated on the 282-keV ? Ray in 
135
Sb
Following ?
?
 Decay of 
135
Sn????????????..??????67
3.9 Coincidence Spectra Gated on the 440- and 707-keV ? Rays
in 
135
Sb Following ?
-
 Decay of 
135
Sn????????????.???68
3.10 Coincidence Spectrum Gated on the 798-keV ? Ray in 
135
Sb
Following ?
-
 decay of 
135
Sn????????????????.??..69
3.11 Coincidence Spectra Gated on the 831- and 1027-keV ? Rays
in 
135
Sb Following ?
-
 Decay of 
135
Sn.?????????????.?..69
3.12 Coincidence Spectra Gated on the 733- and 925-keV ? Rays
in 
135
Sb Following ?
-
 Decay of 
135
Sn???????????????.70
3.13Proposed ?
- 
Decay Scheme of 
135
Sn???????????????..72
3.13 Relative Isotopic r-Proces Abundances of Sn Isotopes
Under Freze-Out Conditions??????????????????76
3.15Level Systematics of the Neutron-Rich Odd-A Sb Isotopes??????.77
3.16 Variation of the Energy Diference Betwen the Lowest
5/2
+
 and 7/2
+
 Levels in the N = 72-84 Even-Odd Sb, I, Cs, and
La Isotones?????????????????????????.78
3.17 Comparison of the First 7/2
-
 Level Energies of Bi Nuclei with
the Positions of the 2
+
 Levels in Adjacent Pb cores???????..??79
3.18 Comparison of the Experimental Levels for 
135
Sb with Shel-Model
Calculations??????????????????????.??..82
xii
4.1 Low-Spin Systematics for Levels for the odd-A Sb isotopes
Betwen A=115 and A=131???????????..???????89
4.2 Time-Gated ? Diference Spectrum Obtained for the ?
+
/EC-
Decay of 
111
Te????????????????????????91
4.3 Coincidence Spectra Gated on the 851-keV and 880-keV
? Rays in 
111
Sb Following ?
+
/EC-Decay of 
111
Te??????????..94
4.4 Least-Squares Fit of the Combined Decays of the 851- and
881-keV Transitions in 
111
Sb Following ?
+
/EC Decay of 
111
Te...????.95
4.5?
+
/EC-Decay Scheme for 
111
Te??????????.???????96
4.5 Comparison of Shel Model Calculations with
Experimental Levels of 
105,107,109,111
Sb??????.????????.99
4.6 Comparison of the Various Shel Model Calculations for
Low-Spin Levels of 
101,103,105,107,109,111
Sb??????..???????.102
5.1 Time-Gated ? Diference Spectrum Obtained for the ?
+
/EC-
Decay of 
113
Te????????????????????????110
5.2 Coincidence Spectra Gated on the 645-keV ? Ray in 
113
Sb
Following ?
+
/EC-Decay of 
113
Te???????????..?????.115
5.3 Coincidence Spectra Gated on the 814-keV ? Ray in 
113
Sb
Following ?
+
/EC-Decay of 
113
Te?????????????...???116
5.4 Coincidence Spectra Gated on the 1019-keV ? Ray in 
113
Sb
Following ?
+
/EC-Decay of 
113
Te??????????????..??.117
5.5 Coincidence Spectra Gated on the 1181-keV ? Ray in 
113
Sb
Following ?
+
/EC-Decay of 
113
Te??????????????..??.118
5.6 Coincidence Spectra Gated on the 1257-keV ? Ray in 
113
Sb
Following ?
+
/EC-Decay of 
113
Te??????.??????????..119
5.7Proposed Level Schemes for 
113
Sb Following ?
+
/EC-Decay of 
113
Te?..?.120
5.8Even Jumping Schematic for the ?
+
/EC-Decay of 
113
Te????...???123
5.9 Triton Energy Spectrum Following the (?,t) Transfer Reaction
on 
112
Sn and an Excitation Spectrum for 
113
Sb??????...?????125
xii
5.10 Comparison of the Angular Distribution Ratios of the 1019-
and 1181-keV Peaks with Respect to the d
5/2 
and g
7/2
???.?????..125
5.11 Experimental Level Systematics for the Odd-A Sb
Isotopes From A=109 to A=123????????...????????.128
A.1Facility Layout of ISOLDE, CERN????...???????????134
A.2Schematic of the UC
2
 Target and Neutron Converter?..????.???135
A.3Schematic of the Laser System at ISOLDE, CERN?????..????137
A.4The 
3
He Gas-Proportional Counter Aray?????????????.140
A.5Aray of Plastic Scintilators and HPGe Detectors Used
at ISOLDE???????????????????????...?..141
A.6The Electronics Used in the On-Line Analysis of the
?-Singles Spectra???????????..???????????.146
A.7The Electronics Used in the Five-Detector ?-? Measurements??.???.147
B.1Facility Layout of ATLAS???????????????????.151
B.2Picture and Schematic of the FMA??????????..?????.153
B.3Photo of PPAC??????..?????????????????.154
xiv
LIST OF TABLES
1.1 Summary of ?-Decay Selection Rules????.??????????.8
1.2 Selection Rules for ? Transitions????????..????????.12
1.3 Partial Half Life Estimates for ? Transitions Calculated
Using the Single-Particle Model?????????????????14
2.1  Data for ? Rays and Levels Observed in the ?-decay of 
134
Sn?????..40
2.2 Calculated Log ft Values for Levels Populated in 
134
Sb via ?-
Decay of 
134
Sn?????..??????????????????..41
2.3 Data for ? Rays and Levels Observed in the ?dn-Decay of 
135
Sn?...??..48
2.3 Comparison of Shel Model Calculations with the Experimental
Values of the Positions of the 5
-
, 6
-
, and 7
-
 Levels in 
134
Sb????...??50
3.1 Data for ? Rays and Levels Observed in the ?-decay of 
135
Sn???.??.65
3.2 Log ft Values and I
?
 for Levels Populated via ?-decay of 
135
Sn??...??.74
3.3 Comparison of Experimentaly Observed Levels with Shel-
Model Calculations for Levels in 
135
Sb??????????.????84
4.1 Gama Intensities in 
111
Sb Following 
111
Te ?
+
-Decay????????.93
4.2 Proton and Neutron Single-Particle Energies for these
Calculations and 
133
Sb in MeV??????????..???????100
5.1 Data for ? Rays and Levels Observed in the ?-Decay of 
113
Te?????..111
5.2 List of ? Rays not placed in the 
113
Sb Level Scheme, but
Asigned to the Decay of 
113
Te?????????????????..114
A.1 ?-Ray Energies and Intensities for Calibration Source????????..145
1
Investigation of Shel Model States in Exotic Od-A Antimony Isotopes
Introduction
The basic goal of any fundamental science is the understanding of observed
phenomena in terms of general underlying concepts and laws. Scientists make progres
achieving these goals by one of two methods. One is to construct hypotheses that
describe a given observable, and to use experimentation until the number of possible
hypotheses is reduced to a minimum. When enough possible hypotheses have been
eliminated, a quantitative or qualitative relationship is formulated, and acepted as a valid
explanation of the observed phenomena. Progres is also made by discovery of
unexpected phenomena. These unexplained phenomena must then be integrated into our
understanding of the universe, which then invokes the first type of scientific progres.
The interplay of these two types of scientific methods is necesary for the progresion of
our understanding of the fundamental principles that govern nature.
As nuclear scientists, we are interested in describing the fundamental phenomena that
govern the properties we observe for the atomic nucleus. The field of nuclear physics
originated following an acidental, yet crucial, discovery by Henri Bequerel in 1896.
Shortly after noting that the photographic film he had in his desk had been exposed in the
presence of uranyl salts, it was suggested that there existed a new phenomenon known as
radioactivity. Piere and Marie Curie expanded our understanding of this new
phenomenon by proving that radioactivity was characteristic of the element from which it
was emited. At first, it was discovered that radioactivity could be clasified into one of
thre categories: heavy charged particles (? rays), light-mas charged particles (? rays),
2
and deeply penetrating chargeles particles (? ray). Crookes, Rutherford, and Soddy made
two more important discoveries regarding the nature of radioactivity. The first
observation was that the intensity of the activity of a radioactive substance decreased in
time, and the second was that radioactive proceses were acompanied by a change in
chemical properties. The first of these observations led to the radioactive decay law,
while the later lent understanding of radioactive decay as a transmutation proces.
The next major stepping stone in the field of nuclear science, and the first step
towards understanding the structures of the atom and nucleus, occurred in 1911 when
Rutherford deduced that al of the positive charge, and most of the mas of the atom
resided in a smal dense region caled the nucleus. In the same set of experiments, it was
deduced that the size of the nucleus was on the order of 10
-12
 cm, which is 1/1000 the
radius of the atom. These claims were based on the results from the wel-known Au-foil
experiment. This experiment was pivotal in our understanding of atomic structure, as it
showed that the atom was mostly made up of space. The nuclear implications of the Au-
foil scatering experiment with the aforementioned discoveries relegated the proces of
radioactive decay to phenomena in the nucleus.
Following the Au-foil experiments, there was an explosion of scientific progres in
the field of nuclear science. These acomplishments included such important
contributions as the invention of the cloud chamber for radiation detection (1912),
hypothesis of the presence of isotopes (1913), inducing the first laboratory nuclear
transformation of 
14
N into 
17
O with the use of 
4
He particles (1919), the development of
quantum mechanics by Schr?dinger and Heisenberg, and the development of the particle
acelerator (1931). By 1932, the final piece of the nuclear puzzle was found after the
3
discovery of the neutron by Chadwick. Though al of the constituents of the nucleus had
been discovered, it would be almost twenty years before a valid theoretical framework
would be developed that would explain a variety of experimental trends in the nuclear
landscape.
Since the 1950s, our understanding of the physics that describe the structure of
nuclei has increased tremendously. Experimentaly, the most important advances have
been in detector technology, electronics and signal procesing, and the construction of
high-energy particle acelerators. Of particular importance to the field of nuclear
structure was the development of the solid-state Ge semiconductor detector in the 1960s.
The Ge detector crystals improved the quality of resolution that could be obtained in a ?
spectrum by a factor of forty, thus making it possible to obtain very detailed information
regarding the positions and intensities of nuclear excited states. The combination of al
these advances has alowed us to push the limits for the production and detection of
exotic nuclei far from the valey of stability, and in some cases to the nuclear driplines.
Technical advances also make it possible to perform what would have been inconceivable
calculations in minutes because of the improvements in computer memory and
procesing speed.  As technology has improved, the amount of data has increased
exponentialy, and the field of nuclear science has spilt into diferent branches: high-
energy particle physics, nuclear structure, and nuclear astrophysics. Even within these
subfields, there are several designations for the diferent aspects of research that one
performs.
The focus of the research that wil be discussed in the following chapters is that
which pertains to nuclear structure research, and more specificaly, low-spin nuclear
4
spectroscopy experimentation. As low-energy nuclear spectroscopists, we are interested
in understanding the fundamental forces that govern the interaction of the protons and
neutrons within the nucleus. As these forces cannot be measured directly, the nature of
these interactions must be implied from the level structure of nuclei. By knowing the
positions, ordering, and density of excited states, it is possible to make inferences
regarding the shape of the nuclide of interest, obtain important information regarding the
behavior of the nuclear potential in which al of the protons and neutrons lie, and estimate
the strengths of the various nucleon-nucleon interactions. Obtaining the level structure of
a nucleus gets more dificult, the further that it is from the beta valey of stability. In the
following chapters, structural information for odd-A Sb isotopes on both the proton-rich
and very neutron-rich sides of the beta valey of stability wil be discussed.
5
1 Radioactive Decay and the Shel Model
1.1  Overview
The primary goal of many nuclear spectroscopy experiments is to obtain nuclear
structure data, and to use that information to deduce information about the shape of the
nuclear potential and nucleon-nucleon interaction strengths in the mas region of interest.
One method for obtaining nuclear structure information is to populate excited states in
the decay daughters via ? decay, and then detect the ? rays that depopulate these excited
states to construct the level schemes of the nuclides of interest. Once the level structure of
a nuclide has been identified, theorists select models that incorporate certain input
parameters that encompas specific physical phenomena which enable them to reproduce
the experimentaly observed level scheme. The focus of the experiments that wil be
discussed in chapters 2-5 is to identify the level structures of 
111
Sb, 
113
Sb, 
134
Sb, and
135
Sb, and discuss the results in the context of the shel model. To beter understand the
decay mechanisms by which structural information is obtained, the theoretical context in
which the data is discussed, and the motivations for studying these nuclides; a
pedagogical summary of some basic principles involving ? and ? decay, the shel model,
and r-proces nucleosynthesis wil be presented.
1.2 Theory of Beta and Beta-Delayed Neutron Decay
In experimental nuclear physics, nuclear spectroscopists use ? decay as a
mechanism to populate excited states of nuclei.  Beta decay is a radioactive proces that
6
occurs when the ground state of a nucleus is at an energy that is higher than the
maximum binding energy for a given mas number. The thre types of ? decay that can
occur are:
? 
(a)
A
Z
X?
A
Z+1
Y+?
?
+? 
e
(b)
A
Z
X?
A
Z?1
Y+?
+
?
e
(c)
A
Z
X?
A
Z?1
Y+?
e
+x?rays
, (1.1)
where Eqns. 1.1 (a) and 1.1 (b) are negatron and positron decay, respectively; and 1.1 (c)
is the proces of electron capture (EC). Neutron-rich nuclides decay via ?
-
 decay; while
proton-rich nuclei decay either by ?
+
 emision or electron capture. At mid to low mases,
?
+
 and EC compete as decay branches. For energies 1.02 MeV or higher, ?
+
 decay is
energeticaly possible, and becomes more likely as E
?
 increases. At higher mases, EC
dominates because the atomic K-orbitals are closer to the nucleus, thus increasing the
probability of electron capture.
The ?-decay proces difers from other types of radioactive decay, such as ? or ?
decay, in that the ? particles are not emited at discrete energies, but with a continuous
energy distribution ranging from Q
?
 (which is the energy diference betwen the ground
states of the parent and daughter) to zero. The energy distribution observed in ? decay is
a result of the split in energy and momentum betwen the emited ?
+
 or ?
-
 particle with
the neutrino (?
e
) or antineutrino (?
e
), respectively, at the time of decay. It was the
distribution of energy observed in ? spectra that initialy led to Pauli?s postulate of the
presence of the neutrino in 1932. Experimental evidence supporting the existence of the
neutrino was reported by Reines and Cowen in 1957 [Re57].
7
The quantitative theory of ? decay was developed by Fermi in 1934 [Fe34], and
stil serves as a guideline for our understanding of the proces. As the mathematical
derivation of this theory is quite extensive, only the equations that embody the most
important aspects of the theory as they apply to our understanding of experimental
nuclear structure wil be discussed. Suppose that a nucleus undergoes ? decay from ?
i
 to
?
f
. The rate (?
?
) at which this transition occurs can be estimated by:
? 
?
?
=
0.693
T
1/2
=S
?
(E
i
)f(Z,Q
?
?E
i
)
0
Q?
?
,
(1.2)
where T
1/2 
is the partial half-life of the transition to the state with energy E
i
; S
?
(E
i
) is the
strength of the ? transition, and f(Z, Q
?
 ? E
i
) is the Fermi function which describes the
probability of a transition to the final state ?
f 
[Ha00]. Eqn. (1.2) can be used to yield
information on the average ? feding of a nucleus. However, the low-energy portion of
its excitation spectrum is strongly weighted by the Fermi function, f, which has an energy
dependence of:
? 
f~(Q
?
?E
i
)
5
. (1.3)
The strength of the transition, S
?
(E
i
), is dominated by the amount of overlap
betwen the initial and final wave functions, and is proportional to the square of the
matrix element characterizing the transition from ?
i
 to ?
f
:
? 
S
?
(E
i
)?|M
if
|
2
. (1.4)
From Eqn. (1.4), it can be concluded that the greater the overlap of wave functions, the
faster a transition wil occur. Therefore, as states with similar spin (I) and parity (?) are
more likely to have analogous wave function components, then the likelihood of a
transition betwen these types of states is favorable. The selection rules that categorize
8
the types of transitions that can occur in ? decay are summarized in Table 1.1. For the
mathematical derivation of these selection rules, refer to [Co01].
Experimentaly, ?-transition probabilities are calculated in terms of a value
known as log ft. The log ft value is calculated from the sum of the log of partial T
1/2 
of the
? transition, and the log of the Fermi function, f(Z, E
?
):
? 
logft=logt
1/2
+logf(Z,E
?
)
. (1.5)
Though Eqn. (1.5) can be used to calculate a log ft value, experimentaly there are
not discrete values for a certain type of transition because of the variability of f(Z, E
?
).
There are, however, typical log ft ranges that correspond to diferent types of transitions,
and these are listed in Table 1.1 along with the selection rules. A more detailed derivation
of the formulas for log ft and ?
?
 can be found in [Fr81].
Table 1.1: Summary of ?-Decay Selection Rules.
a
a
The symbols l, I, and ?, correspond to angular momentum, spin, and parity, respectively.
Of the transitions listed in Table 1.1, there are two that have special designations.
A transition for which ?l=0 and ?I=0, is designated as a Fermi transition. Gamow-Teler
Type 
?l
?I
??
Log ft range
Superalowed 0 0 or 1 No 3
Alowed 0 0 or 1 No 4-7
Alowed   (l-forbidden) 0 1 No 6-12
First Forbidden 1 0 or 1 Yes 6-15
First Forbidden (unique) 1 2 Yes 9-13
Second Forbidden 2 2 No 11-15
Second Forbidden  (unique) 2 3 No 13-18
Third Forbidden 3 3 Yes 17-19
Third Forbidden (unique) 3 4 Yes
>20
9
transitions are used to clasify decays for which ?l = 0, ?I=0 or 1, and there is no change
in parity.
Transitions in ?
?
 decay are not restricted to the bound excited states of daughter
nuclei. They can also occur to states that are above the neutron separation energy (S
n
).
When ?
?
 decay populates a state above the S
n
, the unbound neutron is emited, thus
populating states in the (N-1) adjacent ?-decay daughter. The probability for a ?
transition to an unbound state is caled the ?-delayed neutron probability (P
n
).
Quantitatively it is calculated as
? 
P
n
=
S
?
(E
i
)f(Z,Q
?
?E
i
)
n
Q
?
?
S
?
(E
i
)f(Z,Q
?
?E
i
)
0
Q
?
?
,
(1.6)
where P
n
 is defined as the ratio of the integral ?-strength to neutron-unbound states to the
total ?-strength. One obvious consequence of Eqn. (1.6) is that it should be expected that
as the neutron dripline is approached, that the S
n
 wil decrease, thus the P
n
 increases as
more neutron unbound states become available.
The two gross ?-decay properties discussed in this section, T
1/2
 and P
n
, are useful
for making predictions about the nuclear structure determining ? decay. More
specificaly, because the ?-decay transition rates are energy (E
?
), angular momentum (l),
and parity (?) dependent, it is possible to use this information to obtain details regarding
the spins (J) and parities of the states involved in ? decay. For example, by knowing the
log ft and spin and parity (J
?
) of the ground state of the ?-decaying parent, it is easier to
identify the J
?
 of the states populated in the daughter nucleus. The T
1/2 
and P
n
 values
obtained from ? decay can also be used to identify discrepancies betwen experiment and
10
theory. By using acurately measured decay properties, the reliability of nuclear structure
and r-proces calculations can be tested.
1.3 Theory of Gamma Decay
When nuclei undergo ? decay, the transition is not necesarily to the ground state
of the daughter nucleus, but also to excited states. A nucleus in its excited state must then
decay to a lower-energy excited state or ground state by the emision of electromagnetic
radiation. This type of radiation is caled ? radiation, and its frequency is energy
dependent (E = h?). Gama radiation arises from oscilations in either the charge
distribution or current density in the nucleus. Gama transitions are clasified as either
electric (E) or magnetic (M), depending on whether the oscilation is with the charge
distribution or current density, respectively. The probability that a nucleus decays from
an initial state (?
i
) to a final state (?
f
) by an oscilation in the charge distribution resulting
in the emision of a ? ray with angular momentum L is proportional to the overlap of the
initial and final wave functions, as given by the square of the matrix element
? 
????
f
?
|E
L
|?
i
?,
(1.7)
where E
L
 is the electric monopole operator of order L. Similarly, the probability that a
nucleus decays from ?
i
 to ?
f
 by oscilation of the current density is given as
? 
????
f
?
|M
L
|?
i
?,
(1.8)
where M
L
 is the magnetic multipole operator of order L. In both types of transitions, L
gives information about the change in spin. Gama-ray transitions are clasified as either
(EL) or (ML) transitions of multipole order 2
L
. These transitions are also clasified
11
acording to the parity change betwen ?
i
 and ?
f
. The parity change betwen the two
states of an electric transition of multipole order 2
L
 is
? 
?
E
=(?1)
L
,
(1.9)
and the parity of a magnetic transition of multipole order L is equal to
? 
?
M
=(?1)
L+1
.
(1.10)
Now it is necesary to formulate the selection rules for ? transitions from state ?
i
 with
spin J
i
 and parity ?
i
 to state ?
f
 with spin J
f 
and parity ?
f
. Conservation of angular
momentum dictates that
? 
L=J
i
?J
f
.
(1.11)
If L is the angular momentum caried by the ? ray, then vector addition of the two angular
momenta further constrain that L cannot exced J
i
 +J
f
; therefore, for both ML and EL
transitions
? 
J
i
+J
f
?L?|J
i
?J
f
|.
(1.12)
Similarly, the conservation of parity for a nuclear transition requires that
? 
?
i
=?
ft
,
(1.13)
where ?
t
 is the parity of the electromagnetic transition. A summary of the selection rules
for electromagnetic transitions are listed in Table 1.2.
12
Table 1.2: Selection Rules for ? Transitions
As shown in Table 1.2, electric transitions of even order and magnetic transitions
of odd order connect the same parity, and vice versa for transitions betwen states with
opposite parity. There are a few exceptions to the predicted selection rules listed in Table
1.2. In general the lowest multipole order for a transition dominates; however, when the
lowest multipole order is a magnetic transition (ML), deviations from the rules occur. In
this situation, electric transitions with L+1 are competitive with ML transitions because
nuclear current densities are ~10
2
 smaler than charge densities. When magnetic and
electric transitions become competitive, the transition is said to be mixed, and a multipole
mixing ratio is defined as
? 
?=
??
f
?
|E
L+1
|?
i
?
?
f
?
|M
L
|
i
?
.
(1.14)
Another exception to the selection rules in Table 1.2 involves ?J = 0 transitions,
in particular 0?0 transitions. These transitions cannot occur because a photon has spin 1,
and must take away at least one unit of L vectorialy. Thus, 0?0 transitions either occur
by the emision of an internal conversion electron; or if E
i
 ? E
f
 ? 1.02 MeV, by pair
production.
The selection rules defined in Table 1.2 for the ? transitions set constraints that
make it possible to obtain structural information for a nuclide. This can be useful for
?J
Transition (?
if
 = +1)Transition (?
if
 = -1)
0 M1, E2 E1
1 M1,E2 E1
2 E2 M2
3 M3 E3
4 E4 M4
13
asigning a range of spins and parities (J
?
) to an unknown state, if the J
?
 of at least one
state (either ?
i
 or ?
f
) is established. However, the spins and parities of ?
i
 and ?
f
 are not
usualy known when performing spectroscopic studies on new isotopes. One way to
identify the type of transition present is by measuring the lifetime of the decay. The
partial decay constant for ? emision can be expresed as
? 
?
?
?E
2L
A
2L
3
,
(1.15)
where the decay energy (E) is in MeV and A is the mas number. The proportionality
shown in Eqn. 1.15 shows that for a given spin change, the half lives wil decrease
rapidly for a given A, and more rapidly for a given E.  A set of more quantitative
formulas proposed by Weiskopf [We83] using the shel model for the partial half lives
of electromagnetic transitions is listed in Table 1.3.
Though the formulas shown in Table 1.3 are valid for many cases, these are
thought to give lower limits for transitions from ?
i
 to ?
f
. The experimental half-lives are
usualy longer than calculated rates because ? transitions do not just occur betwen pure
single-particle states, but more often, betwen states whose configurations involve
interactions with other nucleons (configuration mixing).  Other deviations from the
formulas listed in Table 1.3 are observed in regions where states are collective in
character (i.e. rotational and vibrational regions). In these regions, E2 transitions are
much faster than calculated. The failure of the shel model to predict the properties of
mid-shel nuclei is discussed further in sec. 1.4.
14
Table 1.3: Partial Half Life Estimates for ? Transitions Calculated Using the Single-
Particle Model.
a
a
E in second column corresponds to ? ray energy in MeV.
1.4 Nuclear Structure and the Shel Model
The theoretical description of the structure of the nucleus poses two major problems.
First, the nucleus is a many-body system, and as such has to be approached in terms of an
approximate theory. Second, the exact nature of the nucleon-nucleon interaction is not
known, but it has been established that this interaction has atractive character and a
range smaler than the nucleus. Though there are a variety of models that can be used to
approximate the nature of the nucleon-nucleon interaction, the model that first
quantitatively described the underlying physical properties of nuclei was the shel model.
Transition TypePartial Half Life (s)
E1
5.7 x 10
-15
 E
-3
A
-2/3
E2
6.7 x 10
-9
 E
-5
A
-4/3
E3
1.2 x 10
-2
 E
-7
A
-2
E4
3.4 x 10
4
 E
-9
A
-8/3
M1
2.2 x 10
-14
 E
-3
M2
2.6 x 10
-8
 E
-5
A
-2/3
M3
4.9 x 10
-2
 E
-7
A
-4/3
M4
1.3 x 10
5
 E
-9
A
-2
15
Following a long discussion with Fermi, the shel model was proposed by Mayer
[Ma50], and then again independently by Haxel, Jensen, and Sues in 1950 [Ha50]. It
was developed to explain trends in experimental data, particularly those that supported
the idea of magic numbers. The term ?magic? refers to nuclei that have 2, 8, 20, 28, 50,
82, or 126 protons or neutrons. It was suggested that, similar to the behavior exhibited by
electrons (the octet rule), nucleons with magic numbers form ?shels? of stability. There
are several pieces of experimental data that support the idea of magic numbers. For
instance, for nuclei that have magic numbers, the neutron separation energy (S
n
) is
significantly higher than that of neighboring isotopes. In addition, nuclei with a magic
number of protons or neutrons have smal neutron capture cross sections (?
n
), while the
adjacent N-1 isotope has a large ?
n
. Further evidence for the presence of magic numbers
is provided by the isotopic abundances of nuclei with magic numbers of neutrons, which
wil be discussed in more detail in sec. 1.5. Additional support for the notion of magic
numbers is provided by the significantly higher energies of the first excited 2
+
 states for
even-even nuclides with magic numbers. The increased 2
+
 energy for these even-even
magic nuclides results from the large shel gap over which a broken pair of neutrons must
cross in order to populate the first excited state above the 0
+
 ground state.
As stated previously, the goal of the shel model was to describe the trends in
diferent observables for nuclei with a magic number of protons or neutrons. The most
important simplification that is made by the shel model is to asume that nucleons in the
nucleus move independently in a central efective potential. This efective potential is
created by the presence of al the other nucleons in the nucleus, and acts on each nucleon
as a function of its coordinates, independent of the position or number of the remaining
16
nucleons in the nucleus. There are two extreme cases for which analytic calculations can
be made for the nuclear potential. One is to asume that the potential is described using
an harmonic oscilator
? 
V(r)=?V
0
[1?(
r
R
)
2
],
(1.16)
where r is the distance of the nucleon from the center of the nucleus, and R is the nuclear
radius, approximated as 1.2A
1/3
 fm. The opposite extreme is to asume the potential of an
infinite square wel:
? 
V(r)=?V
o
,r<R,
=?,r>R.
(1.17)
The imediate deficiencies in both potentials in Eqns. (1.16-1.17) are that the
potential approaches ? as r??, a situation highly improbable as the nuclear force is
short-ranged, and not likely to extend greater than R in distance. A more realistic nuclear
potential is likely to be a hybrid of Eqns. (1.16) and (1.17) in behavior, such as the
Woods-Saxon potential given as
? 
V(r)=?V
0
[1+e
(
r?R
a
)
],
(1.18)
where a is an additional parameter to acount for the difusenes of nuclear surface. A
schematic showing the shapes of these potentials, neglecting the Coulomb efects of the
protons, for an arbitrary nucleus with A = 10 are shown in Fig. 1.1.
17
-60
-40
-20
0
20
40
60
0 1 2 3 4 5
Wood-Saxon
Harmonic Oscillator
Square Well
V
(
r
)
r (fm)
Figure 1.1: Schematic representing thre spherical wels using the potentials mentioned
in Eqns. (1.18-1.20). The potentials shown in the plot were calculated neglecting the
Coulomb force for an arbitrary nucleus with A = 10.
Once a potential is selected, the nuclear wavefunctions, ?
nucl
 must be obtained by
using the nuclear Hamiltonian (H
(0)
):
? 
H
(0)
=H
k
(0)
=[T
k
+V(r
k
)
k=1
A
?
k=1
A
?
],
(1.19)
where T
k
 is the kinetic energy of the k
th
 nucleon. The eigenfunctions of H
(0)
 are products
of the single-particle wave functions as shown below:
 
? 
?=?
?
k
(
r 
 
k
)
k=1
A
?
,
(1.20)
where ?
k
 denotes a set of quantum numbers characterizing the state occupied by the k
th
nucleon, and these single-particle wave functions can be used as solutions to the
Schr?dinger equation,
 
? 
[T
k
+V(
r 
 
k
)]?
?
k
(
r 
 
k
)=?
?
k
?
?
k
(
r 
 
k
),
(1.21)
where ?
?
k
 is the single-particle energy. The eigenvalues of the many-body H
(0)
 are then
equal to sums of single-particle energies:
18
?
(0)
?
 = ??
?k
,
A
k = 1
(1.22)
where ? = (?
1
, ?
2
,??
A
), is a set of states occupied by the nucleons. In order to construct
the many-body wave function, it is necesary to take into acount the Pauli principle. The
Pauli principle requires that the wave function describing identical fermions has to
change sign if the coordinates of any two fermions are exchanged. The Slater
determinant:
 
? 
?
?
(0)
r 
 
1
,
 
 
2
,...
r 
 
A
)=A
?
1
2
?
?
1
(
r 
 
1
)?
?
1
(
r 
 
2
)L?
?
1
(
r 
 
A
)
?
?
2
(
r 
 
1
)?
?
2
(
r 
 
2
)MM
M MO
?
?
A
(
r 
 
1
)L?
?
A
(
r 
 
A
)
, (1.23)
fulfils this requirement as it vanishes for ?
i
 = ?
j
, thus preventing two nucleons from
having the same set of quantum numbers simultaneously. Use of the spherical potentials
in eqns. 1.16-1.18 above yields solutions to the Schr?dinger equation that are factorizable
into two functions: a radial part and an angular momentum part:
 
? 
?
n,m,
l
(r,?,?)=R
n,l
(r)Y
lm
l
(?,?)
. (1.24)
The function Y
l
,m
l
(?,?) is a spherical harmonic of order l,m. Therefore, this state has
angular momentum quantum number (l = 0, 1, 2?), and magnetic quantum number (l
z
 =
m(-l ? m ? l). The eigenvalue of the orbital momentum squared (L
2
) is l(l+1)h, and that
of the z-component (L
z
) is l
z
h. The radial part, R
n,
l
(r), is specified by n, which is the
principle quantum number, and l. The eigenvalue E
n
l
 is a sum of the kinetic and potential
energy for the state.
19
Up to now the specific asignment of the k
th
 nucleon has not been a factor. Just as
with electrons, each particle also has an intrinsic spin, s
z
. The neutron and proton each
posseses a spin of 1/2. The nucleon is in one of two spin states depending on its
projection of the spin on the z-axis (m
s
  =  ?1/2).
Now that al of the pieces of the wave function have been identified, it should be
possible to calculate al possible single-particle states for a given Z and A. Unfortunately,
solving the Schr?dinger equation for the single-particle levels of the nucleus with the
above potential energies in Eqns. (1.16-1.18) does not acount for the experimentaly
observed magic numbers. The predicted single particle states using the harmonic
oscilator and square wel potentials are shown in Fig. 1.2. As shown, the harmonic
oscilator (V
HO
) and the infinite square wel (V
SW
) potentials do predict shel gaps at
nucleon number 2 and 8, but the predictability of these potentials fails to acount for
expected shel gaps at higher A. There are two main problems with the harmonic
oscilator potential. One is that states with the same 2n + l value are degenerate. In
addition, solutions to the harmonic oscilator require that the states of a given energy
must have either al even or al odd l, hence the degenerate states al have the same
parity. Some of the degeneracy of the harmonic oscilator is lifted by use of the square
wel potential. Use of the square wel lowers the potential energy near the edge of the
nucleus, so that orbitals with high l become more bound.
The mising piece of the shel model puzzle that was developed by Mayer, Haxel,
Jansen, and Sues [Ma56] was the addition of a spin-orbit interaction term to the H
(0)
.
Only by coupling the orbital angular momentum and the intrinsic spin was it possible to
20
reproduce the experimentaly observed magic numbers. Quantitatively, the spin-orbit
term is defined as
 
? 
V
SO
=f(r)l?s,
(1.25)
where f(r) is a radial function related to the potential, V(r). The spin-orbit term odifies
the energies by
 
? 
?
n,l,j
|V
SO
(r)|?
n,l,j
=?
1
2
(l+1)f(r)
nl
?j=l?
1
2
and=
1
2
lf(r)
nl
?j=l+
1
2
.
(1.26)
As shown in Eqn. (1.26), addition of the spin-orbit term splits each nl orbital into two j
levels with j= l ? 1/2. As the value of <f(r)>
nl 
? -20 ? A
-2/3
 MeV, it can be sen that the
l+1/2 member of each doublet is reduced in energy relative to the position of the l-1/2
member.
An example of an arbitrary shel model calculation that includes the spin-orbit
coupling is shown in Fig. 1.2. Realistic shel model calculations difer depending on A
and Z. The characteristics of the levels calculated using spin-orbit coupling is that each
orbital can take N
j
 = 2j + 1 nucleons. Each orbital is labeled with nlj.  Values of l = 0, 1,
2, 3, 4,?are denoted as s, p, d, f, g?respectively, similar to the designations made in
atomic physics for electrons. The proton and neutron orbitals fil independently, and
difer in order and spacing at higher A because of the Coulomb interaction. Also of note
is that when the orbitals fil, nucleons pair off imediately, so that there are never two
similar unpaired nucleons in the ground state. As shown in Fig. 1.2, the predicted ?shel
gaps? occur at the experimentaly observed number of nucleons for both protons and
neutrons.
21
2f
0
1
2
3
4
5
1s
1g
2p
1f
2s
1p
2d
1h
3s
1d
1i
1s
1/2
1p
3/2
1p
1/2
1d
5/2
1d
3/2
2s
1/2
1p
1/2
1f
5/2
2p
3/2
1f
7/2
1g
9/2
1g
7/2
1h
11/2
3s
1/2
2d
3/2
2d
5/2
1h
9/2
N = 2
N = 8
N = 20
N = 28
N = 126
N = 82
N = 50
1f
7/2
3p
3/2
1i
13/2
2f
5/2
Z = 2
Z = 8
Z = 20
Z = 28
Z = 82
Z = 50
1g
7/2
1h
11/2
3s
1/2
2d
3/2
2d
5/2
1s
1/2
1p
3/2
1p
1/2
1d
5/2
2s
1/2
1d
3/2
1f
7/2
1p
1/2
1f
5/2
2p
3/2
1g
9/2
3p
1/2
V
HO
V
SW
V
SO
n V
SO
p
3p
[8]
[20]
[40]
[70]
[112]
[2] [2]
[8]
[18]
[20]
[34]
[40]
[90]
[68]
[58]
[132]
[106]
[138]
[92]
Figure 1.2: Energy levels predicted by use of the harmonic oscilator (V
HO
), the infinite
square wel (V
SW
), and the Woods-Saxon potential with the inclusion of spin-orbit
coupling for both the neutrons (V
SO
n) and protons (V
SO
p). The numbers in brackets
represent the total numbers of nucleons of one kind that would have occupied states up to
that orbital. The magic numbers predicted by the shel model are labeled for both the
neutrons and protons in bold Figure taken from [Fr81].
The shel model can be used to predict a variety of diferent nuclear observables;
among them the spins and parities of the ground and excited states for a nucleus. The
ground state of an odd-A nucleus is usualy equal to the spin (j) of the unpaired nucleon.
The spin and parity of a nucleus with an even number of protons and neutrons wil
always have a ground state of 0
+
. The situation for a nucleus with an odd number of
protons and neutrons is significantly more dificult to predict; however, there are
formulas used to approximate the most likely J
?
 for these nuclides.
The excited states of a nucleus can be predicted by solving the Schr?dinger
equation for a many-body system. The formalism for obtaining these states is to solve the
22
Schr?dinger equation and construct unperturbed many-body wave functions for the
valence nucleons. Next, an energy matrix is constructed asuming the presence of a two-
body residual interaction. The mathematics of two-body interactions wil not be discussed
in detail, but their inclusion in a shel model calculation is as a perturbation to H
(0)
. The
next step is to obtain the unperturbed energies E
k
(0)
, for these multibody matrix elements,
and finaly the constructed energy matrix is diagonalized to obtain the wave functions
and energies of the mixed configurations.
The two main input parameters for shel model calculations include the single-
particle energies and the two-body matrix elements (TBME) that describe the residual
interactions betwen the nucleons. The single particle energies are obtained from the
excitation energies of nuclei with a single valence nucleon outside the closed shels. The
TBME can be obtained from experimental level schemes of nuclei with two valence
nucleons outside a closed shel, if available. Otherwise, these can be calculated provided
that the binding energy of the nucleus, binding energy of the core, and single-particle
energies of the coupled particles are wel known. Due to the fact that some two-nucleon
configurations cannot be observed because of experimental limitations, and that some
experimental single-particle states are mixed or even unobservable, sometimes, the
single-particle energies and TBME must be extracted from calculation. In this case, the
experimentaly observed levels for nuclei in a given region are fit by modifying the
TBME and single-particle energies. When the best agrement betwen experimental data
and theoretical predictions for the largest number of nuclei can be obtained, these
parameters are adopted and used for calculating the level structures of other nuclei in the
region of interest.
23
Despite the succes of the shel model for predicting the properties of many
nuclei, it suffers from two limitations. The first is that the shel model has no convention
for describing the phenomenon of collectivity. In addition, the shel model works poorly
for describing mid-shel nuclei, as these species are usualy deformed, and not spherical
in shape. As the nuclei (
111
Sb, 
134
Sb, and 
135
Sb) that wil be discussed in chapters 2-4
have only a few valence particles outside double magic 
100
Sn or 
132
Sn, then the
underlying physical properties responsible for the observed structure of these nuclides is
best described in the context of the shel model.
1.5 r-Proces Nucleosynthesis
Shel efects are not only important for discussing the physics that dictate the
structure of nuclei, but are also of great importance in the field of nuclear astrophysics.
One of the most important observations that would intertwine the fields of nuclear
structure and astrophysics was made in 1956 by Charles Coryel. He noticed that there
was a clear connection betwen the observed elemental abundances and their proximity
to the closed neutron shels. A year later, in a benchmark paper by Burbidge, Burbidge,
Fowler, and Hoyle [Bu57], this correlation was published. The figure in their paper from
which their conclusions were drawn is shown in Fig. 1.3. The observed solar abundances
show distinct peaks for nuclei that have N = 50, 82, and 126. This strong correlation
implies that nuclear structure plays an important role in our understanding of how the
elements were formed.  Another important, and unexpected implication of the data shown
in Fig. 1.3 is that the presence of a doublet at each neutron shel closure suggest there are
actualy two proceses responsible for the synthesis of al the elements.
24
Figure 1.3: Schematic representation of solar system abundances as a function of A.
Features due to specific proceses are indicated (taken from [Bu57]).
Nucleosynthesis is the proces by which heavier nuclei are built up from lighter
nuclei. There are thre types of nucleosynthetic proceses that are responsible for the
buildup of al of the stable elements, but for purposes of brevity, only the two that
proced to the neutron rich side of the valey of stability wil be discussed. The s-proces
or slow neutron capture proces occurs for modest neutron densities over milions of
years, hugs the beta valey of stability, and is partly responsible for the synthesis of
elements up to Bi. In the s-proces, a few neutrons are captured away from the valey of
stability, and neutron capture occurs until the lifetime of the neutron capture reaction
becomes longer than the ?-decay T
1/2
. When the unstable species decays, it does so to the
Z+1 daughter, and then neutron capture resumes.
The r-proces, or rapid neutron capture proces, occurs in explosive environments
(such as supernovae or neutron star mergers) that have dense neutron environments (N
n
 ?
10
20
 to 10
27
n/cm
3
) and have high temperatures (~10
9
 K). The r-proces path is far from
25
the valey of stability in regions where the S
n
 is ~1.2 to 2.0 MeV. The r-proces, similar
to the s-proces, is also responsible for the buildup of heavy elements by subsequent
neutron-capture and then ? decay into the (Z + 1) daughters. The observed elemental
abundances can mostly be atributed to the s- and r-proces. As the contribution to the
elemental abundances from the s-proces (N
s
) can be calculated reliably, the r-proces
contribution (N
r
) to the solar elemental abundances (N
solar
) is estimated as
? 
N
r
?N
solar
?N
s
. (1.27)
As shown in Fig. 1.3, the s-proces is responsible for the buildup of abundances
for A = 90, 140, and 205, while the r-proces is atributed to the increased abundances of
species with A = 80, 130, and 195. The presence of double abundance peaks at magic
numbers of N and the presence of U was the initial motivation for postulating the
presence of the r-proces.
The r-proces difers from the s-proces in that the lifetimes of the (n,?) reaction
(?
n
?
) are significantly shorter than the ?-decay lifetimes (?
?
),  whereas the situation is
reversed for the s-proces. The reason that ?
n
?
 is extremely fast in the r-proces results
from the presence of extremely high neutron densities and intense flux of ? rays that exist
in the explosive environments where this type of nucleosynthesis takes place. Eventualy,
the S
n
 becomes low enough that there is equilibrium betwen the (n,?)?(?,n) reactions. It
is at this point that ?-decay becomes a competitive mechanism for continuation of the r-
proces path up the mas chain. When the r-proces reaches equilibrium, it is staled until
? decay occurs, thus continuing neutron capture in the Z + 1 daughter. The stagnation of
the r-proces until ? decay occurs is known as the ?waiting point? concept.
26
Unlike the s-proces, abundances that build up as a function of A, the time
dependence of the r-proces is governed by Z, and expresed as
? 
dN
Z
(t)
dt
=?
Z?1
(t)N
Z?1
(t)??
Z
(t)N
Z
(t).
 (1.28)
For nuclei far from the valey of stability with these magic neutron numbers, the
Z+1 ?-decay daughters proced to capture to the adjacent N+1 nucleus. However, these
N+1 nuclei have very smal S
n
, and relatively long half lives, thus these nuclei with
closed shels of neutrons represent a special set of waiting points in r-proces flow. These
special sets of waiting points at N= 50, 82, and 126 are shown in Fig. 1.4. At these
neutron numbers, there is a significant vertical rise in the r-proces path, thus elements
with much higher Z are rapidly synthesized. Eventualy, enough neutron-capture/?-decay
proceses occur that the nuclei are close enough to stability that the S
n
 goes up, and
breakout from the N=50, 82, or 126 bottlenecks is possible. As the half lives of the r-
proces nuclei with a magic number of N are significantly longer, the observed elemental
abundances at A = 80, 130, and 195 buildup.
Figure 1.4: Schematic showing the s- and r-proces paths as a function of increasing Z
and A (taken from [Ro88]).
27
The goals of many astrophysicists is to deduce how, when, where, and under what
conditions the r-proces occurs. They then atempt to theoreticaly reproduce these
observed r-proces abundance peaks using diferent sets of conditions. There are many
models that approach this problem by incorporating diferent sets of underlying physical
principles in order to obtain a global fit to the data. However, as there is succes
reproducing the r-proces abundance curve from these diferent approaches, the question
of model reliability becomes important. Currently, the best method for understanding the
r-proces is to have as many decay properties measured for as many nuclei away from the
valey of stability as possible. The decay properties that are critical as the input
parameters to these calculations include the S
n
, ?-decay half lives, and P
n
 values. Also, as
pointed out, there are many nuclear structure efects that determine the r-proces path;
therefore, it is also important that as much structural information is collected as possible.
It has already been suggested that the shel gaps that occur close to stability collapse as
N/Z ? 2. The combination of acurate decay properties and nuclear structure
information wil help constrain extrapolations of decay properties to heavier mas regions
with beter acuracy, which then limits the variety of r-proces calculations, thus aiding
in a true understanding of the path that this type of nucleosynthesis takes.
1.6 Implications of Nuclear Physics and Astrophysics Concepts
The focus of this chapter was to provide a basis for understanding nuclear physics
and astrophysics concepts that wil now be discussed at length. The selection rules
discussed for ? and ? decay are important for understanding spin and parity asignments
for the levels of the odd-A Sb nuclides. The level structures of these nuclides (
111
Sb,
28
134
Sb, and 
135
Sb), are compared with shel-model calculations that are obtained using
diferent input parameters. The results of these calculations have implications for our
understanding of the strengths of the various N interactions and the nuclear potential in
the A~100 and A~132 mas regions. Finaly, it was important to discuss nucleosynthesis
and the r-proces as the ??delayed neutron (?dn) decay data that wil be discussed were
used in r-proces calculations which predict where the ?waiting points? lie as a function
of neutron density in the A=130 region.
29
2 The Structure of 
134
Sb
2.1 Overview
The level structure of odd-odd 
134
Sb (Z=51, N=83) was studied in the ?
-
 decays of
the very-neutron-rich 
134,135
Sn isotopes. Sn isotopes were produced by proton- and
neutron-induced fision at CERN/ISOLDE and ionized using a resonance ionization laser
ion source. In separate experiments ?-ray singles and ?-? coincidences were studied as a
function of time for the decays of 
134
Sn and 
135
Sn following mas separation. From these
data, the position of the 7
-
 ?-decaying isomer in 
134
Sb has been established at 279 keV.
The 5
-
 and 6
-
 members of the ?f
7/2
??g
7/2 
multiplet have also been identified, along with
thre new 1
-
 levels at higher energy. New insight for the proton-neutron interaction is
discussed in the context of the shel model.
2.2 Scientific Motivation
The structures of the odd-odd nuclides that are adjacent to double-magic nuclides
provide the best opportunities to develop and test two-body matrix elements (TBME) for
the proton-neutron interaction. The calculated TBME used to describe the structures of
nuclei in these regions can then be extrapolated to describe the structures of more
complex nuclides further from the double-shel closure. The structures of nuclides near
132
Sn provide a particularly interesting testing ground for understanding the behavior of
TBME because the low-energy structures of these nuclides are dominated by
configurations with high purity and negligible mixing with higher seniority structures that
arise from the breaking of the 4-MeV double-magic core.
30
One of the most succesful approaches to the structure of odd-odd 
134
Sb, which
has a single proton (?) that can occupy orbitals above the Z = 50 shel closure (1g
7/2
,
2d
5/2
, 1h
11/2
, 2d
3/2
, and 3s
1/2 
orbitals, se Fig. 1.2) coupled to a single neutron (?) that can
occupy orbitals above the N = 82 shel closure (1f
7/2
, 1h
9/2
, 3p
3/2
, 3p
1/2
, and 2f
5/2 
orbitals
se Fig. 1.2), was atempted by Chou and Warburton [Ch92] when litle was known
regarding the experimental single-particle levels near 
132
Sn. The first calculation for the
positions of the levels in 
134
Sb was acomplished using TBME developed by Brown and
Warburton [Br91] for the 
208
Pb region. These TBME were taken from the analogous
nuclide, 
210
Bi, and mas-scaled by a factor of (132/208)
-1/3
 for use in the 
132
Sn region. At
the time, a new study had been published by Fogelberg et al. that suggested that the
lowest 1
-
 level was at 318 keV [Fo90]. As the initial calculations indicated that the 0
-
 and
1
-
 levels were nearly degenerate, as is known for 
210
Bi, a second modified set of TBME,
designated as CW5082 interactions, were developed. The revised interactions provided
~300-keV of separation betwen the 0
-
 ground state and 1
-
 first excited state, which was
in agrement with the published data at the time.
Recently, Korgul et al. reported a new study of the low-energy, low-spin level
structure of 
134
Sb populated in the decay of 
134
Sn and identified a new level at 13 keV
that has been asigned as the lowest 1
-
 level [Ko02]. They were also able to identify
additional levels at 330 (2
-
), 383 (3
-
), 885 (1
-
), and 935 (2
-
) keV and infered a possible
level at 555 (4
-
) keV based on data from fision-gama studies. Now, using the original
KH5082 TBME, along with the single-proton and single-neutron energies identified in
133
Sb and 
133
Sn, respectively; the original TBME were sen to provide a remarkably good
fit to the new level structures.
31
The 0
-
, 1
-
, 2
-
, 3
-
, and 4
-
 levels noted above al belong to the ?f
7/2
?g
7/2
 multiplet that
arises from the coupling of the ground states of 
133
Sn (J
?
 = 7/2
-
) and 
133
Sb (J
?
 = 7/2
+
). In
addition to those five levels, there are thre additional levels with spins 5
-
, 6
-
, and 7
-
 that
are needed to completely determine the ground-state multiplet.
The 
134
Sn ?-decay studies by Fogelberg et al. [Fo90] and Korgul et al. [Ko02]
were performed at the Nuclear Research facility in Studsvik, Sweden. Here, exotic
neutron-rich Sn isotopes were produced by thermal fision of 
235
U [Fo90] or more
recently, by fast neutron fision of 
238
U [Ko02]. The fision products are ionized using a
plasma ion source, and then mas separated using a bending magnet. As the proces of
ionization in a plasma ion source is thermal in nature, several elements with the same
mas are ionized simultaneously, and then deposited onto the tape where ? spectroscopy
measurements are taken. The contribution of the ? rays resulting from the decays of the
isobars makes interpretation of collected spectra dificult. The large background in the ?
spectra due to the buildup of isobaric contamination can often hide les intense
transitions, and even render it impossible to identify transitions asociated with the decay
of exotic nuclides whose production cross sections are smal.
The development of the Resonance Ionization Laser Ion Source (RILIS) at
CERN/ISOLDE now provides a method to produce sources of Sn isotopes that are fre of
surface ionized isobars, as the proces of resonance ionization is non-thermal in nature.
Therefore, higher-Z isobars with low-ionization potentials that are closer to stability and
typicaly overwhelm plasma ion sources, are produced in decreasingly lower yields. For
example, the spectra shown by Fogelberg et al. [Fo90] show strong lines from the decay
of 
134
Sb, 
134
Te, and 
134
I that cover up possible weak lines in the decay of 
134
Sn. The RILIS
32
also offers additional selectivity by enhancing the ionization of atoms with a specific Z.
As atomic structure is Z-specific, lasers can be tuned to energies that correspond to
resonant excitations in Sn. Thus in a sequential two-step excitation proces, followed by a
third step which ionizes only the Sn atoms in the target, it is possible to selectively
increase the amount of Sn which becomes ionized. By taking data with the laser on and
also with the laser off, lines originating from the decay of Sn isotopes and the daughters
and granddaughters that grow in can be easily distinguished from other lines as they
disappear when the laser is off.
In this chapter, the results of a new study of the levels of 
134
Sb populated in both
the direct ?
-
 decay of 
134
Sn, and also in the ?-delayed neutron decay of 
135
Sn are
presented. The spins and parities and relative energies of the parent and daughter nuclides
are ilustrated in Fig. 2.1.  The ?
?
 decay of 0
+
 
134
Sn wil populate the negative-parity 0
-
and 1
-
 levels in 
134
Sb via first-forbidden decay, with some smal first-forbidden unique
decay branching possible to 2
-
 levels. Whereas the ?
-
 decay of the 7/2
-
 
135
Sn wil decay
via Gamow-Teler alowed transitions to negative-parity 5/2
-
, 7/2
-
, and 9/2
-
 levels that lie
wel above the neutron separation energy. From previous measurements, the P
n
 value for
these branches was deduced in our 2000 experiment to be 21(3)% [Sh02]. These levels
wil, in turn, decay largely by the emision of l = 0 neutrons to 2
-
, 3
-
, 4
-
, and 5
-
 levels in
134
Sb, with reduced population of 0
-
, 1
-
, 6
-
, and 7
-
 levels by emision of l = 2 neutrons.
Because of the energy dependence of ?
-
 decay, population of levels in 
134
Sb wil be
concentrated at lower energies.
33
2
4
6
8
10
12
0
n
l= 0
135
Sb
135
Sn
7/2
-
5/2
+
282
440
5/2
+
, 7/2
+
, 9/2
+
S
n
 = 3.6 MeV
3/2
+
?
?-
ff-decay
7/2
+
GT-decay
E
n
e
r
g
y
 
(
M
e
V
)
134
Sn
0
+
134
Sb
0
-
0
-
, 1
-
?
-
ff-decay
2
-
, 3
-
, 4
-
, 5
-
?
5/2
-
, 7/2
-
, 9/2
-
Figure 2.1: Possible states in 
134
Sb that can be populated by the ?
?
-decay of 
134
Sn and the
?dn-decay of 
135
Sn.
2.3 Experimental Details
Low-spin levels in 
134
Sb were populated via ?
-
 decay of 
134
Sn and ?dn decay of
135
Sn. Neutron-rich Sn nuclei were produced at ISOLDE/CERN by fision of a UC
2
target (20-cm long, thicknes 52 g/cm
2
 and ~10 g/cm
2
 of graphite) with fast protons and
neutrons. The fast neutrons were produced by impinging 1.4-GeV protons that were
acelerated by the Proton Synchrotron Booster (PSB) onto a tungsten rod located
adjacent to the UC
2
 target. PSB pulses were impinged upon the tungsten rod as often as
34
every 2.4 s, and each pulse had an intensity of approximately 3 ? 10
13
 protons. One-
second data collection cycles were started with each proton pulse, and then halted so that
the longer-lived radioactivity on the tape could be transported away from the counting
station.
In a first Sn decay experiment reported in [Sh02], the ?-ray spectra were
dominated by isobaric contamination from 53-min 
135
Cs
m
 arising from surface-ionized Cs
ions that are produced in proton spalation on the UC
2
 target. As a consequence, despite
the useable yields of 
135
Sn, only 4 strong ? transitions at 282, 318, 732, and 925 keV
below 1.0 MeV, along with a number of higher-energy ? rays, could be observed above
the large 
135
Cs background (the most intense 
135
Cs peaks were at 840 and 787 keV).
In order to lower the production of spalation-produced Cs isotopes, a target setup
that included the tungsten rod was used. Thus, fision was primarily induced by neutrons.
Thus, the reactions in the target were induced by high-energy neutrons produced by
proton interactions in the tungsten rod instead of the 1.4 GeV proton beam.
Consequently, the high-energy neutrons enhance the fision production cross section
relative to the spalation-production cross section, therefore Cs yields were lowered by
several orders of magnitude and dramaticaly improved ?-ray and ?-? coincidence spectra
could be obtained.
Following fision of the UC
2
 target, Sn isotopes were selectively ionized by use of
the resonance ionization laser ion source (RILIS). Previous studies at ISOLDE/CERN
have shown that the use of RILIS can significantly increase the yields of specific nuclides
relative to the inevitable products of surface ionization [Mi93,Er98]. The ionization
35
scheme used for Sn nuclei was based on thre resonant transitions, (?
1
 = 300.9 nm, ?
2
 =
811.4 nm, and ?
3
 = 832.5 nm) leading to an autoionizing state [Mi93].
Beams of 
134
Sn and 
135
Sn ions were produced with average beam intensities of
~10
7
/s for 
134
Sn and ~10
5
/s for 
135
Sn [Jo03]. These ions were extracted into the general
purpose separator for mas separation and implanted into an Al coated tape in a moving
tape station. Five HPGe and thre plastic detectors were positioned around the point of
implantation. The plastic scintilators were used to veto 0? ?-? coincidence events and
gate on 180? coincidence events. For each event, the outputs of the detectors were
recorded along with time-to-amplitude converter information and the time of the event
following the proton pulse. From these data, it was possible to construct a ?-? matrix, a ?-
time matrix, and background reduced ?-gated ?-singles spectra. Projections from the
matrices were used to determine the time-dependence of each ? ray and generate
coincidence spectra. Data were taken with both the laser-on and the laser-off to determine
which transitions in the ? spectra belonged to the decays of 
134,135
Sn and their daughters.
2.4 Identification of the ? Rays which Depopulate Levels in 
134
Sb
2.4.1 ?
-
 Decay of 
134
Sn
Data were taken at A = 134 to study the ?
-
 decay of 
134
Sn to low-spin levels of
134
Sb. Shown in Fig. 2.2 is a ?-gated ? spectrum that resulted from the diference of a ?
spectrum taken betwen 600-1000 ms following the proton pulse from that of a ?
spectrum obtained in the first 300 ms following the pulse. Peaks previously reported by
Korgul et al. are labeled with filed circles, while transitions unique to this study are
denoted with open squares. The data for the ? rays under 1.0 MeV provide strong support
36
for the 
134
Sb level scheme already published by Korgul et al. [Ko02], although there are
some weak transitions that they did not observe betwen established levels. In addition, a
number of new transitions above 1.0 MeV that they did not report were observed.
Korgul et al. [Ko02]
Shergur et al. 
C
o
u
n
t
s
 
Energy (keV)
1
0
1
5
1
2
3
5
1
2
6
5
1
2
8
5
50
100
150
200
1000 1050 1100 1150 1200 1250 1300
50
100
150
200
1600 1650 1700 1750 1800 1850 1900
1
6
5
5
1
8
3
9
0
20
40
60
80
100
1300 1350 1400 1450 1500 1550 1600
1
4
9
5
1
5
4
5
1
5
6
9
2000
4000
6000
8000
10000
100 200 300 400 500
3
1
7
5
3
6
0
4
5
1
1
1000
2000
3000
4000
5000
6000
500 550 600 650 700 750 800
5
5
1
5
5
4
9
6
3
/
9
6
5
9
2
2
8
7
2
8
8
5
1000
2000
3000
4000
5000
800 850 900 950 1000
X
600
1000
1400
330 350 370 390
3
3
1
3
7
1
Figure 2.2: ?-gated ?-diference spectrum obtained by subtracting data taken from 600
ms to 1 s following the proton pulse from that taken from the first 300 ms after the pulse.
An 'x' is used to label the 965-keV peak because most of the counts in this peak arise
from the ?dn decay of 
134
Sn to the 963-keV first excited state in 
133
Sb.
Coincidence spectra resulting from gates on the 872- and 922-keV ? rays are
shown in Fig. 2.3. Transitions in coincidence with the 872-keV ? ray that depopulate the
885-keV level in 
134
Sb are at 1015, 1285, and 1545 keV. Peaks at 965, 1235, and 1495
keV in coincidence with the 922-keV ? ray which depopulates the 935-keV level support
the placement of new levels in 
134
Sb at 1900, 2170, and 2430 keV, respectively. Gates on
the two most intense new ? rays, the 965- and 1015-keV lines are also shown in Fig. 2.3.
37
5
10
15
900 1100 1300 1500 1700
9
6
5
1
2
3
5
1
4
9
5
922-keV Gate
C
o
u
n
t
s
2
4
6
8
1000 1200 1400 1600
1
0
1
5
1
2
8
5
1
5
4
5
872-keV Gate
Energy (keV)
5
15
25
200 400 600 800 1000
5
5
1
6
0
4
9
2
2
3
1
8
965-keV Gate
2
6
10
14
400 600 800 1000
8
7
2
8
8
5
5
5
4
3
1
8
1015-keV Gate
Figure 2.3: Coincidence spectra for gates on the 922-, 872-, 965-, and 1015-keV ? rays
that depopulate levels in 
134
Sb following ?
-
decay of 
134
Sn.
The gate on the 965-keV ? ray shows coincidences at 318, 551, 604, and 922 keV, which
are the thre most intense ? rays that depopulate the 935-keV level. Similarly, the gate on
the 1015-keV ? ray shows coincidences at 318, 554, 872, and 885 keV, which would be
expected if this transition populated the 885-keV level. Further evidence for the
placement and asignments of the new 1
-
 levels and ? rays in 
134
Sb is shown in the
coincidence gate on the 318-keV ? ray in Fig. 2.4(a).
Also of note in the coincidence spectrum shown in Fig. 2.4(a) is a peak at 947
keV. This ? ray could fed either the level at 331 or 384 keV. The weak peak at 1000 keV
in the laser-on singles spectrum that is 53-keV higher than the 947-keV peak, therefore,
these two lines are tentatively asigned as depopulating a new level at 1331 keV to the 1
-
and 2
-
 levels at 330 and 383 keV, respectively. As these two ? rays are within an order of
magnitude of each other, the spin and parity of the new level is likely to be 1
-
 or 2
-
38
because the E2 transitions sen in the rest of this level scheme are quite weak compared
to competitive depopulation by possible M1 transitions. The absence of a higher-energy
0 100 200 300 400
5
3
C
1000 1100 1200 1300 1400 1500
1
0
1
5
1
2
3
5
1
2
8
5
1
4
9
5
1
5
6
9
1600 1700 1800 1900
Energy (keV)
1
8
3
9
1000
1400
500 600 700 800 900
5
5
1
5
5
4
6
0
4
0
10
20
30
900 920 940 960 980 1000
9
4
7
9
6
5
1600 1700 1800 1900
1000 1100 1200 1300 1400 1500
500 600 700 800 900
5
1
1
7
0
7
*
0
5
10
5
10
15
20
20
60
100
50
150
250
0 100 200 300 400
5
3
1
7
1
C
o
u
n
t
s
0
50
100
0
10
20
200
600
0
10
20
(a) (b)
318-keV gate- 
135
Sn ?dn-decay318-keV gate- 
134
Sn ?-decay
5
5
4
5
5
1
6
0
4
8
0
0
C
C
Figure 2.4: Coincidence spectra for gates taken on the 318-keV transition in 
134
Sb
following ?-decay of 
134
Sn (a) and ?dn-decay of 
135
Sn. The '*' on the 707-keV peak in (b)
denotes that the presence of a 319-keV transition in 
135
Sb shows a coincidence in the 318-
keV gate.
crossover transition to the 0
-
 ground state provides support for our tentative asignment of
2
-
 for the spin and parity of this level. This new level at 1331 keV could be directly
39
populated via first-forbidden unique ?
-
 decay or by unobserved ? rays from the higher
energy 1
-
 levels. The log ft value shown in Fig. 2.5 is a lower limit calculated by
134
Sb
1
-
2
-
3
-
1
-
2
-
1
-
1
-
1
-
0
-
0
331
384
885
935
1900
2170
2430
1331 (2
-
)
5.713.4%
8.61.6%
9.90.05%
0.19% 7.0
0.19% 7.1
0.18% 7.2
71.4% 5.2
0
+
134
Sn
0
?
-
Q
? 
= 7.37
13
3
3
7
1
 
(
0
.
6
(
1
)
5
3
 
(
0
.
9
 
(
3
)
)
1
0
0
0
 
(
0
.
2
 
(
2
)
)
9
4
7
 
(
0
.
4
 
(
3
)
)
5
5
1
 
(
9
 
(
1
)
)
 
6
0
4
 
(
3
.
8
 
(
3
)
)
9
2
2
 
(
8
.
0
 
(
1
)
)
9
3
5
 
(
0
.
3
1
 
(
9
)
)
5
5
4
 
(
3
8
 
(
1
)
)
 
8
7
2
 
(
1
0
0
 
(
1
)
)
8
8
5
 
(
2
4
.
1
 
(
2
)
)
3
1
8
 
(
6
2
 
(
2
)
3
3
1
 
(
0
.
2
3
 
(
7
)
)
1
4
9
5
 
(
0
.
9
2
 
(
4
)
)
1
5
4
5
 
(
0
.
4
5
 
(
4
)
)
2
0
9
8
 
(
0
.
3
0
 
(
6
)
)
2
4
1
7
 
(
0
.
5
5
 
(
5
)
)
I
?
% log ft
1
2
3
5
 
(
0
.
8
1
 
(
8
)
)
1
2
8
5
 
(
0
.
9
 
(
2
)
)
1
8
3
9
 
(
0
.
5
 
(
1
)
)
9
6
5
 
(
0
.
5
 
(
3
)
)
1
0
1
5
 
(
1
.
1
 
(
1
)
)
1
5
6
9
 
(
0
.
5
9
 
(
9
)
)
Figure 2.5: Level scheme for 
134
Sb following the ?
-
decay of 
134
Sn. Log ft values were
calculated using the Q
?
 and ground state ? feding reported in [Fo90]. Transitions and
levels identified in this experiment are in blue. Dashed lines indicate tentative level and
??ray placements.
asuming that al of the observed depopulating intensity arises from direct population of
this level in the first-forbidden unique decay of the 0
+
 
134
Sn parent. Based on the above
coincidence relationships, an updated decay scheme for the ?
-
decay of 
134
Sn is shown in
Fig. 2.5.  Gama intensities obtained from this study of the ?
-
decay of 
134
Sn are listed in
Table 2.1. Shown in Table 2.2 are the log ft values calculated by asuming that the
combined feding to the 0
-
 and 1
-
 levels is 71.4 % as reported by Fogelberg [Fo90]. The
40
data obtained in this experiment could not be used to measure the ?-feding to the
individual 0
-
 and 1
-
 levels.
Table 2.1:  Data for ? Rays and Levels Observed in the ?-decay of 
134
Sn.
a
Uncertainty in ? ray energies is ? 0.5 keV. 
b
Relative to the 872-keV transition in 
134
Sb.
Level 
(keV)
J
?
E
?
a
 (keV) I
?
b
Final Level 
(keV)
J
?
331
2
-
3310.2(1) 0
0
-
31862(2) 13
1
-
384
3
-
3710.6(1) 13
1
-
53 0.9(3) 331
2
-
885
1
-
88524.1(2) 0
0
-
872100(1) 13
1
-
55438(1) 331
2
-
935
2
-
9350.31(9) 0
0
-
9228.0(1) 13
1
-
6043.8(3) 331
2
-
551 9(1) 384
3
-
1331
(2
-
)
10000.2(2) 331
2
-
9470.4(3) 384
3
-
1900
1
-
15690.59(9) 331
2
-
10151.1(1) 885
1
-
9650.5(3) 935
2
-
2170
1
-
18390.5(2) 331
2
-
12850.9(2) 885
1
-
12350.81(8) 935
2
-
2430
1
-
24170.55(5) 13
1
-
20970.30(6) 331
2
-
15450.45(4) 885
1
-
41
Table 2.2:  Calculated Log ft Values for Levels Populated in 
134
Sb via ?-decay of 
134
Sn.
a
The log ft values for these levels were calculated using log
1
f values, as the Fermi function for first
forbidden unique transitions are diferent.
2.4.2 ?dn-Decay of 
135
Sn
In the first experiment at ISOLDE [Sh02], the only ? ray observed from the ?dn
decay of 
135
Sn was the strong line at 318 keV. However, the intensity of the 318-keV ?
ray that is shown in Table 2.1 to 18.7% of the intensity of the 282-keV ? ray can be sen
to cary only ~10% of the total decay strength of 
135
Sn.  Moreover, the presence in the ?-
ray spectrum of lines from the decay of high-spin 10-s 
134
Sb
m
 (i.e. the 1297-keV ? ray)
indicates that there must be significant population of that isomer in the ?dn decay of
135
Sn. Thus, as the P
n
 for 
135
Sn is 21%, it is clear that there are quite likely to be several
additional ? rays arising from population of levels in 
134
Sb, mostly at low energy, as a
consequence of the tendency for delayed neutron decay to populate levels near the
ground state in the daughter nuclide. Hence, the first task was to correlate the ? rays in the
A = 135 spectra to specific nuclei.
The strong, wel-established 872 and 922 ? rays depopulating the levels at 885
and 935 keV in 
134
Sb, respectively, were below the level of detection in the A = 135 ?
Level (keV) J
?
I
?
%
Log ft
0,13
0
-
,1
-
71.45.2
885
1
-
13.45.7
935
2
-
1.6 8.6
a
1331
(2
-
)
0.059.9
a
1900
1
-
0.187.2
2170
1
-
0.197.1
2430
1
-
0.197.0
42
singles spectrum, an observation consistent with the statement above concerning the bias
to population of lower-energy levels. In addition, none of the intense ? rays above 500
keV showed a coincidence relationship with any of the previously reported ? rays in 
134
Sb
[Ko02]. Therefore, the only candidates for intense new peaks in the ? spectra that could
correspond to transitions depopulating levels in 
134
Sb were likely to be below 500 keV.
A ?-spectrum obtained by subtracting the peaks asociated with isobaric
contamination (these are identified by their presence in both the "laser-on" and "laser-off"
data collection modes) for 
135
Sn decay is shown in Fig. 2.6. Peaks marked with open
squares denote ? rays that correspond to transitions in 
135
Sb that have been established by
coincidence relationships that wil be discussed in chapter 3. The transitions labeled with
filed circles can then be atributed to 
134
Sb. As previously mentioned, the 53 keV and
171 keV transitions were asigned to 
134
Sb by Korgul et al. [Ko04]. Though the 171-keV
? ray was asigned to 
134
Sb because it had been observed in fision-product spectra, no
coincidence data have been reported that supported their claim. Asignment can now be
confirmed in the gated spectrum shown in Fig. 2.7 on the 53-keV line where both the
318- and 171-keV lines are sen. These placements are consistent with the asignments of
these thre ? rays as an yrast cascade from a 555-keV 4
-
 level to a 384-keV 3
-
 level to a
331-keV 2
-
 level to the 1
-
 level at 13 keV. The coincidence spectrum showing the gate on
the 171-keV ? ray in Fig. 2.7 also shows evidence of feding from a higher energy state.
As the 171-keV ? ray depopulates a wel-established state at 555 keV, the 830-keV peak
in the coincidence spectrum suggests the placement of a new level at 1385 keV.
43
5
3
1
1
4
1
5
8
135
Sn ? decay
135
Sn ?dn decay
1
8
0
1
7
6
1
7
1
2
1
6
1
6
2
5000
10000
15000
20000
25000
50 100 150 200 250
250 300 350 400 450 500
5000
10000
15000
20000
25000
4
4
0
4
3
1
4
0
9
3
1
8
2
8
2
3
3
8
3
7
1
Energy (keV)
C
o
u
n
t
s
2
4
3
2
7
4
Figure 2.6: Residual ?-gated ?-spectrum obtained for the decay of 
135
Sn. This spectrum
was obtained by subtracting the "laser-off" spectrum (only containing isobaric
contaminations) from the "laser-on" spectrum. Peak asignments are listed in the legend
to the left.
0
10
20
30
40
150 200 250 300 350 400 450 500
1
7
1
3
1
8
53-keV gate
100 120 140 160 180 200
1
1
4
1
7
6
20
40
60
80
162-keV gate
C
o
u
n
t
s
Energy (keV)
0
10
20
30
40
50
700 750 800 850 900
8
3
0 1
3
5
C
s
171-keV gate
0
10
20
30
40
50
60
700 750 800 850 900
7
6
8 1
3
5
C
s
338-keV gate
Figure 2.7: Coincidence spectra for gates taken on the 53-, 162-, 171-, and 338-keV ?
rays that depopulate levels in 
134
Sb following ?dn-decay of 
135
Sn.
Gates on the 162- and 338-keV lines are also shown in Fig. 2.7. The line at 162
keV is the strongest of these lines and shows only two coincidences at 114 and 176 keV.
The presence of the 176-keV ? ray in the 162-keV gate indicates a level sequence
44
whereby the upper level decays by both a 338- and 176-keV ? ray.  The presence of no
other strong lines except the 114-keV line supports the notion that these four ? rays arise
from levels in 
134
Sb that are populated in the ?-delayed neutron decay of 
135
Sb, and the
idea that these ? rays populate the 7
-
 ?-decaying isomer in 
134
Sb. As neither the 171-, nor
53-keV lines are found in this gate, placement of the 114-keV line as a transition
depopulating the established 4
-
 level at 555-keV is suggested. This leads to the level
sequence shown in Fig. 2.8 and places the 7
-
 ?-decaying isomer in 
134
Sb at 279 keV.
Further support for the placement of the 114-keV ? ray and for the population of
the 7
-
 state is shown in Fig. 2.9. In Fig. 2.9(a) is shown a ? spectrum obtained during the
first 100 ms of a one-second acquisition period, while the spectrum in Fig. 2.9(b) was
obtained 600 ms later in the counting period. As shown, the 114-keV peak decreases in
intensity by a factor of ~1/2, which is consistent with the 530(25) ms half-life of 
135
Sn. In
addition, the inverted peak ~116 keV in Fig. 2.6 is shown to grow in as a function of time
in Fig. 2.9, and can be atributed to the decay of the 7
-
 isomer in 
134
Sb, thus providing
further support for the population of the 7
-
 level via ?dn decay of 
135
Sn.
45
1
-
2
-
3
-
4
-
5
-
6
-
0
-
7
-
1
3
1
1
4
 
(
0
.
6
 
(
1
)
)
1
7
1
 
(
3
.
5
 
(
4
)
)
1
6
2
 
(
6
.
3
 
(
1
)
)
3
7
1
 
(
0
.
8
3
(
7
)
)
3
1
8
 
(
1
8
.
7
 
(
2
)
3
3
1
 
(
0
.
2
3
 
(
7
)
)
5
3
 
(
1
.
3
 
(
5
)
)
134
Sb
135
Sn
7/2
-
0
?
-
n
7
6
8
 
(
0
.
4
8
 
(
8
)
)
0
279
331
384
441
555
617
1385
8
3
0
 
(
0
.
2
 
(
1
)
)
(5
-
)
1
7
6
 
(
1
.
0
 
(
2
)
)
3
3
8
 
(
3
.
7
 
(
1
)
)
885
935
1
-
2
-
5
5
4
 
(
0
.
4
 
(
2
)
)
5
5
1
 
(
0
.
8
 
(
1
)
)
6
0
4
 
(
0
.
5
 
(
2
)
)
13
Figure 2.8: Level scheme for 
134
Sb following ?dn-decay of 
135
Sn. Transitions and levels
identified in this experiment are in blue. The 171-keV transition and 555-keV level are in
gren, this ? ray and state were mentioned by Korgul et al. [Ko02], but not observed.
Figure 2.9: In (a) is shown a ? spectrum for A= 135 taken during the first 100 ms of a
one-second acquisiton, and (b) a ? spectrum obtained during the last 600 ms of the same
acquisition.
12000
14000
16000
100 110 115 120 125 130 135 140105
1
1
4
1
1
6
(a)
(b)
10000
Energy (keV)
C
o
u
n
t
s
46
Also shown in Fig. 2.7 is a coincidence spectrum that was taken with a gate on the
338-keV ? ray. With the aforementioned placement of the 7
-
 ?-decaying isomer at 279
keV, the presence of the 768 keV peak in the spectrum would correspond to a ? ray that
would also depopulate the level proposed in the proceding paragraph at 1385 keV. This
level at 1385 keV is given a tentative asignment of 5
-
 as it populates levels with spins
and parities of 4
-
 and 6
-
.
The placement and asignments of the new low-energy ? rays are supported by the
five coincidence spectra shown in Fig. 2.4 and Fig. 2.7. In the 318-keV gated spectrum
shown in Fig. 2.4(b), only the 53 and 171 keV ? peaks are present with intensity wel
above background. Smal peaks can also be sen at 551, 554, and 604 keV that indicate
some weak population of the 1
-
 and 2
-
 levels at 885 and 935 keV, even though the higher-
energy ? rays at 872 and 922 keV could not be observed in the singles spectrum.
It should also be mentioned that there are peaks at 707 and 800 keV in Fig. 2.4(b).
The 707 keV ? ray depopulates an established state in 
135
Sb [Bh98]. This suggests the
presence of a 319-keV ? ray in 
135
Sb. The 800-keV peak is very smal, and as such, the
coincidence spectrum for a gate on this ? ray shows no evidence for the 53-keV
transition. As this possibility cannot be excluded, the 800-keV ? ray could either fed the
331- or 383-keV level that would place a low-spin level at 1131 or 1183 keV,
respectively.
The other thre coincidence spectra of importance for supporting the asignment
of the new ? rays to 
134
Sb are those which were gated on the 282-, 440-, and 798-keV ?
rays in 
135
Sb. The 440-keV ? ray depopulates a 3/2
-
 level at 440 keV that wil be
discussed in Chapter 4, and the 282-keV level is already wel established [Sh02]. In the
47
282-keV and 440-keV gated coincidence spectra shown in Fig. 2.10, there are no lines
that can be connected to either of the lowest levels in 
135
Sb. As most of the ? cascades in
135
Sb proced through one of these levels, it is unlikely that the 114-, 162-, and 176-keV ?
rays were unobserved in these gates.
100 200 300 400
C
1
5
8
1
8
0
0
100
200
300
100
200
300
400
500 600 700 800 900
5
1
1
9
7
8
8
3
1
X
7
3
2
X
9
2
5
X
-10
10
30
50
0 100 200 300 400
0
20
40
500 600 700 800 900
1
3
5
C
s
1
3
5
C
s
6
7
3
X
Energy (keV)
(a) (b)
C
o
u
n
t
s
X
X
0 100 200 300 400 500
2
1
6
X
4
0
9
X
100
200
300
400
50
100
150
500 600 700 800 900 1000
5
3
5
6
0
5
8
0
0
X
X
X
(c)
282-keV gate 798-keV gate440-keV gate
C
C
Figure 2.10: Coincidence spectra for gates taken on the 282-, 440-, and 798-keV ? rays
which depopulate levels in 
135
Sb following ?-decay of 
135
Sn. Peaks labeled with an 'x'
have been identified as ? rays which depopulate levels in 
135
Sb.
The 216-keV ? ray depopulates a wel-established level at 1014, as shown by the
coincidence spectrum gated on the 798 keV ? ray in 
135
Sb. The 409-keV peak that
depopulates a wel-established 1207-keV level in the coincidence spectrum further
supports the notion that the 216-keV ? ray belongs to 
135
Sb. Intensities for al new ? rays
that depopulate levels in 
135
Sb obtained from this study are listed in Table 2.3. In
summary, every ? ray below 500 keV shown in Fig. 2.6 has either been positively
observed in coincidence with some strong high-energy lines that support placement in
135
Sb and/or exclude placement in 
134
Sb, or placed in 
134
Sb and shown not to appear in the
strong lines clearly asigned to levels of 
135
Sb.
48
Table 2.3: Data For ? rays and Levels Observed in the ?dn-decay of 
135
Sn.
a
Uncertainty in ? ray energy is ? 0.5 keV 
b
Relative to the 282-keV transition in 
135
Sb. 
c
Unplaced ? ray in
coincidence with the 318-keV transition.
2.5 Shel Model Calculations
A summary of the experimental results for the level structure of 
134
Sb is shown in
Fig. 2.11, along with the single particle levels in 
133
Sb and 
133
Sn, and both a qualitative
schematic of the proton-neutron multiplets expected in 
134
Sb and the quantitative results
of two shel model calculations that used diferent sets of TBME. Included in this figure
are the actual energies for the high-spin 8
-
, 9
+
, and 10
+
 levels reported by Urban et al.
[Ur99], who could only report these energies relative to the previously unknown position
of the 7
-
 ?-decaying isomer in 
134
Sb.
Level 
(keV)
J
?
E
?
a
 (keV) I
?
b
Final Level 
(keV)
J
?
331
2
- 3310.23(7) 0
0
-
31818.7(2) 13
384
3
- 53 1.3(5) 331
2
-
441
5
- 1626.3(1) 279
7
-
555
4
- 1713.5(4) 384
3
-
1140.6(2) 441
5
-
617
6
- 3383.7(1) 279
7
-
1
- 1761.0(2) 441
5
-
885 5540.4(2) 331
2
-
935
2
- 6040.5(2) 331
2
-
5510.8(1) 384
3
-
1385
5
- 8300.2(1) 555
4
-
7680.48(8) 617
6
-
800
c 0.8(4)
49
Sn
50 83
133
7/2
-
      0
3/2
-
      854
?h
9/2
1561
9/2
-
?p
3/2
?f
7/2
1/2
-
      1656
?p
1/2
5/2
-
      2004
?f
5/2
13/2
+
      2694(200)
?i
13/2
S
n
 = 2455 (45)
133 
   51       82
Sb
7/2
+
5/2
+
962
2793
?h
11/2
?d
5/2
?g
7/2
11/2
-
3/2
+
2440
?d
3/2
1/2
+
2xxx
?s
1/2
      0
0
1
2
3
4
5
6
7
2
3
4
5
1
2
3 4 5
6
1
1
1
?f
7/2
?g
7/2
?p
3/2
?g
7/2
?f
7/2
?d
5/2
?h
9/2
?g
7/2
?p
3/2
?d
5/2
?f
5/2
?g
7/2
?d
5/2
?f
5/2
0
1
?d
3/2
?p
3/2
0
1
134 
   51       83
Sb
    01
-
    8
0
-
3582
-
8041
-
9812
-
12872
-
16731
-
21391
-
23341
-
28850
-
30171
-
KH5082
3
-
351
    0
0
-
   131
-
    383
2
-
330
3
-
8851
-
9352
-
19001
-
21701
-
24301
-
?i
13/2
?g
7/2
?h
11/2
?f
7/2
10
+ 9
+
8
    2797
-
    442
5
-
    555
4
-
    6176
-
  1351
8
-
  2407
9
+
  271410
+
3057
-
4225
-
565
4
-
645
6
-
1656
8
-
28619
+
2829
10
+23
1075
6
-
1283
4
-
1328
5
-
1516
5
-
1385
(5
-
)
1307
3
-
14513
-
14754
-
19102
-
2
329
1
-
    0
0
-
4062
-
1268
1
-
1051
2
-
1358
2
-
1858
1
-
2359
1
-
2572
1
-
2759
0
-
3353
1
-
CD Bonn
3
-
581
392
7
-
6045
-
710
4
-
8496
-
15558
-
2809
9
+
282510
+
11116
-
1333
4
-
15195
-
1849
5
-
1535
3
-
1765
3
-
1622
4
-
1973
2
-
2
-
  1330
Experiment Type:
high-spin
134
Sn ? decay
135
Sb ?dn decay
Figure 2.11: In the left portion of the figure are shown the experimental positions of the
neutron (?) and proton (?) single particle levels in 
133
Sn and 
133
Sb respectively. In
betwen these experimental levels are the possible multiplets that arise from the coupling
of a valence neutron and proton that form the low-energy states in 
134
Sb. The triangles
and squares denote 1
-
 and 2
-
 states that can be fed directly by ?
-
 decay of 
134
Sn. In the
right half of the figure is shown a comparison of the experimentaly observed levels in
134
Sb populated both by 
135
Sn ?dn-decay and by 
134
Sn ?-decay along with levels
calculated using both the Kuo-Herling and CD Bonn interactions. For the Kuo-Herling
and CD Bonn interactions, al levels up to 3.1 MeV are shown.
As noted earlier, Korgul et al. presented four diferent sets of calculations
for the ?g
7/2
??f
7/2
 multiplet [Ko02], and Gargano recently published a new set of similar
calculations [Ga04]. The energies calculated in these models for the newly identified 5
-
,
6
-
, and 7
-
 states in Table 2.4, along with the calculated energy diferences are presented.
Two features stand out, first both our Kuo-Herling and the KH5082 presented by Korgul
et al. provide the best overal fits [Ko02], and second, in spite of wide diferences in the
50
absolute calculated energies, most models fit the diference betwen the 6
-
 and 7
-
 levels
rather wel.
Table 2.4: Comparison of Various Calculations with the Experimental Values of the
Positions of the 5
-
, 6
-
, and 7
-
 Levels (keV) in 
134
Sb.
The shel-model calculations presented in this paper in Table 2.4 and in Fig. 2.11
are based on a closed double-magic core for 
132
Sn with the valence protons and neutrons
at positions shown in Fig. 2.11. Chou and Warburton used this model space for
calculations of levels in ?
-
 decay, and in the absence of a renormalized G matrix for the
132
Sn core they used the Kuo-Herling results for these orbits in the region of 
208
Pb
[Ku71]. This interaction was the basis of several studies of valence particle and hole
spectra around 
208
Pb [Br91,Mc75,Br81]. The Kuo-Herling interaction has a bare G matrix
derived from the Hamada-Johnston nucleon-nucleon interaction and contains first-order
particle-hole (bubble-diagram) corrections. Chou and Warburton scaled the two-body
matrix elements by a factor of (208/132)
-1/3
 as estimated from the mas dependence of a
finite range interaction in an oscilator basis. This approach leads to excelent agrement
with experiment at a degre that is perhaps unexpected. The calculated binding-energy
J
?
EXPKuo-HerlingCD Bonn
Gargano 
[a 04]
Korgul 
Empirical 
[Ko02]
Korgul 
H5082N 
[Ko02]
Korgul 
H5082 
[Ko02]
Korgul 
Bonn A 
[Ko02]
Korgul RPA 
[Ko02]
6
-
617645751743620693 695
7
-
279305404421300276 352
6
-
 to 7
-
338340347322320417 343
5
-
 t? 7
-
162117209110120208 184
6
-
 t? 5
-
176223138212200209 159
628900
279521
143231
349379
206148
51
diference betwen 
134
Sb and 
132
Sn of 12.83 MeV is in reasonable agrement with the
experimental value of 12.97(4) [Au95].
The lowest multiplet (0
-
 to 7
-
) has wavefunctions dominated (90% or more) by the
0g
7/2
-1f
7/2
 proton-neutron configuration. It has been learned from the M3Y interaction
[An83] (that gives bare G matrix elements which are similar to Kuo-Herling) that al
components of the N interaction are important. For example, for the 0
-
 state the various
contributions are -0.54 (T=0 central), -0.21 (T=1 central), 0.42 (T=0 tensor), -0.41 (T=1
tensor) and 0.19 (spin-orbit) MeV. Thus, the fact that the total agres with experiment is
an exquisitely sensitive test of the N interaction in nuclei. In addition, the renormalized
(bubble) part of Kuo-Herling gives significant shifts that contribute to the agrement. In
particular, without the bubble diagram the 1
-
 level lies 230 keV above the 0
-
. The
renormalization turns out to act in opposite directions for the 0
-
 and 1
-
 and brings them
into degeneracy as observed in experiment.
Atempts to improve upon the basic Kuo-Herling result have not succeded. The
scaling asumed by Chou and Warburton was apparently not needed, perhaps because the
higher overlap of the proton-neutron wavefunctions in 
132
Sn compared to 
208
Pb that
follows from the oscilator model, is canceled by the possible efects of the neutron skin
in 
132
Sn. The more recent renormalized G matrix obtained by Hjorth-Jensen from the CD-
Bonn potential (the spectrum labeled CD-Bonn in Fig. 2.11) that was used for the
spectrum of 
135
Sb and 
134
Sn in [Sh02] has bare G matrix elements that are similar to Kuo-
Herling but has higher-order renormalizations that in total are diferent from the first-
order corrections used for the Kuo-Herling calculations. Although it might be expected
that going to higher order leads to further improvements, there appears to be a
52
dependence on the underlying single-particle spectrum that needs further investigation
[Hj04]. The CD-Bonn renormalized G matrix gives beter agrement for the T=1
spectrum of 
132
Sn than obtained with Kuo-Herling [Sh02]. A consistent Hamiltonian for
this mas region has yet to be found.
Atention is also directed at the rather large diference in log f
1
t values shown in
Fig. 2.5 for the direct ? population of the two 2
-
 levels in the decay of 0
+
 
134
Sn to levels of
134
Sb.  As can be sen in the schematic shown in Fig. 2.11, the 2
-
 level at 885 keV is most
likely a member of the ?f
7/2
??d
5/2
 multiplet that can be directly populated in an L = 1
first-forbidden unique ? transition in which one member of the ?f
7/2
 neutrons decays to
form the ?d
5/2
 proton. In contrast, decay of the neutron pair to the other 2
-
 level with a
dominant ?p
3/2
?g
7/2
 configuration is highly atenuated, as such a transition involves
change for both the proton and neutron. Even when the neutron pair is occupying the
excited ?p
3/2
 orbital, the decay of a ?p
3/2
 neutron to produce a ?g
7/2
 proton would actualy
involve an underlying L = 3 ? transition that would be highly suppresed.  Hence it is
much more likely that the decay to the proposed 2
-
 level at 1331 keV is a consequence of
a configuration admixture with the lower 2
-
 level with a dominant configuration or
partialy by unobserved ? ray branches from the higher-energy 1
-
 levels.
Previous studies by Urban et al. established the position of a 10
+
 state 2434 keV
above the 7
-
 isomer and asigned it a ?g
7/2
?i
13/2
 configuration. This state, in turn,
depopulated to a 9
+
 level that was asigned a ?h
11/2
?f
7/2
 configuration [Ur99]. From these
energies, those authors then estimated the position of the unbound i
13/2
 neutron level in
133
Sn to be at 2694 keV with an uncertainty of 200 keV. This was determined using
scaled two-body matrix elements taken from 
210
Bi and a position of 260 keV for the 7
-
53
isomer. The new experimental value of 279 keV for the 7
-
 state would place the position
of the i
13/2
 at 2713 keV based on the reasoning discussed in [Ur99].
Although the calculated position of the 10
+
 level appears to be in rather good
agrement with the newly established position at 2714 keV, a note of caution must be
considered. Because the calculated positions for both of the other high-spin levels, the 8
-
level at 1351 keV and the 9
+
 level at 2407 keV, are ~300 and ~400 keV above the
observed positions. These discrepancies suggest that the 10
+
 level should also lie ~400
keV below the calculated position. Such an interpretation suggests that the estimate for
the position of the unbound i
13/2
 level near 2700 keV is, in fact, too low by several
hundred keV. Thus, while the low-energy levels sem to be reasonably reproduced in
both calculations, some seniority mixing may be present for higher-energy configurations
that involve the 
132
Sn core and are beyond the model space used.
2.6 Sumary and Outlook
New experimental data for the decays of mas separated 
134
Sn and 
135
Sn have
been taken at CERN/ISOLDE using a neutron converter to dramaticaly lower isobaric Cs
contamination. From these time dependent ?-ray singles and ?-? coincidence spectra, the
position of the 7
-
 ?
-
decaying isomer has been established at 279 keV, along with the 5
-
and 6
-
 members of the ?g
7/2
??f
7/2
 multiplet and one level at higher energy that are
populated in the ?-delayed neutron decay of 
135
Sn. Thre newly proposed 1
-
 levels above
1.0 MeV have also been identified in 
134
Sb in the ?
-
decay of 
134
Sn. These new data now
permit much more stringent testing of calculations for the structure of the one-proton-
one-neutron levels in 
134
Sb.
54
3  ?
?
 and ?dn-decay Studies of 
135-137
Sn
3.1 Overview
The ?- and ?-decays of the very neutron-rich 
135-137
Sn isotopes were studied in
two diferent experiments at CERN/ISOLDE using a resonance ionization laser ion
source and mas separator to achieve elemental and mas selectivity, respectively. Half-
life and delayed neutron emision probability (P
n
) values were measured for 
135-137
Sn,
along with an estimate of the upper limit for the half-life of 
138
Sn, using a concentric
aray of sixty 
3
He gas-filed proportional counters. ?-ray singles and ?-? coincidence
spectra were collected as a function of time with the laser on and with the laser off. These
data were used to establish the positions of twenty new levels in 
135
Sb, including low-spin
states at 282, 440, and 798 keV, which are given tentative spin and parity asignments of
5/2
+
, 3/2
+
 and 9/2
+
, respectively. The unexpectedly low-lying 282-keV level is cause for
reinvestigation into the shel model and the concept of monopole shifts. In an atempt to
explain the monopole shift of the 282-keV level, efects of a neutron skin are included in
shel model calculations that atempt to reproduce al the observed levels of 
135
Sb.
3.2 Scientific Motivation
Study of the structures and decay of Ag, Cd, In, Sn, Sb, and Te nuclides with
125<A<140 have taken on new importance in recent years owing to the vital role that
these properties play in r-proces nucleosynthesis calculations [Pf01]. Data for nuclides
in this mas region that lie directly in the r-proces path are esential for such
calculations, and also serve to test models that must be used to describe nuclides not yet
55
acesible to experimental measurements. For example, Dilmann et al. recently reported
new measurements for the Q-value and decay of 
130
Cd that revealed significant
divergence from many mas models whose values are widely used as input parameters
for abundance calculations [Di03].
In addition to astrophysical implications that the decay properties of these
nuclides have, the low-energy level structures of the nuclides that have two or thre
particles or holes adjacent to the doubly-closed shel nuclide 
132
Sn are of particular
interest for the determination and testing of two-body matrix elements (TBME) that
underlie calculations of nuclides much further from stability [Br91,Ch92]. More
specificaly, the nuclei 
135
I, 
135
Te, 
135
Sb, and 
135
Sn remain an excelent testing ground for
descriptions of nuclei with only thre nucleons present beyond the 
132
Sn double shel
closure. Relatively detailed data have been available for some time for 
135
I and 
135
Te
[Sa01,Ha02].
Prior to the experiments presented in this chapter, only the high-spin structure of
135
Sb had been reported [Ba98]. In this fision-fragment study, the yrast cascade for states
with spins and parities ranging from 11/2
+
 to 23/2
+
 were identified. The first experiment
used to probe low-spin structure in 
135
Sb was performed by Korgul et al. [Ko01] at the
OSIRIS facility in Studsvik, Sweden, in 1999. Due to the large amounts of isobaric
contamination in their ion source, only the thre most intense transitions
(the 282-, 733-, and 925-keV ?rays) asociated with the decay of 
135
Sn were identified
[Ko01]. The limited, yet important data obtained from their study were not published
imediately because of the presence of an unexpectedly low first excited state at 282
keV. It was not until the first of two ISOLDE/CERN experiments that their finding of the
56
position of the first excited state at 282 keV was confirmed. In this first ISOLDE
experiment (summer 2000), eforts were focused on measuring the ?-decay properties of
136
Sn and 
138
Sn. While simultaneously obtaining ?dn-spectra for A=138 and ?-spectra for
A=135, the 282-keV peak was observed. During the experiment it was possible to
identify levels in 
135
Sb that were populated via ?-decay of 
135
Sn, and the ?-decay
properties of 
135-137
Sn were measured. Owing to the overwhelming amounts of Te, no
data had been obtained for the decay of 
138
Sn.
Reiterating the ideas mentioned in sec. 2.2, the primary reason for choosing the
ISOLDE/CERN facility was for the use of the Resonance Ionization Laser Ion Source
(RILIS), as it provides the chemical selectivity necesary to reduce the overwhelming
amounts of isobaric contamination asociated with more traditional ion sources, such as
the one used at OSIRIS. However, despite the chemical selectivity asociated with use of
a RILIS in the first experiment, only nine new levels and twelve ? rays were identified in
135
Sb [Sh01,Sh02]. The experiment was succesful in the identification of the
aforementioned level at 282 keV, but questions were raised about the positions of the
other low-energy levels in 
135
Sb.
Motivation to undertake an additional study of the decay of 
135
Sn in the summer
of 2002 was initiated because of the development of the use of a neutron-converter for
the UC
2
 target in which the main proton beam was focused on a tungsten rod just below
the target. Thus, the reactions in the target were induced mostly by fast neutrons instead
of 1.4 GeV protons, as mentioned in sec. 2.3. Consequently, spalation-produced Cs was
lowered by several orders of magnitude and dramaticaly improved ?-ray and ?-?
coincidence spectra could be obtained. The amount of improvement of the 
135
Sn:
135
Cs
m
57
ratio is shown in Fig. 3.1 in which two ?-singles spectra are compared with and without
use of the neutron converter. The ? spectrum in Fig. 3.1(b) obtained with the neutron
converter shows a spectrum of much higher quality in terms of beter resolution and a
smaler background that alowed for the detection of numerous low-intensity transitions
in 
135
Sb in the second experiment.
200 300 400 500 600 700 800 900
10
10
4
10
5
3
(a) A=135 Laser-On ?-spectrum without converter (2000)
(b) A=135 Laser-On ?-spectrum with converter (2002)
(a)
(b)
C
o
u
n
t
s
Energy (keV)
135
Sn
135
Cs 135
Cs
Figure 3.1: Comparison of the quality of the data obtained for the decay of 
135
Sn in 2000
without the neutron converter (a) with that obtained in 2002 with the neutron converter
(b). The '+' labels the most intense 282-keV transition in 
135
Sb following ?
?
 decay of
135
Sn, and the 'x's mark the two largest peaks that result from the isomeric decay of
135
Cs
m
 which is the biggest contributor to isobaric contamination. The spectra have been
normalized to the area of the 282-keV peak.
3.3 Experimental Details
135-138
Sn nuclei were produced at ISOLDE/CERN by fision of a UC
2
 target (20-
cm long, thicknes 52 g/cm
2
 and ~10 g/cm
2
 of graphite). In 2000, 1.4 GeV protons were
used to induce fision; while, as previously mentioned, high-energy neutrons produced by
the tungsten converter were used in 2002. In both experiments, the proton pulses were
acelerated by the Proton Synchrotron Booster (PSB), and impinged directly on the target
58
(2000) or upon the tungsten rod (2002) as often as every 2.4 s, with an intensity of
approximately 3 ? 10
13
 protons/pulse.
Following difusion of the fision products out of the target, lasers tuned to the
frequencies mentioned in sec. 2.3 were used to selectively ionize Sn atoms. Tin ions were
then extracted from the target-ion source and mas separated using the general purpose
separator prior to implantation into an Al coated tape in one of two moving tape stations.
At one station, ?-delayed neutrons were counted using the high-eficiency Mainz neutron
long counter. This counter consists of a thre-ring concentric aray of 60 
3
He proportional
detectors. Neutron counts were recorded as a function of time in 1 ms or longer bins. In
both tape stations, the measurement followed implantation using the proton pulse from
the PSB as the start trigger. The tape was moved after each measurement period to avoid
buildup of long-lived isobaric activity in front of the detectors. In both stations, data were
taken with the laser-on and also with the laser-off.
The other detection station was used for counting ? rays and consisted of five
HPGe detectors and thre plastic scintilators. The plastic scintilators were used to veto
0? ?-? coincidence events and gate on the 180? coincidence events. For each event, the
outputs of the detectors were recorded along with time-to-amplitude converter
information and the time of the event following the proton pulse. ?-singles, ?-?
coincidence, and ?-? coincidence data were collected with both the laser-on and laser-off.
59
3.4 Measurement of the T
1/2 
and P
n
 Values for 
135-137
Sn
3.4.1 
135
Sn
In Fig. 3.2(a) is shown the time dependence of the ?-delayed neutron count rate
taken with the laser-on and also with the laser-off. The laser-on spectrum shown has been
corrected for the laser-off contributions. A least-squares fit for the neutrons from 
135
Sn
decay and the neutrons from the growth and decay of daughter 
135
Sb is shown. The
observed decay curve can be deconvoluted into the decay of 
135
Sn and the growth and
decay of 
135
Sb. Using values of 1.68(2) s and 22(3)% for the T
1/2
 and P
n
, respectively for
10
3
10
4
10
5
0 1 2 3 4 5 6
10
2
10
3
0.2 0.4 0.6 0.8 1 1.2 1.4
Time (s)
C
o
u
n
t
s
T
1/2
 = 530(10) ms
(a) (b)
Least-squares Fit
Observed Counts
135
Sn decay:  T
1/2
 = 538(9) ms 
                       P
n
 = 20(2)% 
135
Sb growth and decay: T
1/2
 = 1.68(2)s 

 
 
         P
n
 = 22(3)%) 
Figure 3.2: Shown in (a) is a least squares fit for the background-subtracted ?dn-decay
of 
135
Sn. Both the decay of 
135
Sn and the growth and decay of 
135
Sb are plotted. The least-
squares analysis yielded T
1/2 
and P
n
 values of 538(9) ms and 20(2)%, respectively. In (b)
is shown a least squares fit for the decay of the 282-keV transition in 
135
Sb following the
?-decay of 
135
Sn.
135
Sb [Pf01], a value of 538(9) ms is obtained for the half-life of 
135
Sn along with a P
n
value of 20(2)%. The time spectrum projected from the ?-(t) matrix for the 282-keV ? ray
is shown in Fig. 3.2(b). Corrections have been made for Compton events that also fal in
the 282-keV energy window. A T
1/2
 of 530(10) ms is obtained from these data.
60
Combining both sets of data from the time dependence of the ?dn and ?-ray
measurements, a T
1/2
 of 534(7) ms for 
135
Sn was obtained.
3.4.2 
136
Sn
In Fig. 3.3 is shown the least-squares analysis of the laser-on background
corrected data that includes the reported T
1/2
 and P
n
 values for 
136
Sb and 
135
Sb [Pf01]. The
fit was used to obtain T
1/2
 and P
n
 values of 300(15) ms and 27(4)%, respectively. No ?
rays were found in the time-projected ?-ray spectra that exhibited a short half-life in the
250-ms range. In particular, the 282-keV line in 
135
Sb that would have been populated in
the 30% ?dn branch was not observed owing, in part, to the intense isobaric Cs and Ba
lines present in the ?-ray spectrum. Previous structure studies of this nucleus have only
yielded information regarding a 565(50) ns isomeric state whose depopulation includes a
?-ray at 173 keV [Mi01].
10
4
0 0.5 1 1.5 2 2.5 3
Observed Counts
136
Sn: T
1/2
 = 300(15) ms, P
n
 = 27(4)%
136
Sb: T
1/2 
= 923(14) ms, P
n
 = 23(6)%
135
Sb: T
1/2
 = 1.68(2) s, P
n
 = 22(3)%
Least Squares
10
2
10
3
10
1
Time (s)
L
o
g
 
(
C
o
u
n
t
s
)
 
Figure 3.3 Least squares fit for the background-subtracted ?dn-decay of 
136
Sn. Both the
decay of 
136
Sn, and the growths and decays of 
136
Sb of 
135
Sb are plotted.
61
3.4.3 
137
Sn
A least squares analysis for the laser-on corrected background sum spectrum at A
= 137 is shown in Fig. 3.4. New values for the T
1/2
 and P
n
 were measured to be 250(30)
ms and 33(12)% for 
137
Sn, respectively; and 0.8(2) s and 12(2)% for 
137
Sb, respectively.
Though the values and uncertainties with the new T
1/2
 and P
n
 measurements for 
137
Sn and
137
Sb were improved because of higher counting statistics in the second experiment, the
presence of four unknown fit parameters stil leaves a considerable amount of
uncertainty. Until the T
1/2 
and P
n
 of 
137
Sb can be measured directly, litle more can be
done to report more acurate values for the decay properties of 
137
Sn.
10
2
0 0.5 1 1.5 2
10
3
10
1
Observed Counts
137
Sn: T
1/2
 = 250(30) ms, P
n
 = 33(12)%
Least Squares
137
Sb: T
1/2
 = 0.8(2) s, P
n
 = 12(2)%
136
Sb: T
1/2
 = 923(14) ms, P
n
 = 23(6)%
Time (s)
L
o
g
 
(
C
o
u
n
t
s
)
Figure 3.4: Least squares fit for the background-subtracted ?dn-decay of 
137
Sn. Both the
decay of 
137
Sn, and the growths and decays of 
137
Sb of 
136
Sb are plotted.
As with the data taken at A = 136, no ? rays were observed in the A=137 spectra
either by comparison of laser on and laser off spectra or by time-gated ? spectra from the
projections of the ?-(t) matrices. The lack of peaks asociated with the decays of 
137
Sn
62
and 
137
Sb could be an indication that the production yields are currently too smal to
observe counts above background in the ? spectra.
3.4.4 
138
Sn
As mentioned, least squares analysis of the ?dn-decay data is already too
ambiguous for the decay of 
137
Sn. Therefore, it would be reasonable to asume that the
measurements would be more dificult for the ?dn-decay of 
138
Sn, as its production cross-
section is an order of magnitude lower than that of 
137
Sn. However, it should be noted
that in the second experiment at ISOLDE, 
138
Sn was being produced in the target-ion
source, though the yields were extremely smal. In Fig. 3.5 a background subtracted ?dn
spectrum, taken at A = 138 is shown. It is possible to se a very short-lived component,
which is believed to be evidence for the presence of 
138
Sn. In view of the uncertainties of
the decay properties of the daughters, an upper limit of 150 ms is estimated for the T
1/2
 of
138
Sn.
5 0
1 0 0
1 5 0
2 0 0
0 0 .5 1 1 .5 2 2 .5 3
A  =  1 3 8  
T im e  (s )
C
o
u
n
t
s
Figure 3.5: ?dn spectrum taken at A = 138.
63
3.5 Identification of the ? Rays Asociated with the Decay of 
135
Sn
In Fig. 3.6 is shown a ? spectrum that was obtained by subtracting data taken with
the laser-off from that of data taken with the laser on at A = 135. Only peaks asociated
with the decay of 
135
Sn, its daughters, and granddaughters should remain in the diference
spectrum. The absence of peaks at 787 and 846 keV, asociated with the decay of 
135
Cs
m
,
shows the efectivenes of the RILIS for reducing surface ionized species that usualy
overwhelm the ion source. The peaks in Fig. 3.6 labeled with 'x's designate transitions
that have been identified as ? rays which depopulate levels in 
134
Sb from the ?dn-decay of
135
Sn (se Fig. 2.8). The peaks labeled with open circles correspond to wel-established
transitions in the granddaughter nucleus, 
135
Te following ?
?
 decay of 
135
Sb. The
remaining unlabeled lines are tentatively asigned as ? rays which depopulate levels in
135
Sb.
Further evidence for the peak asignments in Fig. 3.6 is shown in Fig. 3.7. In Fig.
3.7 is shown a ? spectrum that was obtained by subtracting data acquired in the last 200
ms of a 1.0-s run from data obtained during the first 200 ms of the same acquisition. The
short half-life of 
135
Sn (T
1/2
 = 538(9) ms) makes it possible to eliminate peaks asociated
with the decay of 
135
Sb (T
1/2
 = 1.68(2) m) in the time-gated ? spectra. The remaining
peaks in Fig. 3.7 must have short half-lives, or otherwise would have been subtracted to
zero, similar to al of the peaks labeled with open circles in Fig. 3.6.
64
1
0
1
5
1
0
2
7
1
1
2
7
1
1
1
3
1
1
4
3
1
2
0
7
1000
3000
5000
7000
1000 1050 1100 1150 1200 1250
1
1
0
5
1
0
6
7
1
1
7
4
1
1
8
1
1
2
4
7
1
2
9
6
0
1000
2000
3000
4000
5000
1250 1300 1350 1400 1450 1500
1
2
6
9
1
2
7
9
1
4
4
3
1
3
7
2
1
4
5
6
1
3
3
3
1
4
5
2
1
3
8
0
1
3
8
7
1
6
4
9
0
200
400
600
800
1000
1500 1550 1600 1650 1700 1750
1
5
0
5
1
5
4
9
1
6
3
1
1
5
7
4
1
6
5
4
10
30
50
2000 2100 2200 2300 2400 2500
2
0
8
9
2
1
7
9
2
3
7
5
2
4
4
0
2
3
2
2
10
20
30
40
2500 2600 2700 2800 2900 3000
2
7
6
4
10
20
30
3000 3100 3200 3300 3400 3500
3
1
7
3
3
2
6
3
5
2
2
5
2
7
6
0
5
5
7
0
6
2
6
7
3
3
7
0
7
500 550 600 650 700 750
0
4000
8000
6
3
3
6
7
3
5
3
5
6
5
9
1
5
8
1
8
0 2
1
6
0
5000
10000
15000
20000
50 100 150 200 250
5
3
X
1
7
1
X
1
1
4
X
1
6
2
X 1
7
6
X
2
7
4
2
8
1
4
4
0
4
0
9
4
3
1
0
5000
10000
15000
20000
250 300 350 400 450 500
3
3
8
X
3
1
8
X
3
1
9
3
7
1
X
2
9
7
7
9
8
8
3
1
9
2
5
5000
10000
15000
750 800 850 900 950 1000
9
7
6
0
500
1000
1500
2000
1750 1800 1850 1900 1950 2000
1
9
4
3
1
8
0
7
1
8
5
5
1
8
3
7
1
7
5
6
Energy (keV)
C
o
u
n
t
s
8
9
2
2
3
7
0
Figure 3.6: A ? singles spectrum obtained by subtracting data taken with the laser off
from data taken with the laser on at A = 135. Peaks asociated with the ?dn-decay of
135
Sn are labeled with ?X?s, peaks corresponding to transitions in 
135
Te from the ?
-
 decay
of 
135
Sb are labeled with open circles, and peaks that correspond to transitions in 
134
Te are
labeled with squares.  Unasigned peaks are labeled in red.
2000
6000
10000
50 100 150 200 250
5
3
1
1
4
1
6
2
1
5
8
1
7
1
1
7
6
1
8
0
2
1
6
500
1000
1500
2000
500 550 600 650 700 750
5
3
3
6
0
5
6
2
6
6
3
3
6
7
3
7
0
7
7
3
3
2000
6000
10000
250 300 350 400 450 500
2
8
2
X318, 320
3
3
8
4
0
9
4
3
1
4
4
0
1000
3000
5000
750 800 850 900 950 1000
7
9
8
8
3
1
9
2
5
9
7
6
500
1500
2500
3500
1000 1050 1100 1150 1200 1250
1
0
1
5
1
0
2
7
1
1
0
5
1
1
1
3
1
1
4
3
1
2
0
7
1
1
7
4
500
1500
2500
1250 1300 1350 1400 1450 1500
1
2
9
4
1
3
3
3 1
3
8
7
1
3
7
2
1
4
5
6
1
4
5
2
200
600
1000
1500 1550 1600 1650 1700 1750
1
5
7
3
1
6
4
9
1
6
3
1
1
7
3
4
100
300
500
700
1750 1800 1850 1900 1950 2000
1
8
0
7 1
8
5
5
1
7
5
6
50
150
250
2000 2100 2200 2300 2400 2500
2
0
8
9
Energy (keV)
C
o
u
n
t
s
X
X
X
X
X
X
X
3
7
1
1
5
4
9
Figure 3.7: A ? singles spectrum obtained by subtracting laser-on data obtained during
the last 200 ms of a 1.0-s acquisition from data taken during the first 200 ms of the same
acquisition. As in Fig. 3.6, peaks that can be atributed to transitions in the ?dn-decay
daughter, 
134
Sb, are labeled with 'x's.
65
The observed transitions asigned to the ? decay of 
135
Sn into levels of 
135
Sb are
listed in Table 3.1. Their placements were acomplished by the use of ?-? coincidence
spectra, and wil be described in more detail in sec. 3.6.
Table 3.1: Data for ? Rays and Levels Observed in the ?-decay of 
135
Sn.
a
Uncertainty in ? energies is ? 0.5 keV. 
b
Intensities relative to 282-keV transition in 
135
Sb.
c
Unasigned ?
rays with no coincidence relationships.
Level (keV)
J
?
E
?
a
 (keV) I
?
b
Final Level 
(keV)
J
?
282
5/2
+
282 100
0 7/2
+
440(3/2
+
) 4404.1(2) 0 7/2
+
1580.6(3) 282 5/2
+
707 11/2
+
7074.5(2) 0 7/2
+
798(9/2
+
) 79817(1) 0 7/2
+
1014(7/2
+
) 101410.9(4) 0 7/2
+
73337(2) 282 5/2
+
2166.1(1) 798(9/2
+
)
1027(9/2
+
) 102712(1) 0 7/2
+
3200.6(2) 70711/2
+
1113(5/2
+
) 11131.9(4) 0 7/2
+
8312.5(3) 282 5/2
+
6730.6(1) 440(3/2
+
)
1207(7/2
+
) 120716.9(6) 0 7/2
+
92535(2) 282 5/2
+
4093.7(1) 798(9/2
+
)
1801.2(3) 1027(9/2
+
)
1333(9/2
+
) 13333.1(3) 0 7/2
+
6261.07(8) 70711/2
+
5351.5(2) 798(9/2
+
)
1387(7/2
+
) 13876.0(4) 0 7/2
+
11051.3(2) 282 5/2
+
3600.4(1) 1027(9/2
+
)
2740.6(1) 1113(5/2
+
)
1801.0(2) 1207(9/2
+
)
1456(7/2
+
) 145612.4(3) 0 7/2
+
11744.3(5) 282 5/2
+
4291.7(2) 1027(9/2
+
)
1597(11/2
+
,9/2
+
) 8901.6(3) 70711/2
+
7990.9(2) 798(9/2
+
)
66
Table 3.1 cont?
a
Uncertainty in ? energies is ? 0.5 keV. 
b
Intensities relative to 282-keV transition in 
135
Sb.
c
Unasigned ?
rays with no coincidence relationships.
3.6 Analysis of ??? Coincidence Matrices
Placing transitions in a logical level structure for 
135
Sb was possible by using
projections from ?-? matrices to establish orders of ? cascades that depopulate excited
states. The most intense ? ray following ?
?
 decay of 
135
Sn was the 282-keV transition
from the first excited state to the ground state. The spectrum of ? rays in coincidence with
the 282-keV transition in 
135
Sb is shown in Fig. 3.8. The 733-, 925-, 1105-, 1174-, 1452-,
and 1807-keV ? rays were identified in the first experiment [Sh02]. As the spectra gated
on these ? rays only showed a peak at 282 keV, these transitions were asigned to states
Level (keV)
J
?
E
?
a
 (keV) I
?
b
Final Level 
(keV)
J
?
1630 
(5/2
+
,7/2
+
)
1630 1.7(4)
0 7/2
+
243 0.7(2) 13877/2
+
1734(5/2
+
) 17340.6(1) 0 7/2
+
14524.1(3) 282 5/2
+
12942.1(3) 440(3/2
+
)
1831(5/2
+
,3/2
+
) 15490.43(5) 282 5/2
+
13910.7(2) 440(3/2
+
)
1855(7/2
+
) 18554.2(2) 0 7/2
+
15730.9(1) 282 5/2
+
8292.2(3) 1027(9/2
+
)
2038 17561.2(1) 282 5/2
+
2089(5/2
+
) 20891.84(6) 0 7/2
+
18074.8(4) 282 5/2
+
16491.1(1) 440(3/2
+
)
9761.1(3) 1113(5/2
+
)
6331.21(5) 1456(7/2
+
)
2170(9/2
+
,7/2
+
) 13721.0(3) 798(9/2
+
)
11432.0(2) 1027(9/2
+
)
2461(7/2
+
,5/2
+
) 24610.31(4) 0 7/2
+
21790.37(7) 282 5/2
+
2440
c
 0.3(2)
2764
c
 0.7(5)
3263
c
 0.5(2)
67
that directly populated the 282-keV level. The above ??coincidence relationships
established levels at 1014, 1387, 1456, 1734, and 2089 keV. The 1014 and 1207 levels
were further supported by the presence of ? rays that corresponded to ground state
transitions in the laser on spectra. Peaks at 180, 1573, and 1756 keV correspond to
transitions depopulating levels established from the first experiment at 1207, 1855, and
2089 keV, respectively. The 158-, 831-, and 976-keV lines were used to establish the
placement of additional levels at 440 and 1113 keV.
C
o
u
n
t
s
40
80
120
160
200
100 200 300 400 500
400
800
1200
700 750 800 850 900 950 1000
1
5
8
1
8
0
C
7
3
3
9
2
5
8
3
1
9
7
6
Energy (keV)
40
80
120
1000 1100 1200 1300 1400 1500
1
1
7
4
1
4
5
2
1
1
0
5
1
0
6
6
20
60
100
1500 1600 1700 1800 1900 2000
1
5
7
3
1
7
5
6
1
8
0
7
1
3
5
T
e
Figure 3.8: ?-? coincidence spectrum gated on the 282-keV ?-ray transition in 
135
Sb
following ?
?
 decay of 
135
Sn.
Placement of a level at 440 keV is not only supported by the 158-282 keV
coincidence, but also by the presence of a 440-keV peak in Fig. 3.6 and Fig. 3.7 in the
laser-off subtracted and the time-subtracted ? singles spectra, respectively. A gate on the
440-keV ? ray produces the coincidence spectrum shown in Fig. 3.9. The peaks at 1294
and 1649 keV in Fig. 3.9 are transitions that depopulate established levels at 1734 and
2089 keV. The peak at 673 keV in the 440-keV gated spectrum in Fig. 3.9, and the
presence of an 1113-keV ? ray in Fig. 3.6 and Fig. 3.7 would support the notion of an
1113-keV level suggested by the 282-831 keV coincidence relationship shown in Fig.
68
3.8. The 976-keV peak in Fig. 3.8 would then be likely to depopulate the 2089 keV level
to the new 1113-keV level.
Figure 3.9: ?-? coincidence spectra gated on the 440- and 707-keV ?-ray transitions in
135
Sb following ? decay of 
135
Sn.
Also shown in Fig. 3.9 is a gate on the 707-keV ? ray. The 626-keV peak suggests
a new level at 1333 keV. Further support for the placement of this level is shown in the
798-keV gated spectrum in Fig. 3.10. The 216- and 409-keV transitions depopulate
previously reported levels at 1015 and 1207 keV, respectively. The 535-keV peak in Fig.
3.10 provides further evidence for the 1333-keV level, as previously mentioned, and the
1372 keV line establishes the position of a new level at 2170 keV. The 2170 keV level is
supported by the presence of the 1027-1143 keV coincidence relationship shown in the
0
10
20
30
40
500 1000 1500 2000
1
3
5
C
s
6
7
3
1
2
9
4
1
3
9
1
1
6
4
9
1
3
5
C
s
440-keV Gate
0
10
20
30
40
50
600 800 1000 1200 1400 1600
6
2
6
8
9
0
1
5
0
5
707-keV Gate
Energy (keV)
C
o
u
n
t
s
69
1027-keV gated spectrum in Fig. 3.11. Peaks at 570 and 605 keV in Fig 3.10 can be
atributed to the ? decay of 
134
Cs and are part of a known 569-796-605 keV ? cascade.
100
200
300
100 200 300 400 500
2
1
6
4
0
9
20
40
60
80
100
500 600 700 800 900 1000
5
3
5
5
7
0
6
0
5
7
9
8
10
20
30
40
1000 1200 1400 1600 1800 2000
1
3
7
2
C
o
u
n
t
s
Energy (keV)
1
3
4
C
s
1
3
4
C
s
798-keV Gate
Figure 3.10: ?-? coincidence spectrum gated on the 798-keV ?-ray transitions in 
135
Sb
following ?
-
 decay of 
135
Sn.
0
20
40
60
80
100
200 400 600 800 1000
2
8
2
1
0
2
7
9
7
6
1
3
5
C
s
1
3
5
C
s
831-keV Gate
1
8
0
4
2
9
8
2
9
0
20
40
60
80
100
200 400 600 800 1000 1200
1
1
4
3
Energy (keV)
C
o
u
n
t
s
1027-keV Gate
Figure 3.11: ?-? coincidence spectrum gated on the 831- and 1027-keV ? ray transitions
in 
135
Sb following ?
-
 decay of 
135
Sn.
70
Also present in the 1027-keV gated spectrum in Fig. 3.11 are peaks at 180, 429,
and 829 keV.  The 180-keV peak would suggest that there are two consecutive 180-keV
transitions from the 1387-keV level, as there is no transition that depopulates the 1027
level to a state which feds the 282-keV level. The 429 keV peak connects to the
established 1456 keV level, and 829 keV ? ray is likely to depopulate the level at 1855
keV.  The gate on the 831-keV ? ray (with overlap of the 829-keV ? ray), also shown in
Fig. 3.11, shows peaks at 282, 976, and 1027 keV, which would be consistent with the
placement of both the 829- and 831-keV transitions.
Figure 3.12: ?-? coincidence spectra gated on the 733- and 925-keV ?-ray transitions in
135
Sb following ?
?
 decay of 
135
Sn.
5
10
15
20
500 1000 1500 2000
0
500
1000
1500
2000
100 200 300 400 500
2
8
2
20
40
60
80
100 140 180
1
8
0
2
8
2
200
600
1000
400 800 1200 1600 2000
Energy (keV)
C
o
u
n
t
s
0
733-keV gate
925-keV gate
0
20
40
400 800 1200 1600 2000
expanded in spectrum below
925-keV gate
71
The final ?-gated coincidence spectra are shown in Fig. 3.12. In this figure are
gates on the second and third most intense ? rays, the 733 and 925 keV transitions, also
observed by Korgul et al. [Ko01]. The gate on the 733-keV ? ray shows a coincidence
relationship only with the 282-keV ? ray, and would likely depopulate a level at 1015
keV. The gate on the 925-keV ? ray also shows only a coincidence with the 180- and
282-keV ? rays. As shown in the bottom spectrum in Fig. 3.12, no other peaks are present
in the 925-gated ? spectrum. The 925-180 coincidence provides further support for the
level at 1387 keV, and the presence of a 180-180 keV cascade from this level.
3.7 The 
135
Sb Level Scheme
Based on the data presented in Figs. 3.6-3.12, the decay scheme shown in
Fig. 3.13 was constructed for the ?-decay of 
135
Sn. The ground state of 
135
Sb is asigned a
spin and parity of 7/2
+
, which would be expected as there is only a single g
7/2 
proton
outside the Z=50 closed shel. The 282-keV first excited state was originaly asigned a
d
5/2 
single-particle configuration based on level systematics and the spacing of orbitals in
the Z=82 proton shel [Sh02]. This spin and parity asignment, as wel as the single-
particle nature of this state, was recently supported by Mach et al. [Ma04]. The lifetime
of this state was measured to be 6.0(7) ns. Though a 5/2
+
 ? 7/2
+
 transition has ?I = 1, a
long lifetime is expected for this M1 transition because of the ?l = 2 betwen the d
5/2
 and
g
7/2 
states. The long lifetime for the 282-keV transition supports the notion in [Sh02] that
this level has high single-particle character, and that the low energy is not a result of
collectivity or deformation.
72
(5/2
+
,
7/2
+
)
(5/2
+
)
(7/2
+
,9/2
+
)
(7/2
+
)
(3/2
+
,5/2
+
)
(5/2
+
)
(9/2
+
,11/2
+
)
(7/2
+
)
(7/2
+
)
(9/2
+
)
(7/2
+
)
(5/2
+
)
(9/2
+
)
(7/2
+
)
11/2
+
7/2
+
9/2
+
3/2
+
5/2
+
Sn
135
51
07/2
-
?
-
33 5.63
I
?
 %
1.21
<0.29
0.88
12.6
1.49
1.45
13.0
1.32
2.03
4.00
1.40
0.28
2.34
0.16
<0.07
0.70
0.26
log ft
6.51
6.21
6.55
7.20
6.28
7.32
6.77
7.01
>7.53
7.01
5.82
6.75
6.73
5.76
6.72
>8.22
7.28
6.541.58
0.40 7.17
0.58 7.02
Sb
135
52
0
282
707
798
440
1014
1027
1113
1207
1456
1734
1855
2038
2089
2461
1387
1333
2170
1831
1597
1630
7
9
8
 
1
7
(
1
)
7
0
7
 
4
.
5
(
2
)
1
5
8
 
0
.
6
(
3
)
 
4
4
0
 
4
.
2
(
2
)
5
3
5
 
1
.
5
(
2
)
 
6
2
6
 
1
.
0
7
(
8
)
1
3
3
3
 
3
.
1
(
3
)
1
8
0
 
1
.
2
(
3
)
4
0
9
 
3
.
7
(
1
)
9
2
5
 
3
5
(
2
)
1
2
0
7
 
1
6
.
9
(
6
)
6
7
3
 
0
.
6
(
1
)
8
3
1
 
2
.
5
(
3
)
1
1
1
3
 
1
.
9
(
3
)
3
2
0
 
0
.
6
(
2
)
1
0
2
7
 
1
2
(
1
)
2
1
6
 
6
.
1
(
1
)
7
3
2
 
3
7
(
2
)
3
6
0
 
0
.
4
(
1
)
2
8
2
 
1
0
0
1
1
0
5
 
1
.
3
(
2
)
1
3
8
7
 
6
.
0
(
4
)
1
6
3
0
 
1
.
7
(
4
)
7
9
9
 
0
.
9
(
2
)
8
9
0
 
1
.
6
(
3
)
4
2
9
 
1
.
7
(
2
)
1
1
7
4
 
4
.
3
(
5
)
1
4
5
6
 
1
2
.
4
(
3
)
1
1
4
3
 
2
.
0
(
2
)
2
1
7
9
 
0
.
3
7
(
7
)
1
3
7
2
 
1
.
0
(
3
)
2
4
6
3
 
0
.
3
1
(
4
)
6
3
3
 
1
.
2
1
(
5
)
9
7
6
 
1
.
1
(
3
)
1
6
4
9
 
1
.
1
(
1
)
1
8
0
7
 
4
.
8
(
4
)
2
0
8
9
 
1
.
8
4
(
6
)
1
7
5
6
 
1
.
2
(
1
)
8
2
9
 
2
.
2
(
3
)
1
5
7
3
 
0
.
9
(
1
)
1
8
5
5
 
4
.
2
(
2
)
1
3
9
1
 
0
.
7
(
2
)
1
5
4
9
 
0
.
4
3
(
5
)
1
2
9
4
 
2
.
1
(
3
)
1
4
5
2
 
4
.
1
(
3
)
1
7
3
4
 
0
.
6
(
1
)
1
0
1
4
 
1
0
.
9
(
4
)
2
7
4
 
0
.
6
(
1
)
1
8
0
 
1
.
0
(
2
)
2
4
3
 
0
.
7
(
2
)
Figure 3.13: Proposed ?-decay scheme of 
135
Sn, showing population of states in 
135
Sb.
The spins and parities of the other states shown in Fig. 3.13 are in parentheses, as
their asignments were infered using selection rules to determine ?
-
feding and ?-de-
excitation trends. The new level at 440 keV does not appear to be directly populated in ?
-
decay of 7/2
-
 
135
Sn, and depopulates to both the 7/2
+
 ground state and 5/2
+
 first excited
state. A tentative spin and parity asignment of 3/2
+
 is favored for this level as the
reduced transition rate ratio for the 158- and 440-keV transitions (I
158
/I
440
) should be
much smaler if both transitions were M1.
 The very weak E2 component for the 282-keV transition reported by Mach et al.
[Ma04], combined with the weak E2 branches that were observed in the depopulation of
73
levels in adjacent 
134
Sb, can be interpreted to indicate that, in general, E2 transitions in
134
Sb and 
135
Sb are not competitive with M1 transitions in the depopulation of excited
levels of 
135
Sb. Thus, the new level at 440 keV that depopulates to the first excited and
ground states. A tentative spin and parity asignment of 9/2
+
 for the new level at 798 keV
is consistent with that notion in that no depopulation branch has been observed to either
the 282-keV 5/2
+
 level nor the (3/2
+
) level at 440 keV.
For the levels above 1.0 MeV, tentative spin and parity asignments have been
made on the basis that al of the ? rays observed are M1 transitions. Thus, the levels at
1014, 1207, 1387, 1456, and 1855 keV that depopulate to lower energy 5/2
+
, 7/2
+
, and
9/2
+
 levels are al given tentative (7/2
+
) spin and parity asignments. The level at 1027
keV that feds the 11/2
+
 level and not the 5/2
+
 level is asigned a tentative J
?
 = 9/2
+
, as is
the 1333-keV level that depopulates to 7/2
+
, 9/2
+
, and 11/2
+
 states. Levels at 1597, 1831
2170, and 2461 keV that depopulate only to levels with two diferent spin and parity
asignments could have the same spins and parities that the daughter levels are given.
The growth and decay of known 
135
Sb decay ? rays, specificaly the 1127-keV ?
ray, were used to determine the ground-state beta branching for 
135
Sn decay. Using the
reported intensities for 
135
Sb decay [Ho89], the ?-branches for 
135
Sn decay are shown in
the decay scheme presented in Fig. 3.13. These log ft values are, of course, lower limits
as weak transitions populating these levels may not have been observed.  However, 
135
Sb
has only 3 particles outside of double-magic 
132
Sn and a neutron separation energy, S
n
, of
3.6 MeV.  Because the core excitation of 
132
Sn is ~4 MeV, there are only a limited
number of levels in 
135
Sb below that energy and hence, fewer higher-energy levels to be
74
populated and whose weak decay might have been mised. Log ft values for each level in
135
Sb populated via ?
-
 decay of 
135
Sn are listed in Table 3.2.
Table 3.2: Log ft values and I
?
 for levels populated via ?-decay of 
135
Sn.
3.8 Astrophysical Implications of Measured Decay Properties
With respect to rapid neutron-capture nucleosynthesis (the astrophysical r-
proces), ?-decay properties (T
1/2
 and P
n
 values) and nuclear mases (in particular S
n
values) of neutron-rich Sn isotopes heavier than double-magic 
132
Sn are the most
important nuclear-physics quantities. Under typical r-proces conditions, they wil be the
Level (keV)
J
?
log ft
a
I
?
%
b
0 7/2
+
5.63 3
282 5/2
+
7.01 1.21
40 (3/2
+
) >8.2 <0.07
707 11/2
+
>7.53 <0.29
798 (9/2
+
) 7.01 0.8
1014 (7/2
+
) 5.82 12.6
1027 (9/2
+
) 6.75 1.49
113 (5/2
+
) 6.73 1.45
1207 (7/2
+
) 5.76 13
133 (9/2
+
) 6.72 1.32
1387 (7/2
+
) 6.51 2.03
1456 (7/2
+
) 6.21 4
1597 (11/2
+
,9/2
+
) 7.02 0.58
1630 7.17 0.4
1734 (5/2
+
) 6.54 1.58
1831 (5/2
+
,3/2
+
) 7.28 0.26
185 (7/2
+
) 6.5 1.4
2038 7.2 0.28
2089 (5/2
+
) 6.28 2.34
2170 (9/2
+
,7/2
+
) 6.7 0.7
2461 (7/2
+
,5/2
+
) 7.32 0.16
75
clasical 'waiting-point' nuclei just beyond the major A~130 solar-system r-abundance
peak (N
r
,
?
; se, e.g. [Kr01,Kr00,Kr88]). Odd-neutron Sn isotopes (with 'low' S
n
 values)
wil only build up smal progenitor abundances, since they wil either photodisintegrate
back to an (A-1) even-even isotope or capture another neutron to become an (A+1) even-
even Sn nucleus. Therefore, these even-even isotopes (here mainly 
136
Sn and 
138
Sn) wil
be the clasical 'r-proces nuclei' carying the main r-abundances in the Sn isotopic
chain. And only for these even-neutron isotopes is the ?-decay half-life of importance in
the waiting-point concept, which implies the historical N
r
,
?
(Z) X ?
?
(Z) 
? const.
correlation.
In Fig. 3.14 is shown the results of a simple static calculation of the relative r-
abundances of neutron-rich Sn isotopes as a function of neutron density at freze-out
conditions (T=1.35 ? 10
9
 K). As can be sen from this figure, at modest neutron densities
of n
n
 ? 1 ? 10
23
 ? 3 ? 10
24
 n/cm
3
 representative for the build-up of r-abundances in the A
? 130 peak region, 
136
Sn wil be the main waiting-point nucleus with relative abundances
betwen 35 and 90% of the total Sn isotopic chain. Under these conditions, the odd-
neutron neighbors 
135
Sn and 
137
Sn only collect roughly two orders of magnitude les r-
progenitor yields (maximal 0.5%). For higher neutron densities in the range n
n
 ? 3 ? 10
24
? 1 ? 10
26
 n/cm
3
 where the r-mater flow has already pased the A ? 130 'bottle neck'' to
form the rare-earth region and to start the climb up the staircase at the N=126 shel
closure, 
138
Sn becomes the main waiting point isotope with abundances betwen about 50
and 90% of the total yield.
76
0.1
1
10
100
10
21
10
22
10
23
10
24
10
25
10
26
10
27
10
28
132
Sn
134
Sn
136
Sn
138
Sn
140
Sn
R
e
l
a
t
i
v
e
 
A
b
u
n
d
a
n
ce
 
(
%
)
Neutron Density (1/cm
3
)
Figure 3.14: Relative isotopic r-proces abundances of Sn isotopes under freze-out
conditions (T = 1.35 ? 10
9
 K) as a function of neutron density.
The experimental T
1/2 
and P
n
 values can now be incorporated into dynamic (time-
dependent) multi-component r-proces calculations to replace earlier theoretical data. A
first such application (se, e.g. Fig. 3 in [Kr01]) does improve the r-abundance fit in the
A ? 135 region above the A?130 N
r
,
?
 peak; however, the stil existing odd-even
deviations from the N
r
,
?
 values sem to indicate an earlier onset of collectivity in very
neutron-rich Sn and Te isotopes than predicted by common mas models. This would
result in slightly higher S
n
 values in this region, thus shifting the r-proces path further
away from ?-stability involving progenitor isotopes with shorter half-lives and
consequently lower final abundances.
3.9 Anomalous Behavior of the 282-keV Level
The most important new nuclear physics information concerns the low-energy of
the 282-keV first excited state of 
135
Sb, along with the redistribution of the ?-decay
77
strength. The 5/2
+
 spin and parity asignments are based on systematics and the results
from the high-spin states observed in fision-fragment ?-ray spectroscopy [Bh98].
Positive parity is almost certainly indicated, as the only negative parity level identified in
133
Sb is the h
11/2
 level at 2763 keV [Sa99]. With a log ft value of 7.01 (se Table 3.2), the
decay is either alowed or first forbidden, restricting the state to spin values of 5/2
+
, 7/2
+
,
or 9/2
+
. If this state were 9/2
+
, it certainly should have been observed strongly in the
fision-fragment experiment [Bh98]. If this state were to be a 7/2
+
 level, it would pose the
strange situation of two low-energy 7/2
+
 levels in a single nucleus, a situation rarely
encountered.
The sharply lowered position of the first excited 5/2
+
 level was unexpected. The
trend of the monopole increases for the d
5/2
 orbital relative to the g
7/2
 ground state as
N=82 is approached as shown in Fig. 3.15. Hence, the lowest 5/2
+
 level might have been
expected to lie near the 700-keV energy of the first 2
+
 energy of the 
134
Sn core and have a
dominant g
7/2 
? 2
+
 configuration.
37
1427
0
1644
160
000000
332
1890
491
645
798
2793
963
282
Sb
121
51 70
Sb
133
51 82
Sb
131
51 80
Sb
129
51 78
Sb
127
51 76
Sb
125
51 74
Sb
123
51 72
Sb
135
51 84
d5/2
d5/2
d5/2
d5/2
d5/2
d5/2
d5/2
d5/2
g7/2g7/2g7/2g7/2
g7/2
g7/2 g7/2g7/2
h11/2
h11/2
h11/2
h11/2
Figure 3.15: Level systematics of the neutron-rich odd-A Sb isotopes.
78
One method for highlighting the unusual behavior of this 5/2
+
 level is to make
comparisons of the energy gap for the lowest 5/2
+
 and 7/2
+
 orbitals in isotones of higher
Z odd-proton nuclides. The energy diference betwen the lowest 5/2
+
 level and lowest
7/2
+
 level is plotted in Fig. 3.16 for the 
51
Sb, 
53
I, 
55
Cs, and 
57
La isotones with 72?N?84.
Except for the N=84 isotones, a sharp drop in this energy diference occurs as Z increases
from 51 to 53, followed by a more gentle slope. This change, particularly for the 
53
I and
55
Cs nuclides is caused by the depresion of the first 5/2
+
 level through an admixture with
an adjacent 5/2
+
 level arising from the (g
7/2
)
3
5/2+
 configuration. The presence and
character of such states was described by Par [Pa73], Heyde [He94]; and has also been
discussed by Jackson et al. [Ja75], who noted that in closed-shel nuclei this cluster state
typicaly lies at about half of the energy of the 2
+
 level in the adjacent even-even core
nuclide.
0
500
1000
Sb I Cs La
N=72 Isotones
N=74 Isotones
N=76 Isotones
N=78 Isotones
N=80 Isotones
N=82 Isotones
N=84 Isotones
Element
E
5
/
2
+
1
 
-
 
E
7
/
2
+
1
 
(
ke
V
)
Figure 3.16: Variation of the energy diference betwen the lowest 5/2
+
 and 7/2
+
 levels
in the N = 72-84 even-odd Sb, I, Cs, and La isotones. Lines are drawn to guide the eye.
79
For the N = 78 and 80 isotones, with more collective cores and lower 2
+
energies,
a similar pair of 5/2
+
 levels are observed, but at significantly lower energies.  However, in
both cases, a linear extrapolation as the Fermi level rises from Z = 57 to 55 to 53 to the Z
= 51 Sb nuclides would suggest a lower position for the first 5/2
+
 level than is actualy
observed.  Stated another way, an increase in energy of the lowest 5/2
+
 level in going
from the Z = 53 odd-mas iodine nuclides to the Z = 51 Sb nuclides is to be expected
because of the inability of the single-proton Sb nuclides to form the 3-proton cluster
states present in the I and Cs nuclides.
Keping in mind the important role of the cluster states in depresing the lowest
5/2
+
 level in the odd-mas 
53
I nuclides, it is now possible to interpret the smal variation
in energy of the lowest 5/2
+
 level in the N=84 isotones. The absence of the increase in
energy in going from 
137
I to 
135
Sb is interpreted to arise because the majority of the d
5/2
strength in 
135
Sb (and also in 
137
I) is already wel below the energy of the expected
(g
7/2
)
3
5/2+ 
state.
0
200
400
600
800
1000
1200
120 122 124 126 128 130
Pb 2
+
 levels
Bi 7/2
-
 levels
Neutron Number
E
n
e
r
g
y 
(
ke
V
)
1
1
132
Figure 3.17: Comparison of the first 7/2
-
 level energies of Bi nuclei in the region of
double-magic 
208
Pb with the positions of the 2
+
 levels in their corresponding Pb cores.
80
In Fig. 3.17, the positions of the lowest lying h
9/2
 ground states and f
7/2
 low-energy levels
of the odd-mas Bi nuclides and the positions of the first 2
+
 levels in the neighboring Pb
core in the region of the double-magic nuclide 
208
Pb are shown. In these nuclides, the
separation betwen the h
9/2
 ground states and the lower-spin f
7/2
 first excited states is
observed to be nearly constant below the N = 126 shel closure, but then decreases
inenergy as neutrons are added beyond N = 126 in a fashion quite similar to the
observations in the Sb nuclides.
Earlier, we suggested that this low-lying 5/2
+
 state arises from a strong admixture
of the d
5/2
 single-particle configuration; and that such an admixture would require that the
unmixed energy of this single d
5/2
 proton level must lie at a much lower energy than the
963-keV energy observed in 
133
Sb [Sh01]. Support for such an idea has been presented in
a recent paper by Hamamoto et al. [Ha01]. They showed that an increase in the Woods-
Saxon surface difusenes parameter would result in a lowering of low-spin single-
particle shel model levels relative to higher-spin levels.
3.10 Shel-Model Calculations for 
135
Sb
To further investigate the structure of the new low-energy states in 
135
Sb,
calculations were caried out in the proton-neutron formalism with the shel model code
OXBASH [Et85]. The model space consists of a 
132
Sn closed core with (Z-50) valence
protons in the (0g
7/2
, d
5/2
, 1d
3/2
, 2s
1/2
, 0h
11/2
) orbitals and (N-82) valence neutrons in the
(1f
7/2
, 2p
3/2
, 2p
1/2
, 0h
9/2
, 1f
5/2
, 0i
13/2
) orbitals. The single particle energies used in this
calculation were taken from a more recent mas table [Au03]. The proton single-particle
energies of ?9.66, -9.00, -7.22, and ?6.87 MeV were used for the 0g
7/2
, 1d
5/2
, 1d
3/2
, and
81
0h
11/2
 orbitals, respectively. The observed levels of 
133
Sn provided the single-particle
neutron energies of ?0.89, -2.46, -0.45, -1.60, and ?0.80 MeV for the 0h
9/2
, 1f
7/2
, 1f
5/2
,
2p
3/2
, and 2p
1/2
 orbitals, respectively.
The residual two-body interaction was obtained by starting with a G matrix
derived from a more recent CD-Bonn [Hj04] nucleon-nucleon interaction, with 
132
Sn as a
closed core. An harmonic oscilator basis was employed for the single-particle wave
functions with an oscilator energy h? = 7.87 MeV. The G-matrix elements in turn form
the starting point for a perturbative derivation of a shel-model efective interaction. In
this work we derive the efective interaction for the above shel-model space by the Q-
box method which includes al so-caled non-folded diagrams through third-order in the
interaction G and sums up the folded diagrams to infinite order [Hj95,Hj96]. This type of
Hamiltonian has been used to describe spectra of tin isotopes from mas number A=102
to A=130 [Ho98] and the N=82 isotones up to A=146 [Ho97] with good agrement with
data.
Thre calculations were performed using the CD-Bonn interaction. The first
calculation was performed without shifting any of the above mentioned single particle
energies. As previously reported in [Sh02], a beter fit to the observed levels could be
obtained by lowering the 1d
5/2
 proton single-particle energy (SPE) by 300 keV [Sh02].
The second calculation was performed with this lowered d
5/2 
SPE. The third calculation
was performed in which the 1d
3/2
 proton single-particle energy was also shifted by 300
keV so that the spin-obit spliting of the d
5/2
-d
3/2 
pair would not be afected. Both of the
shifts in the single-particle energies support the notion of the presence of a neutron skin
82
for 
135
Sb [Sh02]. The results of these calculations for the low-spin levels are shown in
Fig. 3.18, and are labeled (a), (b), and (c) respectively.
Given the succes of the Kuo-Herling interaction used to describe the levels in
134
Sb by Shergur et al. [Sh04], an atempt to provide a beter fit for the structure of 
135
Sb
using the same TBME was atempted. In these calculations, the CD-Bonn proton-neutron
interaction was replaced using the Kuo-Herling TBME, while stil using the CD-Bonn
neutron-neutron TBME. The results of these calculations are shown in Fig. 3.18, and are
labeled (d). In these calculations, both the 1d
3/2 
and 1d
5/2
 proton single-particle energies
were lowered by 300 keV.
7/2
+
5/2
+
3/2
+
11/2
+
9/2
+
exp
11/2
+
9/2
+
1/2
+
5/2
+
3/2
+
7/2
+
(a)
(b)
11/2
+
9/2
+
1/2
+
5/2
+
3/2
+
7/2
+
7/2
+
5/2
+
3/2
+
11/2
+
9/2
+
1/2
+
(c)
7/2
+
5/2
+
3/2
+
11/2
+
9/2
+
1/2
+
(d)
250
500
750
1000
E
n
e
r
g
y
 
(
k
e
V
)
Figure 3.18: Comparison of the experimental levels for 
135
Sb with shel-model
calculations using the CD Bonn interaction (a) (same as in [Sh02]). In (b), the same
interaction was used with a d
5/2
 single-particle energy lowered by 300 keV, and in (c),
both the d
5/2
 and d
3/2
 single particle energies were lowered by 300 keV. In (d) the Kuo-
Herling interaction replaced the p-n CD Bonn interaction, and both the d
5/2 
and d
3/2 
single-
particle energies were reduced by 300 keV.
Shown in Fig. 3.18 are the experimentaly observed levels of 
135
Sb up to 1.0 MeV
and four calculations. Below 1.0 MeV, positions are now established for five of the six
levels that are predicted using the CD-Bonn interaction in 
135
Sb as shown in Fig 3.18.
83
Population of the 1/2
+
 level would require indirect feding via an E2 transition from a
5/2
+
 state. This type of transition is not likely as M1 transitions are the dominant type of
de-excitation for the levels of 
135
Sb; therefore it is not unexpected that there is no
evidence in the data for the 1/2
+
 level. Use of the Kuo-Herling proton-neutron interaction
in column (d) of Table 3.3 predicts the presence of additional low-lying 7/2
+
 and 5/2
+
levels below 1.0 MeV of which the 5/2
2
+
 is not observed experimentaly; although, the
calculated values for the 7/2
2
+
 state in Table 3.3 agre quite wel with the experimental
level at 1014 keV. The low-lying 5/2
2
+
 level predicted in the Kuo-Herling interaction
might reflect that the interaction strength is too strong in this calculation. Another
discrepancy betwen the CD Bonn and Kuo-Herling predictions below 1.0 MeV is the
relative positions of the 1/2
+
 and 3/2
+
 states with the other levels. Both the 1/2
+
 and 3/2
+
levels are pushed up relative to the 5/2
+
 state. The best agrement below 1.0 MeV is
observed in Fig. 3.18(b). An additional lowering of the d
3/2 
proton single-particle energy
by 300 keV in (c) had very litle efect on the placement of the low-energy levels,
excluding an unnecesary slight shift in the 3/2
+
 state by ~40 keV. Also of interest are the
levels calculated betwen 1.0 and 2.0 MeV. Al four calculations predict ~fiften levels
that could be directly fed by ? decay (se Table 3.3). The exception again is the
calculation shown in column (d) of Table 3.3. Use of the Kuo-Herling interaction results
in a higher level-density betwen 1.5 and 2.0 MeV than does use of the CD Bonn
interaction. Though the spins and parities of the experimental states betwen 1.0 and 2.0
MeV have not been directly measured, eleven levels that have a tentative J
?
 = 5/2
+
, 7/2
+
,
or 9/2
+
, are observed in this energy range, al which show significant ? feding. Of note is
that population of five of the six predicted 5/2
+
 levels is observed, despite the smal ? 
84
Table 3.3: Comparison of Shel Model Calculations with Experimental Levels in 
135
Sb.
a
a
Calculated values listed in column (a) and (b) that difer by ~100 keV are highlighted in gren, while those
that difer ~200 keV are highlighted in red.
feding to the 282-keV state, which is only 1.21%. It was not unexpected that thre to
four of the 3/2
+
 states were not identified, as it is unlikely any of these levels were fed
directly from ?
-
 decay. As for the positions of the high-spin 9/2
+
 and 11/2
+
 states, the use
of the Kuo-Herling interaction instead of the CD-Bonn interaction afects the positions of
the 9/2
+
 and 11/2
+
 states very litle. This would be expected as the configurations of these
J
? ExpCD Bon (a)CD Bon (b)CD Bon (c)KH (d)
1/2
+
0.63 0.502 0.527 0.735
1/2
+
1.48 1.383 1.37 1.087
3/2
+
0.4 0.438 0.365 0.408 0.57
3/2
+
1.36 1.307 1.35 1.093
3/2
+
1.47 1.371 1.372 1.329
3/2
+
1.831 1.867 1.837 1.837 1.69
3/2
+
1.941 1.95 1.849
5/2
+
0.282 0.527 0.306 0.316 0.36
5/2
+
1.13 1.212 1.195 1.18 0.831
5/2
+
1.249 1.24 1.242 1.198
5/2
+
1.468 1.481 1.478 1.281
5/2
+
1.734 1.85 1.68 1.687 1.419
5/2
+
1.831 1.943 1.783 1.805 1.71
5/2
+
 2.089 
7/2
+
0 0 0 0 0
7/2
+
1.014 1.135 1.137 1.134 0.982
7/2
+
1.207 1.246 1.257 1.254 1.158
7/2
+
1.46 1.571 1.361 1.361 1.191
7/2
+
1.592 1.502 1.537 1.342
7/2
+
1.647 1.58 1.585 1.513
7/2
+
1.85 1.963 1.836 1.835 1.673
9/2
+
0.798 0.947 0.85 0.869 0.876
9/2
+
1.027 1.65 1.043 1.039 1.05
9/2
+
1.383 1.495 1.501 1.494 1.218
9/2
+
1.6 1.784 1.78 1.783 1.647
9/2
+
2.17 1.92 1.913 1.914 1.797
11/2
+
0.707 0.62 0.64 0.66 0.729
11/2
+
1.6 1.643 1.625 1.621 1.459
11/2
+
1.65 1.62 1.658 1.563
11/2
+
1.813 1.782 1.79 1.61
85
levels can be described as g
7/2 
? 2
+
 core-coupled states. Therefore, lowering the positions
of the d
5/2 
and d
3/2 
single-particle energies should have litle efect on the positions of
these states.
Overal, agrement with the experimentaly observed levels in 
135
Sb is much
beter using only the CD Bonn interaction while lowering only the d
5/2 
single particle
energy, as shown in Fig. 3.18(b) and Table 3.3. As noted in the introduction, after only
one level had been identified in earlier studies below 1.0 MeV [Sh01,Sh02,Ko01] in
135
Sb, there were questions about the efect of lowering the d
5/2 
and d
3/2 
levels on the fits
to the other low-energy levels. As can be sen, the levels in column (b) provide what
must be termed an excelent fit for the level structure of 
135
Sb up to 2.0 MeV. This high-
quality fit lends support to the idea that neutron-skin efects are important for the
calculation of level structures in this mas region. These calculations can be compared
with a new calculation reported by Sarkar and Sarkar who found the first 5/2
+
 level of
135
Sb at either 618 or 690 keV using unshifted single-particle energies [Sa04].
Atempts to improve the quality of fit levels in 
135
Sb using the Kuo-Herling
proton-neutron interaction have not succeded. The scaling used for this interaction
asumed by Chou and Warburton [Ch92] is apparently not needed, perhaps because the
higher overlap of the proton-neutron wavefunctions in 
132
Sn compared to 
208
Pb that
follows from the oscilator model is canceled by the efects of the neutron skin in 
132
Sn.
The more recent renormalized G matrix obtained by Hjorth-Jensen from the CD-Bonn
potential that was used in Fig. 3.18(a,b,c)  and columns (a,b,c) in Table 3.3 has bare G
matrix elements that are similar to Kuo-Herling but has higher-order renormalizations
that in total are diferent from the first-order corrections used for the Kuo-Herling
86
calculations. Although one should expect that going to higher order is beter, there appear
to be dependencies on the underlying single-particle spectrum that need further
investigation [Ho04]. The CD-Bonn renormalized G matrix gives beter agrement for
the T=1 spectrum of 
132
Sn than obtained with Kuo-Herling [Sh04]. So a consistent
Hamiltonian for this mas region has yet to be found.
3.11. Sumary and Outlook
New experimental data for the decay of mas separated 
135
Sn have been taken at
CERN/ISOLDE using a neutron converter to dramaticaly lower isobaric Cs
contamination. From these time dependent ?-ray singles and ?-? coincidence spectra,
positions for five of the six levels calculated by the CD Bonn potential for 
135
Sb below
1.0 MeV have been established and eleven of the fiften levels predicted to be fed via ?
decay betwen 1.0 and 2.0 MeV have been identified. Tentative spin and parity
asignments have been proposed for al but two levels asuming that M1 transitions
dominate the de-excitation of the levels in 
135
Sb. Of new importance was the
identification of the 3/2
+
 and 9/2
+
 levels at 440 and 798 keV, respectively, which alowed
for more stringent testing of the single particle energies and TBME used in this mas
region.
Comparison of the predictions betwen the CD Bonn and Kuo-Herling
interactions showed that the observed levels of 
135
Sb were best reproduced by using the
CD Bonn proton-neutron TBME instead of the Kuo-Herling proton-neutron TBME, and
by lowering the d
5/2 
single particle energy by 300 keV. As lowering the d
3/2 
single particle
energy by 300 keV resulted in a poorer fit to the data, than either the d
3/2 
energy is higher
87
then expected or the spin-orbit spliting betwen the d
5/2
-d
3/2 
is wider then expected
outside 
132
Sn.
88
4 The Structure of 
111
Sb
4.1 Overview
New low-spin levels in 
111
Sb have been identified following the ?
+
/EC decay of
proton-rich 
111
Te. 
111
Te was produced in the 
58
Ni(
56
Fe,2pn)
111
Te reaction and separated
using the Fragment Mas analyzer at Argonne National Laboratory. ?-ray singles and ???
coincidence spectra were collected as a function of time. Eleven new levels in 
111
Sb were
identified, including levels at 487 and 881 keV that have been tentatively asigned spins
and parities of 1/2
+
 and 3/2
+
, respectively. Shel-model calculations were performed in
which the single-particle d
3/2 
and s
1/2 
basis levels have been adjusted to fit the observed
positions of the low-energy 1/2
+
 and 3/2
+
 levels in 
109
Sb and 
111
Sb. Good agrement for
the known yrast 1/2
+
, 3/2
+
, 5/2
+
, 7/2
+
, and 9/2
+
 levels in 
105,107,109,111
Sb was obtained.
4.2 Scientific Motivation
The systematic behavior of the low-energy levels of the odd-mas Sb nuclides
with 54?N?82 reflect both the monopole shifts in single proton energies and the
interaction of the single proton with the underlying levels in the even-even core Sn
nuclides  [Sh79,Bu95,Lo98,Lob98]. The low-energy levels of the rather wel-studied
odd-mas Sb nuclides with 64?N?80 are shown in Fig. 4.1. The dominant feature of
these levels is the monopole inversion of the d
5/2 
and g
7/2
 levels that takes place around
121
Sb. In spite of that steady change, it can be sen that the higher-spin 9/2
+
 and 11/2
+
members of the particle-phonon multiplet are relatively insensitive to neutron number,
especialy near N = 82 and remain in close proximity to the energy of the 2
+
 level in the
89
adjacent even-even Sn core. This behavior is in sharp contrast to the low-spin 3/2
+
member of that multiplet that first fals to a low at N = 70, and then rises again to a higher
energy at N = 64. The low-energy 1/2
+
 level that arises from coupling the d
5/2 
proton to
the even-even Sn core is also sen to fal to a low at N = 70, and then rise toward N = 64.
The behavior of both the lowest 1/2
+
 and 3/2
+
 levels provides support for the notion of a
rather strong subshel efect for N = 64, at least for Z = 50 and adjacent Sb and In
nuclides, and also demonstrates a sensitivity to the microscopic structure of the excited
states of the even-even Sn core.
0
200
400
600
800
1000
1200
1400
7/2
+
7/2
+
7/2
+
7/2
+
7/2
+
7/2
+
7/2
+
7/2
+
7/2
+
5/2
+
5/2
+
5/2
+
5/2
+
5/2
+
5/2
+
5/2
+
5/2
+
5/2
+
3/2
+
3/2
+
3/2
+
3/2
+
3/2
+
3/2
+
3/2
+
3/2
+
3/2
+
1/2
+
1/2
+
1/2
+
1/2
+
1/2
+
1/2
+
11/2
+
11/2
+
11/2
+
9/2
+
9/2
+
9/2
+
9/2
+
9/2
+
11/2
+
Sb Sb Sb
Sb
121
Sb SbSbSb Sb
115 117 123119 129127125 131
E
n
e
r
g
y
 
(
k
e
V
)
9/2
+
9/2
+
9/2
+
11/2
+
9/2
+
11/2
+
Figure 4.1: Low-spin systematics for levels below 1.5 MeV for the odd-A Sb isotopes
betwen A=115 and A=131. The position of the 2
1
+
 level in the adjacent even-even Sn
core is marked by an "x".
In contrast to the structures of those neutron-rich Sb nuclides for which
considerable data are available, scant data are known for the low-spin levels of the
proton-rich Sb nuclides, especialy at lower spin. In the ?
+
/EC decay of 
109
Te reported by
Resler et al. [Re02], six new levels below 2.0 MeV have been identified in 
109
Sb. These
levels were predicted with reasonable agrement by two separate shel model calculations
[Re02,Di01], including the positions of the surprisingly low 1/2
+
 and 3/2
+
 states at 402
90
and 752 keV, respectively. Although there are significant data for the high-spin levels of
105,107,109,111
Sb, no data are available for the low-spin levels of 
111
Sb. Hence, this
experiment was succesful in identifying new low-spin levels of 
111
Sb that are populated
in the ?
+
/EC decay of 
111
Te.
4.3 Experimental Details
The experiment was performed using the Argonne Tandem Linear Acelerator
System (ATLAS) coupled to the Fragment Mas Analyzer (FMA) at Argonne National
Laboratory. 
111
Te nuclei were produced using the 
58
Ni(
56
Fe,2pn)
111
Te fusion-evaporation
reaction with a beam energy of 225-MeV and a target thicknes of 823 ?g/cm
2
. Reaction
products were separated in the FMA on the basis of their mas to charge (A/Q) ratio at
charge state 24. Following mas separation, the recoils were implanted in the tape of a
moving tape collector (MTC) that was moved periodicaly to a Pb-shielded counting
station. As the half-life of 
111
Te was previously reported to be 19 s [Ha72], count and
collection times were varied from 40 s to maximize coincidence events, to as long as 150
s to permit identification of ? rays belonging to the decay of daughter and granddaughter
nuclides and to the decay of nuclides that are collected on the tape owing to similar A/Q
values.
Two large HPGe detectors (45% and 65%) and two smal Ge detectors (~25%)
were used to detect the ? rays coming from the reaction products that were deposited on
the tape. In addition to the Ge detectors, two plastic scintilators were used to veto 0
o
 ???
coincidences in the same detector, and to obtain 180
o
 ??? coincidences. Analyses of ?
91
singles, ??? coincidences, and ?-time data were used to identify transitions in the
corresponding 
111
Sb daughter nucleus.
4.4 Identification of the ? Rays Asociated with the ?
+
/EC Decay of 
111
Te
Known contributions to the ?-singles and ??? coincidence spectra arose from the
decay of 
111
Sb (T
1/2
 = 1.25 m), 
111
Sn (T
1/2
 = 35 m), 
110
Sb (T
1/2
 = 24 s) and 
110
In (T
1/2
 =
1.15 h) [Bl03,De00]. A ? spectrum resulting from the subtraction of a ? spectrum taken
betwen t = 75 to t = 150 s from the first 30 s of the counting period is shown in Fig. 4.2.
511
8
5
1
2
0
5 2
4
5
2
9
8
3
2
0
3
5
1
6
0
9
6
3
3
6
7
8
100 300 500 700 900
881
1
7
1
2
-2000
-1000
0
1000
50
100
150
200
1500 1600 1700 1800 1900 2000
154
4
8
7
Energy (keV)
C
o
u
n
t
s
1
7
3
5
200
400
600
800
1000
50
100
150
200
8
3
1
*
1000 1100 1200 1300 1400 1500
9
9
9
1
0
3
1
1
1
4
7
1
2
6
9
1
3
9
2
2100 2200 2300 2400 2500
2
1
2
0
2
3
5
7
1
3
9
8
*
2
1
6
1
Unsubtracted Peak 
*
111
Te ?
+
 decay
111
Sb ?
+
 decay
111
Sn ?
+
 decay
110
Sb ?
+
 decay
1
5
7
6
Figure 4.2: Time-subtracted spectrum showing 
111
Sb transitions from the decay of 
111
Te.
The ? energy spectrum shown is the residual spectrum obtained by subtraction of the
spectrum taken during the first 30 s of a 150 s acquisition from the spectrum taken during
the last 75 s of this counting period. Peaks present in the spectrum arise from the decay of
nuclides with half-lives below ~60 s, while dips arise from the decays of nuclides that
grow in during the counting period.
92
The time-gated spectra used in the subtraction were chosen to eliminate the contribution
of transitions asociated with the decay of 1.25 min 
111
Sb. In Fig. 4.2, it can be observed
that the long-lived transitions at 154 and 489 keV from 
111
Sb decay subtracted roughly to
background, while peaks asociated with the growth of the decay daughters appear as
dips. The remaining peaks in the diference spectrum are atributed to either 
111
Te or
110
Sb decay. As the decay lines of 
110
Sb are wel established, peaks in Fig. 4.2 not
asociated with 
110
Sb decay were asigned to the decay of 
111
Te. There were two peaks
whose energies were ambiguous at 999 and 1031 keV. These are both shown with an
uncertainty of 1 keV due to the strong overlap of the 997- and 1032- keV transitions,
respectively, from the decay of 
111
Sb into 
111
Sn. The energies, intensities, and placements
in the 
111
Sb level scheme of the 
111
Te decay lines from this study are summarized in
Table 4.1.
Thre peaks at 487, 851, and 881 keV stand out below 1.0 MeV in Fig. 4.2. The
851-keV transition was previously identified as part of the 
111
Sb yrast cascade by
LaFosse et al. [La94] among the ? rays observed following a heavy-ion reaction. As the
851-keV transition is the most intense peak in Fig. 4.2, the remaining ? rays in the
spectrum were asigned to 
111
Sb with confidence. The gated spectra for the 851- and 881-
keV transitions are shown in Fig. 4.3. The 851-keV gate in Fig. 4.3(a) shows the
coincidence at 547 keV expected on the basis of the data reported by LaFosse et al.
[La94]. Additional peaks are observed at 727, 1031, 1176, 1269, 1310, 1506, and 1762
keV. As placing gates on these peaks show only coincidences with the 851-keV ? ray,
these transitions are likely to depopulate states that fed the 851-keV level directly.
93
Table 4.1: Gama Intensities in 
111
Sb Following 
111
Te ?
+
-Decay.
a
 Uncertainty in E
?
 is ?0.5 keV. 
b
 I
?
 relative to 851-keV transition in 
111
Sb.
Hence, these coincidences, along with ground-state crossover transitions provide support
for the placement of new levels at 1576, 1879, 2027, 2120, 2161, 2397, and 2613 keV.
Level (keV)
J
?
E
?
a
 (keV) I
?
b
Final Level 
(keV)
J
?
487
(1/2
+
)
48745(7) 0
5/2
+
851
7/2
+
851100(2) 0
5/2
+
881
(3/2
+
)
88192(3) 0
5/2
+
1147
9/2
+
296 2(1) 851
7/2
+
114730(2) 0
5/2
+
1268
(7/2
+
)
126825(15) 0
5/2
+
1398
9/2
+
5477.4(1) 851
7/2
+
139816(5) 0
5/2
+
1576 6963.6(4) 881
(3/2
+
)
72714(2) 851
7/2
+
157621(3) 0
5/2
+
1712 831 6(2) 881
(3/2
+
)
171213(3) 0
5/2
+
1879 999(1) 22(5) 881
(3/2
+
)
1031(1) 22(3) 851
7/2
+
 
139225(5) 487
(1/2
+
)
18796.9(4) 0
5/2
+
2027 117619(4) 851
7/2
+
20278.5(9) 0
5/2
+
2120 126930(15) 851
7/2
+
212017(3) 0
5/2
+
2161 13104(1) 851
7/2
+
216115(2) 0
5/2
+
2357 147710(1) 881
(3/2
+
)
150618.1(5) 851
7/2
+
235718(2) 0
5/2
+
2613 176219(3) 851
7/2
+
26136(1) 0
5/2
+
94
The coincidence spectrum obtained by gating on the 881-keV ? ray is shown in
Fig. 4.3(b). Despite the overlap of the 878-keV transition from the ?
+
/EC-decay of 
111
Sb
in the 881-keV gate, clean peaks not asociated with transitions in 
111
Sn are observed at
696, 831, 999, and 1477 keV. The 696-, 999-, and 1477-keV ? rays are placed as de-
populating levels at 1576, 1879, and 2357 keV that have already been established by
ground-state transitions and transitions to the 7/2
+
 level at 851 keV. The 831-keV ? ray
provides support for a new level at 1712 keV that also depopulates via a crossover
transition to the 5/2
+
 ground state. Peaks also appear in Fig. 4.2 at 487 and 1392 keV.
These ? rays appeared in coincidence with each other and support a cascade from the
level at 1879 keV established by other coincidence data through a level at 487 keV to the
ground state.
50
100
150
600 800 1000 1200 1400 1600 1800 2000
5
4
7
S
U
M
7
2
7
1
0
3
1
(
1
)
1
1
7
6
1
2
6
9
1
5
0
6
1
7
6
2
1
3
1
0
(a) 851-keV Gate
50
100
150
600 800 1000 1200 1400 1600 1800 2000
S
U
M
8
3
1
9
9
9
(
1
)
1
4
7
7
(b) 880-keV Gate
C
o
u
n
t
s
Energy (keV)
6
9
6
Figure 4.3: ??? coincidence spectra gated on the 851-keV (a) and the 880-keV (b)
transitions in 
111
Sb following ?
+
/EC-decay of 
111
Te.
95
The time-dependence of the combined decay rates of the peaks at 851 and 880
keV is shown in Fig. 4.4. These data were used to determine an improved half-life
measurement of 26.2(6) s for 
111
Te decay. This value is somewhat longer than the
previously reported value of 19.3(4) s [Ha72]. As those data came from decay rate of ?-
delayed protons that are not directly asociated with any single nuclide, the presence of
any short-lived 
111
I in their sources could give rise to a shorter half-life value.
Time (s)
C
o
u
n
t
s
T
1/2
 = 26.2(6)
10
4
0 5 10 15 20 25 30 35 40
10
3
Figure 4.4: Least-squares fit of the combined decays of the 851- and 881-keV transitions
in 
111
Sb following ?
+
/EC decay of 
111
Te.
4.5 The 
111
Sb Level Scheme
The decay scheme for 
111
Te based on the interpretation of ?-time and ???
coincidence spectra is shown in Fig. 4.5. The levels at 851, 1147, and 1398 keV were
identified by LaFosse et al. [La94], and asigned spins and parities of 7/2
+
, 9/2
+
, and 9/2
+
,
respectively. The 9/2
+
 level at 1398 keV was interpreted as a 1-proton-hole-2-proton
particle prolate intruder state. No coincidence relationships were observed in the gates on
the 1147- and 1398-keV ? rays reported in this previous high spin study.
The ground-state spin and parity for 
111
Te have tentatively been asigned as 5/2
+
by Boston et al., from heavy-ion reaction studies [Bo00]. This asignment is consistent
96
2357
2120
1879
1712
1576
1398
1147
881
851
487
0
4
8
7
 
4
5
(
7
)
2027
2613
Sb
111
51
5/2
+
(1/2
+
)
7/2
+
(3/2
+
)
9/2
+
9/2
+
Te
111
52
5/2
+
0
26.0 (5) s
?
+
1
3
9
8
 
1
6
(
5
)
8
8
1
 
9
2
(
3
)
8
5
1
 
1
0
0
(
2
)
2161
1
7
6
2
 
1
9
(
3
)
2
6
1
3
 
6
(
1
)
1
4
7
7
 
1
0
(
1
)
1
5
0
6
 
1
8
.
1
(
5
)
1
7
1
2
 
1
3
(
3
)
6
9
6
 
3
.
6
(
4
)
7
2
7
 
1
4
(
2
)
1
5
7
6
 
2
1
(
3
)
5
4
7
 
7
.
4
(
1
)
2
3
5
7
 
1
8
(
2
)
1
2
6
9
 
5
5
(
6
)
2
1
2
0
 
1
7
(
3
)
1
1
7
6
 
1
9
(
4
)
2
0
2
7
 
8
.
5
(
9
)
1
3
1
0
 
4
(
1
)
2
1
6
1
 
1
5
(
2
)
9
9
9
 
2
2
(
5
)
1
0
3
1
 
2
2
(
3
)
1
3
9
2
 
2
5
(
5
)
1
8
7
9
 
6
.
9
(
4
)
(1268)
2
9
6
 
2
(
1
)
1
1
4
7
 
3
0
(
2
)
(
1
2
6
8
)
 
 
2
5
(
1
5
)
(7/2
+
)
8
3
1
 
6
(
2
)
Figure 4.5: Levels populated in 
111
Sb following ?
+
-decay of 
111
Te. Level energies and
transitions are shown in units of keV. Levels already established in heavy-ion reaction
studies are denoted with a filed circle. Al transition intensities are given relative to the
intensity of the 851-keV ? ray, with tentative transitions being shown with a dashed line.
with similar spin and parity asignments for 
107,109
Te. Excited levels in 
111
Sb are
populated as a result of a ?-decay phenomenon described by Kislinger and Sorenson as
"even-jumping" [Ki63]. This occurs when the ground state of a ?
+
/EC decaying proton
rich parent has one or more pairs of valence protons (d
5/2
)
2
 or (g
7/2
)
2
 for 
111
Te) and an
unpaired neutron (in this case  d
5/2 
for 
111
Te).
When ?
+
/EC-decay occurs from 
111
Te to the ground state of 
111
Sb, the valence
pair of d
5/2
 protons must be broken as one of the d
5/2
 protons decays to form a d
5/2
 neutron
to pair with the existing d
5/2
 neutron, leaving behind the 
111
Sb nucleus with the single d
5/2
97
proton ground state. The "even jumping" in the case of 
111
Te decay occurs when either a
member of a d
5/2
 or g
7/2
 proton pair undergoes a Gamow-Teler transition to form a d
3/2
 or
d
5/2
 neutron, or a g
7/2
 neutron, respectively, producing a 3-quasiparticle state with one of
the following configurations,  (?d
5/2
?d
5/2
?d
5/2
)
3/2+,5/2+,7/2+
, (?d
5/2
?d
5/2
?d
3/2
)
3/2+,5/2+,7/2+
, or
(?g
7/2
?d
5/2
?g
7/2
)
3/2+,5/2+,7/2+
. As these final states populated in ?
+
 decay have configurations
that involve the single remaining proton coupled to a broken neutron pair, these levels
wil lie above the neutron pairing energy in regions of rather high level density [Ki63].
Consequently, these states wil mix with adjacent levels and give rise to population of a
large number of levels, each fed rather weakly in direct ?
+
 decay that wil, in turn,
cascade to the ground state through the levels below 2 MeV. For this reason, it is not
surprising that it is possible to observe significant population of the two wel-established
9/2
+
 levels at 1147 and 1398 keV in 
111
Sb, even though direct 2
nd
 forbidden ?
+
 decay
from a 5/2
+
 
111
Te parent should be negligible. A measure of the many weak levels whose
depopulation must contribute to the population of these 9/2
+
 levels is the absence of any
identifiable peaks in the coincidence gates on the 1147- and 1398-keV ? rays.
Hence, spin and parity asignments for low-energy levels, including the two new
levels identified at 487 and 881 keV in 
111
Sb cannot be based on implied direct ?
+
 feding
by comparing the diference betwen the intensity of the ? rays that depopulate the level
and the observed ? rays that populate the level. We start by noting that these levels are
not populated in heavy-ion induced reactions, hence, their spins and parities are likely to
be les than 7/2
+
, i.e. 1/2
+
, 3/2
+
, or 5/2
+
. For the lowest excited level at 487 keV, we note
that the lowest excited state in the adjacent 
113
Sb nuclide at 645 keV is asigned as 1/2
+
on the basis of an l = 0 angular distribution in the (
3
He,d) reaction [Co68], and is also
98
populated indirectly in the decay of 5/2
+
 
113
Te [Wi76].  About half of the observed
intensity of the 487-keV line can be acounted for by the feding of the 1392-keV ? ray.
Hence, this level was tentatively asigned as the low-energy 1/2
+
 state. On a strictly
experimental basis, neither 3/2
+
 nor 5/2
+
 can be completely ruled out.  Similarly, the level
at 881 keV can be considered comparable to the 3/2
+
 level at 1018 keV in 
113
Sb that is
populated in an l = 2 transition in the (
3
He,d) reaction. The 881-keV level is
provisionaly asigned a spin and parity of 3/2
+
, but it cannot entirely be ruled out as
either 1/2
+
 or 5/2
+
.
Resler et al. [Re02], noted ambiguities in the literature for the spin and parity
asignments for the levels in 
113
Sb that lie at 1018 and 1181 keV. These ambiguities are
resolved on the basis of new (?,t) transfer data upon which a recent Leter by Schifer et
al., was based [Sc04], and by studies of the decay of 
113
Te, of which both are discussed in
more detail in chapter 5. One result of interest is the observation that the level at 1181
keV shown in Fig. 4.6 is populated by an l = 4 transition and is likely to be the second
7/2
+
 level [Sc04]. There is also a level at 1331 keV in 
109
Sb that is shown in Fig. 4.6 that
also appears to be the second 7/2
+
 level. Both levels are populated in the decay of their
respective Te parents ~30% of the most intense ? ray. Hence, if the positions of the levels
in the odd-A Sb nuclides vary smoothly, expectations of a level in 
111
Sb betwen 1200
and 1300 keV would be reasonable.
99
815851
832
1101
1341
9/2
+
9/2
+
1147
1399
9/2
+
9/2
+
1257
1461
9/2
+
9/2
+
1018
402
752
3/2+
645
880
3/2+
3/2+
487
7/2+ 771
754
395
3/2+
1/2+
1652
7/2+
712
857
498
3/2+
1/2+
9/2+
1338
7/2
+
7/2
+
7/2
+
Sb
Sb
1331
7/2
+
1779
1811
1921
1944
5/2+
7/2+
3/2+
1/2+
1192
1592
1837
1969
1181
7/2+
1878
1712
1576
1996
2096
11/2+
9/2+
(1268)
(7/2+)
109  
 51       58
111 
 51       60
769
1058
1389
9/2
+
9/2
+
7/2+ 702
9/2+
7/2
+
Sb
1063
107  
 51       56
1219
9/2
+
9/2+
Sb
1201
105  
 51       54
0
5/2+
05/2+
05/2+
0
5/2+
3421/2+
6123/2+
5241/2+
6343/2+
558
7/2+
9/2+
3/2+
2019
2106
Sb
0
5/2+
113 
 51       62
1/2
+
1/2
+
1/2
+
exp   calculated exp   calculated exp   calculated exp   calculated exp 
2027
2120
Figure 4.6: Comparison of shel model calculations with experimental levels of
105,107,109,111
Sb. Values are in units of keV. The 2
+
 energies in the even-even Sn core
nuclides at 1259, 1205, 1206, 1212, and 1257 keV for 
104,106,108,110,112
Sn, respectively, are
marked with a smal rectangle in the column with the experimental data. Also shown are
the experimental levels for 
113
Sb. The calculated levels for 
109
Sb shown in column labeled
(133) were obtained using the single-proton d
3/2 
and s
1/2 
energies of 1.48 and 1.7 MeV,
respectively.
In the diference spectrum shown in Fig. 4.2, no peak of that magnitude stands
out. There is a smal peak that decays at 1244 keV, but it is in the correct ratio to be from
the decay of 
110
Sb to levels of 
110
Sn. However, in the gate on the 851-keV ? ray that is
shown in Fig. 4.3, the intensity of the peak at 1269 keV is present at only about half of
the expected intensity, based on the intensities of the 1176- and 1506-keV peaks. Hence,
100
there is a possible level at 1268 keV in the level scheme shown in Fig. 4.5 in which the
level is dashed and parentheses are used to enclose both the energy and spin and parity.
4.6 Discusion and Interpretation
In the paper by Resler et al. [Re02], in which new low-spin levels for 
109
Sb were
identified in the ?
+
/EC decay of 
109
Te, comparisons were made with shel-model
calculations that used literature values [Hj95] for the single-proton and single-neutron
energies that are tabulated in Table 4.2. In the aforementioned Leter by Schifer et al.,
the evolution of the positions of the higher-spin h
11/2
 and g
7/2
 levels in odd-mas Sb
nuclides were reported. The work postulated that the remarkable monopole shift observed
for the g
7/2
 and d
5/2
 levels in these nuclides arises as a consequence of a spin-orbit
interaction that diminishes as N/Z increases [Sc04].  Although the focus of that paper was
the spliting of the proton g
9/2 
and g
7/2
 orbitals, current consideration of the spliting of the
d
5/2 
and d
3/2
 proton orbitals is also possible.
Table 4.2: Experimental 
133
Sb Proton and Neutron Single-Particle Energies along with
Those Used for Calculation of 
105-111
Sb.
Orbital Neutron s.p. Proton s.p. Reduced proton 
s.p.
133
Sb
0h
11/2
3 3 3 1.82
0g
7/2
0.2 0.2 0.2 -0.963
1d
5/2
0 0 0 0
1d
3/2
2.553.55 2.9 1.48
2s
1/2
2.453.45 2.6 ~1.7
101
The monopole shift of the g
7/2 
neutron orbital by ~3.0 MeV as N and Z changed
from 
91
Zr
50
 to 
131
Sn
81
 was pointed out by Heyde [He88] and atributed to the interaction
of the g
7/2 
neutron orbital with the filing of the spin-orbit partner g
9/2 
proton orbital as had
been suggested by Federman and Pitel [Fe79]. Similar efects were pointed out by
Walters in other mas regions [Wa98]. A large shift in position is partialy sen in Fig.
4.1, however, either suggests that the spin-orbit spliting is narowing and drawing the
g
7/2 
orbital deeper into the nucleus, or that the g
7/2 
and g
9/2 
orbitals are both being more
tightly bound with respect to the d
5/2
, d
3/2
, and h
11/2 
orbitals. As these changes surround
shel gaps, direct measurement is often dificult. On the other hand, study of the spin-
orbit spliting for lower-l orbitals such as the d
5/2 
and d
3/2 
orbitals within a major shel can
be more quantitative.
Walters pointed out that, in fact, both results are plausible. In Fig. 2 of [Wa98], it
can be sen that the f
7/2
 to f
5/2
 and p
3/2 
to p
1/2 
spliting changes only slightly (2004 to 1570
keV and 854 to 898 keV, respectively) in going from 
133
Sn
83
 to 
207
Pb
125
, in a region where
N/Z also changes litle. In contrast, Fig. 5 of the same manuscript, shows that the p
3/2 
to
p
1/2 
split changes from 1112 keV in 
57
Ni
29
 to 2023 keV in 
49
Ca
29
 to, as N/Z evolves from
~1.0 to 1.45, an evolution opposite to that suggested by Schifer et al. [Sc04].
Although the parameters of the calculations that reproduce the experimentaly
observed levels in 
111
Sb do not provide a direct measurement of this spliting, they do, at
least, give values that are consistent with available experimental data. In order to test this
idea, the positions of the single-proton basis d
3/2
 and s
1/2
 levels in the shel-model
calculation were varied in order to provide as good as possible a fit for the low-energy
102
1/2
+
 and 3/2
+
 levels in 
109
Sb, and then the usefulnes of these new energies were tested
against the new 1/2
+
 and 3/2
+
 levels in 
111
Sb.
Calculations have also been performed for the lowest five levels of 
109
Sb using the
single-particle energies for the d
3/2 
and s
1/2 
levels shown in Table 4.2 for 
133
Sb, namely,
1.48 and 1.7 MeV, respectively. These results are shown in Fig. 4.6 under the column
marked (133). As can be sen, the calculated positions of the yrast 1/2
+
 and 3/2
+
 levels
are far below the positions of the observed levels, with some lowering for the 7/2
+
 level.
Hence, at least for this interaction, reproduction of the positions of the yrast 1/2
+
 and 3/2
+
levels requires a much larger spin-orbit spliting than is found for 
133
Sb.
Sb
101
Sb
111
Sb
109
Sb
107
Sb
105
Sb
103
5/2
+ 
ground state
}
lowered d
3/2 
and s
1/2
1/2
+
7/2
+
3/2
+
9/2
+
0
200
400
600
800
1000
1200
1400
1/2
+
7/2
+
3/2
+
9/2
+
Ressler 
et al. 
[Re02]
}
E
n
e
r
g
y 
(
ke
V
)
Figure 4.7: Comparisons of the calculated positions of the lowest 1/2
+
, 3/2
+
, 7/2
+
 and
9/2
+
 levels in 
101,103,105,107,109,111
Sb using the unshifted [Re02] (full lines), and lowered
(dashed lines) d
3/2
 and s
1/2
 single-proton energies.
103
The levels for the odd A Sb isotopes with A=101 to A=111 calculated with both the old
and new single proton energies are shown in Fig. 4.7. The new single-proton energies
required a fit to the positions of the lowest 1/2
+
 and 3/2
+
 levels in 
109
Sb are listed in Table
4.2. Currently, one proton and ten neutrons is as far from the 
100
Sn core as such
calculations are practical. Detailed comparisons of the level structure for 
105,107,109,111
Sb
are shown in Fig. 4.6, along with the levels of 
113
Sb that were refered to earlier. The
calculated levels are shown in shaded rectangles and the 9/2
+
 levels that have been
identified in heavy-ion reactions as g
9/2
 proton-hole intruder states are identified with a
shaded oval. These states are not in the calculation. In Table 4.2, the single-proton basis
levels for 
133
Sb to the d
5/2
 state are normalized for easy comparison with the 
101
Sb
energies. The spin-orbit spliting for the d
5/2
 and d
3/2
 orbitals can be sen to have
narowed from 2.9 MeV in 
101
Sb to 1.48 MeV in 
133
Sb [Sa99], a reduction of almost a
factor of two, and quite in line with the postulate set forth by Schifer et al. [Sc04].
However, such a conclusion implies that the 3/2
+
 level at 2440 keV in 
133
Sb caries the
full spectroscopic strength for the d
3/2 
orbital. If, for example, the true position of the d
3/2
orbital lies much nearer to the 4.0 MeV core in 
132
Sn, then the narowing implied by the
energies in Table 4.2 may wel be too large.
Other approaches to these monopole shifts have been stimulated by the evolution
of the N = 16 and N = 20 shel closures, and noted by Otsuka et al. [Ot01] and
Hamamoto [Ha04]. It can be sen that the narowing that was deduced for the d
5/2 
and d
3/2
orbitals as N/Z increases is almost exactly opposite to the widening of the p
3/2 
and p
1/2 
gap
in the N = 29 isotones. Hence, it may be that nuclear size, the N/Z ratio, and the
underlying microscopic structure of the respective neutrons or protons al play a role in
104
the evolution of the positions of nuclear energy levels and that no single feature provides
a simple description for the observed structure changes.
Several features do stand out in Fig. 4.6 and Fig. 4.7.  First, the lowered single-
particle d
3/2
 and s
1/2
 basis states for 
101
Sb give rise to an excelent fit for the lowest
observed 1/2
+
 and 3/2
+
 levels in both 
109
Sb and in 
111
Sb.  At the same time, the energies
for the higher-spin 7/2
+
 and 9/2
+
 levels are almost unchanged.  Second, the fits for the
9/2
+
 level in 
105
Sb and the 7/2
+
 and 9/2
+
 levels in 
107
Sb are also quite good.  It can be sen
that the prolate g
9/2
 intruder appears to have no efect on the position of the particle-core
9/2
+
 levels in 
105,107
Sb, but as N increases, some mixing appears to keep the lowest 9/2
+
level below the calculated position.
More extensive calculations have been performed for 
109
Sb and show the
calculated levels in Fig. 4.6 up through ~2.1 MeV. This nuclide was chosen, as it is the
heaviest for which the time involved in the calculations is reasonable. And, it is also the
lightest odd-mas Sb nuclide for which some low-spin structure is known up to that
energy.  It can be sen that below the ~2 MeV pairing energy, few levels are expected
from this model, and that the level density is reasonably consistent with the observed
levels, inasmuch as the even-jumping ?-decay proces limits the ability to determine
spins and parities. As the level structures are not expected to undergo large changes with
variations in neutron number, these calculated levels for 
109
Sb should give some
indication of the positions of similar levels in 
111
Sb and 
113
Sb.
105
4.7 Sumary and Outlook
The ?
+
/EC and ? decay of 
111
Te to low-spin levels of 
111
Sb has been studied for
the first time using sources produced via recoil separation of the products of a heavy-ion
reaction.  Eleven new levels were identified, including proposed levels at 487 and 881
keV that are tentatively asigned spins and parities of 1/2
+
 and 3/2
+
, respectively. In
addition, a more precise half-life value of 26.2(6) s for 
111
Te has been determined by
following the decay of the two strongest ? rays as a function of time.  New shel model
calculations have been performed in which the positions of the single-proton basis states
were adjusted to fit the observed energies for the lowest 1/2
+
 and 3/2
+
 levels of 
109
Sb.
With this adjustment, the fits for the six lowest excited states in 
111
Sb and, where known,
for the lighter odd-mas Sb nuclides has proven to be excelent.  Comparison of the
relative energies of the d
5/2
 ? d
3/2
 spin-orbit spliting used for these calculations with the
known single-proton energies in 
133
Sb could be evidence of a reduction of ~50% that is
consistent with recent postulations by Schifer et al. [Sc04], for the g
9/2
 and g
7/2
 orbitals.
It can be sen in Fig. 4.6 and Fig. 4.7, that these calculations show a minimum in
the energies for the lowest 1/2
+
 and 3/2
+
 levels in 
107
Sb and then a rapid rise in energy as
N approaches the closed neutron shel at 50. As 
107
Te is known to undergo ? decay with a
3-ms half-life, the low-spin levels of 
107
Sb cannot be readily studied by a ?-decay
experiment. However, the low-spin structure of 
107
Sb (and 
105
Sb) could be studied via the
use of radioactive 
104,106
Sn beams with a 
3
He target in inverse kinematics where the
strongest population should be to the low-l 1/2
+
 and 3/2
+
 levels.
106
5 The Structure of 
113
Sb
5.1 Overview
The level structure of 
113
Sb was studied following the ?
+
/EC decay of 
113
Te. 
113
Te
was produced in the 
60
Ni(
56
Fe,2pn)
113
Te reaction and separated using the Fragment Mas
Analyzer at Argonne National Laboratory. As for the 
111
Te experiment, ?-ray singles and
?-? coincidence spectra were collected as a function of time. Several ? rays were
identified for the first time as depopulating members of a group of newly identified
states, or as transitions connecting previously established levels. Based on the ?-feding
intensities and level scheme, data were used to asign spins and parities of 3/2
+
 and 7/2
+
for the 1019- and 1181-keV levels, respectively. In addition, transfer reaction data were
used to support the 3/2
+
 asignment of the 1019-keV level. The level structure of 
113
Sb is
systematicaly compared with that of neighboring odd-A Sb isotopes.
5.2 Scientific Motivation
The structure of the odd-mas Sb nuclides has atracted interest over the years as
their low-energy, low-spin structures are described by the coupling of the single Sb
proton with the Sn core [Be71]. Specificaly, the neutron deficient odd-A Sb isotopes
provide an important testing ground for shel model calculations based on the heaviest
self-conjugate double magic nucleus, 
100
Sn. As A increases from 
100
Sn, shel model
calculations become dificult because the model space becomes too large for practical
computation. As mentioned in chapter 4, 
111
Sb is currently the heaviest odd-A Sb nuclide
outside 
100
Sn for which shel model calculations are feasible. Experimentaly, the
situation becomes more complex as wel, as some of the states can no longer be described
107
only as the result of the coupling of a proton with particle-hole excitations of the Sn core,
but also as a coupling of the odd proton with collective core phonons. For odd-A Sb
isotopes with A?115, these types of collective states have been wel described by
particle-phonon coupling using the Interacting Boson-Fermion Model (IBFM)
[Be71,Lo98].
As odd-A Sb nuclides with A ? 111 and A ? 129 are best interpreted in the
context of the shel model, and as those with 115 ? A ? 127 are best described using a
particle-core coupling model (IBFM); then 
113
Sb provides a unique testing ground to
observe the overlap and predictive power of both approaches. The low-spin structure of
113
Sb was first investigated by Conjeaud et al. [Co68] in a systematic transfer reaction
study of al odd-A Sb isotopes ranging from A=113 to A=125. It was concluded that the
majority of the 2d
5/2
 and 1g
7/2 
strengths were localized in the ground state and first
excited state, respectively. In the lower mas region, the single-particle strengths of the
3s
1/2
 and 2d
3/2 
levels diminished with decreasing neutron number, and could be beter
represented by collective motions of either the ?d
5/2
 or ?g
7/2 
states coupled to quadrupole
(2
1
+
 level) vibrations in their respective Sn cores. The collective nature of the 1/2
+
 and
3/2
+
 states were supported by their large B(E2) values [Co68].
Many of the levels observed by Conjeaud et al. [Co68] were later corroborated by
a ?-decay study of 
113
Te by Wigmans et al. [Wi76]; however, there was an experimental
contradiction in the implications of both sets of data. Neither experiment reported a J
?
asignment for the level at 1181 keV, but each experiment supported a diferent J
?
asignment for a level at 1019 keV. The 1019-keV level was populated by both the
(
3
He,d) transfer reaction and the ?
+
/EC decay of the proposed 7/2
+
 
113
Te parent. The l=2
108
transfer reaction had a spectroscopic factor of 2.3. If the 1019-keV level is asigned a
5/2
+ 
value, consistent with population of an l=2 transfer, then the sum rule is exceded
when the spectroscopic factor 2.3 is added to that of 4.3 for the six d
5/2 
ground state
protons. Therefore, the transfer reaction data suggest that this level has a J
?
 = 3/2
+
. The
discrepancy betwen these two experiments occurs because the intense ? feding implies
that if the 
113
Te parent has a ground state configuration of 7/2
+
, then the state at 1019 keV
would have to be 5/2
+
, which as mentioned would violate the sum rule with the measured
spectroscopic factor for this state.
One way to satisfy the results of both experiments would be if 
113
Te had a 5/2
+
ground state, then direct feding via ?-decay would not be not in conflict with a J
?
=3/2
+
for that level. Similarities in the transfer strength for the 1071-keV 3/2
+
 level in 
115
Sb
favor this analysis for the J
?
 asignment of 3/2
+
 for the 1019-keV level in 
113
Sb. Another
possibility that would resolve the conflicting results could be that there are, in fact, two
decaying isomers in 
113
Te, with quite similar half-lives. This conjecture is plausible since
this situation occurs in 
115
Te. This chapter primarily focuses on the new ? rays and levels
observed following ?
+
/EC decay of 
113
Te, with some interpretation of data obtained from
a recent transfer reaction study by Schifer et al. [Sc04].
5.3 Experimental Details
The experiment was performed using the Argonne Tandem Linear Acelerator
System (ATLAS) coupled to the Fragment Mas Analyzer (FMA) at Argonne National
Laboratory. 
113
Te nuclei were produced using the 
60
Ni(
56
Fe,2pn)
113
Te fusion-evaporation
reaction with a beam energy of 225-MeV and a target thicknes of 833 ?g/cm
2
. Reaction
109
products were separated in the FMA on the basis of their mas to charge (A/Q) ratio at
charge state 24. Following mas separation, the recoils were implanted in the tape of a
moving tape collector (MTC) that was moved periodicaly to a Pb-shielded counting
station. As the half-life of 
113
Te was previously reported to be 1.7 min [Wi76], count and
collection times were varied from 60 s to maximize coincidence events, to as long as
1000 s to permit identification of ? rays belonging to the decay of daughter and
granddaughter nuclides and to the decay of nuclides that are collected on the tape owing
to similar A/Q values.
Two large HPGe detectors (45% and 65%) and two smal Ge detectors (~25%)
were used to detect the ? rays coming from the reaction products that were deposited on
the tape. In addition to the Ge detectors, two plastic scintilators were used to veto 0
o
 ?-?
coincidences in the same detector, and to obtain 180
o
 ?-? coincidences. Analyses of
??singles, ?-? coincidences, and ?-time data were used to identify transitions in the
corresponding 
113
Sb daughter nucleus.
5.4 Identification of the ? Rays Asociated with the ?
+
/EC Decay of 
113
Te
As with 
111
Te (se 4.4), known contributions to the ?-singles and ?-? coincidence
spectra arose from the decay of longer-lived daughters, granddaughters; and short-lived
species with similar A/Q ratios. In particular, 
113
Sb (T
1/2
 = 6.7 m), 
113
Sn (T
1/2
 = 21.4 m),
113
I (T
1/2
 = 5.9 s), 
112
Sb (T
1/2
 = 51.4 s) and 
111
In (T
1/2
 = 2.80 d) [Bl98,De96]. A ? spectrum
resulting from the subtraction of a ? spectrum taken betwen t = 150 to t = 300 s from one
obtained from t=30 to t = 150 is shown in Fig. 5.1.
110
Figure 5.1: Time-subtracted spectrum showing 
113
Sb transitions from the decay of 
113
Te.
The ?-energy spectrum shown is the residual spectrum obtained by subtraction of the
spectrum taken from t = 150s to t = 300s acquisition from the spectrum taken from t =
30s to t = 120s. Peaks belonging to ? transitions following decay of 
112
Sb and 
111
In are
marked with a gren diamond and an open circle, respectively. Peaks that correspond to
unplaced transitions believed to depopulate levels in 
113
Sb are in red.
Just as with the A = 111 data (se section 4.4) the time-gated spectra used in the
subtraction were chosen to eliminate the contribution of transitions asociated with the
decay of the daughter nuclei, primarily 6.7 min 
113
Sb. The lower limit on the time-gated ?
spectrum was set at t = 30s to eliminate the peaks asociated with the decay of 
113
I. In
Fig. 5.1, it can be observed that the long-lived transitions at 332 and 498 keV from 
113
Sb
decay subtracted roughly to background. The remaining peaks in the diference spectrum
1
1
9
4
111
In
2
4
5
2
7
3
3
5
1
3
9
7
4
8
4
2
0
5
2
9
6
4
4
33
7
0
9
1
1
7
1
2000
4000
6000
100 200 300 400 500
5
4
3
5
8
1
6
1
1
6
4
5
6
7
0
7
1
1
7
2
3
7
3
7
7
6
5
1200
2000
2800
3600
520 560 600 640 680 720 760 800
1000
2000
3000
4000
800 900 1000 1100 1200
8
1
4
8
4
2
8
5
1
8
7
5
8
9
4
9
1
5
9
3
4
9
9
0
1
0
1
9
1
0
3
9
1
0
7
2
1
0
9
6
,
1
0
9
7
1
1
5
3
1
1
8
1
500
1000
1500
2000
1200 1300 1400 1500 1600
1
2
5
7
1
3
0
1
1
3
1
7
1
3
2
5
1
3
3
2
1
3
7
1
1
3
4
8
1
3
5
8
1
3
8
5
1
4
4
9
1
4
6
1
1
5
1
6
1
5
5
1
1
5
6
7
1
5
7
6
1
2
0
5
100
300
500
2200 2300 2400 2500 2600 2700 2800
2
2
2
1
2
3
6
8
2
4
0
2
2
4
2
2
2
4
3
1 2
5
3
5
2
5
5
0 2
6
0
8
2
6
1
9
2
6
8
2
2
7
4
9
2
7
5
7
2
3
8
1
200
400
600
800
1000
1600 1700 1800 1900 2000 2100 2200
1
6
6
3
1
6
9
1
1
7
2
1
1
7
4
1
1
8
0
5
1
8
6
8
1
8
9
0
1
9
4
5
2
0
1
6
2
0
4
8
2
0
9
4
2
1
1
2
2
1
7
2
1
7
6
7
1
9
0
6
1
7
0
3
Energy (keV)
C
o
u
n
t
s
112
Sb
113
Te
3
7
4
*
1
5
4
2
1
1
5
1
0
9
9
111
are atributed to either 
111
In or 
112
Sb decay. As the decay lines of 
112
Sb and 
111
In are wel-
established [Bl98,De96], most of the peaks (excluding the peaks above 2.0 MeV) in Fig.
5.1 not asociated with the decay of these nuclides were asigned to the decay of 
113
Te.
The energies, intensities, and placements in the 
113
Sb level scheme of the 
113
Te decay
lines from this study are summarized in Table 5.1, while the ? rays that were unable to be
placed because of inconclusive coincidence data are listed in Table 5.2.
Table 5.1: Data for ? Rays and Levels Observed in the ?-decay of 
113
Te.
a
Uncertainty of ?-ray energies is ? 0.3 keV. 
b
Relative to the intensity of the 814-keV ? ray in 
113
Sb.
Level (keV)
J
?
E
?
a
 (keV) I
?
b
Final Level 
(keV)
J
?
645 1/2
+
645 28.8(6) 0 5/2
+
814
7/2
+
814 100.000 5/2
+
10193/2
+
101960(1) 0 5/2
+
374 1.3(5) 645 1/2
+
1181
7/2
+
118161(3) 0 5/2
+
1257
9/2
+
125725(3) 0 5/2
+
443 2.0(1) 814 7/2
+
1348
11/2
-
13481.0(7) 0 5/2
+
91 4.2(5) 12579/2
+
1461
9/2
+
146110(1) 0 5/2
+
647 6(1) 814 7/2
+
280 2.8(5) 11817/2
+
204 5.6(7) 12579/2
+
15515/2
+
155113(2) 0 5/2
+
906 0.6(4) 645 1/2
+
737 2.9(3) 814 7/2
+
370 1.4(5) 11817/2
+
1717
10726.5(2) 645 1/2
+
1853
103910(1) 814 7/2
+
112
Table 5.1: continued
a
Uncertainty of ?-ray energies is ? 0.5 keV. 
b
Relative to the intensity of the 814-keV ? ray in 
113
Sb.
Level (keV)
J
?
E
?
a
 (keV) I
?
b
Final Level 
(keV)
J
?
1870
12251.1(7) 645
1/2
+
10561.8(4) 814
7/2
+
851 2(1) 1019
3/2
+
1910
449 ?0.5 1461
9/2
+
2016
20163.3(4) 0
5/2
+
13712.1(4) 645
1/2
+
997 <0.5 1019
3/2
+
2055 12417.8(5) 814
7/2
+
874 2.2(3) 1181
7/2
+
2094 209413(1) 0
5/2
+
14495.3(4) 645
1/2
+
543 <0.5 1551
5/2
+
2115 211510(1) 0
5/2
+
130110.2(4) 814
7/2
+
109613.3(5) 1019
3/2
+
934 4.6(5) 1181
7/2
+
2132 21321.4(2) 0
5/2
+
131710.1(7) 814
7/2
+
875 2.4(3) 1257
9/2
+
581 2.7(3) 1551
5/2
+
2172 21721.7(5) 0
5/2
+
13583.4(5) 814
7/2
+
11534.6(4) 1019
3/2
+
915 4.9(4) 1257
9/2
+
711 2.6(4) 1461
9/2
+
2381
23813.5(7) 0
5/2
+
15674.9(4) 814
7/2
+
2535
25358(2) 0
5/2
+
18906(1) 645
1/2
+
17216(1) 814
7/2
+
15167.4(3) 1019
3/2
+
113
Table 5.1: continued
a
Uncertainty of ?-ray energies is ? 0.5 keV. 
b
Relative to the intensity of the 814-keV ? ray in 
113
Sb.
Level (keV)
E
?
a
 (keV) I
?
b
Final Level 
(keV)
J
?
2608260813(3) 0
5/2
+
19632.1(1) 645
1/2
+
15894(1) 1019
3/2
+
2619261912(2) 0
5/2
+
18052.9(2) 814
7/2
+
2682
26826.1(5) 0
5/2
+
20371.7(6) 645
1/2
+
186810.9(5) 814
7/2
+
16636(1) 1019
3/2
+
275727576(2) 0
5/2
+
21121.7(4) 645
1/2
+
15769(1) 1181
7/2
+
2845
13851.9(2) 1460
9/2
+
292229221.9(5) 0
5/2
+
22771.1(6) 645
1/2
+
17413.6(6) 1181
7/2
+
12054.9(6) 1717
296429641.7(3) 0
5/2
+
19453.1(5) 1019
3/2
+
17831.8(4) 1181
7/2
+
306724221.9(3) 645
1/2
+
20488.3(7) 1019
3/2
+
114
Table 5.2: List of Unasigned ? Rays that Could to Belong to the 
113
Te Decay Scheme.
a
Uncertainty of ?-ray energies is ? 0.5 keV. 
b
Relative to the intensity of the 814-keV ? ray in 
113
Sb.
5.5 The 
113
Sb Level Scheme
The placement of new ? transitions and levels was acomplished using ?-?
coincident spectra. As an extensive 
113
Sb level scheme below 2.5 MeV was previously
reported by Wigmans et al. [Wi76]; most new ? rays and levels were placed using
coincident relationships which could be connected transitions to established states.
Shown in Fig. 5.2 is a ?-ray spectrum gated on the 645-keV 1/2
+
 ? 5/2
+
 transition
in 
113
Sb. Peaks at 1072 and 1449 keV correspond to transitions previously placed by
Wigmans et al. [Wi76]. The peak at 814 keV results from the overlap of the 647-keV
peak with the gate on the 645-keV ? ray. The 647-keV ? ray is known to be in
coincidence with the 814-keV transition, depopulating the 5/2
+
 level at 1551 keV. New ?
rays at 374, 906, and 1890 keV depopulate established levels at 1019, 1551, and 2535
E
?
a
 (keV) I
?
b
Weak ??? Coincidences (keV)
484 8(2) 1019
11941.5(1) 814, 1039
16912.3(3) 331, 988
17032.5(1) 1019
17673.1(3) none
21531.4(4) 645
22216.0(5) 1257
23682.0(4) 1257
24022.0(2) none
24313.6(4) 1181
25500.7(3) 1181
27496(2) 1181
115
keV, respectively. The 1096 keV peak was originaly placed as depopulating a level at
1742 keV, but as wil be shown in the gate on the 1019-keV ? ray, it is part of a 1097-
374-645 keV cascade. The 1738-keV line also shows up in Fig. 5.2 because it is part of a
similar cascade through the 1019-keV level. Peaks at 1225, 1371, 1963, 2037, 2112, and
2277 keV are transitions that provide evidence for the possibility of new levels at 1870,
2016, 2608, 2682, 2757, 2798, and 2922 keV, respectively. These new levels in 
113
Sb
suggested by the gate on the 645-keV transition are further supported by at least two or
more other transitions that depopulate to lower energy states. The 2153-keV peak could
correspond to a transition that depopulates a new level at 2798 keV. However, as there is
no other evidence to support the placement of a new level at this energy, it wil not be
included in the level scheme for 
113
Sb.
Figure 5.2: ?-? coincidence spectra gated on the 645-keV transition in 
113
Sb following
?
+
/EC-decay of 
113
Te. The peaks marked with ?*? were previously reported in [Wi76],
and the ?**? mark the 814-keV peak, as there is an overlap of the 647-keV ? ray in this
gate.
A ? spectrum gated on the most intense transition, the 814-keV ? ray, is shown in
Fig. 5.3.  Peaks at 442, 647, 737, 1039, 1301, 1317, 1358, and 1721 keV were previously
C
o
u
n
t
s
1
7
3
8
1
3
7
1
1
4
4
9
10
30
50
1300 1400 1500 1600 1700
*
Energy (keV)
1
8
9
0
1
9
6
3
2
2
7
7
2
1
1
2
10
20
30
1800 1900 2000 2100 2200 2300
2
1
5
3
2
0
3
7
1
0
7
2
1
0
9
6
8
1
4
9
0
650
100
150
800 900 1000 1100 1200
645-keV gate
*
1
2
2
5
*
*
0
20
40
60
80
100
200 300 400 500 600 700
3
7
4
5
1
1
116
placed in the 
113
Te decay scheme [Wi76]. Transitions with energies of 1241, 1567, 1805,
and 1868 keV suggest new levels at 2055, 2381, 2619, and 2682 keV. The level at 2682-
keV was previously suggested by peaks observed in the gate on the 645-keV ? ray; and
the 2619-keV level is further supported by the presence of a peak in Fig. 5.1, which could
correspond to a ground state transition. The 766-keV peak also depopulates the 2619-keV
level, and populates the 814 via a 766-1039-keV cascade. There is ?-time and ?-?
evidence that the levels at 2055 and 2381 both have additional ? rays that depopulate
these states, providing further support for the validity their placement. The 1194-keV ?
ray was also coincident with the 1039-keV transition (spectrum not shown) that populates
the 814-keV level, but the placement of a level at 3047 keV could not be supported with
additional data.
0
50
100
150
200
250 300 350 400 450
4
4
2
0
50
100
150
200
560 640 720 800 880 960
7
3
7
0
50
100
150
200
1000 1100 1200 1300 1400
0
20
40
60
80
100
1500 1600 1700 1800 1900
1
0
3
9
1
3
0
1
1
3
1
7
1
3
5
8
1
5
6
7
1
7
2
1
1
8
0
5
1
8
6
8
1
7
4
1
Energy (keV)
C
o
u
n
t
s
814-keV gate
1
1
9
4
1
2
4
1
*
6
4
7
*
*
*
*
*
*
*
1
0
5
6
b
a
ckg
r
o
u
n
d
b
a
ckg
r
o
u
n
d
7
6
6
Figure 5.3: ?-? coincidence spectra gated on the most intense 814-keV transition in 
113
Sb
following ?
+
/EC-decay of 
113
Te. The peaks marked with ?*? were previously observed in
[Wi76].
117
C
o
u
n
t
s
1
9
4
5
1
5
1
5
1
6
6
3
1
5
6
7
10
30
50
1400 1600 1800 2000
*
1
9
0
3
1
7
0
3
1
0
9
6
1
1
5
3
7
2
5
10
30
50
800 1000 1200
8
5
1
9
5
8
Energy (keV)
1
5
8
9
9
9
7
b
a
ckg
r
o
u
n
d
1
7
3
8
20
60
100
200 400 6000
511
1019-keV gate
Figure 5.4: ?-? coincidence spectra gated on the 1019-keV transition in 
113
Sb following
?
+
/EC-decay of 
113
Te. The ?*? denotes the same type of peak as in Fig. 5.3 and Fig. 5.4.
The peak labeled in gren corresponds to a coincidence observed in the decay of 
113
Sb.
The peak labeled in red was not placed in the current level scheme.
Of the peaks in the ? spectrum gated on the 1019-keV transition in 
113
Sb shown in
Fig. 5.4, only the 1516 keV line was previously reported. A 238-keV ? ray was
previously reported to populate this level [Wi76], though it was not observed in either the
time-gated ? spectrum in Fig. 5.1 or the spectrum gated on the 1019-keV ? ray in Fig. 5.4.
The 1096- and 1153-keV peaks correspond to transitions that depopulate established
levels at 2115 and 2172 keV, respectively. Peaks at 851, 997, 1589, 1663, 1738, and 1903
keV corroborate the placement of the levels at 1870, 2016, 2608, 2682, 2757, and 2922
keV suggested in the 645-keV gated spectrum in Fig. 5.2. The peak at 1945 keV would
suggest the placement of a new level at 2964-keV. This 2964-keV level is supported by
118
coincidence relationships observed in gated spectra from higher-energy ? rays, and by a ?
ray at 2964 in Fig. 5.1 that could be the transition to the ground state from this level. The
gren 725-keV peak corresponds to the overlap of the 1018-keV peak from 
113
Sb ?
+
/EC
decay.
A spectrum gated on the 1181-keV ? ray in 
113
Sb is shown in Fig. 5.5. No ? rays
have been reported to populate this level previously. The 280-, 370-, 934-, and 1534-keV
peaks de-excite established levels at 1461, 1551, 2115, and 2535 keV [Wi76]. The 874-,
1576-, 1741-, and 1783-keV lines depopulate the previously mentioned levels at 2055,
2757, 2922, and 2964 keV, respectively. The peak at 894 corresponds to a transition that
cannot be placed with additional supporting data.
0
50
100
150
200
0 100 200 300 400 500
0
10
20
30
40
50
560 640 720 800 880 960
0
10
20
30
40
50
1000 1200 1400 1600 1800 2000
1
7
8
3
9
3
4
1
5
7
6
1
7
4
1
3
7
0
8
9
4
8
7
4
Energy (keV)
C
o
u
n
t
s
1
3
5
4
1181-keV gate
2
8
0
b
a
ckg
r
o
u
n
d
Figure 5.5: ?-? coincidence spectrum gated on the 1181-keV transition in 
113
Sb following
?
+
/EC-decay of 
113
Te. The 894-keV peak in red is not placed in this study.
119
The spectrum resulting by seting a gate on the 1257-keV ? ray is shown in Fig.
5.6. The 91- and 915-keV coincidence relationships with the 1257-keV ? ray were
previously established [Wi76]. The 204- and 875-keV lines depopulate known levels at
1461 and 2132 keV, respectively. The 449-keV ? ray would suggest the presence of a
level at 1910 keV via a 449?204?1257 keV cascade, while the 1385-keV coincidence
peak suggests a state at 2845 keV, also cascading through the 1461-keV level. Peaks at
894, 990, and 1097 keV are known to be coincident with the 1257-keV ? ray in 
112
Sn.
5
15
25
1000 1100 1200 1300 1400 1500
1
3
8
5
20
60
100
0 100 200 300 400
20
60
100
560 640 720 800 880 960
9
1 2
0
5
4
4
9
8
7
5
915
Energy (keV)
C
o
u
n
t
s
1257-keV gate
8
9
4
9
9
0
*
1
0
9
7
U
n
su
b
t
r
a
ct
e
d
 
8
1
4
-
ke
V
 
 
p
e
a
k 
Figure 5.6: ?-? coincidence spectrum gated on the 1257-keV transition in 
113
Sb following
?
+
/EC-decay of 
113
Te. The peaks labeled in gren correspond to transitions known to be
coincident to the 1257-keV ? ray in 
112
Sn.
Using the data in Figs 5.2-5.6, the level scheme for 
113
Sb following ?
+
/EC was
constructed, and is shown split into thre parts in Fig. 5.7.
120
Sb
113
51
0
645
814
1019
1181
1257
1348
1461
1551
1717
1853
2016
6
4
5
 
2
8
.
8
(
6
)
8
1
4
 
1
0
0
1
0
1
9
 
6
0
(
1
)
3
7
4
 
1
.
3
(
5
)
1910
1870
1
1
8
1
 
6
1
(
3
)
1
2
5
7
 
2
5
(
3
)
4
4
3
 
2
.
0
(
1
)
part 1 of 3
5/2
+
11/2
-
5/2
+
9/2
+
9/2
+
1/2
+
7/2
+
7/2
+
3/2
+
1
3
7
1
 
2
.
1
(
4
)
2
0
1
6
 
3
.
3
(
4
)
2
0
4
 
5
.
6
(
7
)
1
5
5
1
 
1
3
(
2
)
7
3
7
 
2
.
9
(
3
)
9
0
6
 
0
.
6
(
4
)
3
7
0
 
1
.
4
(
5
)
9
1
 
4
.
2
(
5
)
1
2
2
5
 
1
.
1
(
7
)
1
0
7
2
 
6
.
5
(
2
)
1
0
3
9
 
1
0
(
1
)
3
9
2
 
7
(
1
)
6
4
7
 
6
(
1
)
1
4
6
1
 
1
0
(
1
)
4
4
9
 
?
 
0
.
5
8
5
1
 
2
(
1
)
6
7
2
 
6
.
1
(
2
)
9
9
7
 
?
 
0
.
5
 
1
0
5
6
 
1
.
8
(
4
)
2
8
0
 
2
.
8
(
5
)
1
3
4
8
 
1
.
0
(
7
)
5/2
+
11/2
-
5/2
+
9/2
+
9/2
+
1/2
+
7/2
+
7/2
+
3/2
+
Sb
113
51
0
645
814
1019
1181
1257
1348
1461
1551
2094
2115
2132
2172
8
7
5
 
2
.
4
(
3
)
1
3
5
8
 
3
.
4
(
5
)
9
1
5
 
4
.
9
(
4
)
1
1
5
3
 
4
.
6
(
4
)
5
8
1
 
2
.
7
(
3
)
1
4
4
9
 
5
.
3
(
4
)
2
1
1
5
 
1
0
(
1
)
1
3
0
1
 
1
0
.
2
(
4
)
1
0
9
6
 
1
3
.
3
(
5
)
9
3
4
 
4
.
6
(
5
)
1
3
1
7
 
1
0
.
1
(
7
)
2
0
9
4
 
1
3
(
1
)
2
1
3
2
 
1
.
4
(
2
)
2
1
7
2
 
1
.
7
(
5
)
7
1
1
 
2
.
6
(
4
)
8
7
4
 
2
.
2
(
3
)
1
2
4
1
 
7
.
8
(
5
)
1910
2055
part 2 of 3
5
4
3
 
<
0
.
5
1
3
1
7
 
1
0
.
1
(
7
)
Figure 5.7: Proposed level scheme for 
113
Sb (in thre parts for clarity), showing levels
populated following the ?
+
/EC decay of 
113
Te. In the upper portion of the schematic is the
decay scheme for the lower energy levels, and in the lower portion is the decay scheme
for the higher energy levels.
121
0
645
814
1019
1181
1257
1348
1461
1551
1717
2381
2535
2608
2922
2619
2682
2964
2757
2845
5/2
+
11/2
-
5/2
+
9/2
+
9/2
+
1/2
+
7/2
+
7/2
+
3/2
+
2
3
8
1
 
3
.
5
(
7
)
Sb
113
51
3067
1
5
6
7
 
4
.
9
(
4
)
1
8
9
0
 
6
(
1
)
2
5
3
5
 
8
(
2
)
1
9
6
3
 
2
.
1
(
1
)
1
7
2
1
 
6
(
1
)
1
5
1
6
 
7
.
4
(
3
)
2
6
0
8
 
1
3
(
3
)
1
8
0
5
 
2
.
9
(
2
)
2
6
1
9
 
1
2
(
2
)
1
3
5
4
 
0
.
9
(
6
)
1
5
8
9
 
4
(
1
)
part 3 of 3
1
7
3
8
 
5
.
0
(
5
)
2
6
8
2
 
6
.
1
(
5
)
2
0
3
7
1
.
7
(
6
)
2
1
1
2
 
1
.
7
(
4
)
2
7
5
7
 
6
(
2
)
1
8
6
8
 
1
0
.
9
(
5
)
1
6
6
3
 
6
(
1
)
2
9
2
2
 
1
.
9
(
5
)
1
3
8
5
 
1
.
9
(
2
)
1
5
7
6
 
9
(
1
)
2
2
7
7
 
1
.
1
(
6
)
1
9
4
5
 
3
.
1
(
5
)
1
7
8
3
 
1
.
8
(
4
)
1
7
4
1
 
3
.
6
(
6
)
2
9
6
4
 
1
.
7
(
3
)
1
2
0
5
 
4
.
9
(
6
)
2
4
2
2
 
1
.
9
(
3
)
2
0
4
8
 
8
.
3
(
7
)
1
9
0
3
 
2
.
0
(
5
)
7
6
6
 
1
.
9
(
5
)
1853
Figure 5.7: 
113
Sb level scheme continued.
There are several interesting features for the level schemes presented in Fig. 5.7.
The first involves the spin and parity asignments for the levels at 1019 and 1181 keV.
Wigmans et al. reported only a single ? ray that depopulated the level at 1019 keV
[Wi76]. As previously mentioned in section 5.2, there were discrepancies for the
implications of what spin and parity were asigned for this level, asuming a 7/2
+
 ground
state for 
113
Te. As shown in Fig. 5.7, analysis of the data obtained in this study places a
374-keV transition from the 1019-keV level to the 1/2
+
 state at 645 keV. If the spin and
122
parity asignment of the 1019-keV level is 5/2
+
, then the relative intensity of the 374-keV
? ray would be expected to be <0.4% of the intensity of the 1019-keV ? ray. However, if
the spin and parity asignment for the 1019-keV level is 3/2
+
, which is the proposed
asignment, then the observed intensities for the transitions depopulating this level would
be consistent with expectations of two M1 transitions.
The level at 1181 keV only populates the 5/2
+
 ground state, and shows significant
?
+
 feding. The lack of a transition from this state to the 1/2
+
 level suggests that this level
has a J
?
 > 5/2
+
. The 1181-keV state is populated by the 1461- and 1551-keV levels which
have spins and parities of 9/2
+
 and 5/2
+
, respectively. The 280-keV ? ray that populates
the 1181-keV level has an intensity of 2.8(5). The relative intensity of this transition to
that to the ground state transition would favor this as an M1 transition, thus suggesting a
spin and parity asignment of 7/2
+
 
for this level.
The spins and parities of the 1019- and 1181-keV levels also have implications
for the J
?
 of the 
113
Te parent. As previously mentioned, it is believed that the ground state
spin and parity of 
113
Te is 7/2
+
; however, as there is intense ?
+
 feding to both the 1019-
and 1181-keV levels, the more likely asignment is 5/2
+
; as a 7/2
+
 would not show
significant, if any, ? transitions to the 3/2
+
 level at 1019 keV.
Another feature of the 
113
Sb level schemes presented in Fig. 5.7 is that there are a
considerable number of states above 2.0 MeV that cascade into the lower-energy levels.
This type of phenomenon was discussed in 4.5, and described by Kisinger and Sorensen
as even-jumping [Ki63]. A detailed schematic of even jumping for 
113
Te is shown in Fig.
5.8.
123
?d5/2?d5/2?d5/2
Valence Nucleons
EC/?
+
Q
EC
 = 6.1 MeV
113
Te
?g7/2?g7/2 ?d5/2
Gamow-Teller
    Transition
?d5/2?d5/2?d5/2
?d5/2?d5/2?d3/2
Configuration 
     Mixing
<?
i
|?
j
>
J
? 
= 3/2
+
, 5/2
+
, 7/2
+
113
Sb
?g7/2?d5/2?g7/2
?g7/2?g7/2
3 Quasi-particle 
        States
?d3/2
?d5/2
?d5/2?d5/2
?d3/2
or
OR
OR
Figure 5.8: Even jumping schematic for the ?
+
/EC decay of 
113
Te.
As shown, there is a single unpaired  d
5/2 
neutron and a pair of either d
5/2 
or g
7/2 
protons in
113
Te. For ?
+
/EC decay to occur, the pair of valence protons must be broken, and then one
of the d
5/2 
protons can decay via a Gamow-Teler transition to either a d
3/2 
or d
5/2 
neutron
or one of the g
7/2 
protons can decay to a g
7/2 
neutron. The remaining 3-particles could
have a ?g
7/2
?d
5/2
?g
7/2
, ?d
5/2
?d
5/2
?d
3/2
, or ?d
5/2
?d
5/2
?d
5/2
 3-quasi-particle configuration
with J
?
 = 3/2
+
, 5/2
+
, or 7/2
+
. These states wil then mix with the other core-coupled states
to form levels with highly mixed configurations above 2.0 MeV. As shown in the level
schemes in Fig. 5.7, there are 16 levels above 2.0 MeV that are fed via ?
+
/EC decay.
Most of these levels populate several low-energy states with a range of spins and parities
suggesting that their configurations are quite mixed, which would be expected if the
124
decay of 
113
Te to levels above 2.0 MeV could be described as an even-jumping
phenomenon.
5.6 Transfer Reaction Data
The 3/2
+
 and 7/2
+
 asignments for the levels at 1019 and 1181 keV, respectively,
were not only deduced from the spins and parities of the levels which populate, and are
fed by this state, but also by analysis of data that was obtained from a 
112
Sn(?,t)
113
Sb
transfer reaction study by Schifer et al. [Sc04].  Transfer reaction studies are useful for
probing the structure of nuclides because the outgoing particles generaly show
pronounced resonances corresponding to discrete energy states populated in the product
nucleus. In addition, the angular distributions of the outgoing particles are peaked in the
forward direction and have a shape indicative of orbital angular momentum transfer, thus
it is possible to constrain the spins and parities of these excited states. The transfer of a
single-nucleon is selective; therefore the cross sections are proportional to the extent to
which the state is single-particle in character.
Shown in Fig. 5.9(a) is an energy spectrum that was collected for the outgoing
triton in the (?,t) transfer reaction on 
112
Sn. To acount for the conservation of
momentum in the center of mas reference frame, the triton energy spectrum was
converted into an excitation spectrum for 
113
Sb, as shown in Fig. 5.9(b). Of note is that
the largest peaks are at ~0, 0.8, and 1.3 MeV. The configurations of these levels are
dominated by the d
5/2
, g
7/2
, and h
11/2 
single-particle states, respectively.
125
0
100
200
300
400
500
21 21.5 22 22.5 23 23.5
3
H Energy (MeV)
0
100
200
300
400
500
0 0.5 1 1.5 2
113
Sb Excitation Energy (MeV)
C
o
u
n
t
s
(a)
(b)
Figure 5.9: In (a) is the triton energy spectrum taken at ? = 6
o
 following the (?,t) transfer
reaction on 
112
Sn. By switching to the center of mas reference frame and correcting for
conservation of momentum, an excitation spectrum for the states populated in 
113
Sb could
be constructed as shown in (b).
There are also smaler peaks ~1.0, 1.2, and 1.5 MeV, which correspond to the
states at 1019, 1181, and 1551 keV, respectively. The spin and parity asignment for the
1019-keV state is 3/2
+
 as discussed in 5.5, thus should show significant l = 2 transfer. If
the 7/2
+
 asignment for the 1181-keV level is correct, then the angular distribution for
this ? ray should be consistent with an l = 4 transfer. The 5/2
+
 asignment for the level at
1551 keV is wel-established by both transfer reaction and ?
+
/EC studies [Co68,Wi76].
1018:d
5/2
1018:g
7/2
Detection Angle (?)
R
a
t
i
o
 
o
f
 
C
o
u
n
t
s
0.15
0.25
0.35
0 5 10 15 20 25 30
0.2
0.3
0.4
0 5 10 15 20 25 30
1181:d
5/2
1181:g
7/2
Figure 5.10: Comparison of the angular distribution ratios of the (a) 1019- and (b) 1181-
keV peaks with respect to the d
5/2 
and g
7/2
.
126
Shown in Fig. 5.10 are two plots that show the angular distribution of the ratio of
counts for the (a) 1019- and (b) 1181-keV peaks with respect to the counts of the peaks
asociated with the d
5/2 
and g
7/2
. In Fig. 5.10(a), the 1019:d
5/2 
count ratio (?
2
 = 1.29) is
more nearly constant than that of the 1019:g
7/2 
ratio (?
2
 = 17.23), suggesting that the 1019
level is populated by the l = 2 transfer. As the l = 2 transfer implies states with 3/2
+
 and
5/2
+
, the previous asignment of 3/2
+
 for this level based on ?-feding and ? de-excitation
is plausible. In Fig. 5.10(b), the 1181:g
7/2 
count ratio (?
2
 = 2.38) is slightly more constant
than that of the 1181:d
5/2 
ratio (?
2
 = 2.51), though the data are not as conclusive for
deducing the type of l-transfer as that shown in Fig. 5.10(a). As the angular distribution
of the 1181-keV ? ray shows no discernable preference for either the l = 2 or l = 4
transfers, the data shown in Fig. 5.10(b) do not validate or disprove the 7/2
+
 asignment
for this level suggested from the ?
+
/EC-decay of 
113
Te.
The configuration of the 1019-keVstate should have two main components: the
d
3/2 
single-particle component and d
5/2
?2
+
 single-particle-core component. As the level at
1019 keV shows significant l = 2 transfer (20% as intense as the d
5/2
 ground state), the
wave function does show a significant portion of the expected d
3/2 
strength. What is
known, is that the unmixed d
3/2 
level would lie betwen 2.9 MeV as in 
101
Sb and 1.4 MeV
as in 
133
Sb. That a strong l = 2 transfer to a single-particle state in this transfer reaction is
is not observed is logical as its strength is not localized, but mixed unequaly betwen
several levels above 2.0 MeV, as sen by Conjeaud et al. for  
117,119
Sb .
The configuration of the 7/2
+
 level at 1181 keV also has two main components: a
g
7/2  
single-particle component at 814 keV, and a particle-core d
5/2
?2
+
 component. As the
127
intensity of the 1181 keV peak in Fig. 5.9(b) is ~10% of the intensity of the 814 keV
peak, it is not likely that there is much mixing of this level with the g
7/2
.
5.7 Level Systematics for the Od-A Sb Isotopes Near the N = 64 Subshel Gap
As the spins and parities of the 1181- and 1019-keV levels in 
113
Sb, and low-spin
levels in 
111
Sb have been identified, it is possible to discuss trends in the positions of the
low-spin levels below 2.0 MeV. Shown in Fig. 5.11 are the systematic trends for the low-
spin levels below 2.0 MeV for odd-A Sb isotopes with 109 ? A ? 123. Several features
are of interest as pairs of neutrons are added from 
109
Sb to 
123
Sb. The ground states of al
these nuclides are al 5/2
+
 up to 
121
Sb because of the spherical ?d
5/2 
orbital. One of the
most striking features in Fig. 5.10 is that of the downward shift of g
7/2 
states relative to
the d
5/2 
ground states as soon as additional neutrons are added to 
115
Sb. 
115
Sb is localy
stable, having a semi-magic number of neutrons of N = 64. This monopole shift of the
g
7/2 
level continues until it eventualy becomes the ground state for odd-A Sb nuclides
with A ? 123, while the d
5/2
 single-particle level
 
continues upward in energy until it
reaches 
135
Sb.
The 1/2
+
 level corresponds to a state whose configuration ?d
5/2
?2
+
, that is, this is
the single-particle d
5/2 
proton coupled to the first phonon excitation of the adjacent Sn
core. This coupling is ilustrated in Fig. 5.11. As shown, there is a direct relationship with
the positions of the 1/2
+
 levels and the trends in the 2
+
 energies of the adjacent even-even
Sn cores. The behavior of the 3/2
+
 level is straightforward as its configuration is also
?d
5/2
?2
+
. The 3/2
+
 states follow the trend in the shifts of the 2
+
 energies in the Sn cores;
128
and both the 1/2
+
 and 3/2
+
 levels increase in energy as the position of the d
5/2 
single
particle level shifts up in 
123
Sb.
0
500
1000
1500
2000
2
1
+ 
energies in adjacent even-even Sn core
E
n
e
r
g
y
 
(
k
e
V
)
109
Sb
111
Sb
113
Sb
115
Sb
117
Sb
119
Sb
d
5/2
d
5/2
d
5/2
d
5/2
d
5/2
d
5/2
g
7/2
g
7/2
g
7/2
g
7/2
g
7/2
g
7/2
h
11/2
h
11/2
h
11/2
h
11/2
h
11/2
g
9/2
g
9/2
g
9/2
g
9/2
g
9/2
3/2
+
3/2
+
3/2
+
3/2
+
3/2
+
3/2
+
1/2
+
1/2
+
1/2
+
1/2
+
1/2
+
1/2
+
9/2
+
9/2
+
9/2
+
9/2
+
9/2
+
11/2
+ 11/2
+
11/2
+
11/2
+
11/2
+
121
Sb
g
7/2
h
11/2
h
11/2
g
9/2
3/2
+
1/2
+
11/2
+
11/2
+
123
Sb
g
7/2
d
5/2
h
11/2
g
9/2
3/2
+
1/2
+
9/2
+
11/2
+
9/2
+
9/2
+
7/2
+
7/2
+
Figure 5.11: Experimental level systematics for the odd-A Sb isotopes from A=109 to
A=123.Lines are drawn to guide the eye.
As for the high-spin states, the 7/2
+
, 9/2
+
 and 11/2
+
 levels shown in Fig. 5.11
correspond to the core-coupled ?d
5/2
?2
+
 and ?g
7/2
?2
+ 
states, respectively. The weakly
coupled 7/2
+
 and 9/2
+
 (pink) states follow the trends of the 2
1
+
 energy of their adjacent Sn
cores, until 
111
Sb is approached. As the Sb isotopes become more proton-rich, these state
drifts away from the phonon.  The 11/2
+
 states show the same trends as the 2
+
 energies
from 
115
Sb to 
121
Sb; however, below A=115, the 11/2
+
 state starts to shift several hundred
keV away from the phonon. This upward shift could be a result of increased mixing with
the other 11/2
+
 state that results from the g
7/2
?2
+
 coupling. As for the g
9/2 
intruder states,
129
they are at their lowest in 
121
Sb, where at that point, the ?h
11/2 
orbital is exactly half full.
Here the low-k orbitals are full, while the high-k orbitals are empty.
The positions of the levels shown in Fig. 5.11, are consistent with expectations
from both the low-mas and mid-mas odd-A Sb nuclei. Though the positions of most of
the levels vary smoothly betwen 
109
Sb and 
121
Sb, it is clear that there is not symmetry
with the position of al the states in 
113
Sb and 
117
Sb, both which are two neutrons away
from the shel closure at N = 64 in 
115
Sb. Though thirten nucleons outside of 
100
Sn, this
could suggest that the excitations in 
113
Sb are more single-particle in character, and that
the collective behavior for 
115,117,119
Sb is diminishing quickly as 
101
Sb is approached.
5.8 Sumary and Outlook
The ?
+
/EC and ? decay of 
113
Te to low-spin levels of 
113
Sb has been studied using
sources produced via recoil separation of the products of a heavy-ion reaction.  Several
new levels were identified, and the ambiguities with the spins and parities of the 1019-
and 1181-keV levels have been determined as 3/2
+
 and 7/2
+
, respectively. The spins and
parities of these two levels now provide evidence for the asignment of 5/2
+
 for the
ground state of 
113
Te instead of the previously suggested J
?
 of 7/2
+
.  The low-energy level
structure of 
113
Sb is consistent with systematic expectations from mid-mas, collective
odd-A Sb isotopes; and the levels of this nuclide show smooth shifts in positions as the
low-mas, single particle odd-A Sb isotopes are approached. The level density and ?-
feding to the high-energy states above 2.0 MeV in 
113
Sb provide more evidence for the
even-jumping concept previously mentioned for 
111
Sb. Currently, neither single-particle
models or those which consider collective core-particle coupling have been used to
130
reproduce the observed level structure for 
113
Sb. However, this nuclide would provide a
perfect opportunity to compare the two approaches, as its level structure is consistent
with the single-particle behavior of 
109,111
Sb and the more collective structures of
115,117
Sb.
131
Conclusions
Several types of data were collected in the experiments at ISOLDE and Argonne
National Laboratory. These data are important to both the fields of nuclear structure and
astrophysics. The low-energy level structure of 
134
Sb is useful to theoreticians because it
can be used to beter estimate the strengths of the nucleon-nucleon interactions outside of
132
Sn. Currently, these nucleon-nucleon interactions are obtained from a mas region that
is 76 nucleons higher in mas, therefore our recent data might provide a beter starting
point for the development of new nucleon-nucleon interactions in the A~132 mas
region. 
135
Sb is currently the heaviest nuclide outside of 
132
Sn for which extensive level
structure data have been obtained. Though it is only thre nucleons away from 
132
Sn, the
positions of the low-spin levels indicate that the previous notion of a change in the shape
of the nuclear potential as the neutron dripline is approached, might be occurring for a
smaler N/Z ratio than expected. If indeed the nuclear surface is changing, then these data
provide a starting point for the development of potentials that can be used for level
structure calculations of more exotic nuclides.
The measured decay properties of 
135-137
Sn have already been used in r-proces
calculations. By using measured instead of extrapolated T
1/2 
and P
n
 values for these
nuclides, other physical parameters that afect the results of the r-proces abundance
curve predictions can be identified or further constrained. These data can also be used to
estimate the T
1/2 
and P
n
 values for nuclides even farther from the beta valey of stability,
as it is likely that the nuclear structure that afects the decay properties of 
135-137
Sn wil
also have an efect on the more exotic nuclides in the same mas region.
132
Finaly there are the data on the proton-rich side that were obtained for 
111
Sb and 
113
Sb.
The low-spin states identified in these nuclides are useful for understanding the trends in
the positions of the states as the N = 82 shel is filed. Though experimental data have not
been obtained for the positions of similar low-spin states in 
101
Sb, shel model
calculations that show predictive power out to 
111
Sb indicate that previous estimates for
the single-particle energies of the low-l orbitals could be too high. As the odd-A Sb
nuclides are the heaviest chain of isotopes which can be used to probe the changes in
structure across an entire shel, use of this new data to beter identify the positions of
these single-particle orbitals have great significance for more global calculations.
133
Apendix A: ISOLDE, CERN
A.1 ISOLDE, CERN Facility
At ISOLDE (se Fig A.1), radioactive nuclides are produced in thick high-
temperature targets via spalation, fision, or fragmentation reactions. The targets are
placed in the external proton beam of the Proton Synchrotron Booster (PSB), which has
an energy of either 1.0 or 1.4 GeV and intensities ~2 ?A. The target and ion-source
together provide the necesary selectivity for converting specific nuclear reaction
products into a radioactive ion beam. The instruments in the ion source that make it
possible to study exotic nuclei are the thre copper-vapor pumped dye lasers that are used
for resonance excitation and ionization. An electric field acelerates the ions, which are
mas separated and stered to the experiments using either the General Purpose Separator
(GPS) or the High Resolution Separator (HRS). Currently, as many as 600 isotopes of
more than 60 elements (Z=2 to 88) have been produced with half-lives in the milisecond
range and intensities up to 10
11
 ions/s.
A.2 Proton Synchrotron Booster
The production of exotic radioactive nuclei at ISOLDE begins with the
production of high-energy protons acelerated at the PSB. The PSB is a stack of four
synchrotrons that are used to acelerate protons to energies of 1.0 to 1.4 GeV prior to
injection of the protons into the CERN Proton Synchrotron (PS). The protons acelerated
by the PSB are pre-acelerated by a Linac, and injected into the PS every 1.2 seconds.
134
Figure A.1: Facility Layout of ISOLDE, CERN.
Each pulse contains as many as 3.2 ? 10
13
 protons, and ISOLDE can take up to half of the
proton pulses per 14-pulse supercycle as available, depending on the experimental needs
of other concurrently running experiments at CERN. The above quantity of protons and
frequency with which they are extracted yield a maximum of ~2 ?A dc beam to the
ISOLDE facility. The acelerated protons from the PSB are delivered to the ISOLDE to
either the GPS or HRS target areas.
135
A.3 Target and Ion Source
A.3.1 Target and Neutron Converter
There are many types of targets from which to choose at ISOLDE. For the
investigation of short-lived species, an ideal target would be one that had the highest
production cross section with high-energy particles, had instantaneous liberation of the
radioactive nuclei of interest from the target, and would be impervious to temperatures
exceding 2000? C. UC
2
 is used as a target for the experiments involving nuclei in the
A~135 mas region because it has a high fision production cross section for these
Figure A.2: Schematic of the UC
2
 target and neutron converter.
W neutron-converter
UC
2
 target
HT-oven electrical connections
NeutronsProtons
Ion-source
136
nuclides, difusion of Sn from this material happens on the order of a few ms, and the
material is durable enough to withstand the high currents necesary for difusion of
species out of the target, in addition to the constant bombardment with high-energy
protons or neutrons.  A schematic of the target/ion source is shown in Fig. A.2.
As mentioned, using high-energy neutrons to bombard the target instead of
protons increases the ratio of neutron-rich fision nuclei to proton-rich species produced
by spalation. The neutron converter is a W rod that absorbs the 1.0 or 1.4 GeV proton
pulse, and via a (p,xn) reaction, releases high-energy neutrons, which then strike the UC
2
target. The one disadvantage of using the neutron converter is that the emited high-
energy neutrons subtend a smal solid angle of the surface area of the UC
2
 target, thus the
net fision production yields of the nuclides of interest is decreased.
A.3.2 Laser Ionization System
The primary reason for studying the decay of neutron-rich nuclei at ISOLDE is
that the Resonance Ionization Laser Ion Source (RILIS) provides the needed selectivity to
suppres the large amounts of isobaric contamination that can render impossible the
detection of exotic species in what are usualy overwhelming backgrounds present in
plasma ion sources. The technique of resonance ionization was first investigated at the
Geselschaft f?r Schwerionenforschung (GSI) in Darmstadt, Germany. Though a RILIS
system was not constructed for the purpose of performing nuclear physics experiments at
GSI, initial development of the technique influenced Profesor Kratz at the Universit?t
Mainz to investigate the possibility of using this technique to enhance the fision
production yields of exotic neutron-rich species far from stability. Throughout the 1990s
137
a lot of research and funding were used to develop the present day RILIS at ISOLDE,
CERN.
The purpose of the laser ionization system is to chemicaly select one element
from the reaction products that are produced in the UC
2
 target. The selectivity of the laser
ion source relies on the fact that each element has a unique atomic structure. By tuning
lasers that correspond to energies of atomic states specific for a certain element, it is
possible to selectively ionize atoms with a specific Z. The laser ionization system (se
Fig. A.3) consists of thre copper-vapor lasers, tuneable dye lasers, and non linear
crystals for frequency doubling or tripling offering the possibility for the most eficient
two or thre step ionization. Ionization of the elements that have difused out of the target
is achieved by tuning the lasers to two atomic resonant excitations for an element with a
specific Z, and a third laser is used to ionize the species into the continuum or to an auto-
ionizing state.
Figure A.3: Schematic of the Laser System at ISOLDE, CERN.
138
A.4 Mass Separators
Ions are extracted from the target/ion source using a 60 kV potential into one of
two isotope separators (se Fig. A.1) that are used to purify beams at the ISOLDE PS-
Booster facility. The first separator, the GPS, has the advantage of alowing thre
simultaneous beams within a mas range of ?15% to be selected and delivered to
diferent counting stations within the experimental hal. The GPS separator has one
double focusing H-magnet with a bending angle of 70? and a mean bending radius of 1.5
m. The mas resolving power  (M/?M) is estimated to be ~2400. The second separator,
the HRS, has a much beter mas resolution (M/?M = 5000) because ions travel through
two bending C-magnets with bending angles of 90? and 60?, respectively. Though the
HRS has a much beter resolution, it can only deliver one mas beam to the experimental
stations at a time.
A.5 Ion Implantation and Data Acquisition
After traveling through the separator, radioactive ions are focused and implanted
into an Al-coated mylar tape that is positioned such that the deposition spot is located in
the center of one of two detector arays (se section A.5.2). One aray consists of a
concentric aray of sixty 
3
He gas-filed proportional counters used to detect beta-delayed
neutrons. The other aray consists of a combination of Ge detectors and plastic
scintilators to detect ? rays and ?
?
 particles, respectively.
139
A.5.1 Tape Station and Timing Module
The 35 m Al-coated mylar film where the ions are implanted is threaded on a
track of spools and moves back and forth betwen two separate rels inside a moving
tape collector (MTC). The MTC, is mounted directly to the beam flange, is made of
aluminum, and is kept under high vacuum (~10
-7
 torr) to alow transmision of the
radioactive beam to the deposition spot. The primary function of the MTC is to move the
longer-lived radioactivity from the implantation spot following data collection.
Movement of the tape is necesary because the radioactive nuclides studied in the heavy
Sn decay experiments (chapters 2,3) have significantly shorter half-lives than their
daughters, granddaughters, or surface ionized species. Therefore, by moving the longer-
lived radioactivity away from the counting station, it is possible to minimize the buildup
of a large background in various spectra. Movement of the tape is acomplished using a
step motor that is controlled with a custom-built tape-control module. The timing of the
tape-control module is determined by software which controls a master timing module
that wil be described in more detail in section A.5.3.
A.5.2 ?-?, and Neutron Detector Arays
Two detector arays are used, one at the end of a separate beam line, each for
either beta-delayed neutron or ? spectroscopy. The detector aray (Fig. A.4) used to count
beta-delayed neutrons consists of sixty 
3
He gas-filed proportional counters. These
detectors are encased in parafin to moderate the neutrons to thermal energies, and this
alows for higher detection eficiency. Signals for the detection of neutrons are generated
by collecting a charge pulse produced by ionization of the 
3
He gas which occurs when
140
positive ions from the n(
3
He,p)
3
H reaction disipate their energy in the gas-filed tube.
The voltage applied to the each tube in the 
3
He proportional counter is ~1300 V, and this
provides gains of up to a few thousand. On average, ~25,000 electrons are collected at the
anode per reacting neutron, and these electrons produce negative charge signals which
can then be amplified, procesed, and stored.
Polyethylene Moderator
3
He Gas detector Preamplifiers
Cylindrical detector wells
Opening for deposition tape and Ge detector
Figure A.4: The 
3
He gas-proportional counter aray. The 
3
He gas tubes are not shown,
but are inserted into the holes in the parafin.
The other aray  (Fig. A.5) consists of thre plastic scintilators and five HPGe
detectors. The scintilators are placed betwen the HPGe detectors and the implantation
site. These detectors are used to detect ?
?
 particles emited from the decaying parents.
The ?
?
 particles are detected when there is a collision betwen the incident particle and a
scintilating molecule. When the ?
?
 particle hits the scintilating molecule, which is
usualy a hydrocarbon, fre electrons are excited to ?-molecular orbitals. These
molecules rapidly de-excite by emiting photons or heat. These photons are then guided
141
to a photomultiplier tube for amplification via internal reflections of the photons inside
the scintilating material.
Reflection of the light inside the plastic scintilator is possible because this
material has a very high index of refraction (n = 1.49?1.51). Wrapping the plastic
scintilator in Al foil enhances the probability of internal reflections for the photons. In
addition, the Al foil does not directly have contact with the scintilator, which alows a
thin layer of air with n = 1.0 to surround the detector. The diferences in refractive indices
betwen the air and the scintilator reflection of the light inside the detector. The
scintilator and foil are then wrapped in black tape to prevent light from outside the
detector reaching the photomultiplier tube  (PMT) from which the electronic signal is
taken.
Figure A.5: Aray of plastic scintilators and HPGe detectors used at ISOLDE.
MTC
Beam
HPGe detectors
142
The PMT generates a useful electronic signal by converting the photons emited
by the scintilator into electrons. These electrons are produced when light from the
scintilator strikes the photocathode located at the end of the PMT, and causes emision
of photoelectrons, which are then atracted to the anode. Prior to reaching the anode, the
electrons hit a series of dynodes that increase the number of electrons that reach the
anode as each dynode induces the emision of more electrons.  After a series of about 8-
12 dynodes, the gain in electron number is ~10
7
 for a typical PMT. The pulse height at
the anode is proportional to the amount of light produced inside the scintilator, which in
turn is proportional to the amount of energy deposited in the scintilator by the beta
particle.
In addition to the plastic scintilators, there are five high-purity germanium
(HPGe) detectors (also known as intrinsic germanium detectors) in the aray (Fig. A.5)
that are used to detect ? rays asociated with the de-excitation of the ?-decay daughters.
The HPGe detector belongs to a clas of detectors known as solid-state semiconductors.
HPGe detectors have the advantage of providing high-energy resolution and good
eficiency. The principle behind the semiconductor detector is that Ge crystals have a
band structure that is divided into the valence and conduction bands. The diference
betwen these bands, or band gap, is about 0.66 eV, thus it is possible at room
temperature to promote electrons from the valence band to the conduction band,
therefore, Ge crystals are cooled to 77 K with liquid nitrogen when in use.
When a ? ray hits the cooled crystal, enough energy may be deposited so that an
electron is promoted from the valence band to the conduction band, and an electron-hole
pair is created. The number of electron-hole pairs created is proportional to the energy of
143
the incoming ? ray. The electron and the hole migrate through the crystal to the cathode
and anode under the influence of an externaly applied potential, and creates an electric
signal that can be used to detect the presence of the pasing radiation.
HPGe detectors are characterized acording to their resolution (FWHM),
eficiency, and peak-to-Compton ratios. Resolutions are usualy reported as the FWHM
of the 1332 keV peak from the decay of 
60
Co. The resolutions for the five detectors used
averaged ~1.7 keV. Eficiencies for HPGe detectors are measured relative to a standard
detector that is taken as a 3 X 3 inch cylindrical NaI(Tl) crystal for a source 10 inches
from the detector. The larger the crystal, the beter the detection eficiency. The five
HPGe detectors used in this experiment al had an eficiency ~65%. The peak-to-
Compton ratio refers to the number of counts in the 1332 keV 
60
Co peak compared to a
number of counts in a selected region of the Compton continuum. The higher the value,
the beter, though most HPGe detectors have a value of ~50 for this parameter.
A.6 Data Acquisiton
The electronic signals produced by al of the detectors in both arays are
converted into useful information by a series of modules that manipulate the signals for
data procesing and storage. In each of the arays, the amount of data being procesed can
be filtered using Boolean logic and timing constraints to enhance the quality of the
diferent types of spectra.
144
A.6.1 ?dn-Decay Data
In the 
3
He detector aray, negative charge signals from al of the gas detectors are
amplified using a custom-built preamplifier, and the number of events per unit time for
each detector is stored in a Canbera 2015A Single Channel Analyzer. The data from the
single channel analyzers are consolidated using a custom-built module, constructed at the
Universit?t Mainz. This module groups data as a function of detector position inside the
aray. A total of four 1024-channel spectra are acumulated, which correspond to the
integral counts taken from the inner ring of detectors, the middle ring of detectors, the
outer ring of detectors, and the total integration of the thre rings. The data are then
stored in an Ortec 7884 analog to digital converter (ADC). The data in the ADC are
observed in real time using the MC-Win spectroscopy analysis program.
Data collection in this aray is triggered by use of the master timing module
mentioned in A.5.1. The master timing module controls the beam gate of the separator,
the data acquisition software, and the MTC. The master timing module is triggered by a
signal that starts when the proton pulse is extracted into the ISOLDE facility. Following
the initial proton pulse, the following sequence of events occurs before the subsequent
pulse hits the target: the beam gate opens to alow transmision of radioactive beam, the
beam gate closes to reduce buildup of longer-lived nuclides, data acquisition starts, data
acquisition stops, and then the tape is moved to move longer-lived radioactive nuclides
away from the point of implantation. The data collected in this aray are used for
measuring the half-lives (T
1/2
) and ?-delayed neutron probabilities (P
n
 values) of neutron-
rich radioactive nuclei.
145
A.6.2 Data Collection in the ?-? Detector Aray
Data collection in the ?-? detector aray involves more extensive signal filtering
and procesing than that obtained in the ?dn-detector aray, mainly because of the
complications that arise with the timing signals. At ISOLDE, two data acquisitions are
taken from the ?-? detector aray for both on- and off-line analyses. The primary purpose
of the on-line analysis is to monitor the experiment to make sure that radioactive species
of interest are being produced, ionized, and deposited on tape at the end of the MTC. On-
line data are analyzed using the Interwinner program for comparison of laser on and laser
off ?-singles spectra. In addition, the events are recorded as a function of time relative to
the signal from the proton pulse. This alows for the comparison of time-dependent
?-singles spectra to observe the growth and decay of peak intensities. A ?-singles
measurement is a determination of ? rays emited from a radioactive sample. The ?-
singles spectra in these experiments were calibrated using 
60
Co and 
152
Eu sources. The
energies and intensities of the peaks in the spectra asociated with the decays of these
nuclides are given in Table A.1. Both the detector energy calibration curves and detector
eficiency curves were fit to second order polynomials.
Table A.1: ?-Ray Energies and Intensities for Calibration Sources.
RadionuclideE? (keV) Intensity
152
Eu
121.8
28.4
152
Eu
244.7
7.51
152
Eu
344.326.6
152
Eu
778.913
152
Eu
964.114.5
152
Eu
1112.113.6
60
Co
1173.2
100
60
Co
1332.5
100
152
Eu
1408.020.8
146
Signals used for the on-line ?-singles data acquisition are procesed using only
two modules. The positive or negative signal from the HPGe detector (depending on the
polarity of the applied potential to the detector) is first amplified in a preamplifier that is
atached to the back of an Ortec 572 amplifier. The Ortec 572 module both amplifies and
shapes the incoming signal that is then input to the Canbera 8077 ADC where it is stored
acording to pulse height in a ??energy spectrum. The spectra are analyzed in real time
using the Interwinner spectroscopy program. The schematic for this acquisition system is
shown in Fig. A.6.
HPGe Detector
Ortec 572
Amplifier
Canberra 8077
       ADC
  Interwinner
Figure A.6: The electronics used in the on-line analysis of the ?-singles spectra.
The off-line part of the data analysis system was more complex, and was used for
collecting ?-singles, ?-? coincidence data, and ?-time data. The crucial data needed for
off-line analysis was that obtained in the ?-? coincidence measurements. ?-? coincidence
measurements are needed because the excited states in the daughter nucleus populated in
?-decay can decay to the ground state by the emision of succesive ? rays. In order to
determine which ? rays are emited in succesion, two or more detectors are placed
around the radioactive sample, and a ?-? coincidence event is recorded whenever two
events are observed in a pair of ?-ray detectors within a given time separation (~100 ns).
147
The type of information recorded per coincidence event include the energy of each ? ray
tagged with the detector in which it was observed, and the time that separated the
detection of the two ? rays. The advantage in using five detectors to measure coincidence
data is that roughly ten times as much data can be obtained than with a single pair of
detectors, depending on the geometry of the detectors.
Ortec 572
Amplifier
 474
   TFA
T
?
 signals
Ortec 474
   TFA
Ortec 474
   TFA
Ortec 474
   TFA
Ortec 474
   TFA
Ortec 584
   CFD
Ortec 584
   CFD
Ortec 584
   CFD
Ortec 584
   CFD
Ortec 584
   CFD
   from 
HPGe #1
   from 
HPGe #5
   from 
HPGe #4
   from 
HPGe #3
   from 
HPGe #2
Ortec 416
  G & D
Ortec 416
  G & D
Ortec 416
  G & D
Ortec 416
  G & D
Ortec 416
  G & D
HPGe Detector #1
HPGe Detector #2
HPGe Detector #3
HPGe Detector #4
HPGe Detector #5
Ortec 572
Amplifier
Ortec 572
Amplifier
Ortec 572
Amplifier
Ortec 572
Amplifier
Ortec 572
Amplifier
E
?
 signals
 Canberra 
     1446
Coincidence
       Unit
Delay
Delay
Delay
Delay
Delay
TPHC out
   Stored as
Listmode Files
Ortec 572
Amplifier
  Sil na 
  ADC
Ortec 572
Amplifier
  Sil na 
  ADC
Ortec 572
Amplifier
  Sil na 
  ADC
Ortec 572
Amplifier
  Sil na 
  ADC
Ortec 572
Amplifier
  Sil na 
  ADC
C
A
M
A
C
Ortec 572
Amplifier
  Sil na 
  ADC
TAC
E
? 
#1
E
? 
#2
E
? 
#3
E
? 
#4
E
? 
#5
out
Ortec 416
  G & D
  Level 
Adapter
{repeat for all   }
{detector pairs }
Ortec 567
    TAC
start
stop
Master 
 Gate
ECL 
Bus
Figure A.7: The electronics used in the five-detector ?-? measurements.
148
A diagram showing the electronics used for the five HPGe detectors for ?-?
coincidence measurements is shown in Fig. A.7. The energy signals obtained from the
HPGe detectors for off-line analyses are the same as used for ?-singles spectra as those
taken for the on-line analysis except that the signal from the amplifier is sent to an ADC
adapter which transforms the signal from an ECL signal to a TL signal, and then it is
stored in the Silena 4418 ADC prior to being sent to the data bus which then writes the
data to listmode files.
The same type of signal from each HPGe detector used to obtain ?-singles spectra
are also used to obtain timing information for each event. Time signal information is
crucial for building ?-? matrices, ?-time-matrices, and filtering out unwanted events to
reduce the background in various types of spectra. The same energy signal used in on-
line analysis from the Ortec 572 amplifier is input to an Ortec 474 timing filter amplifier
(TFA). The TFA shapes and amplifies the signal so that al of the output pulses have a
uniform pulse shape. The benefit of using a TFA to shape the detector signals is that this
module has a very fast procesing time. The output of the TFA is then sent to the Ortec
584 constant fraction discriminator (CFD) that operates as an integral discriminator for
al incoming signals. The CFD delivers a signal when a valid event in one detector has
occurred, and these timing signals are used to determine the logic of the coincidence
setup.
The positive outputs of the CFDs are fed into a Canbera 1446 coincidence
module that gives an output if at least two signals arive within a specified time span. The
output of the coincidence unit is then procesed by a gate and delay generator to provide
the master gate for the camac ADCs. The signals that are produced by the Ortec 572
149
TACs (se Fig. A.7) or the Ortec 572 amplifiers must then be adjusted to ensure that the
signals fal within the width of the master gate. The coincidence unit provides a start and
stop pulse to the Ortec 567 TAC betwen a pair of detectors (i.e. Ge #1 and Ge#2)
whenever a pulse arives at the start input from Ge #1 followed by a pulse at the stop
input from the Ge #2. To ensure that a detector cannot start and stop itself, an extra 64 ns
delay (denoted by paralel broken lines in Fig. A.7) is added to the start side of the timing
pulses from Ge#2 betwen the gate and delay generators and the coincidence unit. If a
start and stop pulse arive within the designated resolving time of the TAC, then the TAC
sends a 5 V coincidence enable signal to the Silena ADC, where it is stored as buffers.
The buffers are filed when 256 coincidence events have been acumulated. The data are
stored as listmode files, and later events are sorted and filtered using Fortran or C
+
programing codes. In addition to analysis of the ?-singles spectra, the codes are
primarily used to generate ?-? and ?-time matrices. These matrices are then used to
generate ?-gated coincidence spectra with programs such as DAPHNE or PAW.
150
Apendix B: Argonne National Laboratory
B.1 Argonne National Laboratory Facility
At Argonne National Laboratory, heavy-ion reactions are used to produce exotic
nuclei on both sides of the beta valey of stability. Beams of elements up to U can be
acelerated to as high as 17 MeV per nucleon using the Argonne Tandem Linac
Acelerator System (ATLAS) shown in Fig. B.1. The primary method of obtaining exotic
radioactive nuclei for study involves separating specific reaction channel products
following fusion-evaporation of the compound nucleus formed in the heavy-ion collisions
in the target chamber. Separation of reaction products of interest is achieved by using the
Fragment Mas Analyzer (FMA) that separates species based on their mas/charge (A/Q)
ratios. Experiments and data collection occur at the focal point of the FMA.
B.2 ECR Ion Source
Ion beams at ATLAS are produced using an electron cyclotron resonance (ECR)
source. The ECR source is a plasma device designed to provide highly-charged ions at
low velocities. Before ions can be created in the ECR source, atoms must be in a gaseous
state. For metals, this is achieved by the use of an extremely hot oven. Once the atoms are
vaporized, a magnetic field created by a hexapole magnet confines the gas long enough to
alow enough collisions with electrons (which are kept in motion using microwaves) such
that nearly fully-stripped ions can be extracted from the source. Ions are then acelerated
using a 12-MV low-velocity linac that injects ions into a 20 MV Booster linac that then
feds the 20-MV ATLAS linac.
151
Figure B.1: Facility layout of ATLAS.
B.3 ATLAS
The ATLAS is a superconducting acelerator capable of acelerating projectiles
heavier than the electron up to U. The key elements in the ATLAS are the sixty-two
superconducting Nb split-ring resonators. These Nb resonators are cooled with liquid
helium and oscilate with radio frequencies of 97 MHz. The estimated potential
diference generated with this charge oscilation betwen each of the rings in each
resonator is ~0.8 MV. Ions that are injected into the ATLAS system gain energy by being
in phase with the electromagnetic waves produced in each resonator. The resonators are
aranged so that ions of a given velocity are acelerated and remain in phase with the
acelerating field. These velocities can be adjusted for each resonator by adjusting their
152
RF phases independently. Magnetic fields and solenoids are used throughout the ATLAS
linac to ster and focus the ion beams to the target area in one of thre experimental hals.
B.4 Fragment Mass Analyzer (FMA)
Following the collision of the beam with the target in Target Area II (se Fig.
B.1), a variety of nuclides produced from diferent reaction channels are produced. As the
production cross section for exotic nuclei is usualy very smal compared to the main
reaction channels, the FMA is necesary to separate the nuclides of interest from the
beam. The FMA is a recoil mas separator used to separate nuclear reaction products
from the primary heavy ion beam and disperse them by their A/Q at the focal plane.
The components of the FMA (se Fig. B.2) include two magnetic quadrupoles, an
electric dipole, a magnetic dipole, another electric dipole, and two more magnetic
quadrupoles. The first pair of magnetic quadrupoles is used for focusing the recoils into
the FMA. A pair of quadrupoles is used for providing focusing in both the x and y planes.
The ions are then pased into the first electrostatic dipole that separates the ions by
energy to charge (E/Q) ratios using curved electrodes. The electrostatic dipole is set such
that the species of interest pases through the center of the apparatus. Next, further beam
purity is achieved by alowing ions with a specific momentum to charge (p/Q) ratio
through the magnetic dipole. The ions are again dispersed based on their E/Q ratios, and
the ions which exit the FMA are focused with another pair of magnetic quadrupoles to
the focal plane of the apparatus where the detection of radiation occurs. A/Q separation is
possible using this apparatus because the magnetic dipole is tuned to counter the electric
dispersion of both electrostatic dipoles, so focusing becomes a function of A/Q.
153
Q1Q2 Q3 Q4
ED1
MD
ED2
target
Beam
Fragment Mass Analyzer
Focal Plane 
 Detectors
Figure B.2: Picture and Schematic of the FMA.
It should be noted that the FMA is kept under high vacuum (~ 10
8
 torr), and has an
estimated transmision eficiency of 10%. The mas resolution of the FMA is not as good
as the mas separators discussed in A.4 having a M/?M value of only ~350.
B.5 Focal Plane Detectors and Moving Tape Collector
Once the recoils are focused with the last pair of quadrupoles, they imediately
pas through a paralel plate avalanche counter (PAC). This gas-filed proportional
counter is used at the focal plane of the FMA to measure the ion energy and position of
the recoils.  The PAC consists of two crossed wire planes within isobutene gas (se Fig.
154
B.3). An anode and cathode plate is placed on either side of the x-wire plate, and a
voltage is applied to the plates to create an electric field betwen the anode and cathode
plates. Similar to the 
3
He gas proportional counters (se A.5.2), the incoming ions fre
electrons from the gas molecules that are then acelerated in the electric field, thus
freing more electrons producing an avalanche of electrons at the anode.
Figure B.3: Photo of PPAC.
The signal at the anode triggers the start of a time-to-digital converter (TDC).
Both the x and y wire plates are coupled to the anode; and their signals are delayed, and
used as stops to the TDC. It is possible to obtain position information on the event from
the time diference of the observed signals. The x-position of the actual event wil
produce a signal to the side that it is closer to in a shorter period of time. Therefore, by
taking the time diference betwen signals on the left and right of the detector, it is
155
possible to estimate its position. This information is coupled to the up and down
information from the y-plate, thus making it possible to obtain a two-dimensional beam
profile.
The PAC also can be used as a tool to filter out unwanted data. While the
electrons are acelerating towards the anode, the positive ions drift toward the cathode.
These positive ions near the cathode produce electrons that induce larger avalanches, as
the distance traveled by these electrons to the anode is larger. The number of ions formed
in the detector is proportional to the energy lost by the ions in the gas, so the energy loss
in the PAC can be extracted from the cathode signal. A software generated gate can be
placed on events that belong to low-energy recoils, so that events due to scatered beam
making it through the FMA can be vetoed in the data acquisition, thus filtering out a
higher percentage of useful events asociated with the recoils at the back of the FMA.
Before counting the radioactivity, the recoils are implanted into an Al-mylar tape
housed in a MTC. The MTC used at ATLAS is similar to the one described in A.5.1, with
a few diferences. Similar to the MTC used at ISOLDE, the tape is kept under high
vacuum. At ATLAS, the tape is moved using a step motor whose controls can be
triggered using an external pulse, which in this case was a periodic signal induced by a
timing module. The main diference betwen the two MTCs is that the radioactivity at
ANL is not implanted into the Al-mylar tape in the center of the detector aray. Instead,
the radioactivity is collected continuously for a period of ~ 2 to 3 times the half-life of the
species of interest to saturate the activity, and then moved to a location perpendicular to
the focal plane of the FMA for counting. The other diference with this MTC is the
mechanical design. The tape is spooled through a series of rollers which move the tape in
156
a continuous path which cycles inside the tape storage box that is also perpendicular to
the focal plane, but on the opposite side of the counting station to prevent unnecesary
background events.
Once the tape is moved to the detector aray, the radioactivity is counted using
four HPGe detectors and two plastic scintilators. The detector aray at ATLAS is
surrounded by Pb bricks to minimize the amount of background radiation hiting the
detectors from the MTC. The details of the operation of these detectors and the
procesing of these signals for data analysis are similar to those described in A.5-A.6.
One experimental diference from the setup at ISOLDE is that the electronic signals from
the detectors at ATLAS are patched to separate room for signal procesing. Data
collection at ATLAS involves ?-singles, ?-? coincidence, and ?-time measurements.
Similar to the data obtained at ISOLDE, ?-singles spectra are purged of unnecesary
background by gating on 180? ?-? coincidences and vetoing 0? ?-? concidences. The data
are writen to magnetic tape as listmode files. These files are then transfered to hard disk
and analyzed using PAW software.
157
Apendix C: Radioactive Decay and Statistical Eror
C.1 Radioactive Decay Proces
C.1.1 The Radioactive Decay Law
The radioactive decay law was established experimentaly by Rutherford and
Soddy. They determined that the activity of a sample decays exponentialy in time. For
example, suppose there is a sample of N nuclei. The mean number of nuclei decaying in a
time dt would be
? 
dN=??dt
, (C.1)
where N is the total number of nuclei and ? is the decay constant. Equation (C.1) can be
rearanged to give
? 
dN
N
=??t
, (C.2)
which after integrating and  rearanging becomes
? 
N(t)=N(0)e
(??t)
, (C.3)
where N(0) is the number of nuclei at t = 0. The exponential decrease in the activity of a
radioactive sample is governed by ?, which is related to the mean lifetime of the sample
by
? 
?
m
=
1
?
 . (C.4)
The mean lifetime is the time it takes for the sample to decay to 1/e of its initial activity,
but in nuclear physics, the rate with which a radionuclide decays is caled the half-life
(T
1/2
). The half-life is defined as the time it takes for a radioactive sample to decay to
one-half of its original activity. Use of 1/2 for N(t)/N(0) in Equation (C.3) yields
158
? 
1
2
=e
(??T
1/2
)
, (C.5)
which implies
? 
T
1/2
=(
1
?
)ln2=
0.693
?
 .  (C.6)
C.1.2 Radioactive Decay Chains
Often in nature, a situation is encountered in which the decay daughter of the
radioactive species is also radioactive, and starts to decay with a diferent ?. This proces
can also occur for the granddaughter radionuclide as wel. This is an example of a
radioactive decay chain. Asume a decay chain of A ? B ? C, where C is stable.
Applying the radioactive decay law to each species in the chain yields the following set
of equations
? 
dN
a
dt
=??
a
N
a
dNb
dt
=?
a
N
a
??
b
N
b
dNc
dt
=?
b
N
b
, (C.7)
where ?
a
 nd ?
b
 are the corresponding decay constants. If N
b
 and N
c
 are asumed to be
zero at t = 0, then the amount of A, B, or C at any time t, can be calculated using
? 
N
a
(t)=N
a
(0)e
(??
a
t)
,
N
b
(t)=N
a
(0)(
?a
b?a
)[e
(??
a
t)
?e
(??
b
t)
],
N
c
(t)=N
a
(0)[1+(
1
?b?a
)][?
b
e
(??
a
t)
??
a
e
(??
b
t)
]
, (C.8)
The above sets of equations can be simplified depending on the relative values of ?
a
 nd
?
b
. If ?
a
 > ?
b
, then ?
b
N
b
/?
a
N
a
 wil always increase as a function of time. If ?
b
 > ?
a, 
then
159
transient equilibrium is reached, and ?
b
N
b
/?
a
N
a 
becomes constant at large t. Finaly, if ?
b
? ?
a
, then secular equilibrium is reached, and ?
b
N
b
/?
a
N
a
 rises quickly, and levels off to
?1.
The above discussion is a simplification of what is usualy observed
experimentaly. Experiments that investigate the decay of extremely proton- or neutron-
rich species can be complicated by additional decays of the granddaughter, decay to
multiple daughters (each with a branching ratio), or the presence of isomers in the
daughters. For example, in the ?-delayed neutron decay of 
137
Sn, there are two daughters:
137
Sb and 
136
Sb. These nuclides each have two daughters that also undergo
?-delayed nuetron decay (
137
Te and 
136
Te), with the decay of 
136
Sb also populating 
135
Te.
Considering that each of these decays is divided into a ?-decay and ?-delayed neutron
decay branch, it can be sen how the set of Equations in (C-8) could get significantly
more complicated.
C.2 Counting Statistics and Eror Propagation
When measuring the half-lives of radionuclides, huge eforts are usualy taken to
design and perform the measurements in such a way that as much determinant eror is
eliminated as possible. Due to the statistical nature of radioactive decay, T
1/2
measurements and determination of
 
branching ratios wil always involve intrinsic eror.
As mentioned in C.1, radioactive decay is an event that occurs with a certain probability
within a certain time interval; therefore, the number of decays in a given interval of time
wil naturaly fluctuate. When collecting time-dependent data, especialy for purposes of
a half-life determination, it is necesary to calculate an eror asociated with an observed
160
number of counts in time duration, ?t. The eror in the number of observed counts
defines the range of possible true values for which the measured value is contained. The
spread of the range that the probability of observing N counts in a period ?t is given by a
Poison distribution,
? 
P(n,?t)=(
mN
!
)e
(?m)
, (C.9)
where m is the average number of counts in the period ?t. The standard deviation of this
distribution is given by
? 
?
N
=
1
2
,   (C.10)
which also happens to be the eror asociated with a single measurement of N. The reality
of obtaining N is that there is usualy a background, B, asociated with the measurement.
The true measured value of N would be obtained by
? 
N
net
=N?B
, (C.11)
where B is measured separately. The calculated eror for N
net
 is given by
? 
?
N
net
=(?
N
2
+?
B
2
)
1
2
. (C.12)
If a sample is counted for a time ?t, and the background for a time ?t
b
, then the measured
rate of radioactive decay (A) is expresed as
? 
A=
N
?t
?
B
?t
?[(
?N
?t
)
2
+(
?B
?t
)
2
]
1
. (C.13)
Typicaly, measurement of A is one of many points that are used to gather more
important information regarding the decay of a radionuclide.
161
C.3 Curve Fiting by Least Squares Analysis
When performing experiments measuring the decay properties of a radionuclide,
N is counted as a function of time. The T
1/2
-
 
and P
n
-values for the decay of these nuclides
is obtained by using the least-squares method to generate theoretical curves which
describe the observations. More specificaly, the T
1/2 
and P
n
 values in the radioactive
decay law are parameterized until this theoretical curve reaches a minimum value of S
where S is calculated by
? 
S=[
yi?f(xi;aj)
?
i
i=1
n
?
]
2
. (C.14)
Equation (C.14) is valid for fiting any function f(x) with a given set of parameters: a
1
,
a
2
,?a
j
, for the observed variable, y
i
. To find the values of a
j
 which minimize Equation
(C.14), a system of equations that solve the system of equations
? 
(
?S
a
j
)=0
. (C.15)
The analytical solution to Equation (C.15) may not always be obtained, depending on
f(x). For dificult equations of f(x), such as those for the radioactive decay law equations
for complicated decay chains, software has been developed to minimize Equation (C.15)
through iterative calculations.  The eror asociated with parameters used for the
minimization of Equation (C.14) is calculated by forming the covariance matrix, V
ij
,
? 
(V
?1
)
ij
=
1
2
(
?S
a
ij
)
, (C.16)
where the second derivative is evaluated at the minimum. The diagonal elements, V
ij
 can
then be shown to be the variances for a
i
, while the off-diagonal elements V
ij
 represent
covariances betwen a
i
 and a
j
.
162
Apendix D: List of Thesis Experiments
D.1 
135-137
Sn Decay Studies [IS378] at ISOLDE, CERN, Sumer 2000
D.1.1 Participants
J. Shergur,
1
 B. A. Brown,
2
 V. Fedoseyev,
3
 U. K?ster,
4
 K.-L. Kratz,
5
 D. Seweryniak,
1,6
 W.
B. Walters,
1
 A. W?hr,
7
 D. Fedorov,
8
 M. Hannawald,
5
 M. Hjorth-Jensen,
9
 V. Mishin,
3
 B.
Pfeifer,
5
 J. J. Resler,
1
 H. O. U. Fynbo,
4
 P. Hoff,
10
 H. Mach,
11
 T. Nilson,
4
 K.
Wilhelmsen Rolander,
12
 H. Simon,
4
 A. Bickley,
1
 and the ISOLDE Collaboration
4
1
Department of Chemistry, University of Maryland, College Park, Maryland, 20742-
2021, USA
2
Department of Physics and Astronomy and National Superconducting Cyclotron
Laboratory, Michigan State University, East Lansing, Michigan 48824-1321, USA
3
Institute of Spectroscopy, Russian Academy of Sciences, RU-142092 Troitsk, Russia
4
Experimental Physics Division, ISOLDE, CERN, CH-1211 Geneva 23, Switzerland
5
Institut f?ur Kernchemie, Universit?t Mainz, D-55099 Mainz, Germany
6
Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA
7
Department of Physics, Oxford University, Oxford, England
8
Petersburg Nuclear Physics Institute, RAS 188350, Gatchina, Russia
9
Department of Physics, University of Oslo, NO-0316 Oslo, Norway
10
Department of Chemistry, University of Oslo, NO-1163 Oslo, Norway
11
Department of Neutron Research, Uppsala University, S-61182 Nyk?oping, Sweden
12
Department of Physics, Stockholms Universitet, S-11385 Stockholm, Sweden
D.1.2 Representative Publications
Decay of 
135,136
Sn Isolated by Use of a Laser Ion Source and Evidence for a More
Harmonic-Oscilator-Like Nuclear Potential
J. Shergur et al., Nucl. Phys. A682, 493 (2001).
?-decay Studies of 
135-137
Sn Using Selective Resonance Laser Ionization Techniques
J. Shergur et al., Phys. Rev. C 65, 034313 (2002).
163
D.2 
135-137
Sn Decay Studies [IS378] at ISOLDE, CERN, Sumer 2002
D.2.1 Participants
J. Shergur,
1,2
 A. W?hr,
1,3
 W. B. Walters,
1
 K.-L. Kratz,
4
 O. Arndt,
4
 B. A. Brown,
5
 J.
Cederkal,
6
 I. Dilmann,
4
 L. M. Fraile,
6,7
 P. Hoff,
8
 A. Joinet,
6
 U. K?ster,
6
 B. Pfeifer,
4
 and
the ISOLDE Collaboration
6
1
Department of Chemistry, University of Maryland, College Park, Maryland, 20742-
2021, USA
2
Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA
3
Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556
4
Institut f?ur Kernchemie, Universit?t Mainz, D-55099 Mainz, Germany
5
Department of Physics and Astronomy and National Superconducting Cyclotron
Laboratory, Michigan State University, East Lansing, Michigan 48824-1321, USA
6
Experimental Physics Division, ISOLDE, CERN, CH-1211 Geneva 23, Switzerland
7
 Departamento de F?sica At?mica Molecular y Nuclear, Universidad Complutense, E-
28030 Madrid, Spain
8
Department of Chemistry, University of Oslo, NO-1163 Oslo, Norway
D.2.2 Representative Publications
New Level Information on Z = 51 isotopes, 
111
Sb
60
 and 
134,135
Sb
83,84
J. Shergur et al., to be published in Eur. Phys. J. A.
Level Structure of Odd-Odd 
134
Sb Populated in the ?
-
 Decays of 
134,135
Sn
J. Shergur et al., submited to Phys. Rev. C (2004).
Identification of New Shel-Model States in 
135
Sb
J. Shergur et al., submited to Phys. Rev. C (2005).
164
D.3 
111,113
Te Decay Studies at ATLAS/Argonne National Laboratory, Fall 2002
D.3.1 Participants
J. Shergur,
1,2
  D. J. Dean,
3
 D. Seweryniak,
2
 W. B. Walters,
1
 A. W?hr,
1,2,4
 P. Boutachkov,
4
C. N. Davids,
2
 I. Dilmann,
5
 A. Juodagalvis,
3,6
 G. Mukherje,
2
 S. Sinha,
2
 A.
Teymurazyan,
4
 I. Zartova
4
1
Department of Chemistry, University of Maryland, College Park, Maryland, 20742,
USA
2
 Physics Division, Argonne National Laboratory, Argonne, Ilinois 60439, USA
3
Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge,
Tennese 37831, USA
4
Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
5
Institut f?r Kernchemie, Universit?t Mainz, D-55128 Mainz, Germany
6
Department of Physics and Astronomy, University of Tennese, Knoxvile, Tennese
37996, USA
D.3.2 Representative Publications
Identification of Low-Spin States in 
111
Sb: Test of Spin-Orbit Coupling in Light Nuclei
J. Shergur et al., to be published Phys. Rev. C (2005).
New Level Structure for 113Sb:  Resolving Ambiguities and Observation of Even-
Jumping Phenomenon
J. Shergur et al., work in progres.
165
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