β DECAY AND ISOMERIC STUDIES OF PROTON RICH
NUCLEI NEAR THE ENDPOINT OF THE RP-PROCESS
By
Ana Delia Becerril Reyes

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Physics
2012

ABSTRACT
β DECAY AND ISOMERIC STUDIES OF PROTON RICH NUCLEI NEAR THE
ENDPOINT OF THE RP-PROCESS
By
Ana Delia Becerril Reyes

Neutron-deficient nuclei in the vicinity of the N = Z = 50 doubly-magic shell closure were produced at the National Superconducting Cyclotron Laboratory to study
their structure and their relevance in the astrophysical rp-process. The 100 Sn nucleus
is the heaviest particle-stable N = Z nucleus, and it is also thought to be doubly magic. Additionally, 100 Sn and its closest neighbors lie in the path of rp-process,
therefore, the production and study of the decay properties of these nuclei are of great
interest for the experimental and theoretical nuclear physics and astrophysics community. Previous attempts to produce these nuclei were hampered by large amounts
of contaminants produced with higher abundances than those of the nuclides of interst. The Radio Frequency Fragment Separator was designed and built at the NSCL
in order to purify rare neutron-deficient secondary beams. The implementation of
this device has made a number of β-decay experiments feasible at the NSCL. The
experiment described in this work (NSCL Experiment 07034) was the second one to
utilize the RFFS to successfully determine β-decay half-lives, β-delay proton emission
branching ratios and β-delayed gamma spectroscopy.
The nuclei of interest were produced at NSCL via fragmentation of a 112 Sn primary beam accelerated to 120 MeV/nucleon, impinging on a 9 Be target. The secondary beam was first selected by the A1900 Fragment Separator and purified further with the RFFS. The N = Z nuclei 100 Sn, 98 In and 96 Cd were produced and
their β decay was studied. The observed production cross sections of these nuclei are
lower than predicted by factors of 10-30. Their β-decay half-lives were found to be

0.55+0.70 s for 100 Sn, 0.66(40)s for an isomeric state in 98 In, and 47(13) ms for
−0.31
its ground state, and 1.03+0.24 s for 96 Cd. The experimental determination of the
−0.21
half-life of 96 Cd was of special interest as it was the last rp-process waiting point to
be measured. The effect of the half-life of 96 Cd on the nuclear abundances produced
by an rp-process and the origin of the light-p nucleus 96 Ru was explored.
Other exotic nuclei produced in Experiment 07034 include 102 − 101 Sn, 100, 99 In,
98, 97 Cd, 96 − 94 Ag, 94 − 92 Pd, 92, 91 Rh and 90, 91 Ru. For the cases with sufficiently high statistics their β-decay half-lives were determined and compared with
previous measurements and theoretical predictions. Several isomeric states were found
and their decay modes analyzed. In particular, a new microsecond isomer decaying
by a γ cascade was observed in 96 Ag for the first time and the level scheme of this
nucleus is presented, together with the results of two shell-model calculations performed within the (p1/2 g9/2 ) and (p3/2 p1/2 f5/2 g9/2 ) model spaces, respectively. It
was found that the shell model calculation with the larger model space reproduced
level energies and isomeric decay half-lives reasonably well.

Para mi familia

iv

ACKNOWLEDGMENTS
I would like to thank all the people and institutions that provided me with support
and encouragement in my journey through grad school.
I thank my advisor, Professor Hendrik Schatz, for all of his support, dedication
and patience during these years. I admire his passion for science and the enthusiasm
that he shares about it. I had the privilege to work in his research group at the
NSCL, which always provided a friendly and professional atmosphere to learn and
grow. Additionally, being part of JINA gave me the opportunity to meet many of the
experts in nuclear astrophysics, by attending schools, workshops and conferences. I
thank Hendrik for being always willing and happy to discuss research, and to let me
learn and re-learn at my own pace.
I thank Professors Edward Brown, Joey Huston, Andreas Stolz and Vladimir
Zelevinsky for serving in my guidance committee and for providing advise and helpful
comments on this dissertation.
I want to acknowledge the hard work of all the people who made Experiment
07034 possible. I am specially thankful to Daniel Bazin, with whom I also had the
opportunity to collaborate in a few other projects, and from whom I always admired
his experimental expertise as well as his ability to remain calmed and optimistic even
when things were not going as planned (which ocurred often). Thanks also to Paul
Mantica for insightful discussions about the analysis and interpretation of our data. I
would like to thank Alex Brown for providing the shell model calculations included in
this work, and for his help in interpreting experimental results. I also want to thank
Sean McDaniel, Dirk Weisshaar and Alexandra Gade for their help with γ-ray related
analysis.
I am specially thankful to Fernando Montes for being very helpful since the day
we met. He shares much of the credit of this work. I appreciate very much the time
that he dedicated to discuss data analysis and physics questions with me, was well

v

as many other practical and impractical questions almost every day. I thank him for
being a great friend and guide.
I want to acknowledge the help and guidance provided by everyone in the Nuclear
Astrophysics group at the NSCL. Past and present members of the group that I am
specially thankful to are Jorge Pereira for useful discussions, advise and an interesting
sense of humor, Marcelo Del Santo, Sebastian George, Zach Meisel and Karl Smith.
Two characters that (for me, at least) defined an era in the group are Alfredo Estrade
and Giuseppe Lorusso. I am glad we had the chance to attend conferences and schools
together, as well as delightful operas. I am glad we became friends and shared many
good times.
I want to acknowledge the encouragement and support from Sean McDaniel throughout our years in grad school. For all the good and bad times shared, for all the late
nights studying for the subject exams, for all the discussions about physics, life and
non-sense that we had, for making sure I ate lunch most days, and for being the best
friend I could have: thank you Sean!
Many other grad students in the lab were also supportive, helpful and friendly,
specially my office mates, who maintained a nice and quiet atmosphere at our workplace. Hui Wang was particularly good at keeping me sane and happy by listening
to me every time I needed to talk, and also by keeping a good supply of cookies at
hand.
I want to thank all the amazing people that I found in East Lansing and that made
my life in grad school so happy. I have the fortune to say that these are so many people
that I cannot list them all here, but there are a few ones that will actually read this
page, and so I should make sure to write their names: thanks very much to my dinner
club friends Kim, Erin, Carol, Neil and Catherine for wonderful dinners and great
times. Thanks to Ileana Marquez for being so helpful, loving and caring, particularly
when I arrived to East Lansing. Thanks to my family in Michigan: Zenaida, Edith,
Cecilia, Itza and Lourdes. To Lupi specially for making me realize how hillarious it

vi

can be to discuss nuclear astrophysics with a social scientist. To Steve, thank you for
your support, patience and love. Thank you for having faith in me.
With all my heart I want to thank my family and friends in Mexico who always
supported me, loved me and pushed me to work hard and get done (finally) with
school. Thanks to Arturo Menchaca and Ruben Alfaro for guiding me through my
first research projects. Special thanks also go to Claudia, Karin and Yox for always
being there for me. To Vicky, Vale, Hugo, Aldo and Abue Delia for believing in me,
and loving me so much, thank you.
A mis padres y a mis hermanos les debo todo, y les dedico mi esfuerzo. Los amo.
Muchisimas gracias!

vii

TABLE OF CONTENTS
List of Tables

x

List of Figures

xi

1 Introduction
1.1 Origin of the light p-nuclei . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Type I X-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 The rp-process . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Nuclear Physics
2.1 Nuclear Structure
2.2 Beta Decay . . .
2.3 Gamma Decay . .
2.4 Isomeric States .

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3 Experimental Setup
3.1 Projectile Fragmentation at NSCL . . .
3.2 Radio Frequency Fragment Separator . .
3.2.1 Design . . . . . . . . . . . . . . .
3.2.2 Performance . . . . . . . . . . . .
3.3 Experimental Station . . . . . . . . . . .
3.3.1 Beta Counting System . . . . . .
3.3.2 Segmented Germanium Array . .
3.4 Rare Isotope Beam Production Settings .

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around 100 Sn
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4 Data Analysis
4.1 Particle Identification . . . . . . . . . . . .
4.1.1 µs-isomers . . . . . . . . . . . . . .
4.2 Fragment - Decay Correlations . . . . . . .
4.2.1 Determination of β-decay Half-lives
4.3 Prompt γ Radiation Measurement . . . .
4.4 β-Delayed γ Radiation Measurement . . .

viii

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5 Experimental Results
5.1 N = Z Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 96 Cd . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 98 In . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 100 Sn . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Other neutron-deficient nuclei produced in Experiment 07034 .
5.2.1 Isomeric decay of 96 Ag . . . . . . . . . . . . . . . . . .
5.2.2 Isomeric decay of 94 Pd . . . . . . . . . . . . . . . . . .

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92

6 Astrophysical Impact
6.1 rp-process reaction network . . . . . . . . . .
6.2 Impact of our measurements on the rp-process
6.2.1 The half-life of 96 Cd . . . . . . . . . .
6.2.2 The microsecond isomers in 96 Ag . . .
6.3 Conclusions and Outlook . . . . . . . . . . . .

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102

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107

ix

LIST OF TABLES
2.1

β decay angular momentum and parity selection rules. . . . . . . . .

27

2.2

Weisskopf single-particle estimates for the lowest electric (Eλ) and
magnetic (Bλ) transition probabilities. . . . . . . . . . . . . . . . . .

27

3.1

SeGA energy calibrations. . . . . . . . . . . . . . . . . . . . . . . . .

47

4.1

Known µs isomers used for particle identification . . . . . . . . . . . .

67

5.1

100 Sn cross section values determined in the various fragmentation experiments dedicated to its production and identification. The acronyms
GSI and GANIL stand for “Gesellschaft fur Schwerionenforschung” and
“Grand Accelerateur National d’Ions Lourds”, respectively. . . . . .

5.2
5.3

79

Energies, intensities, and coincidence relationships of γ rays assigned
to the isomeric decay of 96 Ag. . . . . . . . . . . . . . . . . . . . . .

90

Energies, intensities, and coincidence relationships of gamma rays assigned to the isomeric decay of 94 Pd. . . . . . . . . . . . . . . . . .

93

x

LIST OF FIGURES
Section of the chart of nuclides indicating the light p-nuclei 92 Mo,
94 Mo, 96 Ru, and 98 Ru. . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.2

Artist rendition of an X-ray binary. . . . . . . . . . . . . . . . . . . .

8

1.3

The rp-process path. . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

1.4

Schematic view of the SnSbTe cycle. . . . . . . . . . . . . . . . . . .

15

2.1

Single-particle energy levels calculated by the nuclear shell model. . .

18

2.2

The region of interest for Experiment 07034 in the chart of nuclides. .

20

2.3

Calculated level scheme of 96 Cd. . . . . . . . . . . . . . . . . . . . .

26

3.1

Ion beam production and delivery to the experimental station at NSCL. 43

3.2

LISE++ calculation of production rate of 100 Sn as a function of Bρ
at the exit of the A1900 Fragment Separator. . . . . . . . . . . . . . .

44

Layout of the NSCL RF Fragment Separator installed in the S1/S2
vaults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

3.4

Photograph of the RF Fragment Separator at the NSCL. . . . . . . .

45

3.5

Drawing of the RFFS cavity. . . . . . . . . . . . . . . . . . . . . . . .

46

3.6

LISE++ calculation of the vertical deflection of the secondary beam
caused by the RFFS. . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

3.7

Deflection of a primary beam by the RFFS during its commissioning.

48

3.8

Particle identification at the focal plane of the RFFS. . . . . . . . . .

49

3.9

Picture of the SeGA array surrounding the beamline at the position of
the BCS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

3.10 Observed energy shifts in SeGA detectors. . . . . . . . . . . . . . . .

51

3.11 SeGA efficiency curve. . . . . . . . . . . . . . . . . . . . . . . . . . .

52

1.1

3.3

xi

3.12 Production rates of N=50 isotones obtained from the RFFS commissioning run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1

53

Particle identification spectrum obtained with energy loss from the
PIN1 detector of the BCS and XFP scintillator time-of-flight. . . . .

57

Particle identification spectrum obtained with energy loss from the
PIN2 detector of the BCS and XFP scintillator time-of-flight. . . . .

57

Particle identification spectrum obtained with energy loss from the
PIN3 detector of the BCS and XFP scintillator time-of-flight. . . . .

66

Particle identification spectrum of the heavy nuclei implanted in the
DSSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

β-detection efficiency of the BCS as a function of the amount of background observed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

Two-dimensional matrix of prompt γ-ray energies measured with SeGA
for the 96 Ag implants. . . . . . . . . . . . . . . . . . . . . . . . . . .

70

Two-dimensional matrix of prompt γ-ray energies measured with SeGA
as a function of time in the SeGA TAC. . . . . . . . . . . . . . . . .

71

5.1

Particle identification spectrum from the RFFS commissioning run. .

74

5.2

Number of decays observed for 96 Cd as a function of logarithmic time
and fit obtained with MLH method. . . . . . . . . . . . . . . . . . . .

75

β-decay curve of 96 Cd and fit obtained with a Poisson distribution
log-likelihood function. . . . . . . . . . . . . . . . . . . . . . . . . . .

75

5.4

β-delayed γ-ray spectrum of 96 Cd. . . . . . . . . . . . . . . . . . . .

77

5.5

Prompt γ-ray spectrum of 96 Cd. . . . . . . . . . . . . . . . . . . . .

77

5.6

Comparison of the half-life of 96 Cd measured in this work to theoretical
predictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

5.7

Number of decays observed for 98 In as a function of logarithmic time.

80

5.8

β-delayed γ-ray spectrum of 98 In. . . . . . . . . . . . . . . . . . . . .

80

5.9

β-decay curve of 100 Sn . . . . . . . . . . . . . . . . . . . . . . . . . .

81

5.10 Prompt γ-ray spectrum of 96 Ag. . . . . . . . . . . . . . . . . . . . .

83

5.11 Decay curves and fits of the microsecond isomers in 96 Ag. . . . . . .

85

5.12 Background-corrected fragment-γγ coincidence spectra of isomeric transitions in 96 Ag, part 1. . . . . . . . . . . . . . . . . . . . . . . . . . .

87

4.2
4.3
4.4
4.5
4.6
4.7

5.3

xii

5.13 Background-corrected fragment-γγ coincidence spectra of isomeric transitions in 96 Ag, part 2. . . . . . . . . . . . . . . . . . . . . . . . . . .

88

5.14 Proposed level scheme of 96 Ag compared to the results of shell-model
calculations made with the SLGT interaction and the jj44b interaction. 89
5.15 β-decay curve of the 96 Ag implants which were correlated with the
470-keV transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

5.16 Prompt γ-ray spectrum of 94 Pd. . . . . . . . . . . . . . . . . . . . .

93

5.17 Decay curves and fits of the microsecond isomers in 94 Pd. . . . . . .

95

5.18 Decay time spectrum obtained by gating on the 1651 keV transition of
94 Pd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

5.19 Experimental level scheme of 94 Pd obtained in this work. . . . . . . .

96

6.1

Reaction path of an rp-process calculated with a single zone X-ray
burst model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.2

Effect of 96 Cd half-life in rp-process predicted nuclear abundances. . 102

6.3

Effect of 96 Cd half-life in rp-process predicted energy generation as a
function of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

xiii

Chapter 1
Introduction
The origin of the heavy elements and the nature of explosive events in the cosmos
are two of the most exciting open questions in science. These are two closely related puzzles. The field of Nuclear Astrophysics is concerned with finding answers to
these and other questions by taking a multidisciplinary approach to the problem: it
brings together observational astronomers, nuclear experimenters and theorists to develop models of the various astrophysical scenarios based on reliable nuclear physics;
and conversely, uses astrophysical observations to understand the behavior of nuclear
matter at extremely high densities.
It is now understood that most elements up to iron are synthesized by fusion
reactions in stars. When stars run out of nuclear fuel they eject their metal-enriched
envelopes into the interstellar medium. Neutron capture processes create most of the
heavy elements beyond iron. These processes occur during hydrostatic burning in
massive stars and possibly in explosive events that provide temperature and densities
high enough to induce nuclear reactions that would otherwise be unfeasible. The ashes
of a variety of nucleosynthesis events enriches the interstellar medium with material
of high metallicity (anything beyond H and He), thus providing material for new
stars to form. Such nucleosynthetic cycling in our galaxy resulted in the abundance
distribution currently observed in the solar system. Detailed understanding of the

1

nucleosynthesis of elements beyond iron is still far from complete. New observations
of explosive events in the universe have reached unprecedented quality and they must
be interpreted in terms of the underlying physics of the nuclear reactions responsible
for the energy generation.
Many experimental programs at rare isotope facilities worldwide are currently
dedicated to the production and study of the exotic nuclei that play key roles in the
different astrophysical scenarios thought to contribute to the origin of the heavy elements. At the National Superconducting Cyclotron Laboratory (NSCL), the question
of the creation of the heavy elements is addressed through experiments dedicated to
investigate the nuclear structure, half-lives and masses of the relevant isotopes, as
well as the nuclear reactions in which they participate.
The work presented here describes a β-decay experiment performed at the NSCL
with a twofold motivation: one was to gather experimental data on the structure of
neutron-deficient nuclei along the path of the astrophysical rapid proton capture process (rp-process). The aim of this chapter is to provide an overview of the astrophysics
motivation of our study of heavy N ≈ Z nuclei. Of particular interest for us was the
determination of the β-decay half-life of 96 Cd, a waiting point in the rp-process and
a proposed progenitor of 96 Ru via β + decay.
β-decay spectroscopy measurements close to the proton drip-line are needed not
only to determine the last unknown β-decay half-lives in the rp-process, but also to
clarify the detailed structure of the decays. This is necessary to calculate corrections
for the lifetimes of these nuclei in the astrophysical environment. For instance, isomeric states occurring along the process path may have a significant impact on the
time scale and final abundances. If an isomer is populated in sufficient quantities it
could create a non-thermal population of states, and therefore, their separate identities must be considered in nuclear reaction networks. A β-decaying spin-gap isomer
with a half-life of 0.5 seconds was predicted in 96 Cd by Ogawa in [1]. Details on the
shell model predictions for 96 Cd will be given in Chapter 2. It is important to realize

2

that if this isomeric state exists and if it is populated significantly in the fragmentation reaction of our experiment, then a mixed half-life from ground and isomeric
states would be measured. Since 96 Cd β-decays into 96 Ag, we searched for isomeric
states in this nucleus too, which could potentially also affect the production of A = 96
mass in the rp-process.
The second motivation for the present study was to gain understanding of the
shell evolution close to the predicted doubly magic nucleus 100 Sn. An interesting
phenomenon in this region of the chart of nuclides is the ocurrence of high-spin
isomeric states, which exhibit various decay modes (e.g. β, β-delayed proton, γ). With
over 20 different neutron-deficient species produced in in their ground and isomeric
states in our experiment, various decay modes were observed and their half-lives were
determined, ranging from a few hundred nanoseconds to several seconds. A brief
theoretical framework on the nuclear structure in the region studied will be presented
in Chapter 2.
Details of the experiment are provided in Chapter 3, together with a brief description of the devices utilized. Particular attention is given to the Radio Frequency
Fragment Separator, a velocity filter that improved the purity of the rare isotope
beam to a level adequate for decay studies. This device was built at the NSCL especifically to purify neutron-deficient beams that cannot be separated by the A1900
Fragment Separator alone.
In Chapter 4 a detailed description of the data analysis is presented, and the results
are discussed in Chapter 5. Finally, the effect of our measurements on the abundances
produced by an rp-process reaching the Sn region is explored by incorporating the
experimental results into a reaction network calculation. This will be the subject of
Chapter 6.

3

1.1

Origin of the light p-nuclei

Most of the nuclides heavier than iron are synthesized through a series of neutron
captures and β − decays in the so-called slow and rapid (s- and r-, respectively)
neutron capture processes. Exotic neutron-rich nuclei are created through succcesive
neutron captures, and stable isotopes are formed when the newly formed neutron-rich
nucleus β − decays. However, the stable isotopes on the proton-rich side of the valley
of stability cannot be reached through such processes as they are shielded by more
neutron-rich stable isotopes. These proton-rich nuclei are referred to as p-nuclei, of
which 74 Se is the lightest and 196 Hg the heaviest [2]. The solar system abundances
of the p-nuclei is one to three orders of magnitude lower than their more neutronrich isotopes, and any model attempting to describe their synthesis must account
for this fact. A long standing question in nuclear astrophysics has been the origin
of the light p-nuclei 92 Mo, 94 Mo, 96 Ru, and 98 Ru (see Fig. 1.1) found in the solar
system with rather large isotopic abundances of 14.84%, 9.25%, 5.52% and 1.88%,
respectively [3, 4].
The p-nuclei can be made in nature, in principle, via the p-process, which consists of γ-induced photodisintegration of heavy nuclei previously created by neutron
capture processes. The p-process is thought to occur in the shock front of Type II
supernovae, or in the deflagration flame of a Type I supernova detonation [3, 4], or
alternatively in pre-explosive or explosive O/Ne burning [2]. While the p-process can
reproduce the synthesis of the majority of the proton rich stable isotopes found nature, it fails to account for the large abundances of nuclei in the 92 ≤ A ≤ 98 mass
range (e.g. [2, 4, 5]).
Another possible mechanism to create p-nuclei could be a series of proton captures on lighter nuclei. High Coulomb barriers would have to be overcome for the
(p, γ) reactions to proceed on high Z nuclei, therefore, high temperature and density
environments with a high proton flux are required. The rp-process in X-ray bursts was

4

p-process

96Ru

98Ru

99Ru

100Ru

101Ru

102Ru
u

99Mo

100Mo

99Tc

92Mo

94Mo

95Mo

93Nb

90Zr

91Zr

92Zr

96Mo

97Mo

98Mo

95Zr

96Zr

95Nb

93Zr

94Zr

r-process

s-process

Figure 1.1: For interpretation of the references to color in this and all other figures,
the reader is referred to the electronic version of this dissertation. Section of the
chart of nuclides indicating the light p-nuclei 92 Mo, 94 Mo, 96 Ru, and 98 Ru. These
nuclei cannot be created through neutron capture nucleosynthesis mechanisms. Figure
adapted from [3].

5

proposed as a possible source of the p-nuclei [5,6]. This scenario provides the required
proton-rich environment, as well as the high temperature needed to compensate for
Coulomb repulsion during proton captures. However, an argument against significant
contribution of X-ray bursts to the synthesis of p-nuclides in the Mo-Ru region is the
presence of live 92 Nb in the early solar system [7]. This nucleus cannot be produced
by the rp-process because it is shielded against β + decay by 92 Mo, which is stable.
Thus, 92 Nb must be produced by Type II supernovae. Based on Galatic Chemical
Evolution models, Dauphas et al. concluded that if X-ray bursts produced most of the
p-nuclides then the 92 Nb/92 Mo ratio in the interestellar medium would have been
lowered by a factor of 10 relative to supernovae because X-ray bursts do not produce
92 Nb.
The so-called νp-process [8–10] may also contribute to the creation of light pnuclei. The proposed site of the νp-process are the proton-rich ejecta created by a
strong neutrino flux in supernovae. In this scenario, neutrons produced by the reaction
ν + p → n + e+ would be captured by neutron-deficient nuclei. This would allow the
¯
flow to bypass the slow β decays via (n,p) reactions, resulting in nucleosynthesis above
A = 64 [8].

1.2

Type I X-Ray Bursts

Type I X-Ray Bursts were discovered as a sharp rise in the luminosity of an Xray source followed by a slower cooling phase lasting for tens of seconds to about a
minute and repeating on timescales of hours to days [11, 12] (see for example [13] for
a review). They have been interpreted as the result of thermonuclear explosions on
the surface of a neutron star that accretes hydrogen- and helium-rich matter from
the outer layers of a low-mass companion. In such binary systems, the neutron star
has an average mass of ≈ 1.4 M⊙ (or larger, according to recent photospheric radius
expansion burst studies [14]), a radius of about 10-15 km and a density of the order

6

of 1014 g/cm3 [15]. The companion (or donor) star is, typically, a metal poor low
mass star (

1.5 M⊙ ). An artistic rendition of an accreting neutron star in a binary

system is shown in Fig. 1.2.
Proton-rich matter is transferred to the neutron star via Roche lobe overflow.
The Roche lobe is a gravitational equipotential surface around a star that outlines
the volume within wich material is gravitationally bound to the star. The location
where the two Roche lobes in a binary system touch is called the inner Lagrangian
point [15]. When the donor star fills its Roche lobe, matter from its envelope will
flow out towards the neutron star though the inner Lagrangian point, creating an
accretion disk around the neutron star and spiralling down to its surface.
The falling of mass onto the neutron star releases gravitational energy, heating
the surface of the neutron star to temperatures around 107 K [15]. As a result, a
continuous X-ray flux is emitted. At typical accretion rates of 10−8 − 10−10 M⊙ /yr,
mass accumulation causes an increasing temperature and density until temperaturesensitive fusion reactions ensue. These reactions in turn generate heat that further
accelerates the thermonuclear reaction rates, which increase the temperature even
further, thus triggering even more reactions and so on. The result is a thermonuclear
runaway in which, typically, 1039 − 40 ergs of energy are released. The time rise in the
light curve is fast (1 to 10 s), reaching peak temperatures of 1.5 to 2 GK in the nuclear
burning zone [16], and it is followed by a slower decline of about 10 to 100 seconds
that reflects cooling of the neutron star surface. With recurrence times of the order
of hours to days, type I X-ray bursts are the most frequent thermonuclear explosive
events observed in nature. To date, more than 3000 bursts have been observed. A
large amount of observational data, accumulated during the past few decades, has
made possible the discovery and monitoring of various X-ray burst properties with
high precision, such as millisecond oscillations [13, 17]. The thermonuclear origin of
these phenomena therefore requires detailed understanding of the underlying nuclear
physics in order to construct a complete description of the X-ray bursts.

7

Figure 1.2: Artist rendition of an X-ray binary system. The neutron star (left) accretes hydrogen- and helium-rich matter from its companion (right), which undergo
a thermonuclear runaway in the surface of the neutron star, resulting in the observed
Type I X-ray bursts (see text for details). Image credit: David Hardy.

8

The nuclear processes responsible for the energy generation during X-ray bursts
depend upon several parameters of the binary system, such as accretion rate and
composition of the accreted material, which in turn are related to distance and rotational period between the two stars and to the nature of the companion [13, 15]. For
bursts accreting at rates between 10−8 to 10−10 M⊙ /yr nuclear burning is ignited
at densities above ρ = 105 g/cm3 mostly via the triple-α process [5]. As a result of
these reactions the temperature can reach 3 × 108 K, which in turn triggers the αp
and the rp-process. The rp-process determines the light curve of the X-ray burst and
sets the initial composition for all subsequent processes occurring deeper in the crust
of the neutron star.

1.2.1

The rp-process

The rp-process consists of a sequence of fast (p,γ) reactions competing with photodisintegration and β + -decays. The reaction path runs mostly along the proton-drip
line. Figure 1.3 shows the reaction flow of the rp-process in an X-ray burst. When the
Q-value for further proton capture is either too small or negative, photodisintegration
or proton decay can occur. At this point, the reaction flow has to wait for the nucleus
to β + decay (so that proton capture on the daughter nucleus can resume the process), and therefore mass accumulation occurs at the corresponding nuclide. These
long-lived nuclei along the reaction path are referred to as waiting points [5] and their
β-decay half-lives determine the processing time scale and the final abundances of the
rp-process. The even-even N = Z nuclei beyond 56 Ni represent the major waiting
points, together with a few more stable isotopes, depending on the exact conditions.
Among these, 96 Cd was the only one with a still unknown β-decay half-life. As mentioned above, the origin of 96 Ru in the solar system is not understood, and the isotope
could at least in principle, be produced in the rp-process. The produced amount of
96 Ru in the burst ashes scales with the half-life of 96 Cd. Additionally, a long 96 Cd
half-life would reduce the amount of heavier nuclei produced in the rp-process.
9

Xe (54)

SnSbTe Cycle

Sn (50)
Pd (46)
58

Mo (42)

56

Sr (38)

54
50

Se (34)

52

48
44

Zn (30)
40
36

Fe (26)
32

Protons

30

Ti (22)
28

rp process

24

Ar (18)
22
20

Si (14)
16
14

Ne (10)

p process

12
10

C (6)
8
He (2)
0 2

4

6

3 reaction

Neutrons

Figure 1.3: Section of the chart of nuclides indicating the path followed by the rpprocess in an X-ray burst. Figure adapted from [18].

10

Abundance pattern
The long lived waiting point nuclei along the rp-process reaction path store most of
the material until the burning ends, therefore, their half-lives determine the resulting
isotopic abundances. The effective lifetimes of the rp-process waiting points are a
crucial ingredient in abundance calculations. One needs to take into account the
possibility of population of excited states in the astrophysical environment and use
the appropriate half-lives determined experimentally.
The abundance pattern created by an X-ray burst can be calculated through a
nuclear reaction network. The isotopic abundances Yi = Xi /Ai , defined as the mass
fraction divided by mass number, are modeled as a function of time using set of differential equations in order to determine the reaction path of the process and the
amount of energy released [5]. Crucial input for these reaction networks, besides parameters of the astrophysical environment, are proton-capture reaction rates, proton
separation energies and half-lives of all the nuclei involved.
The rp-process could produce light p-nuclei through the β + decay of the unstable
proton-rich isobars created by proton captures. Using a nuclear reaction network
that included all proton rich nuclei from hydrogen to xenon, Schatz et al. [19] found
large overproduction factors (produced abundance normalized to solar abundance
≈ 109 ) for the p-nuclei 98 Ru, 102 Pd and 106 Cd. However, in order for X-ray bursts
to contribute to galactic nucleosynthesis, it is required that the processed material
escapes the neutron star and enriches the interstellar medium [20].
Characterization of the final abundance pattern of X-ray bursts is not only important for nucleosynthesis considerations, but also for probing the properties of neutron
stars. Most of the ashes of the rp-process will become part of the neutron star crust,
and will set the initial conditions for all subsequent crust processes, some of which
could be directly linked to observables [13, 15].

11

Endpoint
Determination of the endpoint of the rp-process is crucial in order to estimate the
abundance pattern, as well as the amount of hydrogen left after burning is over.
The endpoint of a particular X-ray burst depends on system parameters and
initial ignition conditions.Several rp-process simulations for X-ray bursts showed that
the reaction path reached the end of their respective reaction networks, in the Kr-Y
region [21–25], or up to Cd [26] and Sn [5]. When a large amount of hydrogen is
present in the accreted matter the rp-process can extend into the A ∼ 92 − 110 mass
region, where the SnSbTe cycle represents a natural endpoint [19]. Schatz et al. [19]
showed that nucleosynthesis in the rp-process is limited to nuclei with Z ≤ 54 under
all rp-process conditions as a consequence of the low α separation energies of the
106 − 109 Te isotopes.
The SnSbTe cycle is schematically shown in Figure 1.4. Once the reaction flow
reaches the light tin nuclei, further processing will occur if the corresponding Sb
isotone is sufficiently proton bound for the (γ, p) photodissintegration to be small
[19]. The β + -decays of 99 − 104 Sn followed by proton captures on the corresponding
indium isotopes drive the flow towards greater stability. When 105 Sn is reached,
proton capture can proceed towards 106 Sb and then to 107 Te. At this point, however,
the (γ, α) photodisintegration rate will dominate and the flow will return to 103 Sb,
forming a cycle that forbids processing towards heavier nuclei. 105 Sn is a branching
point, that sends part of the reaction flow towards 105 In via β + -decay, thus forming
the weaker cycle shown in Figure 1.4.
New experimental data on reaction rates and masses of rp-process nuclei have lead
to a better estimate of the final abundances. A recent one-dimensional X-ray burst
model calculation with updated reaction rates showed that significantly less material is processed toward the end of the rp-process, resulting in accordingly reduced
abundances beyond A = 80 [27].
New and improved mass measurements of 104 − 108 Sn and 106 − 110 Sb and de12

termination of their respective one-proton separation energies lead Elomaa et al. [28]
to suggest an earlier termination of the rp-process. The new, low proton separation
energy (Sp =424(8) keV, in contrast to the previously adopted value of 930(210) keV)
determined for 106 Sb implies that the branching into the SnSbTe cycle is weaker.
Therefore, cycling is almost absent in current X-ray burst calculations and the reaction path runs closer to stability. This affects the final abundances, in particular, it
reduces the late-time 4 He production by the SnSbTe cycle.
The remaining uncertainties in the determination of the endpoint are the protoncapture rates on 105, 106 Sb. Larger rates could potentially increase the amount of
cycling in the SnSbTe cycles [28].
Consequences on crust composition
The rp-process, besides powering the light curve of X-ray bursts, sets the composition
of the liquid ocean and solid crust of the underlying neutron star. As the mass transfer
continues in the binary system, the reaction products of the rp-process are pushed
deeper in the crust of the neutron star. Therefore, the ashes of previous bursts determine the initial composition for subsequent bursts or even superbursts. Superbursts
are extremely powerful X-ray bursts in which the energy release is ∼ 103 times that
of a regular burst, and are thought to be the result of carbon burning. They occur
with less frequency but have longer cooling timescales [13].
When ashes of the rp-process are compressed even further the electron chemical potential rises with increasing density, switching on electron capture reactions.
These reactions produce very neutron-rich unstable nuclei and their energy generation contributes to the heating of the crust. Gupta et al. [29] showed that the exact
composition of the ashes needs to be known to determine heating processes in the
crust and ocean of the neutron star that directly influence observables such as superbursts ignition depth. In addition, knowledge of the composition of the crust is
essential for models to determine the thermal and electrical conductivities, as well as

13

evolution of magnetic fields in the neutron star (e.g. [7, 30] and references therein).
Also, cooling of the crust determines the quiescent luminosity in transients (neutron
stars with intermittent periods of rapid accretion) [31].
On the other hand, observables from nuclear processes in the crust and envelope of
the neutron star can be used to constrain its mass and radius, thus providing valuable
information to determine the equation of state of nuclear matter at high densities and
low temperatures ( [14, 32, 33] and references therein).
Ejection of ashes
Whether the rp-process in X-ray bursts contribute or not to nucleosynthesis of heavy
proton-rich isotopes is still a matter of debate. Identifying an ejection mechanism of
the rp-process ashes, given the strong gravity on the surface of a neutron star, is a challenging task. It is estimated that at most a few percent of the synthesized matter can
escape the gravitational potential of the neutron star (Egravitational /Enuclear

40

[7]).
Weinberg et al. [20] demonstrated that such an ejection mechanism in principle
exists. Their calculations showed that heavy-element ashes of nuclear burning can be
transported via convection to the surface of the neutron star, where they could be
ejected in the strong radiative winds of photospheric radius expansion (PRE) bursts
and produce strong spectral absorption features. Later, in ’t Zand and Weinberg
[34] showed observational evidence of the exposure of ashes of nuclear burning in
superexpansion bursts.
Accurate determination of the burst ashes, together with a better understanding
of the possible ejection mechanisms will help identify abundance signatures for future
X-ray observational explorations.

14

(γ,a)
105Te

106Te

107 Te

108 Te

104Sb

105Sb

106

107Sb

Sb

(p,γ)
103Sn

104Sn

105Sn

106Sn

102In

103In

104In

105In

β+

Figure 1.4: Schematic view of the SnSbTe cycle. The solid line represents flow of more
than 10% and the dashed line corresponds to 1%-10%. Figure adapted from [19].

15

Chapter 2
Nuclear Physics
The importance of the nuclear physics of the stable and radioactive isotopes participating in the rp-process was established in the preceding chapter. The following
sections provide an overview of the theoretical framework of the physics of neutron
deficient nuclei in the region around 100 Sn. Also, an introduction will be given to
some of the observables that allow us to probe the structure of these exotic neutrondeficient nuclei.
The atomic nucleus is a quantum many-body system, and analyzing the interactions among its constituents in order to understand its behaviour as a whole is a
daunting mathematical task. Approximations are therefore requiered to describe all
but the lightest nuclei. The shell model of the nucleus, in analogy to the atomic shell
model, describes the motion of a single nucleon as governed by the average potential
created by all other nucleons. Solving the Schr¨dinger equation for a suitable singleo
particle potential (consisting, for example, of a central Woods-Saxon potential plus
a strong spin-orbit coupling term) one gets bound single-particle states characterized
by a quantum number n, orbital angular momentum l, and total angular momentum
j = l + s (with s = 1/2 for both protons and neutrons). The resulting energy levels
are arranged in a structure that resembles that of the atomic shell model, the filling
of shells proceeds in accordance with the Pauli exclusion principle, and the maximum

16

number of particles in a given level is equal to (2j +1). Full shells correspond to an energetically favorable configuration and therefore to enhanced stability of the nucleus.
Particles left out of a closed shell (valence nucleons) will, as in the case of the atomic
shell model, determine the properties of the nucleus, such as its spin, parity (equal to
(−1)l ), excitation energy and possible decay modes. The single-particle energy levels
predicted by a shell model are illustrated in Figure 2.1. The relative positions inside
a major shell as well as gaps between the shells are different in various versions of the
shell model. A shell-model calculation is based upon a subset of single-particle states
together with their interaction via an effective two (or more) body hamiltonian [35].
One of the main successes of the shell model is its ability to predict the occurrence
of the so-called magic numbers, which correspond to the filling of major shells. Such
magic numbers of proton and neutrons are 2, 8, 20, 28, 50, 82 and 126. Nuclei with
a magic N or Z number exhibit extra stability and correspond to major gaps in the
spacings of the single-particle energies. When a nucleus has both, a magic number of
neutrons and a magic number of protons, it is called doubly-magic. With N = Z = 50,
100 Sn is believed to be a doubly magic nucleus, and it is therefore of great interest
for both experimental and theoretical studies.

2.1

Nuclear Structure around

100

Sn

Neutron deficient nuclei in the neighborhood of the expected doubly magic 100 Sn are
an important testing ground for shell model calculations. The low-energy structure
of these nuclei is of great importance to confirm the closure of shells at N = Z =
50. Shell-model calculations rely on the closed-shell property of the doubly-magic
nuclei, which provides a good zeroth-order wave function that can be systematically
improved using perturbation theory [36]. Additionally, the equal number of protons
and neutrons provides excellent conditions for the study of the residual proton-neutron
interaction in identical orbits (π − ν pairing) and the role of core excitations [37]. One

17

184
1j15/2
4s1/2 2d3/2
1i11/2 2g7/2
2g9/2 3d5/2

16
4
2
8
12
6
10

126
14
2
4
6
8
10

1i13/2
3p3/2 3p1/2
2f5/2
2f1/2
1h9/2
82
1h11/2
2d3/2 3s1/2
2d5/2
1g7/2
1g9/2
1f5/2 2p1/2
2p3/2

50

12
2
4
6
8
10
2
6
4

28
8

1f7/2
1d3/2
2s1/2
1d5/2
1p1/2
1p3/2

20

4
2
6

8
2
4

2
2

1s1/2

Figure 2.1: Schematic representation of single-particle energy levels calculated by
the nuclear shell model. Neutrons and protons are counted separately. Spectroscopic
notation (nlj) is used to label the states, where n is used to number the various states
of given l and j. The magic numbers are indicated. The number of identical nucleons
allowed at a given level is indicated on the right.

18

of the current challenges for nuclear physics is to explore the limits of prediction for the
existing models and to develop extrapolations for those nuclei which are not yet within
reach of experimental facilities but that are relevant for models of nucleosynthesis in
astrophysical scenarios.
Numerous experiments in recent years have been dedicated to the production and
study of N ∼ Z nuclei in the vicinity of 100 Sn. β decays with large Q-values, βdelayed proton emission, and spin-gap isomers can observed in this mass region, and
the results have challenged shell model calculations (e.g. [?, 38–41]). Shown in Fig.
2.2 is the portion of the chart of nuclides of interest in this study, the nuclei produced
in our experiment are highlighted.
A variety of model spaces and effective interactions have been used by shell model
calculations to explain observed properties of N ∼ Z nuclei that were previously
not predicted, such as some of the recently observed high-spin isomers. To cite an
example, the observed 21+ state in 94 Ag has been reported to decay by a variety of
channels and raised much discussion about its nature ( [42] and references therein).
A shell model with a minimum model space comprising p1/2 and g9/2 protons
and neutrons generally provided a good description of the structure of these nuclei.
It successfully reproduced observed energy levels and half-lives in 95 Ag, 95 Pd, and
94 Pd, but it failed to predict the isomerism of the 21+ state in 94 Ag [43, 44]. Use of
a larger model space is therefore required to explain some of the new observations.
Shell model calculations including the p3/2 , f5/2 and g7/2 orbitals and using realistic
interactions were developed for this purpose [45].
Shell model calculations with larger model spaces have investigated the role of
deformation and shape coexistence in the isomers observed in this region of the chart
of nuclides. Also, core excitations have been found to be necessary to explain some
high-spin isomeric states, such as those occurring in 98 Cd [41], 94 Ag [43] and 94 Pd
[46] (See section 2.4 below).

19

99Sn

100Sn

98In

99In

96Cd

97Cd

98Cd

99Cd

100Cd

94Ag

95Ag

96Ag

97Ag

98Ag

99Ag

93Pd

94Pd

95Pd

96Pd

97Pd

98Pd

Produced in Exp.
07034

Z

92Pd

101Sn

102Sn

100In

101In

N

Figure 2.2: Section of the chart of nuclides of interest in the present study. The N = Z
line is indicated, and the nuclei produced in Experiment 07034 are highlighted in dark
blue.

20

2.2

Beta Decay

Nuclei sufficiently far on the neutron-deficient side of the valley of stability may
undergo β + decay. Through β + decay a proton within the nucleus is transformed
into a neutron via the following process:

A X →A
′
+
Z
Z − 1 XN + 1 + e + ν
As the mass number A remains constant, β + decay provides a means for the
nucleus to approach the stable isobar of the chain. The Q value of the decay can be
calculated as [47]:

Q+ = [m(A X) − m(A X ′ ) − 2me ]c2
β

(2.1)

where m(A X) denote neutral atomic masses:

m(A X)c2 = mN (A X)c2 + Zme c2 −

Z

Bi

(2.2)

i=1
with mN the nuclear mass, me the mass of the electron and Bi the binding
energy of the ith electron. β + decay is energetically possible when the atomic mass
energy difference is at least 2me c2 =1.022 MeV. The sum of the kinetic energies of
the positron and the neutrino is equal to the β-endpoint energy, ignoring the recoil
of the residual nucleus. Measuring the energy spectrum of the positrons emitted in
β + decay therefore provides a measurement of the Q value, which in turn yields
information about the energy difference between initial and final nuclear states.
Several final states can be populated in the daughter nucleus following β decay.
Angular momentum and parity selection rules for β decay dictate which nuclear states
can be populated. These rules are summarized in Table 2.1. The listed logf t-values,
also known as comparative half-lives, represent standard measures of the strength of a
given β-decay transition. As the range of half-lives in β decay is large, log10 f t values
21

(with t given in seconds) are quoted for convenience. They are useful in comparing
β decay probabilities in various nuclei as the differences in f t values must be due to
differences in the nuclear wave function and therefore to differences in nuclear matrix
elements [47].
Measurements of branching ratios can therefore constrain the spins and parities
of the nuclear states involved. Furthermore, some nuclei studied in this work were
created in excited states, which exhibited competing decay modes (see Section 2.4).
Detailed nuclear structure is therefore elucidated from the detection of the different
decay products and from the corresponding half-life measurements. Besides nuclear
masses, β-decay half-lives are among the most important nuclear physics ingredients
in the prediction of the rp-process path, energy generation rate and final composition.
The half-life measurements performed in our experiment are reported in Chapter 5,
and their incorporation into an rp-process reaction network is presented in Chapter
6.

2.3

Gamma Decay

Most of the nuclear excited states populated through β + decay in our experiment
decayed by emission of γ-rays. As the energy of a γ transition corresponds to the
energy difference between initial and final nuclear states, one can obtain information
on the excitation energy of the states populated in the β decay by performing βdelayed γ spectroscopy. Additionally, as the lifetimes characteristic of γ de-excitation
are usually very rapid compared to β decay, β-delayed γ emission occurs with a
half-life characteristic of the β decay, and γ transitions can then be used to obtain a
virtually background-free β-decay curve of the parent nucleus, which helps disentangle
the various decay components (see Chapter 5).
Also, some of the nuclei produced by fragmentation were created in long-lived
excited states (isomers) that decayed by γ-ray emission within a few microseconds of

22

reaching the experimental endstation. In the cases where the statistics were sufficient,
we were able to obtain γγ coincidences, that is, two or more γ transitions were detected
simultaneously, indicating that they correspond to the consecutive de-excitation of
states in a given nucleus (i.e. a γ cascade). This information, combined with that from
β decay, allowed us to extract information on the level scheme of the parent nucleus.
The emitted electromagnetic radiation during γ de-excitation is generated by a
reconfiguration of the protons and neutrons in the nucleus. The resulting electromagnetic radiation field is of multipole order 2L , where L corresponds to the angular
momentum carried away by the emitted photon. The γ transitions can be of electric (E) or magnetic (M ) nature depending on the relative parity of the initial and
final levels. The angular momentum and parity selection rules for electromagnetic
transitions are:

|If − Ii | ≤ L ≤ If − Ii

(no L = 0)

∆π = no :

even electric, odd magnetic

∆π = yes :

odd electric, even magnetic

When Ii = If the lowest possible γ-ray multipole order is dipole, and therefore
L = 1. In the case of If − Ii = 0 the state can only decay by internal conversion, or if
the energy is sufficiently high, by pair emission. In the electron conversion process the
nucleus transfers its excitation energy directly to an orbital electron without emission
of a γ-ray. The atomic electron is therefore ejected with a kinetic energy

Te = ∆E − Be

which is equal to the transition energy minus the binding energy of the electron. The

23

vacancy left by the emitted electron is quickly occupied by another electron from a
higher shell, followed by the emission of a characteristic X-ray (with energy equal to
the difference between initial and final electronic orbits).
Internal conversion is an electromagnetic process that competes with γ decay. The
ratio of the two decay modes is defined as the internal conversion coefficient α

α=

λe
λγ

The total decay probability will therefore have two components: λt = λγ + λe , or

λt = λγ (1 + α)

(2.3)

In a simplified model of the γ decay we can regard the electromagnetic transition as
the result of a single proton changing from one state to another. Then, the probability
per unit time (λγ ) for photon emission can be calculated using perturbation theory,
and the result is known as the Weisskopf single-particle estimate for the λth multipole.
These estimates can be used to compare measured decay rates and to infer their
multipolarities. The Weisskopf estimates for the first four multipole orders are listed
in Table 2.2.

2.4

Isomeric States

As mentioned in the previous chapter, characterization of isomers along the rp-process
path is necessary to calculate corrections for the lifetimes of these nuclei in the astrophysical environment. The role of an isomer in the rp-process will depend on the
amount of isomer produced, the time scale for thermalization, and on how different
proton capture and β-decay rates of ground and isomeric states are. The half-lives of
isomeric states and of the ground state of a nucleus must therefore be disentangled
for astrophysical calculations.

24

Nuclear isomers can be caused by either deformation (shape isomers), or by a
large change in spin required for decay (spin-gap isomers), or by a large difference in
spin orientation relative to an axis of symmetry (K-isomers) [49]. These excited states
decay often by electromagnetic processes (γ decay or internal conversion). Also α, β,
electron capture, proton, neutron or even nuclear fission are possible decay modes [50].
One reason for the appearance of high-spin isomers in the 100 Sn region is an extra binding energy due to the large attractive proton-neutron (pn) interaction in the
maximally aligned particle-particle or hole-hole configurations. The residual interaction between a proton and a neutron in the g9/2 shell produces states with large
spin differences, which are very close in energy [42, 50]. A number of isomers have
been predicted to exist in the region around 100 Sn (e.g. [1]), and several have been
experimentally confirmed. Some remarkable examples of high-spin γ-decaying isomers
are the 23/2+ and 37/2+ states in 95 Ag [40, 51], 14+ in 94 Pd [43, 51], and 12+ in
98 Cd [41]. β- and β- delayed proton (βp)-decaying isomers have also been found in
the region, examples of which are the 21+ level in 94 Ag [43, 44, 52] and the 25/2+
level in 97 Cd [53].
A β-decaying 16+ spin-gap isomer was predicted at an excitation energy of 5.30
MeV in 96 Cd [1, 42], with a half-life of 0.5 seconds. The predicted level scheme of
96 Cd is shown in Fig. 2.3. One of the goals of Experiment 07034 was to search for
this isomer.
An additional goal of our experiment was the search for isomers in isotopes with
previously measured half-lives as it is possible that experiments with limited statistics
measured mixed half-lives of ground and isomeric states. For instance, the half-life of
97 Cd was measured in a low statistics experiment [50] in which it was not possible
to dissentangle different decay components.

25

Excitation energy (MeV)

7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0

+

12

+

14+
12+
+
16 10
10+

8+
6+

8+
6++
4+
2
0+

4+

1.5
1.0

2+

0.5
0.0

0+
96 Cd

Figure 2.3: Calculated level scheme of 96 Cd. A 16+ β-decaying spin-gap isomer is
predicted at an excitation energy of about 5.3 MeV. Figure adapted from [42].

26

Table 2.1: β decay angular momentum and parity selection rules. ∆J = |Ji − Jf |
∆π represents the change in parity between initial and final states, equal to (−1)l .
Adapted from [48]
Transition type
Superallowed
Allowed
First forbidden
Second forbidden
Third forbidden
Fourth forbidden

∆J
+ → 0+
0
0,1
0,1,2
1,2,3
2,3,4
3,4,5

∆π

log10 f t1/2

no
no
yes
no
yes
no

3.1 - 3.6
2.9 - 10
5 - 19
10 - 18
17 - 22
22 - 24

Table 2.2: Weisskopf single-particle estimates for the lowest electric (Eλ) and magnetic
(Bλ) transition probabilities (in units of s−1 ). E is the energy of the γ transition in
MeV. Values from Ref. [48]
Electric transitions
λ(E1) = 1.02 × 1014 A2/3 E 3
λ(E2) = 7.28 × 107 A4/3 E 5
λ(E3) = 3.39 × 10A2 E 7
λ(E4) = 1.07 × 10−5 A8/3 E 9

Magnetic transitions
λ(M 1) = 3.15 × 1013 E 3
λ(M 2) = 2.24 × 107 A2/3 E 5
λ(M 3) = 1.04 × 10A4/3 E 7
λ(M 4) = 3.27 × 10−6 A2 E 9

27

Chapter 3
Experimental Setup
The experiment described in this work, Experiment 07034 “Study of the β-decay
of 100 Sn”, was performed at the National Superconducting Cyclotron Laboratory
at Michigan State University. The NSCL is a rare-isotope facility where radioactive
ion beams are produced by fragmentation of a primary beam impinging upon a light
target. Two superconducting cyclotrons coupled together accelerate the primary beam
up to 40% of the speed of light, and the fragments resulting from the collision with
the target are identified and separated by the A1900 Fragment Separator [54] through
the Bρ-∆E-Bρ selection technique, and, in the case of proton-rich nuclei, through an
additional velocity selection provided by the Radio Frequency Fragment Separator
[55]. The purified secondary beam is then sent to an experimental station for its
detailed study. Figure 3.1 shows a schematic layout of the laboratory, indicating the
areas associated with the production, separation and study of rare ion beams. In the
following sections the experimental setup and techinques used in our study will be
described in detail.

28

3.1

Projectile Fragmentation at NSCL

In projectile fragmentation high-energy nuclei are broken into smaller residue nuclei
that retain most of the vector momenta of the beam [56]. The process can be understood in terms of the so-called abrasion-ablation model, which consists of two basic
steps. In the abrasion step, the overlapping portions of projectile and target nuclei are
sheared away by the collision, and the remaining projectile, also called prefragment,
continues to travel forward with a minor decrease of velocity [57]. The projectile is
left, however, with a region of extra surface area exposed by the collision, which translates into an excitation energy according to the semiempirical mass equation of about
1 MeV per excess fm2 of surface area [58]. In the ablation step, the excess surface
energy becomes available as excitation energy and the prefragment subsequently decays by emission of γ radiation and/or nucleons, leading to a secondary product, or
nuclear fragment whose properties are then studied.
The secondary beam is initially composed of a variety of fragments, which must be
separated in order to obtain a sufficiently pure radioactive nuclear beam. At the NSCL
this separation is done by the A1900 Fragment Separator, which uses a separation
method based on magnetic rigidity analysis and energy loss in degrader materials [59].
The A1900 Fragment Separator uses four superconducting dipole magnets to bend
the ions for momentum-to-charge ratio selection, according to:

Bρ = p/q = γmv/q

(3.1)

The first half of the device selects the secondary fragments with magnetic rigidities
Bρ within a given acceptance. The momentum acceptance can be adjusted by slits
placed at the dispersive planes. Further selection is achieved by inserting an energy
degrader at the intermediate image (Image 2 in Fig. 3.1), in which the ions lose different energies depending on their atomic number, and emerge with different magnetic
rigidities. At Image 2, a thin plastic scintillator can be used for fragment tracking. The

29

second half of the device provides elemental separation by an additional bend after
the rigidity change in the wedge and provides an achromatic image of the target spot
that results in a small beam that can be transported through the beamline. At the
final focal plane, prior to sending the purified beam to the experimental vault, unambiguous particle identification is perfomed. Diagnostic detectors are inserted during
the setup of the separator and then removed to send the beam to the experimental
vault. A thin plastic scintillator (XFP scintillator) is used to provide a time signal
for Time-of-Flight (TOF) determination. A pair of Parallel Plate Avalanche Counters
(PPACs) can be used to measure the position and angle of the fragments, which are
then stopped in a stack of silicon PIN detectors in front of a HPGe detector. This
method is used to tag ions in isomeric states with half-lives in the microsecond range,
which decay by emission of γ-rays. The detection of known isomers is then used to
verify the particle identification of the rest of the fragments (See section 4.1.2).
Two key characteristics of the projectile fragmentation mechanism that determine the properties of the radioactive beam are the cross sections and the fragment
momentum distributions. The cross-sections are largest for fragments close in mass
to the projectile, and decrease within an isotopic chain for higher and lower mass
number [56]. The momentum distributions are characterized by a small decrease in
velocity compared to the incident beam and a nearly Gaussian spreading, which is
larger than the velocity decrease. However, the momentum distributions of neutrondeficient fragments produced by primary beams in the energy regime between 50 and
200 MeV, as is the case at NSCL, are asymmetric, exhibiting long tails on the low
momentum side due to additional dissipative processes during the collision.
The momentum distributions of neutron-deficient isotopes are peaked at lower
magnetic rigidities than that of their more stable isotopes upon exiting the A1900
Fragment Separator. The low momentum tails of these more abundant contaminants
therefore overlap with the peak of the momentum distribution of the fragments of
interest for a given magnetic rigidity setting of the separator, thus creating a serious

30

problem of contamination for decay studies. Figure 3.2 illustrates this contamination
problem for the case of production and separation of 100 Sn, as calculated with the
program LISE++ [60]. Successful decay studies under these conditions would not
be possible due to an overwhelming number of random ion-decay correlations (See
Section 4.2). Therefore, further purification of the secondary beam is necessary.
However, one can see from equation 3.1 that, for a constant Bρ, the different mass
to charge ratios m/q correspond to different velocities. That is, particles in the low
momentum tails of the contaminants (i.e. with higher m/q than the neutron-deficient
fragments of interest) have lower velocities compared to the particles of interest that
are selected at the maximum of their momentum distribution.
These differences in velocity can thus be used as an additional mechanism to
select the desired isotopes in the secondary beam and separate them from the more
stable low momentum contaminants. At the NSCL, the Radio Frequency Fragment
Separator (RFFS) (described in section 3.2) provides this additional purification by
applying a transverse electric field to the secondary beam, which causes a vertical
deflection of the fragments according to their velocity. A slit downstream of the device
eliminates unwanted fragments, leading to beams sufficiently pure for decay studies
[55].

3.2

Radio Frequency Fragment Separator

As discussed in Section 3.1, a velocity filtering of the mixed rare isotope beam is necessary to improve beam purity for decay experiments. The Radio Frequency Fragment
Separator (RFFS) was proposed, designed and built at the NSCL in order to achieve
this velocity filtering [55]. The principle of operation of the RFFS is based on the
fact that after some distance from the production target, where all ions are produced
simultaneously with the primary beam pulses from the K1200 cyclotron, velocity
differences between the various ion species translate into a phase difference relative

31

to the cyclotron frequency. Therefore, a transverse radio frequency electric field can
be used to cause a phase-dependent deflection, which leads to an effective velocity
filtering. The proof of principle had been demonstrated before at RIKEN, where a
similar device was constructed and is now operational albeit with a lower purification
performance compared to what is required for decay experiments at NSCL [61].

3.2.1

Design

The study of the β-decay of 100 Sn was the primary motivation for the construction
of the RFFS at the NSCL. Therefore, its performance requirements were aimed at
enabling this experiment. Proper correlation of implanted ions and decays requires
that an implanted fragment β-decays before another implantation occurs in the same
pixel of the implantation detector (see section 3.3.1 for details). To measure half-lives
of the order of 1 second and smaller, the average time between implantations should
be greater than 10 s. With a detector pixelation of about 1000, this can be achieved
by keeping the average implantation rate below about 10 Hz.
Figure 3.3 shows a schematic diagram of the RFFS, installed in the combined
S1/S2 vault of the NSCL. The RF-kicker is the most important component of the
RFFS. A photograph of the RF-kicker is presented in Fig. ??, and Fig. 3.5 depicts
the inside of the device, which consists of a cylindrical cavity that contains a pair of
parallel plates that act as electrodes, in between which a uniform RF vertical electric
field is created. The dimensions of the electrode plates are critical parameters in
order to obtain the best filtering performance, they are 1.5 m in length, 10 cm wide,
and are separated by a 5 cm gap. When a particle of mass m and charge q moving
with a velocity v (or alternatively, having a magnetic rigidity Bρ) travels through a
transverse RF field, it is deflected by an angle ∆b given by

∆b =

V
(cos(φ) − cos(ωT + φ))
Bρgω

32

(3.2)

where V is the sinusoidal voltage across the electrodes, g the gap in between, ω
the RF frequency, φ the phase difference between the particle and the cavity, and
T the time it takes the particle to traverse the field region. Clearly, the maximum
deflection is attained when the particle arrives in phase with the RF field (φ = 0)
and it traverses the full cavity in a time T = π/ω. The RF-kicker is located 54 m
away from the production target, and it is operated at the K1200 Superconducting
Cyclotron frequency, which for our experiment was 21.81 MHz, for a primary beam
energy of 120 MeV per nucleon. The RFFS was operated at its maximum peak voltage
of 100 kV. After traversing the cavity, the beam is transported to the focal plane box,
located 5.3 m downstream of the RF-kicker, where a set of vertical slits is used to
block out unwanted species. The slit gap and center position settings are adjusted to
optimize beam purity and transmission. Once the secondary beam is selected, it is
transported further to the experimental endstation. The RFFS focal plane box also
contains detectors for beam diagnostics that allow proper tuning of the device. A pair
of Parallel Plate Avalanche Counters, one on either side of the selection slits, is used
to determine the position of the beam species before and after filtering. The PPACs
are followed by a thin plastic scintillator that provides a signal for time-of-flight
measurements, and a stack of Si detectors that is used for particle identification. In
addition, a re-entry port allows the insertion of a high efficiency Ge detector in order
to identify γ-rays emitted by short lived isomers that aid in the particle identification
process (see section 4.1).

3.2.2

Performance

The effect the RF-kicker has on the secondary beam is illustrated in Figure 3.6, where
the vertical position of the fragments is plotted as a function of the time-of-flight, as
calculated with the program LISE++. The positions of the fragments follow the
periodic function described by equation 3.2. The phase of the RFFS can be adjusted
so as to cause a maximum deflection for the nuclei of interest, while keeping most of
33

the contaminants in a region where they will be blocked by a single slit (represented
by the yellow area in the figure), thus limiting the total implantation rate at the
experimental endstation. These settings have the additional advantage that, in case
the RFFS fails, the full secondary beam will be blocked at the slit, thus avoiding
potential damage to the implantation detectors.
The RFFS was commissioned with beam in May of 2007. A primary beam of
124 Xe at 140 MeV/u was initially sent directly to the RFFS in order to test the
vertical deflection caused as a function of the RF phase of the cavity. During the
commissioning run the rf power available was just 6 kW, which generated a 55 kV
maximum deflecting voltage. Figure 3.7 shows the vertical position of the 124 Xe
beam measured at the slit position, as a function of the RF phase. The two curves
correspond to different RF voltages, and it can be observed that the deflection follows
a sinusoidal and scales linearly with the magnitude of the applied voltage, as expected.
A test of the filtering capability of the device then followed. The primary 124 Xe beam
was therefore impinged onto a 9 Be target in order to produce 100 Sn and its closest
neighbors by fragmentation. The secondary beam was first filtered with the A1900
Fragment Separator and then sent to the RFFS. A few hours were dedicated to finding
the optimum production and filtering settings, which then allowed the removal of a
large amount of contaminants from the secondary beam (about a factor of 15) and
permitted the identification of the exotic N = Z nucleus 96 Cd.
Soon after the commissioning run a 50 kW power supply was installed in the
RFFS, and the cavity could then operate at its nominal maximum voltage of 100 kV.
During EXP07034, the RFFS effectively removed the majority of the most abundant
contaminants present in the secondary beam, thus reducing the total rate at the
implantation detector by about a factor of 200, to an average of about 50 counts per
second. This powerful filtering is evident in Figure 3.8, acquired during preparation
runs for 100 Sn production. The phase of the RF field was adjusted to let the N = Z
heavy ions and closest neighbors pass to the experimental end station. The left panel of

34

Figure 3.8 shows the particle identification when the slits of the RFFS are completely
open. When the slits are closed a large fraction of the undesired species is removed, as
shown in the right panel of Figure 3.8, and the overall rate thus becomes acceptable
for decay studies. The actual vertical deflection of the fragments is shown in the lower
left panel of Figure 3.8, where the phase was adjusted to push the ions of interest to
the lowest position. The majority of the contaminants is then removed from the beam
by lowering the upper slit, indicated by a yellow band in the figure. The contaminants
that enter the RFFS cavity in phase with the fragments of interest cannot be removed.
They correspond, however, to lower Z isotopes with half-lives of the order of several
seconds, which will therefore only contribute to the decay activity as a constant
background (see section 4.2 for details). This selective rejection is crucial as it allows
us to remove key contaminants while leaving the counting rate of the fragments of
interes unaffected.

3.3

Experimental Station

The experimental end station was composed of the NSCL Beta Counting System
(BCS) [63] and sixteen detectors from the SeGA array [64]. The BCS included three
silicon PIN detectors, used to perform particle identification through energy loss and
time of flight measurements. Downstream of the PIN detectors there was a 1 mm
thick Double Sided Silicon strip Detector (DSSD) in which the ions were implanted
and their decay products (positrons and protons) were detected and correlated with
previously implanted ions within time and position windows in order to determine
half-lives. Following the DSSD there were six 1 mm-thick Single Sided Silicon strip
Detectors (SSSDs) to perform beta calorimetry, and a 1 cm-thick planar germanium
detector to veto light particles coming in with the beam. Sixteen high purity Ge
detectors from the SeGA array were placed in close geometry around the DSSD in
order to measure prompt and β-delayed γ-rays within a predefined time window after

35

a charged particle triggered the data acquisition.

3.3.1

Beta Counting System

The beta-decay of the fragments of interest was measured with the BCS [63]. The
BCS consisted of a stack of three Si PIN detectors (PIN1, PIN2, and PIN3), with
thicknesses of 297 µm, 297µm, and 488µm respectively, used to measure energy loss
and to provide time signals necessary for particle identification (PID). The thicknesses
of the PINs were chosen so as to cause enough energy loss to the nuclei of interest
to stop them within the DSSD. The implantation of fragments is predicted by the
program LISE++ to occur at a depth between 200 and 300 µm into the DSSD.
The most important component of the BCS was the DSSD, placed downstream
of the PIN detectors, a 985 µm-thick Si wafer segmented into 40 1 mm-wide vertical
strips on the front, and 40 1 mm-wide horizontal strips on the back, thus effectively
creating 1600 individual pixels. The DSSD detects both, implanted ions and their
subsequent decays, which are later correlated via software such that half-life information can be extracted. Each of the strips of the DSSD was connected to a dual gain
pre-amplifier. The signals amplified with low gain were used to detect implanted ions,
which deposit a few GeV of energy. Signals amplified with high gain were used to
detect the β particles, which deposit up to a few hundred keV. A master gate signal
was generated by a logical OR of the front and back signals of the DSSD, which,
together with a computer-not-busy signal provide a master live signal, which in turn
starts the data acquisition. Each event is time stamped using a 50 MHz clock and a
32 bit counter providing the capability to determine time differences of events with
a resolution of 5.12 µs. Decay times are then determined by subtracting the time of
implantation of a fragment from the time of its associated β-decay. Downstream of
the DSSD there was a set of six SSSDs, with thicknesses of 975, 981, 977, 989, 988
and 985 µm, respectively, used to perform beta calorimetry and to veto light particles
coming in with the beam. The SSSDs are segmented into sixteen strips, and they
36

were setup so that the orientation of their strips alternated between horizontal and
vertical directions. The last element of the BCS was a planar high purity germanium
detector used to create a veto for light particles present in the beam. This veto is
needed because light particles can be mistakenly identified as beta particles in the
DSSD, but as they travel downstream with the beam, they enter the Ge detector,
where they deposit much more energy than any beta particle that happens to be
emitted towards the downstream direction.

3.3.2

Segmented Germanium Array

Sixteen high purity Ge detectors from the Segmented Germanium Array (SeGA) were
used to detect γ rays from the decay of excited states in both implanted fragments
and their decay daughter nuclei. Once an implant or a decay event was registered in
the BCS, a gate was opened for 20 µs to allow SeGA to detect time and energy of
emitted γ-rays. This enabled the detection of microsecond isomeric states in implanted
fragments, which aided the particle identification (see section 4.1), and also enabled us
to identify new isomers. The detectors were arranged in two rings situated as close as
possible to the beamline, and centered around the DSSD. Each detector was read out
individually, providing time and energy measurements for each detected transition.
The absolute gamma detection efficiency of the array was 6.1% at an energy of 1
MeV, as determined by using calibrated radioactive sources of 56 Co, 125 Sb, 154 Eu,
and 155 Eu. A picture of the SeGA array around the beamline is shown in Fig. 3.9.
SeGA Energy Calibrations
In order to generate gamma spectra with sufficient statistics for data analysis, the
data taken by all SeGA detectors were combined into a single spectrum for each
nuclear species. This requires each individual detector to be calibrated in energy, so
that all sixteen spectra can be aligned and combined into a single gamma spectrum.
With the purpose of monitoring the performance of all SeGA detectors throughout
37

the experiment, three energy calibrations were performed at different times during the
experiment, the first two with a Standard Reference Material source (SRM), which
contains 125 Sb, 152 Eu, 154 Eu, and 155 Eu, which emit γ-rays in the range of 40 keV
to 1500 keV. For the last calibration an additional 56 Co source was used to calibrate
higher energies. For the calibrations, the data acquisition was triggered with an OR
of all SeGA detectors. The peaks in each of the resulting γ spectra were fitted with a
Gaussian function using the program Tv [65] and the channel number of each centroid
was correlated to the known energy of the emitting source. The energy resolution of
all detectors was ≤3.5 keV full-width at half-maximum (FWHM) for the 1332 keV
transition of 60 Co (present as background).
A third order polynomial calibration function relating ADC channel with energy
was obtained with this method for each one of the sixteen detectors. Fit residuals were
then calculated for all the calibrated spectra as the differences between calibrated and
known source energies.
The stability of the energy calibration was monitored using the channel location of
the 511 keV peak from positron anihilation that was present in the β-delayed spectra
of all Ge detectors. Several such shifts were observed, requiring the use of different
calibrations for different detectors and runs. Figure 3.10 illustrates this point and
shows the centroid of the 511-keV peak is plotted for detectors 4, 9 and 16 as a
function of run number using each one of the three calibrations. For detector 4, for
instance, the calibration “4634” works fine througout the entire experiment, yielding
the smaller residual. However, that was not the case for detector 9, as can be seen
in 3.10b, from run 4190 to around run 4425, the calibration that yielded the smallest
deviation of the centroid of the observed 511-keV peak from the actual value was the
first one, labeled “4267” in the figure, but starting at run 4425 the best calibration
to use is the third one, labeled “4634”. The case of detector 16 is also illustrated in
Fig. 3.10c, the best calibration for runs 4196 to around 4414 is the first one, labeled
“4267”, then the “4424” calibration works best, and starting at run 4470 the best

38

calibration to use is the third one, labeled “4634”. This analysis was done for all 16
SeGA detectors and resulted in five different run-dependent energy calibration files as
energy shifts occurred for different detectors at different times. Table 3.1 summarizes
the run-dependent SeGA energy calibrations incorporated into our analysis software.
It was found that detector 2 showed a poor energy resolution and was therefore not
used for data analysis.
SeGA Efficiency Calibrations
The SeGA detectors were calibrated for efficiency using the aforementioned sources
prior to the start of the experiment. The calibration sources were placed at the position of the DSSD, and γ-ray spectra were acquired with all detectors for a preset
collection time of 3600 seconds. The observed peaks were fitted using the program
Tv, and the area, corrected for dead time, was used to determine an observed rate
which was then normalized to the known emission rate of the calibration source.
This was done for each individual detector and the results were added to determine
the efficiency of the entire array, the errors were added in quadrature. It should be
noted here that one of the detectors (Detector number 2 in the electronics) had a bad
resolution during many runs, and also shifted in energy too many times, so it was
decided not to include it in the total gamma spectrum; therefore the efficiency was
determined considering only the other 15 SeGA detectors. The obtained efficiency
data as a function of the γ-ray energy, Eγ , were fitted with an empirical formula of
the form

ǫ = Ae−Bln(Eγ − C)
in the energy range of 43 to 3273 keV, and the resulting efficiency curve is shown
in Fig. 3.11.

39

3.4

Rare Isotope Beam Production Settings

The production and separation of doubly magic 100 Sn and its closest neighbors has
been a major experimental challenge for nuclear physics in the last few decades. However, projectile fragmentation had proven to be a promising production mechanism in
previous experiments performed at GSI and GANIL. The first successful identification of 100 Sn was achieved at GSI [66], produced from a beryllium target bombarded
by a 1095 MeV/u 124 Xe beam. Seven events were reported as 100 Sn from that experiment. Around the same time, 100 Sn was also produced at GANIL [67], from a
primary beam of 112 Sn accelerated to 63 MeV/u impinging on a nickel target. The
production cross section reported from this work was σ ≥ 120(pb). A second attempt
at GSI with 112 Sn fragmentation on beryllium yielded only one 100 Sn identification
during 60 hours of beam on target [68].
Low production rates combined with high levels of contamination had hindered detailed decay studies of 100 Sn and its closest neighbors at the NSCL. The first attempt
to produce 100 Sn at the NSCL (Experiment 01006) utilized a 124 Xe primary beam
accelerated to 140Mev/u, impinging on a 390 mg/cm2 9 Be target. Unfortunately, high
amounts of contaminants were produced with half-lives of tens of seconds or more,
thus preventing attempts to correlate implanted fragments with their subsequent β
decays. The measured rate of 100 Sn during experiment 01006 was 1.3+1.2 × 10−3
−0.7
pps/pnA for a momentum acceptance of 5%, based on the observation of two 100 Sn
events.
During the commissioning run of the RFFS (see Section 3.2.2 below), an attempt
was made at identifying 100 Sn. Two events were identified as 100 Sn, but not unambiguously, since only one time-of-flight measurement could be done due to the
prohibitively high rate on the A1900 image 2 scintillator. Based on the observed
rates for other N = 50 isotones (see Fig. 3.12), a production yield of 100 Sn was
estimated as 7 ×10−5 pps/pnA, derived from the observed maximum rate of 99 In,

40

5×10−4 pps/pnA. This estimated rate of 100 Sn production was an order of magnitude lower than the one assumed in the proposal for Experiment 07034, of 6.5+6.0
−3.5
× 10−4 pps/pnA for this combination of primary beam (140MeV/u 124 Xe at 2 pnA
intensity) and target (berillyum).
With an order of magnitude less yield than expected with the 124 Xe beam, it was
decided to perform the Experiment 07034 with a 112 Sn primary beam instead, as
it was considered a suitable projectile for 100 Sn production according to the 120 pb
lower limit established at 63 MeV/u on a nickel target [67].
Targets of both, 9 Be and 58 Ni (backed with a 47 mg/cm2 -thick 9 Be foil) with
equivalent energy losses were tested in order to study the effect of the reaction mechanism on the production of 101 − 104 Sn isotopes and to extrapolate a production
rate for 100 Sn. This study revealed a higher yield by a constant factor of 5 for the
9 Be target [69].
Settings for production and separation of 100 Sn, such as Bρ, thicknesses of the
wedge and ∆E detectors, as well as RFFS parameters, were calculated with the
program LISE++ [60], and used to set the experiment up. These were chosen to
minimize the production of lower charge states without affecting 100 Sn production.
The very low expected production rate of 100 Sn prevented identification of fragments
at the A1900 focal plane, due to the long time that would be needed to accumulate
sufficient statistics. Therefore, with the purpose of finding the optimum Bρ settings
for the production of 100 Sn, a momentum distribution scan was done with heavier
(and more abundantly produced) Sn isotopes, starting with 104 Sn and going step
by step down to 101 Sn. For each tin isotope setting the beam was implanted in the
RFFS focal plane silicon stack, where its rate was measured. The location of the peak
of the momentum distribution of each of the 104 − 101 Sn isotopes was determined
by taking five measurements changing the Bρ by 1% each time. The Bρ setting for
100 Sn was then extrapolated based on measurements of its heavier siblings, assuming
that the production mechanism is similar.

41

The actual production settings for the neutron-deficient nuclei of our study were
therefore: fragmentation of a 120 MeV/u 112 Sn primary beam on a 195 mg/cm2 thick
9 Be target, at an average intensity of 10.7 pnA. The secondary beam containing the
fragments of interest was selected with the NSCL A1900 Fragment Separator [54],
operating in achromatic mode. A 40.6 mg/cm2 curve-shaped Kapton foil located at
the intermediate focal plane acted as an achromatic degrader. The magnetic rigidity
Bρ of the first half of the A1900 was set to 2.8802 Tm, and the second half to 2.7701
Tm, past the Kapton wedge. These settings were optimum for centering fully stripped
100 Sn fragments, and, in an effort to reduce the intensity of contaminant species, the
momentum acceptance of the separator was limited to 1%. The use of this narrow
acceptance allowed the separation of neighboring isotopes in the particle identification
with a simple time of flight measurement (see Section 4.1). This was convenient in our
experiment because the scintillator at the intermediate image of the A1900 Fragment
Separator, which is typically used for position measurements, was degraded due to
the high intensity of the beam.

42

K500
cyclotron
Secondary beam
(p-rich nuclei)
to experimental vault

Primary beam:112Sn
at 120
A1900
Fragment
Separator

Image 2
Kapton wedge, energy
degrader (40.6 mg/cm2)
Momentum acceptance = 1 %
K1200
cyclotron

Be target
195 mg/cm2

Figure 3.1: Ion beam production and delivery to the experimental station at NSCL.
A primary beam of stable ions is accelerated in the coupled cyclotrons and impinged
upon a Be target. Exotic fragments of interest are separated with the A1900 Fragment
Separator in conjunction with the RFFS to be delivered to the experimental station.

43

ρ
Figure 3.2: Production rates of 100 Sn and closest neighbors as a function of Bρ at
the exit of the A1900 Fragment Separator, as calculated with LISE++ [60]. More
stable fragments are produced orders of magnitude more abundantly, and their low
momentum tails leak into the momentum acceptance of the fragment separator, thus
causing an overwhelming background and making decay studies unfeasible. Figure
adapted from [55]

Beam

Focal Plane

Experiment

Figure 3.3: The incoming beam enters the RFFS from the left and after filtering it
is delivered to the experimental station. All white boxes represent quadrupoles. The
collimation slits and diagnostics detectors are located at the RFFS focal plane. Figure
adapted from [62].
44

Figure 3.4: Photograph of the RF-kicker, installed in the S1/S2 vaults. The vacuum
vessel is a cylindere made of copper-plated steel with an inner diameter of 0.9 m. The
beam enters the cavity from the left. The end of the RF guide connected to the RF
coupler is visible at the top right. Figure reproduced from [55].

45

RF coupler

beam

Electrodes
(parallel deflecting plates)
1.5m long, 5 cm gap

Fine tuner
(60 kHz of tuning
range)
RF electric field:
Maximum peak voltage of 100 kV
Frequency range: 17MHz to 27 MHz.

Capacitive (coarse) tuners: their
distance to the deflecting plates is
adjusted in order to match the RF
frequency of the cyclotrons.

Figure 3.5: Drawing of the RFFS cavity. The interior parts are made of solid copper and steel, and employ a water cooling system. The coarse tuners are adjusted
prior to the experiment to match the RF frequency of the cyclotrons, while the fine
tuner is used for frequency regulation necessary due to temperature fluctuations while
operating the cavity at different voltages.

46

Figure 3.6: LISE++ calculation of the vertical deflection of the secondary beam caused
by the RFFS. The vertical position of fragments in the secondary beam is plotted as
a function of their time of flight after passing through the RFFS. The yellow band
represents a slit to block unwanted fragments. 100 Sn and the ions with

Table 3.1: SeGA energy calibrations implemented in the data analysis of Experiment
07034 according to run number. Detector 2 was excluded from the data analysis due
to technical problems.
Det. No.
Cal1
Cal2
Cal3
Cal4
Cal5
Runs
Runs
Runs
Runs
Runs
4196-4414 4415-4424 4425-4469 4470-4659 4600-4632
1
4424
4424
4634
4634
4634
3
4634
4634
4634
4634
4634
4
4634
4634
4634
4634
4634
5
4634
4634
4634
4634
4634
6
4634
4634
4634
4634
4634
7
4634
4634
4634
4634
4634
8
4634
4634
4634
4634
4634
9
4267
4267
4634
4634
4634
10
4267
4267
4267
4267
4267
11
4267
4267
4634
4634
4634
12
4267
4267
4634
4634
4424
13
4634
4634
4634
4634
4634
14
4267
4267
4634
4634
4634
15
4267
4424
4424
4634
4634
16
4267
4424
4424
4634
4634

47

Figure 3.7: Deflection of a primary beam by the RFFS during its commissioning. The
vertical position of 124 Xe ions is plotted as a function of the RF phase of the cavity.
The two curves correspond to different applied voltages. Figure adapted from [55]

48

Figure 3.8: Particle identification at the focal plane of the RFFS. The two lower panels
show the vertical position of the fragments as a function of ToF at the exit of the
RFFS. The total number of counts in all spectra are similar, the spectra on the left
were taken with the blocking slits open, and the ones on the right were integrated
with the slits closed and much more primary beam. The filtering capabilities of the
device are evident, the purification factor achieved was around 200 at the experimental
station. Figure adapted from [55]

49

Figure 3.9: Experimental endstation. Sixteen SeGA detectors surrounding the beam
line and centered around the DSSD. The beam enters from the left.

50

2

(a)

1

0

-1

-2

Residual (keV)

1.5

(b)

1
0.5
0
-0.5
-1
-1.5
2

(c)

1

0

-1

-2
4200 4250 4300 4350 4400 4450 4500 4550 4600 4650

Run Number
Calibration4267

Calibration4424

Calibration4634

Figure 3.10: Observed energy shifts in SeGA detectors (a) 4, (b) 9 and (c) 16 used in
Experiment 07034. The residual from the determination of the centroid of the 511-keV
peak is plotted as a function of run number for each of the three energy calibrations
performed.

51

0.2
f(x)=A*exp(-B*log(x-C))

0.15

0.15

1.0

0.1

0.05

0.05

0
0

0
500

1000

1500 2000 2500
Energy (keV)

3000

Residuals

SeGA Efficiency (Det02 excluded)

2.0

3500

Figure 3.11: γ-detection efficiency for the fifteen SeGA detectors used in the data
analysis (Detector No. 2 was excluded because of technical problems). Residuals are
shown in bottom panel.

52

Rate (pps/pnA)

10

-1

99In
97Ag
98Cd

-2

10

-3

10

10

-4

3.12

3.16

3.20

3.24

Magnetic Rigidity Bρ (T.m.)
Figure 3.12: Production rates of N = 50 isotones obtained from the RFFS commissioning run. The rates (in pps/pnA) are plotted as a function of the magnetic rigidity
of the A1900 Fragment Separator. A Bρ scan was performed to find the peak of the
momentum distribution of the most neutron-deficient isotopes produced.

53

Chapter 4
Data Analysis
The present chapter is dedicated to the description of the offline treatment given to the
raw data collected during Experiment 07034 in order to extract and interpret structure
information about the nuclei of interest. The main goal of this experiment was to
investigate the β decay of the doubly magic nucleus 100 Sn into 100 In. However, as was
described in Chapter 3, the beam reaching the experimental station is not 100% pure,
rather, it contains a group of nuclear species close in charge and mass to the nucleus of
interest, i. e. its neighbors in the chart of nuclei. The following sections describe how
these beam impurities are used to our advantage in providing unambiguous particle
identification of the most exotic fragments present. Additionally, this gives us the
opportunity to obtain new information on the neighboring nuclei that are also of
great interest for nuclear physics. These findings are presented and interpreted in
Chapter 5.

4.1

Particle Identification

Particle identification was a crucial aspect of our experiment. As described in Chapter
3, detectors installed at suitable points along the beam path are used to measure
energy loss and Time-Of-Flight (TOF) of the nuclei present in the secondary beam.

54

Each nuclear species in the secondary beam is uniquely characterized by its mass
and charge. According to the Bethe-Bloch equation, the energy lost by fast ions with
charge q and velocity v in matter is given by:
4πq2 e2
dE
=
NB
−
dx
m0 v 2
with
B ≡ Za ln

2m0 v 2
− ln(1 −
I

v2
)−
c2

(4.1)

v2
c2

where N and Za are the number density and atomic number of the absorbing
material, m0 is the electron rest mass, and e is the electron charge. The parameter I
represents the mean excitation energy of atomic electrons in the absorber, and is, in
practice, regarded as an empirical constant with a value in eV. Additionally, as Bρ is
fixed in the A1900, a measurement of the time-of-flight of the particles over a known
distance is a direct way to determine their mass to charge ratio (m/q). Therefore,
by independently determining dE/dx and TOF, both the charge and the mass of the
ions in the beam can be determined. The fragments produced with the highest yields
in our experiment corresponded to fully stripped ions. Charge state contamination,
i.e. from lower mass ions with orbital electrons resulting in the same m/q than the
fragments of interest, was negligible as such isotopes would be more exotic (i.e. more
neutron deficient).
The three Silicon PIN detectors installed at the experimental endstation provided
redundant energy loss measurements. Two TOF measurements were made, one was
determined from the time difference between a start signal from PIN1 and a stop
signal given either by a scintillator placed at the focal plane of the A1900 Fragment
Separator (XFP scintillator), or by the cyclotron RF signal. Figures 4.1, 4.3 and ??
show the particle identification spectra obtained with each of the three PIN detectors.
As expected, the fragments with the highest atomic numbers had the largest energy
loss in each detector. Each blob represents a particular nuclear species, and their

55

widths in time-of-flight are proportional to the momentum acceptance of the A1900
Fragment Separator. The requirement that each implanted particle at the DSSD leaves
valid signals in all three PINs is used to clean up the particle identification spectrum
at the DSSD. Additionally, the two TOF measurements must be proportioinal to each
other, and this proportionality can be used as a cleaning requirement as well.

4.1.1

µs-isomers

Several nuclei in our secondary beam were produced in excited states with half-lives
in the microsecond range. A large fraction of them was therefore able to reach the
experimental station after about 600 ns of flight path. These long-lived excited states,
or isomers, decay mostly by emission of gamma radiation, which we detected with
the SeGA array within a few microseconds after their implantation in the DSSD.
The decay information from well known isomers was used to confirm the particle
identification via the γ-ray tagging method [59]. The most abundant isomers detected
during runs in which the RFFS slits were open include 90 Mo, 93 Ru, and 96 Pd. When
the slits of the RFFS were closed the isomeric decays of 88 Zr and 94 Pd were used
for final particle identification confirmation. A list of the isomeric γ-transitions used
for particle identification is provided in table 4.1. Slice gates were made in the SeGA
spectrum at the energies of each of the known transitions and were used to gate
the ∆E (from PIN1) vs TOF spectrum, and the blob corresponding to the parent
nucleus was identified. Then the inverse was done for confirmation, a fragment in the
particle identification spectrum was used to gate the SeGA spectrum and the lines
corresponding to the correct fragment were clearly observed. The identification of the
rest of the isotopes was then done based on their position with respect of the known
isomers in the ∆E vs TOF spectrum.
Once the charge and mass of each fragment was unambiguously determined, it
was possible to produce the particle identification plot presented in Figure 4.4, with
the nuclear charge in the vertical axis, and the mass-to-charge ratio on the horizontal
56

PIN 1 energy loss (a.u.)

2200

2000

1800

1600
3300

3340

3380

3420

XFP Time of Flight (a.u.)
Figure 4.1: Particle identification spectrum obtained with energy loss measurement
from the PIN1 detector of the BCS and time-of-flight from XFP scintillator.

PIN 2 energy loss (a.u.)

1500

1400

1300

1200

1100
3300

3340

3380

3420

XFP Time of Flight (a.u.)
Figure 4.2: Particle identification spectrum obtained with energy loss measurement
from the PIN2 detector of the BCS and time-of-flight from XFP scintillator.
57

one. This plot does not include the lower Z nuclei which were not eliminated with
the RFFS, and that also reached the DSSD. Gates around the centers of each blob
were then used to select the data events corresponding to each particular isotope. In
the case of the most exotic nuclei of this study, fits applied to the mass spectra were
used in an effort to deal with the small contamination from neighboring nuclei. These
mass fits were used to determine a probability for the nature of a specific implanted
nucleus that was taken into account in the half-life determination in the MLH analysis
described below.
Based on the particle identification spectrum of Fig. 4.4, gates drawn around each
blob were used to identify each nucleus implanted into the DSSD with its unique
time stamp and pixel location. Then, time-stamps files were saved for each isotope so
that the analysis could be carried out for each different species independently. The
majority of the analysis of this experiment was done using the NSCL data analysis
program SpecTcl, which was modified to read the time-stamp files as input, and then
search the corresponding decays in the event files according to the time stamps of
interest only.
Isomeric Production Fraction
The isomeric production fraction F is defined as the number of nuclei produced in
the isomeric state as a fraction of the total number of nuclei produced for a particular
nuclide. Once corrections for decays during the time-of-flight from the production
target to the experimental station are taken into account, the isomeric production
fraction can be determined from the number of implanted nuclei and the number
of those implanted in their isomeric state. The number of nuclei implanted in the
isomeric state was estimated (following the procedure outlined by Daugas et al. [70])
from the number of counts in the observed γ-ray transitions, after correcting for the
relative γ-ray intensities inferred from the decay scheme and the photopeak efficiencies. A correction for decays occurring during the time-of-flight requires knowledge of

58

the decay half-life. This half-life can be different from the measured isomeric decay
half-life of the ions implanted in the detector as during flight ions are fully stripped
and therefore decay by electron conversion cannot occur. For neutron-deficient nuclei,
a correction for the suppression of electron capture and, more importantly, of electron conversion decay must therefore be applied. The following equation was used to
calculate the isomeric fractions reported in this work [70]:

F=

T
Nisom
exp ln(2) TOF
Q
Nions
γT
1/2

(4.2)

where Nisom is the number of detected isomers and Nions the number of implanted nuclei with mass A and atomic number Z, TT OF is the time-of-flight of the
Q
is the half-life of the isomer for charge
nucleus from the target to the DSSD, T
1/2
state Q, and γ is the relativistic factor. For fully stripped ions:
Q=0
Q=Z
(1 + αtotal )
=T
T
1/2
1/2

(4.3)

where αtotal is the total internal conversion coefficient.

4.2

Fragment - Decay Correlations

All the events registered in the DSSD were classified as either an implanted fragment
or a β particle based on thresholds established via software on the various detectors
of the BCS. An event was classified as an implantation when it produced a signal
above threshold in PIN1 (which ensured that the particle was a heavy ion in the
secondary beam), and signals above threshold in the low gain channels of the front
and back strips of the DSSD. The implantation pixel was therefore defined as the
intersection of the front and back strips in which the low-gain signals were maximum.
A β particle was identified as an event that did not produce a valid signal in PIN1,
but with signals above threshold in the high gain channels of the front and back strips

59

of the DSSD. Additionally, some light particles that may come with the secondary
beam are discarded by setting an upper threshold in the signals from the SSSDs and
on the planar Ge detector.
The correlation of a decay with its coresponding parent was done in software
using the time and position information of each event. The specific time and position
correlation settings used in the analysis of each nuclear species varied depending on
the half-life of the parent, the background rate, and the information sought. The
fragment-decay correlation in position was performed with a correlation area larger
than a single pixel to account for β particles that deposit only a small fraction of their
energy in the implantation pixel but that pass through a neighboring pixel, and also
to account for uncertainties in the determination of the implantation pixel. It will be
shown below that the β-detection efficiency scales with the size of the area chosen for
implant-decay correlations, but so does the amount of false implant-decay correlations
(background). A study to determine the ideal efficiency-background compromise was
performed, and the results are shown in Fig. 4.5. It was found that a 5-pixel correlation
area consisting of the implantation pixel plus its four nearest neighbors was optimum,
and such a geometry was used to determine the β-decay half-lives of the N = Z nuclei
96 Cd, 98 In, and 100 Sn. For most other nuclei the statistics were high enough to allow
the use of a single pixel for correlation, at the cost of lower β-detection efficiency in
favor of a lower amount of background.
A decay and a fragment correlated in position were also correlated in time if they
both occurred within a time window of about 10 (estimated) half-lives of the parent
nucleus. Making the correlation time larger only adds background to the decay curve,
wich however, can be useful to the fit, since by fixing the background level the number
of free parameters decreases.
The production rates of the very exotic N = Z nuclei was the lowest of all.
Therefore, in an effort to minimize the wrong correlation of their decay products
to other, more recent, implanted ions, a “Beam Off” gate was implemented, which,

60

upon detection of an implanted ion in a predefined area of the particle identification
spectrum of PIN1 vs PIN1.RF time-of-flight, dephased the cyclotron RF for 5 seconds,
preventing the beam from reaching the DSSD.

4.2.1

Determination of β-decay Half-lives

The β decay half-lives of the implanted nuclei were determined using two different
methods, both of which assumed Poisson statistics, but differed in the treatment of
data. The methods were chosen based on the number of fragment-decay correlations
observed for each particular isotope. For the cases with high statistics, the differences
in time between the implantation of the fragment and its correlated decay events were
binned into ∆t intervals, from zero to the maximum correlation time. The resulting
decay curve was then fitted with the ROOT Minuit least-square minimization procedure that determines a constant level of background and the decay constant of the
parent nucleus, considering the activities of the parent, daughter, and grandaugther
nuclei according to the Bateman equations for nuclear decay. In the Bateman equations the activity of the nth member of the decay chain is given in terms of the decay
constants of all preceeding members [47]:
n
An = N0

c1 e−λi t

(4.4)

i=1
Necessary input parameters for the ROOT fitting routine were the desired bin
size, daughter and grandaughter half-lives, and initial guess values for the parent
decay constant, initial activity, and background level. The β-decay half-life curves are
presented in the next chapter.
For the most exotic nuclei of this study, the statistics was too low for the above
method to be effective in the half-life determination. Therefore, a Maximum Likelihood (MLH) method was applied, which used all of the information available, event
by event, to find the parent decay half-life that maximized a joint probability density

61

called the likelihood function. Inputs to the MLH are daughter and grandaughter
half-lives, background rate and β-detection efficiency. The probability density function for up to three decay events within the correlation time window is calculated
taking into account all possible scenarios leading to the observation, including background events [71]. The determination of the half-lives for the N = Z implants was
then performed by calculating the likelihood for the observed event sequences as a
function of assumed parent half-life. The maximum of the likelihood function corresponded to the decay half-life. The width of the likelihood function is then used to
estimate error bars.
β Detection Efficiency
The β detection efficiency of the DSSD (ǫβ ) was determined from the fit to the decay
curves of isotopes with high statistics and known half-lives, such as 93 Pd, 95 Ag,
96 Ag, and 100 In. The fit allows the calculation of the total number of parent decays
Nd , which, compared to the total number of implanted nuclei Ni , yields ǫβ .

ǫβ =

A0 T1/2
Nd
=
Ni
Ni ∆tln2

(4.5)

where A0 is the number of counts in the first bin, T1/2 the half-life determined
from the fit, and ∆t the bin size of the histogram. The average β efficiency of the DSSD
was 37(2)%, using a 5-pixel correlation area. Since the energy loss of the β particles
in the DSSD is only a few hundred keV (i.e. only a small fraction of their energy),
it was assumed that the efficiency is independent of the Qβ value and therefore the
same for all nuclides. This was confirmed by comparing the efficiencies obtained for
95 Ag, 97 Cd, 98 Cd.

62

β Background
A large number of decays ocurred at any given time all over the DSSD, which resulted in incorrect fragment-decay correlations. Therefore, the decays assigned to the
incorrect fragment become a source of background in the implant-decay histograms.
As the vertical deflection caused by the RFFS to each particular fragment depended
on its time-of-flight, each nuclear species was implanted in slightly different overlapping regions of the DSSD. Therefore, the resulting β-decay background was isotopedependent.
For the exotic N = Z nuclei, the background was determined from the history
of implantations in each pixel of the DSSD. A background rate was then calculated
by summing the background contribution from each isotope implanted in that pixel,
provided their half-lives were known.
For the species observed with high statistics, the background was determined from
the fits to their decay curves. By allowing a sufficiently long correlation time, it was
possible to clearly observe most of the decay of the parent nucleus, until the remaining
activity could be assigned to background, which was constant over the observation
period.

4.3

Prompt γ Radiation Measurement

As described in section 4.1.1, our experimental setup allowed the detection of γrays from isomeric states within a window of around 12 µs after the implantation
of the parent nucleus. We call these γ-rays prompt. For each isotope in our particle
identification, a total prompt γ-ray energy spectrum was constructed in SpecTcl by
combining the energy-calibrated spectra from the fifteen SeGA detectors. Such spectra
were analyzed using the program Tv [65], where the γ-rays peaks were fitted with
Gaussian distributions for the case of high statistics, and with Poisson distributions
in the case of low statistics. Tv outputs centroids, FWHMs and peak areas, with

63

their respective uncertainties. Relative γ-ray intensities were obtained by correcting
the peak areas for the efficiency of the SeGA detectors, and normalizing them to 100
for the most intense peak.
When an isotope emits multiple cascade γ rays in its decay, additional peaks may
appear in the recorded spectrum. If no isomeric states are involved, the lifetime of
the intermediate state is generally so short that the two γ rays are, in effect, emitted
in coincidence. It is then quite possible for both γ-ray photons from a single decay to
interact with the material of the detector and deposit all their energy within a time
that is short compared with the response time of the detector or the resolving time of
the following electronics [72]. If enough of these events occur, a sum coincidence peak
will be observable in the spectrum that occurs at a pulse height that corresponds to
the sum of the two individual γ-ray energies. A continuum of sum events will also
occur at lower amplitudes due to the summation of partial energy loss interactions.
Two-dimensional matrices of prompt γ-ray energies were constructed in order to
study the coincidence relationships of the observed transitions. One example of such
matrices is shown in Fig. 4.6 for the case of 96 Ag. One-dimensional projections of
each matrix were done at the energies of interest in both, horizontal and vertical
axes, then the pair was added in Tv to obtain a γγ spectrum for each transition.
Relative intensities and coincidence relationships obtained this way are the usual
method utilized in the construction of decay schemes, as will be explained in more
detail in the next Chapter.
Isomeric half-lives can be determined from a two-dimensional matrix of the prompt
γ-ray energies vs time, like the one presented in Fig 4.7. The time between implantation of a fragment and its subsequent γ emission was measured by a time-to-amplitude
converter (TAC), started by an master gate (MG) Live signal, and stopped by an OR
of all SeGA detectors. A cut around the energy of the transition of interest was projected into the time axis in order to obtain a decay curve, which was then fitted with a
single exponential component and a constant background. The SeGA-TAC spectrum

64

shows a large amount of counts at early times due to the overload of the germanium
detectors from X- and γ-rays created when the heavy ions are implanted in the silicon
detector, therefore all of the µs-isomeric decay curves were fitted starting at around
1.5 µs, ignoring data at earlier times.

4.4

β-Delayed γ Radiation Measurement

Following β-decay, some nuclei reach an excited state of the daughter nucleus, which
is quickly de-excited by the emission of γ-rays. These γ-rays are therefore referred to
as β-delayed, and are typically emitted with the half-life characteristic of the β-decay
of the parent. Since these γ transitions uniquely identify a parent decay, they can
be used to determine decay curves and half-lives free of contamination from random
correlations with other isotopes or daughter decays, although with reduced statistics,
due to the limited γ-ray detection efficiency.
Fragment-β − γ coincidence spectra were obtained for all isotopes in our particle
identification, and they were analyzed in the same way as the prompt γ spectra
described above in order to extract γγ-coincidence information.

65

PIN 3 energy loss (a.u.)

2200

2000

1800

1600

3300

3340

3380

3420

XFP Time of Flight (a.u.)
Figure 4.3: Particle identification spectrum obtained with energy loss measurement
from the PIN3 detector of the BCS and time-of-flight from XFP scintillator.

66

Table 4.1: Known γ-rays from µs isomers used for particle identification.
Parent nucleus
88 Zr

T1/2 (µs)
1.320(25)

90 Mo

1.12(5)

93 Ru

2.20(17)

94 Pd

0.468(0.019)

96 Pd

2.2(3)

67

Eγ (keV)
77.0
271.8
671.2
399.4
1082.5
1057.0
809.6
262.8
546.7
1054.1
948.0
146.3
544.2
1392.1
95
324
659
814
905
994
1092
106.4
325.1
683.8
1415.4

1000

50

48
Z

100

46
10

44
1

1.98

2

2.02 2.04 2.06 2.08
A/Z

Figure 4.4: Particle identification spectrum of the heavy nuclei implanted in the DSSD.
The low-Z contaminants are not shown in this figure. Figure adapted from [69]

68

Beta-detection efficiency (%)

60 %

50 %
3x3square
pixel
40 %

cross pixel

30 %

20 %

cross-no-center

single pixel

10 %

corner pixels

0%
0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Background rate (1/s)

Figure 4.5: β-detection efficiency of the BCS as a function of the amount of background observed. The labels indicate the correlation pixel considered in each case:
single-pixel means that both, implant and decay were detected in the same pixel;
cross-pixel refers to the implantation pixel plus its four nearest neighbors; 3 × 3
square means a 9-pixel area centered around the implantation pixel; corner-pixels
refers to the four corner pixels of the 3 × 3 square pixel; and cross-no-center pixel
means the 4 nearest neighbors, without considering the implantation pixel.

69

250
1600

γ-Energy (keV)

1400

200

1200
150

1000
800

100
600
400

50

200
0

0

200 400 600 800 1000 1200 1400 1600

0

γ-Energy (keV)
Figure 4.6: Two-dimensional matrix of prompt γ-ray energies measured with SeGA
for the 96 Ag implants. A cut around an energy of interest in each axis is projected
along the opposite one in order to extract γγ coincidence information.

70

1800

600

γ−ray Energy (keV)

1600
500

1400
1200

400

1000
300

800
600

200

400
100
200
0

0

2

4

6

8

10

12

0

Time (µs)
Figure 4.7: Two-dimensional matrix of prompt γ-ray energies measured with SeGA
as a function of time in the SeGA TAC. This spectrum was generated for the 96 Ag
fragments implanted in the DSSD. A cut around an energy of interest in the energy
axis is projected along the time axis in order to construct a decay curve for that γ
transition.

71

Chapter 5
Experimental Results
Fourteen exotic neutron-deficient nuclei were studied in Experiment 07034. As described in previous chapters, the region in the chart of nuclides close to 100 Sn is
characterized by the occurrence of high-spin isomers. Several such long-lived excited
states were observed in our experiment and they are presented in the following sections. Diverse decay modes were identified in this study, namely γ, internal conversion, β or β-delayed proton emission. Results on β-decay half-lives, and prompt and
β-delayed γ spectroscopy are presented in the current chapter, along with the interpretation of the results in terms of the underlying nuclear structure. The possible
implications of our results on the astrophysical rp-process are discussed in Chapter
6.

5.1

N = Z Nuclei

The particle identification plot presented in Fig. 4.4 represents the accumulated statistics for the most exotic nuclei produced in Experiment 07034. Experimental results
are presented in this section for the N = Z nuclei 96 Cd, 98 In and 100 Sn. The β-decay
half-life of 96 Cd was determined in this work for the first time, and its possible consequences on the production of mass A = 96 in the rp-process explored. The β-decay

72

half-lives of 98 In and 100 Sn had been measured previously, and the results obtained
in the present study are in agreement with those measurements.

5.1.1

96

Cd

96 Cd was first observed at the NSCL during the commissioning run of the RFFS
in May of 2007, produced by fragmentation of a primary beam of 124 Xe impinging
on a 188 mg/cm2 9 Be target at an energy of 140 MeV/u. The particle identification spectrum is presented in Fig. 5.1, with 96 Cd marked in the upper right corner.
The particle identification was confirmed through observation of known γ transitions
from the de-excitation of a microsecond (µs)-isomer in 94 Pd. The experimental setup
during the RFFS commissioning was not suited for β-decay studies. The measurement, nevertheless, allowed us to unambiguously identify eighteen 96 Cd events and
to determine the production rate of 96 Cd as 2.03 ± 0.48 × 10−4 pps/pnA for these
production settings. A lower limit for the half-life of 96 Cd was estimated at around
475 ns, based on the time-of-flight of the fragments from the target position to a Si
PIN detector installed at the RFFS focal plane.
During Experiment 07034, 274 (24) implantation events of 96 Cd were registered at
the DSSD. β-decays occurring within the implantation pixel and its nearest neighbors
within 10 seconds of a 96 Cd implantation were correlated to the fragments. The time
distribution of observed decay events within the 10 seconds of correlation time is
shown in Fig. 5.2. The time axis was plotted on a logarithmic scale with the intention
to improve the visualization of different decay components, in case more than one
was present. The event rates of decays plotted on a logarithmic time scale show a
bell-shaped distribution peaked around the mean life time [73]. Thus, when two or
more decay components are present and their half-lives differ by at least an order of
magnitude, such logarithmic plot will show the corresponding decay curves clearly
separated.
There is a long-standing shell model prediction of a β-decaying 16+ spin-gap
73

∆E(a.u.)

96

Cd

700

94Pd
350

1

TOF (a.u.)
Figure 5.1: Particle identification spectrum from the RFFS commissioning run. Nuclei
in this plot were produced by fragmentation of a primary beam of 124 Xe at 140 MeV
impinging on a beryllium target. Shown are ion energy-loss in a silicon detector versus
time-of-flight. The particle identification was confirmed by the observation of known
isomeric γ-rays, such as those of 94 Pd.
isomeric state in 96 Cd with a half-life of 0.5 s [1, 42]. The time distribution of 96 Cd
decays, however, does not show an indication for more than one component (Fig.
5.2). A maximum likelihood analysis was implemented in order to estimate the decay
constant of the 96 Cd data. The resulting likelihood function is also displayed in Fig.
5.2, and it reaches its maximum at the value corresponding to a half-life of 1.03+0.24
−0.21
s. For this analysis, the time distribution and intensity of the expected background
for each individual 96 Cd event was predicted from the implantation history in each
pixel and the known half-lives of the implanted nuclei and their decay daughters,
resulting in an average rate of 0.1 s−1 over the 10 seconds of correlation time (see
Section 4.2.1 for a description of the determination of β-decay half-lives).
As a cross check, a binned decay curve of 96 Cd was fitted based on the maximization of a Poisson probability log-likelihood function. The fit is presented in Fig. 5.3,

74

Counts

10
0.1
1
0.1

0.01

Maximum likelihood

1

Log(time) (seconds)
Figure 5.2: Number of decays observed for 96 Cd as a function of logarithmic time.
The fit shown was obtained through a MLH analysis, and includes the contributions
from the decay of the daughter and contaminant nuclei. The blue curve peaks around
zero, which corresponds to a half-life of 1 second. The background is observed as a
straight line (dot dashed red line), and was calculated as a function of time and pixel
position. The likelihood function is also shown (dotted curve), with its scale on the
right-hand side. Figure reproduced from [69].

Total
Parent
Daughter
Background

40

Counts/0.5s

35
30
25
20
15
10
5

0

2

4

6

8

10

Time (s)

Figure 5.3: β-decay curve of 96 Cd, obtained within a correlation time of 10 seconds.
The fit is the result of the maximization of a Poisson distribution log-likelihood function. The curve labeled “Total” is the result of the sum of the Bateman equations
corresponding to contributions from the parent and daughter decay, in addition to a
constant background.

75

and considered the decay of the parent and daughter plus a constant background.
The half-life of 96 Cd obtained with this method is 0.8 ± 0.36 s, consistent with that
obtained with the MLH analysis. It was found that the best fit corresponded to the
assumption of a single component in the decay.
As noted in the previous chapter, β-delayed γ transitions can provide a way to
isolate different parent β-decay components. The β-delayed γ spectrum of 96 Cd is
shown in Fig. 5.4. As can be seen, the statistics of β −γ coincidences was not sufficient;
no clear γ-ray peaks are visible appart from the positron annihilation peak at 511 keV.
Therefore, it is not possible to draw a conclusion about the existence of a β-decaying
16+ spin-gap isomer as predicted by Ogawa in [1] (see Section 2.1), with a half-life
of 0.5 s. Our statistics were not sufficient to exclude the possibility that the β-decay
half-life determined in this work is a mixed half-life from ground and isomeric states.
To investigate the possibility of a γ-decaying isomer, the prompt γ spectrum of
96 Cd is presented in Fig. 5.5. This spectrum was obtained within 12 µs of a 96 Cd
implantation. There is no indication of a γ-decaying isomer. However, we cannot
exclude the possibility of a γ-decaying µs isomer with a production fraction smaller
than about 7%, assuming a typical isomeric γ transition energy of 100 keV. Such a
decay would have been below the sensitivity of our experiment.
Figure 5.6 shows the comparison of the half-life of 96 Cd determined in this work
to the predicted half-lives in references [74–77]. Our measurement agrees, within error
bars, with the prediction by M¨ller, wich used a QRPA global model [76].
o

5.1.2

98

In

The odd-odd 98 In nucleus was previously investigated by Faestermann et al. [78].
The nuclei in that experiment were produced by fragmentation of a 112 Sn primary
beam, accelerated to 1 GeV/u, impinging on a Be target. Two β-decaying states were
observed: a short-lived component, with a half-life of 32+32 ms, assigned to the 0+ →
−11
0+ superallowed Fermi decay of the ground state, and a longer component with a
76

14

Counts/ 1 keV

12
10
8
6
4
2
0
100

500

1000

1500

2000

2500

3000

3500

Energy (keV)

Figure 5.4: γ-ray spectrum in coincidence with β-decay events of 96 Cd, ocurring
in the same and the four nearest neighbor pixels within 10 seconds of a fragment
implantation. The 511 keV peak from positrion annihilation is clearly distinguished.
No γ transitions could be identified and assigned to the β-decay of 96 Cd.

Counts/ 1 keV

4

3

2

1

0
200

400

600

800

1000 1200
Energy (keV)

1400

1600

1800

2000

Figure 5.5: Prompt γ-ray spectrum in coincidence with 96 Cd implantation events. No
γ transitions could be identified and assigned to the decay of excited states in 96 Cd.

77

half-life of 1.2+1.2 s, attributed to an isomeric state, possibly with a high spin.
−0.4
In this work, 216 (21) fragments of 98 In were implanted in the DSSD. The distribution of observed β-decay events that followed 98 In implantations is presented
as a function of the logarithmic time in Fig. 5.7. We confirm the existence of two
β-decay components, with half-lives of 47 (13) ms, and 0.66 (40) s, which presumably correspond to the ground and isomeric states, respectively. The contribution to
the observed decay from the isomeric state was deduced as 42 (20)% from the twocomponent fit. The β-delayed γ spectrum of 98 In is shown in Fig. 5.8. No transitions
associated with the 98 In β-decay were found. The prompt γ spectrum of 98 In does
not show any lines either.

5.1.3

100

Sn

As was described in previous chapters, production and separation of 100 Sn has been
a major experimental challenge for the field. At the NSCL, a production study was
done in order to determine the production settings that would maximize production
of

100

Sn. Based on production cross sections reported by previous experiments, pri-

mary beams of

124

Xe and

112

Sn were tested on 9 Be and 9 Be+nat Ni targets of various

thickeness and an estimate of the yield (in particles per second) was made in each
case. An overwiew of previous experiments that successfully produced 100 Sn, together
with a brief summary of the tests performed at NSCL was presented in Section 3.4.
In Experiment 07034, fourteen events were identified as 100 Sn during 11.5 days
of measurement. This yielded a production cross section of 0.25 (15) pb. Our result,
together with those from other measurements utilizing fragmentation as production
mechanism, is reported in Table 5.1. Our value is in sharp constrast with the 120 pb
lower limit established at an incident energy of 63 MeV/nucleon of the same primary
beam [79].
The LISE++ predictions of the fragment yields of N = Z nuclei for Experiment
07034 were between a factor of 10 and 30 higher than the actual measured rates. The
78

reported cross sections measured at relativistic energies do not show such discrepancy
[71, 80].
The time distribution of the 100 Sn β decay events observed in Experiment 07034
is shown in Fig. 5.9. Using an MLH analysis, a β-decay half-life was determined as
0.55+0.70 s. With such low statistics it was impossible to detect either prompt or
−0.31
β-delayed γ radiation.

5.2

Other neutron-deficient nuclei produced in Experiment 07034

Besides the N = Z nuclei presented in the previous section, we studied several N =
Z + 1 and N = Z + 2 nuclei. Results on β-decay half-lives and prompt and β-delayed
γ spectroscopy will be presented in the following sections for some of these nuclei.

5.2.1

Isomeric decay of

96

Ag

96 Ag is a T = 1 nucleus (i.e. (A − 2Z)/2 = 1 ), with three proton holes and one
z
neutron hole relative to 100 Sn. It was first identified by Kurcewicz et al. [81] using
the 60 Ni(40 Ca,p3n)96 Ag reaction. A half-life of 5.1(4) s was deduced for this nucleus
from the analysis of β-delayed protons, and spin and parity of 8+ or 9+ was suggested
for its ground state. Later, Batist et al. [39] identified two β-decaying states in 96 Ag
with half-lives of 4.40(6) and 6.9(6) s and tentative spins and parities of 8+ and 2+ ,
respectively; however, none of them was assigned as the ground-state. Evidence for
additional excited states in 96 Ag was reported by Grzywacz et al. [38], who discovered
the existence of an isomeric state with a half-life of 0.7 (2) µs and observed two γ
transitions with energies of 470 keV and 667 keV originating from the γ decay of
the isomer; however, statistics were not sufficient to construct a level scheme. Based
on a shell model prediction in the proton-neutron (p1/2 , g9/2 ) model space using

79

2.50

Halflif e (s)
-

2.00

1.50

1.00

0.50

0.00

Takahashi73 Biehle92

Moller97

Herndl97

This work

Figure 5.6: Comparison of the half-life of 96 Cd measured in this work to the theoretical
predictions by [74–77].

Table 5.1: 100 Sn cross section values determined in the various fragmentation experiments dedicated to its production and identification. The acronyms GSI and GANIL
stand for “Gesellschaft fur Schwerionenforschung” and “Grand Accelerateur National
d’Ions Lourds”, respectively.
Reference
NSCL [69]
GSI [80]

Production
112 Sn + Be
124 Xe + Be

Primary beam energy
120 MeV/u
1 GeV/u

GSI [68]

112 Sn + Be
112 Sn + Ni

1 GeV/u

GANIL [79]

63 MeV/u

80

σ (pb)
0.25(12)
11+5.5
−3.7
1.8+2.9
−1.1
≥ 120

102

Counts

Total
Parent
Isomer
Background

10

1
-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

Log(time)(seconds)

Figure 5.7: Number of decays observed for 98 In as a function of logarithmic time.
The blue curve peaks around -1.3, which corresponds to a half-life of 47 ms. The
dashed curve yields a half-life value of 0.66 s. The fit considers the decay of two
components, and includes the daughter decay and a predicted constant background,
which is observed as a straight line in the plot (dot-dashed). The total is indicated
by a thick black solid line.
16

Counts/ 1 keV

14
12
10
8
6
4
2
0
100

500

1000

1500

2000

2500

3000

3500

Energy (keV)

Figure 5.8: γ-ray spectrum in coincidence with β-decay events of 98 In, ocurring within
a 5-pixel correlation area, and within 10 s of a fragment implantation. Apart from
the 511 keV, no γ transitions were identified.

81

10

Counts

Total
Parent
Background

1

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

Log(time)(seconds)

Figure 5.9: Number of decays observed for 100 Sn as a function of logarithmic time.
The fit is the result of an MLH analysis that, as in the case of 96 Cd, considered a
calculated background, and the information of the known half-lives of the implanted
nuclei and their decay daughters.
an empirical interaction [82], Grzywacz et al. suggested the decay of a 15+ or 13−
isomer followed by a few γ transitions. In this work, we report a new measurement
of the lifetime of this isomer, and the observation of several new γ transitions, one of
which indicates the existence of a second, longer-lived µs isomeric state in 96 Ag.
The spectrum of γ rays observed between 1.2 and 12 µs after implantation of a
96 Ag ion is shown in Fig. 5.10. The lower time limit of 1.2 µs was chosen to eliminate
prompt X-rays and low-energy γ-rays produced by beam fragments interacting with
the silicon detectors. Apart from the 470-keV and 667-keV transitions, which were
previously reported by Grzywacz et al. [38], all of the γ transitions in Fig. 5.10 were
observed in the present experiment for the first time.
The time distribution of each of the γ lines of interest was analyzed to assign
them to the decay of a specific isomer and to determine isomeric half-lives. The 257-,
630-, 667-, and 1506-keV transitions decay with the same half-life. An OR of these
82

Counts / 1 keV

470

(a)

500
400

667

300
257

200

630

100

*
100

300

400

500

600

700

800

1506

(b)

140
100
1249

60
20 *
800

Counts / 1 keV

200

6

887

Counts / 1 keV

0
180

743

*

*

*

*

900 1000 1100 1200 1300 1400 1500
1719

(c)

2173 S

4

*
1976 S

2
0

1600 1700 1800 1900 2000 2100 2200 2300

Energy (keV)
Figure 5.10: γ-ray spectrum collected between 1.2 and 12 µs after an 96 Ag implantation. Transitions belonging to the isomeric decay of 96 Ag are labeled by their energies
in keV. Lines marked with an asterisk are known background from neighboring 94 Pd.
Summing peaks are marked by the letter S.

83

energies was used to obtain the isomeric decay curve shown in Fig. 5.11(a). A fit
to the decay curve taking into account a single exponential decay plus a constant
background resulted in a half-life of 1.45(7) µs, more than two times longer than the
previously-reported value of 0.7(2) µs [38]. The 743-keV transition, however, appears
to decay with a longer half-life (see Fig. 5.11(b)). The fit to this decay curve needed to
consider the time dependence of the background attributed to the contribution from
the decay of the shorter-lived isomer. The low intensity of the 743-keV transition and
the short 12 µs collection time results in large error bars in the half-life determination:
8.6±6.3µs. Nonetheless, we interpret this as an indication that the 743-keV transition
corresponds to the decay of an additional, longer-lived microsecond isomer in 96 Ag.
The isomeric fractions were calculated following the procedure outlined by Daugas
et al. [70], considering the number of counts in the 630-keV and 667-keV peaks, the
total number of implanted 96 Ag ions, and the 475 ns flight time of the fragments from
the target to the DSSD. An isomeric production fraction of 10.8 (12) % was estimated
for the short-lived isomer in the fragmentation process. Similarly, by comparing the
number of counts in the 743-keV peak to the total number of 96 Ag implants, a
0.59 (9) % production of the long-lived isomer was estimated.
A 2-dimensional γγ coincidence matrix was constructed for γ rays which occurred
within the first 12 µs after a 96 Ag implantation. 1-dimensional coincidence spectra
were then obtained by setting energy gates on the lines of interest in the γγ matrix
(Figs. 5.12 and 5.13). Table 5.2 summarizes the observed γγ coincidence relationships,
as well as the intensities of all transitions, normalized to the transition with an energy
of 470 keV. A total of 1.1 × 104 counts were detected in the 470-keV peak, several
orders of magnitude higher than in the previous measurement. Based on these coincidences, their relative intensities, and energy-sum relationships, the decay scheme
for 96 Ag presented in Fig. 5.14 (a) is proposed. The 470-keV line was placed at the
bottom of the level scheme based on two observations: it was the most intense transition and it was in coincidence with nearly all other transitions (with exception of

84

Counts / 0.2292 µs

(a) T1/2 =1.45 ± 0.07µs

100

parent
10

background
1
2

4

6

8

10

Time (µs)
15

Counts / 3.5 µs

(b) T1/2 =8.6 ± 6.3µs

10

parent
backg
background

1

2

4

6

8

10

12

Time (µs)
Figure 5.11: Decay curves and fits of the microsecond isomers in 96 Ag. (a) Decay
curve obtained by gating on the 257, 630, 667, and 1506-keV γ-ray transitions. The
curve was fitted with a single exponential and constant background. (b) Decay curve
obtained by gating on the 743-keV γ-ray transition, fitted with a single exponential
decay and a time-dependent background.

85

the transition with energy 1718 keV). Energy-sum relationships were used to place
the 1506-keV transition that is proposed to connect the levels with energies 1976 and
470 keV; and the 1718-keV ground-state transition. The 630-keV and 667-keV γ-rays
are not in coincidence with each other, or with the 743-keV line, so they were placed
on top of the cascade, both feeding the 1976 keV level.
The β decay of two low-lying states in 96 Ag with proposed spins and parities 2+
and 8+ , and half-lives of 6.9(6) and 4.40(6) s, respectively, was reported by Batist
et al. [39]. Implanted nuclei correlated with the 470-keV line were tagged to determine which of these two β-decaying states was populated following the decay of the
microsecond isomers. The β-decay curve of the tagged nuclei is shown in Fig. 5.15.
The deduced half-life of 4.74(95) s is consistent with that reported by Batist et al.
for the 8+ β-decaying level [4.40(6) s]. Furthermore, the β-delayed γ spectrum of the
tagged nuclei was compared to that of all the 96 Ag implanted nuclei. A considerable
decrease of more than 30% was observed in the relative intensity of the 1415-keV
γ-ray transition in the daughter 96 Pd. The 1415-keV transition, according to Batist
et al., is mostly fed by the β decay of the 2+ level (see Fig. 3 in Ref. [39]). Therefore,
the 1.45 µs isomer most likely populates the 8+ β-decaying state.
To gain a better understanding of the nature of the isomeric states observed, and
to tentatively assign spins and parities to the inferred energy levels of 96 Ag, two
different shell-model calculations were performed, hereafter referred to as the SLGT,
and the jj44b calculations, respectively. In Fig. 5.14 the level scheme of 96 Ag as
inferred from our experiment is compared with the predictions of both shell-model
calculations. Both shell-model calculations were performed by B. Alex Brown and
reported in [83].
The SLGT calculation was performed with the code OXBASH, within the g9/2 , p1/2
model space using the SLGT effective interaction [77], and assuming a 100 Sn core.
This calculation predicts one potentially isomeric state located at 3148 keV above
the 8+ state (3351 keV above the 2+ state), with spin and parity 15+ [see Fig. 5.14

86

80

470

60

(a) 257 keV gate

667
1249

20

1719

630

40

0
160
120

667
257

1506
630

80

Counts / 1 keV

(b) 470 keV gate

1249

40
743
0
40

470

(c) 630 keV gate

30
20

1506
257

10

1249

0
160

470

(d) 667 keV gate

120
80

1506

257
40
1249
0

200

400 600 800 1000 1200 1400 1600 1800

Energy (keV)
Figure 5.12: Background-corrected fragment-γγ coincidence spectra obtained by applying gates on the (a) 257-keV, (b) 470-keV, (c) 630-keV, (d) 667-keV γ rays. These
coincidences together with those shown in Fig. 5.13 were used to deduce the 96 Ag
level scheme.
87

12

470

(a) 743 keV gate

8

1249

4
0
-4
257 470

40

(b) 1249 keV gate

30

Counts / 1 keV

630

10

743

667

20

0
470

100

(c) 1506 keV gate

80
667

60

630

40
20
0
3

200

400 600 800 1000 1200 1400 1600 1800
257

(d) 1719 keV gate

2
1
0

-2

200

400

600

Energy (keV)

800

1000

Figure 5.13: Background-corrected fragment-γγ coincidence spectra obtained by applying gates on the (a) 743-keV, (b) 1249-keV, (c) 1506-keV and (d) 1719-keV γ rays.
These coincidences were used to deduce the 96 Ag level scheme.
88

15+
13 13+
12+
10+
X+2643
X+2606

2523

2140 11+
10+

2069
1937

X+1976 10+

(11+ )

1719
1249

(10 +)

2376

11+

X+1719

1506

743

630
887
667

X+2460

257

(13 - )

3060
3020
2914
2782
2770

13-

(13+ )
(12+ )

3351
3222
3158 15+
3148 12+
+
2988 1311+
10

(9 )

8+

203
0

9+

689

8+
2+

105
0

470

X+470

741

2+

+

9+

X+0

(8 +)

Experiment

SM SLGT

SM jj44b

(a)

(b)

(c)

Figure 5.14: (a) Proposed level scheme of 96 Ag, compared to the results of shellmodel calculations made with the SLGT interaction (b) and the jj44b interaction (c).
Tentative spins and parities were adopted from the results of the jj44b calculation.
Deduced level energies are relative since the energy of the 8+ state is unknown. The
newly-identified 15+ isomeric level is not drawn in the experimental level scheme. See
text for details.

89

Table 5.2: Energies, intensities, and coincidence relationships of γ rays assigned to
the isomeric decay of 96 Ag.
Eγ (keV)
Iγ(%) Coincident transitions (keV)
257.2 (2) 17.3 (16)
470, 630, 667, 1249, 1719
470.0 (2) 100.0 (67) 257, 630, 667, 743, 1249, 1506
630.1 (2) 21.8 (20)
257, 470, 1249, 1506
667.4 (2) 71.1 (51)
257, 470, 1249, 1506
742.7 (3)
4.5 (9)
470, 1249, 1719
887.4 (6)
1.0 (4)
1248.8 (2) 21.9 (23)
257, 470, 630, 667, 743
1505.9 (2) 81.4 (63)
470, 630, 667
1718.9 (3)
1.8 (4)
257, 743

T 1/2 = 4.74 ± 0.95 s

Counts / 0.5 s

400
300
200

background

100
parent

0

2

4

6

8

10 12

14

16

18

20

Time (s)
Figure 5.15: β-decay curve of the 96 Ag implants which were correlated with the 470keV transition. The resulting half-life of 4.74 (95) s agrees with the known half-life of
the β-decaying state in 96 Ag with tentative spin and parity 8+ .

90

(b)]. The predicted half-life of the E2 15+ → 13+ transition is around 15 ns, much
shorter than the half-life of 1.5 µs reported here. Using the B(E2) strength from the
SLGT calculation and our measured half-life of 1.5 µs, the energy of the isomeric
transition can be estimated as 77 keV; this energy is 116 keV smaller than predicted
by the shell model, but well within typical shell model uncertainties. Such a 77-keV
transition is predicted to be highly converted [α=3.67(6)]. No evidence of a 77 keV
γ-ray was found in our data, which is consistent with the expected small statistics
and signal to background ratio in that energy range. Our experimental setup was also
not sensitive to the low-energy electrons expected from this transition.
The second shell-model calculation was carried out in the (p3/2 p1/2 f5/2 g9/2 )
model space considering a 56 Ni core and using the jj44b Hamiltonian. The jj44b
Hamiltonian was obtained from a fit to about 600 binding energies and excitation
energies with a method similar to that used for the JUN45 Hamiltonian [84]. Most
of the energy data for the fit came from nuclei with 28 ≤ Z ≤ 30 and 48 ≤ N ≤ 50.
Using a fit with 30 linear combinations of the J − T two-body matrix elements,
which conserve isospin, varied, the rms deviation between experiment and theory for
the energies in the fit was about 250 keV. Proton and neutron effective charges of
ep =1.5 and en =0.5 were used. Predictions obtained with the jj44b Hamiltonian have
been compared to experimental data for Ga [84, 85] and Cu [86, 87] isotopes, showing
remarkable agreement. The jj44b calculation predicts a 0.99 µs (partial) half-life for
a 146 keV 15+ → 13+ E2 transition [see Fig. 5.14 (c)] that feeds a cascade to the 8+
level. Again, given the experimental conditions, a 146-keV transition of the expected
intensity would not be observed. Additionally, the jj44b calculation predicts a lowlying 13− state, which could explain the longer-lived isomer as a slow E3 transition.
Since most of the E3 strength comes from orbitals outside the model space, the
reduced E3 transition strength measured in a nearby nucleus was used as reference
to estimate the expected lifetime. The closest nucleus to 96 Ag for which a measured
E3 value is available is 93 Tc [88], with B(E3) = 540 e2 fm6 , resulting in a 13− →

91

10+ half-life of 18 µs. The 13− → 11+ transition is expected to have mixed M2/E3
character, with a partial half-life of a few hundred microseconds, as calculated using
the values of the B(M2) and B(E3) obtained in 93 Tc. The small branching ratio for
this transition would not have been detected in the present experiment. The resulting
half-life of the 13− state of 18 µs is within a factor of two of the deduced value of
8.6 ± 6.3µs reported here.
Overall, both shell model calculations reproduce the observed level sequence and
γ-ray cascades for the short-lived isomer. The jj44b calculation, with its larger model
space, predicts excitation energies better than the SLGT one, and reduces the excitation energy of the 13− state sufficiently to provide an explanation for the longer-lived
isomer identified in the present work. The jj44b results were used to tentatively assign
spins and parities to the experimental levels presented in Fig. 5.14 (a).

5.2.2

Isomeric decay of

94

Pd

94 Pd is also a T = 1 nucleus, and, similarly to 96 Ag, it also exhibits high-spin
z
isomeric states. Excited states in 94 Pd were investigated by La Commara et al. [52],
Marginean et al. [51], and by Plettner et al. [43] through analysis of the β-decay of
94 Ag. A microsecond isomer with spin and parity of 14+ was established, de-exciting
through a cascade of γ-transitions with energies of 95, 324, 660, 814, 905, 994 and 1092
keV. The isomeric half-life had been measured in previous experiments as 0.8 ± 0.2 µs
by Gorska et al. [89] and 0.530(10) µs by Grzywacz et al. [38]. Five new γ transitions
with energies of 267, 408, 597, 979 and 1545 keV were reported in [52] as prompt lines,
not in delayed coincidence with the cascade de-exciting the 14+ isomer, and placed
tentatively in the level scheme. This placement was later confirmed by Plettner et al.
In Experiment 07034, 94 Pd nuclei were produced in the fragmentation process
in their excited states in sufficient quantities to perform γ spectroscopy. Fig. 5.16
shows the γ-ray spectrum collected within 12 µs of a 94 Pd implantation event. Table
5.3 summarizes the observed γγ coincidence relationships, as well as the intensities
92

4000
50

Counts / 1 keV

3500

324

1651

40
30

3000

20

95
2500

10

659

0

2000

1580

814

1620

1660

1700

1740

905 994

1500

1092

500

347
408

267

1000
745
1651
0
200

400

600

800

1000

1200

1400

1600

1800

Energy (keV)

Figure 5.16: γ-ray spectrum collected within 12 µs of a 94 Pd implantation. Transitions
belonging to the isomeric decay of 94 Pd are labeled by their energies in keV.

93

of the γ transitions observed in 94 Pd. Additionally, the inset of Fig. 5.16 shows a
1651-keV transition, which had not been seen before, and that suggests the existence
of a second high-spin isomeric state (see below).
The time distribution of each of these γ lines of interest was analyzed to assign
them to the decay of a specific isomer and to determine isomeric half-lives. The 96,
324, 347, 660, 745, 814, 906, 994 and 1092-keV transitions decay with the same halflife. An OR of the 324, 660, 814, 905, 994 and 1092 keV-transitions was used to
obtain the isomeric decay curve shown in Fig. 5.17. A fit to the decay curve taking
into account a single exponential decay plus a constant background resulted in a
half-life of 482 (14) ns, which is within the range of values reported before [38, 90].
The 1651-keV transition has a half-life shorter than that of the known 14+ isomer,
its decay curve and fit are presented in Fig. 5.18. The fit to the decay curve of the
1651 keV transition yields a half-life value of 219 ± 55 ns. We therefore conclude
that there exists another isomeric state in 94 Pd, not observed before through the
β-decay of 94 Ag, and located above the known 14+ isomer. The 267-keV, 347-keV
and 408-keV lines, which were previously reported as prompt in fusion-evaporation
experiments studying the β decay of 94 Ag, are present in the γ spectrum of Fig.
5.16, i.e. approximately 475 ns after fragmentation. Their low intensities and the
contribution to Compton background from higher energy lines de-exciting the known
14+ state make it hard to extract a half-life for these lines. However, their intensities
are very similar and also consistent with that of the 1651-keV line, thus leading to
the conclusion that they originate from the same cascade, above the known 14+ →
0+ one.
Following the same procedure as in the case of the 96 Ag isomer, coincidences,
relative intensities and energy-sum relationships were deduced for the isomeric γ
transitions of 94 Pd, and the resulting level scheme is presented in Fig. 5.19, which
is in agreement with previous works. Placement of the 1651-keV transition in the
level scheme is suggested, as part of the γ cascade de-exciting a high-spin µs isomer,

94

Counts / 0.18 µs

Table 5.3: Energies, intensities, and coincidence relationships of gamma rays assigned
to the isomeric decay of 94 Pd.
Eγ (keV)
Iγ (%)
Coincident transitions (keV)
95.4 (2) 21.0 (16)
324, 659, 814, 905, 994, 1092, 1651
267.7 (3)
3.3 (4) 95, 324, 347, 408, 659, 814, 905, 994, 1092, 1651
324.1 (2) 97.5 (70) 95, 268, 347, 659, 745, 814, 905, 994, 1092, 1651
347.2 (2)
7.8 (7)
95, 324, 659, 745, 814, 905, 994, 1092
408.3 (3)
3.0 (4)
95, 267, 324, 659, 814, 905, 994, 1092, 1651
659.5 (2) 95.7 (69)
95, 325, 659, 745, 814, 905, 994 1092, 1651
745.2 (2)
7.7 (7)
324, 347, 659, 814, 905
814.3 (2)
96.3 (7)
95, 324, 347, 659, 745, 905, 994, 1092, 1651
905.5 (2)
96.6 (7)
95, 324, 347, 659, 745, 814, 994, 1092, 1651
994.2 (2) 100.0 (73)
95, 324, 347, 659, 814, 905, 1092, 1651
1092.4 (2) 93.6 (68)
95, 324, 659, 814, 905, 994, 1092, 1651
1544.7 (5)
0.7 (2)
95, 268, 324, 408, 659, 814, 905, 994, 1092
1651.1 (16)
4.0 (4)
95, 268, 324, 408, 659, 814, 905, 994, 1092

100

10

1

2

3

4

5

6
7
Time (µs)

8

9

10

Figure 5.17: Decay time spectrum obtained by gating on the 324, 660, 814, 905, 994,
and 1092 keV transitions of 94 Pd. The resulting decay curve was fitted with a single
exponential and a constant background.

95

located at 7210 keV.

96

Counts / 0.183 µs

10

1

1

1.5

2

2.5

3
3.5
Time (µs)

4

4.5

Figure 5.18: Decay time spectrum obtained by gating on the 1651 keV transition of
94 Pd. The resulting decay curve was fitted with a single exponential and constant
background.

97

7210 219(55) ns
7103

( 18+)

1651
1545

( 16+)

5559

( 15+)

268

14+
12+

408
95

5291
4883
4788

482(14) ns

994
10+

3794

1092
(8+ )

3049
347
2702

8+
6+

745

324

2378

659
4+

1719

905
2+

814
814

0+

0

Figure 5.19: Experimental level scheme of 94 Pd obtained in this work (only observed
transitions are included). Level spin and parity assignments are based on previous
results. The 1651-keV transition is new and its placement is suggested, de-exciting a
high-spin isomeric state, at 7210 keV, and with a half-life of 219(55) ns.

98

Chapter 6
Astrophysical Impact
The neutron-deficient nuclei studied in this work are in the path of the astrophysical
rp-process. Possible implications of our measurements on the isotopic abundances
produced in an rp-process that reaches the 100 Sn region were therefore explored by
incorporating the new results into a one-zone X-ray burst model. A brief introduction
to the reaction network used is presented in this chapter, followed by the results of
the calculations performed.

6.1

rp-process reaction network

A single zone X-ray burst model was used to study the impact of our measurements
on an rp-process that reaches the A ≈ 100 region. This model has been used before to
explore the mass processing beyond tin to determine for the first time the endpoint of
the rp-process [19], and it is based on the physics outlined in Ref. [91]. The network
includes 690 proton-rich nuclei, from hydrogen to xenon. The reaction rates used are
from ReaclibV1, provided by JINA Reaclib online database [27].

99

6.2

Impact of our measurements on the rp-process

Presented in figure 6.1 is the rp-process reaction path calculated with our code. The
nuclei produced in this experiment are indicated. The goal of this study was to find
out whether or not the rp-process could be a viable production mechanism for

96

Ru,

a p-nuclei observed with high abundance in the solar system (see Sections 1.1 and
1.2.1). Thus, the following discussion focuses on the impact of the measured half-life
of 96 Cd.
Nuclei with A = 96 produced in the rp-process decay into 96 Ru at freezeout. Therefore, our calculations were done under the most favorable conditions for production
of A = 96 nuclei, which were the same used in Ref. [19]. The initial conditions corresponded to a high accretion rate and low metallicity of the accreted matter, which
minimizes hydrogen burning in the neutron star prior to burst ignition, and leaves
about 66% of the hydrogen for burning during the X-ray burst. During freezeout, the
A = 96 nuclei produced during the burst as 96 Cd are destroyed through proton capture on 96 Rh. This destruction rate depends in turn on the freezeout timescale. An
instant freezeout was therefore chosen at the time of maximum A = 96 production.

6.2.1

The half-life of

96

Cd

Nuclei with A = 96 are produced during the rp-process due to the accumulation of
mass at 96 Cd, which is a waiting point [5]. Previous rp-process calculations which
included 96 Cd had to use a theoretically predicted half-life (ranging from 0.30 [74]
to 2.18 seconds [77]). The experimental determination of its half-life was therefore
crucial in order to reliably calculate the final composition of the ashes of an X-ray
burst that reaches this mass region. The half-life of 96 Cd was determined in this work
as 1.03+0.24 s.
−0.21
The final rp-process abundance pattern reflects the composition of the ashes of the
X-ray burst after the proton captures have ended and the newly formed proton-rich

100

nuclei had time to decay towards stability. As the most proton-rich stable A = 96
isobar, 96 Ru is the only one that can be produced by β + decays of heavier isobars.
Thus, the final abundance of mass A = 96 in the rp-process will correspond to that
of 96 Ru. Fig. 6.2 shows the overproduction factors, defined as the ratio of the mass
fraction of an isotope produced in a particular process to its mass fraction in the
solar system. The two curves correspond to the minimum and maximum predicted
values of the half-life of 96 Cd. For the rp-process to be the mechanism responsible
for the origin of 96 Ru, a large overproduction factor is required for A = 96, of the
order of 1010 [69]. Such a large overproduction factor would be necessary in order to
compensate for the small amount of ashes that could be ejected, and the relatively
small amount of mass processed by X-ray bursts in our Galaxy [20, 69]. In addition,
the overproduction factor must peak significantly higher than for isotopes that are
known to be produced in the s-process, such as A = 97. Fig. 6.2 shows that with our
new data such conditions are not met. Therefore, the rp-process can be ruled out as
the scenario responsible for production of 96 Ru.
Additionally, Fig. 6.3 shows the energy generation as a function of time during
an X-ray burst. The two curves correspond to the shortest (0.3 s) and longest (2.2
s) predicted half-lives of

96

Cd, respectively. The effect of varying this value is rather

small, differences can only be noticed during the cooling phase, the inset shows a
zoom-in of the time range where the two calculations differ the most.

6.2.2

The microsecond isomers in

96

Ag

During the rp-process freezeout, 96 Cd β + decays to 96 Ag, where the 96 Ag(p, γ)
reaction rate then governs how many A = 96 nuclei survive and how many are
converted into heavier nuclei. Isomers may affect proton capture rates significantly by
creating a non-thermal population of levels, thus the importance of their identification
and characterization. Experimental data on isomers in 96 Ag can therefore shed light
on the question of the production of mass A = 96 in the rp-process.
101

In this work, a γ-ray cascade was identified from the decay of a 1.45(7) µs isomeric
state in 96 Ag. Evidence for a second µs isomer, along with the γ-ray transitions
associated with its decay, was also found. Its half-life was determined as 8.6(63) µs.
The new data show that the microsecond isomers in 96 Ag are at excitation energies of
at least 2.5 MeV and likely have spins and parities of 15+ and 13− , respectively. At
such high excitation energies, these states are unlikely to be populated in astrophysical
environments by thermal excitation of lower-lying states in 96 Ag. The high spin makes
population by proton capture on 95 Pd (expected ground state 9/2+ ) or by β decay
from 96 Cd (ground state 0+ ) also unlikely. The 15+ state in 96 Ag could be populated
by the β decay of the predicted 16+ isomer in 96 Cd, though the existence of this
state has not been confirmed by experiment. However, population of that isomer by
proton capture is, again, unlikely because of its high spin. The microsecond isomers
characterized in this work are therefore unlikely to play a role in the rp-process.

6.3

Conclusions and Outlook

The development of science and technology over the 20th century to the present day
has been vertiginous. We have come to the realization that the elements that make
up everything in our planet, including ourselves, are the result of billions of years
of nucleosynthesis, taking place in a variety of scenarios, some of them still to be
understood, or even, discovered.
One of such nucleosynthesis scenarios was explored in this work: that of the rpprocess in Type I X-Ray Bursts occurring in accreting neutron stars. It was proposed
as a possible production mechanism of some of the stable nuclides on the proton-rich
side of the valley of β stability, such as 96 Ru. Our new data ruled out this possibility,
indicating that X-ray bursts are not the main source of 96 Ru, found so abundantly in
the solar system [69]. The mystery therefore remains, and new models will have to be
developed in order to explain the nucleosynthesis of 96 Ru. Several works on νp-process

102

in Type II Supernovae show that an important contribution to the abundances of light
p-nuclei can come from this process. However, the νp-process is very sensitive to the
details of the explosion mechanism and mass of the proto-neutron star. The variuos
model uncertainties together with nuclear physics uncertainties result in different
nucleosynthesis from event to event, and therefore to a lack of consensus between
the different studies [8–10] (see also [92] and references therein). In a recent work by
Travaglio et al. [93] different models of Type Ia supernovae were analyzed and the
different s-process distributions, and their consequences for the p-process explored.
They found that a flat s-seed distribution directly translates into a flat p-process
distribution with average production factors directly proportional to the adopted level
of s-seeds. This demonstrated that p-nuclei can be produced with similar enhancement
factors relative to

56

Fe, including the light-p nuclei

92,94

Mo and

96,98

Ru.

There are still plenty of open questions regarding accreting neutron stars. New and
improved nuclear physics measurements will play a crucial role in gaining a better understanding of these phenomena. Our work showed an example of the sensitivity of the
X-ray burst energy generation and mass processing to nuclear physics uncertainties.
Besides half-lives, masses and particle induced reaction rates of the neutron-deficient
nuclei in the rp-process nuclei are needed.
On the nuclear structure side, our measurement contributes to the understanding
of the shell structure of N ≈ Z nuclei very far from stability. For instance, the
comparison of the level scheme determined for 96 Ag from our experiment to the shell
model predictions indicated that a larger model space was needed in order to correctly
reproduce observations. The calculation within the larger (p3/2 p1/2 f5/2 g9/2 ) model
space reproduced excitation energies and half-lives of the isomeric states better than
the one performed in the limited (p1/2 g9/2 ) model space. These results will in turn
serve as reference for future experimental and theoretical work.

103

Xe (54)
I (53)
Te (52)
Sb (51)
Sn (50)
In (49)
Cd (48)
Ag (47)
Pd (46)
Rh (45)
Ru (44)

59
57 58

Tc (43)
Mo (42)
Nb (41)
Zr (40)
Y (39)
Sr (38)

Protons

56
54 55
53

Rb (37)
Kr (36)
Br (35)
Se (34)

51 52
49 50
45 46 47 48

As (33)
Ge (32)
Ga (31)
Zn (30)

42 43 44
41
37 38 39 40

Cu (29)
Ni (28)
Co (27)
Fe (26)
Mn (25)
Cr (24)

Neutrons

33 34 35 36
31 32

Figure 6.1: The nuclei produced in the present experiment are marked in green.

Over-abundance ratio to solar

11

10

0.3 s
2.2 s
this work

10

10

9

10

8

10

7

10

90

92

94

96
98
100
Mass number

102

104

106

Figure 6.2: Predicted overabundances relative to solar as a function of mass number,
from rp-process calculations using a 96 Cd half-life ranging from 0.3 to 2.2 s, and
our measured vale. A pronunced peak at mass 96 would indicate that 96 Cd plays a
significant role as a waiting point. Figure adapted from [69].

104

1.2e+18

2.5e+16
2e+16

Energy generation

1e+18

1.5e+16
1e+16

8e+17

T1/2=0.3s
T1/2=2.2s

5e+15
200

6e+17

240

280

320

4e+17
2e+17
0

150

200

250

300

Time
Figure 6.3: Effect of 96 Cd half-life in rp-process predicted energy generation as a
function of time. The two curves correspond to the shortest and longest half-lives
predicted for 96 Cd. The inset shows a zoom of the region where the two cureves
differ the most.

105

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