Decay Studies of Neutron
Deficient Antimony Near the
Endpoint of the rp-Process
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of
Philosophy in the Graduate School of The Ohio State University
By
Edward E. Smith, B.S., M.S.
Graduate Program in Physics
The Ohio State University
2011
Dissertation Committee:
Evan Sugarbaker, Advisor
Richard Furnstahl
Thomas Humanic
Richard Kass
c Copyright by
Edward E. Smith
2011
Abstract
The rp-process or rapid proton capture process, produces nuclei through a series of proton
capture or (p,γ) reactions and β + decays along the proton drip-line and above the line of
β stability. In astrophysical models, the rp-process on accreting neutron stars produces
energy output in general agreement with light curves from type I X-ray bursts. For some
bursts, the resulting reaction network can extend up to the region of the closed nuclear
shell at Z = 50. Further progress is prevented due to the α decay of the light Te isotopes
resulting in a Sn–Sb–Te cycle.
Models of the rp-process require accurate input from thermonuclear reaction rates and
decay half-lives in order to produce results which can be compared to observations. This
dissertation describes a 2003 experiment designed to reduce uncertainties in the decay properties of neutron deficient Sb isotopes beyond the proton drip-line and in the vicinity of the
Sn–Sb–Te cycle. In this study, the Sb isotopes were produced through the fragmentation
method at the National Superconducting Cyclotron Laboratory (NSCL). In this experiment, a 140 MeV/nucleon
124 Xe
beam impinged upon a Be target. The fragments of the
secondary beam were separated in the recently commissioned NSCL A1900 fragment separator and selected nuclei were implanted in a position-sensitive double-sided silicon strip
detector (DSSD). The DSSD is the primary detector in the NSCL’s β decay endstation,
where both the implanted nuclei and their subsequent decays were observed and correlated
within the analysis software.
Due to limitations at the NSCL at that time, it was not possible to eliminate many
unwanted fragments from the beam. Several isotopes were implanted at rates three or more
orders of magnitude greater than those of the Sb isotopes of interest. Some of these had
ii
decay half-lives on the order of minutes or longer. The high rate of implantation by these
nuclei created a large and persistent β decay background within the data that presented
itself as time-dependent when correlated to implanted nuclei.
This dissertation describes how implanted nuclei were separated within the analysis
and presented onto a 2-D particle identification spectrum (PID). It explains how decays
were correlated to implanted nuclei of a given isotope, and how the background decays were
characterized and predicted at high precision with a parameterized model. It then describes
a curve-fitting procedure to measure the decay half-lives.
Results include a remeasurement of the 104 Sb half-life that is in agreement with previous
values. A grouping of implantations on the PID presented as a possible observation of the
previously unmeasured isotope,
103 Sb.
Investigation of the resulting decay curve, however,
suggests that this spectrum may largely be the result of contamination from
could not be sufficiently resolved from the lightly produced
103 Sb
101 Sn,
which
within the A1900 at that
time.
The results of this study are presented in the context of other recent observations. The
on-going development of experimental techniques and their applicability to recent and future
decay studies are also discussed.
iii
To Wendy.
iv
Acknowledgments
It has often been suggested to me that writing one’s dissertation is “just like running a
marathon.” However, speaking as someone who has run 26.2 miles on more than one
occasion, I can assure you that completing one’s doctoral dissertation is the considerably
more difficult task of the two. It is also not something that can be done under your own
steam. I have had many companions, supporters, collaborators, and guides along the way.
First and foremost, I’d like to thank my adviser, Evan Sugarbaker. Without his patience,
encouragement, and support I might not have ever completed this document. Thanks also
to the other members of my advisory committee. Richard Kass, Tom Humanic, and Dick
Furnstahl have each been great teachers during my time here.
I’d also like to thank my initial adviser at Ohio State, Dick Boyd. He was not frequently
present on campus for very long after I joined the nuclear astrophysics group, but even after
relocating to the NSF in Washington, made the time to come to campus on Saturdays to
give me a very personalized version of his course covering the field. It is an odd thing to be
on the tail end of the burst of light that was the nuclear astrophysics group at OSU. Still,
I’m thankful for the illumination others have provided. Thanks especially to Mike Famiano
and Arthur Cole who departed not long after I arrived, but continued to be friends and
positive influences.
The experiment described in the pages that follow was performed at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. I can hardly
say enough about what a unique and special working environment the NSCL provides. I’m
very lucky to have had the opportunity to work there as a visitor through the Joint Institute
of Nuclear Astrophysics (JINA) and to have participated on so many experiments. Thanks
v
foremost to Hendrik Schatz who served as my adviser during my time there and who, along
with his students, made me feel at home in his group. Thanks to Andreas Stolz for giving
me the opportunity to work on this experiment. Thanks also to Paul Mantica, Colin Morton, and Elaine Kwan who each did some of the initial calibration and offered insightful
conversations. Thanks to Paul Hosmer for advice regarding the analysis code and to Fernando Montes for finding a long-lost electronics diagram. Thanks also to Alfredo, Thom,
Dani, Cedric and so many others at the NSCL who shared their time and friendship.
Between Ohio State and Michigan State I’ve been assigned at least eight different desks
during my years in graduate school. There are more people with whom I’ve shared time,
friendship, and office space than I’m able to name here. The one person who has been
present more than anyone else on this journey is Meredith Howard. I’m so thankful for our
friendship and for the words of encouragement that she has provided to me over the years,
just when I most needed to hear them.
To my family, who has never stopped rooting for me, my parents and my sisters, thank
you for always encouraging me. Finally, I’m so blessed to have a beautiful daughter who
brightens my every day and a wife whose endless faith and love continue to amaze me.
vi
Vita
1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.S. Physics, Dickinson College,
Carlisle, Pennsylvania.
2003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M.S. Physics, The Ohio State University,
Columbus, Ohio.
2000–2009, 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graduate Associate,
The Ohio State University.
2004 (Summer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . JINA Visiting Student,
Joint Institute for Nuclear Astrophysics,
Michigan State University,
East Lansing, Michigan
2009–2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lecturer,
The Ohio State University.
Publications
G. Perdikakis, R. G. T. Zegers, Sam M. Austin, D. Bazin, C. Caesar, J. M. Deaven, A.
Gade, D. Galaviz, G. F. Grinyer, C. J. Guess, C. Herlitzius, G. W. Hitt, M. E. Howard,
R. Meharchand, S. Noji, H. Sakai, Y. Shimbara, E. E. Smith, and C. Tur. “Gamow-Teller
unit cross sections for (t,3 He) and (3 He,t) reactions”. Phys. Rev. C, 83(5):054614, 2011.
D. Galaviz, A.M. Amthor, D. Bazin, B.A. Brown, A.A. Chen, A. Cole, T. Elliot, A. Estrade,
Zs. Fülöp, A. Gade, T. Glasmacher, A. Heger, M.E. Howard, R. Kessler, G. Lorusso,
M. Matos, F. Montes, W. Müller, J. Pereira, H. Schatz, B. Sherrill, F. Schertz, Y. Shimbara, E. Smith, K. Smith, A. Stolz, A. Tamii, D. Weisshaar, M. Wallace and R.G.T. Zegers.
“Nucleosynthesis of proton-rich nuclei. Experimental results on the rp-process.”. J. Phys.
Conf. Ser., 202:012009, 2010.
G.W. Hitt, R.G.T. Zegers, Sam M. Austin, D. Bazin, A. Gade, D. Galaviz, C.J. Guess,
M. Horoi, M.E. Howard, Y. Shimbara, E.E. Smith, and C. Tur. “Gamow-Teller transitions
to 64 Cu measured using the 64 Zn(t,3 He) reaction”. Phys. Rev. C, 80(1):014313, 2009.
vii
J. Pereira, S. Hennrich, A. Aprahamian, O. Arndt, A. Becerril, T. Elliot, A. Estrade,
D. Galaviz, R. Kessler, K.-L. Kratz, G. Lorusso, P.F. Mantica, M. Matoš, P. Moller,
F. Montes, B. Pfeiffer, H. Schatz, F. Schertz, L. Schnorrenberger, E. Smith, A. Stolz,
M. Quinn, W.B. Walters, and A. Wohr. “β-decay half-lives and β-delayed neutron emission probabilities of nuclei in the region A . 110, relevant for the r-process”. Phys. Rev.
C, 79(3):035806, 2009.
M. Matoš, A. Estrade, M. Amthor, D. Bazin, A. Becerril, T. Elliot, M. Famiano, A. Gade,
D. Galaviz, G. Lorusso, J. Pereira, M. Portillo, A. Rogers, H. Schatz, D. Shapira, E. Smith,
A. Stolz, and M. Wallace. “Time-of-flight mass measurements and their importance for
Nuclear Astrophysics”. Acta Physica Polonica B, 40(3):695, 2009.
M.E. Howard, R.G.T. Zegers, Sam M. Austin, D. Bazin, B.A. Brown, A.L. Cole, B. Davids,
M. Famiano, Y. Fujita, A. Gade, D. Galaviz, G. W. Hitt, M. Matos, S. D. Reitzner,
C. Samanta, L.J. Schradin, Y. Shimbara, C. Simenel and E.E. Smith,. “Gamow-Teller
strengths in 24 Na using the 24 Mg(t,3 He) reaction at 115A MeV”. Phys. Rev. C, 78(4):047302,
2008.
D. Galaviz, A.M. Amthor, D. Bazin, B.A. Brown, A. Cole, T. Elliot, A. Estrade, Zs. Fülöp,
A. Gade, T. Glasmacher, R. Kessler, G. Lorusso, M. Matos, F. Montes, W. Müller, J. Pereira,
H. Schatz, B. Sherrill, F. Schertz, Y. Shimbara, E. Smith, A. Tamii, M. Wallace and R.G.T.
Zegers. “New experimental efforts along the rp-process path”. J. Phys. G, 35(1):014030,
2008.
M. Matoš, A. Estrade, M. Amthor, A. Aprahamian, D. Bazin, A. Becerril, T. Elliot,
D. Galaviz, A. Gade, S. Gupta, G. Lorusso, F. Montes, J. Pereira, M. Portillo, A.M. Rogers,
H. Schatz, D. Shapira, E. Smith, A. Stolz,and M. Wallace. “TOF-Bρ mass measurements of
very exotic nuclides for astrophysical calculations at the NSCL ”. J. Phys. G, 35(1):014045,
2008.
J. Pereira, A. Aprahamian, O. Arndt, A. Becerril, T. Elliot, A. Estrade, D. Galaviz, S. Hennrich, R. Kessler, K.-L. Kratz, G. Lorusso, P.F. Mantica, M. Matoš, P. Moller, F. Montes,
B. Pfeiffer, H. Schatz, F. Schertz, L. Schnorrenberger, E. Smith, A. Stolz, W.B. Walters,
and A. Wohr. “Beta-decay of r-process nuclei at the National Superconducting Cyclotron
Laboratory”. Proceedings of Science, PoS(NIC X)027, 2008.
G.W. Hitt, Sam M. Austin, D. Bazin, A. Gade, C.J. Guess, M. Horoi, M.E. Howard,
D. Galaviz-Redondo, Y. Shimbara, E.E. Smith, and R.G.T. Zegers. “Studying electroncapture in supernovae with the (t,3 He) charge-exchange reaction” Proceedings of Science,
PoS(NIC X)105, 2008.
A. Estrade, M. Matoš, M. Amthor, A. Aprahamian, D. Bazin, A. Becerril, T. Elliot,
A. Gade, D. Galaviz, S. Gupta, G. Lorusso, F. Montes, J. Pereira, M. Portillo, A.M. Rogers,
H. Schatz, D. Shapira, E. Smith, A. Stolz,and M. Wallace. “Time-of-flight mass measurements of neutron rich nuclides” Proceedings of Science, PoS(NIC X)184, 2008.
viii
J. Pereira, A. Aprahamian, O. Arndt, A. Becerril, T. Elliot, A. Estrade, D. Galaviz, S. Hennrich, P. Hosmer, R. Kessler, K.-L. Kratz, G. Lorusso, P.F. Mantica, M. Matoš, F. Montes,
B. Pfeiffer, H. Schatz, F. Schertz, L. Schnorrenberger, E. Smith, B.E. Tomlin, W.B. Walters, and A. Wöhr. “β-decay studies of r-process nuclei at the NSCL”. Nucl. Phys. A,
805:470, 2008.
A. Estrade, M. Matoš, A.M. Amthor, D. Bazin, A. Becerril, T. Elliot, A. Gade, D. Galaviz,
G. Lorusso, F. Montes, J. Pereira, M. Portillo, A. Rogers, H. Schatz, D. Shapira, E. Smith,
A. Stolz,and M. Wallace. “TOF–Bρ mass measurement of neutron rich nuclides at the
NSCL” AIP Conf. Proc., 947(1):383, 2007.
G.W. Hitt, Sam M. Austin, D. Bazin, A.L. Cole, J. Dietrich, A. Gade, M.E. Howard, S.D.
Reitzner, B.M. Sherrill, C. Simenel, E.E. Smith, and R.G.T. Zegers. “Development of
a secondary triton beam for (t, 3 He) experiments at intermediate energies from primary
16,18 O beams”. Nucl. Instrum. Methods A, 566:264, 2006.
D. Galaviz, M. Amthor, D. Bazin, B.A. Brown, A. Cole, T. Elliot, A. Estrade, Zs. Fülöp,
A. Gade, T. Glasmacher, R. Kessler, G. Lorusso, M. Matos, F. Montes, W. Müller, J. Pereira,
H. Schatz, B. Sherrill, F. Schertz, Y. Shimbara, E. Smith, A. Tamii, M. Wallace and
R. Zegers. “High precision measurements along the rp-process path” Proceedings of Science,
PoS(NIC-IX)099, 2006.
J. Pereira, A. Becerril, T. Elliot, A. Estrade, D. Galaviz, L. Kern, G. Lorusso, P. Mantica,
M. Matos, F. Montes, H. Schatz, S. Hennrich, K.-L. Kratz, O. Arndt, R. Kessler, F. Schertz,
B. Pfeiffer, M. Quinn, A. Aprahamian, A. Whr, E. Smith, and W. Walters. “r-process experimental campaign at the National Superconducting Cyclotron Laboratory” Proceedings
of Science, PoS(NIC-IX)162, 2006.
M. Quinn, A. Aprahamian, S. Almaraz, B.B. Skorodumov, A. Wöhr, J. Pereira, A. Becerril,
T. Elliot, A. Estrade, D. Galaviz, L. Kern, G. Lorusso, P. Mantica, M. Matos, F. Montes,
H. Schatz, S. Hennrich, K.L. Kratz, B. Pfeier, and E. Smith. “New experiments on neutron
rich r-process Ge–Br isotopes at the NSCL” Proceedings of Science, PoS(NIC-IX)168, 2006.
E.E. Smith, M.E. Howard, B. Mercurio, S. D. Reitzner, A. Estrade, P.T. Hosmer, E. Kwan,
S.N. Liddick, P.F. Mantica, F. Montes, A.C. Morton, H. Schatz, A. Stolz, and B.E. Tomlin..
“Decay studies at the end of the rp-process” Proceedings of Science, PoS(NIC-IX)178, 2006.
Fields of Study
Major Field: Physics
ix
Table of Contents
Abstract . . . . . .
Dedication . . . .
Acknowledgments
Vita . . . . . . . .
List of Tables . .
List of Figures .
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Page
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iv
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v
. vii
. xiii
. xiv
Chapters
1 Background
1.1 Introduction and Overview . . . . . . . . .
1.2 Origins of the p-nuclei . . . . . . . . . . . .
1.2.1 Abundances of p-nuclei . . . . . . .
1.2.2 The p-process on type II supernovae
1.2.3 rp-Process . . . . . . . . . . . . . . .
1.3 Nuclear physics of the rp-process . . . . . .
1.3.1 Nuclear physics models and inputs .
1.3.2 Explosive hydrogen burning . . . . .
1.3.3 Endpoint of the rp-process . . . . .
1.3.4 Nuclear physics points of interest . .
1.4 Astrophysical considerations . . . . . . . . .
1.4.1 Cataclysmic binary systems . . . . .
1.4.2 Other astrophysical scenarios . . . .
1.5 General properties of radioactive decay . . .
1.5.1 Decay rate, half-life, and activity . .
1.5.2 Decay chains . . . . . . . . . . . . .
1.5.3 Branching . . . . . . . . . . . . . . .
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2 Experimental Setup
2.1 Introduction: NSCL experiment 02012 . . . .
2.2 Isotope production and delivery . . . . . . . .
2.3 Experimental endstation . . . . . . . . . . . .
2.3.1 Endstation electronics . . . . . . . . .
2.3.2 Energy calibration of silicon detectors
2.4 γ-ray detection with SeGA detectors . . . . .
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41
41
42
44
49
51
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53
55
57
63
64
64
65
66
67
68
68
4 Discussion
4.1 Evaluation of β detection method and half-life measurement . . . . . . . . .
4.1.1 Application to measurement of known half-lives of 104 Sb and 103 Sn .
4.1.2 β detection efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Application of fits to the 103 Sb region of the PID . . . . . . . . . . . . . . .
4.2.1 Previous experimental measurement of neutron-deficient Sb half-lives
4.2.2 Calculation of neutron-deficient Sb half-lives . . . . . . . . . . . . .
4.2.3 Relative rates of proton decay . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Possible contaminates and the re-analysis of the 103 Sb gate . . . . .
4.3 Proton emission among neutron deficient Sb . . . . . . . . . . . . . . . . . .
4.4 Recent technological progress in β studies . . . . . . . . . . . . . . . . . . .
4.4.1 Improvements to the NSCL . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Decay studies at GSI . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Possible implications for the Sn–Sb–Te cycle of the rp-process . . . .
4.5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
71
71
74
75
75
76
77
79
79
81
81
83
83
84
86
2.5
2.4.1 Segmented germanium array setup . . . .
2.4.2 SeGA electronics . . . . . . . . . . . . . .
2.4.3 Energy calibration of SeGA . . . . . . . .
Data acquisition system and analysis framework
3 Experiment analysis
3.1 Particle identification . . . . . . . . . . . . . .
3.1.1 Isomer identification with SeGA . . .
3.1.2 Separation and identification of nuclei
3.2 Event correlation in the DSSD . . . . . . . .
3.2.1 Implanted nuclei . . . . . . . . . . . .
3.2.2 Correlated decay events . . . . . . . .
3.3 Characterization of background . . . . . . . .
3.3.1 Fitting background spectra . . . . . .
3.3.2 Parameterization of background rate .
3.3.3 Generalized background rate . . . . .
3.4 β decay measurements . . . . . . . . . . . . .
3.4.1 Fit of 103 Sn gated decays . . . . . . .
3.4.2 Fit of 104 Sb gated decays . . . . . . .
3.4.3 Fit of 103 Sb gated decays . . . . . . .
3.4.4 Additional uncertainties . . . . . . . .
3.5 β-decay detection efficiency . . . . . . . . . .
3.6 The search for proton-decay . . . . . . . . . .
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Appendices
A Detector channel assignments
96
B Spectra from SeGA
98
xi
C Fitting a time-dependent background
xii
103
List of Tables
Table
Page
1.1
1.2
Abundances of the p-nuclei. . . . . . . . . . . . . . . . . . . . . . . . . . . .
The hot CNO cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
14
2.1
2.2
Properties of detectors within the beamline. . . . . . . . . . . . . . . . . . .
The photopeak efficiencies for SeGA . . . . . . . . . . . . . . . . . . . . . .
29
37
3.1
3.2
3.3
3.4
3.5
3.6
Known isomers in mass region. . . .
Transition energies in 100 Cd isomer.
Symbols and values used. . . . . . .
Background fit results. . . . . . . . .
β + decay chains and half-lives . . . .
β detection efficiency. . . . . . . . .
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42
44
48
57
63
69
4.1
Improved photopeak efficiencies for SeGA . . . . . . . . . . . . . . . . . . .
82
A.1 Detector TDC channel assignments . . . . . . . . . . . . . . . . . . . . . . .
A.2 Detector ADC channel assignments . . . . . . . . . . . . . . . . . . . . . . .
96
97
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xiii
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List of Figures
Figure
Page
1.1
1.2
1.3
1.4
1.5
1.6
Elemental abundances by the r-, s-, and p-processes. . . .
Reaction flow resulting from one- and two-body reactions.
The path of the rp-process with experimental data. . . . .
The CNO and hot CNO cycles. . . . . . . . . . . . . . . .
The rp-process path and the Sn–Sb–Te cycle. . . . . . . .
Roche lobes of an accreting binary system. . . . . . . . .
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3
8
12
14
16
20
2.1
Schematic diagram of the Coupled Cyclotron Facility and
ment Separator. . . . . . . . . . . . . . . . . . . . . . . . .
Location of endstation detectors in the N3 vault. . . . . .
Diagram of the β-decay end station. . . . . . . . . . . . .
DSSD electronics . . . . . . . . . . . . . . . . . . . . . . .
PIN detector electronics . . . . . . . . . . . . . . . . . . .
Si detector calibration–lower energy range . . . . . . . . .
Si detector gain matching . . . . . . . . . . . . . . . . . .
The Segmented Germanium Array (SeGA). . . . . . . . .
The signal processing system. . . . . . . . . . . . . . . . .
the A1900 Frag. . . . . . . . . .
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26
28
30
31
32
34
35
36
38
100 Cd
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43
46
46
50
50
51
52
54
56
59
60
61
62
65
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
level scheme. . . . . . . . . . . . . . . . . . .
PID plot: Z versus A/q. . . . . . . . . . . . . . . .
I2 position example spectrum. . . . . . . . . . . . .
Comparison of calculations of Z. . . . . . . . . . .
DSSD multiplicity. . . . . . . . . . . . . . . . . . .
PID of implanted nuclei with and without cuts. . .
Z distribution (in arbitrary bins) of implantations.
Z distribution with cuts. . . . . . . . . . . . . . . .
Four parameter fit to background in 95 Ru gate. . .
Fitted values of λBG1 . . . . . . . . . . . . . . . . .
Fitted values of λBG2 . . . . . . . . . . . . . . . . .
Fitted values of RBG1 . . . . . . . . . . . . . . . . .
Fitted values of RBG2 . . . . . . . . . . . . . . . . .
103 Sn decay spectrum. . . . . . . . . . . . . . . . .
xiv
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3.15
3.16
104 Sb
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
104 Sb
half-life measurements compared. . . . . . . . . . .
half-life measurements compared. . . . . . . . . . .
Z distributions of A − 2q = 1, 2, groupings from the PID.
Half-lives for 102-110 Sb. . . . . . . . . . . . . . . . . . . . .
103-105 Sb half-life measurements compared. . . . . . . . . .
101 Sn half-life measurements compared. . . . . . . . . . .
Comparison with PID from recent GSI experiment. . . . .
Photodisintegration rates for 103 Sb and 104 Sb. . . . . . . .
B.1
B.2
B.3
B.4
γ-ray
γ-ray
γ-ray
γ-ray
103 Sb
decay spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
decay spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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72
73
75
76
78
80
84
85
0–300 keV range. . . .
300–600 keV range. . .
600–1000 keV range. .
1000–1500 keV range.
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99
100
101
102
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104
105
106
107
108
109
110
111
112
113
103 Sn
energies
energies
energies
energies
C.1 Background
C.2 Background
C.3 Background
C.4 Background
C.5 Background
C.6 Background
C.7 Background
C.8 Background
C.9 Background
C.10 Background
correlated
correlated
correlated
correlated
activity
activity
activity
activity
activity
activity
activity
activity
activity
activity
to
to
to
to
within
within
within
within
within
within
within
within
within
within
100 Cd
implants,
implants,
100 Cd implants,
100 Cd implants,
100 Cd
95 Ru
gate. .
gate. .
97 Rh gate. .
98 Pd gate. .
99 Pd gate. .
94 Tc gate. .
93 Tc gate .
99 Ag gate. .
100 Ag gate .
100 Cd gate.
96 Ru
xv
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66
67
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Chapter 1
Background
1.1 Introduction and Overview
In 1957 Burbidge, Burbidge, Fowler, and Hoyle (B2 FH), presented a landmark paper that
described much of our modern understanding of nucleosynthesis [1]. Al Cameron independently authored a paper that same year giving essentially the same description [2]. B2 FH
presented three astrophysical processes responsible for producing elements heavier than iron.
Two of these are neutron capture processes. The slow neutron-capture process (s-process),
a network of reactions that proceeds along the line of stable nuclei, is thought to occur in
environments such as massive stars or low mass AGB stars. The rapid neutron capture
process (r-process) evolves far from stability among neutron-rich nuclei and is theorized to
occur at high temperature and pressure in environments where copious amounts of neutrons
are available. Core collapse supernovae (SNII) are the most frequently proposed r-process
environment. A third process, the p-process was proposed by B2 FH as a possible mechanism to resolve a problem observed by the authors. Unlike the other processes presented
in the paper, the p-process was entirely theoretical. The authors noted at that time, “No
astrophysical evidence is at present available for the occurrence of this process.”[1]
Abundances of most radionuclides can be attributed as being produced in either one or
both of the s- and r-processes. The need for an additional production mechanism becomes
apparent, however, due to the several dozen nuclei that lie on the neutron-deficient side
of stability. These could not be produced by neutron-capture and β-decay. This chapter
presents the rp-process as a partial explanation to the origins of these so-called p-nuclei and
1
describes the progression of rp-process reactions beginning with the breakout from the CNO
cycles to the possible culmination of these reactions into a Sn–Sb–Te cycle. Chapters 2 and
3 describe the setup and analysis of a decay experiment at the National Superconducting
Cyclotron Laboratory and chapter 4 discusses the results and outlook following this study.
1.2 Origins of the p-nuclei
1.2.1 Abundances of p-nuclei
Observations of solar and cosmic abundances are made through a variety of methods. Decomposition of absorption spectra allow for the study of elemental abundances in many
locations, but generally do not allow isotopic abundances to be distinguished, and represent
only thin layers of hot astrophysical objects. They are therefore combined with data from
other sources, including cosmic rays, and planetary studies. Abundance analyses are primarily based, however, on a class of rare meteorites, the CI1 carbonaceous chondrites.[4, 5, 6, 7].
Figure 1.1 shows the decomposition of nuclei by process as described in B2 FH. Note
that the abundances of p-nuclei are minimally an order of magnitude smaller than the
abundances of nuclei produced by either the r-process or s-process. A list of these nuclei
and their abundances are given in table 1.1. It is worth noting that the Mo and Ru isotopes
occur at a significantly larger abundance than neighboring nuclei. Also, the vast majority
of p-nuclei are even proton-even neutron nuclei, which tend to have greater stability due
to pairing effects. Notable examples are the very rare
138 La
and
180 Tam ,
an isomer with a
long half-life relative to its ground state.
1.2.2 The p-process on type II supernovae
The modern conception of the p-process (reviewed at length in [6]) is still very similar in
spirit to the description given in B2 FH. Previously produced seed nuclei beyond iron are
acted upon by a series of capture reactions, primarily (p, γ), and photodisintegrations.
(γ, n) and (γ, α) are of greatest importance, but (γ, p) occur as well. In some of the
2
Figure 1.1: Elemental abundances by the r-, s- and p-processes. (Figure from B2 FH [1]
in which the elemental abundance data of Seuss and Urey [3] are decomposed by relevant
nucleosynthesis process.)
3
Table 1.1: The p-nuclei, adapted from tables in [4, 8,
relative to an elemental abundance of Si at 106 .
Nuclide Z N
Abundance t1/2
74 Se
34 40
0.58
78 Kr
36 42
0.20
84 Sr
38 46
0.131
92 Nb
41 51
0.0
3.5×107 yr
92 Mo
42 50
0.386
94 Mo
42 52
0.241
96 Ru
44 52
0.105
98 Ru
44 54
3.55×10−2
102 Pd
46 56
1.46×10−2
106 Cd
48 58
1.98×10−2
108 Cd
48 60
1.41×10−2
113 In
49 64
7.80×10−3
112 Sn
50 62
3.63×10−2
114 Sn
50 64
2.46×10−2
115 Sn
50 65
1.27×10−2
120 Te
52 68
4.60×10−3
124 Xe
54 70
6.94×10−3
126 Xe
54 72
6.02×10−3
130 Ba
56 74
4.60×10−3
132 Ba
56 76
4.40×10−3
138 La
57 81
3.97×10−4 1.5×1011 yr
136 Ce
58 78
2.17×10−3
138 Ce
58 80
2.93×10−3
144 Sm
62 82
7.81×10−3
146 Sm
62 84
0.0
1.03×108 yr
156 Dy
66 90
2.16×10−4
158 Dy
66 92
3.71×10−4
162 Er
68 94
3.50×10−4
168 Yb
70 98
3.23×10−4
174 Hf
72 102 2.75×10−4
180 Tam
73 107 2.58×10−6 1.2×1015 yr
180 W
184 Os
190 Pt
196 Hg
74
76
78
80
106
108
112
116
1.53×10−4
1.33×10−4
1.85×10−4
6.3×10−4
4
9]. Abundances are from [7] and are
Possible additional processes
rp-process?
rp-process?
rp-process?
[β-decay to 92 Mo]
rp-process?
s-process & rp-process?
rp-process?
rp-process?
r-process & s-process
s-process
[β-decays to
138 Ce]
[α-decays to
146 Nd]
s-process
[β − -decays to 180 W,
or e− -captures to 180 Hf]
s-process
literature this process is referred to as the γ process differentiating it from other processes
that may be involved in the production of p-nuclei [8, 10, 11].
The favored astrophysical scenario for the p-process occurs within the shock wave following the collapse of a type II supernova [12]. The previous evolution of a massive star
would provide the needed seed nuclei from the s-process, and the explosion would provide
the needed conditions of temperature and density as well as the required radiated flux for
the photodisintegration reactions.
Models of this scenario suffer from a persistent under-production of the abundances of
a number of elements [13, 14]. Neutron deficient isotopes of Mo and Ru are consistently
under-produced relative to other p-nuclei [6] and in some models,
113 In
and
115 Sn
have
been under-produced as well. Some plausible explanations within the context of type II
supernovae have been suggested. There are uncertainties regarding the effects of rotation
and mixing in core collapse supernovae, and some key reactions may have larger-thanestimated errors [6]. Still, the production of the Mo and Ru isotopes remains an unresolved
problem.
1.2.3 rp-Process
The rp-process was proposed as a “new kind of nucleosynthesis process” in 1981 by Wallace and Woosley [15]. They explored the nucleosynthesis possible in very hydrogen rich
environments at high temperature (T >> 0.1 GK) and showed that heavy elements could
be produced up to and beyond the iron group through a series of rapid proton capture
reactions either on seed nuclei or on the products of hydrogen burning if no heavier nuclei
are present. Wallace and Woosley suggested a number of astrophysical applications for this
process, but the candidate that is favored by far in the literature is within the model of
Type I X-ray bursts. Further discussion of astrophysical considerations will be presented
in section 1.4. Some X-ray burst scenarios now extend the rp-process into the mass region
of the light p-nuclei [16]. This has raised the possibility that the rp-process might be a
contributor to the observed abundances under-produced in p-process models.
5
1.3 Nuclear physics of the rp-process
The rp-process is essentially a network of nuclear reactions occurring within some thermodynamic system (albeit a rather complex one). Current modeling efforts deeply intertwine
the reaction network, including its rates, element production, and energy outputs, with
astrophysical aspects of an X-ray burst or other native environment. It is, however, instructive to first independently discuss the nuclear physics aspects of the reaction network
independent of environment. A more detailed description of astrophysical conditions will
be presented in section 1.4.
1.3.1 Nuclear physics models and inputs
Calculations of the rp-process require a great deal of data input from nuclear physics. These
include reaction cross sections, nuclear masses (which relate to reaction Q-values as well
as proton and α separation energies) and beta decay properties (half-lives, level structures,
etc.)
A reaction network
General discussion of the time evolution of isotopic abundances can be found in several texts
([5, 17, 18]) and given in the context of the rp-process in [19, 20, 21]. Isotopic abundances
are given as mass fraction divided by mass number or equivalently written in terms of
number density and matter density:
Yi =
ni
Xi
=
,
Ai
NA ρ
(1.1)
where Xi is the mass fraction of isotope i, Ai , its mass number (in g/mole), and ni its
number density. NA is Avogadro’s number and ρ is the density of matter.
A reaction network is then formed from the set of differential equations written for each
6
isotope and including all relevant production and depletion reaction rates [5, 20]:
X
X
dYi X i
i
i
=
Nj λj Yj +
Nj,k
ρNA < σv >j+k Yj Yk +
Nj,k,l
ρ2 NA 2 < σv >j+k+l Yj Yk Yl .
dt
j
j,k
j,k,l
(1.2)
Each of the three terms of this equation represent reaction types. The first term represents
all possible channels of decay and photodisintegration with rates given by λi . The second
are the two particle interactions in which j and k are reactants with a rate ρNA < σv >j+k .
The third represents a three-body reaction between particles j, k and l .
The time integrated reaction flow between radionuclides from i to j is given by
Z Fi,j =
dYj
dYi
−
dt.
dt (i→j)
dt (j→i)
(1.3)
Thus, the solution of the above system of equations also establishes the path of the rpprocess. The reaction channels relevant to rp-process calculations and their corresponding
flow across the chart of the nuclides are summarized in figure 1.2.
Particle capture reactions
Any calculation of explosive hydrogen burning processes will depend heavily upon proton
capture reaction rates. Most important are the (p, γ) rates, but (p, n) rates are relevant as well. At sufficiently high temperatures (α, p) rates play an important role in the
8 . Z . 21 region, starting with the breakout from the hot CNO cycles (discussed further in section 1.3.2. There is a scarcity of experimental information on these reactions
[22]. Only two of the relevant (p,γ) reactions have been measured directly,
[23] and
13 N(p,γ)14 O
21 Na(p,γ)22 Mg
[24]. Few of the relevant (α, p) reactions are even experimentally
derived. For example,
14 O(α,
p)17 F, a possible exit channel from the hot CNO cycle to
the rp-process, has been calculated using corresponding levels experimentally observed in
18 Ne.
As reactions progress to higher masses and farther from stability, the availability of
experimentally-derived rates decreases quickly. Typically reaction cross sections are calculated from statistical models such as Hauser-Feshbach [25].
7
Z + 1, N − 1
β − decay
or
(p,n)
@
I
@
Z, N − 1
Z + 2, N + 2
(α,n)
(α,γ)
Z + 1, N
Z + 1, N + 2
3
(p,γ)
(α,p)
6
Z, N
Z, N + 1
original
nucleus
-
?
Z − 1, N − 2
Z − 1, N
+
(p,α)
(γ,p)
@
R
@
(γ,n)
Z + 2, N + 1
(n,γ)
Z − 2, N − 2
Z − 2, N − 1
(γ,α)
(n,α)
Z − 1, N + 1
β + decay,
e− capture,
or (n,p)
Figure 1.2: Reaction flow resulting from one- and two-body reactions. Z and N indicate
the initial proton and neutron number of the nucleus prior to decay, photodisintegration,
or capture reaction.
8
Photodisintegration
Photodisintegration reactions, including (γ, p), (γ, n), and (γ, α), are essentially reverse
particle capture reactions and thus have negative Q-values. These rates, and inverse rates
in general have been derived using the detailed balance principle of statistical physics [20].
In the rp-process, the most important of these reactions are photodisintegrations involving
(γ, p). The relative rates of photodisintegration to proton capture reactions are highly
sensitive to reaction Q-value and temperature, with photodisintegrations dominating at
higher temperatures [20]. The (γ, α) rate plays a significant role at a couple of points along
the rp-process path. Mass models predict Q-values of < 1.5 MeV for α capture on
82 Zr, 84 Nb,
80 Sr,
and 84 Mo [20]. The endpoint of the rp-process (discussed further in section 1.3.3
occurs above the closed nuclear shell at Sn, where the (γ, α) reaction has a positive Q-value
for all of the Te isotopes reached. In addition to temperature, photodisintegration rates also
depend upon other environmental conditions, namely, matter density, ρ, and 1 H abundance.
β-decay and electron capture
Both β decay processes and photodisintegration are included in the first term of equation 1.2.
Most general discussions of β decay include three basic processes:
β − decay (electron emission) :
AX
Z N
→
A 0
Z+1 X N −1
+ e− + ν¯e
(1.4)
β + decay (positron emission) :
AX
Z N
→
A 0
Z−1 X N +1
+ e+ + νe
(1.5)
electron capture (ε) :
AX
Z N
+ e− →
A 0
Z−1 X N +1
+ νe
(1.6)
Where X and X 0 represent the nucleus before and after each decay process with the numbers
of nucleons indicated. The presence of the neutrino or antineutrino (νe or ν¯e ) distinguishes
the weak decay processes from other charged-particle decay processes (such as α decay).
In each case the nearly-massless neutrino carries away part of the energy and is generally
undetected experimentally. Although β − decay may be the more familiar process, it is
the other processes that are relevant to the rp-process and are the primary subject in
the present study of neutron deficient nuclei. The rates of these processes are generally
9
treated together. Both positron emission by β + decay and electron capture result in the
same reaction flow. They do, however, differ energetically in terms of Q-value by twice the
electron’s rest energy (Qε = Qβ+ + 2me c2 ). Rates from β decay half-lives are among the
most important input to a reaction network. β + decays occur more slowly than many of
the other reactions discussed above allowing some regulation of the timescale for reaction
network calculations. The ground-state half-lives are known experimentally for many of the
nuclei along the rp-process. Where they are unknown, calculated values are used. In the
higher temperature stellar environments, heavier isotopes (A > 20), are likely to undergo
decays from thermally populated energy levels above the ground state. For these cases,
temperature-dependent half-lives must be calculated.
Three-body reactions
The third term in equation 1.2 is representative of the less frequent three-body reactions.
This includes the triple-α reaction, important in the formation of 12 C. This rate has recently
been determined through the experimental observation of the reverse process [26]. Also,
two-proton capture reactions, (2p, γ), have been investigated in a number of rp-process
studies. It has been suggested that these may offer a means to connect reaction pathways
at long-lived waiting points that have been blocked by the proton drip line [20, 27].
The equilibrium approximation
The most critical data needs for the rp-process can be better understood by considering an
approach using a simplified approximation. The conditions of the rp-process fall just short
of nuclear statistical equilibrium, but allow some equilibrium clusters to form along isotonic
chains. Once the rate of proton capture, (p, γ) and disintegration, (γ, p) reach equilibrium
the evolution of the system is limited by the β + decay of so-called “waiting point” nuclei
(typically at the point where the isotonic chain reaches the proton drip line [28]).
Under this equilibrium condition the relative abundance of neighboring nuclei can be
10
related together by the Saha equation [28]
G(Z+1,N )
Y(Z+1,N )
= ρp
Y(Z,N )
2G(Z,N )
A(Z+1,N ) 2π~2
A(Z,N ) mu kT
3/2
exp
Sp(Z+1,N )
kT
,
(1.7)
where Y(Z,N ) is the abundance of nucleus Z, N , T is the temperature, ρp is the proton
density, G is the partition function, A is the mass number, mu is the atomic number, k is
the Boltzmann’s constant, and Sp is the proton separation energy, given by:
Sp(Z+1,N ) = M (Z, N ) + M (1H) − M (Z + 1, N ).
(1.8)
Under this equilibrium condition the rp-process evolves independently of two and three
particle reaction cross-sections and the critical data needs are mass measurements and β +
decay half-lives of the waiting point nuclei.
The equilibrium model does not apply well to the rapid heating and cooling phases that
occur during an X-ray burst. Also, at sufficiently high energies, (α,p) reactions begin to
compete with proton capture and provide another channel to move the reaction flow to exit
the isotonic chain. Thus, other data are needed.
Additional nuclear data needs
Among the most critical input to reaction network calculations are not the masses of nuclei
themselves, but the energy production or consumption from each reaction, the Q-values
that result from the differences in the masses of products and reactants. The energy output
of the reaction network dictates the behavior of the astrophysical model.
Whereas many very few of the reaction rates are known experimentally, most are calculated using statistical models such as Hauser-Feshbach with well-known codes such as
NON-SMOKER [25]. Various approaches have been used to calculate unknown half-lives
(see section 4.2.2 for examples).
The nuclear masses (and reaction Q-values) are perhaps the most important input to
rate calculations. It has been suggested that a mass uncertainty of less than 500 keV/c2 is
needed to prevent a contribution to the rate uncertainty in excess of a factor of two [20].
Another important ingredient to such models are the nuclear level densities. The output
11
Figure 1.3: The path of the rp-process in an X-ray burst model [16] shown with the current
status of experimental data. Stable nuclides are gray, nuclides with mass experimentally
known to better than 10 keV are red, other nuclides with experimentally known masses
are orange, nuclei with measured half-lives are in green, and nuclei that have only been
identified are indicated in blue. Modified from 2006 figure in [28] and updated with the
recent 96 Cd half-life measurement [29] and numerous mass measuremnts [30, 31, 32, 33, 34,
35, 36, 37, 38, 39, 40, 41, 42, 43].
12
of such models can be improved by including experimentally known level structure. One
recent measurement at the NSCL, for example, has probed the level structure of 30 S through
neutron removal in an effort to reduce the uncertainties in the
29 P(p,
γ)30 S rate [22].
Figure 1.3 shows the current status of the available mass and half-life data in the rpprocess region. A great deal of recent progress has occured due to high-precision mass
measurements from Penning-trap mass spectrometry experiments around the world [30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43]. Also, the half-life of
96 Cd
was recently
measured, the last experimentally unknown waiting point half-life of the rp-process, at the
NSCL [29].
A recent effort by the Joint Institute for Nuclear Astrophysics (JINA) has made reaction
rate data more accessible. The REACLIB database [44] provides a current and accurate
library of reaction rates for astrophysical applications. The rate data is made publicly available online through a Web interface. Updates are transparently documented and version
tracked. Users can choose from a recommended set of rates or a variety of other available
experimental and theoretical rates.
1.3.2 Explosive hydrogen burning
Network calculations of the rp-process are generally designed to accommodate scenarios with
or without heavier seed nuclei. Many reaction sequences are included. Some are identical to
processes that occur in other environments, such as hydrogen burning via the p-p-chains, or
the fusion of helium into carbon through the triple-α reaction. Other processes are unique
to conditions where explosive hydrogen burning is favored.
The Hot CNO cycles
The hot CNO cycles (also known as the HCNO cycles or the β-limited CNO cycles [15])
can occur in a star when there are sufficient quantities of catalyst nuclei (C, N, O, as well
as F, and Ne) and the temperature is elevated into the range of 0.1-0.4 GK. Below 0.1 GK
reactions tend to favor the cycles of the “cold” CNO cycles, and above 0.4 GK breakout
reactions occur leading to the rp-process [9]. As the heavy elements are processed through
13
13
(p,γ)
14
C
β
(p,α)
N
17
(p,γ)
14
O
β + decay
(p,α)
(α,p)
18
β+
decay
(p,γ)
(p,γ)
13
F
+
(p,γ)
β+
decay
18
O
N
15
17
O
β+
decay
Breakout
to rp−process
β+
decay
F
Ne
19
Ne
(p,γ)
β+
decay
(p,γ)
(α,γ)
12
C
(p,α)
15
N
16
(p,γ)
18
O
T < 0.1 GK,
CNO cycles
T > 0.1 GK, Hot CNO cycles
O
19
(p,γ)
F
(p,α)
(p,α)
T > 0.4 GK, rp−process
Figure 1.4: Flow chart of the CNO reaction cycles as they occur in stellar interiors are
shown with black lines. Alternative reaction pathways that result in the Hot CNO cycle
are included in blue. Breakout reactions that allow the start of the rp-process are shown in
red. (Inspired by a similar figure by [45])
Hot CNO1
Hot CNO2
Hot CNO3
12 C(p,γ)13 N
15 O(β + ν)15 N
15 O(β + ν)15 N
15 N(p,γ)16 O
15 N(p,γ)16 O
16 O(p,γ)17 F N
16 O(p,γ)17 F
13 N(p,γ)14 O
14 O(β +
ν)14 N
14 N(p,γ)15 O
15 O(β +
ν)15 N
15 N(p,α)12 C
17 F(β + ν)17 O
17 O(p,γ)18 F
18 F(p,α)15 O
17 F(p,γ)18 Ne
18 Ne(β +
Table 1.2: The hot CNO cycles.
14
ν)18 F
18 F(p,α)15 O
the reactions of these cycles there is no net change in their abundance, but their presence
helps facilitate the burning of hydrogen. The net effect of any one of these cycles is the same
as the collective result of the pp-chains, four 1 H atoms are fused into one 4 He and copious
amounts of energy are released as a result. Each cycle occurs on a time scale limited by
the cycle’s slowest β + decay [9]. Figure 1.4 and table 1.2 illustrate the reaction sequences
involved in each of the hot CNO cycles.
Lower temperature rp-process
The hot CNO cycle below 0.4 GK constrains reactions to the mass region A . 20. However,
if seed nuclei exist in the region A > 20, an rp-process can occur on the seed nuclei in a lower
temperature range (0.1–0.4 GK [9]). Such a process could act within a mass range of A =
20-30 and would likely be impeded by any of the waiting point nuclei in this region, such
as:
22−23 Mg, 25−27 Si, 29−31 S, 34−35 Ar, 38−39 Ca, 43 Ti
(Note: Different sources cite different
isotopes of the same nuclei as waiting points. Where a network crosses an isotopic chain is
model dependent [9, 46, 47]). Rather than moving up the isotonic chain through a (p,γ)
reaction, a (p,α) reaction might direct the flow towards lower mass and start a cycle of
reactions similar to the CNO cycle. Examples of this include Ne–Na–Mg and Mg–Al–Si
cycles [8].
Hot CNO breakout and the αp process
At higher temperature (T ≈ 1.5 GK),an abundance flow can break out of the hot CNO cycle
through a series of (α, p) and (p, γ) capture reactions following one the two sequences:
19 Ne(p,
γ)20 Na(p, γ)21 Mg(α, p)24 Al(p, γ)25 Si(α, p)28 P
18 Ne(α,
p)21 Na(p, γ)22 Mg(α, p)25 Al(p, γ)26 Si(α, p)29 P(p, γ)30 S(α, p)30 Cl
This series of reactions is referred to as the αp-process [15]. Since this sequence does
not include any β + decays it is able to bypass the waiting points in the lower mass region
of the rp-process. The series of (p, γ) and (α, p) reactions may continue to A ≈ 40 (just
above the Z = 20 shell closure at Ca).
15
Figure 1.5: The rp-process path for a Type I X-ray burst from [16, 48] Helium burning can
be seen in the lower mass regions. The reaction: 3α →12 C, is shown in blue, a series of
(α,p) and (p,γ) reactions that connect the Hot CNO cycle to the 40 Ca region are shown in
green. The higher mass region (p,γ) reactions advance up isotonic chains until reaching the
proton-drip line where a series of β + decays occur (shown in pink). INSET:The Sn-Sb-Te
cycle, also from [16], the primary cycle is shown with solid, orange arrows, a secondary cycle
is indicated with dashed arrows.
16
High temperature rp-process
A significant bottleneck for the abundance flow as an rp-process reaches higher temperatures
occurs at the Z = 28 shell closure near doubly magic
56 Ni.
Many early simulations of the
rp-process didn’t extend beyond Z = 28 arguing that negligible hydrogen burning could
occur in this region [16]. At temperatures less than 1 GK proton captures likely will not
be able to overcome the coulomb barrier. F.-K. Thielemann suggests that the maximum
temperature must be below 2 GK to prevent photodisintegrations from dominating the
reaction sequence [47]. Beyond Ni are additional waiting points including
72 Kr,
60 Z, 64 Ge, 68 Se,
any of which may limit the further extension of the reaction flow [9, 28]. An extended
network for a high temperature rp-process is shown in figure 1.5.
1.3.3 Endpoint of the rp-process
Schatz [16] has shown within an X-ray burst model that the reaction flow may reach up to
the A ≈ 100 region. The endpoint for an individual burst may depend upon conditions such
as peak temperature and amount of available H for ignition. Reaction network calculations
show that the natural limit of the rp-process occurs due to a Sn–Sb–Te cycle [16]. The cycle
is shown in the inset of figure 1.5. When reaction flows reach the range of light Sn nuclei
near doubly magic
100 Sn,
β + decay of Sn nuclei and proton capture by In nuclei allow the
reactions to follow a path along the chain of Sn isotopes towards greater β-stability. The
primary path of the reaction flow passes from
105 Sn
to
106 Sb
to
107 Te
following the first set
of isotones that are sufficiently proton-bound to allow (p,γ) proton capture to dominate the
rate of photodisintegration, (γ,p). Upon reaching 107 Te, however, (γ, α) photodisintegration
produces
103 Sn
once again and thus creates the cycle.
The nature of the cycle at the endpoint of the rp-process has consequences for the
composition of the resulting ashes. For one, it suggests that an upper mass limit near A =
107 is imposed. More generally it allows for the production of a broad range of nuclei in the
mass region, A = 64-107. Furthermore, the cyclic nature of the Sn-Sb-Te cycle also allows
for the build-up of the relatively long-lived
104 Sn
17
nuclei (t1/2 = 20.8 ± 0.5 s), alters the
relative abundances of hydrogen and helium, and increases energy production at late times
within the light curve of the burst. These various factors have consequences for the X-ray
burst luminosity curve which may be observed as having a longer tail. The potential for
X-ray burst ashes to contribute to the abundances of p-nuclei, such as
92,94 Mo
and
96,98 Ru,
depends on both this cycling and the ability of the ash to escape the neutron star and
enter the interstellar medium [16]. While it is clear that the Sn-Sb-Te cycle forms once the
rp-process reaches the neutron deficient Te isotopes, it is still uncertain at which Sn isotope
the reaction flow breaks through the weakly bound Sb isotopic chain and whether there are
significant secondary branches. The neutron deficient 105−108 Te isotopes are experimentally
known ground state alpha emitters and have long been known to be alpha unbound by
3-4 MeV [49, 50]. Decay properties and proton separation energies among the antimony
isotopes, however, are less certain. These values play roles in determining the degree to
which the primary isotonic chain is followed into the cycle (105 Sn-106 Sb-107 Te) or a possible
sub-cycle, such as (106 Sn-107 Sb-108 Te) or(104 Sn-105 Sb-106 Te) [16].
1.3.4 Nuclear physics points of interest
In addition to the astrophysical applications the study of neutron deficient nuclei along the
rp-process path are of great interest to nuclear structure theorist as well. It is worth making
note of some points of interest along the rp-process path. It is no coincidence that the most
significant bottlenecks to impede the rp-process and even its proposed end point occur in
close proximity to closed proton shells at Z = 20, 28, and 50. In some cases the nuclei along
the path are doubly magic, having closed neutron shells as well (56 Ni and
100 Sn).
The path
of the rp-process follows very closely to the N=Z line, which has provided opportunities to
study and apply models of mirror nuclei (with equal, but opposite isospin) [51]. Studies
in this region also probe the structure of the relatively accessible proton-drip line which is
tremendously influential in determining the rp-process path [52].
18
1.4 Astrophysical considerations
1.4.1 Cataclysmic binary systems
The most common astrophysical models of the rp-process involve a mass transfer within a
cataclysmic binary star system. Such systems include a compact object (such as a white
dwarf star, a neutron star, or a black hole) and a companion star (typically a main sequence
star). Figure 1.6 shows such a system. Dashed lines in the figure indicate the contour of
the system’s Roche Lobes. The Roche Lobes form an equipotential gravitational surface.
All matter within one of the lobes is gravitationally bound to the star in that lobe. In very
close systems, when the companion star ages and eventually expands beyond the confines of
its own lobe matter will fall from the companion’s surface and will accrete onto the compact
object. Due to rotation of the system, transferred material will generally spiral into the
form of an accretion disk.
Novae
When the compact object described in the above scenario is a white dwarf, the result is a
nova. Novae have become the lead candidate for the low temperature rp-process described
in section 1.3.2. These systems have modest mass transfer rates (dM/dt ≈ 10−9 Msun /yr)
and achieve peak burning temperatures of 0.1-0.2 GK for C-O white dwarfs and 0.4-0.5 for
a O-Ne-Mg white dwarfs. The timescale for thermonuclear runaway is 100-200s [46].
Type-I X-ray bursts
When the compact object in a cataclysmic binary system is a neutron star the resulting
system is a Type I X-ray burster. Superficially this system may seem very similar to a Nova.
Mass is transferred from a companion star and accretes onto the surface of the degenerate
neutron star. The gravitational potential, however, is much greater in this case resulting in
a much higher density and temperature (ρ = 106 –108 g·cm−3 , T = 0.2–1.5 GK [46]). The
bursts themselves last tens to hundreds of seconds and release ∼ 1039 –1040 ergs. The bursts
recur on timescales of hours to days. Typically bursts have a sudden sharp rise and fall in
19
Figure 1.6: Roche lobes of an accreting binary system. A compact object (left) accretes
matter through the Lagrange point from a massive star that has expanded to fill its Lobe.
intensity which is followed by an extended tail [53]. Understanding how the energy output
of the rp-process evolves over time and where its end point lies is key to understanding
these variations in intensity.
1.4.2 Other astrophysical scenarios
A number of more exotic scenarios for the rp-process have been proposed. In addition
to novae and accreting neutron stars, Wallace and Woosley’s initial description of the rpprocess suggested possible scenarios such as exploding supermassive stars (SMS) or even
some chaotic cosmology [15]. Accretion onto a Thorne-Źytkow object (TŹO) has been proposed as well [10]. TŹOs are hypothetical stellar objects in which a red giant or supergiant
has merged with and eveloped a neutron star.
1.5 General properties of radioactive decay
Two decay processes dominate the neutron-deficient (also known as proton-rich) side of the
nuclear landscape. First, essentially by definition, these nuclei are unstable to β + decay
and are thus both susceptible to spontaneous emission of a positron or β + particle and
may, under the right conditions, be likely to undergo electron capture reactions. Second,
for nuclei farther from stability, decay by the spontaneous emission of a proton is observed.
Proton-stability defines the other important boundary for nuclear structure in the region,
20
the so-called proton drip-line. The experiment described in the chapters that follow was
proposed as a probe of both of these decay modes. The nuclei of primary interest lie on the
far side of the proton drip line. This section discusses nuclear physics concepts common to
radioactivity in general.
1.5.1 Decay rate, half-life, and activity
Decay of a radioactive nucleus is a statistical process that may be described by half-life, t1/2 ,
or the related disintegration rate constant, λ. The latter is defined such that the probability
that a given nucleus will decay in a short time, dt, is given by λdt. For a sample of N nuclei,
the expected number to disintegrate in the same short time is given by:
dN = −λN dt.
(1.9)
Integration of this expression gives the fundamental law of radioactive decay in exponential
form:
N (t) = N0 e−λt ,
(1.10)
where N is the number of nuclei present after a time, t, and N0 is the initial number of
nuclei present (N = N0 , at t = 0).
Half-life, the time at which half of the initial nuclei may be expected to have decayed is
then related to the disintegration rate constant by:
t1/2 =
ln 2
.
λ
(1.11)
The activity, R, of a sample of radioactive nuclei undergoing a single decay process
will have a proportionality to the disintegration rate and will have an exponential timedependence similar to equation 1.10:
R(t) =
dN
= λN (t) = λN0 e−λt .
dt
21
(1.12)
1.5.2 Decay chains
While the above description of decay and activity is sufficient for describing a simple case
where a parent undergoes a single decay process to produce a stable daughter, often, the
initial decay is the beginning of a series of decays:
λ
λ
λ
1
2
3
N1 −→
N2 −→
N3 −→
··· ,
(1.13)
where N1 , N2 , N3 , . . ., are the numbers of successive generations of unstable nuclei produced
by a series of decay processes and λ1 , λ2 , λ3 , . . ., are their respective disintegration rates.
In such a case, the activity will be the sum of the activities from each decay process:
R(t) = λ1 N1 (t) + λ2 N2 (t) + λ3 N3 (t) + . . .
(1.14)
Where each of these terms is coupled with the others in a series of linear differential equations:
dN1
dt
dN2
dt
dN3
dt
= −λ1 N1
= λ1 N1 − λ2 N2
= λ2 N2 − λ3 N3
(1.15)
..
.
If the initial conditions are assumed such that N1 = N0 at t = 0, and Ni = 0 at t = 0 for
all other values of i 6= 1 (i.e. N2 , N3 , . . ., are not initially present), a general solution can
be given to the nth term of equation 1.14 by the Bateman equations (as presented in [54],
and discussed in [55]). The activity of each process in the decay chain is given in terms of
coefficients that depend upon the constants used to describe the preceding processes:
Rn (t) = λn Nn (t) = N0
∞
X
ci e−λi t
n=0
= N0 c1 e−λ1 t + c2 e−λ2 t + c3 e−λ3 t + . . . + cn e−λn t ,
22
(1.16)
with coefficients given by:
n
Y
ci =
λj
j=1
=
n
Y0
(λj − λi )
λ1 λ2 λ3 . . . λn
.
(λ1 − λi )(λ2 − λi ) . . . (λn − λi )
(1.17)
j=1
On the lower product rule, the prime indicates that the factor with i = j is to be omitted.
In the present decay study of neutron-deficient Sb, these are applied explicitly to the first
three terms of equation 1.14:
R1 (t) = λ1 N1 (t) = N0 λ1 e−λ1 t ,
R2 (t) = λ2 N2 (t) = N0
(1.18)
λ1 λ2 −λ2 t
λ1 λ2 −λ1 t
e
+
e
,
λ2 − λ1
λ1 − λ2
(1.19)
R3 (t) = λ3 N3 (t)
(1.20)
−λ
t
−λ
t
−λ
t
1
2
3
λ1 λ2 λ3 e
λ1 λ2 λ3 e
λ1 λ2 λ3 e
= N0
+
+
.
(λ2 − λ1 )(λ3 − λ1 ) (λ1 − λ2 )(λ3 − λ2 ) (λ1 − λ3 )(λ2 − λ3 )
The n = 1 term represents the activity of the parent nucleus and is essentially unchanged
from equation 1.10. The n = 2 and n = 3 terms represent decay processes by daughter
and granddaughter nuclei. In studies where the parent decay process is of primary interest,
if the activity of the granddaughter process is sufficiently low and/or sufficiently timedelayed from the parent decay, three generations prove a sufficient approximation of the
total activity. Equations 1.18–1.20 can also be written in terms of the initial activity of the
parent, R0 = λ1 N0 , by coupling N0 with a factor of λ1 from each of the terms. This form of
the Bateman equations is the basis of the curve-fitting procedure described in section 3.4.
1.5.3 Branching
In addition to the multiple decay processes that occur from subsequent generations, some
isotopes have access to more than one decay channel. The fraction of nuclei that decay by
each process may be expressed by a branching fraction. For example, an isotope beyond
23
the proton drip-line might decay by either β + decay or proton emission:
dN = dNβ + dNp = (bβ + bp )dN,
(1.21)
where bβ and bp are the branching fraction for each process and bβ + bp = 1. The total
decay rate, is then related to the partial rates of each branch:
λT otal = (bβ + bp )λT otal = λβ + λp .
(1.22)
The branching fraction can then be used to express a partial half-life for each decay mode.
In the present example, the partial β decay half-life is given by:
t1/2,β =
t1/2
ln 2
ln 2
=
=
.
λβ
bβ λT otal
bβ
(1.23)
Although this definition of partial half-life is analogous to the total half-life, it does not
suggest that half of the β + decays occur within time, t1/2,β .
24
Chapter 2
Experimental Setup
2.1 Introduction: NSCL experiment 02012
The experiment to measure the decay properties of nuclei near the endpoint of the rp-process
(NSCL experiment 02012) was conducted at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The NSCL is the preeminent facility in the
United States offering rare isotope beams for study of short-lived unstable nuclei. Isotopes
are produced at the NSCL using the projectile fragmentation method: a primary beam
is accelerated and then collides with a target to produce a secondary beam of stable and
unstable nuclei. The fragments of the secondary beam are then selected in flight by the
NSCL’s A1900 fragment separator. In the case of β decay experiments, the selected nuclei
are stopped in a position-sensitive silicon detector where the timing of both the implantation and subsequent decay of the nuclei are observed. This experiment was one of seven
in a campaign of β decay experiments to use the recently commissioned A1900 device at
the NSCL throughout February–May of 2003. The set-up was very similar to a preceding
experiment to study the β-decay of 100 Sn, also using the NSCL’s β-decay end station (NSCL
experiment 01006).
2.2 Isotope production and delivery
The production, separation and identification of neutron deficient nuclei in the A≈100
mass region at the NSCL’s Coupled Cyclotron Facility (CCF) [57, 58] began with the
25
Figure 2.1: Schematic diagram of the Coupled Cyclotron Facility and the A1900 fragment
separator. Modified from [56].
injection of
124 Xe
nuclei from an Electron Cyclotron Resonance (ECR) source into the
K500 cyclotron where they were accelerated to about 12.25 MeV/nucleon and stripped to
a charge state of
124 Xe20+ .
48
The beam was then transported through a coupling line for
injection into the K1200 cyclotron, where the nuclei were further accelerated to approxi48+ state. The beam current varied
mately 140 MeV/nucleon and stripped fully to the 124
48 Xe
considerably over the course of the experiment with an intensity primarily in the range of
1-5 pnA.
The primary beam then impinged on a thin Be production target (188 mg/cm2 ), where
interactions produced a degraded primary beam and a secondary beam with a mix of stable
and neutron deficient nuclei with a large forward momenta. The resulting secondary beam
was then analyzed and separated using the NSCL A1900 fragment separator. The A1900
(shown in figure 2.1 with the superconducting coupled cyclotrons) is a high-resolution and
high-acceptance magnetic spectrometer [59, 60]. It is an upgrade to the NSCL’s previous
A1200 device and represents a third generation projectile separator (relative to early work
done at Lawrence Berkeley Lab). The A1900 includes 40 large diameter superconducting
multipole magnets and four 45◦ dipoles, each with a maximum rigidity of 6 Tm, a solid
angle of 8 msr, and a momentum acceptance of up to 5%. The A1900 has three intermediate
26
images. Maximum dispersion occurs at image 2 (I2). As the beam passes through this
region, there is a linear relationship (to first order) between momentum and horizontal
position for nuclei of the same charge.
The first two dipole magnets of the A1900 were set to Bρ1,2 = 3.1544 Tm to maximize
transmission of
104 Sb
and other fragments of similar rigidity to image 2 or I2. Magnetic
rigidity is the ratio of the fragment’s momentum to its charge, q. More often it is written as
the product of the magnetic field normal to the particle’s path, B, with radius of curvature
ρ:
Bρ =
γmv
p
=
.
q
q
(2.1)
An achromatic energy degrader and a plastic scintillator were located at image 2. Energy
loss of fragments passing through the Al wedge degrader (effectively 180 mg/cm2 thick),
is proportional to nuclear charge. As a result, nuclei of different atomic numbers emerged
with different momenta. The effective rigidity of each fragment was decreased as well. With
the exception of a few of the initial data runs, the remaining two dipoles in the second half
of the A1900 were set to Bρ3,4 = 2.5830 Tm to maximize the transmission of
104 Sb
from I2
to the focal plane of the A1900.
The thin plastic scintillator at I2 is attached to photomultiplier tubes on opposites
sides, providing the so-called I2N or North and I2S or South signals. Each of these signals
is processed by a constant-fraction-discriminator (CFD) and is further processed to record
the timing of nuclei transmitted.
The horizontal position of ions passing through the scintillator was determined by the
timing difference between the I2S signal and a delayed I2N signal, which provided the start
and stop signal for a time-to-amplitude-converter (TAC). Each of these signals also provided
the stop signal to a time-to-digital converter (TDC) which measured timing relative to the
master gate signal (see figure 2.9 and later discussion for details). The horizontal position
of nuclei passing through the I2 scintillator was used to determine the rigidity of individual
fragments.
Nuclei were transferred from the focal plane of the A1900 through an additional beam
27
Figure 2.2: Layout of experimental vaults at the NSCL. The bright green arrow shows the
path of the beam from the primary target to the endstation detectors in the N3 vault.
line to the NSCL N3 vault. The location of the experimental vault is shown in figure 2.2.
The TOF of nuclei transmitted to the experimental vault from image 2 is measured between
the I2N signal and a signal from the N3 scintillator (positioned just upstream from the
experimental endstation and 38.5 m downstream from image 2). The N3 scintillator provides
a start signal to a TAC which then receives a delayed stop signal from I2N.
The calibration of the TOF and position of nuclei at image 2 had to be adjusted for
various running conditions within the analysis and is further discussed in section 3.1.2. A
broader overview of the signal processing system is included in section 2.5.
In addition to the scintillator and energy degrader, the image 2 of the A1900 also
includes a system of slits that were used to control the selection of particles transmitted to
the endstation. A set of slits upstream from the energy degrader were set to a momentum
acceptance (∆p/p) of 2% throughout the experiment. During the first day and a half of
the experiment a second set of slits downstream from the degrader at I2 further limited the
acceptance to 0.5%. The yield of
104 Sb,
however, was only a few per hour. In an effort to
increase this yield, the downstream slits at I2 were removed and a set of slits at image 3
were adjusted to control the beam current. However, relatively low yield rates continued
28
Detector
I2 Scintillator
N3 Scintillator
Pin 1
Pin 2
Pin 2a
DSSD
SSSD 1
SSSD 2
SSSD 3
SSSD 4
SSSD 5
SSSD 6
Pin 3
Pin 4
Thickness
130 µm
5 mm
470 µm
309 µm
303 µm
979 µm
990 µm
977 µm
981 µm
975 µm
989 µm
988 µm
993 µm
998 µm
Position
image 2 of A1900
beamline, N3 vault
beamline, N3 vault
calorimeter stack
calorimeter stack
calorimeter stack
calorimeter stack
calorimeter stack
calorimeter stack
calorimeter stack
calorimeter stack
calorimeter stack
calorimeter stack
calorimeter stack
Number
Bias
-1900 V
+120 V
1442-9
1442-10
2034-3
2194-1
2194-12
2186-5
2186-10
2194-14
2194-4
2103-14
2103-12
-140
-230
-230
-200
-180
-210
-230
-170
-170
V
V
V
V
V
V
V
V
V
Table 2.1: Properties of detectors within the beamline. Ordered by position along the path
of the beam.
throughout experiment 02012.
2.3 Experimental endstation
The NSCL β-decay calorimeter has been developed to study the decay properties of rare
isotopes [62, 63, 64]. The β-decay calorimeter includes the Double-sided Silicon Strip Detector (DSSD) and the stack of five silicon PIN detectors and six Single-sided Silicon Strip
Detectors (SSSD) that surround it. The primary detector, the DSSD is 979 µm thick with
a 4 cm wide square surface that contains an array of 40 horizontally oriented front strips
followed by 40 vertically oriented back strips (1600 pixels) giving high position sensitivity
for nuclei upon implantation and decay. The correlation of an implanted nucleus and its
subsequent decay at the same position is evaluated in the analysis of the experiment.
Upstream of the DSSD the beam first encounters a series of three silicon PIN detectors
labeled PIN1, PIN2, and PIN2a in figure 2.3. These PIN detectors each have a thickness of
470 µm, 309 µm, and 303 µm, respectively. The first two of these were used as energy loss
detectors to determine the nuclear charge state of the incoming fragments.
29
Figure 2.3: Diagram of the β-decay endstation. Detectors are not drawn to scale. Modified
from [61].
A series of six Single-sided Silicon Strip Detectors (SSSD) with alternating horizontal/vertical strip orientation and two PIN detectors (PIN3 and PIN4) were placed downstream of the DSSD to further characterize events. Events that register signals downstream
from the DSSD may be disregarded in the analysis as “punch-through” events. Implanted
nuclei should coincide with signals in PIN1, PIN2, and the DSSD while decays should register only in the DSSD. The properties of each of the beamline detectors are outlined on
table 2.1. Details of how events are defined by the analysis are described in section 3.2.
2.3.1 Endstation electronics
The DSSD electronics system (shown in figure 2.4) must be capable of detecting implantation and β decay events occurring over different energy ranges. Implanted fragments may
deposit energy on the order of a few GeV, while β particles are likely to deposit a couple
hundred keV. These two different needs are met by using Multi Channel System (MCS)
preamplifiers having both low-gain (0.1 V/pC) and high-gain (2 V/pC) analog outputs.
Signals from the low-gain outputs are sent directly to analog-to-digital converters (ADCs).
Signals from the high-gain outputs are processed by Pico Systems shaper/discriminator
modules. The slow signal from the discriminator is sent to an additional ADC, while the
fast signal is sent to a scaler and into the master gate logic system. All signals from a
30
Multi Channel
System
preamp
DSSD
(in 16
strip
blocks)
high−gain
signal
low−gain signal
shaper /
discriminator
analog−to−digital
converter
slow
analog−to−digital
converter
fast
80 strips total
(40 front/back)
scaler
to OR of 40 strips (front/back)
DSSD front signal
AND
DSSD back signal
master
gate
bit register
AND
master
gate live
scaler
analog−to−digital conv.
VME gates
computer NOT busy
time−to−digital conv.
start signals
Figure 2.4: Electronics setup for the DSSD during experiment 02012. The setup for a block
of channels is shown (top) along with the trigger conditions (bottom).
31
preamp amplifier
PIN
1
fast
analog−to−digital
converter
slow
const. frac.
disc.
100ns
delay
scaler
bit register
NIM
ECL
stop
time−to−digital
converter
master gate live
start
AND
PIN
2, 2a,
3,4
preamp amplifier
fast
A1900 trigger
analog−to−digital
converter
slow
const. frac.
disc.
200ns
delay
scaler
bit register
NIM
ECL
stop
time−to−digital
converter
master gate live
start
Figure 2.5: Schematics for the PIN detector electronics setup during experiment 02012, for
PIN1 (top) and the setup used for each of the other PIN detectors (bottom).
32
given side of the detector are processed through a common OR logic gate. The front and
back DSSD signals are processed through an AND gate which triggers the master gate,
the primary trigger for all production data runs. If the master gate coincides with a NOT
busy signal from the data-acquisition system, the master gate live signal is triggered and
the data are read. Since 16 channel electronic modules are used to process a detector with
40 channels on each side, the channels on each side are bundled together in groups, 1-16,
17-32, and 33-40.
The SSSD electronics setup is similar to the one used for the DSSD. The 16 channels of
each detector are amplified by a Multi Channel System. In this case, the low-gain signal is
not used. A general schematic of the overall signal processing system, including the SSSDs
can be seen in figure 2.9.
The schematics configuration of the PIN detectors is shown in 2.5. The signal from
each PIN detector was sent to a preamplifier (Tennelec TC 178) and then to an amplifier
that provided fast and slow signals (Tennelec TC 241S). The slow signals were sent to a
VME ADC (CAEN 785) to provide an energy readout. The fast signal was processed by a
constant fraction detector (CFD, a Tennelec TC 455) and then was sent to a bit register and
a scaler. The fast signal also provided the stop to a time-to-digital converter (TDC, a CAEN
V775), giving a time measurement relative to the master gate live. As an alternative option
to the primary trigger from the DSSD, an A1900 trigger to the master gate was available
and was triggered by signals present in both PIN1 and the I2 scintillator. PIN2, PIN2a,
PIN3 and PIN4 each shared identical configurations as shown in figure 2.5.
2.3.2 Energy calibration of silicon detectors
Experiment 02012 ran back-to-back with another experiment with nearly the same setup.
Many of the same calibrations were employed and adjustments to the hardware were made
on an as-needed basis. Additional calibration spectra were collected mid-way through the
experiment during a shutdown of the coupled cyclotrons, and again immediately after the
experiment for use in the off-line analysis.
A
90 Sr
source was used to establish low-energy threshold levels for hardware triggering.
33
Figure 2.6: Representative calibration spectra of the lower range energy for Silicon detectors.
Both spectra are for the uncalibrated high-gain energy on front strip number 18 of the DSSD.
Left shows a background run without any radioactive sources. Right shows the same energy
range on the same detector with a 90 Sr β source present. The features used to determine the
offset and threshold energies are indicated. Units are counts on a logarithmic scale versus
arbitrary bin numbers.
90 Sr
produces a β − spectrum with a mean energy of 195.8(8) keV and an end-point energy
of 546.0(14) keV [65]. Spectra with and without the
90 Sr
source present were collected to
establish software thresholds in the offline analysis. Individual strips of the DSSD and SSSD
needed to be set independently. Figure 2.6 shows a representative energy spectrum from a
single high-gain strip of the DSSD and indicates the low-energy threshold. The high-gain
channels of the DSSD and SSSDs used the background peak to establish an offset (also
shown in figure 2.6).
The strips of the DSSD and the SSSDs were gain-matched using the offset and the 5.423
MeV α-decay energy from a
228 Th
through and after the experiment.
source.
228 Th
228 Th
source data were collected both mid-way
and its decay daughters release eight or more α
particles in the 5–7 MeV range. A representative spectrum is shown in figure 2.7 with the
three most prominent decays indicated.
An absolute energy calibration was not required to measure decay half-lives, however, it
is assumed that the gain-matched values offer a linear relationship to energy loss of fragments
in each detector. Some recent studies have developed an energy calibration by comparing
the energy loss of known fragments to the simulated energy loss of the same fragments
34
Figure 2.7: Representative spectrum for gain matching of Silicon detectors. Spectrum
resulting from a chain of α decays from a 228 Th source shown for the uncalibrated high-gain
energy on front strip number 18 of the DSSD. Left shows the full energy range recorded
in the data. Right shows α decay energies that have been identified from 228 Th and its
daughters. Units are counts versus arbitrary bins. (Decay energies from [65]).
[66]. During the present study, a calibration to the
228 Th
spectrum was approximated
by applying a fit function summing eight Gaussian peaks. This approach found the gainmatched spectra to have an energy scale of about 1.7 keV per bin when viewed as 12-bit
spectra in SpecTcl and determined the variance to be σ ≈ 50 keV. This is in agreement
with a previous study of the DSSD, which suggested the energy resolution to be “better
than 80 keV” and estimated the intrinsic β detection efficiency to be 50+
− 10% [64].
2.4 γ-ray detection with SeGA detectors
2.4.1 Segmented germanium array setup
The β calorimeter assembly was surrounded by a set of 12 high-purity Germanium detectors
from the NSCL Segmented Germanium Array (SeGA) [67]. The crystals of these detectors
were placed parallel to the beam line and adjacent to the plane of the DSSD; six were directly
upstream and six directly downstream, this is known as the betaSeGA-12 configuration [68]
and is shown in figure 2.8. The SeGA detectors were used to observe γ rays of isomers
shortly after implantation. Each of the 12 detectors includes a cylindrically-symmetric ntype coaxial germanium crystal with a diameter of 70 mm and a length of 80 mm. Each
35
Figure 2.8: The Segmented Germanium Array (SeGA): Model showing the position of the
12 HPGe crystals from SeGA (shown in blue) relative to the position of the DSSD (shown
in green).
crystal is divided into 32 segments (split radially into quarters and laterally in eight equal
parts). The high segmentation of these detectors may be used for the Doppler correction to
the observed energy of γ rays [69, 70]. In β-decay studies, such as the present experiment,
gammas are observed from stopped fragments and no correction is needed. Signals are
processed from the detector’s central contact which provides a total energy signal of each
SeGA detector. The typical energy resolution is estimated to be 3.5 keV for a 1.3 MeV γ
ray. The estimated photopeak efficiency is given in table 2.2.
2.4.2 SeGA electronics
A schematic representing the electronics for each of the 12 SeGA detectors in the context
of the larger data acquisition system is included in figure 2.9. The central contact of
each SeGA detector is operated through the use of a field effect transistor (FET) which is
then attached to a charge-sensitive preamplifier (not shown in figure) The signal from the
36
γ-ray energy [keV]
100
250
500
1000
2000
3000
Efficiency
14.4%
12.6%
8.0%
5.3%
3.5%
2.6%
Table 2.2: The photopeak efficiencies for the SeGA configuration used in experiment 02012
(from [68]).
preamplifier is further processed into two separate lines for energy and timing. The energy
signal is connected to a spectroscopic amplifier and is processed through an analog-to-digital
converter (ADC; Ortec AD413). The timing signal is connected to a timing filter amplifier
(TFA; Ortec 863) and is further processed through a constant fraction discriminator (CFD;
a Tennelec TC 455) before it is split. One signal follows a 100 ns delay and is sent to both
a bit register and a scaler (LeCroy 2551). The second line provides the stop signal to a
time-to-digital converter (TDC). Since the DSSD served as trigger during the experiment,
observed γ rays could be correlated with either implantation or decay events. Appendix B
shows the energy spectrum of the SeGA detector coincident with
100 Cd
implantations.
2.4.3 Energy calibration of SeGA
The calibration of the SeGA detectors was performed with data from runs 2149 and 2151
using a Standard Reference Material (SRM) 4275-C69 source and a
56 Co
source. Both
of these source runs were performed at the end of experiment 02012. During calibration
runs the SeGA detectors themselves were used as a trigger to the data acquisition system.
A quadratic fit was applied to the ADC output from the SeGA detectors. An additional
0.5 keV was added to the intercepts determined by the fits to account for truncation within
the analysis software.
37
Figure 2.9: Schematic of the signal processing system during experiment 02012. Numbers
within circles correspond to delays in nanoseconds.
38
2.5 Data acquisition system and analysis framework
A schematics diagram of the electronic signal processing setup for experiment 02012 is shown
in figure 2.9. Some details relevant to specific detectors have been discussed in previous
sections. For all data runs an event occurring in the DSSD served as the trigger for the
“master gate.“ An AND gate of master gate with a “not busy” signal from the computer
created the “master gate live” signal which triggered the data readout. The data were
stored in up to 32-bit data words and packed into binary .EVT (or event) files using the
NSCL DAQ system software. Both the online monitoring of the experiment and the offline
analysis were facilitated by the NSCL SpecTcl analysis software [71].
In addition to the readout of all ADC and TDC data, each DSSD-triggered event is
given an associated timestamp. Event timing for each experimental run is maintained by a
pair of coupled clock modules. A fast clock module driven by an internal pulser operated
at 215 Hz, thus giving a precision of 30.5 µs per tick of the clock. As the fast clock module
reached the upper limit of its range every 2 seconds, an overflow signal was sent to a slow
clock module used to maintain a count of the resets. The output of each module was stored
as a 16-bit word, and data from both were combined into a single 32-bit parameter during
analysis using the following relation:
clock.current = clock.f ast + 65536 × clock.slow,
(2.2)
where clock.current provided the timestamp for all implant and decay events. It is the
difference in the precision timing of events that is ultimately used to determine β decay
half-lives in the analysis that follows in chapter 3.
The assignment of detectors to channels in the data structure is included in appendix A.
The NSCL SpecTcl analysis software uses a C++ application framework controlled by an
extended Tcl/Tk interpreter. The framework includes a series of user defined event processors that are applied sequentially to each data event. Processors included in experiment
02012 unpack the binary data, apply calibrations, check software thresholds, and to correlate implant and decay events. For parts of the analysis additional extensions were added
39
to filter data subsets and to draw a representation of detector output for selected events.
40
Chapter 3
Experiment analysis
At least 22 different radionuclides were identified in the β-decay endstation during NSCL
experiment 02012. Some species were produced with rates several orders of magnitude larger
than the anticipated rates of the nuclei of interest. The chapter that follows describes how
these data were analyzed to separate and identify specific nuclei, how the background data
were characterized, and how β-decay half-lives were measured.
3.1 Particle identification
The separation of radioisotopes in the analysis was achieved by the Bρ–∆E–Bρ method
described in section 2.2. Upon detection of events in the β-decay endstation, this allowed
isotopes to be distinguished by their energy-loss, measured in either PIN1 or PIN2, and
time-of-flight. Measurements of these parameters were further refined and used to calculate
the atomic number, Z, and the mass/charge ratio, A/q, for each radionuclide (it is assumed
for this analysis that nuclei are fully stripped, hence Z = q). The process used to create
the particle identification plot (PID) of Z versus A/q is described in section 3.1.2. The
development of the PID (e.g. figure 3.2) is completed in parallel to application of cuts on
the PID to verify the identity of nuclei observed. In the following description, the procedure
to identify individual nuclei is presented first.
41
Isomer
93 Tc
94 Tc
95 Rh
96 Rh
97 Rh
99 Ag
100 Ag
100 Cd
103 In
t1/2
43.5 m
52.0 m
1.96 m
1.51 m
46.2 m
10.5 s
2.24 m
60 ns
34 s
Table 3.1: Nuclei with known isomers in the mass region of experiment 02012 and their
half-lives from [65].
3.1.1 Isomer identification with SeGA
As described in section 2.4, the SeGA detector allowed for the observation of γ rays. Some
γ rays may have resulted from short-lived isomers of nuclei implanted in excited states,
others may have been delayed by β decay and resulted from transitions within the decay
daughter nucleus. Other detected γ energies, however, were simply background. These
background energies may have been associated with implanted nuclei with moderately long
half-lives (several minutes or more) that become saturated in the DSSD, or may exist due
to environmental factors within the detector, or may have been created through electronpositron pair annihilation.
The spectrum of γ energies observed in the SeGA detector from the full data set is
about two orders of magnitude more intense than the subset of γ rays observed to occur
in coincidence with implanted nuclei or β decay. From this spectrum a catalog was formed
listing energies not associated with specific events.
In order to unambiguously identify the nuclei in the PID, characteristic features of one
or more nuclei must be observed. One approach is to observe γ rays associated with shortlived isomers that correlate to a nucleus in the PID. In order to observe these γ energies, the
parameters that define the PID were created for the subset of data that represent implanted
nuclei and gates were drawn on the parameters of the PID to isolate data to specific nuclei
42
Figure 3.1: 100 Cd level scheme and γ transition energies below the J π = 8+ isomer (generated from [65]).
implanted.
Table 3.1 lists the half-lives of known isomers of nuclei thought to be included in the
PID. Most of the isomers have half-lives that are too long to produce γ rays in coincidence
with implantation. Ideally we would seek isomers having a half-life on the order of 1 µs.
The 60 ns half-life of the
100 Cd
isomer is an order of magnitude less than the time-of-flight
of fragments through the A1900. Over 99% of nuclei in this state are expected to have
decayed in-flight, prior to implantation in the DSSD. None-the-less, the characteristic γ
energies associated with this decay were observed.
Measured values of the
100 Cd
isomer half-life range from 40-73 ns [72, 73]. It is the
more recent measurement of 60 ± 3 ns by [74] that appears to provide the accepted value
[65]. In experiment 02012,
100 Cd
was the fifth most highly implanted nucleus (with 34,776
events occurring within the gate). The high yield of
100 Cd
may have made it possible to
observe decays from this short-lived state. The energy spectrum of the SeGA detector cut
on
100 Cd
is displayed in appendix B, but is described briefly here. The 60 ns
43
100 Cd
isomer
Jiπ →
8+ →
4+
2 →
6+
1 →
6+
2 →
6+
2 →
8+ →
6+
2 →
4+
1 →
2+ →
4+
2 →
Jfπ
6+
2
4+
1
4+
2
6+
1
4+
2
6+
1
4+
1
2+
0+
2+
Iγ
23(4)
4(2)
947(31)
103(8)
24(8)
874(25)
38(9)
981(32)
1000(33)
19(11)
Eγ[NuDat] [keV]
90.7(1)
247.3(1)
296.4(2)
362.5(1)
411.5(1)
452.6(1)
658.4(2)
794.9(1)
1004.1(1)
1042.1(2)
observed peak?
background peak
none
background peak
none
none
yes
yes
yes
yes
none
Eγ[SeGA] [keV]
91(1)
—
298(1)
—
—
453(1)
658(1)
796(1)
1005(1)
—
Table 3.2: Available transitions of the 100 Cd isomer, relative intensities from [74], and
energies from [65] with energy peaks observed in SeGA. “Background peak” indicates that
a peak was present, but one that was also observed in background spectra.
is known to occur in the J π = 8+ , E = 2548 keV state. A level scheme is presented in
figure 3.1. Table 3.2 shows the energy, Eγ and relative intensity, Iγ of allowed transitions
from the J π = 8+ isomeric state towards the ground state. Four of the transitions showed
distinct peaks above background in the SeGA total spectrum. Each of the observed energies
were within one keV of the known transition. The only gamma energy known to occur at
high relative intensity (Iγ > 0.1Iγ,M AX ) that did not present a definitive peak was at
Eγ = 296.1 keV. These γ rays, however, may have contributed to a peak at 298 keV that
was also present in background spectra. Many of the remaining unobserved γ energies were
produced at too low an intensity to be observed.
The known values of Z = 48 and A/q ≈ 2.08 for
100 Cd
served as a reference point for
nearby nuclei in the PID.
3.1.2 Separation and identification of nuclei
The particle identification plot (PID) in this analysis is defined by the parameters of A/q
and Z. Once the identity of one of the nuclei in Figure 3.2 is confirmed, the identity of
others can be deduced. The vertical groupings of nuclei all share similar values of A/q.
100 Cd
is part of a series including 98 Ag,
100 Cd, 102 In,
44
and 104 Sn, having A/q = 2.085, 2.083,
2.081, and 2.080 respectively. An alternative, and perhaps more precise way to differentiate
this group from others on the PID is to say that they all satisfy the relation A − 2q = 4.
Each step vertically upward within the group represents a step of Z + 1 and A + 2. Nuclei
of the same element (same Z) neighbor one another horizontally. One step to the left of
100 Cd
is 99 Cd.
99 Cd
is part of a vertical grouping that also includes 101 In,
103 Sn,
and 105 Sb,
all having A/q ≈ 2.06, and satisfying the relation A − 2q = 3. In this same manner, the
identity of additional nuclei present can be deduced from the identity of neighboring nuclei
and neighboring groups of nuclei.
These parameters of A/q and Z are calculated from other parameters, such as rigidity
(Bρ), time-of-flight (TOF) and energy loss in one of the PIN detectors (dE1 or dE2 ). At
virtually every step of the calculations, a calibration is applied to these parameters. Some
of the variables used for these calibrations required repeated adjustment when applied to
data collected over the course of the experiment’s nine day run. This is the result of various
changes to the conditions of the experiment. These included adjustment of slit settings at
images 2 and 3, changes in the beam due to issues with the ion source, and changes in the
rigidity settings of the dipole magnets between I2 and the experiment, Bρ3,4 . In all, 13
variations of the calibration were applied to the off-line analysis, each to one or more data
runs. Each group of runs with similar conditions had a unique set of defined calibration
variables.
Image 2 position and corrections to the rigidity
As described in section 2.2, a time-to-amplitude-converter (TAC) measures the timing difference between photomultipiers on the north and south sides of the image 2 (I2) scintillator
detector. The north-south direction lies perpendicular to the beam path and I2 represents
the plane of maximum dispersion of the A1900. The TAC output is processed through an
analog-to-digital converter (ADC) and the timing difference is scaled to position in mm
based on the distribution of the data into channels and the known slit settings at image 2
(I2). Figure 3.3 shows the uncallibrated position spectrum for a group of runs. The raw
data for position were then calibrated, for each run group, using a linear or quadratic fit as
45
Figure 3.2: Particle identification plot (PID) of Z versus A/q, compiled from the full data
run of the experiment; including implantations and pass-through events. Color indicates
the number of counts on a logarithmic scale.
Figure 3.3: An example spectrum of the I2 position for a series of runs. Position of the
centroid is used to determine the offset (or zero position). The width of the spectrum in
channels is used to determine the scaling factor from bins to position in mm.
46
needed, the location of the centroid of the primary peak and other features served as reference points. Each peak representing a group of nuclei with similar rigidity. In general, for
data runs where the downstream I2 mask was employed to limit the momentum acceptance
of the spectrometer, the TAC data spanned fewer channels, and a linear fit to position was
sufficient. The I2 mask was removed for the majority of production runs, allowing for the
full acceptance of the spectrometer. In this case the TAC data spanned a much greater
range of channels and a quadratic fit was often beneficial.
The position separation of nuclei at I2 is the result of variations in the intrinsic rigidity of
fragments about the setting of the first two dipoles (Bρ1,2 ). The presence of an achromatic
energy degrader at I2 reduces the momentum of all fragments. The wedge geometry and
differences in nuclear charge, Z, result in greater variation in the momentum of fragements
as they emerge from I2. Between I2 and the focal plane of the A1900, the intrinsic rigidity
of transmitted fragments varies about the settings of the third and fourth dipoles (Bρ3,4 ).
A small correction to the set value of Bρ (on the order of 1%) is assigned based on the
position of the centroid, and a scaling factor is applied to further correct Bρ of individual
fragments in proportion to their I2 positions.
Time of flight and velocity
As noted in section 2.2, the time-of-flight (TOF) is measured by a TAC receiving a start
signal from the N3 scintillator just upstream of the experimental endstation, and a delayed
stop signal from the I2 scintillator at the dispersive image. As with the image 2 position, the
TAC signal is processed by an ADC. Since these signals are received in reverse chronological
order relative to when they were created, the fit function has a negative slope. Projectile
velocity, β is calculated from the mean distance traveled between scintillators (38.52 m)
and the TOF. A reduction factor to the velocity is applied to calculations using the energy
loss, as measured in PIN2 to reflect the momentum decrease due to passage through PIN1.
47
Symbol
Bρ
Z
A
q
dE
dx
Zabs
Aabs
I
e
K
NA
re
me c2
T
M
β
γ
δ(βγ)
Definition
rigidity
Atomic number of projectile
Atomic mass of projectile
Charge of incident projectile
Energy loss in absorber
Distance in absorber
Atomic number of absorber
Atomic mass of absorber
Mean excitation energy
elementary charge
4πNA re2 me c2
Avogadro’s number
Classical electron radius
Electron rest energy
Kinetic energy
Incident particle mass
velocity
Lorentz factor
Density effect correction
Units or Value
T·m (corrected magnet settings)
equivalent to q for fully stripped nuclei
g·mol− 1
units of e
MeV (measured in Si PIN detector)
m (measured thickness from table 2.1)
14.0 for a Si target
28.0855 g·mol− 1 for a Si
173.0 eV for Si
1.60217646 ×10−19 C
0.307075 MeV·cm2 /g
6.0221415 ×1023 mol− 1
2.817940325 fm
0.510998918 MeV
MeV (see equation 3.4)
MeV/c2
c
0 (low-energy regime)
Table 3.3: Symbols used in the equations of this section, with data from [75, 76, 77].
Mass-charge ratio, A/q
The atomic mass number-to-charge can be related to the previously discussed equation for
rigidity (2.1):
Bρ =
γmv
γAβ c
≈
.
q
q NA e
(3.1)
All of the symbols are as defined in table 3.3. Using values from the table and solving
for A/q shows a direct proportionality to corrected rigidity and an inverse relationship to
velocity:
Bρ
A
=
q
3.10713γβ
(3.2)
Calculation of atomic number (the Bethe equation)
The energy loss, velocity, atomic number and mass of a charged projectile passing through
an absorber are related together within an accuracy of a few percent by the “Bethe” equation
for stopping power [75]:
−
dE
dx
1 1 2me c2 β 2 γ 2 Tmax
δ(βγ)
2
= Kq
ln
−β −
,
Aabs β 2 2
I2
2
2 Zabs
48
(3.3)
where the symbols are described in table 3.3. Simplifications are applied to the above
equation. First, in the case of a Si target, the density correction due to polarization δ(βγ)
is effectively zero for β . 0.846 [76]. Second, we use the “low energy” approximation for
the maximum energy transfer per single collision (for 2γme /M 1):
Tmax =
2me c2 β 2 γ 2
≈ 2me c2 β 2 γ 2
1 + 2γme /M + (me /M )2
(3.4)
Atomic number can be found for fully stripped nuclei (Z = q) by combining these approximations into equation 3.3 and using values from table 3.3:
v u
u
Aabs
1
dE
Z = t−
dx KZabs 12 ln 2me c2 β 2 γ 2 − 1
I
β
(3.5)
In practice, several of the constants of proportionality (K, Zabs , Aabs , and dx) are absorbed
into a scaling factor that matches known values of Z. Since the calculation can be performed
independently using the energy lost in either PIN1 or PIN2 (with some adjustment to the
velocity for PIN2), two calculations are performed for each event (Z1 and Z2 ). A comparison
of the two calculated values is shown in figure 3.4. Cuts applied to this figure were employed
as a means to improve resolution of the PID.
3.2 Event correlation in the DSSD
The calculation of A/q and Z allow for event by event identification. As events are read into
the analysis software, they are either designated as “punch -through” events, implantations,
or decays depending on the event’s profile in the β calorimeter. Any energy readout above
software threshold settings for a given detector is designated as a “hit” for that detector.
In the case of any SSSD, a single slit with energy above threshold registers as a hit for the
detector. Hits on the front and back of the DSSD are tracked separately as are the high and
low-gain readout for each side. Implantations represent fragments stopped in the DSSD,
the criteria used to identify an implantation in software are hits in both front and back
low-gain channels of the DSSD, and a hit on PIN1, upstream of the calorimeter, while not
having a hit downstream of the DSSD in SSSD1. The “punch-through” label is assigned to
49
Figure 3.4: Independent calculations of Z compared for nuclei implanted in the DSSD.
The vertical axis is Z2 (as calculated from PIN2 energy loss). The horizontal axis is Z1
(calculated from PIN1). The orange circular regions are cuts that were applied collectively
to improve separation of nuclei in the PID.
Figure 3.5: Strip multiplicity for implantation events in the DSSD for a series of data runs.
Gray bars represent the back strips, black bars represent the front.
50
Figure 3.6: Particle Identification plot similar to figure 3.2, but for implanted nuclei only.
The plot on the right shows the same data filtered through the cuts applied from figure 3.4.
The positions of 103 Sb and 104 Sb are indicated. The vertical axis indicates Z, and the
horizontal axis represents A/q (with an arbitrary scale).
any event that has a hit on PIN2A (just upstream of the DSSD), and a hit on any detector
downstream of the DSSD (SSSD1–6 or PIN3,4). A decay is defined as any event that has
a hit on the front and back of the high-gain channels of the DSSD, that does not have
hits on either of the upstream detectors PIN1, and PIN2, and is not already tagged as a
punch-through.
3.2.1 Implanted nuclei
The strip multiplicity of implantation events in the DSSD is shown in figure 3.5. About 90%
of events registered as a “hit” in just one or two channels on a given side. The front and
back channel with the largest energy signal from each side is used to designate the position
of the implanted nucleus. Once an event is designated as an implantation, its properties are
recorded in association with its position in the DSSD. These include a timestamp recording
when the implantation occurred, the energy loss in the first two PIN detectors, the time51
Figure 3.7: Z distribution of observed nuclei implanted, grouped according to the value of
A − 2q (regions outlined in figure 3.6). Five of the observed isotopes are implanted at rates
three or more orders of magnitude greater than the rates of Sb isotopes, resulting in a high
rate of background β activity.
52
of-flight, and calculated values of Z and A/q.
Figure 3.6 shows the PID (as calculated from PIN1 data) for implanted nuclei compiled
from various fragment settings over the duration of the experiment. The data are shown
both with and without filtering from cuts shown in figure 3.4. The additional filtering from
cuts on the Z2 versus Z1 plot had a minimal effect on the Sb spectra and was not used
in the final analysis. The regions outlined on the PID group together nuclei with similar
values of A/q, and as explained in section 3.1.2, into groups with identical values of A − 2q.
The Z distribution for each of these groups of nuclei are shown in figure 3.7. As shown, at
least five β + emitters,
97 Rh, 98 Pd, 99 Ag, 100 Cd,
and
101 Cd,
are implanted at a rate three
or more orders of magnitude greater than the implantation rates of
103 Sb
and
104 Sb.
These
result in a high rate of background β activity and complicate event correlation between
implantation and decay events.
Figure 3.8 shows the gates applied to the Z spectra. These are used to restrict study to
individual isotopes. Gates for all isotopes present are shown. Regions applied to the study
of Sb isotopes are shaded (in red).
3.2.2 Correlated decay events
Once an event is designated as a decay and is found to have maximum energy in valid front
and back channels of the DSSD, the decay is correlated to the most recent implantation at
the same position. In this study, only single pixel correlations were used. A number of β
decay studies using similar apparatus have found it to be beneficial to expand correlation to
include the nearest neighboring pixels. Due to the high rate of background events caused by
contaminants, expanding the correlation to additional pixels greatly increased the presence
of background decays correlated to the nuclei of interest.
3.3 Characterization of background
The high rate of undesirable nuclei within the beam presented a number of challenges.
Regions of the DSSD receiving the highest intensity of the beam have nuclei implanted at
53
Figure 3.8: Similar to figure 3.7, but with a different binning scheme and showing cut
regions. Shaded areas are regions designated for decay analysis of Sb isotopes.
an average rate of 1 every 10 to 20 seconds per pixel. The majority of these nuclei have
half-lives that range from 1–30 minutes. Decays from these species create a substantial
and persistent background of decay events unrelated to the nuclei of interest. Also, since
nuclei are correlated only to the most recent implant, correlation windows for data collection may be cut short when an additional implant interrupts. As these effects lead to a
time-dependent background for decay events following an implantation, the challenge is to
accurately characterize this background. One approach is the development of a function
that predicts the background spectra given the number of nuclei implanted. To develop
this model, β-decay time spectra for events correlated to stable and long-lived nuclei were
created. Since these events produced little or no decay activity in the detector themselves it
is assumed that whatever events were observed were representative of the background. All
decay time spectra in this analysis were produced using a compilation of the full data set,
grouping together events recorded under various run conditions at various positions within
54
the DSSD. The beam was defocused during the experiment to maximize exposure to a large
surface area of the DSSD. The profile of Sb events across the DSSD surface was similar to
that of other nuclei, but at a much lower intensity. Sb events were also well-distributed
across the runs of the experiment. The stable and long-lived isotopes used to characterize
the background events are sampling the same range of positions and experimental conditions
from which the Sb data were collected.
3.3.1 Fitting background spectra
Several different functions were used in an attempt to fit the background spectra observed
in the longer-lived nuclei. A two-parameter fit using a single decay function yielded results
that did not fit the spectra. A preliminary analysis presented in [78] used a three-parameter
fit that included a constant component and a single exponential decay curve to create a
background activity function of the form:
RBG (t) = RBG1 · e−λBG ·t + RBG0 ,
(3.6)
where the three parameters of the fit were λBG , the apparent decay rate, RBG1 , the initial
activity of the time dependent component, and RBG0 , the constant background activity.
Each of the free parameters have units of s−1 . Fitting using this method worked reasonably
well. Fits applied to various background spectra (“decay“ spectra cut on long-lived or stable
nuclei) yielded similar values of λBG ; RBG0 and RBG1 scaled well with the number of nuclei
implanted within the selected gate, NI . However, the curve fits did not reproduce some
of the background spectra particularly well. In some cases the reduced chi-squared value
(χ2 /number of degrees of freedom) of the fit was ∼ 10, suggesting a better model might be
found.
An additional analysis has used the following form for background activity:
RBG (t) = RBG1 · e−λBG1 ·t + RBG2 · e−λBG2 ·t ,
(3.7)
a four-parameter fit of two decay curves. λBG1 and λBG2 are the apparent decay rate
of each component, one occurring more slowly, the other more quickly. RBG1 and RBG2
55
Figure 3.9: A representative plot of the four parameter fit from equation 3.7 applied to
the background following the implantation of 95 Ru. In this example, the black line that
represents the fit applied only to the data shown is almost completely concealed by the pink
line–the parameterized background formula developed in section 3.3.2. Additional plots for
other nuclei appear in appendix C.
56
Gated
NI
nucleus (implants)
93 Tc
7085
94 Tc
7966
95 Ru
29774
96 Ru
6249
97 Rh
149186
98 Pd
629117
99 Pd
12293
99 Ag
531706
Weighted mean (93 Tc
t1/2
Results of a 4-parameter fit
(s)
χ2 /ndf RBG1 /NI
λBG1
9900
1.28
0.011(8)
0.018(17)
17580
1.02
0.026(3)
0.040(4)
141955
1.00
0.020(2)
0.035(3)
stable
1.28
0.023(3)
0.038(3)
1842
0.97
0.0188(8) 0.0321(14)
1062
1.01
0.0189(5)
0.0328(8)
1284
1.10
0.0234(24)
0.040(4)
124
1.06
0.0200(5)
0.0334(7)
and 99 Ag excld.)
0.019(3)
0.033(4)
to background
RBG2 /NI
λBG2
0.031(6) 0.12(37)
0.026(4) 0.29(10)
0.021(2)
0.20(3)
0.022(3)
0.23(6)
0.0235(7) 0.20(1)
0.0228(4) 0.194(7)
0.026(2)
0.25(5)
0.0238(4) 0.201(7)
0.023(2)
0.20(4)
Table 3.4: Results of a 4-parameter fit of the formula in equation 3.7 applied to the background observed when gates are applied to long-lived nuclei. Mean values are weighted by
number of implantations within a given gate. The adopted uncertainties are the unweighted
standard deviation.
represent the initial activity rates of each component of the function and are expected to
scale with NI . For each fit, the time distribution of β background events were placed into
0.64 s bins. The rate given by equation 3.7 was multiplied by the bin size in seconds in
order to correlate with the number of counts per bin provided by the histogram. All of
the background fits used a χ2 minimization within the CERN program ROOT, which uses
a C++ implementation of the Minuit code [79]. The results of eight fits are compiled in
table 3.4, in the case of RBG1 and RBG2 the proportionality of the fit value to the number
of implantations (NI ) is reported rather than the parameters themselves. A representative
plot of the fit applied to the
95 Ru
spectrum is shown in figure 3.9. The additional fitted
spectra are presented in appendix C.
3.3.2 Parameterization of background rate
Both the χ2 /ndf values presented in table 3.4 and the fitted plots themselves show a much
improved representation of the data. In order to parameterize the results of these fits to
predict background activity for other spectra, results from six of the spectra were used to
compute mean values of the fit parameters weighted by number of implantations. The mean
values are also presented in table 3.4. Due to the high statistics provided by spectra for
57
98 Pd
and
97 Rh,
the standard deviations of the weighted mean values are quite small and
are not representative of the uncertainty in the background parameters for low statistical
cases, therefore the standard deviations of unweighted values were adopted as uncertainties.
Figures 3.10 through 3.13 present a comparison of the results of each fitted parameter with
uncertainties in comparison to the weighted mean.
93 Tc
and
99 Ag
are included in the
table and on the plots for comparison, but were excluded from calculations of the mean and
standard deviation. The fit results for 93 Tc were of low quality and the resulting parameters
did not agree well with the rest of the data. Fit data for
of the data, but as
99 Ag
99 Ag
did agree well with the rest
has a half-life of 124 ± 3 s and may produce a small, but not
insignificant, amount of β activity of its own, it was excluded as well. The remaining nuclei
used all have half-lives in excess of 17 minutes.
Exponential rate constants, λBG1 and λBG2
The values of λBG1 and λBG2 have been established by weighted means of the data shown
in table 3.4 and on figures 3.10 and 3.11. The resulting weighted means of hλBG1 i =
0.0330 ± 0.0035 s−1 and hλBG2 i = 0.197 ± 0.040 s−1 correspond to half-lives of 21 s and
3.5 s, respectively, representing slow and quick-decay components of the background. These
timescales complicate the application of the parameterized background to the evaluation of
half-lives for most of the nuclei on the PID which have half-lives known to be within this
range or longer, such as
103 Sn
, with a half-life of t1/2 = 7.0 s.
Initial activity rates, RBG1 and RBG2
The initial background activity rates RBG1 and RBG2 are assumed to scale in direct proportion to number of gated nuclei implanted, NI , and therefore to parameterize the background, it is the proportionalities, that must be determined. These are presented in table 3.4 and on figures 3.12 and 3.13. Weighted means are determined to be hRBG1 /NI i =
0.0191 ± 0.0029 s−1 and hRBG2 /NI i = 0.0230 ± 0.0020 s−1 .
58
Figure 3.10: Fitted values of λBG1 compared to the weighted mean (solid red line). Red
dashed lines indicate the standard deviation about the weighted mean. Blue dashes indicate
unweighted standard deviation. 93 Tc and 99 Ag are shown, but not used in the calculation.
59
0.4
0.35
94
Tc
0.3
99
-1
λBG2 (s )
Pd
0.25
96
Ru
97
Rh
95
Ru
99
Ag
0.2
98
Pd
0.15
93
Tc
0.1
0.05
1000
10000
1e+05
NI (Implantations in gate)
Figure 3.11: Same as figure 3.10, but for fitted values of λBG2 .
60
1e+06
Figure 3.12: Fitted values of RBG1 in proportion to NI compared to the weighted mean
(solid red line). Red dashed lines indicate the standard deviation about the weighted mean.
Blue dashes indicate unweighted standard deviation. 93 Tc and 99 Ag are shown, but not
used in the calculation.
61
Figure 3.13: Same as figure 3.12, but for fitted values of RBG2 /NI .
62
Parent →
Nucleus
t1/2
103 Sn
7.0(2)
101 Sn
1.7(3)
105 Sb
1.22(11)
104 Sb
0.44+15
−11
103 Sb
> 1.5
s
s
s
s
µs
Daughter →
Nucleus
t1/2
103 In
65(7)
101 In
15.1(3)
105 Sn
34(1)
104 Sn
20.8(5)
103 Sn
7.0(2)
s
s
s
s
s
Granddaughter
Nucleus
t1/2
103 Cd
7.3(1) m
101 Cd
1.36(5) m
105 In
5.07(7) m
104 In
1.80(3) m
103 In
65(7) s
Table 3.5: β + decay daughters and granddaughters with evaluated ground state experimental half-lives and uncertianties from [65].
3.3.3 Generalized background rate
Using the mean values described above, The formula given by equation 3.7 may be written
to give a parameterized, time-dependent general background rate depending only on the
number of implantations and time:
RBG (t) = 0.0191NI · exp(−0.0330 · t) + 0.0230NI · exp(−0.197 · t),
(3.8)
where t is time in seconds and background activity is in s−1 . This generalized background
rate formula has been applied to all of the nuclei included on table 3.4 and others. The
function is included on the plots of the fitted spectra in appendix C. The function represents
the data of the spectra for
95 Ru, 97 Rh,
and
98 Pd
at the same level of precision as the indi-
vidual four-parameter fits to each of those spectra. It also gives excellent representation of
the spectra for some shorter-lived (t1/2 ≈ 2 minutes) nuclei, including 99 Ag, and 100 Ag. The
function slightly underestimates 100 Cd activity, but the difference is easily attributable to β
decay from
100 Cd
(t1/2 = 49.1 s). What can not easily be explained is an underestimation
of background activity in parts of the spectra for
96 Ru, 99 Pd,
and
94 Tc,
in some cases, by
∼ 10%. This may indicate some possible systematic errors with this approach. It is worth
noting that all of these nuclei lie in the lower right corner of the PID (figure 3.6); nuclei in
this region are of lower Z and higher A/Q. The nuclei of interest in this study lie in the
top left corner (higher Z and lower A/Q) and the same systematic errors may not apply.
In none of the spectra evaluated, does the function significantly overestimate background.
63
3.4 β decay measurements
Decay half-lives must be short in order for implanted nuclei to produce a measurable activity
above the background observed in the present experiment. For example, if one were to
suppose a β detection efficiency of ∼ 10%, a half-life of 9 s or less would be required to
observe an initial activity equal to the background predicted by equation 3.8.
For shorter-lived nuclei it should be possible to fit spectra with a formula of the form:
RF it (t) = RBG (t) + R1 (t) + R2 (t) + R3 (t),
(3.9)
Where the first term, RBG , represents the generalized background formula (equation 3.8),
and the remaining terms, R1 , R2 , and R3 , are the activity rates of the gated parent nucleus and its daughter and granddaughter nuclei as given by the Bateman equations (equations 1.18–1.20). If the half-lives of the daughter and granddaughter nuclei are known, then
it is possible to write RF it such that the only free parameters are the initial activity of the
parent nucleus, R0 , and the parent decay rate, λ1 . Table 3.5 shows the decay daughters
and granddaughters and the half-lives used in the present analysis.
Due to the low event rate within the spectra to which the curve fit is being applied, the
number of events per bin is low enough that Gaussian statistics may not apply. The chisquared minimization approach is not as effective in such cases. Therefore a log-likelihood
maximization option within Minuit was chosen. Also, for this fit, the data were placed in
narrower bins (∆t = 10 ms), improving the decay event time precision by a factor of 26 .
3.4.1 Fit of
103
Sn gated decays
When equation 3.9 is applied to the decay spectrum in the
103 Sn
gate, the decay rate is
found to be λ1 = 0.149 ± 0.018 s−1 , which corresponds to a half-life, t1/2 = 4.7 ± 0.6 s. The
initial activity is at t = 0, is R0 = 123 ± 15 decays/s. The fitted half-life is nearly four
standard deviations shorter than the previous experimental value of 7.0 ± 0.6 s, but this
is not surprising when the additional uncertainty from the background is considered. The
initial β activity from
103 Sn
only accounts for 23% of the initial activity in the spectrum
64
Figure 3.14: 103 Sn decay spectrum with fit function and components. The results have been
rescaled from 10 ms to 0.64 s bins.
with one component of the background decaying more quickly and the other more slowly
than the
103 Sn
decay rate. The results of this fit, rescaled into 0.64 s bins are shown in
figure 3.14.
Attempts to gate on the
105 Sb
region of the PID, give similar results to those found for
this spectrum. This is due to the poor Z resolution of the PID and the relatively high yield
of
103 Sn
as shown in figure 3.7. It is not possible to resolve
3.4.2 Fit of
104
105 Sb
from
103 Sn.
Sb gated decays
Figure 3.15 shows the fit applied to decays gated on
104 Sb.
The fit gives a decay rate
of λ1 = 1.30 ± 0.32 s−1 , which corresponds to a half-life of t1/2 = 0.54 ± 0.13 s, and an
initial activity of R0 = 50±13 decays/s. This measurement of the half-life provides sufficient
agreement with previous experiment (t1/2 = 0.44+0.15
−0.11 s [65]) to offer additional confirmation
65
Figure 3.15: 104 Sb decay spectrum with fit function and components. The results have been
rescaled from 10 ms to 0.64 s bins.
of the position of nuclei in the PID. It also provides some validation of the fitting procedure
using equation 3.9 and suggests that the generalized background formula does apply well
to nuclei in this region of the PID.
3.4.3 Fit of
103
Sb gated decays
The results of the fit applied to decay events in the
103 Sb
gate are shown in figure 3.16.
The fit value for the decay rate, λ1 = 0.47 ± 0.17 s−1 corresponds to a half-life of t1/2 =
1.48 ± 0.54 s, and an initial activity of R0 = 13.4 ± 5.0 decays/s.
The β half-life of
103 Sb
has not previously been measured, and its non-observation in
recent radioactive ion beam experiments has been noted [80]. This measurement is an
order of magnitude larger than calculated predictions of the 103 Sb β half-life. It is, however,
similar to the previously measured half-lifes of two other nuclei that may be present in the
66
Figure 3.16: 103 Sb decay spectrum with fit function and components. The results have been
rescaled from 10 ms to 0.64 s bins.
data.
105 Sb,
with t1/2 = 1.22±0.11 s [65] has the same value of Z as 103 Sb and if a significant
horizontal displacement in the PID could be explained, might produce a spectrum similar
to figure 3.16. Also,
101 Sn
has a similar value of A/q, and due to poor Z resolution may
be a likely contaminant of the
103 Sb
spectrum. A recent measurement of the
101 Sn
half-life
(t1/2 = 1.7 ± 0..3 s [65]) suggests that this too could produce the given spectrum. These
issues are further discussed in chapter 4.
3.4.4 Additional uncertainties
In addition to the uncertainties derived from the fit of data to the function in equation 3.9,
there are additional uncertainties relating to the half-lives of daughter and granddaughter
nuclei and to the strength of the parameters derived to create the generalized background
formula (equation 3.8). Additional iterations of the fit were performed on each data set with
67
each of these parameters varied one standard deviation above or below the accepted value.
The results of these fits were used to estimate the additional contribution to the uncertainty
in the measured half-lives. Variation of the granddaughter half-life had a negligible effect
on the fit. The deviation in half-life caused by altering the daughter half-life was also small.
104 Sb
Even coupled together, the deviation for
slight for
103 Sb
was negligible (σdaughter < 0.002 s), and
(σdaughter ≈ 0.034 s). Uncertainties derived by varying the strength of the
background function were slightly more significant, with σbackground ≈ 0.054 s for 104 Sb, and
σbackground ≈ 0.14 s for
103 Sb.
Assuming these contributions to the overall uncertainty to be independent, the standard
deviations were added in quadrature:
σ=
q
2
2
.
+ σbackground
σf2it + σdaughter
The resulting decay half-life for the
1.5 ± 0.6 s. For
104 Sb,
103 Sb
(3.10)
data is t1/2 = 1.48 ± 0.56 s or, more concisely,
the result is t1/2 = 0.54 ± 0.14 s
3.5 β-decay detection efficiency
The β detection efficiency is defined by the ratio of the number of parent decays detected
to the number of gated nuclei implanted, εβ = Nβ /NI . Nβ is calculated for each isotope
using the fitted values for initial parent activity, R0 , and the parent decay rate, λ1 :
εβ =
Nβ
R0
=
.
NI
NI λ1
(3.11)
Obtaining Nβ in this manner is equivalent to determining a time-integration of the parent
function in figures 3.14, 3.15, and 3.16. The calculated efficiencies and their uncertainties
are presented on table 3.6.
3.6 The search for proton-decay
Results of a search for proton-decay activity were inconclusive. In order to differentiate
proton decays from β decays, proton-candidate events were defined in software to be decays
68
Gated nucleus
103 Sn
104 Sb
103 Sb
β efficiency
0.08±0.01
0.14±0.05
0.29±0.16
Table 3.6: The β decay detection efficiency and standard deviation for fitted isotopes.
that occurred within five seconds of the nucleus being implanted, and occurred in a single
channel of both the front and back of the DSSD. Candidates were then plotted on a 2dimensional histogram with the dimensions of front and back energies measured in the
DSSD. If the front and back energies differed by greater than the 50 keV resolution of the
DSSD, the decays were disregarded. Ultimately no events gated on
of the criteria. The two events within the
105 Sb
103 Sb
or
104 Sb
met all
gate that met the criteria were not at
the same energy and did not have the energies in agreement with a previously suggested
proton separation energy. Non-observation of proton decay is in agreement with other recent
experiments of neutron deficient Sb. The low statistics of this study do not allow for any
greater upper limit on the proton branching ratios than has already been stated in [80].
69
Chapter 4
Discussion
At the time when experiment 02012 was proposed, two distinct scientific goals were suggested, both related to the rp-process. One goal was to measure the decay properties of
96 Cd.
At that time,
96 Cd
was the final waiting point along the rp-process path with no
experimentally determined β-decay half-life. The second goal was to measure lifetimes,
proton emission ratios, and proton decay energies for the
103-105 Sb
isotopes. It was rec-
ognized early during the experimental run that the first goal could not be achieved. The
experimental conditions needed to produce, separate, and measure the decay of
96 Cd
could
not be met at the NSCL. Thanks to many subsequent technological advances at the NSCL
and improved analytical techniques, the measurement of the 96 Cd half-life has recently been
measured [29]. The second goal, measurement of the properties of neutron-deficient Sb, has
been met with only partial success in the present study. However, the intervening years,
and additional studies of these nuclei that have been conducted since have shown that this
goal also was more complicated than initially might have been supposed.
Recent Penning trap studies have extended direct mass measurements of Sb isotopes
out to the proton drip line at
106 Sb
[33]. Direct mass measurements allow for the reli-
able determination of a range of reaction Q-values. Where direct mass measurements are
unavailable, studies of particle emission and measurements of separation energies provide
an alternative means of relating masses together. The
103-105 Sb
isotopes have long been
thought to be likely proton emitters and their proton separation energies and branching
ratios have remained a subject of lively discussion and study.
70
β + decay half-lives in this region are also of great interest as decays are important
reaction pathways in the neighborhood of the Sn–Sb–Te cycle. Direct measurements exist
for
104 Sb
and
105 Sb.
Although a previous observation of
103 Sb
has been reported [81], no
direct measurement of half-life has been made.
This chapter will first offer an assessment of the general methodology in the present
study. Then the attempt to apply this method to seek new data on 103 Sb will be considered,
ultimately resulting in the re-analysis of the
neighboring nuclei in the PID,
101 Sn.
103 Sb
gate data as the decay of one of the
This will be followed by brief discussions of proton
radioactivity in 103-105 Sb, recent improvements and technological progress for studies of this
type, and possible implications of these results and others for the Sn–Sb–Te cycle of the
rp-process.
4.1 Evaluation of β detection method and half-life measurement
The decision to run experiment 02012 with a wider momentum acceptance was an attempt
to permit a greater yield of
103-105 Sb
nuclei to the experiment. It also allowed a greater
number of contaminants to be implanted into the DSSD and may have contributed to a
poor resolution between nuclei in the PID. The high rate of implantation by contaminants
created a persistent background in the DSSD. When correlation procedures where employed
in software, the background presented itself as time-dependent.
The method of analysis used attempted to take advantage of the high-statistics of the
background to give a high precision description of the background. This allowed a fit of the
data by including a parameterized background formula in the fit function. The success of
this method depended upon the nuclei themselves.
4.1.1 Application to measurement of known half-lives of
104
Figure 4.1 shows a comparison between the half-life measurement of
104 Sb
study and two previously published measurements.
71
104 Sb
Sb and
103
Sn
in the current
has been measured as t1/2 =
0.8
104
104
0.7
Sb in present experiment
Sb in previous experiments
Half-life (s)
0.6
0.5
0.4
Schneider 1995
0.3
Faestermann 1996
Figure 4.1: Comparison between previous 104 Sb half-life measurements and the present
study. The fit results are in excellent agreement with previous studies and offer similar
precision. (Measurements from [82, 83, 84])
72
103
Sn half-life
10
Present experiment
Previous experiments
9
8
Half-life (s)
7
6
5
4
3
2
1
0
1980
1990
2000
Year published
2010
Figure 4.2: Comparison between previous 103 Sn half-life measurements and the present
study. The fit results from the spectrum in 3.14 fall short of recent measurements (from
[65]).
73
+0.15
0.52+0.18
−0.13 s by [82, 83], and t1/2 = 0.44−0.11 s by [84], the latter of which is given in [65].
The measurement from the present study, t1/2 = 0.54 ± 0.14 s agrees well with both prior
measurements and offers a similar level of precision.
Figure 4.2 shows a comparison between the half-life measurement of
103 Sn
in previous
experiments to the present result of t1/2 = 4.7+1.5
−2.1 s. The present result is within one standard deviation of some past measurements, but falls short of the most recent measurement
of 7.0 ± 0.3 s
The reason for the difference in effectiveness of this method can be seen in the fitted
spectra (figures 3.14 and 3.15). Parent decays account for 82% of the initial activity in the
104 Sb
spectrum, but only 23% of the initial activity in the 103 Sn spectrum. Longer half-lives
coincide with lower initial activity. It is likely that the accuracy of this technique will begin
to decrease noticeably for half-lives of a few seconds and longer.
4.1.2 β detection efficiency
The decision to only correlate decays to implants in the same pixel in the DSSD was
made to avoid an increase in background. However, this also contributed to a reduced
detection efficiency (see table 3.6) when compared to similar experiments where the DSSD
was employed more fully. The average detection efficiency in this experiment was 0.17±0.11.
In an other analysis, Stoker was able to achieve an efficiency of 0.34 ± 0.02 by using the
four nearest neighboring pixels. Hosmer obtained an efficiency of 0.40–0.43 by including
the block of eight pixels surrounding the decay pixel.
Some variation in efficiency for different isotopes is not unusual. The wide range of
efficiency seen in table 3.6, however, is not typical. Some of the lower efficiency seen
in the
103 Sn
may be the result of the background. The cause of the differences in the
spectra for the
103 Sb
and
104 Sb
gates is not obvious, but might be explained if there are
differences in the nature of the decays occurring in these two spectra (e.g. if one of the decay
processes included β delayed protons which would be detected with a greater efficiency than
positrons).
74
Figure 4.3: Z distribution (in arbitrary bins) of A − 2q = 1, 2, groupings from the PID.
The regions labeled 103 Sb and 104 Sb cover the same range of bins and both appear to have
separation from the regions designated as isotopes of Sn, In.
4.2 Application of fits to the
103
The region of the PID gated and labeled as
103 Sb
Z distribution of
104 Sb
Sb region of the PID
was given this designation based on the
in a parallel group. In both cases, a Gaussian-like distribution
appeared to have some separation from isotopes of Sn and In (bins in the range of 3400–
3550 in figure 4.3). The discussion that follows is to ultimately give an explanation as to
why the fit result of t1/2 = 1.5 ± 0.6 s is not likely to be attributed to
103 Sb,
and offer an
alternative explanation for the distribution.
4.2.1 Previous experimental measurement of neutron-deficient Sb halflives
Although both nuclei lie beyond the proton drip line, the β + half-lives of 104 Sb, as discussed
in section 4.1.1, and
105 Sb
have each been established by multiple experiments.
105 Sb
has
been measured at t1/2 = 1.12 ± 0.16 s by [81, 85] and at t1/2 = 1.30 ± 0.15 s by [82, 83].
The accepted value of 1.22 ± 0.11 s in [65] is a weighted average of these two measurements.
In the present study, attempts to gate on the
results to the measurement for
the dominance of
103 Sn
103 Sn.
105 Sb
region of the PID resulted in similar
This is likely an indication of poor Z resolution and
in this region of the PID. The history of
103 Sb
in β + decay studies
is somewhat more complicated than that of the other two isotopes beyond the proton drip
line. The first reports of the isolation and identification of
75
103 Sb
came in 1995 [81, 85]
+
β half-lives for Sb isotopes
Experimental and Calculated
1e+05
Present experiment
Previous experiment
Zhang 2007 (fit + even-odd effect)
Moller 1997 (QRPA)
Hirsh 1993 / Moller 1981 (pn-QRPA)
Hirsh 1993 / Groote 1976 (pn-QRPA)
Hirsh 1993 / Hilf 1976 (pn-QRPA)
Hirsh 1993 (pn-QRPA)
10000
Half-lives (s)
1000
100
10
?
1
0.1
0.01
0.001
96
98
100
102
104
106 108 110
A (mass number)
112
114
116
118
120
Figure 4.4: A comparison of calculated and experimentally measured β + decay half-lives
for 102-110 Sb on a logarithmic time scale. Calculated values typically offer an order of
magnitude estimate of experimental results. (Experimental values are from [65], calculated
values from [86, 87, 88])
when it was reported among the products following the fragmentation of a
produced at the LISE spectrometer in GANIL. The
103 Sb
112 Sn
beam
half-life was assigned a lower
bound t1/2 > 1.5 × 10−6 s, based on the time-of-flight of fragments in the experiment.
To date, no additional experimental observations have confirmed the existence of
103 Sb
in
fragmentation studies.
4.2.2 Calculation of neutron-deficient Sb half-lives
When experimentally known half-lives are not available as input to astrophysical models,
calculated results must be used. These results can sometimes be used to compare experimental results. There are relatively few calculations of decay half-life for nuclei in this mass
region. Where available, the preferred calculations for astrophysical models are those based
on the nuclear shell model [20]. These, however, are not often available in this mass region.
A number of studies have presented calculations for a select set of nuclei (e.g. the rp-process
76
waiting point nuclei [89]), but neglect the nuclei near the Sn–Sb–Te cycle. The most wideranging and frequently cited calculations for β + decay are, by far, the quasiparticle random
phase approximation model (QRPA) calculations by Möller et. al.[87]. A less often cited,
and slightly more dated set of calculations have been done by Hirsh et. al.[86] using a
proton-neutron quasiparticle random phase approximation model (pn-QRPA). Hirsh uses
experimentally derived Q-values as input where available, as he does for
104−108 Sb.
When
experimentally derived values are not available, he presents three different calculations for
three different mass models. A very different approach to predicting decay half-lives has
been offered by Zhang et. al. [90, 88], not based on a physical model, but rather grouping
together known half-lives with the same order of transition and fitting an exponential function based on atomic and neutron number (Z, N ). An additional term is added to account
for even-odd effects.
All available calculations of these models for the full range of neutron-deficient antimony isotopes are shown in figure 4.4 along with experimental values. As shown there,
many of the calculations offer an estimate of experimental values within an order of magnitude. Therefore, close agreement or disagreement with models, within that range, may not
be of great significance to an experimental measurement. For the previously unmeasured
103 Sb
half-life the results from curve-fitting in the present study appear to be an order of
magnitude greater than many of the predicted values. The models that do provide some
agreement for
103 Sb
are two calculations by Hirsh using the older mass models (published
in 1976). Most calculations offer estimates in the range of ∼0.1–0.3, about an order of
magnitude lower than the fit value for the
103 Sb
gate data at t1/2 = 1.5 ± 0.6 s.
4.2.3 Relative rates of proton decay
It is not the expected β + decay rate that has made observation of
103 Sb
in fragmentation
experiments difficult, it is the expected rate of decay due to proton emission. There have
been a number of calculations suggesting this rate to be something less than the time of
flight of particles through the A1900. Woods et. al. [91] suggest a half-life for 103 Sb ground
state proton emission of approximately 10−11 s. If this model is correct it is highly unlikely
77
+
β half-lives for
103-105
Sb
Experimental and Calculated
Present experiment
Previous experiment
Zhang 2007 (fit + even-odd effect)
Moller 1997 (QRPA)
Hirsh 1993 / Moller 1981 (pn-QRPA)
Hirsh 1993 / Groote 1976 (pn-QRPA)
Hirsh 1993 / Hilf 1976 (pn-QRPA)
Hirsh 1993 (pn-QRPA)
Half-life (s)
3
2
103
Sb gate fit
105
with Sb
daughters
103
Sb gate fit
103
with Sb
daughters
103
Initially the Sb data appear similar
105
to previous Sb experiments.
1
0
103
104
A (mass number)
105
Figure 4.5: Half-lives for 103-105 Sb. The fit results of the 103 Sb gate data initially appeared
to share some agreement with the 105 Sb half-life, however, the fit results shift significantly
when the decay chain daughters of 105 Sb are used in the fit.
that
103 Sb
could reach the endstation detector in the NSCL vault, much less be found to
have a β + half-life of 1.5 s. Therefore, alternative explanations of the decay spectrum within
the “103 Sb gate” must be considered. Experimental evidence of the decay of
103 Sb
on very
short timescales has been found in a recent study using SIMBA at GSI [92]. Although the
results do not yet appear to be officially published, conference presentations have indicated
an upper limit on the
103 Sb
half-life that is smaller than previously expected, based on
non-observation relative to calculated yield predictions.
78
4.2.4 Possible contaminates and the re-analysis of the
Initial inspection of the nuclei in the PID suggested that the
103
105 Sb
Sb gate
half-life offered some
agreement with the fit result of the data in the 103 Sb gate, however, when this fit is reapplied
using the daughter and granddaughter of the
105 Sb
decay chain, the result is shifted from
1.5 ± 0.6 s to 2.4 ± 0.8 s, as shown in figure 4.5 this is no longer in agreement with the
105 Sb
half-life. Also, even exotic explanations could not explain why 105 Sb might be in that
region of the PID.
A simple and logical explanation is that a neighboring nucleus in the PID,
101 Sn,
has a
spread of implantations that, due to poor Z resolution, extend into this region of the PID.
Very recent measurements of the 101 Sn half-life (shown in figure 4.6) are in good agreement
with the half-life from the fit. Agreement improves when the daughters of the
101 Sn
decay
chain are used. Therefore, a very possible, and perhaps likely, explanation of the data is
to suggest that the bulk of
103 Sb
produced by fragmentation decayed in flight, allowing for
the observation of a decay curve by
101 Sn
with a half-life of 1.8 ± 0.6 s.
4.3 Proton emission among neutron deficient Sb
The non-observation of decay by proton emission in the present study is in agreement
with recent experiment. The possibility of an observable proton decay and the proton
separation energy (Sp = −Qp , see also equation 1.8) of Sb isotopes beyond the proton
drip-line has been an interesting topic of study in recent years. Evidence of proton decay
at Sp = −483 ± 15 keV and a branching ratio of ∼ 1% was reported 17 years ago in
[96]. Although various techniques have been applied, no recent experiment has succeeded
in verifying this result (see, e.g. [80, 81, 97]). A recent study of the α decay of
105 Sb
109 I
to
has permitted the indirect determination of Sp = −356 ± 22 keV [98]. This suggests a
partial half-life on the order of t1/2,p = 4 × 106 s and a branching ratio of bp = 3 × 10−7 [98].
Much more rare and on a much longer timescale than suggested by the previous experiment.
No experimentally derived proton separation energy has yet to be determined for
or
104 Sb.
103 Sb
Available estimates are based on systematics. Cyburt et. al. [44] suggest that
79
4
103
Present experiment "
Previous
3.5
101
Sb" gate
Sn experiments
Half-life (s)
3
2.5
Fit using
Kavatsyuk 2007
101
Sn daughters
Fit using
2
Janas 1995
103
Sb daughters
Seweryniak 2007
1.5
1
Figure 4.6: Comparison of previous measurements of the 101 Sn half-life with results of fits
to the 103 Sb gate data. Agreement improves when the 101 Sn decay chain daughters are
used. (Including measurements by [93, 94, 95].)
80
the value of Sp = −510 keV for
104 Sb
given in [65] is barely consistent with its observed
half-life and adopt a limit of Sp > −590 keV. Meanwhile, Mazzocchi et. al. [98] propose
a limit of Sp > −378 keV and even raise the possibility that
104 Sb
may be proton-bound
(Sp > 0). Cyburt et. al. [44] adopt a limit of Sp > −890 keV for
103 Sb
based on its
reported observation in [81] and the preliminary analysis of the present study [78]. This
value is considerably less bound than the value of Sp = −1462 ± 326 keV given in the 2003
Atomic Mass Evaluation [99].
4.4 Recent technological progress in β studies
The present study indicates some of the limitations of the experimental techniques employed
at the time. It offers some insights into areas where improvements were needed. This section
discusses some of the advances that have been developed both at the NSCL and elsewhere
that have improved the outlook for decay studies in general and particularly for studies on
the neutron deficient side of stability.
4.4.1 Improvements to the NSCL
General improvements
Systems in all areas of the NSCL are constantly being improved. From improvements
in software design and increased computing power of data acquisition systems to source
development and better beam intensity. When this experiment was proposed the available
124 Xe
primary beam offered was at an energy of 120 MeV/nucleon with a current of 1.5 pnA.
The NSCL primary beam list as of April 2011 offers an energy of 140 MeV/nucleon with a
current of 10 pnA [100]. The improved energy and current should improve the production
rates of
103 Sb
and
104 Sb
by approximately a factor of nine (according to rate calculations
in Lise++ [101, 102]).
81
γ-ray energy [keV]
100
250
500
1000
2000
3000
betaSeGA-12
14.4%
12.6%
8.0%
5.3%
3.5%
2.6%
betaSeGA-16
20.5%
18.6%
11.7%
7.3%
4.6%
3.5%
Increase
+42%
+48%
+46%
+38%
+31%
+35%
Table 4.1: The photopeak efficiencies for the SeGA configuration used at the NSCL for βdecay studies from [68, 103]. Experiment 02012 used the betaSeGA-12 configuration, more
recently a betaSeGA-16 configuration has offered a much improved efficiency.
Improved γ-ray detection
Another significant area of improvement at the NSCL has been in the area of γ-ray detection.
Experiment 02012 used 12 Ge crystal detectors in the betaSeGA-12 configuration, with
four detectors above and four detectors on either side of the β-calorimeter. All β studies
at the NSCL now use a 16 detector configuration, adding four additional detectors on the
underside of the calorimeter. The newer configuration offers a 30-48% improvement in
efficiency depending upon the energy of the γ-rays. Table 4.1 shows the efficiencies of both
configurations and the relative gain in efficiency. Some recent studies have improved gamma
detection further by placing an additional Ge crystal downstream of the β calorimeter
beyond the end of the beamline. [66, 104]
Radio Frequency Fragment Separator
The major improvement at the NSCL with respect to this study of nuclei on the neutron
deficient side stability has come with the commissioning of the Radio Frequency Fragment
Separator (RFFS) or the “RF-Kicker” [105, 106]. The RFFS has been implemented at
the NSCL specifically to purify beams of neutron deficient nuclei. The device works in
conjunction with the A1900 Fragment Separator. It is placed downstream of the A1900 in
one of the experimental vaults and in β-decay studies, adds an additional layer of beam
filtering of nuclei prior to the beam reaching the detector endstation. The device consists of
82
two parallel horizontal plates 5 cm apart. A time-varying electric field is applied across the
plates with an amplitude up to 100 kV. The electric field is varied sinusoidally at a frequency
matched to the K1200 cyclotron. The time-of-flight (TOF) separation of various incoming
fragments causes different species of nuclei to encounter the variable field at different phases
of the cycle. Each receive a vertical “kick” in proportion to the field intensity encountered.
The downstream end of the RFFS contains a system of detectors and slits. Manipulation
of the slits in conjunction with adjustments to the phase difference between the RFFS and
the K1200 allow experimenters to select desired nuclei from the peaks, troughs or central
nodes of the sinusoidally separated incoming nuclei. This provides experimenters with an
additional means of removing unwanted fragments based on differences in velocity.
4.4.2 Decay studies at GSI
A newer implantation detector has been developed for use with the FRS Fragment Separator
at GSI in Darmstadt, Germany. The Silicon Implantation Detector and Beta Absorber
(SIMBA) is a detector stack that includes 12 SSSDs upstream of 3 DSSDs with an additional
10 SSSDs downstream. Each of the DSSDs has dimensions of 60 × 40 × 0.7 mm3 and 60 × 40
strips. The overall implantation region increases the number of pixels available to a factor
of 4.5 greater than the single DSSD used in the present study. The choice of using thinner
implantation detectors (0.7 mm as opposed to ∼ 1.0 mm in the present study) also improves
spatial resolution which may be helpful when attempting to differentiate protons from beta
decays. Figure 4.7 shows a comparison between the PID from the present experiment with
a similar PID of nuclei in the same region observed at GSI using SIMBA.
4.5 Summary and conclusions
This NSCL experiment to observe and measure the decay properties of neutron deficient Sb
near the endpoint of the rp-process encountered many technical issues and achieved only
limited success. The high implantation rate of unwanted nuclei and the resulting presence
of a persistent β background both complicated the decay correlation process and interfered
83
Figure 4.7: Comparison of PID from the present study (left) with that of a recent GSI
experiment from [92] (right). Ovals and abels added. Note the greatly improved resolution
of nuclei, the reduced intensity of contaminants, the additional nuclei far from stability
included, and the scarcity of implants in the 103 Sb region.
with the statistical analysis of the results. The high implantation rate, and possibly other
issues with the detector systems, led to a poor resolution between nuclei included on the
particle identification plot (PID).
As a result,
105 Sb
was observed in the PID, but could not be sufficiently separated in
order to make a measurement. The half-life measurement of 104 Sb at t1/2 = 0.54±0.14 s is in
excellent agreement with previous results but does not significantly reduce the uncertainty
of this quantity. Implantation and decay events were observed in the region of the PID
where
103 Sb
was expected, but analysis of the resulting decay curve suggests these data
are better explained as decays from the poorly resolved neighboring isotope
resulting measurement, presumed to be the
101 Sn
101 Sn.
The
half-life (t1/2 = 1.8 ± 0.6 s) may have
been a more accurate and precise measurement than was available during the experiment
run, but does not improve upon more recent measurements.
4.5.1 Possible implications for the Sn–Sb–Te cycle of the rp-process
The results of the present study have little to add to the on-going discussion regarding the
behavior of reaction networks near the endpoint of the rp-process. One comment may be
that the
101 Sn
β + decay reaction rate may need to be updated in REACLIB as it appears
84
Figure 4.8: Calculated rates for (γ, p) photodisintegration on 103 Sb (top) and 104 Sb (bottom) in REACLIB over a range of T = 0.1–10 GK. The currently recommended rates
(shown in blue) differ significantly from previous models at lower temperatures. The newer
rates would appear to be more consistent with recent predictions that these nuclei may be
significantly proton unbound.[44].
85
to be based on the half-life t1/2 = 3 ± 1 s from the 1995 measurement in [93]. Both the new
measurement suggested in this study and the current compiled value of t1/2 = 1.7 ± 0.3 s
given in [65] suggest a decay rate that is nearly double the currently recommended value.
In general reaction rate libraries appear to have recently improved significantly for nuclei
in this region. Figure 4.8 shows one example where a newer recommended model appears
to be more consistent with the expectation that
103 Sb
and
104 Sb
are significantly proton
unbound.
Recent rp-process calculations in [98] and in [44] show that both the path that the Sn–
Sb–Te cycle follows through the Sb isotopes [98] and the precise shape of the X-ray burst
light curve [44] show sensitivity within these models to the remaining uncertainties among
nuclei in this region.
4.5.2 Outlook
Many uncertainties among the decay properties of
103-105 Sb
remain. Hopefully, new ex-
perimental developments will help to resolve these issues. Either a direct measurement of
the
103 Sb
decay half-life or a statistically significant limit based on its non-observation may
soon be available. Likewise, improved data for the half-lives and branching ratios of
and
105 Sb
104 Sb
may help to reduce some of the uncertainties regarding the Sn–Sb–Te cycle, its
chemical production and its energy output.
86
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95
Appendix A
Detector channel assignments
Table A.1 shows the TDC channel assignments to beam line detectors used in the readout/analysis of the data for experiment 02012. Table A.2 shows the same for ADC data.
See also figure 2.9 for a schematic of the signal processing system.
Table A.1: Assignment of TDC channels to timing of beam line detectors.
Device Channel
Detector
Notes
TDC 01
0
PIN1
1
PIN2
2
PIN3
3
PIN4
4
N3 scintilator
5
I2 scintilator North PMT
6
I2 scintilator South PMT
7
PIN2a
96
Device
ADC 01
ADC 02
ADC 03
ADC 04
ADC 05
ADC 06
ADC 07
ADC 08
ADC 09
ADC 10
Table A.2: Assignment of ADC channels to all beam line detectors.
Channel(s)
Detector
Parameter
Notes
0–15
DSSD front strips 1–16 high-gain energy
16–31
DSSD front strips 1–16
low-gain energy
0–15
DSSD front strips 17–32 high-gain energy
16–31
DSSD front strips 17–32 low-gain energy
0–7
DSSD front strips 33–40 high-gain energy
8–15
[Not used]
16–23
DSSD front strips 33–40 low-gain energy
24–31
[Not used]
0–15
DSSD back strips 1–16 high-gain energy
16–31
DSSD back strips 1–16
low-gain energy
0–15
DSSD back strips 17–32 high-gain energy
16–31
DSSD back strips 17–32 low-gain energy
0–7
DSSD back strips 33–40 high-gain energy
8–15
[Not used]
16–23
DSSD back strips 33–40 low-gain energy
24–31
[Not used]
0–15
SSSD1 strips 1–16
energy
16–31
SSSD2 strips 1–16
energy
0–15
SSSD3 strips 1–16
energy
16–31
SSSD4 strips 1–16
energy
0–15
SSSD5 strips 1–16
energy
16–31
SSSD6 strips 1–16
energy
0
PPAC
up
PPAC not biased
1
PPAC
down
2
PPAC
left
3
PPAC
right
4
PIN1
energy
5
PIN2
energy
6
PIN3
energy
7
PIN4
energy
8
Scintilator
energy
9
TAC
RF TOF
10
TAC
I2 TOF
11
TAC
I2 Position
12
PIN2a
energy
97
Appendix B
Spectra from SeGA
Here spectra from the SeGA detectors are presented, showing γ energies coincident with
100 Cd
implants and used to identify the 60 ns isomer as described in section 3.1.1. The
energy spectrum is split into four plots, each of a different energy range. In each figure, three
histograms are shown covering the same energy range. They are labeled “SEGATOTAL,”
“SEGAXMATRIX,” and “SEGAYMATRIX.” The first γ energy associated with an event
is recorded in the SEGATOTAL plot. If a second or third γ ray is detected with the same
event, it’s energy is recorded on the SEGAXMATRIX or SEGAYMATRIX plot respectively.
These spectra are compilations from the full data set of the experiment. These histograms
represent the raw data. Intensities are not corrected for variations in photopeak efficiency
(see table 2.2)
98
Figure B.1: γ-ray energies correlated to
99
100 Cd
implants, 0–300 keV range.
Figure B.2: γ-ray energies correlated to
100
100 Cd
implants, 300–600 keV range.
Figure B.3: γ-ray energies correlated to
100 Cd
101
implants, 600–1000 keV range.
Figure B.4: γ-ray energies correlated to
100 Cd
102
implants, 1000–1500 keV range.
Appendix C
Fitting a time-dependent
background
Here fits of background spectra to equation 3.7 are presented. Results of these fits have
been previously presented in table 3.4:
Gated
NI
t1/2
nucleus
(implants)
(s)
χ2 /ndf
RBG1 /NI
λBG1
RBG2 /NI
λBG2
93 Tc
7085
9900
1.28
0.011(8)
0.018(17)
0.031(6)
0.12(37)
94 Tc
7966
17580
1.02
0.026(3)
0.040(4)
0.026(4)
0.29(10)
95 Ru
29774
141955
1.00
0.020(2)
0.035(3)
0.021(2)
0.20(3)
96 Ru
6249
stable
1.28
0.023(3)
0.038(3)
0.022(3)
0.23(6)
97 Rh
149186
1842
0.97
0.0188(8)
0.0321(14)
0.0235(7)
0.20(1)
98 Pd
629117
1062
1.01
0.0189(5)
0.0328(8)
0.0228(4)
0.194(7)
99 Pd
12293
1284
1.10
0.0234(24)
0.040(4)
0.026(2)
0.25(5)
99 Ag
531706
124
1.06
0.0200(5)
0.0334(7)
0.0238(4)
0.201(7)
excld.)
0.019(3)
0.033(4)
0.023(2)
0.20(4)
Weighted mean (93 Tc and
99 Ag
Results of a 4-parameter fit to background
Mean values in the above table are weighted by number of implantations within a
given gate. These values have been used to produce a generalized background formula
(equation 3.8) which is also included on each of the plots here. Additional spectra for 100 Ag
and
99 Cd
are also presented.
103
Figure C.1: Background activity within the 95 Ru gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
104
Figure C.2: Background activity within the 96 Ru gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
105
Figure C.3: Background activity within the 97 R gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
106
Figure C.4: Background activity within the 98 Pd gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
107
Figure C.5: Background activity within the 99 Pd gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
108
Figure C.6: Background activity within the 94 Tc gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
109
Figure C.7: Background activity within the 93 Tc gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
110
Figure C.8: Background activity within the 99 Ag gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
111
Figure C.9: Background activity within the 100 Ag gate. The black curve is a four-parameter
fit of equation 3.7 to the displayed data, the pink curve is the general background function
(equation 3.8) applied to the number of implantations within the same gate.
112
Figure C.10: Background activity within the 100 Cd gate. The black curve is a fourparameter fit of equation 3.7 to the displayed data, the pink curve is the general background
function (equation 3.8) applied to the number of implantations within the same gate.
113