QUANTIFYING THE URCA COOLING IMPACT OF MASS 61 NUCLEI

IN X-RAY BURSTING SYSTEMS

By

Wei Jia Ong

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Physics — Doctor of Philosophy

2018

QUANTIFYING THE URCA COOLING IMPACT OF MASS 61 NUCLEI IN X-RAY

ABSTRACT

BURSTING SYSTEMS

By

Wei Jia Ong

Early-time observations of cooling crusts of neutron stars in Quasi-persistent X-ray tran-

sients cannot be explained by current astrophysical models, suggesting an incomplete under-

standing of the physical and nuclear processes that occur in the crust. An as yet unidentified

strong, shallow heat source has been postulated to account for these discrepancies. Compli-

cating this issue is the recent discovery of Urca cooling, β decay-electron capture cycles that

release neutrinos, in neutron star crusts. The strength of Urca cooling depends critically on

the magnitude of the ground state to ground state transition between the parent-daughter

pair, because the electron degeneracy under neutron star crustal conditions forbids β decay

transitions to excited states. Current predictions of Urca cooling in neutron star crusts are

highly reliant on theoretical QRPA predictions. Experimental data are needed to test these

predictions and characterise their uncertainties. Of particular importance is the possible

existence of strong ground state to ground state electron capture and β decay transitions,

and the strength of these transitions.

This work reports an experimental measurement of the transition strength for the β

decay of the ground state of 61V to states in 61Cr. Most importantly, the ground state to

ground state transition strength was determined to be 7.4+13.8

−5.8 % (corresponding to a log
−0.6). This result confirms the existence of a considerable ground state to
ground state transition that enables Urca cycle cooling in accreted neutron star crusts at

f t value of 5.5+0.8

the boundary of the 61Cr and 61V layers. However, the log f t value is significantly larger

than the theoretically predicted log f t value of 4.35, resulting in a slower than expected Urca

cycle. This result was achieved through the measurement of the β-delayed γ rays using the

total absorption spectrometer SuN and the measurement of the β-delayed neutron branch

using the neutron long counter system NERO at the National Superconducting Cyclotron

Laboratory (NSCL) at Michigan State University. The use of the combination of SuN and

NERO helps to mitigate the impact of the Pandemonium effect that tends to significantly

skew studies using more traditional high-resolution, low-efficiency detectors.

The impact of this experimental result on the cooling strength of the A = 61 mass

chain was investigated using a nucleosynthesis network evolved under neutron star crustal

conditions. The results show that the mass 61 chain is amongst the strongest cooling chains

in crusts composed of X-ray burst ashes. Updated cooling strengths using the latest state of

experimental knowledge were also folded over realistic crust compositions for X-ray bursting

systems to identify other strong cooling chains, as well as to pinpoint Urca pairs of particular

interest for future studies using the same technique as developed in this work.

In memory of Frank and Ernst, without whom I would never have begun this journey.

iv

ACKNOWLEDGMENTS

There is a proverb that says that it takes a village to raise a child, and the same can

be said about completing a PhD- Thank you to everyone who played a role in helping me

throughout graduate school, no matter how small. I unfortunately cannot name everyone

here, but please know I sincerely appreciate your time and help. Thanks must go out to

everyone who keep the lab running, and who help to make experiments happen.

I must especially thank my advisor Hendrik Schatz, who was an incredible mentor to me.

He constantly challenges me to be a better scientist, and his guidance helps me to become

a better one. I can only hope that I do not disappoint him too much. I would also like

to thank members of Team Schatz, in particular: Christoph Langer, for his patience and

mentorship during my first years in graduate school; Fernando Montes, for many interesting

conversations and for his invaluable help preparing for my thesis experiment; Zach Meisel,

for being an outstanding example to a younger graduate student (I learnt my backronym

skills from the very best); as well as “Cowboy” Tony Ahn, Konrad Schmidt, Jin Shilun,

Justin Browne, and Sara Ayoub for making the lab a fun and welcoming place to work.

I am also grateful to the members of my committee: Artemis Spyrou, who served as

a semi-advisor and who also did her best to ensure my well-being as a graduate student;

Alexandra Gade, with whom I was able to discuss scientific topics of any kind and whose

unrelenting work ethic always inspired me to work harder; Ed Brown, for his extraordinarily

clear explanations of any question I had for him, no matter how silly, and his constant

encouragement; and Carl Schmidt, for being a kind and patient teacher to a young graduate

student.

Thanks also to: members of the SuN and Beta groups, especially Professor Sean Liddick

v

and Alexander Dombos, for their help preparing for my experiment and with my analysis;

Professor Vladimir Zelevinsky for always letting me bounce ideas off him and for not laughing

at them; Jill Berryman and Carol Lentz for being good listeners and even better friends.

I have been very lucky throughout graduate school to have the support of amazing friends.

Amy “Bear Hunter” Lovell and “Becky” Lewis, whom I cannot thank enough for their

friendship.

I would not have been able to do this without them. Thanks for all the fun

cooking/baking and football days, and for providing surrogate (if competing) teams to cheer

for when the Rams abandoned St Louis. Josh “Brad” Bradt and Chris “no relation to

Tom” Izzo, for their great company and senses of humour. Walter Buhro, who made me a

better person. Juan Manfredi, Katie Childers, Zach “Batman” Matheson and other transient

residents of office 1022, for being the very best officemates and fellow Guardians of the Sign

I could ask for. To the lovely Nanyang girls who’ve had my back for more than a decade,

you guys are the best, most enthusiastic cheer squad ever.

I have to thank Christine Floss, whose encouragement kept me going even when I was

struggling the most, and who always opened her home to me when I needed somewhere to

go.

Finally, none of this would have been possible without the support and love of my family.

Mum, Dad, 大姐, 二姐, and Brian, thanks for always believing in me and for helping me

chase my dreams. As mum loves to say: “吃饱饭，没事做。 船到桥头自然直。”

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Open questions in neutron star crustal physics . . . . . . . . . . . . . . . . .
1.3 Nuclear processes in neutron star crusts . . . . . . . . . . . . . . . . . . . . .
1.4 Urca cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5
. . . . . . . . . . . . . .
1.6 Motivation for the measurement . . . . . . . . . . . . . . . . . . . . . . . . .
1.7 Outline of dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Impact of Urca cooling on neutron star observables

Chapter 2 Experimental Method . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Overview of the technique . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Bateman equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 β-delayed γ decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 β-delayed neutron emission . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Experimental Description . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Beam delivery from CCF and A1900 . . . . . . . . . . . . . . . . . .
2.5.2 Particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3 Detectors
2.5.3.1 NERO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3.2
SuN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3.3 Double-Sided Strip Detectors (DSSDs) . . . . . . . . . . . .
2.6 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 Digital Data Acquisition System . . . . . . . . . . . . . . . . . . . . .
2.6.2 NSCLDAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
2.6.3 Defining a physics event
2.7 Experimental End Station . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.1 NERO set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.2
SuN set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 NERO Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.1 Moderation time of neutrons in NERO . . . . . . . . . . . .
SuN Energy Calibrations . . . . . . . . . . . . . . . . . . . . . . . . .
Silicon Detector Calibrations . . . . . . . . . . . . . . . . . . . . . . .
3.1.3.1 Energy calibration and resolution of PIN detectors
. . . . .
. . . . . . . . . . . . . . . . . . . . .
3.1.3.2 Calibration of DSSDs

3.1.2
3.1.3

vii

ix

xi

1
1
4
5
7
10
11
13

14
14
18
19
21
22
23
25
25
25
28
31
32
32
36
37
38
38
44

47
47
47
51
52
54
54
56

3.1.4 Light Particle Veto Calibrations . . . . . . . . . . . . . . . . . . . . .
3.2 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Correlating implants and decays . . . . . . . . . . . . . . . . . . . . . . . . .
β Correlation efficiency . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1
3.3.2 Reverse-time correlations . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Simulating β-delayed radiation in SuN . . . . . . . . . . . . . . . . . . . . .
3.4.1 GEANT4 construction of SuN . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Neutron and electron signals in SuN . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 GEANT4 simulation of β decay events in SuN . . . . . . . . . . . . .
3.5 Extracting β-feeding intensities from SuN γ ray spectra . . . . . . . . . . . .
. . . . . . . . . .

58
62
64
68
72
72
72
74
74
75
76
77
3.5.1 Generating templates of the decay of known states
77
3.5.2 Generating templates of the decay of unknown states with DICEBOX 81

3.4.2.1 Neutrons
3.4.2.2 Electrons

Chapter 4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 β Decay of 61V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Half-life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
β-delayed neutron branch . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2
β feeding intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3
4.1.4
ft-value and Urca strength . . . . . . . . . . . . . . . . . . . . . . . .

83
83
83
88
88
97

Chapter 5 Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98
. . . . . . . . . . . . . . . . . . . . . . . 101

5.1 Urca cooling of neutron star crusts

Chapter 6

Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . 106

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

viii

LIST OF TABLES

Table 1.1: Measured log f t values for A = 61 nuclei and the QRPA predicted log f t
. . . . . . . . . . . . . .

for the ground state to ground state transitions.

Table 1.2: List of spin/parity assignments for the neutron-rich A = 61 isobars. As-
signments in parentheses are tentative. . . . . . . . . . . . . . . . . . . . .

12

13

Table 2.1: Angular momentum and parity selection rules for β decay . . . . . . . . .

16

Table 2.2: List of detectors and properties used in the NERO set-up. . . . . . . . . .

40

Table 2.3: List of detectors and properties used in the SuN set-up.

. . . . . . . . . .

44

Table 3.1: Isotopic composition of the source on the source preparation date (left,
provided by source manufacturer) and on the α calibration date (right,
calculated). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 3.2: NERO detection rate of neutrons for a representative background run dur-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ing the experiment.

Table 3.3: Source characteristics and NERO efficiencies by quadrant and detector type
. . . . . . . . . . . . . . . .

before (left) and after (right) the experiment.

Table 3.4: DDAS slow filter parameters and highest achieved energy resolution of the
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

PIN detectors.

Table 3.5: Rate of implants for the major beam species at the centre of the position
distribution in the plane of the detector in different correlation field sizes.
The implantation efficiency (fraction of implants to beam particles) for each
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
species is also given.

Table 3.6: Calculated efficiencies for the correlation of implanted isotopes for the BCS
. . . . . . . . . . . . . . .

DSSD (top) and the SuN miniDSSD (bottom).

Table 3.7: Summary of correlation efficiency as a function of correlation field size for
both DSSDs. The result for a 5×5 field for the miniDSSD was not included
as a reduced χ2 of below 2 was not achieved by the best fit.
. . . . . . . .

Table 4.1: Comparison of measured values in this work with previously measured val-
ues of the half-life of 61V. . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

49

50

58

66

69

70

87

ix

Table 4.2: List of β feeding intensities to the identified states in the 61Cr excitation
scheme from [36], and the corresponding apparent β feedings deduced by
[29] from [36].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 4.3: Table of log f t values for the β decay from 61V to the known states in
61Cr. The L34 values are only given for the ground state and the first
excited state because β decay to the higher-lying excited states is highly
suppressed and do not occur in Urca cycling.
. . . . . . . . . . . . . . . .

94

97

x

LIST OF FIGURES

Figure 1.1: Left: Structure of a neutron star (layers not to scale) [6, 7]. Right: The
light curve with the corresponding portion of the star that is probed.
(Adapted from [8].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.2: Cartoon showing the source of crustal heating from consequtive electron
captures in even-A, even-Z nuclei. . . . . . . . . . . . . . . . . . . . . . .

Figure 1.3: Left: Crust composition change boundary at non-zero temperature, show-
ing the co-existance of A, Z nuclei and A, Z − 1 nuclei in the Urca shell.
Right: Crust composition change boundary at zero temperature, showing
the sharp transition boundary with no Urca shell. . . . . . . . . . . . . .

Figure 2.1: Left: Layout of the NERO tubes. Right: Cross-section schematic of
NERO. Adapted from [50]. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.2: Left: Schematic of SuN. Right: Lengthwise cross-section of SuN. Adapted
from [52] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.3: The total absorption (solid blue) and sum of segments (dashed black)
. . . . . . . . . . . . . . . . . . . . . . . . . .

spectra for a 60Co source.

Figure 2.4: Example of an event in the DDAS data stream. The top panel shows the
event as it is recorded in the data stream. The bottom panel shows the
same event with each separate component commented out. . . . . . . . .

Figure 2.5: Example of a trace (red diamonds), the trigger filter output (black circles),
and the energy filter output (blue triangles) from a representative DSSD
high gain signal. The energy filter output has been scaled down to fit on
the same scale as the trigger filter output. The trigger filter parameters
are L = 80 ns and G = 500 ns. The energy filter parameters are L = 100
ns and G = 700 ns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.6: A cartoon showing the components of the set-up for the NERO portion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

of the experiment.

4

6

9

26

29

30

33

35

39

Figure 2.7: BCS/NERO electronics logic.

. . . . . . . . . . . . . . . . . . . . . . . .

42

Figure 2.8: BCS DSSD electronics logic. . . . . . . . . . . . . . . . . . . . . . . . . .

43

xi

Figure 2.9: A cartoon showing the components of the set-up for the SuN portion of the
experiment. Here, the BCS chamber has been removed from the set-up,
indicated by the hollow bore of NERO. . . . . . . . . . . . . . . . . . . .

45

Figure 2.10: SuN electronics logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

Figure 3.1: Left: Spectrum from a representative 3He tube. Right: Spectrum from a
representative BF3 tube. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.2: Moderation time of neutrons in NERO. The time for half the neutrons to
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

be detected is ∼34 µs.

Figure 3.3: Gain-matched room background spectrum for all 24 PMTs of SuN. The
peak at ∼1000 ADC units is the 1461 keV line from the decay of 40K in
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
the room background.

Figure 3.4: The source γ rays used for the calibration of SuN from 241Am (left), 60Co
(centre), and 137Cs (right), marked by diamonds. The second peak in the
137Cs spectrum is produced by two γ rays at 662 keV from two separate
decays being detected by the same segment, and is a result of the high
activity of the 137Cs source used.
. . . . . . . . . . . . . . . . . . . . . .

Figure 3.5: Calibration residuals for all 8 segments of SuN for the energy calibration
. . . . . . . . . . . . . . . . . . . . . . . . .

from before the experiment.

Figure 3.6: Calibration residuals for all 8 segments of SuN for the energy calibration
from after the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.7: 228Th spectrum. The six α peaks from the decay chain are at 5.42, 5.69,
. . . . . . . . . . . . . . . . . . . . . . .

6.05, 6.29, 6.78, and 8.78 MeV.

Figure 3.8: BCS DSSD front side calibration residuals with a 228Th source. Strip 1
. .

shows no residuals as it was not operational due to a broken contact.

Figure 3.9: BCS DSSD front side calibration residuals with a 228Th source. The
shared pre-amlifier for strips 33-40 had a gain high enough that the 8.8 MeV
α from 228Th was outside the ADC range.
. . . . . . . . . . . . . . . . .

Figure 3.10: SuN miniDSSD front side (top four rows) and back size (bottom four rows)
calibration residuals with a 228Th source. Strips are ordered left to right,
then top to bottom.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

51

53

54

55

55

57

59

60

61

xii

Figure 3.11: 90Sr spectrum in a representative DSSD strip. The threshold used is
indicated by the dashed line. The peak to the left is due to electronic
noise, and the broad peak to the right is the β spectrum measured from
the 90Sr source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.12: Scintillator spectrum for a representative NERO run. The dashed line
indicates the 12 MeV upper threshold used to eliminate light particle
signals from the DSSD high-gain channels. . . . . . . . . . . . . . . . . .

62

63

Figure 3.13: Uncorrected (left) and corrected (right) particle identification plots.

. . .

64

Figure 3.14: The spatial distribution of correlated 61V decays in the BCS DSSD. The

low-event strip in the middle is due to a noisy channel with a high threshold. 67

Figure 3.15: The spatial distribution of correlated 61V decays in the miniDSSD.

. . .

68

Figure 3.16: Top: Implant distribution for 61V (red), 62Cr (magenta), and 64Mn (blue)
for the front (left) and back (right) sides of the BCS DSSD. Bottom:
Implant distribution for 61V (red), 62Cr (magenta), and 64Mn (blue) for
the front (left) and back (right) sides of the SuN miniDSSD.
. . . . . . .

Figure 3.17: Total absorption spectrum (left) and sum of segments spectrum (right)
comparing background-subtracted 60Co source data (dashed red), and
GEANT4 simulation with a 60Co source (solid black).
. . . . . . . . . .

Figure 3.18: Total absorption spectrum for mono-energetic 1 MeV neutrons, showing
the sum peak for the inelastic scattering populating the first excited state
of 127I where the neutron is not captured and the 7.8 MeV peak from
neutron capture on 127I.
. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.19: Simulated total absorption spectrum (black) and energy deposited in the
DSSD (red) for allowed β decay of a species with a Q value of 1 MeV
. . . . . . . . . . . . . . . .
(left), 3 MeV (centre), and 10 MeV (right).

Figure 3.20: Level scheme showing the known excitation levels in 61Cr populated by β
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

decay.

Figure 3.21: Total Absorption spectrum of γ rays correlated with β decay events from
implants in the 61V PID gate. Black triangles, blue circles, and red squares
denote levels in 61Cr, 60Cr, and 61Mn respectively.
. . . . . . . . . . . .

Figure 3.22: The sub-templates representing the three different γ decay cascades from
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

the 224 keV state.

71

73

74

76

78

79

80

xiii

Figure 3.23: Top: Contributions of individual templates of the decay to the ground
state (green), through the first excited state (magenta), and through the
second excited state (red). Bottom: Comparison between the best fit of
the templates (blue) and the data (black).
. . . . . . . . . . . . . . . . .

Figure 4.1: Top: Decay curve fit for the SuN miniDSSD. Bottom: Decay curve fit for
the BCS DSSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.2: Decay curve from the SuN miniDSSD when gated on the 1028 keV cascade
(inset) from the corresponding state in 61Cr . . . . . . . . . . . . . . . .

80

84

86

Figure 4.3: Decay curve from the BCS DSSD when gated on coincident neutrons. . .

87

Figure 4.4: Panels (a)-(c) show the components of the decay curve still remaining in
the corresponding TAS spectra shown in panels (i)-(iii). Panel (iv) shows
the background-subtracted total absorption spectrum used for fitting. . .

Figure 4.5: Data (black) and best fit from GEANT4 simulated templates (red) for
the total absorption spectrum (top) and the sum of segments spectrum
(bottom).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.6: Data (black) and best fit from GEANT4 simulated templates (red) for
the total absorption spectrum (top) and the sum of segments spectrum
(bottom) up to Ecrit = 2270 keV. . . . . . . . . . . . . . . . . . . . . . .

Figure 4.7: Beginning bottom left, clockwise: Reduced χ2 as a function of (i) the
sum of the two ground state transition intensities; (ii) Iβ(61Cr ground
state); (iii) Iβ(60Cr ground state); and (iv) contour plot demonstrating
the correlation between the two parameters. The increasing warmth of
the colour denotes increasing χ2.
. . . . . . . . . . . . . . . . . . . . . .

Figure 4.8: Beginning bottom left, clockwise: Reduced χ2 as a function of (i) the sum
of the two transition intensities; (ii) Iβ(61Cr 632 keV); (iii) Iβ(60Cr 644
keV); and (iv) contour plot demonstrating the correlation between the two
parameters. The increasing warmth of the colour denotes increasing χ2. .

90

91

92

95

96

Figure 5.1: Top: Abundance plot of A = 61 nuclei as a function of column depth.
Bottom: Cooling profile as a function of column depth. The grey band
shows the uncertainty in the cooling profile prior to the experiment and the
green band shows the uncertainty following the experiment. The uncer-
tainty bands shown only reflect the uncertainty in the 61V-61Cr transitions.100

xiv

Figure 5.2: Chart of the nuclides (only odd-A nuclei are shown) showing the compar-
ison between QRPA predictions for ground state transitions and whether
allowed transitions are possible based on the experimentally-determined
spins of the ground states. The red (yellow) squares denote nuclei where
there is a QRPA-predicted transition and there is (is not) an allowed tran-
sition based on spins. The blue (green) squares denote nuclei where there
is no QRPA-predicted transition and there is (is not) an allowed transition
based on spins. Magenta squares denote nuclei where the spins have not
yet been experimentally determined.

. . . . . . . . . . . . . . . . . . . . 102

Figure 5.3: Cooling strengths of individual mass chains in X-ray burst ashes.

‘Old’
refers to the calculations presented in [22], and ‘new’ refers to the calcu-
lations done following the prescription described in the text, representing
the state of experimental knowledge before the 61V result. The new cool-
ing strength of the mass 61 chain using the results of this experiment is
given by the black octagon, with error bars (solely from the uncertainty
in the 61V decay strength) denoted by the up and down black triangles. . 104

xv

Chapter 1

Introduction

1.1 Neutron Stars

Neutron stars are compact stellar objects which are formed when the core of an evolved

star implodes. With masses of ∼1M(cid:12) and radii of ∼10km, they have densities roughly
equivalent to a billion tonnes per teaspoon, and are thus good laboratories for the way

that nuclear material behaves at extreme densities. Neutron stars can be partitioned into

layers (Fig. 1.1). The outermost layer of a neutron star is the neutron star atmosphere,

which is on the order of a centimetre thick, where the atmospheric material behaves like

a gas and there are no correlations between nuclei. Below the atmosphere is the envelope,

which behaves like an ideal gas. Further beneath is the ocean where densities are sufficient

such that the behaviour of a nucleus is correlated with other nuclei in close proximity to

it. Deeper still is the outer crust, in which nuclei exist in a solid lattice with a Fermi gas

of degenerate, relativistic electrons that provides most of the pressure supporting the crust

against gravitational collapse. As the neutron-richness of the material increases, eventually

the extra neutrons cannot bind to the nuclear matter. This is known as neutron drip, and

marks the transition of the outer crust to the inner crust. In the inner crust, the neutron

pressure exceeds the electron pressure (since the number density of neutrons is much higher

at this point than the electron number density) and becomes the dominant resistance against

1

gravitational collapse. The crust-core transition occurs when the density is ∼0.08 nucleons
per fm3 (where 1fm = 10−15m), about half of nuclear saturation density. The state of matter

of the inner core of the neutron star is still unknown, and what the equation of state is that

governs it is one of the biggest open questions in nuclear physics.

Quasi-persistent transients are a subset of observed neutron stars that exist in low-mass

X-ray binaries (LMXBs). They are characterised by particularly long outburst periods pow-

ered by accretion from their companion star where their X-ray luminosities are on the order

of 1037 erg/s, followed by a similarly long quiescent phase where the X-ray luminosity drops

many orders of magnitude. It is hypothesised that the transition from the accreting phase

to the quiescent phase occurs when the accretion from the companion star slows to a negli-

gible level or stops completely [1, 2]. The mechanism responsible for this accretion turn-off

is not yet fully understood, but it is the most likely physical reason for the large drop in

X-ray luminosity. As material accumulates on the neutron star surface during the accretion

phase, it undergoes nuclear burning. Depending on the accretion rate, the nuclear burning

can potentially be unstable, where a layer of fuel accumulates for hours to days before it

burns explosively within 10-100s, causing an observable X-ray burst [3]. Burst luminosities

can reach 1038 erg/s, which is observed on top of the persistent X-ray flux generated by the

release of gravitational energy by infalling material during accretion.

X-ray bursts are caused by a thermonuclear runaway where the temperature sensitivity

of the nuclear reaction rates leads to an increase in energy production when temperatures

increase, creating a positive feedback loop. The thermonuclear runaway is triggered when

it becomes hot and dense enough for the 3α reaction to ignite and for breakout from the

CNO cycle through the 15O(α, γ)19F reaction to occur. This then triggers the (α, p) and

(p, γ) reactions which dominate the rise of the X-ray flux up to the peak of the X-ray

2

light curve, producing elements in the intermediate mass range (A ∼ 40). At this point,
the Coulomb barrier becomes too high for α-induced reactions to be fast even for the hot

and dense conditions of the burning material, and the rapid proton capture process (rp-

process) becomes the dominant source of energy powering the X-ray lightcurve [4, 5]. The

rp-process is characterised by a series of fast proton captures and slower β decays, with a

reaction flow near or at the proton drip line. Depending on the conditions of the burst, it

predominantly produces nuclei in the mass A ∼ 60–70 range, potentially up to Tellurium,
Tin and Antimony [5]. These ashes will be pushed down into the ocean and then the crust

under the weight of continued accretion, and replaces the ocean and crust completely. Thus,

understanding the ashes of the bursting phase nucleosynthesis is important for a correct

determination of the properties of the neutron star ocean and crust.

During the accreting phase, the nuclear reactions heat the crust of the neutron star

and bring it out of thermal equilibrium with the core. During the quiescent phase, when

accretion has ‘turned off’, the star cools through neutrino and radiative emission. The surface

luminosity as a function of time of the neutron star, known as the cooling curve, probes the

thermal structure of the crust at increasing depth as the crust cools. This is because the

thermal relaxation time of the material depends on its matter properties and depth. At

a given time, the thermal profile can be understood as two separate parts: the innermost

material has not yet cooled, and its thermal character is essentially equivalent to the steady-

state condition during the accretion phase. The outer part of the material has thermally

relaxed and has an approximately constant outward flux. Therefore, a series of observations

following the beginning of quiesence will probe increasingly deeper layers of the neutron star

(Fig. 1.1). Observations of transient neutron stars present a unique opportunity to probe

the inner layers of the neutron star crust because the cooling timescales are on the order of

3

years, as opposed to the expected thousands of years for the entire neutron star.

Figure 1.1: Left: Structure of a neutron star (layers not to scale) [6, 7]. Right: The light
curve with the corresponding portion of the star that is probed. (Adapted from [8].)

1.2 Open questions in neutron star crustal physics

Several major mysteries remain that suggest our understanding of neutron star crust physics

is incomplete. Present models of neutron star crust cooling systematically produce lower

temperatures in the early stages of cooling, right after the beginning of quiescence [8, 9].

To produce temperatures consistent with observations, a shallow heat source is required.

Though nuclear reactions in the neutron star crust do produce heat, it has been shown that

the heat produced by nuclear reactions (further discussed in section 1.3) is insufficient in the

most-observed quiescent quasi-persistent transients to explain the cooling profile [9].

Another big question is that of superburst ignition. Superbursts are similar to X-ray

bursts but last for hours to days with a recurrance period of months to years. They are

about three orders of magnitude more energetic than X-ray bursts (1042 ergs compared to

4

SurfaceCoreSuperfluid neutronsNuclear PastaOuter crust1039 ergs), and therefore cannot be the product of explosive He burning. Hence, superbursts

are theorised to be powered by C burning [10]. Observed superburst light curves have

constrained the superburst ignition depth to much shallower layers than neutron star crust

models predict [11, 12], and require a shallow heat source (likely the same heat source that

explains hotter-than-expected crusts discussed above) for ignition to occur at shallow depths.

Together with a sound understanding of the astrophysics of quasi-persistent transients,

precise knowledge of the nuclear processes that heat and cool neutron star crusts is required

to provide stringent constraints on the strength and origin of the shallow heat source, as well

as superburst ignition. These nuclear processes are discussed in the following section.

1.3 Nuclear processes in neutron star crusts

Several nuclear heating processes can occur in the crust of neutron stars during the accretion

phase when ashes of burning are pushed deeper into the star [13,14]. With increasing depth,

the Fermi energy of the relativistic degenerate electrons becomes high enough for electron

captures to occur on increasingly neutron-rich nuclei in the solid lattice. In even-A chains,

due to the odd-even mass stagger, when the electron capture of A, Z (where Z is even) to

A, Z − 1 becomes energetically possible, the electron capture of A, Z − 1 to A, Z − 2 is also
possible because QEC(A, Z → A, Z − 1) is larger than QEC(A, Z − 1 → A, Z − 2). In the
case shown in Fig. 1.2, the difference between the electron Fermi energy and the electron

capture Q-value is shared between deposited heat (∼25%) and the emitted neutrino (∼75%)
which carries its energy away. However, if there is an excited state in the A, Z − 2 nucleus
that is populated by the electron capture, heat deposition increases as all the energy from

the electromagnetic de-excitation of the excited state is deposited as heat [14].

5

Figure 1.2: Cartoon showing the source of crustal heating from consequtive electron captures
in even-A, even-Z nuclei.

Another source of heat is pycnonuclear, or density-driven, fusion in the inner crust [15].

Continued electron captures in the inner crust lower the Coulomb barrier for fusion reactions.

This, combined with the decreasing distance between nuclei in the solid lattice of the crust,

can trigger fusion reactions that release heat into the crust.

In addition to pycnonuclear fusion and electron capture heating which release on the

order of a few MeV/u into the crust, observations of early cooling indicate that there is

a yet-unidentified strong heat source near the surface of the neutron star [8]. Depending

on the observed source, current models of early cooling require on the order of 1 MeV per

accreted nucleon [16, 17], up to 10 MeV per accreted nucleon [9]. One hypothesis for the

physical origin of this heat source is accretion-induced shear [18]. Infalling material carries

angular momentum to the neutron star which is mostly deposited at shallow depths, leading

to shear between differentially rotating layers and potentially viscous heating.

6

EFA, ZA, Z-1QECEFA, Z-2QEC’Heat + NeutrinosMost recently, it has been proposed that there is heating from the decay of charged

pions produced by high-energy nuclear reactions on the surface of the neutron star during

the accretion phase [19]. Strong gravitational acceleration of infalling material can lead to

nuclear collisions with nuclei at the surface of the neutron star. If the kinetic energy of the

incident particle is above the pion production threshold (∼ 290 MeV), such that the centre-
of-mass energy of the collision is higher than the pion rest mass, then it is possible for pions

to be produced. The decay of π+ produces a muon neutrino and an anti-muon, which itself

decays to a positron, an electron neutrino, and an anti-muon neutrino. The muon neutrinos

are thought to mostly leave the star, but the electron neutrinos are absorbed and heat the

deep crust.

1.4 Urca cooling

In certain cases, electron capture-β decay cycles can form which cool the crust and core

through neutrino emission, or Urca cooling. Urca cooling was first proposed by Mario

Schenberg and George Gamow during a visit to the Cassino da Urca in Rio De Janerio

as an explanation for the rapid cooling of neutron stars following their formation [20]. The

direct Urca process that occurs in neutron stars can be described in Eqn. 1.1. The pro-

duced neutrinos and anti-neutrinos barely interact with the star, and stream freely out of

the system, thus cooling it.

p + e− → n + νe
n → p + e− + ¯νe

7

(1.1a)

(1.1b)

The direct Urca process is possible when the protons, neutrons and electrons are highly

degenerate, such as in the dense environment of the neutron star core, and their Fermi

energies are such that momentum conservation is possible. In certain cases, depending on

the mass of the neutron star and the equation of state, the direct Urca process is forbidden

even in the core because the fermion number densities are not high enough, and the modified

rather than direct Urca process occurs. In the modified Urca process, spectator particles

(denoted A in Eqn. 1.2) are required to fulfil momentum conservation.

A + p + e− → A + n + νe
A + n → A + p + e− + ¯νe

(1.2a)

(1.2b)

Finally, the nuclear Urca process [21] has been understood to occur in white dwarves, but

has recently been reported to occur in the crust of neutron stars [22].

Z

N A + e− →Z−1
Z−1
N +1A →Z

N +1 A + νe

N A + e− + ¯νe

(1.3a)

(1.3b)

In the accreted crust of the neutron star, electron capture processes cause nuclei to become

increasingly neutron-rich as they get pushed deeper into the crust. For a given isobar A

in a zero-temperature crust, at a certain depth, it will exist as a single species Z

N A. As

it sinks, eventually the electron Fermi energy will equal and then exceed the Q-value for

electron capture, and the species will transition to Z−1

N +1A, which will have a distinct and

sharp boundary separating it from the layer of Z

N A material.

However, at non-zero temperature, the electron Fermi surface is no longer mono-energetic

8

and there exists some phase space (within ∼ kBT of the Fermi energy) for electrons produced
by β decay, thus allowing for β decays of Z−1
N A. For this to happen, the β

N +1A nuclei back to Z

decay has to go to the ground state (or a very low-lying state), and the neutrino has to carry

away a small portion of energy so that the electron can be produced at or just below the

Fermi energy, within this window. Instead of a sharp boundary separating the two layers,

there now exists a thin layer of material where Z

N A and Z−1

N +1A co-exist (Fig. 1.3). This layer

is known as an Urca shell, where repeated cycles of Urca processes can occur and emit a

potentially large neutrino luminosity. The Urca cooling rate scales with T 5, therefore with

sufficiently strong heating the Urca shell will effectively lead to a thermal decoupling of the

layers above and below it, acting as a heat sink. This prevents heat produced by the outer

layers to reach the interior of the star, and prevents any heat from deep crustal processes to

reach the surface.

Figure 1.3: Left: Crust composition change boundary at non-zero temperature, showing the
co-existance of A, Z nuclei and A, Z − 1 nuclei in the Urca shell. Right: Crust composition
change boundary at zero temperature, showing the sharp transition boundary with no Urca
shell.

9

A, Z-1A, ZA, ZA,Z-1kTEFEFT ≠0KT = 0K1.5

Impact of Urca cooling on neutron star observables

The impact of Urca cooling on superburst ignition has been assessed [23]. Because the Urca

layer prevents heat produced by nuclear processes deeper in the crust from reaching the

layer of C ignition in the neutron star ocean, it drives the layer of C ignition deeper into the

ocean. The limitation on the amount of nuclear heating that increases the temperature of

the ocean also places a lower limit on the strength of the shallow heat source. Ref. [24] has

also shown that the observed light curve of source MAXI J0556-332 cannot be fit by current

crust models if Urca cooling in present at the strengths expected from the composition of

typical X-ray burst ashes. This was used to constrain the total accreted mass from the

companion star during the accretion phase.

The magnitude of crust Urca cooling can be approximated as

(cid:18) g14

(cid:19)−1

Lν ≈ L34 × 1034 ergs s−1XT 5

9

2

R2
10

(1.4)

where T9 is the temperature in GK, g14 is the surface gravity in 1014 cm−2, R10 is the

neutron star radius in units of 10 km, and L34 is a function only of nuclear properties:

(cid:18)106s

(cid:19)(cid:18)56

(cid:19)(cid:18) QEC

(cid:19)5(cid:18)

f t

A

4 MeV

(cid:19)

(cid:104)F(cid:105)∗
0.5

L34 = 0.87

,

(1.5)

and f t is the comparative half-life of the β-decaying transition, QEC is the electron capture

10

Q-value, (cid:104)F(cid:105)∗ is

(cid:104)F(cid:105)∗ =
and (cid:104)F(cid:105)± ≈

F +F−
F + + F−
2παZ

,

|1 − e(∓2παZ)|

(1.6)

(1.7)

and α is the fine structure constant (≈ 1/137).

In terms of nuclear physics, Eqn. 1.5 shows that the two chief requirements for strong

crust Urca cooling are: (1) a large abundance of the isobar in the ashes of the burst phase

(i.e. a large X); (2) a low f t value, or strong ground state to low-lying state transition during

the β decay. Urca cycles are hindered from forming in even-A nuclei due to the occunce of

two consecutive electron captures. For the second electron capture, the Fermi energy of the

electrons is higher than the β decay Q-value of the A, Z − 2 nucleus, and β decay in this
case is phase space blocked. Hence, though even-A nuclei are typically more abundant in

X-ray burst ashes, Urca pairs tend to form most strongly in odd-A chains [23, 24]. [24] also

demonstrated that Urca cooling has an observable impact on the light curves of quiescent

neutron stars if the crust achieved a temperature of ∼109 K for nuclei with ground state to
ground state electron capture and β-decay transitions with log f t of around 5.

1.6 Motivation for the measurement

The goal of this thesis is to provide nuclear data that allow us to more reliably determine the

strength of Urca cooling in accreting neutron star systems that exhibit X-ray bursts. Mass

61 nuclei are among the most abundant odd-A isobaric chains produced by the rp-process,

largely due to the waiting point at 64Ge, and can be present in X-ray burst ashes up to

11

β decay parent Measured log f t Reference

QRPA prediction

61Ti
61V
61Cr
61Mn
61Fe

-
-
5.1
4.7
7.1

-
-

[26]
[27]
[28]

5.9
4.35

no transition predicted

4.84
4.69

Table 1.1: Measured log f t values for A = 61 nuclei and the QRPA predicted log f t for the
ground state to ground state transitions.

several %. Measured log f t values for ground state to ground state β decay transitions

among the neutron-rich mass 61 nuclei suggest that the A = 61 chain has the potential

to significantly cool the neutron star crust. The experimentally-determined ground state to

ground state log f t values to date and corresponding QRPA predictions [25] are given in

Tab. 1.1. Data are not available for the decays of 61V and 61Ti, and QRPA calculations

predict that the ground state to ground state decay of 61V is the strongest transition in the

chain with the lowest log f t value. However, there are large discrepancies of many orders

of magnitude between measurements and QRPA predictions for 61Fe and 61Cr. Therefore,

experimental data are mandatory to reliably estimate Urca cooling.

The ground-state spins of the neutron-rich mass 61 nuclei are given in Tab. 1.2 [29]. The

spins for Ti-Cr were taken from shell model calculations using the TBLC8 interaction [30],

but are supported by systematics [31]. The spin for Mn was calculated using the extended

pairing-plus-quadrupole model with monopole corrections (EPQQM), which supports the

log f t result from [27] for the transition from the 61Mn ground state to the ground state of

61Fe, indicating an allowed transition. The spin for Fe is from an experiment and supported

by a shell model calculation, both from [32], using a truncated pfg model space [33].

The ground state spins indicate a possible allowed ground state to ground state β decay

transition for 61V and therefore a possible 61Cr-61V Urca pair. The next step is to exper-

12

Element N Z
22
23
24
25
26
27

Ti
V
Cr
Mn
Fe
Co

39
38
37
36
35
34

J π

(1/2−)
(3/2−)
(5/2−)
(5/2−)
(3/2−)
7/2−

Reference

[34]
[34]
[34]
[35]
[32]
[29]

Table 1.2: List of spin/parity assignments for the neutron-rich A = 61 isobars. Assignments
in parentheses are tentative.

imentally determine the log f t value for the β decay of 61V to the ground state of 61Cr.

A previous β-decay study of 61V [36] determined some branchings to excited states in the

daughter nucleus 61Cr, but did not derive a branching to the ground state due to incomplete

information of the 61Cr excitation scheme. The goal of this experiment is to experimentally

determine the ground state to ground state transition strength of the decay of 61V to assess

the viability of the A = 61 mass chain as a strong Urca cooling chain.

1.7 Outline of dissertation

Chapter 2 discusses the experimental technique for measuring β decays and β-delayed ra-

diation and the experimental set-up (detectors and electronics). Chapter 3 discusses the

analysis of the data, including detector calibrations and efficiency measurements, and the

data analysis techniques used for the extraction of the ground state branch of the β decay

of 61V. Chapter 4 details the results from the experiment, including the β decay half-life,

β-delayed neutron emission branch, and the deduced ground state to ground state transi-

tion and f t value. Finally, chapter 5 discusses the astrophysical impact of the experimental

result, as well as other potential Urca cooling candidates.

13

Chapter 2

Experimental Method

This experiment studies the β-decay of 61V with the goal of determining the ground-state

to ground-state transition strength of the decay of 61V to 61Cr. The ground state to ground

state transition is difficult to measure directly because it does not emit any characteristic

radiation in the form of γ rays or neutrons that can be used to constrain the number of such

decays. Furthermore, β-decay electrons are not monoenergetic and thus cannot be used to

discriminate the ground state to ground state transition from other transitions. In contrast,

β-decay feeding to excited states can be identified by the sum energy of the γ rays emitted

in the de-excitation cascade from the excited state to the ground state. The ground state to

ground state feeding intensity can then be determined by subtracting the sum of all feeding

to excited states and the total β-delayed neutron emission branch from the known total

number of decays.

2.1 Overview of the technique

β decay involves the conversion of a proton to a neutron (β+), if the nucleus is overly

proton-rich, or a neutron to a proton (β−), if the nucleus is overly neutron-rich. β decay

has been extensively used in a large variety of nuclear physics experiments. For instance,

it has been used to study the properties of resonances important for astrophysical reaction

rates (e.g. [37]). β decay end-point studies utilise the fact that the electron energy spectrum

14

ranges from 0 keV to the energy difference between the mass of the parent nucleus and

sum of the masses of the electron, electron neutrino, and daughter nucleus to make mass

measurements of nuclei (e.g. [38, 39]). Analysis of the decay radiation also allows for the

reconstruction of the ordering of excitation energies, or level scheme, of the daughter nucleus,

and provides information about the nuclear properties of the daughter nucleus since the

transition strengths depend on the nuclear matrix elements.

There are three different modes of β decay: (1) β−; (2) β+; and (3) electron capture

(EC) and the underlying processes can be expressed as

β− : n → p + e− + ¯νe,
β+ : p → n + e+ + νe,
and EC : p + e− → n + νe,

where p is the proton, n is the neutron, e− is the electron, e+ is the position, νe is the

electron neutrino and ¯νe is the electron anti-neutrino.

β decays follow quantum mechanical selection rules (table 2.1). The increasing suppres-

sion of of the decays as the difference in angular momentum of the initial and final states,

|Jf − Ji|, increases is because large changes in angular momentum carried away by the
electron require the electron to be localised far from the nucleus since the electron’s momen-

tum is relatively small. This scenario is unlikely due to the concentration of the electron

wavefunction close to the nucleus.

There are two types of β decay, the Fermi transition, where the spins of the neutrino/anti-

neutrino and the positron/electron are anti-parallel (∆I = 0), and the Gamow-Teller tran-

sition, where the spins of the neutrino/anti-neutrino and the positron/electron are parallel

15

Class

Allowed

First Forbidden
Second Forbidden
Third Forbidden

∆J ∆π
no
0,1
yes
0,1,2
2,3
no
yes
3,4

Table 2.1: Angular momentum and parity selection rules for β decay

(∆I = 0 or 1). Most transitions are a mixture of Fermi and Gamow-Teller transitions; how-

ever, Fermi transitions only signifiantly contribute to transitions between isobaric analogue

states, and β-decay transitions strengths are in general referred to Gamow-Teller strengths.

This experiment is concerned with β− decay:

Z

N A →Z+1

N−1 A(cid:48) + e− + ¯νe,

(2.1)

where Z

N A is referred to as the parent and Z+1

N−1A(cid:48) is referred to as the daughter. The decay

releases energy equivalent to the difference between the masses of the daughter nucleus,

electron, and electron neutrino and the mass of the parent, known as the Q-value. Ignoring

the mass of the neutrino and the binding energy of the electron to the daughter nucleus,

(cid:20)

(cid:21)

c2,

Q(β−) =

m(Z

N A) − m(Z+1

N−1A(cid:48))

(2.2)

where the masses used are the neutral atomic masses (hence why the electron mass does not

appear). The daughter nucleus, electron, and the anti-neutrino share the energy released

in the β decay. When the β decay populates the ground state in the daughter nucleus, the

energy released is referred to as the reaction Q-value. In the case where the parent nucleus

decays to an excited state of the daughter nucleus, the total energy of the electron and

16

anti-neutrino is simply the difference between the Q-value and the excitation energy

Ke + K¯ν = Q − Ex.

(2.3)

Because this is a three-body process, the energy spectrum of the electron is not single-valued

but rather follows the following distribution (for the simplest case of allowed transitions) [40],

N (Ke) = |Mf|2
2π3¯h7c5

g2(K2

e + 2Kemec2)1/2(Q − Ke)2(Ke + mec2)F (Z(cid:48), pe),

(2.4)

where F (Z(cid:48), pe) is the Fermi function, which takes into account the attraction (repulsion)
of the produced electron (position) to the daughter nucleus with charge Z(cid:48), |Mf i|2 is the
nuclear matrix element, related to the transition strength, and g is a constant representing

the strength of the weak interaction.

In general, β decay will populate a number of states in the daughter nucleus and the

strengths of these transitions, or the feedings, depend on the nuclear properties of the parent

and daughter, and follow the angular momentum and parity selection rules (Tab. 2.1).

The β-decay strength for a particular transition is often represented in terms of the

comparitive half-life or f t value. In terms of the transition half-life t,

f t = ln2

2π3¯h7
g2|Mf i|2m5

ec4 .

The f t value of a specific transition is then

f t = f (Z(cid:48), Q) ×

t1/2
Iβ

,

17

(2.5)

(2.6)

where t1/2 is the parent half-life, f (Z(cid:48), Q) is the Fermi integral, and Iβ is the β branching,

or the fraction of total β decays that undergo the specific transition.

The log f t value is a measure of the intrinsic physical properties of the decay and can be

determined experimentally from the β-decay branching, Iβ, and the Q-value of the transition.

Systematic comparisons across many nuclei show that the f t value is an indication of the

“forbidden”-ness of the transition [41]. The f t value is often tranformed into log(f t) because

of the large range of f t values.

2.2 Bateman equations

The rate of β-decay of a parent nucleus Z

N A to its daughter is described by first-order

kinematics, where the decay rate is proportional to the number of parent nuclei, N , at a

given time t:

dN (t)

dt

= −λN (t),

where λ is defined as the decay constant. Integration of the decay equation gives

N (t) = N0e−λt

(2.7)

(2.8)

where N0 is the initial number of parent nuclei at t = 0. The half-life of the nucleus is defined

as the time it takes for half of the nuclei to decay and is related to the decay constant λ:

(2.9)

t1/2 =

ln2
λ

.

18

For N(cid:48) daughter nuclei that are being produced by β decays of parent nuclei and are them-

selves β decaying, the net rate of change is given by the sum of the rate of production by β

decay of the parent and the rate of destruction by its own β decay. The rate equation for

such a species can be expressed as

dN(cid:48)
dt

= λN − λ(cid:48)N(cid:48).

(2.10)

The amount of nuclei of the parent and daughter, and any subsequent decays from the

daughter nuclei, are described in general by the Bateman equations [42]:

N (t) = N0e−λt
N(cid:48)(t) = N(cid:48)0e−λ(cid:48)t − N0

(cid:2)e−λ(cid:48)t − e−λt(cid:3),

λ

λ(cid:48) − λ

The general solution to the kth decaying product is [43]:

Nk(t) =

Aje−λj t

j=1

l=j

k(cid:88)

l=k−2(cid:89)

−λl+1
λl+1 − λj

,

(2.11)

(2.12)

(2.13)

where Aj are constants related to the initial quantity of the jth species and λj are the decay

constants of the jth species.

2.3

β-delayed γ decay

β decay of a parent nucleus can populate, in addition to the ground state, excited states

in the daughter nucleus. For low-energy states below any particle emission thresholds, the

dominant decay mechanism is γ-ray emission to a lower-lying state. Theoretically, the β-

19

feeding intensities to each excited state in the daughter can be calculated by determining

the (efficiency-corrected) number of γ rays emitted from a given state, and the number of

γ rays that feed the state. The transition strength to the daughter ground state is then

simply 100% less the sum of the transition strengths to the excited states. Practically, this

method requires a full understanding of the level scheme of the daughter nucleus so that

observed γ rays can be correctly assigned to corresponding transitions between states in the

daughter nucleus. To do so, the γ-ray detector used has to have a high-enough resolution

to be able to isolate individual γ-ray energies. The use of high-resolution Ge detectors in

β decay experiments trades the ability to distinguish individual transitions for efficiency.

For nuclei where the level density is low, or where the low Q-value limits the number of

possible states which can be populated by β decay, such a trade-off is acceptable. For nuclei

which have large β-decay Q-values where the number of possible γ transitions is large, or

nuclei where level densities are high, the method fails due to the difficulty in deriving a

complete level scheme. For low-efficiency, high-precision detectors, it is likely that only the

strongest transitions are detected, and that the weak transitions which can still constitute

a non-negligible fraction of the β-decay scheme will be missed. This is especially true in

γ decays involving high multiplicity cascades, where the likelihood of detecting the entire

cascade diminishes with each additional γ ray, or high-energy γ rays, where the efficiency of

detecting each γ-ray is relatively low. The β-feeding intensity to a given state i is determined

as the difference between the number of γ rays depopulating i and the number of γ rays that

populate i from higher-lying states. A large number of weak β-decay transitions to higher-

lying states, which are hard or impossible to detect, can still lead to significant population

of i by γ decay. Missing these weak transitions thus leads to a systematic overestimation of

the β-feeding intensity to i.

20

This effect is known as the Pandemonium effect [44], and has been a long-standing prob-

lem in β decay studies. The effect was first studied using a Monte Carlo simulation of the

β decay creating a fictional nucleus “Pandemonium” in [44], and it was demonstrated that

with the exception of light nuclei with low Q-values, it is likely that the Pandemonium ef-

fect will manifest itself in high resolution γ ray spectroscopy studies, leading to unreliable

determinations of β strengths.

We employ a method called Total Absorption Spectroscopy (TAS) or Total Absorption

Gamma Spectroscopy (TAGS) to address this effect, using a large, high-efficiency Summing

NaI (SuN) detector to provide 4π coverage of the source of radiation. Though TAS detectors

often have low energy resolution, their extremely high efficiency enables the measurement

of even the weakest branches in the β decay. This method focuses on measuring the total

energy of γ ray cascades rather than indiviual γ transitions. In this case, instead of separately

identifying populating and depopulating transitions for a given state, the β-feeding intensity

is obtained directly from the number of cascades depopulating a state.

2.4

β-delayed neutron emission

When the decay Q-value is larger than the neutron separation energy Sn, it is possible for

the decay to populate states above the neutron separation threshold that subsequently emit

neutrons. This is known as β-delayed neutron emission. Because this is a two-body process,

the neutron will be emitted with energy

En = Ex,i − Ex,f − Sn,

(2.14)

21

where Ex,i and Ex,f are the excitation energies in the emitter and the produced nucleus

(hereafter referred to as the neutron daughter) respectively, and Sn is the neutron separa-

tion energy. The sum of all neutron-emission probabilities is referred to as the total β-delayed

neutron emission branch or Pn value. Since the decay to the ground state of the neutron

daughter also does not emit any characteristic γ radiation and therefore is otherwise indis-

tinguishable from the decay to the ground state of the daughter, it is imperative to know the

Pn value to correctly determine the ground state to ground state transition to the daughter.

2.5 Experimental Description

The experiment, NSCL experiment E14041, took place at the National Superconducting

Cyclotron Laboratory (NSCL) between the 8th and 15th of August 2015. The purpose of the

experiment was to determine the ground state to ground state transition strength in the β

decay of 61V to 61Cr; it involves the use of high-efficiency detector systems to determine the

total decay strength to the excited states. The set-up to measure the radiation from the beta-

decay of 61V consisted of (i) a set of Si PIN detectors, which provided particle identification

from energy loss and flight time between the PIN detectors and the Image 2 scintillator of the

A1900; (ii) a Si Double-Sided Silicon Strip Detector (DSSD) for implant and decay energy

loss and location of the implants and decays; (iii) a NaI(Tl) Total Absorption Spectrometer

(TAS) for the measurement of β-delayed γ ray emission and; (iv) a neutron long counter

system for the measurement of β-delayed neutron emission.

22

2.5.1 Beam delivery from CCF and A1900

The primary beam was a 35 pnA 82Se beam at 140 MeV/u , impinging on a Be target,

producing a cocktail beam that was purified by the A1900 fragment separator. 82Se was

selected based on LISE++ [45] calculations because it produced a combination of the highest

rate and purity of 61V in the cocktail secondary beam.

The A1900 fragment separator [46, 47] consists of a series of four magnetic dipoles that

discriminate between beam components by their momentum-to-charge ratio and also has an

additional 24 magnetic quadrupoles for beam focusing. The Image 2 (I2) position is located

between the second and third dipoles; at this position, there was a plastic scintillator with

a thickness of 254 µm as well as an Aluminium wedge with 0◦ thickness of 450 mg/cm2.

The plastic scintillator provided time-of-flight information, acting as the ‘stop’ signal; to do

this, the signals from the scintillator were time-delayed such that they reached the Time-to-

Amplitude Converter (TAC) after the ‘start’ signal from the experimental end station. This

was done because the separation of unwanted beam by ion optic components downstream

of the I2 scintillator meant that only a small fraction (0.1-0.01%) of beam particles incident

on the scintillator were transmitted to the experimental end station.

In the case of this

experiment, the rate at the I2 scintillator was ∼10,000 pps, whereas the rate at the first
detector at the experimental set-up was more than two orders of magnitude lower. The plastic

scintillator was read out by two different photomultiplier tubes (PMTs) located on opposite

sides of the scintillator, referred to I2N and I2S. The time difference between the firing of

these two PMTs gave the position along the dispersive plane for momentum corrections.

Particles travelling through a magenetic dipole with a constant magnetic field obey the

23

equation of motion,

Bρ =

mv
q

,

(2.15)

where B is the magnetic field strength, ρ is the radius of curvature, mv and q are the

momentum and charge of the particle respectively, and Bρ is collectively defined as the

magnetic rigidity. For light nuclei, in this case 61V, it is possible for the nucleus to be fully

stripped of its electrons such that q is equal to the nuclear charge Z of the nucleus. Fragments

produced by the primary beam impinging on the Be target that are transported to the A1900

have a limited velocity range. The A1900 fragment separator transports only particles with

a fixed Bρ (within some percentage acceptance of up to ±2.5%), thus allowing for m/Z
selection. At the I2 position, the fragments passed through an Aluminium wedge, and lost

energy depending on the fragment nuclear charge. At the beam energies of ∼100 MeV/u,
the energy loss of heavy ions in matter depends on the thickness of the material, the energy

of the ion, and the charge of the ion in the following manner:

dE
dx ∼

Z2
E

.

(2.16)

At 100 MeV/u, the energy loss through a thin foil is insignificant relative to the total energy,

thus the right side of the above equation can be considered to be constant, and the total

energy loss through the material can be well approximated by

∆E ∼

tZ2
E

,

(2.17)

where t is the thickness of the material. Because this energy loss is Z dependent, the change

in Bρ is also Z dependent and leads to a broader Bρ distribution following interaction with

24

the wedge. This allowed for further purification of the beam, as the second set of A1900

dipoles also have a fixed Bρ acceptance. The shape of the wedge in this case was chosen

to ensure achromatic focus to maximise transport of the secondary beam to the end of the

A1900. For the experiment, the A1900 delivered a secondary beam of ∼36% 61V, with only
three major beam contaminants 62Cr, 64Mn and 65Fe.

2.5.2 Particle identification

To distinguish between the beam components, particle identification was done on a event-

by-event basis with the δE-TOF method, using the energy loss through the Si PIN detector

at the experimental station to discriminate by nuclear charge, and the time-of-flight from the

I2 plastic scintillator at the focal plane of the A1900 to the Si pin detector to discriminate

by velocity. The particle identification was also further improved through a momentum

correction ascertained from the position along the dispersive axis where the beam particle

hits the I2 scintillator, allowing for better separation between isotopes of the same element.

2.5.3 Detectors

The experiment utilized many different types of detectors, and their characteristics and

purpose will be explained.

2.5.3.1 NERO

The Neutron Emission Ratio Observer (NERO) [48] is a neutron long counter system con-

sisting of 44 BF3-filled tubes and 16 3He-filled tubes housed in a high-density polyethylene
matrix (ρ=0.93(1) g/cm3) 60×60×80 cm3 in size. The matrix has a cylindrical bore of radius
11.4 cm, which was designed to hold the NSCL Beta Counting System [49]. The neutron

25

counters are co-axial to the beam axis and centred on the detector located in the target

position in the BCS chamber. The 60 detectors are arranged in 3 concentric rings, with the

innermost ring comprising of the 16 3He detectors, and the outer two rings comprising of

the remaining BF3 counters.

Figure 2.1: Left: Layout of the NERO tubes. Right: Cross-section schematic of NERO.
Adapted from [50].

Long counter systems operate on the principle of neutron-induced reactions by neutrons

thermalised by a moderating material. The cross-section for neutron-induced reactions at

low energies depends inversely on the velocity of the neutron

σ ∝

1
√E ∝

1
υ

(2.18)

due to the lack of a Coulomb interaction and the dominance of s-wave capture. For max-

imising efficiency, it is thus advantageous for the neutron to have as low energy as possible.

26

BF3Proportional Counters3He Proportional CountersNeutrons emitted from the centre of NERO are moderated by interactions with the polyethy-

lene. The energy loss of a neutron collision with a nucleus of mass A is given by

Ef
Ei

=

A2 + 2Acosθ + 1

(A + 1)2

(2.19)

where Ef and Ei are the final and initial energies of the neutron respectively, and θ is the

scattering angle. In the limit where A is large, the quadratic terms dominate and

Ef
Ei ∼

A2

(A + 1)2 ∼ 1.

(2.20)

Therefore it is ideal to choose a moderating material with as low mass as possible such that

fewer scattering events are needed to thermalise the neutron; Polyethylene is an ideal mod-

erator due to the high density of protons. As the neutrons are moderated, they ultimately

induce the reactions 10B(n, α)7Li and 3He(n, p)3H in the BF3 and 3He tubes respectively.

The produced charged particles then ionise the gas in the tube and the voltage difference

applied through the tube triggers and extracts electron cascades (hence the term ‘propor-

tional’ counters), indicating a neutron detection. Long counters have the advantage of high

efficiency for low-energy neutrons, but the disadvantage of losing all initial momentum infor-

mation of the neutron. The NERO detector was designed to optimize the efficiency for the

detection of neutrons lower than 2 MeV. The detector was commissioned in 2005 and cali-

brated using a series of resonant and non-resonant reactions, as well as a 252Cf source [48].

Monte Carlo N Particle (MCNP) [51] simulations of the efficiency curve (as a function of

neutron energy) well-reproduced the trend of the experimentally-determined efficiency curve

seen from data, but showed a systematic over-estimation of the efficiency. Thus, the MCNP-

27

simulated efficiency curve was scaled to the measured efficiency values to obtain the detector

efficiency curve at low neutron energies.

2.5.3.2 SuN

The Summing NaI (SuN) detector [52] is a total absorption spectrometer that is primarily

used as a γ ray detector. A summing detector was chosen for the experiment to resolve the

issue of the Pandemonium effect. Because the β decay transition strengths are extracted

from the size of the sum peak at a given energy, it is important for the summing efficiency

to be as high as possible. SuN consists of 8 half-annular crystals of Tl-doped NaI, forming a

barrel 1ft in length and diameter (Fig. 2.2). Total absorption spectrometers require several

properties that the design of SuN takes into account. NaI was chosen because of the ease

of producing large monocrystalline volumes, this is simply so that the interaction volume

is large, increasing the efficiency. The crystal is doped with Tl, introducing states into the

band gap between the conduction and valence bands of pure NaI. These intermediary states

are desirable because the wavelengths of photons produced overlap well with the response of

photomultiplier tubes.

SuN has several advantages over more precise Germanium detectors for this experiment

as the number of transitions is predicted to be extremely high due to the large reaction

Q-value and high level density [53], resulting in a significant Pandemonium effect. Firstly,

since the level scheme of the daughter nucleus of the 61V β decay, 61Cr, is only known up

to ∼2.26 MeV compared to the β-decay Q-value of ∼12 MeV, individually detected γ rays
may not easily be associated with a particular nuclear transition. Secondly, there are likely

to be a number of weak transitions to states in 61Cr which themselves can decay through a

multitude of different cascades, and Ge detectors simply do not have the intrinsic efficiency to

28

Figure 2.2: Left: Schematic of SuN. Right: Lengthwise cross-section of SuN. Adapted from
[52]

measure every one of these transitions. SuN, with its high geometric and intrinsic efficiency,

is better suited for this measurement because summing detectors are designed to measure

the total energy of an entire γ-ray cascade (or sum peak), rather than individual transitions.

The total absoprtion technique is demonstrated using the decay of 60Co to stable 60Ni.

This is an ideal case as the decay scheme is simple due to the low reaction Q-value of 2.8228

MeV and the low density of states at low energy in 60Ni. There are only three excited states

which can be populated by the β-decay; the first 2+ excited state at 1332.5 keV, the second

2+ excited state at 2158.6 keV, and the first 4+ excited state at 2505.7 keV. Of these three

states, the β-feeding intensity to the 4+ state dominates (99.88%) since the ground state of

60Co has J π = 5+. The remainder of the decays will populate the 1332.5 keV state, while

there is virtually no population of the 2158.6 keV state. In this example, we will focus on

the γ decays following a β decay to the 2505.7 keV state.

29

Figure 2.3: The total absorption (solid blue) and sum of segments (dashed black) spectra
for a 60Co source.

The 2505.7 keV state can decay directly to the ground state or to the first or second

excited 2+ states. The predominant branch is the cascade decay through the first excited

state, with two γ rays of 1173.2 keV and 1332.5 keV. The cumulative spectrum of the indi-

vidual scintillator segments in SuN, hereafter referred to as the sum of segments spectrum,

is shown in Fig. 2.3.

The two individual peaks at 1332.5 keV and 1173.2 keV dominate the spectrum. The

small peak at 2505.7 keV demonstrates the much weaker branching of the direct to ground

state transition, or the case where both γ rays in the spectrum are detected in the same

crystal. The total absorption spectrum is constructed by adding together the total energy

detected in each segment for each γ ray event.

In the total absorption spectrum for the

30

Energy (keV)50010001500200025003000Counts / keV 0100002000030000400005000060000Total AbsorptionSum of segmentssame 60Co decay, the peak at 2505.7 keV dominates, with smaller peaks at 1332.5 keV and

1173.2 keV due to incomplete summing when one of the γ rays is missed.

2.5.3.3 Double-Sided Strip Detectors (DSSDs)

Nuclei in the secondary beam delivered to the experimental area were implanted in the

DSSD and subsequently decay, emitting a β decay electron which can also be detected by

the DSSD. The DSSD used for the NERO portion of the experiment (hereafter referred to

as the BCS DSSD) was a Micron Semiconductor BB1 (979 µm), with each side of the DSSD

segmented into 40 strips with ∼1 mm pitch, for a total of 80 strips and an active area of 39.90
× 39.90 mm2. The front and back sides of the DSSD are segmented orthogonally, creating
1600 1 mm2 pixels. Each channel is read out by a Multi-Channel Systems CPA-16 dual-gain

pre-amplifier, for a total of 160 channels, allowing the detection of both the implanted ion

(low gain, GeV range) and the β-decay electron (high gain, MeV range). The DSSD used

for the SuN portion of the experiment (hereafter referred to as the miniDSSD) was a Micron

Semiconductor BB8 type (1030 µm), with each side of the DSSD segmented into 16 strips

with 1.25 mm pitch, forming a total of 32 strips and an active area of 20.0 × 20.0 mm2;
each strip is read out by a Multi-Channel Systems CPA-16 dual-gain preamplifier. Similar

to BCS DSSD, the front and back strips are segmented orthogonally, forming a total of 256

pixels.

31

2.6 Data Acquisition

2.6.1 Digital Data Acquisition System

The signals from the detector systems in the experiment were processed with the NSCL

Digital Data Acquisition System (DDAS) [54, 55]. NSCL DDAS utilises the XIA digital

gamma finder class of electronics, currently all of the Pixie-16 (16 channel) type. Each

channel is FPGA-programmable, and can independently read out a pulse arrival time and

pulse-processed energy. In total, 24 100 Mega-sample per second (MSPS) Pixie-16 modules

were used in a three-crate system. Each module also has the ability to transmit and receive

another module’s clock signal, allowing for a system-wide timing synchronisation to within

one clocktick (10 ns). Each DDAS event is stored as four 32-bit words. An annotated

example event is given in Fig. 2.4. The first 32 bits store the crate and channel information

and the event length. The next 32 bits store the least significant bits of the timestamp in

units of clock ticks. The third 32 bits has two 16 bit segments, with the first recording the

most significant bits of the timestamp in units of clockticks, for a total of a 48-bit timestamp

(∼782 hours), and the second recording the constant fraction discriminator (CFD) time for
sub-timestamp clock precision. The final 32 bits also has two 16 bit segments, with the first

storing the pulse-processed energy and the second storing the trace length (if recorded).

DDAS has an advantage over analog electronics systems in terms of throughput. The

vast majority of analog acquisition systems, when triggered, will store the peak point of

the signal in a capacitor, which is then converted to a digital value for the data acquisition

system. When this conversion process occurs, the analog system will be in the interrupt

state and cannot accept more signals, a period of time known as the ‘dead time’ of a system.

Digital electronics do not require such a conversion, and its dead time is mostly determined

32

l o n g

Event 56 b y t e s
0038 0000 9bb0 01 f c 0000 0000 0002 0000
0020 0000 0000 0000 0020 0000 001 e 0000
000 c 0000 00 f a 0 f 0 e 42 ac 0008 9376 003 f
0000 0000 0017 0000

0038 0000

0000 0000

0020 0000

0020 0000

9bb0 01 f c

0002 0000

0000 0000

001 e 0000
000 c 0000 00 f a 0 f 0 e
42 ac 0008

0000 0000

9376 003 f

0017 0000

e v e n t
l e n g t h = 56 b y t e s
timestamp = 33332144 ns

data s o u r c e = s o u r c e 2
fragment

l e n g t h = 32 words

l e n g t h = 32

i d e n t i f i e r

timestamp

fragment
data type = 30 ( p h y s i c s e v e n t )
DDAS f i r m w a r e
4 word evt ,
l o w e s t b i t s o f
t o t a l
e n e r g y = 23 ADC u . ;

timestamp = 4166518 c l o c k t i c k s
t r a c e l e n g t h = 0

c r a t e 2 , mod 1 0 , ch 12

Figure 2.4: Example of an event in the DDAS data stream. The top panel shows the event
as it is recorded in the data stream. The bottom panel shows the same event with each
separate component commented out.

33

by the length of the filter used to calculate if a trigger is accepted or not. This is useful for

a detector such as SuN, which in self-trigger mode will have thousands of counts per second

just from room background. Another advantage of DDAS is the ease with which it can be

set up, especially if the filter parameters are already known from previous calibrations or

experiments (assuming the pre-amplifiers are the same).

The input traces are analysed using a short filter, called the trigger or fast filter, that

determines if a rising edge of a signal is detected. DDAS uses a type of filter called a trapezoial

filter. A trapezoidal filter is characterised by two windows with length L separated by a flat

top time G. The application of the filter subtracts the signal heights in the first section

of length L from the signal heights in the second section of length L. The advantage of a

trapezoidal filter over a triangular filter (where G = 0) is that it avoids summation over the

region where the signal height is changing rapidly. Consider a pulse with some height H-

the determination of H by DDAS uses a simple subtraction of the points before the pulse

trigger and after the pulse trigger to determine H. For a trapezoidal filter with rise time L

and gap time G, the signal height H is found by the following equation:

k(cid:88)

k−L−G(cid:88)

Hi

(2.21)

LHk =

Hi −

k−L+1

i=2L−G+1

where k is a signal point. This procedure is repeated for every new signal point k until the

filter threshold is passed. If the trigger threshold set in DDAS is passed by the output of the

trigger filter, it is timestamped and the trace passes through a longer trapezoidal filter, called

the energy or slow filter. The output of the energy filter at time PEAKSAMP (determined

only by parameters of the energy filter) after the trigger point is then stored as the energy

value of the event. An example of filter output of a signal is given in Fig. 2.5.

34

Figure 2.5: Example of a trace (red diamonds), the trigger filter output (black circles), and
the energy filter output (blue triangles) from a representative DSSD high gain signal. The
energy filter output has been scaled down to fit on the same scale as the trigger filter output.
The trigger filter parameters are L = 80 ns and G = 500 ns. The energy filter parameters
are L = 100 ns and G = 700 ns.

35

-10-50510152025303540400450500550600650500100015002000ADC OutputFilter OutputTime (ns)Signal TraceTrigger Filter OutputEnergy Filter OutputEnergy Sampling PointTrigger ThresholdPEAKSAMPTrigger PointWhen determining which filter parameters are best for a signal, the following guidelines

were useful: (a) The ‘flat top’ time of the trapezoidal filter should be approximately the

rise time of the signal; (b) the rise time of the trigger filter is primarily determined by the

signal-to-noise ratio, and the longer the trigger filter rise time, the more baseline of the

signal is averaged over such that a lower trigger threshold can be set without triggering on

noise. The trade-off by choosing a long filter rise time is that the effective dead-time of the

system increases with the length of the trigger filter; (c) the rise time of the energy filter will

determine the energy resolution of the slow filter.

Finally, another important DDAS parameter is τ , the decay time of the signal. Due to the

high trigger rates in the experiment, signal pile-up occurs where the signal does not return

to the baseline before the second pulse arrives. Therefore, it is necessary to know the extent

to which the first signal has decayed or decreased for an accurate baseline subtraction. As a

result, the position of the energy peak in ADC units is fairly sensitive to τ . In contrast, the

resolution is less sentitive to τ . For the experiment, the filter parameters were optimised for

each channel individually and τ was obtained by fitting signal traces.

2.6.2 NSCLDAQ

The data acquisition used during the experiment was the NSCL Data Acquisition suite

of softwares (NSCLDAQ) which is well-suited for processing and merging data flows from

different sources. This capability was especially relevant for the experiment as there were

three separate DDAS crates read out by three separate computers. NSCLDAQ provides

flexibility by allowing each individual crate to run its acquisition (termed ‘readout’) inde-

pendently (useful for troubleshooting), or to be controlled by a master system that enforces

time-ordering of events from different sources. In a multi-crate system, each crate has its

36

own onboard computer (spdaq) device which is read out independently of each other. The

on-board buffer acquires data and is polled continuously by readout, and upon hitting a

user-defined threshold, the data are transferred to a ringbuffer that is specific to each spdaq

device or data source. Each data source is subsequently read out into a ring buffer or cir-

cular buffer, termed within the NSCLDAQ system as a ‘raw ring’. The advantage of ring

buffers for continuous data acquisition is that it easily preserves a first-in first-out (FIFO)

queue without pointer reassignment, such that event triggers that occur first temporally are

also read from the ring buffer first in the data stream. Each raw ring is then fed to the

NSCLDAQ on-line event builder, a system designed to merge data from different sources in

a time-ordered fashion. A data packet from a raw ring is wrapped in a header which provides

information on the data source and the global timestamp (compared to system clockticks,

which is what raw data usually stores) such that systems with different clock frequencies can

be run. The second part of the NSCLDAQ event builder is the glom software, which collects

all triggers occuring within a user-defined correlation time into an event.

2.6.3 Defining a physics event

The use of digital data acquisition allows for the timestamping of each accepted trigger.

Instead of relying on external triggers, triggers are gathered into groups defined by a time

period, similar to the glom software in the NSCLDAQ event builder. A group of triggers is

hereafter referred to as a physics event, meaning that the triggers originate from the same

physical event such as a beam particle being stopped or a β decay. In this manner, triggers

from SuN or NERO that follow the detection of a DSSD signal are grouped together with the

DSSD trigger. In the case of the NERO portion of the experiment, this coincidence window

is defined to be 200 µs to accomodate the moderation time of neutrons in NERO (discussed

37

in section 3.1.1.1). In the case of the SuN portion of the experiment, the coincidence window

was defined to be 300 ns to minimise the contribution of background γ rays.

2.7 Experimental End Station

The experiment was run in two segments, first with the beam focused on the DSSD centred in

NERO (9.8 hours) and then on the miniDSSD centred in SuN (90 hours). The most upstream

part of the end station consisted of a cross containing (from upstream to downstream) two

Si PIN detectors and passive beam degraders. SuN was located downstream of the cross and

NERO was downstream of SuN. Though the two detectors were not used simultaneously,

this configuration was chosen to optimise the use of beam time. 8 hours were allocated

following the NERO run to remove the NERO target chamber and insert the SuN target

(different to the NERO target) in the centre of SuN. To achieve such a rapid switchover time,

both SuN and NERO were set up initially and an empty beampipe connected the upstream

cross to the NERO target chamber. Once the NERO measurement was completed, the SuN

miniDSSD was inserted into the beam pipe in the centre of SuN and the SuN measurement

was subsequently conducted. Because the two segments only share the two PIN detectors in

common and essentially function as two independent end stations, the set-up for the NERO

and SuN runs will be described separately.

2.7.1 NERO set-up

A schematic of the NERO set-up is shown in Fig. 2.6, and a table of the detectors used

along with their characteristics is given in Tab. 2.2.

The passive degraders were placed downstream of PIN2 in the PIN stack so that the

38

Figure 2.6: A cartoon showing the components of the set-up for the NERO portion of the
experiment.

PINs would not have to be moved when the passive degraders were changed for the SuN run.

PIN3 and PIN4 were read out by low-gain pre-amplifiers for additional particle identification

information (eventually not used for this function) and for determining transmission of the

secondary beam through to the DSSD. PIN5 was read out by a high-gain pre-amplifier as

a secondary light particle veto, but this information was not used in the analysis. A Si

Double-Sided Strip Detector (DSSD) was at the target position at the centre of NERO. A Si

Single-Sided Strip Detector (SSSD) was located directly downstream to veto particles which

39

SuNBCS StackNEROSi PIN stackDetector

Thickness (µm) Voltage (V)

Si PIN Stack

PIN1
PIN2

Al Degrader

525
1041
250

40
75
-

Detector

Thickness (µm) Voltage (V)

BCS Stack

PIN3
PIN4
PIN5
DSSD
SSSD

488
503
991
979
982

Scintillator

∼ 25400

NERO

50
-30
-150
280
-210
-850

Gain
Low
Low

-

Gain
Low
Low
High

Low and High

High
High

Detector

Type Voltage (V)
3He
NERO A 1-4
3He
NERO B 1-4
3He
NERO C 1-4
3He
NERO D 1-4
NERO A 5-15 BF3
NERO B 5-15 BF3
NERO C 5-15 BF3
NERO D 5-15 BF3

1130
1130
1080
1350
2620
2620
2620
2620

Table 2.2: List of detectors and properties used in the NERO set-up.

did not lose all their energy in the DSSD (termed ‘punchthroughs’), followed by a thick

plastic scintillator which was used as the primary light particle veto. Light particles such

as He ions that can be part of the fragment beam deposit approximately the same energy

in the silicon detectors as β decay electrons and can mimic decay signals. The thick plastic

scintillator enables the differentiation of β decay electrons from light particles, as the light

particles will deposit far more energy in the scintillator than the maximal β decay electron

energy of 11.95 MeV, which was chosen as the upper threshold above which all β-like signals

in the DSSD are vetoed.

40

The data acquisition electronics are shown in Figs. 2.7 and 2.8. A coincidence between

a signal from a front strip and a back strip of the DSSD was required for a valid signal to be

read out. The DDAS signals were passed to DDAS breakout modules, which were used to

extract a 16-channel OR over all the channels in a module. The TTL signals that contain the

AND signals from the front and back strips were then passed back into the DDAS breakout

modules as an external trigger for DDAS. For all other detectors, the signals were processed

in self-trigger mode, and did not require any external validation. This was possible because

the lack of dead time of DDAS enabled the recording of high trigger rates.

41

Figure 2.7: BCS/NERO electronics logic.

42

PIN 3PIN 4Pre-ampDDAS (c1,m7,ch4)DDAS (c1,m7,ch5)PIN 3PIN 4PIN 1PIN 2Pre-ampAmplifierDDAS (c1,m8,ch3)AmplifierPIN 2CFDFIFOTACTACPIN 1Start (PIN 2)Cyc. RF or FP Scint. StopStartCyc. RFStopDDAS (c1,m7,ch2)DDAS (c1,m7,ch4)TACStartFP ScintillatorDDAS (c1,m7,ch3)StopDDAS (c1,m8,ch2)PIN 1Pre-amp (Quad A)Pre-amp (Quad B)Pre-amp (Quad C)Pre-amp (Quad D)NERO Quad A (15 ch)DDAS (c2,m1,ch1-15)DDAS (c2,m2,ch1-15)DDAS (c2,m3,ch1-15)DDAS (c2,m4,ch1-15)NERO Quad B (15 ch)NERO Quad C (15 ch)NERO Quad D (15 ch)SSSD 1 (16 ch)Pre-ampDDAS (c1,m13,ch1-16)DDAS (c2,m13,ch1-16)High-gainLow-gainPIN 5Pre-ampDDAS (c1,m7,ch5)TennelecTC178TennelecTC178mesytecMPR-1MCS CPA-16 dual gainTennelecTC241  TennelecTC241  Abbreviationsc –crate numberm –module numberch–channel numberCFD –constant fraction discriminatorFIFO –fan-in/fan-outTAC –time to amplitude converterFigure 2.8: BCS DSSD electronics logic.

43

BCS DSSD (40 ×40)DSSD front pre-amp 3Front HIFront LODDAS (c1,m1,ch1-16)DDAS (c1,m7,ch1-16)DDAS (c1,m2,ch1-16)DDAS (c1,m8,ch1-16)DDAS (c1,m3,ch1-8)DDAS (c1,m9,ch1-8)DDAS breakoutDDAS breakoutDDAS breakoutDDAS breakoutDDAS breakoutFIFOTTL to NIMTTL to NIMAND 1AND 2NIM to TTLDSSD front pre-amp 2DSSD front pre-amp 1DDAS breakoutFIFONIM to TTLFIFOFIFODSSD back pre-amp 3Back HIBack LODDAS (c1,m4,ch1-16)DDAS (c1,m10,ch1-16)DDAS (c1,m5,ch1-16)DDAS (c1,m11,ch1-16)DDAS (c1,m6,ch1-8)DDAS (c1,m12,ch1-8)DDAS breakoutDDAS breakoutDDAS breakoutDDAS breakoutDDAS breakoutFIFOTTL to NIMTTL to NIMAND 1AND 2NIM to TTLDSSD back pre-amp 2DSSD back pre-amp 1DDAS breakoutFIFONIM to TTLFIFOFIFONon-InvertingInvertingi4o6MCS CPA-16 dual gainMCS CPA-16 dual gainMCS CPA-16 dual gainMCS CPA-16 dual gainMCS CPA-16 dual gainMCS CPA-16 dual gain2.7.2 SuN set-up

For the SuN set-up, the beam line vacuum was vented and the beam tube and the BCS

chamber were removed so that the SuN miniDSSD could be installed. Behind the miniDSSD

was a Si barrier detector which functioned as a veto for the light particles and punchthroughs.

At the same time, the passive degraders in the PIN flange in the cross located upstream

were replaced for a thicker set of 2300 µm thickness, shown by LISE to provide the optimal

implantation depth of 61V. The list of detectors and degraders in the SuN set-up is listed in

Tab. 2.3. A schematic of the SuN layout is shown below in Fig. 2.9.

Detector

PIN1
PIN2

Al Degrader

Si PIN Stack
Thickness (µm) Voltage (V)

525
1041
2300

SuN Stack

40
75
-

Detector

Thickness (µm) Voltage (V)

DSSD
Veto

979
982

280
-210

Table 2.3: List of detectors and properties used in the SuN set-up.

The data acquisition electronics are shown in Fig. 2.10. For a valid SuN signal to be

recorded, the three PMTs in each segment had to fire within a 0.5 µm coincidence window.

The summing module acts as a 24 channel OR for the CFD to get the time of any SuN

triggers. Similar to that of the BCS DSSD, there was also a coincidence condition for the

miniDSSD where a signal had to be recorded from both a front strip and a back strip to be

recorded. There were no external triggering conditions for any of the other detectors.

44

Figure 2.9: A cartoon showing the components of the set-up for the SuN portion of the
experiment. Here, the BCS chamber has been removed from the set-up, indicated by the
hollow bore of NERO.

45

NEROSuNSi PIN StackminiDSSDand Si vetoFigure 2.10: SuN electronics logic.

46

SuN(24 ch)AmplifierDDAS (c1,m1, ch1-12)DDAS (c1,m2, ch1-12)Summing ModuleMiddle PMTsCFDTACPIN 1PIN 2Pre-ampDDAS (c1,m8,ch2)AmplifierDDAS (c1,m8,ch3)AmplifierPIN 1PIN 2CFDFIFOTACTACPIN 1Start (PIN 2)Cyc. RF or FP Scint. StopStopStartStartCyc. RFStopDDAS (c1,m7,ch1)DDAS (c1,m7,ch2)DDAS (c1,m7,ch4)SuNvetoAmplifierDDAS (c1,m8,ch1)SuNDSSD (16 ×16)DSSD front pre-ampDSSD back pre-ampDDAS (c1,m3,ch1-16)DDAS (c1,m4,ch1-16)DDAS (c1,m5,ch1-16)DDAS (c1,m6,ch1-16)Front HIFront LOBack HIBack LODDAS breakoutDDAS breakoutDDAS breakoutDDAS breakoutTTL to NIMTTL to NIMANDAND16 chOR16 chOR16 chOR16 chORNIM to TTLTACStartFP ScintillatorDDAS (c1,m7,ch3)StopNIM to TTLAbbreviationsc –crate numberm –module numberch–channel numberCFD –constant fraction discriminatorFIFO –fan-in/fan-outTAC –time to amplitude converterTTL –transistor-transistor logicNIM –nuclear instrumentation moduleTennelecTC178TennelecTC178Pico systems32-channelMCS CPA-16 dual gainMCS CPA-16 dual gainTennelecTC241  TennelecTC241  Chapter 3

Data Analysis

3.1 Calibrations

3.1.1 NERO Efficiency

A 252Cf source efficiency measurement was performed using the same 252Cf source (NSCL

source ID Z7153) used in NERO efficiency measurements in [56] and [57]. 252Cf produces

neutrons through spontaneous fission, with a spontaneous fission branching of 3.39% and

0.116 neutrons/decay [58]. The source had a nominal activity of 50 µCi on November 19th

1990, but this value only takes into account the presence of 252Cf. In addition to 252Cf,

there are two other main contributors to neutron production in the source, 250Cf, which also

produces neutrons following spontaneous fission (0.0027 n/decay) [59], and 248Cm (the α

decay daughter of 252Cf), which produces neutrons at a rate of 0.2611 n/decay [59]. Since

the nominal value of the source has a large error bar of 10 %, a more precise value of the

source neutron activity has to be determined for a precise efficiency calibration of NERO.

The total source α activity, together with knowledge of the original source isotopic com-

position, can be used to determine the neutron activity on any date thereafter. The most

recent α calibration of Z7153 was performed in October 2014. Tab. 3.1 shows the source

properties on December 1st 1989 and on this date.

The α activity of the source was measured using a Si barrier detector with an active

47

December 1st 1989
Amount
(atom %)

Nuclide

249Cf
250Cf
251Cf
252Cf
245Cm
246Cm
247Cm
248Cm

7.32
13.11
4.55
75.02

0
0
0
0

Nuclide

249Cf
250Cf
251Cf
252Cf
245Cm
246Cm
247Cm
248Cm

October 16th 2014
Amount Neutron Activity
(atom %)

(s−1)

6.972
3.506
4.463
0.110
0.351
9.583
0.087
74.907

0

49.8

0

331.7

0
0.1
0
3.9

Table 3.1: Isotopic composition of the source on the source preparation date (left, provided
by source manufacturer) and on the α calibration date (right, calculated).

area of radius 0.5 cm at a distance of 0.62 cm. After correction for the geometric efficiency

of the Si detector [60], the α activity of the source was 22964/s. Taking into account the

contributions of other α-emitting nuclides in the source, the total neutron activity on the

date of α calibration was calculated to be 385.4 n/s, with 49.8 n/s from 250Cf, 331.7 n/s from

252Cf, and 3.9 n/s from 248Cm. This calibration is increasingly important as the source ages

because the proportion of neutron activity from 250Cf and 248Cm will increase (compare

Tab. 3.1 and Tab. 3.3) and ignoring these sources of neutrons will lead to an inaccurate

efficiency measurement.

In the presence of electronics-induced noise, the efficiency of NERO depends on the

hardware thresholds used. Example spectra from a 3He tube and a BF3 tube are shown in

Fig. 3.1. In some cases there was a clear separation between the noise peak and the neutron

signals, but this was not true for all of the tubes. For the experiment, the hardware threshold

was set so that the noise peak was visible. These noise signals were then eliminated by the

use of software thresholds in analysis on a run-by-run basis. The software thresholds were

set at the minimum point between the low-frequency noise peak and the neutron signals if

48

Figure 3.1: Left: Spectrum from a representative 3He tube. Right: Spectrum from a repre-
sentative BF3 tube.

Quadrant Rate (n/s)

A
B
C
D

Total

1.1
0.4
0.4
0.3
2.2

Table 3.2: NERO detection rate of neutrons for a representative background run during the
experiment.

there was not good separation, and at the beginning of the neutron signals if there was good

separation.

The rate of background neutrons was also investigated. Tab. 3.2 gives the neutron count

rate per quad, applying the same software thresholds, for a representative background run

during the experiment. This background rate was used to determine the level of false β-n

correlations, where a true β decay is correlated to a background neutron, when the β decay

curve is fit to extract the number of true β-n events.

The background-subtracted NERO efficiencies by quadrant before and after the experi-

49

ment are listed in Tab. 3.3. The total NERO efficiencies for a 252Cf source were measured

at 31(5) % (before) and 32(2) % (after). The efficiencies are very similar, with the biggest

difference from the change in quadrant C BF3 efficiency due to a detector which was not

working in the calibration before the experiment that was fixed prior to the experiment. The

larger error bar from the pre-experiment efficiency measurement comes from the assumption

that the broken detector could contribute up to the average of the other detectors in the

same ring. These measurements are compatible with the value of 31.7(2)% reported in [48]

which is considered the benchmark efficiency for 252Cf. Therefore, the same scaled efficiency

factor of 37(5) % as in [57] was used in the calculation of the Pn value.

Before

After

Nuclide

Amount Neutron Activity
(atom %)

(s−1)

Nuclide

Amount Neutron Activity
(atom %)

(s−1)

249Cf
250Cf
251Cf
252Cf
245Cm
246Cm
247Cm
248Cm

6.96
3.36
4.46
0.09
0.36
9.74
0.09
74.93

0

47.7

0

267.6

0
0.1
0
3.9

249Cf
250Cf
251Cf
252Cf
245Cm
246Cm
247Cm
248Cm

6.96
3.35
4.46
0.088
0.36
9.74
0.09
74.93

0

47.6

0

265.1

0
0.1
0
3.9

Quadrant

3He (%)

BF3 (%)

Quadrant

3He (%)

BF3 (%)

A
B
C
D

3.06
2.99
3.07
2.80

Total

11.92

4.57
5.06
4.59
4.72

18.94

A
B
C
D

3.17
3.05
3.14
2.74

Total

12.10

4.88
5.20
5.26
4.89

20.23

Table 3.3: Source characteristics and NERO efficiencies by quadrant and detector type before
(left) and after (right) the experiment.

50

3.1.1.1 Moderation time of neutrons in NERO

Because the β-delayed neutrons are moderated by the NERO polyethylene matrix (according

to Eq. 2.20) before detection in the proportional counter tubes, the time delay of neutron

detection following the detection of the β-decay electron is significant, unlike for β-delayed

γ rays. Therefore, the moderation time of neutrons in NERO must be considered for the

successful correlation of neutron detections to β decay events. Fig. 3.2 shows the time differ-

ence between a β decay signal and the neutron detection by a tube in NERO demonstrating

that 98.4% of neutrons are detected within a 200µs window of the β decay event. Therefore,

during the analysis, all neutrons arriving within a 200 µs window following the detection of

a decay signal (defined in section 3.3) were considered to be β-n events.

Figure 3.2: Moderation time of neutrons in NERO. The time for half the neutrons to be
detected is ∼34 µs.

51

Time (ns)020406080100120140160180200310·Counts / microsecond0501001502002503003504003.1.2 SuN Energy Calibrations

Each SuN segment is read out by three PMTs which must be gain-matched so that each

PMT reads out the same signal voltage when receiving the full light from the detection

of a specific a γ ray. This is so that the energies detected in each PMT can be summed

together correctly. Gain-matching was done using the 1460 keV line from 40K in the room

background which will not produce strong geometric effects in the PMT spectra, which using

a source at the centre of the SuN detector would [61]. First, the PMTs were gain-matched

by adjusting the PMT voltages until the peaks in the spectra from the three PMTs in a

segment overlapped (Fig. 3.3).

52

Figure 3.3: Gain-matched room background spectrum for all 24 PMTs of SuN. The peak at ∼1000 ADC units is the 1461 keV
line from the decay of 40K in the room background.

53

ADC channel400  8001200 1600400  8001200 1600400  8001200 1600400  8001200 1600400  8001200 1600400  8001200 1600Counts / 2keV10410310210104103102101041031021010410310210Figure 3.4: The source γ rays used for the calibration of SuN from 241Am (left), 60Co
(centre), and 137Cs (right), marked by diamonds. The second peak in the 137Cs spectrum
is produced by two γ rays at 662 keV from two separate decays being detected by the same
segment, and is a result of the high activity of the 137Cs source used.

The SuN segments were also calibrated so that the ADC units of the energy recorded

by the energy filter of DDAS matched the energy of the γ ray in keV. Four lines from three

sources were used for this calibration, the 59.5 keV line from 241Am, the 661.7 keV line from

137Cs, and the 1173 keV and 1332 keV lines from 60Co (Fig, 3.4).

The calibration was applied using a linear least squares fit to the position of the four

peaks, determined using a Gaussian fit, for each segment. Calibrations were performed both

before (Fig. 3.5) and after (Fig. 3.6) the experiment to ensure that the effects of any voltage

drift of the PMTs throughout the experiment were taken into account during the analysis.

3.1.3 Silicon Detector Calibrations

3.1.3.1 Energy calibration and resolution of PIN detectors

For the Si PIN detectors to be useful for particle identification, the energy resolution has

to be sufficient to distinguish between the different components of the incoming beam. Ac-

cording to LISE++ [45] calculations, a ∆E/E resolution of less than 3% was necessary to

separate all beam components. The energy calibrations and resolutions of the primary par-

54

Energy (keV)50100150200250300350400450500Counts / 10 keV0100200300400500600310·Energy (keV)50010001500200025003000Counts / 10 keV010000200003000040000500006000070000Energy (keV)200400600800100012001400160018002000Counts / 10 keV0200400600800100012001400Figure 3.5: Calibration residuals for all 8 segments of SuN for the energy calibration from
before the experiment.

Figure 3.6: Calibration residuals for all 8 segments of SuN for the energy calibration from
after the experiment.

55

−10−50540080012001600−10−505400800120016004008001200160040080012001600Energy(keV)Residual(keV)−50510152040080012001600−505101520400800120016004008001200160040080012001600Energy(keV)Residual(keV)ticle identification PINs (1 and 2) were determined with an 241Am source, which has two

visible α lines at 5442.80(13) keV an 5485.56(12) keV which require a 0.8% resolution to

separate. The DDAS energy filter rise and flat top parameters were adjusted to achieve

the best resolution possible for the stronger 5485.56 keV α line and are listed in Tab. 3.4.

Although the resolution required to separate the two α lines was not achieved, the resolu-

tion was good enough for the purpose of particle identification (also listed in Tab 3.4). The

calibrations and resolutions of PINs 3,4, and 5 were determined using a 228Th source, which

has 6 well-known α lines of energy 5.4-8.8 MeV from α decay of 228Th and nuclei in the

daughter chain (Fig. 3.7). The signals from PINs 1, 2, 3, and 4 were passed through a

Tennelec 4-channel (TC-178) pre-amiplifier unit, which has three gain settings of 100 MeV,

1 GeV, and 10 GeV. Based on LISE++ calculations of the amount of energy expected to

be desposited in each PIN detector (300-900 MeV), the pre-amplifier settings for all four

low-gain PINs for the experiment were set to 1 GeV. On this gain setting, a ∼5 MeV α
would not produce detectable signals. Thus, for these PINs, the resolution optimisation and

energy calibrations were performed with the 100 MeV gain setting and assumed to hold for

the 1 GeV gain setting. The poor energy resolution of PINs 3 and 4 are caused by noise in

the pre-amplifier channels used. This did not end up affecting the analysis, since PIN3 and

PIN4 were used to confirm transmission through the BCS chamber to the BCS DSSD rather

than precise particle identification.

3.1.3.2 Calibration of DSSDs

Energy calibrations of the high-gain channels of both the BCS DSSD (and SSSD) and the

miniDSSD were determined using a 228Th source. Signals from the different DSSD strips

were gain matched to facilitate the position distribution. A linear least squares fit was

56

Figure 3.7: 228Th spectrum. The six α peaks from the decay chain are at 5.42, 5.69, 6.05,
6.29, 6.78, and 8.78 MeV.

57

ADC units9000100001100012000130001400015000160001700018000Counts / 10 keV020406080100120Detector Rise time (µs) Flat top time (µs) FWHM resolution (%)

PIN1
PIN2
PIN3
PIN4
PIN5

9.52
9.52
9.52
9.52
4.96

0.640
0.640
0.640
0.640
0.240

1.2
2.24
10.1
4.25
1.8

Table 3.4: DDAS slow filter parameters and highest achieved energy resolution of the PIN
detectors.

performed for the energy vs channel data for the 6 α lines from the 228Th source (Fig. 3.7).

The residuals of the calibration for the 228Th source measurements for the BCS DSSD and

SuN miniDSSD are shown in Figs. 3.8 (front) and 3.9 (back), and 3.10 respectively. The

offsets for the calibration were at a reasonable level of ∼100-200 keV at ADC channel 0.

The low energy thresholds were set by using a 90Sr source, which has a well-known β-

decay electron spectrum. The thresholds were set high enough such that it minimised the

inclusion of noise as false β decay signals, but as low as possible to include as many true

β decay signals as possible (Fig. 3.11). The low-gain channels of the DSSDs could not be

tested using sources before the experiment since source αs are not energetic enough, so these

were gain-matched online with the energy deposition by beam particles.

3.1.4 Light Particle Veto Calibrations

For the NERO portion of the experiment, the thick plastic scintillator downsteam of the

SSSD was used as the light particle veto. The light particles which come with the beam

are much more energetic than the β decay electrons, but mimic β decay signals in the

comparatively thin DSSD and SSSD. However, the LISE prediction for the energy deposited

in the scintillator by the light particles is much higher (>50 MeV) than the β decay Q-value

of 61V (∼12 MeV), and gating out the high energy portion of the scintillator spectrum helps

58

Figure 3.8: BCS DSSD front side calibration residuals with a 228Th source. Strip 1 shows
no residuals as it was not operational due to a broken contact.

59

−20−1001020−20−1001020−20−1001020−20−1001020−20−1001020−20−1001020−20−100102055007500−20−100102055007500550075005500750055007500Energy(keV)Residual(keV)Figure 3.9: BCS DSSD front side calibration residuals with a 228Th source. The shared
pre-amlifier for strips 33-40 had a gain high enough that the 8.8 MeV α from 228Th was
outside the ADC range.

60

−20−1001020−20−1001020−20−1001020−20−1001020−20−1001020−20−1001020−20−100102055007500−20−100102055007500550075005500750055007500Energy(keV)Residual(keV)Figure 3.10: SuN miniDSSD front side (top four rows) and back size (bottom four rows)
calibration residuals with a 228Th source. Strips are ordered left to right, then top to
bottom.

61

−20−1001020FrontStrip1−20−1001020−20−1001020−20−1001020FrontStrip16−20−1001020BackStrip1−20−1001020−20−100102055007500−20−1001020550075005500750055007500BackStrip16Energy(keV)Residual(keV)Figure 3.11: 90Sr spectrum in a representative DSSD strip. The threshold used is indicated
by the dashed line. The peak to the left is due to electronic noise, and the broad peak to
the right is the β spectrum measured from the 90Sr source.

to eliminate the light particles event from the β decay spectrum seen in the DSSD (Fig.

3.12).

3.2 Particle Identification

As previously discussed in section 2.5.2, the particle identification for this experiment was

performed using the δE-TOF method. The energy loss ∆E used was the energy loss in PIN1,

and the time-of-flight used was the time between a (delayed) signal from the I2 scintillator

and a signal in PIN1. The uncorrected PID is shown in Fig. 3.13. The I2 slits were open

to allow a momentum acceptance, dp/p, of 2%, and momentum corrections were performed

using the position along the I2 scintillator to account for the distribution in the time of

flight. This correction was done by assuming that the position in the I2 scintillator was a

62

ADC units200400600800100012001400160018002000Counts / 5 keV020406080100120140160Figure 3.12: Scintillator spectrum for a representative NERO run. The dashed line indicates
the 12 MeV upper threshold used to eliminate light particle signals from the DSSD high-gain
channels.

linear function of the TOF, and calculating a corrected time of flight which is independent

of the position in the I2 scintillator (effectively performing a rotation of the trendline).

In the case of this experiment, the tune was such that the beam contained only a few

fragments, and only a single isotope of each element. The cause of the double peak structure

in the I2 position spectrum for 61V and 64Mn is uncertain. However, following momentum

correction, the double-peaked structure is resolved into a single peak, and the γ ray spectra

gated on each peak shows that they are the same isotope. The γ ray spectrum in coinci-

dence with implantation events does not show any isomeric transitions for either 64Mn or

61V. Analysis gates for each isotope were defined by selecting regions in the corrected PID

(Fig. 3.13) so that the β decays and β-delayed radiation could be analysed for each isotope

separately.

63

Energy (ADC units)50001000015000200002500030000Counts / 10 ADCu110210310Figure 3.13: Uncorrected (left) and corrected (right) particle identification plots.

3.3 Correlating implants and decays

After being implanted in the DSSD, the beam particle eventually decays and emits an elec-

tron. Both the decaying ion, referred to as the implant, and the β decay electron, referred to

as the decay, will deposit energy in the DSSD. To be classified as an implant, the following

conditions were required: (1) a signal in PINs 1-4; (2) a signal in the low-gain channels of

both the front and back side of the DSSD; (3) no signal in the SSSD; and (4) no signal

in the plastic scintillator. Events where conditions (1) and (2) are met but (3) is not are

considered punchthrough events. These events are excluded because the decay electron from

implantation in the SSSD is not localizable by a single SSSD, making correlation challenging.

To be classified as a decay, the following conditions were required: (1) no signal in PINs

1-4; (2) no signal in the low-gain channels of the DSSD; (3) a non-overflow signal in the high-

gain channels of the DSSD that also passes the hardware noise thresholds; and (4) a signal

in the plastic scintillator under the 12 MeV threshold. Events where conditions (1)-(3) are

fulfilled but condition (4) is not are considered light particle events, which otherwise behave

the same as β decay events, but have to be vetoed as they can occur at a much higher rate

depending on the secondary beam delivered to the experimental end station.

64

Time of Flight (arb. units)1000010500110001150012000125001300013500140001450015000Energy Loss (arb. units)3000320034003600380040004200440046004800500020406080100120Time of Flight (arb. units)1500015500160001650017000175001800018500190001950020000Energy Loss (arb. units)24002600280030003200340036003800051015202530354045Each time a decay was detected, it was correlated to all implants within the given corre-

lation time window (a time chosen to be ten times the half-life of the decaying parent, 500 ms

in the case of 61V) and within the correlation area (defined below) of the decay pixel. This

was done to generate a flat random background. If the decay had been correlated only to the

most recent implant within its correlation field, this would bias the background toward lower

time differences between the implant and decay, and lead to a slowly decaying background.

Correlations between implants and decays are complicated by the fact that other species

implanted in the detector can also emit decay electrons, whether they be other components

of the implanted beam or daughter nuclei from previously implanted species that undergo

further decays. The first problem was dealt with by using gates in the particle identification

so that only implants of a certain species are considered. Additionally, fewer false correlations

were achieved by choosing an implantation rate where the time between implants is much

longer than the half-life of the implanted isotope of interest.

Another strategy used was to utilise the fine pixelisation of the DSSD to spatially localise

both the implant and decay, and to correlate implants and decays which are in proximity to

each other (since it is likely that the decay electron will be detected near the implant which

emits it). Once an implant is localised, the correlation field can be defined to be either

the implant pixel itself, or can be widened to include the neighbouring pixels (including

diagonally adjacent pixels) to create a 3×3 field of 9 pixels or a 5×5 field of 25 pixels. The
presence of a high-gain signal (not vetoed by the light particle vetoes) in any of the pixels

in the correlation field is then considered a correlated β decay electron.

The maximum rate of implants of major beam species in correlation fields of different

sizes for a representative run during experiment is given in Tab. 3.5. For a 3×3 pixel2
correlation field, the average time between implants for 61V is ∼15000 ms, or about 300

65

Species Correlation field size Rate of implantation (ms−1)

Implantation efficiency

61V
61V
62Cr
62Cr
64Mn
64Mn

1 × 1
3 × 3
1 × 1
3 × 3
1 × 1
3 × 3

1.2 × 10−5
6.6 × 10−5
1.5 × 10−5
8.7 × 10−5
3.6 × 10−5
1.5 × 10−4

80%

86%

76%

Table 3.5: Rate of implants for the major beam species at the centre of the position dis-
tribution in the plane of the detector in different correlation field sizes. The implantation
efficiency (fraction of implants to beam particles) for each species is also given.

times longer than the half-life of 61V. This is a sufficiently large time between implants to

minimise ambiguities in correlating decay events to implantation events.

The decay electrons and implants typically cause more than one strip on each side to

trigger, and were localised based on the distribution of energy in the front and back strips.

The implants deposited energies on the order of 2 GeV in the DSSDs and the ranges of the

pre-amplifiers were not large enough such that the implant signals frequently overflowed.

This prevented localisation of the implant by simply selecting the strips with the highest

energy deposition. Instead, two different procedures were used: (1) the central of the set

of consecutive overflowed strips was selected if the number of overflowed strips is odd and

randomly selected from the central two of the set of strips if the number of overflowed strips

is even, referred to as Cof ; and (2) the energy-weighted average strip number was selected

(overflowed strips were assigned the value 32767, the maximum of the 16 bit range), referred

to as Cwa.

Cwa =

(cid:80)i=39
(cid:80)i=39

i=0 iEi
i=0 Ei

For all correlated events, Cof and Cwa were the same or adjacent to each other. Similarly

66

(3.1)

for the decays, localisation was used by taking the strip with the highest energy deposition

in the front and the back. There was no need to perform the same procedure as was done for

the implants because the high-gain signals did not overflow the range of the pre-amplifier.

The spatial distributions (in the plane of the detector) of correlated β decays for the BCS

DSSD and the miniDSSD are shown in top row and bottom row of Fig. 3.14 respectively.

The procedures used to determine the positions of the implants and decays can be checked

by determining the correlation efficiency (section 3.3.1) and were found to be appropriate.

Figure 3.14: The spatial distribution of correlated 61V decays in the BCS DSSD. The low-
event strip in the middle is due to a noisy channel with a high threshold.

The total number of implants and correlated decays are given in Tab. 3.6.

67

Back Strip Number0510152025303540Front Strip Number0510152025303540010002000300040005000Figure 3.15: The spatial distribution of correlated 61V decays in the miniDSSD.

3.3.1 β Correlation efficiency

The β correlation efficiency refers to the fraction of detected β decays correlated to an

implantation event, and includes both the detection and correlation efficiencies. Experimen-

tally, the Bateman equations have to be corrected by the β correlation efficiency for each

isotope, such that

N (t) = 
N0e−λt
N(cid:48)(t) = 
(cid:48)N(cid:48)0e−λ(cid:48)t − 
N0

(cid:2)e−λ(cid:48)t − e−λt(cid:3)

λ

λ(cid:48) − λ

(3.2)

(3.3)

68

Back Strip Number0246810121416Front Strip Number0246810121416500100015002000250030003500400045005000BCS DSSD

Isotope

61V
62Cr
64Mn

Implants Correlated Decays
164736
154559
377259

61847
59300
138412

Efficiency

37.5 (2.0) %
38.4 (2.3) %
36.7 (1.6) %

SuN miniDSSD

Isotope

61V
62Cr
64Mn

Implants Correlated Decays
1185155
927977
3480589

223910
186584
752020

Efficiency

18.9 (1.1) %
20.1 (1.2) %
21.6 (1.0) %

Table 3.6: Calculated efficiencies for the correlation of implanted isotopes for the BCS DSSD
(top) and the SuN miniDSSD (bottom).

where N , 
 and N ’, 
(cid:48) are the number of correlated decays and β correlation efficiencies of

the parent and daughter respectively. The β correlation efficiency for all the components of

the secondary beam have been determined by taking the ratio of correlated decays (N (t))

obtained from the decay curve fit to the number of implanted ions (N0(t)). The β correlation

efficiencies of the components of the implanted beam are listed in Tab. 3.6.

A potential cause for differences in efficiencies could be the position distribution of the

implants in the plane of the detector. The closer the centroid of the beam spot is to the

edge of the detector, the more likely that the decay electrons will not be detected by the

DSSD. Fig. 3.16 shows the planar position distribution in the front and back sides of the

two DSSDs for the beam components. For the BCS DSSD, there is no significant difference

in the beam position between 64Mn and 61V, but the 62Cr beam position is more centred

and does not show the same run-off the sides of the detector as 64Mn and 61V, which could

account for the slightly elevated correlation efficiency of 62Cr. For the SuN miniDSSD, all

three beam positions are encompassed mostly within the miniDSSD, and beam position

is thus unlikely to have had an impact on correlation efficiency. Given the similarity of β

69

BCS DSSD

SuN miniDSSD

Efficiency

Signal-to-Background

Efficiency

Signal-to-Background

14.2 (0.8) %
37.5 (2.0) %
42.8 (2.3) %

26.4
8.17
3.51

18.9 (1.0) %
25.9 (1.4) %

-

9.49
3.25

Size
1×1
3×3
5×5

Table 3.7: Summary of correlation efficiency as a function of correlation field size for both
DSSDs. The result for a 5×5 field for the miniDSSD was not included as a reduced χ2 of
below 2 was not achieved by the best fit.

correlation efficiencies for the different beam components studied here and previously [56,62],

we fellow the approach in previous work and assumed that the β efficiencies are the same for

parent and daughter decays. In this case, the efficiency term in the experimental Bateman

equations is simply a scaling factor.

The correlation efficiency will also depend on the size of the correlation field- the efficiency

can be increased if the correlation field is widened to a 3×3 pixel2 field instead of a single
pixel field because the decay electron may deposit its energy predominantly in a neighbouring

strip, or because the implant was localised incorrectly. This gain in efficiency tapers off as

the correlation field is subsequently widened. The trade-off when using a larger correlation

field is that the signal-to-noise ratio (defined here as the N0 term over the background level)

will decrease as the background increases at a faster rate than the number of true decay

events. Tab. 3.7 lists the correlation efficiencies and signal-to-background ratios for the

BCS DSSD for 1×1, 3×3, and 5×5 pixel2 correlation fields, and 1×1 and 3×3 pixel2 fields
for the SuN miniDSSD. All results in this work were obtained using a 3×3 and 1×1 pixel2
field for the BCS DSSD and the SuN miniDSSD respectively. For the BCS DSSD, a 3×3
correlation field was chosen because the significant increase in efficiency outweighted the

derease in signal-to-noise.

70

Figure 3.16: Top: Implant distribution for 61V (red), 62Cr (magenta), and 64Mn (blue) for
the front (left) and back (right) sides of the BCS DSSD. Bottom: Implant distribution for
61V (red), 62Cr (magenta), and 64Mn (blue) for the front (left) and back (right) sides of the
SuN miniDSSD.

71

BCS DSSD Front Strip no.0510152025303540BCS DSSD Back Strip no.0510152025303540SuN DSSD Front Strip no.0246810121416SuN DSSD Back Strip no.02468101214163.3.2 Reverse-time correlations

Running the correlation algorithm on the time-reversed event sequence (hereafter referred

to as reverse-time correlations) extracts the rate of false correlations, or background. There

are many potential sources of background- for example, long-lived nuclei in the decay chain

of the implanted nuclei will decay at a much later time, emitting β decay electrons that

are then erroneously correlated with newly implanted events; light particles that are part of

the incoming beam that were not vetoed by the plastic scintillator. All of these events have

different and uncorrelated rates, and therefore should generate a flat background of correlated

events. The reverse time correlation should correctly reproduce the same background rate

as the forward time correlation.

3.4 Simulating β-delayed radiation in SuN

3.4.1 GEANT4 construction of SuN

A GEANT4 [63] simulation of the SuN set-up, consisting of the SuN detector [61], the

beampipe and the miniDSSD [64] was used to analyse the β-delayed γ ray spectra. Because

of the low resolution of the SuN detector, it is often impossible to analyse individual γ ray

peaks. Furthermore, the purpose of using SuN was to extract the β decay transition strengths

by considering the total cascade energy rather than single γ rays. The summing efficiency of

SuN is not 100% (for example, the summing efficiency for the 662 keV 137Cs line is 82% [52]),

and the summing efficiency will vary from cascade to cascade. Since each excited state can

decay through multiple cascades, it is not straightforward and in some cases impossible to

determine the population of a given excited state by counting the number of events in a

72

Figure 3.17: Total absorption spectrum (left) and sum of segments spectrum (right) compar-
ing background-subtracted 60Co source data (dashed red), and GEANT4 simulation with a
60Co source (solid black).

given total absorption peak and unfolding the efficiency. Instead, it is more feasible to use

the GEANT4 simulation to automatically take the detector response into account.

To ensure that the GEANT4 simulation of the detector is trustworthy, it was bench-

marked against a source measurement. Utilising the properties of a well-characterised 60Co

source as input to the simulation, the accuracy of the simulation was verified. Fig. 3.17

demonstrates that the GEANT4 simulation does reproduce the measured γ ray sum of seg-

ments spectrum, as well as the total absorption spectrum. In Fig. 3.17, the counts in the

total absorption spectrum for the simulation was normalised to the counts in the spectrum

from the data, since this represents the total number of detected events. Integration of the

total absorption peaks for both cases gave a summing efficiency of 61.2(1)% and 62.6(1)% for

the data and simulation respectively, in good agreement with the 62.4(1.2)% result from [61].

More details regarding the previous benchmarking of the SuN GEANT4 simulation are dis-

cussed in [61].

73

Energy (keV)5001000150020002500300035004000Counts / 4 keV020004000600080001000012000Energy (keV)5001000150020002500300035004000Counts / 4 keV0200040006000800010000120001400016000Figure 3.18: Total absorption spectrum for mono-energetic 1 MeV neutrons, showing the
sum peak for the inelastic scattering populating the first excited state of 127I where the
neutron is not captured and the 7.8 MeV peak from neutron capture on 127I.

3.4.2 Neutron and electron signals in SuN

3.4.2.1 Neutrons

In addition to β-delayed γ rays, SuN also detects neutrons and the high-energy electrons

from the β decay. The neutron signal in SuN arises through inelastic scattering reactions,

127I(n, n(cid:48)γ)127I and 23Na(n, n(cid:48)γ)23Na, or neutron capture on 127I (Q = 6.826 MeV) [65].

The neutron signatures in SuN are demonstrated with a GEANT4 simulation of SuN using

mono-energetic neutrons at 1 MeV emitted isotropically from the centre of the detector (Fig.

3.18). The presence of 58 keV γ rays from inelastic scattering of neutrons on 127I is seen, as

is the sum peak around the neutron capture threshold of 127I at 7.8 MeV (with the capture

Q-value summed with the energy deposited by inelastic scattering) [66].

74

Energy (keV)10002000300040005000600070008000900010000Counts / 10 keV 110210310Though SuN in principle detects neutrons, the efficiency is not high, and the neutron

capture peak is overwhelmed by decay cascades from states in 61Cr at that energy. As

part of this thesis, some work was done comparing GEANT4 simulations of (p, n) events to

SuN data measuring 92Zr(p, n) and 64Ni(p, n) from experiments carried out at Notre Dame.

However, on the whole, the response of SuN to neutrons has not been well-benchmarked,

unlike its response to γ rays. As such, the neutron data from NERO are needed to determine

the β-delayed neutron branch of the decay of 61V.

3.4.2.2 Electrons

To simulate the SuN detector response to β electrons, it is important to include the beampipe

and the miniDSSD because the additional material shifts the electron spectrum seen in SuN

to lower energies. Low-energy electrons up to ∼400 keV will be stopped in the miniDSSD.
Electrons up to ∼1 MeV are stopped in the SuN beam-pipe. Higher-energy electrons will
enter SuN and be detected, and can be summed together with the β-delayed γ rays, compli-

cating the extraction of γ rays cascade strengths. Thus, in addition to generating γ rays, the

SuN GEANT4 simulation included neutron and electron emission. The neutrino is ignored

as the likelihood of interaction is effectively nil.

The simulated electron spectrum in SuN following an interaction with the DSSD and the

SuN beam-pipe is shown in Fig. 3.19. As the average electron energy increases (with increas-

ing β decay Q value), less energy is deposited in the DSSD and the beampipe. Consequently,

the fraction of total electron energy deposited in the SuN detector will increase.

75

Figure 3.19: Simulated total absorption spectrum (black) and energy deposited in the DSSD
(red) for allowed β decay of a species with a Q value of 1 MeV (left), 3 MeV (centre), and
10 MeV (right).

3.4.3 GEANT4 simulation of β decay events in SuN

Each β decay event in GEANT4 begins with a decay that occurs in the miniDSSD at the

target position of SuN. The γ ray cascade associated with this decay event is read in from

an input file and the total energy of the cascade is subtracted from the β-decay Q-value.

The remainder of the energy is shared between the electron and the neutrino. The electron

energy is randomly generated, sampling the β-decay distribution for allowed transitions, and

the electron is emitted from the centre of SuN, following an isotropic angular distribution.

For templates for βn decays, the neutron is emitted isotropically, and its energy, En, is given

by Eqn. 3.4,

En = Ef − Ei − Sn,

(3.4)

where Ef is the energy of the state in 60Cr populated by the neutron emission, Ei is the

energy of the state in 61Cr which is first populated by the β decay of 61V, and Sn is the

neutron separation energy of 61Cr.

76

Energy (keV)1002003004005006007008009001000Counts / 5 keV010203040506070Energy (keV)50010001500200025003000Counts / 5 keV020406080100120140Energy (keV)10002000300040005000600070008000900010000Counts / 5 keV0204060801001203.5 Extracting β-feeding intensities from SuN γ ray

spectra

The total β decay radiation spectrum from SuN was considered to be the sum of the β decay

radiation spectra for the decays to single states. Instead of attempting to simulate the full β

decay spectrum in SuN, templates of the β decay specta for β decays to individual states in

61Cr and βn decays to states in 60Cr are generated, and the total spectrum is then a linear

combination of the templates. The β decay transition strengths, including the βn feeding,

are the normalised co-efficients from the fit to the data. In the following sections, a ’template’

refers to the simulated γ ray spectrum of β decays to a given state, and a ’sub-template’

refers to the simulated γ ray spectrum of a specific γ decay cascade following β decays to a

given state (Fig. 3.22).

3.5.1 Generating templates of the decay of known states

Several levels in 61Cr populated by the β decay of 61V have been identified in a previous

study using the high purity Germanium array SeGA [36] (Fig. 3.20). Together with states

in 60Cr populated following β-delayed neutron emission, and states in 61Mn populated by

the decay of 61Cr, these are marked out in Fig. 3.21. No new states in 61Cr were definitively

identified in this study, as the limited resolution of SuN makes it challenging to identify

individual states. Additionally, because of the contribution of the β decay electrons to the

total absorption spectrum, the background was too high to effectively identify peaks.

Cascade branchings from known levels were found by recursively fitting the contribution

of cascades from lower-lying states. This is described using the 224 keV level as an example.

First, three GEANT4 sub-templates were generated, representing the decays through the

77

Figure 3.20: Level scheme showing the known excitation levels in 61Cr populated by β decay.

78

(5/2-)065972244024515646327167741028123320552262Quasi-continuumNeutronSeparationEnergy(3/2-)0T1/2=49(2)msQβ=12.0(9)MeV61Cr61VFigure 3.21: Total Absorption spectrum of γ rays correlated with β decay events from
implants in the 61V PID gate. Black triangles, blue circles, and red squares denote levels in
61Cr, 60Cr, and 61Mn respectively.

first excited state to the ground state, second excited state and the direct to ground state

transitions respectively (Fig. 3.22). Strictly speaking, there is a possibility that the second

excited state might populate the first excited state by γ decay, but this transition is not

expected to play a role because of its low energy of 33 keV. Once the sub-templates are

generated, a χ2 minimisation was performed using MINUIT to determine the contribution

of each sub-template to the sum of segments spectrum from data when gated on the 224 keV

sum peak (Fig. 3.23).

Once the decay branchings of the 224 keV state have been determined, it can be used

to generate a template of the decay of the 224 keV state and used to fit the decay of the

79

659822440245156563271677410271222206222616441461181911421497186120322378Figure 3.22: The sub-templates representing the three different γ decay cascades from the
224 keV state.

Figure 3.23: Top: Contributions of individual templates of the decay to the ground state
(green), through the first excited state (magenta), and through the second excited state (red).
Bottom: Comparison between the best fit of the templates (blue) and the data (black).

80

Sub-template 1Sub-template 2Sub-template 3224 keV224976502249765022497650159 keV65 keV97 keV127 keVCounts / 2 keVCounts / 2 keVCounts / 2 keVEnergy (keV)Energy (keV)Energy (keV)Counts / 10 keVEnergy (keV)next excited state at 402 keV through the 224 keV state. A comprehensive template for an

known entry state that implements all possible decay cascades, using the prior determined

branchings, is then generated to represent the spectrum for the γ decay when that state is

populated by β decay. This procedure is done for all 12 excited states identified in [36].

3.5.2 Generating templates of the decay of unknown states with

DICEBOX

β decay of 61V can populate states in 61Cr up to the decay Q-value. In this case, the level

scheme of 61Cr is known only up to 2.26 MeV, whereas the Q-value is 11.97(90) MeV. While

the decay strength to each of these unknown states could be small, the total decay strength

to states above 2.26 MeV could be substantial and must be considered. In lieu of complete

knowledge of the excitation scheme of 61V, levels above 2.26 MeV are treated as a quasi-

continuum, with pseudolevels inserted every 50 keV up to 3.2 MeV, every 100 keV up to

3.95 MeV and every 200 keV up to the Q-value. Because of the coarse resolution of SuN,

it is impossible to separate total absorption peaks to within 6%, and so each pseudolevel

represents all states within the band given by the difference in energy between pseudolevels.

The decay scheme of each pseudolevel is simulated using the Dicebox statistical code.

A detailed explanation of the Dicebox code can be found in [67], but the main procedure

of the code is as follows: The Dicebox code adopts a dichotomous approach to generating

decay cascades. For levels below a energy cut-off termed Ecrit = 2.262 MeV, the decay

scheme is determined by known excitation energies, spins and parities, and decay branchings

(taken as input to the code, in this case, the results from the the procedure in section 3.5.1).

For levels above Ecrit, the levels (and their spins and parities) are distributed according

81

to an input level density prescription [53]. The first step of Dicebox discretises the level

density function, generating a set of states (here-after referred to as a nuclear realisation)

between an input energy Ee, termed the entrance energy, and Ecrit. Transitions between

levels are governed by input photon strength functions (PSFs), with the assumption that the

only radiation multipolarities that present are electric dipole (E1), magnetic dipole (M1),

and electric quadupole (E2) radiation. The total decay scheme for decay for a given entry

state at energy Ee, with spin and parity J π, is then generated by a Monte Carlo simulation

using these parameters. For each nuclear realisation, a sufficiently large number of Monte

Carlo steps have to be used to ensure that the set of generated cascades is statistically

representative of the input distributions.

For each Monte Carlo step, the state at Ee is populated, and is allowed to decay to a

secondary state of lower energy. The cascade continues following the PSFs, if the inter-

mediate level is still above Ecrit, or the input branching ratios, if the intermediate level is

below Ecrit. This procedure is repeated for all pseudolevels, and spin/parity combinations

for allowed transitions from the 61V ground state (J π = 3/2−), and the decay scheme for

each pseudo-level is given by a simple average of the three spin/parity combinations for an

allowed transition (J π = 1/2−, 3/2−, and 5/2−).

Once the templates were generated, a least squares fit was performed to determine the

contribution of each template to the total absorption spectrum. This was done with MINUIT

[68] in the ROOT C++-based data analysis toolkit [69,70]. The resulting co-efficients of the

fit, when properly normalised, will give the β feeding intensities. The results of this fit are

discussed in the following chapter.

82

Chapter 4

Results

4.1

β Decay of 61V

4.1.1 Half-life

The correlated β decay events using a correlation window of 500 ms and gated on 61V in the

PID are shown in the decay curve in Fig 4.1. The total fit includes contributions from: (1)

the decay of 61V; (2) the decay of the daughter 61Cr (t1/2 = 237±11 ms); (3) the decay of
the neutron daughter 60Cr (t1/2 = 490±10 ms); (4) the decay of the grand-daughter 61Mn
(t1/2 = 709±8 ms); (5) the decay of the neutron grand-daughter 60Mn (t1/2 = 280±20 ms);
and (6) a flat background.

The contributions of the decaying nuclei were modelled using the Bateman equations

(Section 2.2), using the experimentally-known half-lives for the set of daughters and grand-

daughters, as well as the Pn obtained from the NERO data (disucssed later). The magnitude

of the background is also not a free parameter, as it is determined from reverse-time corre-

lation (Section 3.3.2) over the same correlaton interval of 500 ms.

The half-lives from these fits are 46 ± 3 ms and 44 ± 3 ms for the SuN miniDSSD and
BCS DSSD data respectively. The error in the extracted half-lives have both systematic and

statistical components. The systematic component arises from the uncertainties in the half-

lives of the nuclei in the decay chain (listed above) and the uncertainty in the Pn value, and

83

Figure 4.1: Top: Decay curve fit for the SuN miniDSSD. Bottom: Decay curve fit for the
BCS DSSD.

84

Time between implant and decay (ms)050100150200250300350400450Counts / 1ms050010001500200025003000350040004500V-61Cr-61Cr-60Mn-61Mn-60BackgroundDataTotal Decay CurveTime between implant and decay (ms)050100150200250300350400450Counts / 1ms02004006008001000V-61Cr-61Cr-60Mn-61Mn-60BackgroundDataTotal Decay Curvewas evaluated by a Monte Carlo calculation. For each Monte Carlo instance, the half-lives

of the decay chain nuclei were varied within their uncertainties and the decay curve was fit.

The systematic error was then extract from the distribution of the half-life of 61V from the

fits. The statistical error was determined from the error in the fit co-efficients, derived from

the statistical error of each bin.

For the SuN portion of the experiment, γ rays were detected in coincidence with β decay

signals. By gating on a γ ray associated with the decay of 61V to an excited state in 61Cr,

the half-life of 61V can be determined more accurately than the total fits. In this case, the

gated decay curve will have only an exponential contribution from the decay of 61V and a flat

background, eliminating all contributions from nuclei in the decay chain. This eliminates all

systematic errors associated with the error bars of the daughter/grand-daughter half-lives.

The β decay curve gated on total absorption γ cascades from the decay of 61V is shown in

Fig. 4.2. The extracted half-life from this fit is 49(2) ms, in agreement with the previously

measured values (Tab. 4.1).

For the NERO portion of the experiment, neutrons were detected in coincidence with β

decay signals. Similar to gating on a γ ray, a gate on β decay events that produce a neutron

will reduce the complexity of the fit. The predicted β-delayed neutron emission branches of

the nuclei in the 61V decay chain are small or zero (Pn(61Cr) = 0.6%, Pn(60Cr) = 0.00%,

Pn(61Mn) = 0.01%, Pn(60Mn) = 0.00% [71, 72]), such that the neutron-gated decay curve

should only contain contributions from a flat background, an exponential background, and

the parent decay. The flat background arises from background neutrons arriving close in time

to falsely correlated decay events, and the exponential background arises from β-delayed

neutrons arriving in coincidence with falsely correlated decay events or from background

neutrons arriving in coincidence with true β decay events. The β decay curve gated on

85

Figure 4.2: Decay curve from the SuN miniDSSD when gated on the 1028 keV cascade
(inset) from the corresponding state in 61Cr

86

coincident neutrons is shown in Fig. 4.3. The extracted half-life from this fit is 48(1) ms.

Figure 4.3: Decay curve from the BCS DSSD when gated on coincident neutrons.

Reference

Half-life (ms)

Sorlin et al. 1999 [73]
Sorlin et al. 2003 [74]

Gaudefroy et al. 2005 [75]

Daugas et al. 2011 [76], Matea 2002 [77]

Suchyta et al. 2014 [36]
This work (BCS DSSD)

This work (SuN miniDSSD)

This work (BCS DSSD gated on neutrons)
This work (SuN miniDSSD gated on γ ray)

43 ± 7
47.0 ± 1.2
47 ± 1
52.6 ± 4.2
49 ± 1
46 ± 3
47 ± 3
48 ± 1
49 ± 2

Table 4.1: Comparison of measured values in this work with previously measured values of
the half-life of 61V.

87

Time between implant and decay (ms)050100150200250300350400450500Counts / 2 ms020406080100120Total Decay CurveV-61BackgroundData4.1.2 β-delayed neutron branch

The β-delayed neutron branch of 61V was determined using

Pn =

Nβn − Bn


nNβ

(4.1)

where Nβn is the number of neutrons detected in coincidence with β decays, Bn is the number

of background β-neutron coincidences, Nβ is the total number of correlated β decays, and


n is the neutron detection efficiency of NERO. Here, the assumption is made that the β

correlation efficiency is the same for β decays to states above and below the neutron emission

threshold, supported by the analysis in section 3.3.1.

The energies of β-delayed neutrons can range from zero to Qβ -Sn (∼ 8 MeV in this
case), where Sn is the neutron separation energy of 61Cr (3880 ± 220 keV [65]). As discussed
in [57], the expected neutron energy distribution favours low energy neutrons below 1 MeV,

and it is likely that most of the neutrons are below 500 keV where the efficiency of NERO

is fairly constant. This is supported by QRPA calculations which predict that the strongest

transitions to states above the neutron separation threshold in 61Cr lie below 5 MeV that

emit neutrons of up to 1.1 MeV. Therefore, similar to [57], a flat efficiency of 37 ± 5% was
assumed for NERO, and a Pn value of 14.5 ± 2.0 % was determined. The dominant source
of error in the Pn value is the systematic error associated with the efficiency of NERO and

the lack of knowledge of the neutron energy distribution.

4.1.3 β feeding intensities

The β feeding intensity to a state in 61Cr, or the number of times that a state in 61Cr is

populated by 100 β decays of 61V, was determined from the strength of the total absorption

88

peak at the energy of the state as measured by SuN. To minimise the contribution of un-

wanted γ rays from background and other decays (e.g. daughter and grand-daughter decays)

to the γ ray spectra, three things were done (illustrated in the first three rows of Fig. 4.4

respectively). Firstly, the γ ray spectra from the backwards time correlation were subtracted

from the spectra from the forward time correlation. This eliminates the contribution from

randomly correlated background (the green lines in panels (a) and (i) in Fig. 4.4). Secondly,

the spectra that were fit were gated to include only events where the time difference between

the implant and decay was less than 50 ms (∼ one half-life of 61V) indicated by the solid line
in panel (b) of Fig. 4.4. This limits the contribution (relative to the number of 61V decays)

of decays of the 61Cr daughter nucleus to 6.97%, producing the magenta spectrum in panel

(ii) in Fig. 4.4; and lastly, the spectra from a later time (60-80.98 ms) in the correlation time

plot were subtracted to eliminate the contribution of the decays of 61Cr and 60Cr completely

(panels (c) and the grey line (iii) in Fig. 4.4). The grand-daughters contributed only at the

0.01% level, and were ignored. The end result is the red spectrum shown in panel (iv) of

Fig. 4.4.

The best fit (reduced χ2 = 1.3) of the GEANT4-generated templates to the background

subtracted total absorption spectrum is shown in Fig. 4.5, along with the corresponding sum

of segments spectrum. Within the resolution of the SuN detector, the observed peaks in the

total absorption spectrum can be matched to the level scheme in [36] (see Fig. 3.21). The

single exception is the 565 keV state that is not detectable above background in the total

absorption spectrum, but was reported to have a 1.5% branching by [36].

To assess the error in the β-feeding intensities extracted from the fit, a Monte Carlo

was performed where all the fit co-efficients were simultaneously varied using a lognormal

distribution. A lognormal distribution was chosen to provide fine-grained sampling of the

89

Figure 4.4: Panels (a)-(c) show the components of the decay curve still remaining in the
corresponding TAS spectra shown in panels (i)-(iii). Panel (iv) shows the background-
subtracted total absorption spectrum used for fitting.

90

Figure 4.5: Data (black) and best fit from GEANT4 simulated templates (red) for the total
absorption spectrum (top) and the sum of segments spectrum (bottom).

91

Figure 4.6: Data (black) and best fit from GEANT4 simulated templates (red) for the
total absorption spectrum (top) and the sum of segments spectrum (bottom) up to Ecrit =
2270 keV.

92

reasonable values for the fit co-efficients. The width of the distribution was set so that the

reduced χ2 boundary of the fit was located definitively. A uniform distribution varying each

co-efficient from 0 to 104 was also used to demonstrate that the location of the reduced χ2=2

boundary is independent of the shape or width of the input distribution used in the Monte

Carlo.

The NERO Pn result of 14.5 (2.0) % was also used to narrow the distributions of the

extracted β feeding intensities. A 1-σ cut of 12.5 % ≤
+ Iβ(60Cr 1460 keV) + Iβ(60Cr 1819 keV))≤ 16.5 % was imposed on the results of the
Monte Carlo. The results from the best fit and Monte Carlo, along with a comparison to

(cid:80)(Iβ(60Cr g.s.) + Iβ(60Cr 644 keV)

the inferred β feedings from [36] are given in Tab. 4.2.

The results from this work demonstrate the Pandemonium effect in the results from the

previous β decay study. The β feedings to low-lying excited states in 61Cr obtained using

the TAGS method are systematically lower than those from [36], where HPGe detectors were

used. It is only at higher energies, above 1 MeV, where the feedings from this study exceed

those from the previous study.

There exist several degeneracies between certain templates which lead to particularly

large uncertainties in feeding for the states represented by those templates. Firstly, between

the templates of the decays to ground states of 61Cr and 60Cr, as neither of them have

distinct γ rays. Even though the Q-values of each of the transitions is different (Qβ−(61V)
= 11969 (900) keV and Qβ−n(61V) = 8092 (915) keV) [65], and the electron spectrum
measured by SuN should be different, it is still expected that the templates are to some

extent degenerate as the shapes are fairly similar. Another degeneracy is that of the 632 keV

state in 61Cr and the 644 keV first excited state in 60Cr. To assess the degeneracy within

these two sets of templates, a Monte Carlo simulation was performed where the fit co-

93

State (keV)

This work (%) Suchyta et al. [29, 36] (%)

0

65

97

224

402

451

564

632

716

774

1028

1233

2055

2262

Quasi-continuum

7.4+13.8
−5.8
2.6+3.7
−1.8
2.1+2.6
−1.6
2.0+2.8
−1.5
0.3+0.3
−0.26
3.0+3.1
−2.2
0.3+0.9
−0.2
0.3+0.3
−0.3
4.3+4.0
−3.2
3.0+3.7
−2.4
8.8+5.3
−4.2
4.5+4.0
−3.1
4.1+4.9
−3.4
5.6+5.6
−4.2
31.9+27.8
−17.2

<40

6.0 (1.2)

10 (6)

7.1 (1.1)

1.7 (0.5)

5.7 (0.7)

1.5 (0.4)

1.7 (0.7)

6.1 (0.8)

3.2 (0.7)

8.4 (0.8)

1.4 (0.3)

2.2 (0.7)

2.5 (0.8)

-

Table 4.2: List of β feeding intensities to the identified states in the 61Cr excitation scheme
from [36], and the corresponding apparent β feedings deduced by [29] from [36].

94

efficients for each set templates were varied (separately) while all other co-efficients were

held constant at the values obtained by the χ2 minimisation performed by MINUIT.

Figure 4.7: Beginning bottom left, clockwise: Reduced χ2 as a function of (i) the sum of
the two ground state transition intensities; (ii) Iβ(61Cr ground state); (iii) Iβ(60Cr ground
state); and (iv) contour plot demonstrating the correlation between the two parameters. The
increasing warmth of the colour denotes increasing χ2.

The Monte Carlo results demonstrate that the goodness-of-fit is most strongly dependent

on variations of the sum of the parameters, and is less dependent on variations of the indi-

95

0.000.050.100.15Iβ(61Crg.s.)1.41.61.82.0χ20.000.050.100.15Iβ(60Crg.s.)1.41.61.82.0χ20.00.10.20.3Iβ(61Crg.s.)+Iβ(60Crg.s.)1.41.61.82.0χ260Crg.s.co-efficient(arb.units)61Crg.s.co-efficient(arb.units)1.4941.5541.6141.6741.7341.7941.8541.9141.9742.034Figure 4.8: Beginning bottom left, clockwise: Reduced χ2 as a function of (i) the sum of
the two transition intensities; (ii) Iβ(61Cr 632 keV); (iii) Iβ(60Cr 644 keV); and (iv) contour
plot demonstrating the correlation between the two parameters. The increasing warmth of
the colour denotes increasing χ2.

vidual parameters themselves. The contour shape of the χ2 as a function of two parameters

is linked to the correlation between the two parameters. If there were no or only a weak

correlation, the contour would be more circular, whereas the high ellipticity of the contours

in Fig. 4.8 and 4.7 are indicative of a strong correlation between the two parameters.

96

0.000.050.100.15Iβ(61Cr632keV)234χ20.000.050.100.15Iβ(60Cr644keV)234χ20.00.10.20.3Iβ(61Cr632keV)+Iβ(60Cr644keV)234χ261Cr632keVco-efficient(arb.units)60Cr644keVco-efficient(arb.units)1.321.591.862.132.402.672.943.213.483.754.1.4 ft-value and Urca strength

With the determined Iβ of the transitions, the log f t values for the lowest transitions were

calculated using a Qβ = 11.969 MeV. Tab. 4.3 summarises the log f t values for all known

excited states as well as the intrinstic Urca luminosity L34 of the ground state and the 65 keV

first excited state in 61Cr. The value found experimentally for the ground state transition

is higher than the value calculated by QRPA of 4.35.

State

log f t L34

507

34

Ground state

65 keV

97 keV

224 keV

402 keV

451 keV

564 keV

632 keV

716 keV

774 keV

1028 keV

1233 keV

2055 keV

2262 keV

5.5+0.8
−0.6
6.0+0.6
−0.6
6.1+0.7
−0.5
6.1+0.7
−0.5
6.9+1.0
−0.5
5.8+0.8
−0.4
6.8+0.7
−0.8
6.5+∞
−0.2
5.6+0.8
−0.4
5.8+0.8
−0.5
5.3+0.4
−0.4
5.5+0.7
−0.4
5.4+0.9
−0.5
5.0+1.0
−0.3

Table 4.3: Table of log f t values for the β decay from 61V to the known states in 61Cr. The
L34 values are only given for the ground state and the first excited state because β decay to
the higher-lying excited states is highly suppressed and do not occur in Urca cycling.

97

Chapter 5

Astrophysics

We can now implement the new ground state to ground state log f t value for the decay of

61V into a model for an accreted neutron star crust and determine the strength of crust Urca

cooling from the 61V-61Cr pair.

The ground state to ground state log f t value of 5.5+0.8

−0.6 is higher than the QRPA pre-
diction of 4.35. Prior to the measurement, the upper limit of 40% estimated by [36] would

impose a lower limit on the log f t value of 4.6. To assess cooling strength of the 61Cr-61V

pair, crust calculations similar to those in [22] were performed using the 1-σ range of the log

f t value deduced from the experimental results.

The simulation, same as that used in [22], follows a fluid element in the crust as it travels

deeper into the crust such that the electron chemical potential increases. A nucleosynthesis

network was run with a starting composition of 61Ni, and allowed to evolve for ∼1010s,
corresponding to a column depth of ∼2×1015 g/cm2 and a mass density of ∼1010 g/cm3,
at a temperature of 0.5 GK. At this depth, neutrons become abundant enough to enable

neutron capture and neutron-emitting reactions that transform nuclei from one mass chain

to another, effectively eliminating the possibility of Urca cooling. Masses (and therefore

Q-values) were taken from AME2016 [65], and the measured log f t values for the ground

state to ground state β decays of 61Fe, 61Mn, 61Cr, and 61V were used. Electron capture

transitions were assumed to have the same f t value as the β-decay transitions.

98

To evaluate the cooling impact of an isobaric chain, the time-integrated nuclear energy

release per accreted nucleon Qnuc (Eqn. 5.1) was calculated. The effects of compressibility

and lattice energy due to changes in density are not included in Qnuc to isolate the effect

arising solely from nuclear reactions.

(cid:88)

(Y ∆M + µedYe − 
ν)

Qnuc =

(5.1)

The steps in the cooling profile (Fig. 5.1) indicate transitions between isobars, as in-

dicated in the abundance plot in the upper panel of Fig 5.1. The abundance plot shows

that the electron capture transition between nuclei does not occur at a sharp boundary, but

instead occurs over a range of depth due to the finite temperature.

The experimental results presented in this work establish the 61V-61Cr pair as a major

cooling mechanism in accreting neutron stars with crusts that contain A = 61 nuclei. Within

our uncertainties, the cooling from 61V-61Cr is at least as strong as more shallower tran-

sitions, and likely much stronger. About 20% of the uncertainty in the log f t value arises

from the large uncertainty in the mass of 61V and therefore the uncertainty in the β decay

Q-value. An improvement in the precision of the mass measurement would thus help further

decrease the uncertainty in cooling strength.

The other experimentally-measured ground state to ground state β decay log f t values

characterising the shallower Urca cooling pars in the mass 61 chain (61Fe, 61Mn, and 61Cr)

were performed either with high-purity germanium detectors or with small-angle NaI detec-

tors and are likely subject to the Pandemonium effect. Hence, as suggested in the original

works [26–28], these log f t values should be considered as lower limits. A true assessment of

the cooling strength of this mass chain (as with another other) is predicated upon realistic

99

Figure 5.1: Top: Abundance plot of A = 61 nuclei as a function of column depth. Bottom:
Cooling profile as a function of column depth. The grey band shows the uncertainty in the
cooling profile prior to the experiment and the green band shows the uncertainty following
the experiment. The uncertainty bands shown only reflect the uncertainty in the 61V-61Cr
transitions.

100

1013101410150.00.51.0Abundance101310141015ColumnDepth(g/cm2)−25−20−15−10−50MeV/uCurrentuncertaintyQRPApredictionPreviouslimit61Ti61V61Cr61Mn61Feerror bars for these transition strengths, which can be obtained by using the method pre-

sented in this work. The subsequent pair of 61Ti-61V is another potential cooling pair (with

a QRPA prediction for the log f t value of 5.9), and should be also experimentally measured.

5.1 Urca cooling of neutron star crusts

It is important to consider the complete picture of Urca cooling in a crust consisting of

X-ray burst ashes. Several methods have been used to identify potential Urca cooling pairs

amongst the majority of nuclei where ground state to ground state transition strengths have

not been measured experimentally. These include using Quasiparticle Random Phase Ap-

proximation (QRPA) calculations [25], and using typical measured f t value distributions [41]

together with knowledge of ground state spins. The QRPA method has been shown to be

less consistent with experimental measurements of f t values than shell-model based calcu-

lations [78, 79]. However, the usage of shell model-based calculations for β decay transition

strengths is still limited to certain mass regions due to the prohibitive computational chal-

lenges associated with the large configuration spaces requires for heavier nuclei far from close

shells. Here, we compare QRPA predictions with the latest state of experimental knowledge

of log f t values and spins.

Fig. 5.2 shows the comparison of QRPA and a simple spin-based assessment of whether

a ground state to ground state transition should be allowed and therefore strong. There are

114 cases where QRPA and spins provide compatible information: 47 cases where QRPA

predicts a transition from the parent ground state to the daughter ground state (or an

extremely low-lying state of below 30 keV) and the spins of the parent-daughter pair enable

an allowed transition; and 87 cases where QRPA does not predict such a transition and the

101

Figure 5.2: Chart of the nuclides (only odd-A nuclei are shown) showing the comparison
between QRPA predictions for ground state transitions and whether allowed transitions
are possible based on the experimentally-determined spins of the ground states. The red
(yellow) squares denote nuclei where there is a QRPA-predicted transition and there is (is
not) an allowed transition based on spins. The blue (green) squares denote nuclei where
there is no QRPA-predicted transition and there is (is not) an allowed transition based on
spins. Magenta squares denote nuclei where the spins have not yet been experimentally
determined.

spins of the parent-daughter pair do not enable an allowed transition. There are 102 cases

where QRPA and spins provide incompatible information: 50 cases where QRPA does not

predict an allowed transition where the parent-daughter pair spins imply the likely existence

of such a transition, and 52 cases where the opposite is true. Cases of disagreement are

clustered in mid-shell regions, where QRPA typically predicts strong ground state to ground

state transitions (red boxes in Fig 5.2) due to the larger nuclear deformation in these regions.

We update the list of Urca cooling chains from [22], where only QRPA calculations for

102

QRPA ✓spins ✗QRPA ✓spins ✓QRPA ✗spins ✓QRPA ✗spins ✗Spins unknownthe allowed β decay and electron capture transitions were used. We follow the following

prescription: (1) Experimental log f t values are used where they are available; (2) if the

ground state spins of pairs of parent and daughter nuclei are known to enable an allowed

transition (∆ J ≤ 1) and there is a QRPA prediction for the transition, then the QRPA
prediction is used; (3) if the ground state spins of the pairs are known to enable an allowed

transition and there is no QRPA prediction for the transition, then a ground state to ground

state transition with a typical log f t = 4.9 is added (similar to [24]); (4) if the ground

state spins of the pairs are known to forbid an allowed transition, the transition is removed

regardless of whether there is a QRPA prediction or not; finally (5) if one (or both) of the

spins in the pair is not known, then the QRPA prediction for whether the transition occurs

is used. QRPA predictions of transitions to states with excitation energies of 30 keV or

lower are treated as ground state transitions. This is to account for uncertainties in the

QRPA energies or population by thermal excitation. Furthermore, even if the energies are

correct, these extremely low-lying states can be significantly populated by β decays from

the parent ground state at neutron star crust temperatures, and can therefore participate in

Urca cycles.

To obtain a realistic estimate of the importance of various Urca cooling transitions, we

calculated total heating or cooling in each mass chain independently and folded the result

over a realistic crust composition with mass fractions X(A), determined by thermonuclear

burning near the surface of the neutron stars. Here we use the composition from the ashes

of typcial mixed hydrogen and helium bursts from [80].

In the original calculations, the mass 61 chain was found to be one of the weaker cool-

ing chains. However, newer calculations taking experimental information for the shallower

cooling pairs into account suggest that it is still significant. Inclusion of the result from this

103

Figure 5.3: Cooling strengths of individual mass chains in X-ray burst ashes.
‘Old’ refers
to the calculations presented in [22], and ‘new’ refers to the calculations done following the
prescription described in the text, representing the state of experimental knowledge before
the 61V result. The new cooling strength of the mass 61 chain using the results of this
experiment is given by the black octagon, with error bars (solely from the uncertainty in the
61V decay strength) denoted by the up and down black triangles.

work somewhat mitigates this strength since the experimentally-determined log f t value of

5.5 is higher than the QRPA prediction of 4.35. Furthermore, many of the other transi-

tions in strong cooling chains are either experimentally-unmeasured, or rely on experimental

measurements likely heavily subject to the Pandemonium effect and maybe weaker than

reported. Though the exact cooling strength depends the ash composition and therefore on

the X-ray burst ignitition conditions (such as the composition of the accreted material), the

abundances for the mass 50–80 region are likely to be the least condition-dependent.

Other important cooling chains for X-ray burst ashes are A = 55, 31 and 33. Of these,

104

2030405060708090A10301031103210331034XA·LνOldHeatersOldCoolersNewHeatersNewCoolersthe mass 33 chain is the most experimentally well-characterised, with β decay ground state

to ground state measurements of log f t for 33Na (5.2 [81]), 33Mg (5.2, [82]),33Al (4.3 [83]),

and 33Si (4.96 [83, 84]). The strongest cooling pair in the mass 31 chain is the 31Na-31Mg

pair, with a measure log f t of 4.9 [85, 86]. The strengths of the A = 31 and A = 33 chains

is highly dependent on the conditions of the X-ray burst. In scenarios the so-called extreme

rp-process scenario, where there is an extended rp-process, there is very little abundance in

the mass 30 region, drastically limiting the importance of the A = 31 and A = 33 chains for

Urca cooling. The strength of the mass 55 chain, also extremely important for crusts made

of superburst ashes [23], is almost entirely dependent on the strength of the unmeasured

55Ca-55Sc transition, by far the strongest cooling transition.

105

Chapter 6

Summary and Outlook

The experimental result presented in this work demonstrates that there is a non-negligible β-

decay transition strength between the ground states of 61V and 61Cr of 7.4%, corresponding

to a log f t value of 5.5. This is the first reporting of an f t value for a high Q-value β decay

transition with realistic error bars. This result was achieved by using a combination of a

high-efficiency neutron detection system and a total absorption spectrometer to mitigate the

impact of the Pandemonium effect. The impact of the new measurement on the strength of

Urca cooling by A = 61 ashes was investigated by incorporating the result into a reaction

network calculation of a pure A = 61 neutron star crust. This revealed that the A = 61

mass chain is a moderately strong Urca cooling chain, though not one of the strongest.

However, within the errors of the ground state to ground state strength, there is still an

order of magnitude uncertainty in the Urca luminosity, which casts doubt on the reliability

of current predictions of Urca cooling in neutron star crusts based on measured log f t

values where the Pandemonium effect may have systematically skewed the results. More

experimental measurements of ground state to ground state transition strengths using the

method developed in this work are required to bolster the effort towards understanding

and properly quantifying the role of Urca cooling in cooling X-ray transients. With the

implementation of this technique at the National Superconducting Cyclotron Laboratory,

with its access to neutron-rich radioactive isotope beams, other exotic Urca pairs can be

106

investigated. For example, the A = 55 mass chain is predicted to be the strongest Urca

cooling chain for superbursting systems [23], due to the strong ground state to ground state

transition from 55Ca to 55Sc. A future experiment at NSCL utiilising the technique presented

in this work to measure the ground state to ground state feeding of the β decay of 55Ca will

be conducted to determine if Urca cooling is effective in superbursting X-ray transients.

107

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108

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