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This is to certify that the
dissertation entitled

Study of 69Br Ground State Proton Emission and
Effects on the rp-Process 68Se Waiting Point

presented by

Andrew Michael Rogers

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Physics

 

 

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SIDS K:IProj/Aoc&Pres/ClRC/DateDue.indd

Study of 69Br Ground State Proton Emission and
Effects on the rp-Process 68Se Waiting Point

By
Andrew Michael Rogers

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Physics
2009

ABSTRACT

STUDY OF 69Br GROUND STATE PROTON EMISSION AND EFFECTS ON THE
RP-PROCESS 685e WAITING POINT

By
Andrew Michael Rogers

The rp-process determines the characteristic properties of the tail in X-ray burst
lightcurves and the nucleosynthesis occurring during such events. In high temper-
ature, hydrogen-rich environments the rp-process results from the breakout of the
hot CNO cycle leading to a series of fast proton captures and fi-decays involving
nuclei along the proton drip-line up to masses possibly as heavy as Te. Type I X-
ray bursts are thought to be key sites for this process. To realistically model the
rp-process in these systems experimental data such as masses, lifetimes, and pro-
ton capture rates along the proton drip-line are required. Such data are currently
lacking for many of these nuclei.

The 685e waiting point is of particular interest, where a long beta-decay half-
life coupled with inhibited proton capture restricts the amount of material that is
processed beyond mass 68 in the rp-process. However, the reaction rate for the
2p-capture process 68Se+p —>6gBr+p —+7°Kr depends exponentially on the 693r
proton separation energy and may bypass the waiting point. This separation en-
ergy is poorly constrained.

The first direct measurement of the proton separation energy for the proton un-
bound nucleus 693r has been performed. The newly developed MSU High Reso-
lution Array (HiRA) and a MicroChannel Plate (MCP) beam tracking system were
used for the first time together with the existing 3800 spectrograph at the National
Superconducting Cyclotron Laboratory (NSCL). The experiment was designed to
reconstruct the decays of proton unbound nuclei, specifically 69 Br, by detecting the

decay protons using HiRA in coincidence with a heavy residue, e. g. 685e, which is

measured in the large acceptance $800 magnetic spectrograph. We find that the
proton separation energy of 69Br is Sp = 78533 keV. In addition, the influence of

this new measurement on the rp-process is investigated using a one-zone X-ray

burst model.

To my family,

who have supported me during this long journey . . .

iv

ACKNOWLEDGMENTS

I would like to begin by expressing my deepest thanks to my adviser Bill Lynch.
His support over these past few years and his guidance have been invaluable. I will
always appreciate his ability to continue to hammer away at a problem until it is
understood and solved.

I would also like to thank Mike Famiano and Mark Wallace. Without their hard
work and determination this dissertation would not have been possible. I am in-
debted to both of you.

I would like to thank all of the members of the HiRA group that I have had
the pleasure of working with during my time as a graduate student. In particular,
I would like to thanks Betty Tsang for all her work and encouragement. I would
also like thank Vladimir and Daniela Henzl who are both wonderful and inspiring
colleagues as well as an excellent pair of friends.

I would like to thank all of my collaborators that I have had the privilege to
work with over the years. It was always an adventure running experiments with
Lee Sobotka, Bob Charity, Ion Elson, Romualdo de Souza, and Dan Shapira. I
learned a lot from all of them and I am greatly appreciative for everything they
have done for me.

I would like to thank all of the laboratory staff that have contributed in so many
different ways to my experiences at NSCL. I would like to thank in particular Len
Morris and Ronan Fontus who were always helpful when anything needed to be
designed (especially for all those parts that needed to be done now).

I would like to thank all of my friends that I have made during my time as
graduate student. I would especially like to thank Karinita for making so many of
my days so much brighter.

Finally, I would like to thank my family. Without the support of my parents,
Mike and Marlene Rogers, and my brother Matt and sister Michelle I would not be

where I am today. Whenever I needed them they were always there.

Contents

List of Tables ........................ ' ............. x

List of Figures .................................... xvii
Acronyms ....................................... xviii

1 Introduction .................................... 1

1.1 Nuclear Masses and their Relevance to Nucleosynthesis ........ 3

1.1.1 Nuclear Masses ........................... 5

1.2 Proton Emission from Nuclei ....................... 10

1.3 rp-Process .................................. 12

1.3.1 685e Waiting Point .......................... 15

1.4 Previous Studies and Observations .................... 19

1.4.1 First Attempts ............................ 20

1.4.2 Recent Predictions by Non-Observation ............. 21

1.4.3 Recent Predictions by Indirect Methods ............. 22

1.4.4 Summary ............................... 24

1.5 Dissertation Organization ......................... 27

2 Experimental Setup ............................... 28

2.1 Overview ................................... 28

2.1.1 Experimental Technique ...................... 30

2.1.2 Secondary Beam Production .................... 33

2.2 The $800 Spectrograph ........................... 36

2.2.1 Principle of Operation ....................... 37

2.2.2 Coordinate System ......................... 40

2.2.3 Inverse Map Reconstruction .................... 41

2.2.4 Cathode Readout Drift Chambers (CRDC) ........... 43

2.2.5 Ionization Chamber ......................... 44

2.2.6 Focal Plane Scintillators ...................... 44

2.3 Secondary Beam Tracking ......................... 45

2.3.1 Parallel Plate Avalanche Counters (PPAC) ............ 45

2.3.2 Micro-Channel Plate Detectors (MCP) .............. 46

2.3.3 Coordinate System ......................... 49

2.4 HiRA ..................................... 49

2.4.1 Silicon Detectors .......................... 50

2.4.2 CsI(Tl) Detectors .......................... 54

2.4.3 Coordinate System ......................... 55

2.4.4 ASIC (Application Specific Integrated Circuit) Electronics . . . 55

vii

3 Data Analysis ................................... 59

3.1 Monte Carlo Methods ............................ 60
3.2 Data Reduction Techniques ........................ 61
3.3 HiRA Calibration and Analysis ...................... 63
3.3.1 Pulser Calibrations ......................... 63
3.3.2 III-Source Calibrations ........................ 65
3.3.3 ASIC Readout Order Correction ................. 67
3.3.4 Light Nuclei Elastic Scattering ................... 72
3.3.5 Particle Identification Results and Discussion .......... 80
3.3.6 Detector Efficiency ......................... 81
3.4 MCP Calibration and Analysis ...................... 82
3.4.1 MCP Mask Calibrations ...................... 82
3.4.2 Calibration and Fitting Procedure ................. 86
3.4.3 Results and Discussion ....................... 88
3.5 5800 Calibration and Analysis ....................... 92
3.5.1 E1 Scintillator Corrections ..................... 93
3.5.2 CRDC Pad Calibration and Corrections ............. 95
3.5.3 CRDC Mask Calibration and Corrections ............ 98
3.5.4 Secondary Beam Identification .................. 101
3.5.5 Particle Identification ........................ 104
3.6 MCP 8: S800 Optics ............................. 107
3.7 69Br Proton Emission ............................ 112
3.7.1 Relative Energy Spectrum Construction ............. 112
3.7.2 Beam Energy and CsI(Tl) Calibration Correction ........ 115
3.7.3 Interpretation and Discussion ................... 118
4 69Br Proton Separation Energy and
Consequences for the rp-Process ....................... 123
4.1 Formation Process .............................. 124
4.2 Local Structure and the 695e Mirror Nucleus ............... 128
4.3 Lifetime Effects ............................... 133
4.4 Barrier Penetration in the WKB Approximation ............. 135
4.5 Fitting Methods and the 69Br Proton Separation
Energy .................................... 139
4.6 Possible Influential Factors on the Proton Separation Energy ..... 147
4.7 X-Ray Burst Calculations .......................... 153
4.7.1 No 2p-Capture (Q(p, 'y) = —2000 keV) .............. 155
4.7.2 Non-observation Limit (Q(p, 7) = —500 keV) .......... 155
4.7.3 Slightly Unbound (Q(p,'y) = —200 keV) ............. 157
4.7.4 Comparison of Results and Conclusion ............. 157
4.8 Extended Duration X-Ray Burst ...................... 161

viii

5 Summary ..................................... 171

5.1 Results .................................... 172
5.2 Outlook .................................... 172
5.2.1 The Influence of the 64Ge Waiting-Point ............. 173
Appendices ...................................... 177
A Kolmogorov-Smirnov Test ........................... 178
Bibliography ..................................... 183

ix

List of Tables

1.1

3.1

3.2

3.3

4.1

4.2

Previous predictions for the 69Br proton separation energy. For con-
sistency and where applicable the separation energy is calculated
using data from AME 2003 and Coulomb displacement from [1]. A
t denotes those values not explicitly stated in the reference but cal-
culated in this dissertation. A § denotes values that were originally

reported but altered for comparison using AME2003 and reference [1]. 25

Resolutions for the 8.784 86 MeV Ix-source peak for front strips for

each telescope .................................

Elastically scattered nuclei used in the CsI(Tl) energy calibration and

their kinetic. energies. ............................

Si detector manufacturer thicknesses and their inferred thicknesses

from deuteron elastic scattering. .....................

Summary of the predictions for the 693r proton separation energy

67

73

from this dissertation and their corresponding assumptions. ..... 145

Estimated electromagnetic spin-orbit shift, level energy, and excita-
tion energy assuming a (1 /2‘, 5 / 2‘, 3 / 2') ordering for the various
I” values being considered. The assumed proton separation energy
(636 keV) is predicted using the Schury [2] and Savory [3] mass mea-

surements + Coulomb displacement energies of reference [1] ...... 152

List of Figures

1.1

1.2

1.3
1.4

1.5

1.6

2.1
2.2
2.3

2.4
2.5
2.6
2.7
2.8
2.9

Segre chart. (Original image from NSCL INTRA image repository) . . 4

Illustration of quantum tunneling of a proton through the Coulomb
barrier. Neutrons, unlike protons, are charge neutral and are only

confined by the strong nuclear interaction ................. 12
Hot CNO cycle and breakout through 15003:, 'y)19Ne ........... 13
68Se waiting-point region of the nuclear chart ............... 16

Effective stellar half-life of 6’3Se as it depends on the 69Br proton
separation energy for various relevant temperatures and densities.
Here, 68Se is removed from the stellar environment either through B-
decay or 68Se(p, 'y)69Br capture reactions. (The temperature is given

in units of GK and the density in units of gm/cm3.) .......... 19
Comparison of the effective 688e stellar half-life for selected values

of the 69Br proton separation energy. ................... 26
Overhead view of the NSCL Coupled Cyclotron Facility. ....... 28
Cartoon of the 698r breakup reaction .................... 31

Schematic rendering of the coupled cyclotrons, A1900 fragment sep-
arator, and beamline to the S800. HiRA and the MCP tracking system

are located inside the target chamber .................... 34
S800 analysis line and spectrograph. ................... 37
S800 focal plane box. ............................ 39

S800 focal plane coordinate system translated into the target chamber. 40

MCP amplification process due to secondary electron emission. . . . 47
Top down schematic of an MCP beam tracking detector ......... 48
A HiRA telescope ............................... 50

2.10 HiRA configuration for experiment 02023. The secondary beam en-
ters from the left of the photo and exits the scattering chamber in
the gap between towers 1 and 2. (a) Two targets are viewable in the
photo. The upper target is a viewer used for beam tuning. Just be-
low is a Au target used for CsI elastic scattering calibration. (b) HiRA
configured with 4 towers of 4 telescopes each. (c) Copper bars and
lines used to cool the CsI preamplifiers. (d) Asic electronic box for

tower 3. (e) CsI pulser distribution box. ................. 51
2.11 HiRA telescope positions and their ID labels. .............. 52
2.12 Photographs of the unmounted HiRA E (DSSD) and AE (SSSD) de-

tectors. .................................... 53
2.13 Block diagram of a single channel of the HINP16C ASIC chip. . . . . 56
2.14 HiRA ASIC electronics setup. ....................... 58
3.1 Block diagram for the general data reduction procedure. ....... 62
3.2 Telescope 5 CsI 0 pulser ramp ........................ 64
3.3 Linear Fit of the telescope 5 CsI 0 pulser ramp. ............. 64

3.4 Telescope 9 228Th a-source calibration for all front strips of the DSSD. 66
3.5 Diagram of the chip/ channel / strip mapping for the HiRA DSSD. . . 68

3.6 ASIC readout order correction of the a-SOLII'CE calibration for Tele-
scope 5. The upper figure is the a-source spectrum for the front strips
before the correction while the lower figure is the spectrum after the
correction. .................................. 70

3.7 Distribution of channels per event that are readout from HiRA Tower
1. Events where 2, 3, or 4 strips are readout compose most, but not
all, of the data. Events with less than 2 channels are suppressed in
the plot. ................................... 71

3.8 Light nuclei elastic scattering peaks for uncalibrated telescope 5 C513. 73
3.9 CsI(Tl) x-offset dependence on Si thickness ................ 76

3.10 Calibration points taken from MS. (a) The proton PID band used to
obtain calibration points. The profile histogram is overlaid on the
rebinned histogram. (b) Linear fit relating the calculated CsI(T1) en- '
ergy as a function of the CsI(Tl) ADC channel. ............. 77

xii

3.11 Natural 3rd-order cubic spline interpolation of LISE++ calculation.
This provides an accurate conversion from energy loss in the DSSD
to calculated energy in the CsI(Tl). .................... 78

3.12 Telescope 5 CsI 2 calibration. Two points are used in the fit; the pro-
ton elastic scattering point and an zero energy x-offset point deter-

mined from a linear fit of the DSSD energy loss points. ........ 79
3.13 Spectra showing cleanly resolvable HiRA PID bands for p, d, t, 3He,

and 4He. ................................... 80
3.14 HiRA geometric efficiency as a function of the relative energy. . . . . 81

3.15 (a) Photograph of a rear view of the inserted MCP 1 calibration mask
and MCP 1 detector. The beam enters from the right of photograph.
(b) Schematic drawing of the MCP mask. All holes are separated by
5mm. The diameter of the smaller holes is 1 mm while the larger
holes that make up the L pattern are 2 mm. ............... 83

3.16 Photograph of the MCPO tracking detector during an Ix-source cali-
bration. The beam enters the chamber from the left side of the photo-
graph. Also shown is the upstream beam blocker in the background(left)
as well as a scintillator(right) used for detecting a coincidences. The
target drive enters at 60° supporting an aluminized mylar foil and
calibration mask. The bias cable attached to the target ladder is also
visible. .................................... 84

3.17 MCP a-source uncalibrated mask pattern for (a) MCP 0 and (b) MCP 1. 85

3.18 MCP secondary beam uncalibrated mask pattern for (a) MCP 0 and

(b) MCP 1. .................................. 85
3.19 MCP 1 mask pattern for (a) pedestal values —10 channels, (b) pedestal

values 0 channels, and (c) pedestal values +10 channels. ....... 87
3.20 Example of MCP pedestal stability tests .................. 87
3.21 MCP 1 corrected Y-position dependence on the sum signal ....... 89
3.22 Final MCP mask calibration spectra. ................... 90
3.23 Beam spots at (a) MCP 0 and (b) MCP 1. ................. 91
3.24 Timing signal for the E1 scintillator ..................... 94

3.25 The (a) uncorrected and (b) corrected E1 scintillator timing signal as
a function of the dispersive position in the focal plane .......... 94

xiii

3.26 Uncalibrated and calibrated CRDC 1 summed induced charge signal

spectra. .................................... 96
3.27 Saturation of CRDC 2 pad 52. ....................... 97
3.28 CRDC 1 uncalibrated non-dispersive mask calibration spectrum. . . . 98

3.29 CRDC uncorrected and corrected drift time signal as a function of
dispersive position. ............................. 99

3.30 CRDC Y1 / Y2 (a) uncorrected and (b) corrected non-linear tinting

signal correction. .............................. 101
3.31 Secondary beam PID based on the XFP and OB] ToF signals. ..... 102
3.32 Parameters for the TOP derivation. .................... 103
3.33 Components of the secondary beam. ................... 104

3.34 Uncorrected ToF signal as it depends on CRDCl (a) X and (c) Y com-
pared to the corrected dependence on CRDCl (b) X and (d) Y (gated
on 69Se). Similar corrections are done for ion chamber MS as well as

the dependencies on CRDC2 X / Y and APP. ............... 106
3.35 PID of reaction products in the S800 focal plane for (a) uncorrected

and (b) corrected ToF stabilization. .................... 107
3.36 8800 particle identification (PID). ..................... 108

3.37 MCP 1 mask image illustrating the unique correlation between (a)
the X-position and S800 ATA and (b) the Y-position and 8800 BTA (b). 109

3.38 Correlation of the Y-position at the target (YTA) for MCP 1 and the
3800 ....................................... 110

3.39 3800 and MCP angular correlations at the target position ........ 111

3.40 Plots illustrating the method for manually generating an improved
inverse transfer map based on the MCP data. .............. 113

3.41 Correlation between the 5800 and MCP dispersive angles (ATA),
from MCP mask calibration data, using the (a) 5800 inverse trans-
fer map and using the (b) manually created MCP inverse transfer
map ....................................... 114

3.42 HiRA 68Se and S800 proton coincident yields ............... 116

xiv

3.43 Simulation illustrating the effect of a CsI miscalibration due uncer-

tainty of the true secondary beam energy. ................ 117

3.44 Difference between the peak position for forward and backward

proton emission angles (in the COM frame) for the low p+685e rel-
ative energy peak as a function of scaled total proton kinetic energy.
The forward and backward peaks overlap when the energy is re-
duced by ~ 0.8 % ............................... 118

3.45 Relative energy (Q-Value) spectrum for coincident p+685e events. . . 119

3.46 Relative energy (Q-Value) spectrum for proton emission from 695e,

4.1

4.2

4.3
4.4

4.5

4.6

4.7

4.8
4.9

68Se, 68As, and 67As normalized to the p+685e spectrum from [6, 10]
MeV as compared to the 69 Br decay. ................... 122

68Se momentum distributions associated with the 71 Br and 70Se sec-
ondary beams. The peaks are fit using the methods in the fragmenta-
tion study of Mocko et al. [4]. High momentum events for reactions
involving the 71 Br beam are clearly missing due to the acceptance of
the 5800 spectrograph. ........................... 125

685e momentum distributions corresponding to the proton emission
peak compared to the momentum expected from the simple proton
fusion and transfer models described in the text. ............ 125

Level diagram for the low-lying states in the 69Se mirror nucleus. . . 129
Comparison of low-lying states in the 71 Br, 73Br, and 753r isotopes. . 132

Illustration of finite particle lifetimes on the determination of the

emitted proton angle ............................. 134
Simulation of proton emission from states with finite lifetimes in
698r for Q = 810 keV. ............................ 135
Line shape dependence on CsI energy resolution. Changes in energy
resolution effect the width of the peak distribution ............ 136
Typical potential used for the WKB approximation. .......... 137

(a) The various components of the optical model + centrifugal po-
tential used to estimate lifetimes in the WKB approximation and (b)
the summation of all potential components ................ 139

XV

4.10 Gaussian fits of simulated decay peaks produced over a range of
relevant Q—values for (a) l = 1 and (c) l = 3 orbits. A comparison
of the observed to actual decay Q—value is shown in figures (b) for
l = 1 and (d) for l = 3. ........................... 140

4.11 Simulated decay spectra from the 698e mirror states and the compar-
ison of the simulation to data. ....................... 141

4.12 Best-fit of simulated decay from 69Se mirror level adjusted for our
Sp value. ................................... 143

4.13 Best-fit of the experimental data from a set of simulations with the
level in 69Se but with the 5 / 2' level unconstrained in energy. The
best-fit suggests that the 5/ 2" and the 3/2" are inverted compared
to the mirror nucleus ............................. 144

4.14 Systematic trends and the predicted level spacing in 69Br based on
the known structure of the nearest Br isotopes. ............. 145

4.15 Comparison of the 69Br proton separation energies obtained in this
dissertation to previous works. ...................... 146

4.16 Comparison of simulated decay from a 9/ 2+ (1 = 4) to the experi-
mental data where the lifetime has been estimated using the WKB
approximation. The tail at lower Q-values does not match the data
indicating that the decay peak is not due to decays from a long-lived
9/ 2+ state. .................................. 151

4.17 X-ray luminosity, nuclear energy generation, and abundance versus
processing time where the 2p-capture on 685e has been effectively
removed from the network calculation. This was accomplished by
setting the (p, '7) to a large (Qpfl = -—2000 keV) value. ......... 156

4.18 X-ray luminosity, nuclear energy generation, and abundance versus
processing time for QM, = —500 keV. .................. 158

4.19 X-ray luminosity, nuclear energy generation, and abundance versus
processing time for Qpfl = —200 keV. .................. 159

4.20 X-ray luminosity, nuclear energy generation, and abundance versus
processing time for Qpfl = —785 keV. .................. 160

4.21 Comparison of the luminosity, nuclear energy generation, and tem-
perature for 685cm, ’rl6gBr Q—values of —200, —500, and —785 keV. . . 162

xvi

4.22 Final abundances versus mass number for the Q—values used in the
one-zone X-ray burst model. The recommended 64Ge(p, '7) Q—value
was used in this calculation. ........................ 163

4.23 Difference between the final abundances for Qp,7 = —785 keV and
Qpfl = —500 keV. .............................. 164

4.24 X-ray luminosity, nuclear energy generation, and abundance versus
processing time for Qpfl = —2000 keV for the extended duration burst. 165

4.25 X-ray luminosity, nuclear energy generation, and abundance versus
processing time for (2p,7 = —500 keV for the extended duration burst. 166

4.26 X-ray luminosity, nuclear energy generation, and abundance versus
processing time for Qpfl = —200 keV for the extended duration burst. 167

4.27 X-ray luminosity, nuclear energy generation, and abundance versus
processing time for QP/r = -785 keV for the extended duration burst. 168

4.28 Comparison of the luminosity, nuclear energy generation, and tem-
perature for 68Se(p, 'y)69Br Q—values of —200, —500, and —785 keV
for the extended duration burst ....................... 169

4.29 Difference between the final abundances for Qpfl = —785 keV and
Qpfl = —500 keV for the extended duration burst. ........... 170

5.1 Comparison of the luminosity, nuclear energy generation, and tem-
perature for 68Se(p, 'y)6gBr Q-values of —200, —500, and —785 keV at
high and low 64Ge(p, 'y)65As Q-values corresponding to the current
uncertainty in the waiting point. ..................... 174

5.2 Comparison of the luminosity, nuclear energy generation, and tem-
perature for 68S€3(p, ’7)693r Q—values of ——200, —500, and —785 keV
for the extended burst. ........................... 175

A.1 Empirical distribution function (EDF) for the example dataset in Equa-
tion A3. The EDF increases by 1 / n at each data point in the set. . . . 180

A2 Example of the Kolmogorov-Smirnov test using a randomly sam-
pled Landau distribution. ......................... 180

IMAGES IN THIS DISSERTATION ARE PRESENTED IN COLOR.

xvii

Acronyms

ADC analog-to-digital converter.
AME Atomic Mass Evaluation.

ASIC application specific integrated circuit.

CB chipboard.

CCF Coupled Cyclotron Facility.

CDE Coulomb displacement energy.
CDF cumulative distribution function.
CED Coulomb energy difference.

CFD pseudo-constant fraction discriminator.
COM center of momentum.

CPT Canadian Penning Trap.

CRDC cathode readout drift chamber.
CSA charge sensitive amplifier.

CSSl first cyclotron.

CSSZ second cyclotron.

DAC digital-to-analog converter.
DAQ data acquisition.

DSSD double-sided strip detector.

EB E-back.

ECR electron cyclotron resonance.
EDF empirical distribution function.
EF E-front.

FEE front end electronics.

FPGA field-programable gate array.

xviii

FRDM Finite-Range Drop Model.
FW HM full width at half maximum.

HCNO hot CNO.
HiRA High Resolution Array.

IAS isobaric analog states.
IMME Isobaric Mass Multiplet Equation.
ISOL Isotope Separator On-Line.

LMXB low-mass X-ray binary.

MCP micro-channel plate.

NSCL National Superconducting Cyclotron Laboratory.
0B] object plane.

PAC proposal advisory committee.
PCB printed circuit board.

PID particle identification.

PMT photomultiplier tube.

PPAC parallel plate avalanche counter.
QDC charge-to-digital converter.

SNR signal-to-noise ratio.

SSSD single-sided strip detector.

TDC time-to-digital converter.

ToF time of flight.
TPC Time Projection Chamber.

TVC time-to-voltage converter.
WKB Wentzel-Kramers-Brillouin.

XFP extended focal plane.

XLM universal logic module.

xix

Chapter 1

Introduction

Man is slightly nearer to the atom than to the star. ... From his
central position man can survey the grandest works of Nature
with the astronomer, or the minutest works with the physicist.
...Knowledge of the stars leads through the atom; and
important knowledge of the atom has been reached through the
stars.

Lecture 1. Stars and Atoms (1928, 2007)

SIR ARTHUR STANLEY EDDINGTON

We interact with a world made of atomic nuclei. Atoms are composed of three
fermions; protons, neutrons, and electrons. Altering the numbers of protons and
consequently the number of electrons in the atom results in the vastly different
properties of the chemical elements as is seen throughout the periodic table. These
basic building blocks give rise to much of the complexity observed within the nat-
ural world.

One of the long-standing scientific problems of our time is a fundamental un-
derstanding of the origin and evolution of the universe and the material of which
it is composed. It is now known that the universe is 13.734183}? billion years old [5].
In this vast time the matter composition of the universe has changed dramatically.
Approximately 10‘6 s after the Big Bang conditions existed in the universe that

allowed for the formation of baryons such as protons and neutrons. Light nuclei

soon followed after ~ 10 s resulting in primordial mass fractions for hydrogen and

deuterium of X 2 0.76, 3He and 4He of Y 9: 0.24, and all heavier elements, generi-
cally referred to as ”metals”, of Z s 0.01 [6]. From this initially hot, dense plasma
galaxies, stars, and even planets eventually formed. The subject of nucleosynthesis
describes how the matter composition of the universe has evolved from the light
nuclei characteristic of the early universe into the distribution of heavy element
abundances that we observe today. In general, eight processes, first suggested by
Burbidge, Burbidge, Fowler, and Hoyle (BZFH) [7], are capable of generating al-
most all known nuclear species. These processes are at the core of more than 50
years of investigations into the chemical evolution of the cosmos.

Both astronomical observations and nuclear physics knowledge play critical
roles in quantifying and constraining the synthesis of the elements. The energy
generation in stars is due to nuclear fusion, where lighter nuclei combine to form
heavier ones and release energy. Stars do not live forever however. They burn, ex-
haust their fuel, and die, in some instances, in energetic and violent explosions
known as supernova. Other violent explosions, such as novae, can also occur on
white dwarfs or in the form of X-ray bursts on the surfaces of neutron stars. Evi-
dence for the active production of the heavy elements is found, for example, in ob-
servations of short-lived 44Ti, which can only be produced in supernova events [8].
In general, precise nuclear physics data is often necessary to describe the nucle—
osynthetic processes in such explosions and provide a quantitative modeling of
the observational data obtained by astronomers. These extreme astrophysical en-
vironments can be the factories that produce the heavy elements and eventually
spew them into the interstellar medium. The measurements in this dissertation
can have a bearing on the rapid proton capture process in these environments and
on the nucleosynthesis that occurs during X-ray bursts.

In the remainder of this chapter, some basic concepts of nuclear physics and

nuclear astrophysics are discussed; the concepts are important to later chapters in

this dissertation. Section 1.1 provides an overview of the chart of nuclides and basic
properties of the nuclear landscape. Subsection 1.1.1 introduces concepts relevant
to nuclear masses and separations energies. Section 1.2 discusses proton emission
from nuclei. Section 1.3 discusses the astrophysical rp-process and the rp-process
68Se waiting-point. Section 1.4 provides a review of the previous works on the 6E’Se
waiting point and the ground state mass of 698r. Finally, Section 1.5 provides a

brief outline of the remaining chapters.

1.1 Nuclear Masses and their Relevance to
Nucleosynthesis

Nuclei are composed of two types of fermions, protons and neutrons, that together
are called nucleons. The nucleus itself contains over 99 °/o of the mass of the atom.
The number of protons, Z, in the nucleus defines the element. The number of neu-
trons, N, defines the isotope of that element. The total number of nucleons is de-
noted by the mass number A = N + Z. While in principle any number of Z protons
and N neutrons can be combined, not all combinations are bound. Suppose one
places points on a graph of a specific color for each combination of proton number
and neutron number where a nucleus has been observed. Or, one chooses another
color to label nuclei that have not been observed but may ”exist” long enough to
someday be observed. Then, one produces a Segre chart such as the one shown in
Figure 1.1. Here, the known stable (black squares) and unstable (blue squares) nu-
clei are shown together with the yet unexplored regions, ”Terra Incognita”, shown
as the red region that represents possible nuclei that may be observed in the future.
We define a nucleus as existing if it has a lifetime on the order of milliseconds since
unbound nuclei typically have lifetimes shorter than this. In general, this means
that the nucleus decays by ,B-decay, or in the case of heavy nuclei, by a-decay. En-
ergetically, unstable nuclei try to minimize their energy through decay to the stable

nuclei and, eventually, reach the ”Ii-stable valley of stability.”

 

120_ I I I I I I I I l_‘

100-

60-

Proton number

40*

   

Observed nuclei
I Stable nuclei

 
 

—:

 

 

q.
0 1 I I I I I I I

o 20 40 60 80 100 120 140 160 180
Neutron number

 

Figure 1.1 — Segre chart. (Original image from NSCL INTRA image repository)

There are a number of fundamental issues that govern the trends displayed
by Figure 1.1. First, for a fixed stable Z, neutrons can be added or removed mak-
ing heavier or lighter isotopes, respectively, until one creates nuclei that have no
bound states. At the limits where the least bound nucleon is energetically unbound
(negative separation energies) the nuclei are very short lived. Such nuclei decay by
proton emission if they are at the left boundary and by neutron emission if they
are at the right boundary. These boundaries are often called the proton and neutron
drip-lines, respectively.

Clearly, the drip-lines on the Segre chart are not symmetric with respect to the
N = Z line, indicating differences in the properties of the proton and neutron.
These differences are mainly due to the symmetry and Coulomb energies. The
symmetry energy, which is o< (N — Z)2A‘1, tends to increase the binding for nu-

clei with the same number of neutrons and protons. This is the case for the light-

 

est stable nuclei which have equal numbers of neutrons and protons. However,
the Coulomb repulsion of the protons brings in an energy term o< ZZA‘1/3. This
term reduces the binding energy for proton-rich nuclei. As the mass number, A,
increases so does the ratio of neutrons to protons in stable nuclei. The resulting
change in Coulomb energy shifts the proton drip-line closer to and the neutron
drip-line farther away from the N = Z line.

1.1.1 Nuclear Masses

Limits on the domain of particle bound nuclei shown by the Segre chart are de-
fined by the possibility of proton and neutron decays. These decays can occur if
they are energetically allowed; this is governed by nuclear binding energies, i.e.,
by the masses of nuclei. Nuclear and atomic masses are intimately tied to model
calculations of the rp-process. Consequently, these concepts will be defined in this
section, and are key to the remainder of this chapter and to this dissertation as a
whole. Furthermore, this dissertation focuses on the experimental determination
of the 69Br proton separation energy which is equivalent to the 68Se(p, '7) ground
state capture Q—value. When combined with recent measurements of the mass of
683e, the proton separation energy yields the mass of 69Br. These quantities are de-
fined in this section. In addition, one may estimate masses using calculations of
the Coulomb energy differences between ”mirror nuclei.” This relationship will

also be discussed.
Masses, Binding Energies, and Q-Values

The invariant mass, m, for a single particle is defined by the well known relation,

me2 = E2 —- lp'CI2 (1.1)

where E is the total energy of the particle and p is its spatial momentum. This
relationship is true regardless of whether the particle is point-like or a composite
system composed many elementary particles. For a composite system the invari-
ant mass, Mcz, includes contributions from the internal energy of its components
as well as from any fields, such as the Coulomb, or nuclear mean fields which
contribute to its binding. Consequently, the invariant mass of a composite system
will in general be different from the sum of the individual masses of which it is
composed.

For a neutral atom with Z protons and N neutrons the atomic mass is defined

as,
MA(Z, Me2 = Z(Mp + Me)c2 + NM..c2 — BE(Z, N) (1.2)

where B E(Z, N) is the total binding energy of the atom and Me, MP, and Mn are
the free electron, proton, and neutron masses respectively. In addition, the nuclear

mass can be given in terms of the atomic mass by,
MNuc(Z, N)c2 = MA(Z, N)c2 — 2M..c2 + 3139(2) (1.3)

where BEe(Z) is the binding energy of the electrons and Me is the free electron
mass. Generally, unless otherwise stated, most mass tables use atomic masses as
opposed to nuclear masses. It should be noted that the atomic binding energy is
small compared to the nuclear binding energy. For the purposes of this dissertation
one can calculate nuclear masses using the formula for the electron binding energy

from Lunney, Pearson, and Thibault [9],

BE, 2 14.4381 - 22-39 + 1.554 68 x 10-6 - 25.35 eV (1.4)

 

as is suggested by the Atomic Mass Evaluation (AME) 2003 [10].
For calculating the energetics of nuclear reactions the atomic mass excess, A (Z, N),

is a useful quantity,

A(Z, N) = [MA(Z, N) —— AM,,]c2 (1.5) I

= [MA(Z, N) [amu] — A] - 931.478 MeV. (1.6)

Here, Mu is the atomic mass unit and is defined to be 1/ 12 the mass of a neutral
12C atom. In a reaction of the type 1+2 —> 3+4 the Q-value, or the energy absorbed
or released in the reaction, is given by the difference of initial and final atomic

masses,

Q = (M + M2 — M3 — M4)c2 (1.7)

= A1 + A2 — A3 *- A4 (1.8)

where the A’s are the respective atomic mass excesses. If the total nuclear charge
changes as it does in the case of B-decay, then one must calculate the Q—value from
the nuclear masses. As this dissertation is focused mainly on (p, 7) ground state

capture Q—values we have,

Qm = [M(Z, N) + MH — M(Z + 1, N)]c2 (1.9)

 

Finally, we can define the proton separation energy as the energy required to re-

move a proton from the nucleus and take it out to infinity,

sp(z, N) = BE(Z, N) — BE(Z —- 1, N) (1.10)
= [—M(Z, N) + M(Z —- 1, N) + MH]c2 (1.11)
2 —(2p (1.12)
= QM. (1.13)

In case of proton decay from the ground state, the separation energy is equal in
magnitude but opposite in sign to the ground state proton decay Q-value, QP. How-

ever, the proton capture Q-value, me is equivalent to the proton separation energy.
Coulomb Energy Differences (CED)

This method of determining masses relies on the isospin independence or invari-
ance of nuclear forces [11]. In the isospin formalism, the proton and neutron are
treated as two states of a nucleon (Isospin is completely analogous to spin). All nu-
cleons are assigned an isospin of t = 1 / 2, where the 3rd component of the isospin
vector determines whether the nucleon eigenstate is a proton (tz = —1 / 2) or a
neutron (t2 = +1/ 2). The total isospin quantum number, T, of a nucleus is the
magnitude of the vector sum of the individual nucleon isospins. The group theory
formalism for isospin is similar to spin: one constructs corresponding T+ (raising)
and T‘ (lowering) operators acting within isospin space. The isospin operators
commute with the strong interaction part of the Hamiltonian. If one operates with
T T on an eigenstate of a nucleus with (Z, N), one either creates an eigenstate of
the nucleus with proton number Z + 1 and neutron number N — 1 or zero. The
latter occurs when the orbit of the new proton that would be converted from a
neutron by the operator T‘ is already occupied. T“ and T" do not change A or

the total isospin T. These operators only convert states in the same isospin multi-

plet, i.e., states with the same isospin quantum number, T. Such states are known
as isobaric analog states (IAS). Additionally, the 3rd component of total isospin,
T2 = (N — Z ) / 2, defines the nucleus with mass number A.

The nuclear part of the binding energy is the same for two analog energy states
in neighboring nuclei because T commutes with the strong interaction Hamilto-
nian. The Coulomb part of the binding, however, does not: energy differences be-
tween the same IAS in neighboring nuclei are due to isospin non-conserving inter-
actions (particularly the Coulomb interaction). These energy differences are gener-
ally known as the Coulomb energy difference (CED)*. The Coulomb displacement
energy (CDE), D(T, Tz, k), refers to the total binding energy difference between any

two members of an isospin multiplet,

D(A, T2, k) = BE(A, :rZ + k) — BE(A, T2) (1.14)

= M(A, 13).:2 — M(A, T2 + k)c2 + kAanz. (1.15)

where k is the number of protons exchanged for neutrons, TZ is the projection of
the nucleus with the largest Z, and Ann is the neutron-Hydrogen atomic mass
difference [13]. The binding energy of 69Br can therefore be predicted from the

known binding energy for 69Se by calculating

313(69Br) —_— BE(69,TZ = —%) = BE(69,TZ = %) — D(69,T = —%,1) (1.16)

The atomic mass for 693r is,

M(69Br)c2 = M(69Se)c2 + D(69, T, = £, 1) — Aan2 (1.17)

' A thorough review of Coulomb energy differences can be found in [12].

 

and the proton separation energy for 69Br is,

5., = M(685e)c2 — M(69Br)c2 + mm2 (1.18)
= D(69, T = é) — Aan2. (1.19)

As will be discussed in Section 1.4, calculations of the Coulomb displacement en-
ergy (CDE) have been used to predict the 69Br mass in many previous studies.
The fundamental importance of CDEs and their application to extracting nu-
clear structure information has resulted in extensive theoretical studies. Most no-
tably, CDEs for a number of experimentally known isobaric analog states (IAS)
were calculated in the review of Nolen and Schiffer [12]. In their calculations Nolen
and Schiffer initially included the three most dominant terms to the CDE: the
direct, exchange, and electromagnetic spin-orbit terms (the electromagnetic spin-
orbit term will be discussed in more detail in Section 4.6). However, these calcu-
lations were unable to account for the full Coulomb displacement energies de-
termined from the experimental data. Additional ”correction” terms were then
calculated which included Coulomb perturbation, spreading width, nuclear rear-
rangement, isospin impurities in the core, intrashell interactions, and correlation
terms; but even then there was still, on the average, a ~ 7% under-estimate of the
CDE [13]. This under-estimate of the CDE, which persists to this day, is know as
the Nolen-Schzfi‘er Anomaly. In the discussions based on CDEs that follow in this
dissertation it should be kept in mind that while there have been improvements in

the theoretical calculations, some contributions still remain poorly understood.

1.2 Proton Emission from Nuclei
Moving away from the valley of stability toward more proton-rich nuclei we find
that fi+-decay is usually the favored decay mode. However, as one approaches

the proton drip-line, the nuclear force is no longer able to bind the last proton. As

10

 

the proton becomes more unbound, decay by emission of a proton can compete
with B+-decay. In some nuclei it becomes the dominant mode of decay. The bal-
ance between these two decay modes depends sensitively on the Coulomb and
centrifugal barriers. Moreover, in certain cases, decay by two-proton emission is
also possible [14].

Decay by proton emission, sometimes referred to as proton radioactivity", was
first outlined in a review by Goldanskii [15]. While proton emission from long-
lived excited states has been investigated since the 19705 in 53mCo+ [16], the first
clear experimental evidence for ground state decay, the decay of 147Tm [17], was
not found until the early 1980s. Subsequent discoveries of proton emission from
151 Lu [18], 113Cs, 109I [19], and eventually other exotic heavy isotopes like 117La [20]
and 135Tb [21] have motivated additional measurements. Today, experiments have
identified approximately 25 ground state proton emitters [22]. Their properties are
mostly well understood theoretically [23, 24] and, since p-decay is similar to a-
decay, reasonably accurate estimates of decay lifetimes can often be made [25].

The decay rates for proton emission from proton-rich nuclei near the drip-line
is almost completely determined by quantum mechanical tunneling through the
Coulomb barrier. Protons, unlike neutrons, even at unbound energies (E > 0), are
still confined by the Coulomb barrier. Classically, protons with energies less than
the height of the Coulomb barrier would not be emitted; the nucleus would there-
fore only undergo B-decay. However, as illustrated in Figure 1.2, quantum mechan—
ics allows the unbound proton to tunnel through the ”classically forbidden” region
and be emitted as proton radioactivity. The tunneling penetrability is determined

by the width and height of the barrier through which the proton must tunnel. For
unbound protons with energies near the barrier momentum the barrier is thin and

the tunneling time is short. At much lower proton energies the proton must tunnel

 

 

f. This is actually a slightly deceptive term as it implies that it is the proton that is undergoing decay.
The letter ”m” denotes that the nucleus was in an excited isomeric state.

11

 

_ O Proton
E Coulomb BarrIer . Neutron

 

Figure 1.2 — Illustration of quantum tunneling of a proton through the Coulomb bar-
rier. Neutrons, unlike protons, are charge neutral and are only confined by the strong
nuclear interaction.
through a thick barrier due to the long 1/ r tail of the Coulomb interaction. This
reduces the penetrability so much that B-decay can be the dominant decay mode

even when the nucleus is energetically unbound with respect to proton decay.

1.3 rp-Process
While certain processes, like the r and 5 process, proceed mainly through neu-
tron captures some processes proceed mainly through proton captures. Nucleosyn-
thesis processes that burn hydrogen synthesize elements only accessible from the
proton-rich side of the valley of stability. In particular, the rp-process (rapid pro-
ton capture process) has been identified as a possible contributor to the light nuclei
abundances as well as elements beyond the iron group. The formal description of
the rp-process was initially detailed by Wallace and Woosley [26]. It occurs follow-
ing the breakout from the hot CNO (HCNO) cycle and is characterized by rapid
proton captures on seed nuclei that drive the composition towards the proton drip-
line interspersed with B-decays that drive the composition toward the valley of B-
Stability The nuclear energy generated during the rp-process is thought to power

the light curves in explosive hydrogen burning events in sites where the rp-process

12

 
          

21Na 22Na

19Ne 20Ne 21Na

Figure 1.3 — Hot CNO cycle and breakout through 15O(a, 'y)19Ne.

is expected to occur, such as Type I X-ray bursts. However, modeling of the rp-
process path and the abundances of nuclei, especially those heavier than Fe, are
limited by uncertainties in the nuclear physics of the involved nuclei.

In principle, all allowed decay and capture processes between nuclear species
can occur during stellar burning. However, the conditions of the system (i.e., tem-
perature, density, composition, etc.) and nuclear properties dictate which processes
dominate. In hot hydrogen rich environments where temperatures exceed 8 X 107 K

hydrogen burns in the HCNO cycle [27, 28],
12C(Pr7)13N(PI7)140(5+)14N(P1 ’Y)150(/3+)15N(P1“)12C (120)

as shown in Figure 1.3 and can be the major source of energy production. At tem-
peratures exceeding 5 x 108 K the reactions 150(a,’)')19Ne and 18Ne(oc,p)21Na al-
low "breakout” from the HCNO cycle. Proton capture on 19Ne removes it from the

HCNO cycle and allows the production of heavier masses via rapid proton cap-

13

tures. These captures, however, are limited by the proton drip-line, B+-decay rates,
and the abundance of protons. In addition, as Z increases so does the Coulomb bar-
rier that charged particles must overcome. This reduces the capture rates for higher
masses which is especially relevant to any or induced reactions. On nuclei along the
rp-process path proton capture can be inhibited by Q-values or Coulomb barriers.
If these nuclei have long B-decay half-lifes compared to proton capture rates or B-
decay rates of other nuclei in the process, they are called waiting-point nuclei. This
is because the capture process has to wait for the relatively slow B-decay, resulting
in large abundances of nuclei accumulating at these points.

While a number of rp-process sites have been proposed [29, 30] one of the most
likely scenarios are Type I X-ray bursts found in low-mass X-ray binary (LMXB)
systems. A LMXB is formed in a system with a typically low mass companion
in orbit with a compact stellar object such as a neutron star. Matter that becomes
gravitationally unbound from the companion star is transferred to the compact
object [27]. A persistent flux of X-rays is observed from such systems due to the
conversion of gravitational potential energy of the infalling material. The compo-
sition of the accreted material is typically rich in both hydrogen and helium, which
is the thermonuclear fuel for the burst. Eventually, the accreted fuel accumulates
on the neutron star surface where it is compressed and heated to high temperatures
(T 2 0.5 x 109 K) and densities (p ,2 104 gcm’3) [31]. This environment provides
the necessary conditions for helium to ignite due to a thin shell instability in which
the layer is heated more efficiently than it can cool and the burning becomes ex—
tremely temperature sensitive. The resulting release of nuclear energy is observed
as a large transient increase in the X-ray luminosity.

These sudden energetic X-ray burst events are capable of generating ~ 1039 ergs
of energy or more and have been observed with X-ray observatories such as Chan-

dra and XMM-Newton. The observed X-ray flux typically has a short rise time on

14

the order of 1 s driven by the initial unstable helium burning. As the initial explo-
sive burning ends, the up and rp-processes, responsible for the extended energy
generation in the tail of the burst profile, produce heavy nuclei. The duration of
these bursts are found to be typically on the order of ~ 10 s to 100 s. This implies
that any nucleosynthesis process must occur on a timescale of this order. Further-
more, if the accretion of material continues, these bursts may occur periodically
with recurrence times typically on the order of hours or days. The properties of the
burst depend critically on the accretion rate, composition of the accreted material,
and the composition of the surface layers of the neutron star. Since these bursts
reoccur, incomplete burning will contribute ”ashes” from previous bursts to the
initial composition of the next burst [32, 33].

In regard to rp-process nucleosynthesis, it may be possible to reconcile large
observed overabundances of certain A ~ 80 —— 100 nuclei and account for the solar
abundance of a number of nuclei, such as 92Mo and 96Ru [27, 34], that cannot be
produced in the p-process. The ejection of only ~ 0.3% of the ashes produced
via the rp-process in type I X-ray bursts would be needed to account for the solar
abundance patterns" [31]. The possibility of processing material as high as Te has
also been proposed [35] although it is uncertain as to how plausible this actually
may be [36]. Furthermore, it is thought that no material will escape from the X-ray
burst due to the large gravitational potential of the neutron star [26]. If another site
for the rp-process is found where the gravitational potential can be overcome this

issue could be resolved.

1.3.1 5882 Waiting Point

Waiting points along the rp-process path significantly control the abundance flow
from lighter to heavier masses along the proton drip-line. The 64Ge, 68Se, and 72Kr

 

‘ The ejection factor (escape factor) was estimated using assumptions about abundance overpro—
duction factors, total galactic nucleosynthesis time, and the galactic disk mass as well as X-ray burst
birth rate, system lifetime, and mass transfer rate [31].

15

 

Half-Life

n ~minutes
E] ~seconds
I ~ms

I <ms

[:j Unknown

AZ

 

 

 

 

Drip-Um

 

 

Process

I (10.7)
n B+-decay
I mp)

655a
<50ms

 

 

 

 

 

 

Figure 1.4 — 68Se waiting-point region of the nuclear chart.

waiting points are keys to understanding the amount of material that can be pro-
cessed through this region and ultimately affect the observed properties of astro-
physical events such as X-ray bursts. In particular, the 68Se waiting point has been
an intense source of interest, both from astrophysical and nuclear structure points
of View. Its long B+-decay half-life combined with its Q-value inhibited proton
capture rates greatly reduces processing isotopes to Kr and above. However, the
waiting point may be bypassed through 2p-captures to 70Kr [31], potentially al-
tering the final isotopic abundances significantly. The extent to which this occurs
depends exponentially on the 68Se(p, 'y)6gBr Q-value.

Following the general rp-process flow, under the correct conditions, into the
Se region one finds a large fraction of the matter contained in 6”Se nuclei. As illus-
trated in Figure 1.4, proton captures through the 64Ge waiting point (“Ge(p, 7)65As)
reach 66Se just below the proton drip-line. Proton captures on 66Se produce 67Br
which is believed to be sufficiently proton unbound that it will immediately decay

by proton emission. The abundance flow of 66Se will instead proceed through 5-

16

decay to 66As. Proton captures on 66As produce 678e, which also eventually under-
goes B-decay to 67As because proton captures to 688r are expected to be inhibited
by the drip-line. Proton capture reactions on 67As generate 68Se: proton captures on
68Se are again expected to be suppressed by the large Q-value characteristic of nu-
clei on the proton drip-line. If proton capture on 68Se cannot occur, the rp-process
must wait for the B-decay of 68Se to 68As (T1 /2 2 35.5 s) in order to continue cap-
turing protons and processing to higher masses. The 6E’Se lifetime is comparable to
the timescale (~ 10 s to 100 s) for a typical X-ray burst. So, the rate for proton cap-
ture on 685c, though small, may be a significant factor in allowing the generation
of nuclei in the rp-process beyond A z 68.

Whether or not‘proton captures to unbound nuclei like 69Br play a role in the
rp-process depends closely on details of the locations and excitation energies of
the low-lying levels in the unbound 69Br nucleus, and the structure of these states.
In principle, the existence of low-lying states in 69Br means that, given sufficient
hydrogen, 685c, and sufficient time a second proton can be sequentially captured
on an equilibrium abundance of 69Br to produce 7°Kr, which is bound. As the 70Kr
B-decay half-life is relatively short (T1 /2 = 52 ms) this opens an additional channel
through which the 685e waiting point can be effectively bypassed, allowing the
rp-process to continue to heavier masses without waiting for the B-decay of 68$e.

The role of 2p-capture reactions in X-ray bursts was first thoroughly investi-
gated by Schatz et al. [31]. Here, they derived the approximate stellar 2p-capture
reaction rate (for T ,S 1.5-2.0 GK) in terms of the proton capture Q-value and tem-

perature as,

 

 

271712 3/2 G (T) Q (pr '7)
2 2 2 (Z+1,N) (Z,N)
_— Y p N ( ) ZG(Z.N)(T) exp( kT )(Pr’7>(z+1,N) (1.21)

17

where Yp is the proton abundance, p is the density, G(z+1,N) (T) and G(Z,N) (T) are
the partition functions, N A is Avogadro’s number, and (p, 7)( Z+1,N) is the reac-
tion rate for the second proton capture. The exponential whose argument is the
Q—value, or equivalently the proton separation energy (Qp = —Sp), dominates the
dependence of the reaction rate.

The effects on the abundance at the 68Se waiting point can be crudely illustrated
by considering its effective half—life. Further processing in the rp-process is directly
related to how much 68Se is destroyed. Taking into account the destruction of 68Se
through B-decay and proton capture to 693r the effective destruction rate for 6BSe

(for T ,‘S 1.5-2.0 GK) in the stellar environment is [31],

 

27th2 3” G (l') S
2 2 2 Br P
Aeff —— A5 + Yp p NA (—kT ) ZG (T) exp(kT) (Irv)3,. (1.22)

Here, A); is the 68Se B-decay rate, Yp is the proton abundance, p is the density, G3,
and Gs, are the respective Br and Se statistical factors involving spin, and (171/)3, is
the reaction rate for proton capture on 69Br. The effective half-life,

teff __ 111(2)

of 68Se for a density (p = 1 x 106 gm/cm3) and temperature (T = 1.5 GK) of a
typical X-ray burst, as well as for a variety of possible desities and temperatures,
is shown in Figure 1.5. For the most unbound separation energies no 69Br will be
produced through proton capture and the effective half-life of 68Se remains at its
,B-decay value of 35.5 s. As the separation energy becomes more positive the ex-
ponential term begins to dominate, very rapidly destroying 685e below ~500 keV.
Clearly, the proton separation energy has a drastic effect on the lifetime of 68Se in

the stellar environment of an X-ray burst, quickly varying by orders of magnitude.

18

5i.

I I I I I I l I

 

I IIleI II WIT

 

.5

O
I
/

 

 

 

10'1

-2.0 -15 -1.0

10'2
-0.5 0.0 0.5 1.0
sp[MevI

 

 

 

“Se Effective Stellar Half-Life [5]
/

 

 

 

 

Figure 1.5 — Effective stellar half-life of 68Se as it depends on the 69Br proton separation
energy for various relevant temperatures and densities. Here, 68Se is removed from the
stellar environment either through ,B-decay or 68Se(p, 7)69Br capture reactions. (The
temperature is given in units of GK and the density in units of gm/cm3.)

This illustrates the need for precise measurements with minimum uncertainties of
key Q-values along the rp-process path.

1.4 Previous Studies and Observations
Over the past two decades a significant number of studies have been undertaken
and a large amount of effort devoted to searches and measurements on 69Br as
well as nuclei at the proton drip-line. The first experiments simply attempted to
prove the existence of 69Br while at the same time allowing limits to be set on its
lifetime. In later experiments predictions for the mass of 69Br and its proton sepa-
ration energy were determined indirectly through measurements on the masses of
685e and 698a Intimately coupled with these experiments are systematic and the-
oretical studies that in general attempt to predict properties of nuclei for regions

of the nuclear chart where experimental data are lacking. Currently, the most re-

19

cent and precise predictions for the 6gBr mass utilize high precision Penning trap
measurements of both 68Se and 69Se together with theoretical calculations for the
Coulomb displacement energy (discussed in Equation 1.1.1). This results in esti-
mated uncertainties on the order of 100 keV. Therefore, in light of these previous

endeavors, a brief review is in order.

1.4.1 First Attempts

The boundaries of the nuclear landscape are defined by the proton and neutron
drip-lines. Interestingly, the lifetimes of certain unbound nuclei can be exceed-
ingly long compared to the orbital period of a nucleon within the nucleus. The
additional presence of the Coulomb barrier confines the proton to the nucleus, sig-
nificantly increasing its lifetime as mentioned in Section 1.2. Thus, such nuclei can
be considered to ”exist” as a coherent object.

In the past predictions for the location of the proton drip-line and, at the time,
recent discoveries of ground state proton emission from 1091, 113CS [19], 147Tm,
150Lu [37], and 151Lu [18, 38] prompted studies into possible ground state proton
emission from 69Br [39]. One of the earliest attempts was carried out by Hourani
et al. [40]. The experiment, conducted at the Orsay Tandem accelerator, sought to
produce 693r through fusion residues. The residues were then implanted in an
ionization chamber which was used to search for protons in an energy range of
250-600 keV. However, they did not observe any protons with the expected en-
ergy and were able to exclude a range of 10 Its-100 ms for the 6gBr proton decay
half-life. Shortly after, Robertson et al. [39] reported results from a similar experi-
ment involving the bombardment of 2BSi and 328i on a natural calcium target at the
Berkley 88-inch Cyclotron. Fusion residues were implanted on a rotating catcher
wheel and protons were measured and identified using a telescope composed of a

gas energy loss (A E) detector followed by a 300 um Si E detector. Again, no proton

20

groups were detected in the expected energy range and a complimentary upper
limit for the proton decay half-life of 100 us was obtained.

Following this, Mohar et al. [41] reported the first direct observation of 69Br.
They investigated the production of isotopes in the projectile fragmentation of a
78Kr beam using the A1200 magnetic analyzer at the National Superconducting
Cyclotron Laboratory (N SCL). In their fragment identification spectra they ob-
served 7 events which they attributed to 69Br. Subsequent measurements by other

groups could not confirm this result and it is generally believed to be incorrect.

1.4.2 Recent Predictions by Non-Observation

Following the claim of observation of 6gBr and the first searches for proton emis-
sion, improved fragmentation experiments were carried out. The first of these was
conducted by Blank et al. [42] who also investigated the production of proton-rich
isotopes in the projectile fragmentation of 7'8Kr at the SISSI/ LISE facility at GANIL.
In this case the yields of other produced nuclei in the region surrounding 69 Br were
significantly higher compared to the results of Mohar et al. [41], yet no events were
found that could be attributed to 69Br. Consequently, it was concluded that the
proton half-life of 69Br is < 100 us which, given a simple barrier penetration cal-
culation, translates into a proton separation energy of Sp 3 —450 keV. However,
the GANIL experiment differed significantly from Mohar et al. [41] in that the flight
path from the production target to the particle detectors was approximately 6 times
longer. This means that the results of Mohar et al. [41] were not necessarily contra-
dicted since a half-life of 100 ns would allow a small number of 69Br nuclei to reach
the detectors in the A1200.

Further investigations into the fragmentation of 78Kr were again conducted at
NSCL using the A1200 by Pfaff et al. [43]. This experiment aimed to improve upon

the measurement of Mohar et al. [41]. However, with a similar setup and increased

21

statistics no ”Br nuclei were observed, in contradiction with the previous result
from Mohar et al. Assuming the previously measured cross sections of Mohar et al.
for the produced Br isotopes, 300 counts of ”Br were expected but not observed.
This absence of ”Br nuclei and the 14 m flight path of the A1200 separator suggests
a half-life upper limit of 24 ns for ”Br. Following Blank et al. [42], one can estimate
from this value of the half-life combined with a barrier penetration calculation that
the ”Br proton separation energy is S —500 keV. Throughout this dissertation the
value of Sp 5 —500 keV will be taken as a reasonable upper limit on the proton

separation energy.

1.4.3 Recent Predictions by Indirect Methods

While the experiments discussed in Subsection 1.4.1 and Subsection 1.4.2 are capa-
ble of establishing upper limits on the half-life of ”Br, they provided little else. A
precise measurement of the proton separation energy would provide more defini-
tive information about the 68Se waiting-point (see Subsection 1.3.1). As shown
by Equation 1.21, the astrophysical reaction rate depends exponentially on the
68Se(p, 7) capture Q—value; relatively small uncertainties in the Q-value lead to
large variations in the 2p-capture process. Recent measurements have focused on
obtaining and improving mass measurements for 68Se and 6"’Se [44, 45, 46, 2, 3].
When combined with theoretical calculations these increasingly precise mass mea-
surements have led to predictions for the mass of ”Br (and equivalently the pro-
ton separation energy) with significantly reduced uncertainties. These predictions,
however, are less reliable than a direct experiment as they fundamentally rely on
the accuracy of the calculated mass difference between ”Br and ”Se.

In part, because the rp-process in general depends heavily on many experi-
mentally undetermined properties of nuclei close to the proton drip-line, a large

number of studies have provided predictions for masses, binding energies, and

22

separation energies for nuclei that have not been measured experimentally. For
example, the 1995 [47, 48] and 2003 [49, 10] Atomic Mass Evaluation (AME) sys-
tematic studies are often implemented in astrophysical simulations that require
the knowledge of unknown masses. In addition, there are other ways to estimate
the masses such as the Isobaric Mass Multiplet Equation (IMME), the Finite-Range
Drop Model (FRDM) of MOller et al. [50, 51], and various coulomb displacement
calculations [52, 1], which use the available experimental data to provide estimates
for unknown masses.

Soon after the fragmentation experiments of Mohar et al. and Pfaff et al., the
first mass measurements of 68Se were reported by both Lalleman et al. [44] and
Lima et al. [45]. These experiments used very different techniques. The experi-
ment of Lalleman et al. [44] produced 68Se through fusion-evaporation reactions
in the bombardment of a 12C foil with a 56Ni beam accelerated in the first cy-
clotron (CSSl) at GANIL. The residues of fusion-evaporation were then injected
into the second cyclotron (C882), which was used as a mass spectrometer. A mass
excess of AM = —52 347(80) keV was reported corresponding, when taken to-
gether with AME 2003 and Coulomb displacement [1], to a proton separation en-
ergy of Sp 2 1072(190) keV. This value implied that ”Br would be bound, but is
in disagreement with more recent mass measurements of 68Se.

The experiment of Lima et al. [45] utilized the high-resolution energy loss spec-
trometer SPEG, also located at GAN IL, to perform mass measurements of proton-
rich isotopes using a time of flight (TOP) method. The 68Se nuclei were produced by
fragmenting a 78Kr beam on a “‘"Ni target. Masses were obtained for the produced
fragments from the relation M / Z = T pr / (by) which relates the mass, M, and
charge, Z, of the transmitted ion to the magnetic rigidity, Bp (where B is the mag-
nitude of the magnetic field and p is the bending radius of the magnetic system),
of the spectrometer, the flight path length, L, and the ToF of the ion, Tf. A mass

23

excess of AM = —53 620(1000) keV was determined for 688e. Furthermore, Lima
et al. [45] reported a proton separation energy of Sp z 80(1030) keV.

These mass measurements have been recently superseded by high-precision
mass measurements using Penning traps. A new mass measurement of ”Se per-
formed by Clark et al. [46] using the Canadian Penning Trap (CPT) greatly reduced
its uncertainty. They reported a ”Se mass excess of AM = —54 232(19) keV cor-
responding to a predicted ”Br proton separation energy of SP 2 ~813(129) keV
when taking the ”Br mass estimated by the Coulomb displacement energy dif-
ferences of [1] discussed in Equation 1.1.1. Additional measurements of the LEBIT
group at N SCL for the mass of ”Se by Schury et al. [2] and a remeasurement of 68Se
by Savory et al. [3] improved the overall accuracy of masses in the region. The mea-
surement of ”Se with a reported mass excess of AM = —56434.6(1.5)keV differs
by 135 keV from the AME 2003 result, which has a significant effect on the predic-
tions for the ”Br mass previously provided by the AME value. Finally, with the
mass excess of 68Se found to be AM 2 —54 189.3 (5) keV a prediction for the mass
of ”Br, using the mass of ”Se and the Coulomb displacement energy calculations
of reference [1], yield an estimate of Sp 2 —636(100) keV for the proton separation
energy of ”Br. Until the present data, this was probably the best estimate for the
value of this quantity.

1.4.4 Summary

The measurements of the previous section are summarized in Table 1.1. It is clear
from the table that these attempts have provided a relatively large spread in pre-
dicted ”Br proton separation energies with large varying uncertainties. If one com—
bines the recent LEBIT Penning trap mass measurements of ”Se and ”Se with the-

oretical Coulomb displacement calculations, as discussed in the preceding section,

24

 

 

Sp [keV] Error [keV] Data Type Comments

 

 

 

<-450 - Non-Obs. [42] T1/2 < 100 ns 1'

<-500 - Non-Obs. [43] T1/2 < 24 ns

+1072 190 Exp. [44] CSSZ ”Se mass measurement §
-201 1110 Exp. [45] SPEG ”Se mass measurement §
-813 129 Exp. [46] CPI‘ ”Se mass measurement 1'
-766 350 Exp. [53] ,B-endpoint ”Se mass
-679 119 Exp. [2] LEBIT ”Se mass measurement
-636 105 Exp. [3] LEBIT ”Se mass measurement t
4151 610 Syst. [47] AME 1995 'l'
-450 100 Syst. [10] AME 2003
+89 - Theory FRDM t
-663 305 Theory [52] CD
-730 320 Theory [1] CD / Skyrme Hartree-Fock

 

Table 1.1 - Previous predictions for the ”Br proton separation energy. For consistency
and where applicable the separation energy is calculated using data from AME 2003
and Coulomb displacement from [1]. A t denotes those values not explicitly stated in
the reference but calculated in this dissertation. A § denotes values that were originally
reported but altered for comparison using AME2003 and reference [1].

25

 

102 Ifirjilii UITIITFDIIITfiI—[IIIT
:—

 

. cssa GANIL

:1

..L
O

 

\‘ I LEBIT
D on 3.11. Brown

 

 

 

‘ d

10- . Unbound

10"2
‘10“
£3 4
10-1.5 -1 -0.5 0 0.5 1 1.5
sp[Mev1

Figure 1.6 -— Comparison of the effective ”Se stellar half-life for selected values of the
”Br proton separation energy.

 

E ectlve Stellar Half-Life [5]

 

 

 

 

   

 

 

all of the resulting uncertainties in the proton separation energy comes essentially
from the uncertainty in the theoretical Coulomb displacement energy calculations.

To illustrate the possible effects on the rp-process the effective half-life of ”Se
inside the neutron star crust from Subsection 1.3.1 is shown in Figure 1.6 for a se-
lected set of predicted separation energies. According to these estimates and the
uncertainties that exist, even when taking the uncertainties in Coulomb displace-
ment to be correct, it is possible for the effective half-life to vary by a factor of 3.
The experiment to directly measure the proton separation energy described in this
dissertation attempts to reduce the remaining uncertainties in the ”Br proton sep-
aration energy, thereby establishing the validity of ”Se as an rp-process waiting

point.

26

1.5 Dissertation Organization

The remainder of this dissertation is organized as follows. In chapter 2 an overview
of the experimental setup and details of technique for measurements of proton un-
bound nuclei is described. A thorough description of the detectors used in the mea-
surement, including the 8800 spectrograph, MCP beam tracking counters, and the
HiRA array is also provided. In chapter 3 the analysis of the raw data is described.
Key uncertainties of the measurement are discussed as well as the data analysis
strategy, data corrections, and detector calibrations. In chapter 4 the physics data
and results are discussed. Finally, in chapter 5 a summary of this dissertation is

given.

27

Chapter 2
Experimental Setup

2.1 Overview

The ”Br experiment‘ was performed at the National Superconducting Cyclotron
Laboratory (NSCL) Coupled Cyclotron Facility (CCF) located at Michigan State
University in the summer of 2005. This facility is capable of producing a wide
array of common radioactive and exotic, or ”rare” isotope, beams that would oth-
erwise not exist in nature. A fast in-flight fragmentation technique is employed to
produce user requested radioactive beams with the desired energy, purity, and in-
tensity. This will be discussed in more detail in Subsection 2.1.2. An overhead View
of the accelerator and experimental areas is shown in Figure 2.1. The beam delivery

process begins with an electron cyclotron resonance (ECR) ion source. This device

 

‘ proposal advisory committee (PAC) approved experiment number 02023

EC\R K590 N1 N2 N3 N4 N5 N6

     

 

 

 

Figure 2.1 — Overhead view of the NSCL Coupled Cyclotron Facility (CCF) as it was
configured during the ”Br experiment. The experiment was setup in the S3 vault.

28

provides beams of stable‘ positive ions for injection directly into the central region
of the K500 cyclotron where they are accelerated to ~ 14 MeV/u. The advantage
of the CCF is that the K500 provides the first stage of acceleration. In this mode,
ions injected into the K500 are not required to be in a high charge state, result-
ing in higher output intensities from the ECR source and a higher intensity final
primary beam. However, since higher charge states allow for higher final beam
energies, the ions extracted from the K500 are injected radially into the K1200 and
shipped of their electrons by a carbon foil located inside the first dee electrode [54].
Typically, fully stripped ions are accelerated to an energy of ~ 140 MeV/u in the
K1200 and extracted using a high voltage deflector to form a primary beam. The
extracted primary beam is directed onto a production target, typically composed
of beryllium, located just outside the extraction line. Collisions with target nuclei
result in the stochastic production of isotopes via fragmentation. The desired ra-
dioactive nuclei are selected from the distribution of produced isotopes using the
A1900 projectile fragment separator [55] and delivered via a magnetic switchyard
as a ”secondary” beam to any of the various experimental areas for study.

For this dissertation a primary beam of 78Kr at 140 MeV/ u was used in conjunc—
tion with a 775 mg / cm2 beryllium production target to produce a mixed or ”cock-
tail” secondary beam of 71 Br (9.4 ‘70), 70Se (66.7 °/o), and ”As (23.9 ‘70). The beam was
delivered to the S3 vault shown in Figure 2.1 where it underwent collisions with a
5.4 mg / cm2 polypropylene H6C3 target. Reactions with the 1H and 12C result, with
some probability, in the formation of ”Br. This nucleus is energetically unbound
and has a half-life of < 24 ns [42] [43]. This dissertation describes an experiment to
measure the relative energies of the decay products from ”Br—> p+”Se. The ob-
served relative energies of protons corresponding to decays from the ground state

as well as any excited states provide direct information on the relevant two-body

 

‘ Stable in this context typically means the lifetime of the atoms are sufficiently long to be a high
intensity source. Examples of unstable atoms available as primary beam include 48Ca and 238U.

29

decay Q-values. Since this is a two-body decay the Q—value for the ground state in
addition to the mass of ”Se provides a direct measurement of the ”Br mass. The
following sections will describe in more detail the basic technique, the detectors

that were used, and their principles of operation.

2.1.1 Experimental Technique

Nuclei at the drip-lines can be extremely difficult to study. By definition they are
unbound and therefore can have exceedingly short lifetimes. This feature has two
general consequences: First, any kind of direct measurement must be performed
immediately after the nucleus is formed. Second, producing a sufficient number
of these drip-line isotopes required for an experiment becomes a challenge, espe-
cially for higher mass isotopes which generally lie farther from the line of stability.
Due to the inaccessibility of these nuclei experiments are typically limited in their
resolution and specificity.

For this work the method of decay spectroscopy for reconstructing decay events
of unbound nuclei was extended to heavy masses. To measure states in ”Br the
outgoing momentum vectors of the proton and ”Se must be completely deter-

mined. This requires three main detector systems:
1. The S800 spectrograph.
2. Two MicroChannel Plates (MCP) tracking detectors.

3. HiRA: An array of 16 AE-E telescopes composed of silicon strip detectors
backed by CsI(Tl) detectors.

A schematic view of the experimental setup and the general measurement tech-
nique is shown in Figure 2.2. Protons from the decay of ”Br are detected and iden-
tified using HiRA while the heavy, forward focused, ”Se residue is measured in
the $800 spectrograph. Both HiRA and the 5800 provide information on a parti-

3O

cle’s energy and its scattering angle. Two micro-channel plate (MCP) detectors are
used for tracking beam particles to the target. Knowledge of the interaction point
on target allows one to accurately determine the angle of emission for particles
measured in HiRA. In addition, the MCPs provide a time dependent monitor of
the beam optics.

Originally, the experiment was planned to produce ” Br by the reaction,
71Br + target ——) 69Br + 2n —> 68Se + p (2.1)

Specifically, we envisioned a prompt fragmentation of 71 Br in the target during
which two neutrons are emitted leading to the formation of ”Br. The prompt parti—
cles generated in this process, such as the two projectile neutrons, are not detected.
This is not important however, because the decay of 69Br is still determined by the
complete measurement of the kinematics of the 685e+p decay products. To our sur-
prise, other production mechanisms are also present. Indeed, the 7°Se secondary
beam actually provides better results than does the originally planned 71 Br sec-
ondary beam. Details of the beam composition and its properties will be discussed

in Subsection 3.5.5 and the formation process in Section 4.1.

[:I up To 5800

 

Figure 2.2 - Cartoon of the ”Br breakup reaction.

31

With the identification and measurement of the particle final states the relative
energy can be calculated. For a two-body decay in the center of momentum (COM)

frame this is just the total kinetic energy of the decay products and is given by,

Erelative 2 "(mp + mSe)C2

 

1 _. ..
+ El/4(mp + m5€)2c4 + 8(mSeCsz + mPCZTSe + TPTSe ‘ PP ' I’Secz) (2'2)

where mp, mse, Tp, TSe, pp, and p5,. are the masses, kinetic energies, and outgoing
momentum vectors of the decay proton and ”Se residue respectively.

Quantum mechanically the proton may only occupy a discrete set of nuclear
energy levels. Consequently, in the rest frame of the ”Br nucleus the decay prod-
ucts will emerge with discrete values of the kinetic energy corresponding to those
quantum levels due to conservation of energy. At low energies where the level
width is narrow and the density of states is low, the spectra of relative energies
will exhibit peaks corresponding to these quantum states.

In terms of the astrophysics calculations discussed in chapter 1 knowledge of
the ground state Q-value for the ”Se(p, '7)”Br reaction or equivalently the proton
ground state separation energy, Sp, is needed. The relative energy of the ground

state is related to the separation energy by,

Erelative(g-S-) : _3p (23)

The Q—value as mentioned in Section 1.3 is the difference in final and initial kinetic

energies. In the rest frame of the decay this is just,

Q 2 AT 2 Tf - 0 ‘2 Erelative(g-S-) =3 -Sp (2.4)

32

Utilizing Equation 1.9 the mass of ”Br is given by,
M(”Br)c2 = M(”Se)c2 + Mch + Op (2.5)

The proton mass is known to an astounding accuracy‘ of $1.3 x 10—10 u. And, as
discussed in Section 1.4 there are a number of measurements of the mass of ”Se
with an uncertainty of 5 keV. The uncertainty in M (”Br) is therefore currently
dominated by the uncertainty in the Q-value.

This technique therefore provides a measurement of the Q—values for reaction
rate calculations as well as the direct measurement of the ”Br mass via the ground

state decay Q-value.

2.1.2 Secondary Beam Production

There are a number of methods used to produce usable amounts of rare isotopes
for study. These methods include spallation, Isotope Separator On-Line (ISOL)
methods, and in-flight fast fragmentation. It is the latter technique that is currently
used at NSCL.

At N SCL the heavy primary beam nuclei breakup or are fragmented when they
collide with a production target just before the A1900, producing a beam of stable
and unstable nuclei with velocities somewhat less than that of the beam [4]. Fig-
ure 2.3 shows the position of the production target as well as a layout of the ac-
celerator and the A1900 projectile fragment separator. The production target, he
quently composed of beryllium, is usually chosen to maximize the production rate,
the acceptance, and minimize the background rate for a particular fragment at the
required energy. The separator is constructed of large magnets; 24 superconduct-
ing quadrupole and four 45° superconducting dipole. The quadrupole magnets

reside in eight cryostat modules, containing three quadrupole elements; sixteen

 

’ The mass is known more accurately in atomic mass units than in MeV/c2 due to a relatively large
error in the conversion.

33

        
 

    
 

Object %
Scmtlllator 5800 '
XFP fiw
Scintillator , ;, -”<9/ ,
\L 7 _ 3 (’06 J34 ’

 

Target Chamber

 

Figure 2.3 — Schematic rendering of the coupled cyclotrons, A1900 fragment separator,
and beamline to the S800. HiRA and the MCP tracking system are located inside the
target chamber.
out of 24 of the quadrupole triplet elements also contain hextupole and octupole
coils [56]. In general, the quadrupoles act as magnetic lens to focus the beam while
the dipoles bend the beam to provide an A / Z dispersion described by the equation
for the motion of a charged particle in a magnetic field,

Amuc
Z e

 

M
BP = 321376 % fir (26)

Here, B is the magnitude of the magnetic field, p is the bending radius of the dipole,
e is the elementary charge, M and Z are the mass and charge number of the particle,
and )3 = v/c and 7 = (1 — [32)“1/2 are the relativistic factors. The role of the
fragment separator is to select out the desired nuclei of interest and filter away the
unwanted primary beam and fragments.

Filtering and selection of isotopic fragments is carried out in stages along the
separator. The first two dispersive dipole elements select only fragments with a
given magnetic rigidity, or Bp. At image 1 and 2 positions, shown in Figure 2.3,

the beam is dispersed and a slit system blocks any fragments not matching the set
rigidity. However, this only selects fragments with a certain A / Z ratio. To pick out
a fragment with a particular atomic number, and thus obtain isotopic selection,
an energy degrading ”wedge” is used at image 2 after the slits. Charged particles

passing through matter lose energy according to the Bethe formula,

dE 47rnZ2 e2 2 2mec2j62 2
a = meczfiz (4......) [hi—10 — 32>) ‘5 I <2”

where n is the electron density, Z is the charge number of the particle, B = v / c, and

 

I is the average excitation potential of the material. Equation 2.7 governs energy
loss in the wedge and also all of the detector systems described in this thesis. For a
given velocity of fragments, d E / dx ~ Z2. Fragments then emerge from the wedge
with differing momentum, depending on their charge Z; a second dispersive stage
then removes more of the unwanted fragments from the beam. The shape and
thickness of the wedge are chosen so that the image at the focal plane of the A1900
is achromatic, i.e., independent of the momentum to first order.

Secondary beams produced by the in-flight method are characterized by a num-
ber of features. First, the fragmentation process results in fragments with a distri-
bution of momentum and angles. Thus, the emittance, or phase space, of the sec-
ondary beam (typically given in units of mm/mrad), produced in the A1900, is

relatively large compared to those of stable beams. While the emittance can be
improved by cutting the beam with secondary slits, the experimentalist must typ-
ically balance momentum acceptance and purity with intensity.

The secondary beam used for this work was produced by the fragmentation
of a 140.00 MeV/ A 78Kr3‘4+ primary beam with a beam intensity of ~ 800 enA. A
376 mg/cm2 Be production target was used in conjunction with a 240 mg/cm2 Al

wedge to achieve a secondary beam intensity of ~ 2.0 x 106 pps. Typically, most of

35

the data was obtained with a momentum acceptance defined by slits (at the image

1 position) of 1 %.

2.2 The S800 Spectrograph

It is a general feature that secondary beams produced by in-flight fragmentation
often have large emittances reflecting a trade off between beam intensity and the
beam phase space. High resolution experiments can still be done if one can track
the incoming and outgoing particles and determine their momentum on an event-
by-event basis. The 5800 is a large acceptance magnetic spectrometer designed to
identify and analyze beam-like reaction products event-by-event. In the following
sections, details of the principle operation of the 8800 and its various detectors are
described.

The 5800 system is composed of two sections: an analysis line and the spectro-
graph, which are shown in Figure 2.4 (the analysis line is composed of the beam-
line and magnets before the target position). The S800 system is a magnetic op-
tical system with an object plane located at the entrance of the analysis line, an
intermediate image plane, and a focal plane at the end of the spectrograph. The
analysis line is composed of 4 superconducting magnetic dipoles (shown in blue)
and 5 superconducting magnetic quadrupole triplets (shown in green). The 8800
spectrograph is composed of a large bore magnetic quadrupole doublet followed
by two large magnetic dipoles (D1 and D2). The large acceptances of the S800 in
both solid angle and momentum, coupled with a high resolution focal plane de-
tection system [57] allow for particle spectroscopy and identification of nuclear
reaction products generated with secondary beams. A reaction target is generally
positioned at the pivot point of the $800, which lies in front of the entrance of a
large bore quadrupole doublet. In this dissertation the target was placed upstream
of this position by 0.68 m. It should be noted that this distance was obtained from

the mechanical drawings of the S800 scattering chamber and its location with re-

36

5800

Focal Plane :3

    

Figure 2.4 — 8800 analysis line and spectrograph.

spect to the pivot point. The consequences of this will be discussed in more detail

in Section 3.6 and Section 3.5.

2.2.1 Principle of Operation

There are two possible optical modes of operation for the 8800 (dispersion matched
and focused mode) each with its own advantages and limitations [58, 59]. In dis-
persion matched mode the beam is tuned to an achromatic focus on the focal plane
of the $800 spectrograph. This means that all beam particles that originate from a
focused beam spot at the object end up at a focused beam spot in the focal plane.
To achieve this the beam must be dispersed in momentum at the target with high
momenta particles striking higher on the target. To achieve a dispersion match-
ing, however, this displacement must be 10 cm/% of the momentum difference
from the central momentum of the beam. While all beam particles are focused on
this beam spot regardless of initial momentum, momenta altering reactions at the
target will move the reaction products to a different spot on the focal plane. As-

suming an achromatic beam spot at the focal plane of 0.5 cm, this corresponds to

37

a change in the momentum of less than 0.05 °/o. Thus, if a reaction at the target
changes the momentum by more than 0.05 % it can be resolved from the beam, for
example. In principle this allows one to measure reactions with small rigidity dif-
ferences between the beam and the produced fragment. With the large momentum
spreads typical of secondary beams of the CCF, however, the 10 cm / % dispersion
of the S800 results in a very large beam spot at the target position. The large beam
spot for the dispersive mode makes it a problem for many secondary beam ex-
periments that require large momentum acceptances for the beam to achieve the
required beam intensity. In focused mode the image at the target is achromatic.
This mode provides a worse ultimate momentum resolution at the focal plane, but
the achromatic target spot size allows one to use a wider momentum spread in the
beam and thus a large overall beam intensity. For the ”Br experiment the system
was configured for focused mode.

A key idea in any beam optics system is that of the central-ray or reference tra-
jectory. This is the path taken by a particle with a rigidity that perfectly matches
that of the magnetic system. For the S800 this is the central trajectory taken by the
particles that compose the secondary beam that have not undergone any reactions.
It is the deviation from this central-ray together with the particle identification of
the reaction product that contains the information required to reconstruct the re-
action that occurred in the target and achieve the required energy and angular
resolution. Some of the information about the direction is provided by the focal
plane detectors and some is provided by the MCP beam tracking system.

The focal plane box as shown in Figure 2.5 is composed of several detectors that
allow for the reconstruction of a particle’s momentum vector at the reaction target,
measurement of total energy, its particle identification, and a partial measurement
of the interaction point on the target. An analytic method is employed to calcu-

late these properties of beam particles at the target from the quantities measured

38

GEE

Figure 2.5 - 5800 focal plane box.

 

with the focal plane detectors (see Subsection 2.2.3). Information from two position
sensitive cathode readout drift chambers (CRDCs) are used in this reconstruction
and measure the trajectory of the particle entering the focal plane (see Subsec-
tion 2.2.4). Particle identification is carried out using the AE-TOF technique where
the energy loss for particles entering the focal plane is measured using a segmented
ion chamber (see Subsection 2.2.5). Lastly, the successively thicker scintillators la-
beled E1, E2, and E3 at the end of the focal plane box provide measurements of
energy 1035/ total energy with E1 also supplying timing and trigger information
(see Subsection 2.2.6).

39

X (Dls.porslve)
HIM
hloscopos A

IB

B

 

 

D.
B C...z...3 B
B I: :1 Bi"

 

 

IB

Figure 2.6 — S800 focal plane coordinate system translated into the target chamber.

2.2.2 Coordinate System

It is especially important to define the coordinate systems used in this thesis since
three devices, each with their own internal coordinates, are used and must be com-
bined into a unique laboratory frame of reference. The $800 coordinate system is
labeled as shown in Figure 2.5. The z-axis points along the direction of the beam
with x and y oriented so as to be a right-handed system. The x-axis is vertical
(down) and defined to be in the dispersive direction while the y-axis lies in the
non-dispersive direction. This is the coordinate system as it would look for some-
one standing next to the focal plane box at the top of the spectrograph. Standing in
the target chamber and looking downstream along the beam axis this coordinate
system (after translating it along the beamline down to the target chamber) appears
as shown in Figure 2.6. Here, positive x points to beam-up and positive 3; points
to beam-right. This can be a little confusing as one typically expects y to denote a
vertical axis and x to denote a horizontal axis. However, this choice of the x-axis
as the dispersive axis is standard in beam optics. Vectors in this system are usually

defined in terms of dispersive and non-dispersive angles, a and b, respectively.

40

2.2.3 Inverse Map Reconstruction

An important feature of the 5800 is the ability to reconstruct event information
at the target using magnetic field maps combined with an analytically calculated
transfer map. The details of this method are described in reference [60]. In smaller
acceptance spectrometers, correction of higher order field effects and aberrations
is often done with additional coils. To achieve high acceptances the S800 accom-
plishes this through precise magnetic field maps [61] which are used with the ion-
optical code COSY Infinity to generate a matrix known as a transfer map. A trans-
fer map expresses a particle’s final coordinates at the focal plane detector in terms
of its initial coordinates at the target. The transfer map is then inverted and the re-
sulting inverse map expresses the initial coordinates in terms of the final measured
coordinates taken from the 8800 focal plane.

Following reference [60] the transfer map, denoted as S, can be expressed with

the assumption that initial x positions are zero as,

xf a,

Hf : y; 2
yf 8 br ( .8)
b, d,

where (x, a) and (y, b) are the dispersive (position,angle) and the non-dispersive
(position,angle) as denoted in Subsection 2.2.2 and d = 6 E / E is the relative energy
deviation. The subscripts f, i, and r stand for final, initial, and reaction dependent
and label the coordinates as depending on their location. Since the reconstruction
assumes that x,- = 0 any finite X-position along the target folded directly into the
final energy resolution of the spectrometer.

To first order this transfer map can be expressed as,

41

af 310 0 0 813 y;

= 2.
W 0 521 822 0 br ( 9)
bf 0 S31 S32 0 dr

Although higher order terms can have significant contribution for particular irri-
tial coordinates the main dependencies can be understood through Equation 2.9.
In words, the dispersive position in the focal plane is proportional to the relative
energy deviation at the reaction target. The dispersive angle in the focal plane is
proportional to a linear combination of the dispersive angle and relative energy
difference. The non-dispersive position in the focal plane is proportional to a lin-
ear combination of the initial non-dispersive position and non-dispersive angle at
the reaction target. Finally, the non-dispersive angle in the focal plane is also pro-
portional to a different linear combination of the initial non-dispersive position
and the non-dispersive angle at the reaction target. Dispersive and non-dispersive
coordinates are only mixed in the higher order terms. In will be useful to keep this
lst order relationship in mind when the beam optics are discussed in Section 3.6.

This full transfer map can then be inverted to arbitrary order to give,

a, x;

W = -1 “f 21
br 8 yf ( . 0)
dr bf

where 8‘1 denotes the inverse map. For use with the S800 this map is only calcu-
lated to fifth order as this has been determined to be the highest significant order.
To summarize, as shown in Equation 2.10 the inverse map relates the measured

coordinates in the focal plane (x, a, y, b) to the desired coordinates of the reaction

(a, y, b, d).

42

2.2.4 Cathode Readout Drift Chambers (CRDC)

The two CRDC detectors at the beginning of the focal plane of the S800 provide
the XY—position information needed as input for the inverse map reconstruction
discussed in Subsection 2.2.3. The CRDCs are shown in Figure 2.5 and are sepa-
rated by ~ 1.073 m. They each have an active area of 30 cm x 59 cm. Each detector
functions similarly to a single wire drift counter. A mixture of 80 % CF4 (freon 14)
and 20% C4H10 (isobutane) at a pressure of ~ 50 Torr is used as the drift gas.

In the x-z plane (dispersive) the X-position is given by analyzing the distribu-
tion of charge induced on electrode pads that run vertically along one side of the
detector. There are 224 pads that have a pitch of 2.54 mm. The induced signals on
the pads are individually amplified and shaped using front end electronics (FEE)
chips developed by the STAR collaboration [62] for their Time Projection Chamber
(TPC). Two 16 channel chips are mounted on a FEE card with a total of seven cards
needed for readout of each CRDC. The position can be obtained from a Gaussian
fit to the pad charge distribution or by finding the center of gravity of the induced
charge distribution. In this dissertation the center of gravity method was used ex-
clusively.

In the y-z plane (non-dispersive) the Y-position is derived from the drift time
of ionized gas molecules to the anode wire, relative to the trigger generated from
the E1 scintillator. Also, to produce a more uniform drift field metallic strips are
evaporated onto the surface of the CRDC to create field shaping electrodes. These
electrodes produce an electric field that runs perpendicular to the x-z plane (dis-
persive) of the detector.

Additionally, it is important to note that the gas ions drift in opposite relative
directions in each CRDC. This is a consequence of the construction of the focal
plane. CRDC 2 is positioned at the front of the ion chamber. As a result, the FEE
cards which are mounted vertically to CRDC 2, must protrude into the region be-

43

tween the CRDCs. On the other hand, CRDC 1 is mounted in the opposite direction
with the FEE cards facing inward. This means that for CRDC 1 the ions drift from 3;-
max to y-min while for CRDC 2 they drift from y—min to y-max. The consequences

of this will be discussed in Subsection 3.5.3.

2.2.5 Ionization Chamber

The S800 ionization chamber provides a measure of the energy loss (AE) of parti-
cles that reach the focal plane. When combined with a measurement of a particle’s
time of flight (ToF) particles can be identified based on their Z and A. The ion
chamber is divided into sixteen 1 inch segments that are filled with a ~ 300 Torr
of 90 % Ar and 10 "/0 CH4 (methane), a mixture commonly known as P10 gas. As a
particle traverses the chamber it loses energy by ionizing the gas. The gas ions then
drift toward the anodes of the chamber and their signals are summed to provide

the AE signal for the particle identification (PID).

2.2.6 Focal Plane Scintillators

At the end of the focal plane are 3 scintillators that provide timing information as
well as a measurement of a particle’s energy loss (AE) and total energy. As shown
in Figure 2.5 the scintillators are labeled E1, E2, and E3. They are relatively large,
covering the active area of the CRDCs and have thicknesses of 3 mm, 5 cm, and
10 cm respectively. The light that is produced through scintillation by the travers-
ing particle is collected by photomultiplier tubes (PMTs) located at each end of the
scintillator. Both of these PMTs are then used to generate energy and time signals.

The E1 scintillator is particularly important in this dissertation and is the only
one used in the analysis since most of the particles of interest are stopped in this
scintillator. This scintillator serves as the trigger for the $800 as well as providing
a start timing signal for all of the time of flight (ToF) measurements. In addition,

the drift time of the gas in the CRDC, which provide the non-dispersive position

44

information (see Subsection 2.2.4), are taken relative to the E1 trigger. To minimize
energy straggling this scintillator also forms the exit window for the ionization

chamber.

2.3 Secondary Beam Tracking

To track the beam to the reaction target, we used two detector systems during the
experiment. At the intermediate image plane of the analysis line there are two par-
allel plate avalanche counters (PPACs), which provide information via a transfer
map about the beam angle and momentum at the target. In addition, we had two
position sensitive MCP detectors in the reaction chamber, which provide informa-
tion about the position, angle, and arrival time of the beam at the target. Finally,
we have tracking information provided by the S800 focal plane discussed in Sub-

section 2.2.4.

2.3.1 Parallel Plate Avalanche Counters (PPAC)

Two PPACs were installed in the intermediate image box of the S800 analysis line,
where they are separated by 0.7 m. Each PPAC contains an entrance foil, center
foil, and exit foil. The entrance and exit foils have aluminum strips with a pitch of
1.25 mm evaporated onto their surfaces. At the entrance the strips run in the dis-
persive direction while the strips at the exit run in the non-dispersive direction. The
detector volume is filled with isobutane. Ions produced from traversing charged
particles are collected on the strips. The voltage across a resistor chain connecting
the strips can then be readout to give x-y position information. With two PPAC
detectors angular information is also obtained.

The PPAC detectors were included in the experimental system as a backup to
the MCP tracking detectors. After the experiment was performed, we evaluated
the performance of the tracking detectors and determined that the PPACs would

45

not improve the resolution of the experiment, so we do not discuss them further in

this dissertation.

2.3.2 Micro-Channel Plate Detectors (MCP)

MCPs evolved from the invention of the single channel electron multiplier [63].
In general, these channels are constructed of a glass tube coated with a semicon-
ducting layer on their interior. The end surfaces of these channels have an elec-
trode plating that allows a bias to be applied across the channel. Secondary radi-
ation such as electrons, X-rays, photons, etc. enter the channel and strike the inte-
rior semiconducting surface producing electron multiplication. The performance
of such a channel is governed by the ratio of its length and diameter typically
denoted as a = l /d [64]. Consequently, one is able to scale down this technol-
ogy to produce channels with small diameters and short lengths. These channels
can be manufactured through a fiber drawing technique and then bundled, cut,
and plated to form a MCP wafer. Typical wafers can range in thickness from 0.4-
3.0m with ~ 10-100 urn diameter channels spaced 5-15 mm apart. Depending
on the channel design, gain factors up to 109 or more may be reached [63]. This
makes such a device a clear choice for applications of single electron counting.
Furthermore, these detectors can be tailored for specific applications where prop-
erties such as timing [65] are of high importance. When coupled with a stage that
can localize the cascade of electrons to specific channels in the plate, position sen-
sitivity is obtained. This concept has been implemented in a number of nuclear
physics experiments with heavy ions [66, 67, 68, 69].

In this dissertation two MCP detectors were used for position and tinting mea-
surements. The MCP setup was similar to that described in references [68] and [69].
Each detector consisted of a stack of two MCP wafers as shown in Figure 2.7. The

MCPs are stacked in a chevron design with each plate cut to produce a bias angle

46

Secondary
Electrons

 
     
 

MicroChannnel

. .. l\\\\\\\\\\\\\\\\:l\\\\\\\\\
L ///////////////..-”’-ill/ll/l/l ‘

       

! Electrons

 

/
Resistive Layer Anode

Figure 2.7 - MCP amplification process due to secondary electron emission.

of 8°. Stacking the plates serves two purposes. The first is to increase and saturate
the gain of the system due to the multiplicity of firing channels. The second is to re-
duce positive ion feedback by requiring any ions that are generated at the output
of the plate from flowing back toward the input thereby producing after pulses.
By forcing the ions to undergo a significant change in direction these effects can
be mitigated [64]. Each plate is 0.46 mm thick and contains 10 um diameter chan-
nels with a spacing of 12 um which make up a total active diameter of 40 mm. The
full diameter of each plate is 50.05 mm. A vacuum of < 5 x 10‘6 Torr is required
for operation of these detectors which required the use of multiple high vacuum
pumping stages on our chamber.

A resistive anode layer was employed to obtain position information using re-
sistive readout. As a technical note, the resistive layer is not a square but instead
has a ”pincushion” shape which reduces the warping effects of the readout. An
electrode is connected to each corner of the anode and the charge produced during
the electron multiplication process is collected. These signals are sent into a set of

fast amplifiers and then digitized with a Caen V792N QDC. Comparing the rela-

47

 

Beam \ 30° 3
MCP // 9'

Aluminized
Target
-1000V

 

Figure 2.8 — Top down schematic of an MCP beam tracking detector.

tive amplitudes of the digitized corner signals provides XY-position information.
Additionally, a timing signal is taken directly from the anode and sent to a TDC.
The timing signal was not used in this work.

Position signals for the MCP tracking detector originate from electrons scat-
tered by the beam from a foil that intersects it. The MCP setup is shown in Fig-
ure 2.8. A bias voltage of —1000 V is applied to the foil and accelerates the ejected
electrons toward the MCP. Two permanent magnets provide a magnetic field that
tightly confine the electron trajectories to a helical path. The entire device and tar-
get is rotated by 60° with respect to the beam so that the detectors do not block the
incoming particles. As a result of this rotation the Y—position (non-dispersive) res-
olution is improved because the beam is spread over a larger dimension on the foil
and on the channels. (For a square beam relative to box resolution of width L the
x-dimension of the beam on the foil is L while the y-dimension is L / cos(9)). The

electrons entering the micro-channel are then multiplied and the resulting charge

48

is deposited on the anode side behind the MCPs. In a sense the interaction posi-
tion is projected and imaged onto the MCP detector. One signal from the channel
plates can produce a time signal and signals from the four corners of the anode are
averaged by charge division to obtain the beam position.

The detector configuration shown in Figure 2.8 will be referred to as a MCP
tracking detector. Two MCP tracking detectors are positioned 505 mm apart as
shown in Figure 2.2 and thereby track the beam by measuring the trajectory of
each particle at two points. The combination of these two MCP tracking detectors

will hereby be referred to as the MCP tracking system.

2.3.3 Coordinate System

For this dissertation the common frame of reference is the S800 coordinate system
described in Subsection 2.2.2. In this system x labels the dispersive axis while y
labels the non-dispersive axis. Trajectories of incoming particles are defined by the
same two angles as described in Subsection 2.2.2. The dispersive angle is labeled a

while the non-dispersive is labeled b.

2.4 HiRA

The High Resolution Array (HiRA) is a set of 20 AE-E telescopes that cover a large
solid angle, are highly granular, and are used to identify and analyze charged par-
ticles [70] [71]. This dissertation constitutes the first time HiRA, along with our
MCP tracking system, was implemented in an experiment. Moreover, for the first
time the S800 was coupled with HiRA and our new ASIC readout electronics [72].
Each fully mounted telescope, as shown in Figure 2.9, is composed of a thin Si
(65 um) single-sided strip detector (SSSD), a thick Si (1.5 mm) double-sided strip
detector (DSSD), and backed by four 4cm CsI(Tl) crystals”. The thin SSSD is de-

noted as "AE" while the thick DSSD is denoted as ”E”. In should be noted that this

" Due to polishing and other processing the actual thickness of the crystals may vary. On average
they are closer to 3.9 cm thick.

 

49

   

(a) Internal telescope schematic. (b) Actual assembled telescope.

Figure 2.9 — A HiRA telescope.

is just a naming convention since particles with a high enough energy will only
deposit some of their energy in the E detector and thus function as an energy loss
or ”AE” detector.

For this dissertation 16 HiRA telescopes were configured only with the DSSD
and CsI(Tl) in order to detect protons from the decay of ”Br. In the laboratory
frame the protons will be traveling with roughly the velocity of the beam or ~
0.4c. All protons of interest will not be stopped by the thick DSSD. The array was
arranged as shown in Figure 2.10 with all the detectors positioned at a radius of
~ 50 cm from the target. A thin mylar foil attached to an aluminum frame is placed
over the front of the detector cans and serves as a Faraday cage. Four telescopes
are stacked vertically to form what will be denoted as a tower and there are four
such towers. The towers are labeled from left to right as tower 0, 1, 2, and 3. Each
telescope has an unique ID tag that identifies each detector can. More clearly, the

position of each telescope and it’s ID tag are shown in Figure 2.11.

2.4.1 Silicon Detectors

Semiconductor detectors serve an important role in nuclear physics. In general,

they have been available since the early 19603 [73]. They have a number of advan-

50

 

Figure 2.10 - HiRA configuration for experiment 02023. The secondary beam enters
from the left of the photo and exits the scattering chamber in the gap between towers
l and 2. (a) Two targets are viewable in the photo. The upper target is a viewer used
for beam tuning. Just below is a Au target used for CsI elastic scattering calibration.
(b) HiRA configured with 4 towers of 4 telescopes each. (c) Copper bars and lines
used to cool the CsI preamplifiers. (d) Asic electronic box for tower 3. (e) CsI pulser
distribution box.

tages including high energy resolution, compact designs, and good timing char-
acteristics. Wafers can be produced with a wide variety of thicknesses in order to
have the stopping power required for a given experiment. The High Resolution
Array (HiRA) detectors are a good example of such a variety. One of the unique
aspects of these Si detectors is their large relative thicknesses. In terms of Si strip
detectors the 1.5 mm is very thick and is capable of stopping protons with energies
up to 15.534 MeV.

Detectors made of semiconducting material use as information carriers the

electron-hole pairs created by particles that traverse the detector. The electronic

51

 

Figure 2.11 — HiRA telescope positions and their ID labels.

structure of a semiconductor can be viewed in terms of energy bands that char-
acterize the allowed and forbidden electron energies. In general, a semiconductor
can be understood in terms of a valence band and conduction band. The valence
band corresponds to the lowest energy electrons that are bound to specific lattice
sites. The conduction band corresponds to a higher set of allowed electron energies
in which electrons are free to migrate throughout the lattice. In a semiconductor
like silicon the forbidden region, or band gap, between these two bands is small
(1.11 eV at T = 300 K) compared to an insulator. Particles that pass through such
a material excite electrons into the conduction band and leave holes in the valence
band. If these electron-hole pairs are collected through the use of an electric field
a charge signal is produced that is proportional to the energy deposited by the
traversing particle.

For the HiRA Si strip detectors shown in Figure 2.12 the charge carriers are
collected and detectors biased via a flexible 32-pin cable. This cable is coupled to

the Si through wire bonds that are ultrasonically bonded to both the strip surface

52

    

..

’ “’1’? S;- a: .. : '
(a) Photograph of an unmounted HiRA (b) Photograph of an unmounted
AE detector. HiRA E detector.

 

Figure 2.12

on the wafer and electrode pads connected to the cable. For the DSSD used in this
work both sides are metalized with 3000A of aluminum that provides an ohmic
electric contact. The wafer itself is epoxied into a custom designed G-10 frame
the details of which are described in [71]. When mounted in the telescope can the
signal cables run at a 90° angle to a printed circuit board (PCB) at the back plane
of the can which maps each of them to a 32-pin output connector.

Characteristics of semiconductors can be precisely controlled and the perfor-
mance tailored through the use of impurity doping. Impurity doping is generally
defined as being n-type or p-type. N-type impurities are sources of excess electrons
which are more easily promoted to the conduction band than those electrons as-
sociated with the valence band lattice sites. P-type impurities are sources of excess
holes. The HiRA Si strip detectors function as a p-n junction. The bulk silicon wafer
is n-type material while the strip surfaces on the front (junction side) are p—type
which have been created using a p+ ion implantation method. This forms the basis
for the junction. Space charge generated at the interface of the p-n junction induces

an electric field near the junction known as the depletion region [73]. Here, any

53

electron-hole pairs that are created quickly migrate apart. Placing a reverse bias
voltage across the junction results in the extension of the depletion region across
the wafer. The result is that charge carriers migrate rapidly and are efficiently col-
lected generating a high quality signal. The HiRA Si are operated as fully depleted
detectors with typical operating voltages of ~ 350 V. More detailed information
including information on the Si performance, design, and testing methods can be

found in references [71] and [70].

2.4.2 CsI(Tl) Detectors

Protons with energies 2, 15.5 MeV will not be stopped by the HiRA Si detectors.
To obtain AE-E particle identification the Si are followed by four quadrants of CsI
crystals as shown in Figure 2.9a that are capable of stopping protons up to energies
of ~ 116 MeV and provide a total E signal.

In general, CsI are classified as inorganic scintillators. Both 55Cs (an alkali) and
53I (a halogen) with their relatively large atomic numbers provide considerable
stopping power and together form an alkali halide ionic compound. They rely on
the emission of light through the excitation of electron-hole pairs within the band
structure of the crystal. Electrons that are promoted to the conduction band can
eventually recombine with holes in the valence band through the emission of pho-
tons. This process is inefficient, however, and does not typically yield light with
usable wavelengths [73]. To enhance the de-excitation process and shift the pho-
ton frequencies to a desirable range impurities are added. For HiRA the crystals
are doped with thallium (CsI(Tl)). These impurities result in what are known as
recombination sites which allow electrons in the conduction band to quickly de-
excite through, previously unavailable forbidden, states in the band gap.

Light produced in this way has a characteristic wavelength of 540 nm. Light

guides 1.3cm thick couple each HiRA crystal to a Si photodiode which is sensi-

54

tive to this range of wavelengths and has an active area of 18 x 18 mmz. Non-
uniforrnities in the light output ultimately limit the final resolution of the crystals
and were investigated in reference [74]. The diodes are connected to preamps that
are located in the back of end of the telescope can. A 16-pin connector on the back
plane of the can connects to a set of high-vacuum coaxial cables. These cables run
to a pulser distribution box shown in Figure 2.10e. There is one such box for each
tower.

The CsI distribution box serves a couple of purposes. It distributes the common
+12 V preamp power and individual diode biases. In addition, CsI output signals
from each box are routed to two 32-pin ribbon cables that run to a flange at the top
of the scattering chamber. Finally, an internal pulser circuit which is driven by an
external DAC supplies individual test pulses to all the CsI preamps.

Digitizing the CsI signals is accomplished through a more classical set of elec-
tronics instead of the application specific integrated circuits (ASICs). Output sig-
nals carried out of the distribution box are sent to computer controlled PICO sys-
tem CAMAC modules which shape and discriminate the pulses. The shaped sig-
nals are then digitized by a CEAN V785 peak sensing VME analog-to-digital con-
verter (ADC) module.

2.4.3 Coordinate System

The final coordinates of each HiRA pixel is given in terms of the common S800
coordinate system described in Subsection 2.2.2. Figure 2.6 shows the position of

each HiRA telescope and tower in relation to the S800 coordinate system.

2.4.4 ASIC (Application Specific Integrated Circuit) Electronics

Recently there has been a growing demand in nuclear science and in other fields
for high density electronics for analog signal processing. As the number of chan-

nels that must be digitized grows so does the cost of their associated electron-

55

External

Preamp Differential
Amplifier

Peak
..v .E

 

 

Detector
_ I

 

 

 

 

Differential
- Ammumr
External .................
Stoe 65A AVIIT

 

 

 

 

 

Figure 2.13 — Block diagram of a single channel of the HINP16C ASIC chip.

ics. The highly granular nature of the HiRA Si directly translates into a need for
such electronics. If one considers that a fully configured HiRA telescope contains
32 + 2 x (32) = 96 channels, and a typical setup contains approximately 20 tele—
scopes, then a total of 1920 channels need to be digitized. In collaboration with
Washington University in St. Louis, a set of ASIC chips were developed [72]. Each
chip is specifically designed to handle the high capacitance and large dynamic
range required for HiRA. This was the first experiment to utilize these new elec-
tronics.

Each HINP16C ASIC contains most of the components onboard to process the
Si signals. Figure 2.13 shows a schematic drawing of a single channel of the ASIC.
An individual chip contains 16 such channels. Signals generated by the detector
are first amplified by a charge sensitive amplifier (CSA) that has two computer
selectable gains (High and Low). The CSA can also be bypassed and an external
preamplifier can be used instead. This mode of operation has been used for HiRA
experiments where the AB is installed. After amplification the signal is then sent to
a shaper and pseudo-constant fraction discriminator (CFD). The shaper takes the
long decay-time pulses from the CSA and shapes them into a Gaussian-like signal
which has beneficial signal-to-noise ratio (SNR) characteristics. The CFD discrimi-

56

nates signals that are a constant fraction of the peak height and generates a trigger.
Triggers generated in this manner are then independent of the peak height as op-
posed to a threshold trigger which can have problems with time walk. The logic
signal from the CFD then goes to a hit register and time-to-voltage converter (TVC)
circuit. If the signal is above a computer set threshold the CFD triggers and the hit
register is set. The TVC is started by the CFD and generates a voltage signal which
is proportional to the time between the start and an external stop. The resulting two
signals from the shaper and CFD circuits are sent to peak sampling circuits which
are designed to track and hold the maximum value of the input signal. Finally,
both the E and T signals are sent to an off-chip differential amplifier. It generates
two analog levels whose difference in height is proportional to either the E or T
signals.

Two chips are mounted to a chipboard (CB) and provide the necessary 32 chan-
nels to process a single side of the HiRA silicon. A CB is shown Figure 2.14a with
a comparison to a quarter for scale. A 32—pin ribbon cable connects the detector
to the connector on the left side of the CB in Figure 2.14a. The signals are then
processed by the two ASICs and multiplexed off the board. The CBs connect to
a mainboard as shown in Figure 2.14b through the 64-pin high density connector
located on the top of the board in Figure 2.14a. In the center of the mainboard is
a field-programable gate array (FPGA). One key advantage of the ASIC is that the
analog E and T signals along with address information referring to the chip and
channel that generated the signal can be multiplexed out of the system on only
three cables. Otherwise, every channel would have its own signal cable and be
routed into its own digitizer. With the ASICs, each mainboard multiplexes all E
and T signals onto only two double (differential) lemo cables. Addressing infor-

mation is carried out simultaneously on a 64-pin high density ribbon cable.

57

 

(a) Photograph of the HINP16C ASIC chip- (b) Photograph of an ASIC
board. The quarter is shown for scale. Also mainboard configured with 6
shown in the bottom left is a 8 channel pro- chipboards.

totype.

Figure 2.14 — HiRA ASIC electronics setup.

The signals for E and T are sent into pipeline or 1’flash” ADC to be digitized
while the addresses are sent to an universal logic module (XLM). Another FPGA
onboard the XLM controls I/ O flow, logic, and clocks in the streaming data. For
this dissertation 1024 channels need to be digitized. Using the electronic setup just
described only one SiS flash ADC and two XLMs were used. This greatly reduces
the number of cables needed, freeing up space, and reducing the number and com-

plexity of flanges in the setup.

58

Chapter 3

Data Analysis

Ahhh, what an awful dream. Ones and zeroes
everywhere. . . and, I thought I saw a two.

—
BENDER

In general, data produced and recorded during an experiment must undergo
further detailed and rigorous analysis. Experiments in nuclear physics rely on the
electrical signals generated by sensitive detectors which are digitized and acquired
through an electronic data acquisition (DAQ) system. Typically, raw data collected
during a running experiment is encoded and written to a computer file for fu-
ture processing. For complex experiments with many detector channels the data
files can be very large, making them difficult to efficiently manipulate and search.
Transforming the basic raw information into a manageable and physically mean-
ingful data set is one of the main goals in the data analysis process.

The data analyzed in this dissertation is generated by detectors in three main
systems that all must be calibrated and their performance understood in order to
properly process the basic signals into a form from which the physics of inter-
est may be extracted. The processing, calibration, correction, and analysis of data
collected during the experiment (see chapter 2), including obtaining spectral infor-

mation for ”Br proton emission, is the subject of this chapter.

59

3.1 Monte Carlo Methods

To probe the sensitivities to various experimental and theoretical uncertainties a
Monte Carlo code was developed to simulate the setup and ”Br proton decay. The
code was written in C++ and takes advantage of the class libraries available in the
ROOT“ analysis framework. It is designed to simulate the two-body decay of a
nucleus for selected Q-values and then propagate the decay products into the user
defined HiRA detector geometry. A user sets the input values of the simulation
and runs an event generator. The code produces as output a ROOT file containing
a TTree object which holds all the data of the simulation on an event-by-event basis
as well as any histograms generated during the simulation.

A significant number of effects are taken into account in the simulation. These

include,

1. Realistic beam properties: An incoming simulated beam can be defined by
its coordinates at the target. It may be point-like, rectangular, or elliptical in
terms of the beam spot at the target plane. The most realistic beam in the sim-
ulation is defined within a 4-dimensional beam phase space ellipsoid. These
are typical coordinates used in the beam transport community. The coordi-
nates are (x, a, y, b) and represent the dispersive position, dispersive angle,

non-dispersive position, and non-dispersive angle respectively.

2. Detector geometry: An input file defines the positions of HiRA pixels relative
to the target plane.

3. Detector resolution: Actual detector resolutions can be defined for the in-
dividual HiRA detector elements. For the $800 the resolutions are defined
in terms of energy, momentum, and angular resolutions. For the MCPs the

XY-position resolutions are also defined and accounted for in the simulation.

 

t

root.cern.ch/

60

4. Finite HiRA pixel size: Finite surface areas and angles of the HiRA pixels

are taken into account.

5. Bad HiRA detector elements: The simulation allows for cuts to be applied

that tag data associated with malfunctioning detector elements.

6. MCP position corrections: Uncorrected and corrected data based on the in-
teraction position on target is outputted during the simulation for later anal-

ysis and comparison.

7. Single particle lifetimes: Since the lifetime of a state and its width are related
by T o< 1 /I‘, narrow states with lifetimes T 2, 10‘11 s can decay between the
target and HiRA detectors (instead of at the target location). This will be the
discussion of Section 4.3. Consequently, peaks in the the relative energy can
have tails at lower relative energies and must be properly taken into account

for a correct interpretation.

Data generated from the developed Monte Carlo code will be used in a number
of the following sections. In Section 4.3 it is used to illustrate how the finite lifetime
of a state can influence the interpretation of the relative energy. In Section 4.5 sim-
ulated data is used in a fitting method to determine the proton separation energy,

Sp, of ”Br.

3.2 Data Reduction Techniques

A key aspect of data analysis in nuclear and particle physics is the reduction of raw
data to a form that is easier to process and manipulate. For this dissertation a num-
ber of software libraries for data processing were created using the ROOT analysis
framework. All the detector components are described by C++ classes. The classes

contain structures for holding data as well as functions for basic processing.

61

Detector
Signals

 

01100101
01011101
11011100
10001011

 

01011101

Callbratlon Processing

 

 

 

 

 

 

 

 

 

 

 

Stage Stage 1
Calibrated Processed
MCP Tn'ee MCP Tn-ee
Data Flla Data Flla
RAW ROOT Calibrated Processed
E t m
"33.53;" Date Flla MIRA rm. MIRA Tn'ee fizzysks) °
(TTree Structure) Data Flle Data Flla
Callbrated
$800 Tn'ee
Data Flle

Figure 3.1 — Block diagram for the general data reduction procedure.

Data processing is conducted in stages. A basic schematic is shown in Fig-

ure 3.1. First, the raw event data files are unpacked and converted into raw ROOT

event files. Next, calibration parameters are determined, defined, and then applied

to produce a new set of calibrated ROOT event files for each device in the experi-

ment. An additional processing stage for HiRA and the MCPs is applied which is

useful for more advanced analysis of the data. Finally, a ”physics event class” is

used to recombine the data into a single file containing the physical quantities of

interest in the experiment. Partial contents of the data produced with the physics

event class include,

7.1

. Event-by-event PID: Each event is characterized by the initial and final par-

ticles involved in the reaction. The incoming beam particles and detected

outgoing reaction products are identified on an event-by-event basis.

N

. Measured particle properties: The final corrected energies, angles, and etc.

are generated and stored event-by-event.

OJ

4. Calculated relative energy.

. Transformation to a common frame of reference.

Data presented in this dissertation is generated from ~ 20Gb of raw data spread

over 50 files. At the end of the processing sequence a single file of ~ 1 Gb is left con-

62

taining all the interesting physics information. The advantage here is that looping
over and searching through this compact file as well as the modularization of data
processing is considerably more efficient. There also exists the possibility of mod-
ifying the code for future experiments as well as adding additional modularized

processing stages before the creation of the physics event tree.

3.3 HiRA Calibration and Analysis
Decay protons, as well as other light charged particles, are detected and identified

with HiRA telescopes. An accurate and precise measurement of the total kinetic en-
ergy of each particle requires both the DSSD and CsI(Tl) to be properly calibrated.
The calibration has three main parts: A pulser calibration that tests the linearity
and determines the energy offset of the CsI(Tl) and DSSD electronics is discussed
in Subsection 3.3.1, the energy calibration of the DSSD with ac-source data is dis-
cussed in Subsection 3.3.2, and the CsI(Tl) energy calibration from elastic scatter-
ing of light nuclei is discussed in Subsection 3.3.4. In Subsection 3.3.5 the calibrated
particle identification (PID) obtained with HiRA is discussed.Finally, the geometric

efficiency of HiRA and its consequences are described in Subsection 3.3.6.

3.3.1 Pulser Calibrations

The linearity of the CsI electronics, specifically the amplifier and the ADC, was ver-
ified with the pulser system described in Subsection 2.4.2. A single pulser drives
a pulser circuit in the distribution boxes connected to the test input of the CsI(Tl)
preamps. A ramp is done over the full ADC range as shown for a single crystal
in Figure 3.2. The resulting linear fit is shown in Figure 3.3 where the pulser am-
plitude has been converted to the equivalent input signal that would be produced
as light output of the crystal. Since the combination of amplifier and ADC module
begins to show known non-linearities above channel 3500 the fitting is restricted

to this range. All CsI(Tl) channels were pulsed in the same manner and all dis-

63

3000
2500
2000

Counts
-L
0'!
o
O

1000

9°
o

Light Output [mV]
r‘ .-‘ N P
O 01 O 01

99
cm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:- ‘
s , a
I 500 1000 15! DO 2500 3000 3500 4000
Energy [ADC Channel]
Figure 3.2 — Telescope 5 CsI 0 pulser ramp.

x2/ ndf 1.50e—04 / 30

p0 1.33e-03 ' 7.08e-04

p1 7.19e-04’ 3.81e-07 ”'0’“
0 500 1000 1500 2000 2500 3000 3500 4000

Ener rgy [ADC Channel]

Figure 3.3 — Linear Fit of the telescope 5 CsI 0 pulser ramp.

play similar linearities to that shown in Figure 3.3. However, the x-offset from the
pulser data did not provide a correct measure of the true channel corresponding
to zero energy. Instead the offset is extracted from an extrapolation of low energy
CsI(Tl) events as described in Subsection 3.3.4.

A similar pulser ramp was done for the HiRA DSSD using a precision BNC
PB-5 pulser. All channels were tested and found not to have any significant non-
linearities. Additionally, the pulser ramp was to be used to determine the energy
offset of the DSSD calibration that will be discussed in Subsection 3.3.2. However,
the pulser led to inconsistent results for the energy offset as compared to that of
the a-source calibration. Therefore, we chose to use the energy offset obtained from

the a-source calibration.

3.3.2 oc-Source Calibrations

The HiRA DSSD energy calibration is carried out using a 228Th source. In the
decay chain of 228Th there are five main (x-lines that are separated by at least
200 keV, making this an ideal calibration source. In addition, there is an a-decay
from 212Po—>208Pb with an energy of 8.78486 MeV that provides a higher energy
point not available in other common sources. For this dissertation ~ 51 hours of
a-source data were taken. Most of this data was recorded during the actual ex-
periment with the source placed in the upper corner of the scattering chamber.
However, this was not an optimum setup as a small number of strips were not il-
luminated and instead these runs were used mostly for tracking the stability of the
calibration. The final calibration was performed at the beginning and at the end
of the experiment with the source placed at the target location so as to expose all
strips to the source.

A number of factors regarding sources of energy loss are taken into account

for the calibration. The 228Th source has an activity of ~ 1.2 uC and is sealed with

65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

400 - lnztograi 3.1-Mum é
x/ndt 51.94/32 5

35° — Constant 175.3: 4.0 E
300 - Mean 8.56:0.00 §
‘3 250 - Sigma o.oz712:o.ooo47 Li
3 ' :
8 200 - —;
150 - 5 —§
100 - —§
so g— J .g
4.5 5.6 5.5 ' 60 U I I W I '9.

 

6.5 7.0
Energy [MeV]
Figure 3.4 — Telescope 9 228Th a-source calibration for all front strips of the DSSD.

a thin Au (gold) Window that is 50 pig/cm2 thick. Thin 1.9 um thick aluminized
mylar foils cover the entrance of each HiRA telescope and present an additional
source of energy loss. Finally, a thin layer at the surface of the DSSD, known as
the dead layer, is not an active part of the detector volume. This was estimated to
have a thickness of ~ 0.6 um from previous tests. The total energy loss through
all of these layer for each or energy is calculated with the fragment separator and
spectrometer simulation code LISE++”. Stopping powers in LISE++ were set to be
consistent with those listed in [75].

The resulting calibration of telescope 9 for all front strips of the DSSD is shown
in Figure 3.4. Similar calibration spectra were obtained for all other telescopes.
Table 3.1 lists the resolution of the 8.784 86 MeV peak for all combined front strips
for each telescope. It is clear from the table that a reasonable energy resolution
was obtained over the entire array with an average energy resolution of 77.0 keV

FWHM.

' m.nsc1.msu.edu/lise

 

66

 

 

Telescope ID Sigma [keV] FWHM [keV]

 

O 27.9 65.7
1 29.1 68.5
2 42.9 101.0
3 27.7 65.2
4 41.3 97.3
5 31.6 74.4
6 31.4 73.9
7 26.5 62.4
8 29.7 69.9
9 29.8 70.2
10 34.1 80.3
11 30.0 70.6
12 33.5 78.9
16 35.7 84.1
17 35.1 82.7
19 36.6 86.2

 

Table 3.1 — Resolutions for the 8.784 86 MeV a-source peak for front strips for each
telescope.

3.3.3 ASIC Readout Order Correction

This dissertation constituted the first experiment in which the newly designed
HiRA ASIC electronics were implemented. It was quickly realized that there were
a number of issues regarding the ASICs, chipboards (CBS), and mainboard that
needed to be debugged. The most prominent issue for this analysis involved the
influence of the channel readout sequence on the amplitude of the energy signal.
This will be referred to as the readout order problem.

When an event triggers the ASIC system the electronic channels are readout
and digitized according to a specific sequence. First, during the readout process
each mainboard is processed independently. There are two modes of readout; sparse
mode (only channels that triggered the discriminator are readout) or forced mode
(all channels are readout). For this dissertation sparse readout mode is utilized.

Second, CB slots, as shown in Figure 2.14b, are processed from the bottom to the

67

Ch 15151414 I I a a a a a a a a a a a a a a a a a a a a a a 01010000
Pl“ 31 302928 a a a a a .. a a a a I a a a a a a a a a a a a a 03 02 O1 00
strlpoo 01 02 03 a a a a a a a a a a a a a a a a I a a I a I I I 28 29 30 31

00 00
00 01
01 02
01 03

.IIIIIIIIIIIIIIIIIIIII
III-IIIIIICIIIIIIIIIIIII8328

 

EF
Figure 3.5 — Diagram of the chip / channel / strip mapping for the HiRA DSSD.

top slot. This is significant, since each telescope in this experiment requires two
CBS, one for the back side and one for the front side of the DSSD. The CB for the
back is always in a lower slot than the front (since the DSSD output connector for
the back is below the front connector on the rear of the telescope can) and so will
always be processed first. Third, each CB contains two ASIC chips, labeled 0 (even
strips) and 1 (odd strips) as shown in Figure 3.5. During the readout process chip
0 (even strips) is processed first followed by chip 1 (odd strips).

68

During the initial data recording it was found that for a given channel the num-
ber and sequence of channels read previous to that channel affected the value of
its energy. For example, let’s suppose that a particle passes through the DSSD and
a signal is generated on one front strip and one back strip of the detector of equal
amplitude A0. Consequently the amplitude of the signal read out for the back strip
is unaltered as it is the first channel in the sequence processed, Ab = A0. How-
ever, the amplitude of the front strip is altered due to the previously read out back
strip. Fortunately, in general it is found that the amplitude for a particular chan-
nel is modified by a constant shift which only depends on the number of channels
readout prior, n p, to the current channel A = A0 + $01,). In the current example,
the amplitude of the front strip is A f = A0 + 5(1). The results of the readout or-
der problem are clearly observed in the upper a-source spectra in Figure 3.6. The
double-peak structure is a direct consequence of the readout order problem. When
an a particle deposits its energy in the detector the desired response is for an equal
number of holes to be collected on a single front strip as electrons on a single back
strip thus uniquely defining a pixel. However, one possibility is that the collec-
tion of electron-hole pairs is distributed over more than one back strip. The most
probable situation after a two strip event (one front and one back) is a three strip
event where one front strip fires along with two back strips. Since the back strips
are processed first there are now two channels read out prior to the front strip as
opposed to just one. This results in a shift in the amplitude of the energy signal
from the front strip and is observed as a shadow peak at higher energies in the
upper spectra in Figure 3.6.

For this dissertation the key events of interest are only those where a single
proton from the decay of 69Br is detected in HiRA. As this is ultimately a low
statistics experiment, as many of these events as possible need to be corrected.

Shown in Figure 3.7 are the number of channels being readout from tower 1 for

69

 

x2 I ndf 64.7 / 57
Constant 38.5 i 1.9
Mean 8.56 :l: 0.00

 

 

 

Sigma 0 as i 0.001
\

\
but-.- ‘

7.5- u 0.0 8.5-

Counts

 

 

 

 

 

 

 

 

 

 

 

 

     
   
 

4.5 5.0 5.5 6.0 6.5 7.0 9.0
Energy [MeV]
1 . , . . , . . . .
Integral 9559
X2 / ndf 87.5 / 63
Constant 54.2 i 2.2
Mean 8.56 d: 0.00

 

Sigma 0.0282 :l: 0.0008

Lw -... ..--i.
75

6.5 7.0
Energy [MeV]

Counts

 

 

llllllllllllllllllllll

 

 

 

 

 

 

 

 

00
o
90
01
to
a

4.5 5.0 5.5

Figure 3.6 — ASIC readout order correction of the a-source calibration for Telescope

5. The upper figure is the tx-source spectrum for the front strips before the correction

while the lower figure is the spectrum after the correction.
a subset of the experimental data gated on protons. One channel events are of no
interest as they do not provide any pixel information and are ignored. Two channel
events compose most, 57.0 %, of the data in a tower and correspond mostly to one
front and one back strip firing. Three channel events compose 4.7 % of the data in a
tower and correspond to one front and two back strips firing. Four channel events
compose 20.6 "/0 of the data in a tower and correspond to mostly two proton events

in the same tower as well as four strip firing events. Events with more than four

70

 

1w III [III IIII IIII IIII IIII IIII'IIII'IIII'IIII'

105 lll Tower 1
104

103 1'1!
102
10

1 ll llll Illl llll [[11 [Ill IIII I ll lllli

0 5101520253035404550
Number of Readout Mainboard Channels

 

 

 

 

Counts

HEMP—“1L

  

IIII‘ 1’an IIIIIH IIII‘ III.” III

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.7 — Distribution of channels per event that are readout from HiRA Tower 1.

Events where 2, 3, or 4 strips are readout compose most, but not all, of the data. Events

with less than 2 channels are suppressed in the plot.
readout channels in a tower make up the remaining 17.7% of the data in a tower
and correspond to multi-particle and noise events and are not of interest in this
analysis.

To correct the readout order problem the a-source calibration data was used

to obtain the shifts, 3(np) just described. The peak position of the 8.784 86 MeV a
for two channel events is compared to the peak position of three channel events.
Shifts are obtained for each chip since the shifts do not depend significantly on
individual channels for this dissertation. Four channel events and higher could
not be corrected since the at events did not provide enough statistics for this type
of event to make a correction. The lower spectra in Figure 3.6 shows the result
of the correction as applied to the oc—source data for telescope 5. The resolution
of the 8.78486 MeV peak remains practically unchanged after the calibration at
(7 ~ 29 keV. For this dissertation, the final analysis only contains data where a

single proton is detected and where either two or three DSSD strips are triggered.

71

3.3.4 Light Nuclei Elastic Scattering

By definition, the total kinetic energy of elastically scattered particles is conserved.
Only a change in the particle trajectories and in the sharing of this energy between
scattered particles results. As long as one scatters from target nuclei that are much
more massive than the projectile, any recoil of the target nuclei becomes negligible
and the incoming and outgoing kinetic energies of the lighter projectile are nearly
equal. For a stationary heavy target in the laboratory the kinetic energy of a light
elastically scattered projectile nucleus varies only slightly as a function of its labo-
ratory scattering angle. This makes elastic scattering a useful method of calibration
since the projectile nuclei can be scattered into the range of angles where detectors
are located. So long as one knows the identity of the scattered particle and its in-
coming energy, the precisely defined elastic scattering energy provide points of
calibration.

For this dissertation the energy calibrations of the CsI(Tl) detectors were done
via elastic scattering of light nuclei on a 19.5 [Lg/C1112 gold (197Au) target. The Au
target was mounted perpendicular to the beam direction as opposed to the 60°
rotation of the MCP / reaction target. A special frame, just visible in Figure 2.10 (a),
held the Au target to the ladder. The A1900 fragment separator was tuned to a
Bp = 1.371 60 Tm" to allow the passage of p, d, t, 3He, and 4He nuclei produced in
the fragmentation of the primary 78Kr beam. Slits inserted at image 1 and image
2, shown in Figure 2.3, reduced the momentum acceptance of the secondary beam
to ~ 0.4 % thereby providing nuclei with sharply defined kinetic energies. Using
Equation 2.6 and the given A1900 Bp the kinetic energies for each isotope in the
secondary beam are calculated and listed in Table 3.2. The PPACs, extended focal
plane (XFP) scintillator, object plane (OBI) scintillator, and MCP 0 target foil were

removed during the calibration to reduce the energy straggling of the beams.

 

" The units of magnetic rigidity are given in Tesla-meters.

72

 

Isotope Kinetic Energy [MeV/ u]

 

1H 85.4363
2H 22.1106
3H 9.92435
3He 39.0892
4H9. 22.391

 

Table 3.2 — Elastically scattered nuclei used in the CsI(Tl) energy calibration and their
kinetic energies.

 

9V]
N N 00
o 01 o

IIIIIIIIIIIIIIllIrIlflIIlIlllllll

 

EF Energy [M
3 a

01

lllllllllllllllllllIlllllllllll

 

 

I I I l

1000 1200

 

 

'- '4;_§'-‘:.;*J.--' A ' ' ”"3
400 60
Csl Energy [channels]

0

Figure 3.8 - Light nuclei elastic scattering peaks for uncalibrated telescope 5 C513.

Elastic scattering peaks can be easily identified in either a 1D CsI(Tl) energy
spectrum or, since HiRA is a AE-E telescope, in a 2D PID spectrum. An example
of the 2D spectrum for elastically scattered particles into telescope 5 is shown in
Figure 3.8. All other working detectors show similar peaks.

While the energy of the elastically scattered light nuclei is given by the Bp of

the A1900 there are energy losses that must be accounted for in order to determine

73

the energy the particle actually deposited into the CsICTl). Energy loss corrections

are made for,
1. The angle dependent energy loss in the target.

2. Energy losses in the aluminized mylar cover on the front of each HiRA tele-

scope.

3. Energy losses in the dead layer of the DSSDs.

4. Energy losses in the individual DSSD detector thicknesses.

5. Energy losses in the mylar wrapping of the CsI(Tl) crystal segments.

The actual energy of the elastic scattering peak is given by these energy losses
subtracted from the energy determined from the Bp. All of the energy losses just
listed were taken from tables generated with LISE++.

While most of the energy losses and material thicknesses are known, the actual
DSSD thickness can be uncertain by a few percent. Fabricating silicon wafers with
a thickness of 1.5mm and of the quality required for use as a HiRA detector is
difficult. Additionally, it is a challenge to accurately determine the actual thickness
of each silicon wafer. For this dissertation, the actual thickness of each detector
is inferred from the energy loss of the elastically scattered deuteron which loses
~ 7 MeV of energy in the DSSD. For a thin absorber the energy loss, AB, is related
to the thickness, t, of the absorber by,

AB = — (d—E) t (3.1)
dx avg

where —(dE/dx)avg is the linear stopping power given in Equation 2.7 averaged
over the particle’s energy while in the absorber. Values of linear stopping power

are abundantly tabulated for many different particles and commonly used mate-

74

Ia

rials
sort
isre
met
the I
from
in U
4°10
QUE]
EHEI

left

 

 

Telescope Manufacturer Thickness (um) Inferred Thickness (pm) A (um)

 

O 1496 1442.09 53.91
1 1503 1452.71 50.29
2 1490 1453.91 36.10
3 1488 1411.99 76.01
4 1489 1444.93 44.07
5 1499 1447.25 51.75
6 1471 1435.47 35.53
7 1499 1442.38 56.62
8 1460 1420.80 39.20
9 1491 1454.68 36.33
10 1511 1462.66 48.34
11 1491 1457.57 33.44
12 1452 1410.90 41.11
16 1513 1475.43 37.57
17 1496 1333.35 162.65
19 1541 1512.16 28.84

 

Table 3.3 — Si detector manufacturer thicknesses and their inferred thicknesses from
deuteron elastic scattering.

rials. A thick absorber, such as the DSSD, can be viewed as a series of thin ab-
sorbers and Equation 3.1 can be calculated recursively until a desired value of AB
is reached thus yielding the thickness of the absorber. LISE++ which implements a
method similar to that just described is used to calculate the DSSD thickness given
the energy loss of the deuteron for each detector. The inferred detector thicknesses
from this method are listed in Table 3.3. These are the values used in all calculations
in this analysis. With the exception of telescope 17, the values agree to better than
4 % of that given by the manufacturer. It should also be noted that the deuteron
energy loss is in a relatively well calibrated region of the DSSD detector, since the
energies of the a-source calibration cover this range, and provide an accurate indi-
rect measure of the detector thickness.

It was found after the experiment that the pulser system did not function as

expected. The pulser system is driven by a voltage level set by a digital-to-analog

75

l‘l‘
I
I'll

I. III

III

‘

[On

Eli's

the

ene

aP

eff-E

are

Wit}

the‘

 

 

  
  
 
 

 

 

 

; Si Thickness I X-Offset [ch]

5' 30; — 1333.35 um/97.2
g 25;. —1411.99uml94.8 -_
-; 20; — 1447.25 uml93.7 E
2’ ; —1512.160m/92.0 E
215;— ‘3
I.” ; 3
a 10? ‘:
O : 3

5r .7 ‘2

 

 

 

50 "100'"150"'200”‘256"300‘
ADC Value [channels]

Figure 3.9 — CsI(Tl) x-offset dependence on Si thickness.

converter (DAC). However, the grounding of the electronic racks and the detector
systems inside the scattering chamber was not optimal and it is suspected that this
resulted in an offset shift for the pulser signals. Since we are unable to determine
the zero energy offset from the pulser ramp discussed in Subsection 3.3.1, the zero
energy offset is instead found by extrapolating from the energy loss in the DSSD,
a process which will be discussed in the following paragraphs. Therefore it is im-
portant to understand how changes in thickness may effect the zero offset. The
effects of adjusted silicon thicknesses on the zero energy offset of the calibration
are shown in Figure 3.9. While conclusions about the gain is sensitive to changes
in thickness the offset is not.

The response of the CsI(Tl) depends somewhat on the isotope and therefore,
each isotope requires its own calibration. For this dissertation we are concerned
with properly calibrating the response of the CsI(Tl) for protons. Consequently,

the elastic scatting peak provides the only necessary point for the calibration. Ad-

76

1

4| C105: mu<

tGC
Ill

dit

du

his

ht

C01

UTE

l0;

tion

 

 

 
 
   

 

 

 

 

 

 

 

 

 

12Ll_; ' lendf 2087/28 Mi
:§ — g 35 13° -15.32 ‘5
5'1 _ * - :30 p1 0.155 —;
g E 25i—
E g 20:— i
4315:— —:
2 E 3
. - 8105 E
100 t 200 300 ' I ' ‘ ' 500 100 Li50‘ 200 250 “300' L

Csl E [channels] Csl E [channels]

(a) (b)

Figure 3.10 — Calibration points taken from AE. (a) The proton PID band used to ob-
tain calibration points. The profile histogram is overlaid on the rebinned histogram.
(b) Linear fit relating the calculated CsI(Tl) energy as a function of the CsI(Tl) ADC
channel.

ditional lower CsI('II) energy points are obtained based on the energy loss in the
DSSD. These energy loss points are then used to extract the zero energy offset.
A systematic method is used to extract these points and consists of three main
steps. First, histograms of AE-E were constructed with a fine binning of the y-axis
(Si AE) and a coarse binning of the x-axis (Csl E). Second, a profile histogram’,
which displays the mean value of one axis for each bin in the other axis, was pro-
duced, and an example is shown in Figure 3.103 where the red points of the profile
histogram are overlaid with the proton PID band. Finally, points from the profile
histogram are selected over a range of AE energies (from ~ 4MeV-9 MeV) and a
corresponding CsI(Tl) energy calculated using data generated from LISE++. Fig-
ure 3.10b shows the resulting calibration that maps the raw CsI(Tl) ADC channels
to a CsI(T1) energy calculated via the energy loss in the DSSD. This method was

implemented for all detectors by interpolating energy loss tables generated with

 

‘ For a more detailed description of this histogram object consult ROOT online class documenta-
tion under TProfile. http : //root . cern . ch/root/html/TProf ile . html

tic]
wa
thc

COT

int
poi
cor

the

 

 

 

 

 

 

   

 

14 ' I r I T—f T fT Tfi lfi f l I _;
g‘ ‘2 e LISE++ Data ‘3
E 10 _ —_
55 a — Interpolation _f
2 6 -I
III I
273 4 ‘3
2 _"
° ' ‘ '20‘ ‘ ‘40‘ ' 50' Tea L 300‘ 120 i146

Csl Energy [MeV]

Figure 3.11 — Natural 3rd-order cubic spline interpolation of LISE++ calculation. This
provides an accurate conversion from energy loss in the DSSD to calculated energy in
the CsI(Tl).

LISE++. Natural 3rd-order cubic splines were created for each combination of de-
tector angle, energy losses, and elastic scattering energy. For a given incoming par-
ticle energy and angle, in steps of 250 keV, the energy loss in each detector layer
was calculated" and accounted for in the calibration. The interpolations, such as
those shown in Figure 3.11, were used to translate the DSSD AE energies into a
corresponding Csl energy as shown in Figure 3.10b for each detector.

The proton elastic scattering point and the points obtained from the energy loss
in the DSSD are enough to constrain the CsI(Tl) energy calibration. However, these
points do not lie on a single line. This could be a consequence of not having the
correct detector thickness. For this dissertation, the decay protons of interest lie in
the lower AE region of the PID band and therefore deposit most of their energy
in the CsI(Tl). Furthermore the decay protons will have an energy approximately
that of the beam, or ~ 72 MeV. It is therefore important to properly calibrate in the
energy range around the beam energy. The proton elastic scattering point is within

this region and is used as a fixed point to constrain the calibration. It is, however,

 

 

’ The [H-base] ].F. Ziegler energy loss and the ATIMA 1.2 (LS-theory) options were used for the
Calculations.

78

 

— Fit to calibration points (Offset Not Fixed)
— Fit to offset point and elastic point

 

 

 

90 a Low Energy Data
30 1k Elastic Data Point
70

Csl Energy (MeV)
0|
0

lllllilliiillllllIII|llIllililillilllllllillllll

 

 

Alllllllllll|IIIIIIlllllllllllllllllllllllllllllj

" 150 200 250 300 350 400 450 500 550 800
ADC Value (channels)

 

 

Figure 3.12 — Telescope 5 Csl 2 calibration. Two points are used in the fit; the proton
elastic scattering point and an zero energy x—offset point determined from a linear fit
of the DSSD energy loss points.

sensitive to the Bp calibration of the A1900 fragment separator. This complication
is discussed in Subsection 3.7.2. A second point is still required as we found that
the CsI(Tl) pulser system produced unreliable zero offset information due to its
sensitivity to the DC level difference between the towers and the electronic racks.
Proton calibrations of CsI(Tl) detectors are known to be linear. A linear fit of the
DSSD AE points is used to obtain the zero energy offset and is used as the second
point. Figure 3.9 shows how this derived offset is largely independent of the as-
sumed detector thickness. Thus the AE points fix the energy offset and the elastic
scattering point fixes the gain as shown in Figure 3.12 This procedure is repeated
for all HiRA CsI(Tl) crystals and is of sufficient accuracy for the calculations in this

dissertation.

79

 

 

 

EF Energy [MeV]

    

 

. i . . ' i ’ ' '
200 300 400 500 600
Csl Energy [MeV]

Figure 3.13 - Spectra showing cleanly resolvable HiRA PID bands for p, d, t, 3He, and
4He.

3.3.5 Particle Identification Results and Discussion

With both the DSSD and the CsI(Tl) calibrated we obtain PID spectra as shown in
Figure 3.13. Light charged particles up to 4He are cleanly resolved. However, there
are a number of conditions put on the data. First, the middle ships of the DSSD
are always excluded. This is done because they overlap with the gaps between
CsI(Tl) crystals as shown in the schematic in Figure 2.9a. Particles entering this
region can deposit energy in more than one crystal making these events difficult
to properly analyze. Second, (as mentioned in Subsection 3.3.3) only events where
two or three strips are involved are analyzed. Third, even though the energy is
taken from the front strips, it is required that the front and back energy signals
differ by no more than 500 keV. Finally, a number of DSSD strips, ASIC channels,
and CsI(Tl) detectors did not function properly or at all. These signals are excluded
from the analysis of this dissertation.

80

 

§imulated FHA GeometricE-iflciency

 

 

|:| Full Coverage
- Full HIRA Coverage
- Actual HIRA Coverage

 

 

 

2 3 4 5 6 7 8 9 10
Relative Energy [MeV]

Figure 3.14 — HiRA geometric efficiency as a function of the relative energy.

3.3.6 Detector Efficiency

Previous measurements, as discussed in Section 1.4, have set a limit on the lifetime
of 69Br. The non-observation measurement of [43] set a limit on Sp < -—500 keV
which implies the Q—value for the proton decay is (.2p > +500 keV. The geomet-
ric efficiency for HiRA was simulated with the Monte Carlo simulation from Sec-
tion 3.1. Random Q-value decay events generated for 693r proton decay have an
efficiency shown in Figure 3.14. The black histogram is the random Q-value decays
that would be detected assuming HiRA had complete 47r coverage. The blue his-
togram is the events that would be detected for the current HiRA setup. The green
histogram is the events that are actually detected after accounting for non-working
and malfunctioning detectors. Above 500 keV the geometric efficiency is relatively
constant indicating that if 69Br is unbound by at least 500 keV the proton decays

from the ground state should be observed.

81

3.4 MCP Calibration and Analysis

This dissertation constitutes the first implementation of the complete MCP track-
ing system in an actual experiment. Each MCP provides position information at
two points along the beam, thereby providing the incoming angle and interaction
position on the target. The raw position information is taken from the four corners
of the MCP anode as described in Subsection 2.3.2 and sent to a charge-to-digital
converter (QDC). Calibration of the raw charge signals into position is carried out
with a target mask. Mask data was taken both with an a-source and the actual
secondary beam. Finally, a mapping function is applied followed by a position

correction involving the total sum of the corner signal amplitudes.

3.4.1 MCP Mask Calibrations

A brass target mask 0.155 mm thick containing a matrix of holes is used to map
the raw corner signals to physical Cartesian coordinates. Figure 3.15 shows a rear
(downstream) view of the target mask used for MCP 1. The mask is mounted to
an L-shaped G-10 (an insulating fiberglass composite) target ladder so that it can
be biased up to ——1000 V, providing the electric field necessary to accelerate the
secondary electrons ejected from the target foils. The smaller holes have a diameter
of 1 mm while an ”L” pattern, used for orientation of the mask pattern, is composed
of six larger holes, each with a diameter of 2 mm. All holes are separated by a
distance of 5 mm.

Particles that pass through the holes in the target mask are measured in coinci-
dence with a secondary detector to obtain the mask calibration pattern. The calibra-
tion involving the a-source is carried out in coincidence with a plastic scintillator
as shown in Figure 3.16. The photograph shows the MCP 0 (upstream) tracking
detector. A target drive holds a ladder with two target foils; an aluminized target

foil at the end of the drive and the target mask located nearest to the drive shaft. A

82

 

(a) (b)

Figure 3.15 — (a) Photograph of a rear View of the inserted MCP 1 calibration mask and
MCP 1 detector. The beam enters from the right of photograph. (b) Schematic drawing
of the MCP mask. All holes are separated by 5 mm. The diameter of the smaller holes
is 1 mm while the larger holes that make up the L pattern are 2 mm.

green PCB board that carries the corner signals, timing signal, and high voltage is
shown mounted behind the MCP detector and one of the permanent magnets. The
a-source is located upstream (left of the photograph). Particles that are not stopped
in the brass mask and pass through the holes reach the scintillator. Events where a
signal is generated in both the MCP and the scintillator produce a mask pattern as
shown in Figure 3.17.

A calibration was also carried out with the secondary beam. The last quadru-
pole at the end of the last triplet in the S800 analysis line, shown in green just
before the target in Figure 2.4, was turned off. Consequently, the beam is defo-
cused at the target. Moreover, the incoming secondary beam particles arrive at the
target with nearly parallel trajectories, i.e., the incoming angle is ~ 0°. This optical
Configuration turned out to be extremely convenient for comparing information
Provided by the MCP tracking system and the 5800 and is discussed in more de-
tail in Section 3.6. The $800 focal plane is the secondary coincident detector for this

calibration instead of the scintillator that was used in the a-source mask calibra-

83

 

Figure 3.16 - Photograph of the MCPO tracking detector during an tx-source calibra-
tion. The beam enters the chamber from the left side of the photograph. Also shown is
the upstream beam blocker in the background(left) as well as a scintillator(right) used
for detecting ix coincidences. The target drive enters at 60° supporting an aluminized
mylar foil and calibration mask. The bias cable attached to the target ladder is also
visible.

tion. While the a particles are stopped by the brass mask, higher energy secondary
beam particles mostly pass through both the holes and the mask. However, beam
particles passing through the brass lose enough of their energy that they are de-
flected from the spectrometer focal plane due to their reduced magnetic rigidity‘.
Uncalibrated mask patterns for both MCPs 0 and 1 are shown in Figure 3.18 for a

particles and secondary beam particles.

 

‘ A 7OSe beam at 72 MeV/u passing though 0.5mm of brass will emerge with an energy of
12MeV/u.

84

 

0.5

Y Flaw [a.u.]

-0.5 ' I‘

 

-;.- . -‘

t' t
1.._ l - .

..I .. ..-..I.

 

 

0.5 I 0.0 0.5
X Raw [a.u.]

(a)

 

 

  

   

 

i LII . i.

 

-0.5 I 0.0 0.5
X Raw [a.u.]

1.0

(b)

Figure 3.17 — MCP a-source uncalibrated mask pattern for (a) MCP 0 and (b) MCP 1.

 

 

 

 

...l 1’

 

 

 

 

 

5 I 00 I I 05 I I I1.o
XRaw[a.u.]

(a)

-0.

 

0.5

Y Raw [a.u.]

 

  

 

 

   

 

 

-0.5—~~-~I—I' . . ,.
_ I'1. -_ :.\ > ‘ .2: . 1
Z -I_'.' ._ . -;--_'. .
-1nII. . . . l. .jI. .4 .Ii . . . .1
'-‘i.0 -0. .5 1.0

5 I I 0.0 0
X Raw[a.u.]

(b)

Figure 3.18 — MCP secondary beam uncalibrated mask pattern for (a) MCP 0 and (b)

MCP 1.

thi
ga;
tr0.

3.4.2 Calibration and Fitting Procedure

Transforming the uncalibrated position spectra into calibrated physical Cartesian

positions consists of the following steps,

1. Pedestals, or channels corresponding to signals with zero amplitude, are sub-

tracted from the raw data and are initially taken from non-coincident data.
2. Pedestals are finely adjusted to maximize the uniformity of the mask pattern.

3. Position stability of the pedestals is checked as a function of the total sum
of the corner signals (sum signal). This is done by comparing how stable the

centroid positions of the mask holes for different ranges of the sum signal.

4. A 2D polynomial, M(X, Y), is fitted to the mask pattern and maps the uncal-

ibrated positions to physical positions on the target.

In step 1, a pedestal subtraction is done to set the QDC channel corresponding
to zero signal amplitude. Data was taken on random triggers of the data acqui-
sition and provide a best estimate for the pedestal value for each comer of the
MCPs. In step 2, the optimum pedestal values are determined by incrementing
and decrementing the estimated values and finding the pattern that maximizes
the uniformity as shown in Figure 3.19. The pedestal settings will affect the center
of the pattern the most severely since this is the region where the smallest corner
signals are generated.

Once an optimum set of pedestal values is obtained, position stability is checked
in step 3 as a function of the total sum of corner signals. Gates are placed on dif-
ferent holes of the mask pattern as shown in Figure 3.20a and the centroids of
the hole positions calculated. The stability of the X and Y positions is checked by
gating over different ranges of the sum signal. For each sum signal gate the cen—

troid of the hole position is calculated and compared to the original hole position

86

 

 

(b) (c)

Figure 3.19 — MCP 1 mask pattern for (a) pedestal values —10 channels, (b) pedestal
values 0 channels, and (c) pedestal values +10 channels.

 

a
C}

 

 

III IIIIIII'IIIIIII III

"'l'”!

 

-0.3

 

 

 

 

  
  
   

 

iiililiilli All

i
Y Raw [a.u.]

Aniliiiliiiiiii All

 

 

r

l i. ' 1 i
IllllllllllIIIIIIIIiIIIiIII

 

l

1
4
III

 

 

-1.c " '-

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

(3) Gates used to determine the centroid po-

X Raw [a.u.]

sition of holes for testing pedestal stability.

V &

 

X Raw [a.u.]

(b) Illustration of centroid stability for vari-
ous mask holes gated on different sum signal
ranges.

Figure 3.20

87

without a sum gate as shown in Figure 3.20b. This process is iterated over a set of
pedestal values until the process converges to a pedestal setting where the shift of
the centroid with the gate on the sum signal is minimized.

In step 4, a 2D polynomial up to 3rd-order maps the raw position information
to the calibrated mask pattern. Each calibrated position, X and Y, is mapped by
the function,

2 2 3
Mn(xo, x1) = ano + an1x0 ‘i' (1an] ‘i‘ “113350 + an4x1 + anSxo

+an6xI13 + an7xoxl + angxgxl + anngX% (32)

where n=0 or 1 (M0 = X and M1 = Y) and Mn depends on the two raw coordi-
nates (xo,x1). This function takes into account some of the non-linear effects that
are observed in Figure 3.18.

After calibration a correction to the XY—positions is made based on the sum
Signal, Figure 3.21 shows the Y—position dependence on the sum signal for MCP
1- Each Vertical band corresponds to a column of holes on the target mask. Larger
total summed signals are observed to be compressed compared to those with a

smaller sum. After the sum correction an additional mapping function was applied
for MCP 1.

3.4.3 Results and Discussion

The reStilts of the calibrations are shown in Figure 3.22. The position resolution of
the MCPS is clearly much better for the a-source calibration than for the secondary
beam, Also, the background is larger for the secondary beam calibration. There are
a nurtlber of factors that cause the beam and tx-source resolutions to differ. First, the
“‘Pal‘ticles (4He) have Z = 2 while the secondary beam nuclei have Z ~ 34. This
Should make the resolution of the beam better because the number of secondary

eleCtl‘ons ejected from the foil is larger for the beam as compared to that of the a-

88

7000

6000

0) A 01
O O 8
O O

O O O

2000

Sum [channels]

1 000

 

940 -30 -20 -10 0 10 20 30 40
Y-PositionlNon-Dispersive [mm]

Figure 3.21 — MCP 1 corrected Y—position dependence on the sum signal.

particles due to the larger interaction with the Coulomb field. And, it is true that
this results in large amplitude detector signals. The number of electrons is related
to the specific energy loss given in Equation 2.7 which goes as ~ Z2 / (E / A), corre-
sponding to a factor of ~ 4 more electrons for the secondary beam in this disserta-
tion. The angular distribution, however, of the ejected electrons should be greater
than that of the few electrons ejected as a result of an a-particle. Investigations car-
ried out in reference [69] show that this effect is real but it is not significant for the
particle energies used by Shapira et al. More important is the increase in the width
of the momentum distribution of the ejected secondary electrons from the higher
incident energy beam. This results in an initial spot on the first micro-channel plate
that is more broadly distributed in position than that of the a-particle due to the in-
creased radius of the helical orbits of the secondary electrons in the magnetic field.
The electron avalanche that follows is then spread over a broader distribution of

positions. One solution to this problem is to increase the magnetic field so that the

89

FEE.— ‘:.""|.:“‘-.I"al’

X-PositionlDispersive [mm]

X-PositionlDispersive [mm]

  

 

X-PositionlDispersive [mm]

 

-30 -20 -10 0 10 20 30 40 -40 -30 -2o -10 0 10 20 30
Y-PositionlNon-Dispersive [mm] Y-PositionlNon-Dispersive [mm]

(a) MCP 0 a-source mask calibration (b) MCP 1 a-source mask calibration

 

E
E.
0
.2
U.)
L
O
D.
.2
.2 '
:2
U!
0
‘t
X
-30 -20 -10 0 10 20 30 40 -30 -20 -10 0 10 20 30 40
Y-PositionINon-Dispersive [mm] Y-PositionlNon-Dispersive [mm]
(c) MCP 0 beam mask calibration (d) MCP 1 beam mask calibration

Figure 3.22 — Final MCP mask calibration spectra.

90

X-PositionlDispersive [mm]

  

X-PositionlDispersive [mm]

    

-30 -20 -10 0 10 20 30 40 -3o -20 -10 0 10 20 30
Y-PositionlNon-Dispersive [mm] Y-PositionlNon-Disperslve [mm]

(a) (b)
Figure 3.23 — Beam spots at (a) MCP 0 and (b) MCP 1.

trajectories of the secondary electrons take a more tightly confined flight path to
the MCP. Indeed, this has been done in recent HiRA transfer reaction experiments
that are currently under analysis and has resulted in a noticeable improvement in
the position resolution.

For this dissertation it is not a requirement that the entire active area of the
MCPS is accurately calibrated, only the area that overlaps with the beam spot. The
beam spots take on the shape of an ellipse at both MCP positions as shown in
Figure 3.23. At MCP 0 (upstream) the largest axes of the ellipse has a radius at half
maximum of ~ 1 cm while at MCP 1 (downstream), where the beam is at a focus,
the radius at half maximum is ~ 0.7 cm. Comparing the beam spot area to the
calibrated regions in Figure 3.23 one can verify that the majority of beam particles
are in a calibrated active region of the MCP detectors. This is important because
the large size of the beam spot at MCP 1 requires that an event-by-event interaction
correction for the position on the target to achieve the resolution needed for this

experiment.

91

To summarize, the MCP tracking system consists of two MCP detectors posi-
tioned at two points along the beam. MCP 1 is located at the target position and
provides event-by-event tracking of the interaction position on the reaction target.
MCP 0 is located upstream of the target position and provides position informa-
tion at an additional point along the beam thereby allowing for the tracking of the
incoming beam angle. Calibration of the detectors is accomplished by using a tar-
get mask in coincidence with a secondary detector. A 2D polynomial function is
fit to the raw mask pattern to obtain a calibrated position spectrum for each MCP
that gives the physical position of the interaction.

Calibrations were performed using both an a-source and the secondary beam.
However, there was a small difference in the calibration obtained for the 0: particles
and the secondary beam. Therefore, we used the beam calibration for the final
analysis of for MCP 1. For MCP 0 the beam did not cover enough of the active
area, so the alpha source calibration was used and adjusted to match the mask
pattern from the beam. By this procedure we obtain calibrations over the entire

active area that overlaps with the size of the beam spot.

3.5 $800 Calibration and Analysis
The heavy 688c decay product of 69Br is identified and analyzed in the $800 spec-

trograph. Additionally, the coordinates of the 68Se nucleus at the target are deter-
mined through an inverse transfer mapping of coordinates measured in the 3800
focal plane as described in Section 2.2. These measurements rely on the accurate
calibrations and / or corrections of the detectors in the focal plane. A description
of the corrections and importance of the E1 scintillator is given in Subsection 3.5.1.
This is followed by corrections to the pad readout of the CRDCs in Subsection 3.5.2.
The calibration of the non-dispersive direction of the CRDCs is explained in Sub-

section 3.5.3. Identification and analysis of the secondary beam is discussed in Sub-

92

section 3.5.4. Finally, the steps required to resolve the PID spectrum are described

in Subsection 3.5.5.

3.5.1 E1 Scintillator Corrections

For this dissertation the E1 scintillator generates the S800 trigger and timing stop
signal that is a reference for all other timing in the experiment. Typically, because
the scintillator is so large, the timing signal is taken as the mean of combined sig-
nals of the upper, tup, and lower, tdown, PMTs (shown in Figure 2.5 and is calculated

as follows,

tuP + iIdown
= . 3.3
2 ( )

 

The lower PMT did not function properly, however, and the time was instead cal-

culated just from the upper PMT signal,
t : tup (3'4)

The signal from the upper PMT is split. One signal is sent to generate a logic
trigger pulse which is sent into the 5800 time-to-digital converter (TDC) and is
used as the ultimate timing reference. The other signal is sent directly into the TDC
and is the timing signal for the E1 scintillator. In other words, these two signals
are generated from the same source and produce a ”self-trigger”. So, the timing
Signal for the E1 scintillator should be a sharply peaked Gaussian whose width re-
flBCts the intrinsic timing resolution of the E1 scintillator. The actual timing signal
Shown in Figure 3.24 reflects a different structure however; a doubled peak dist-
ribution is observed. The underlying cause of this problem is, as of yet, unknown
but is suspected to be a problem associated with the 5800 trigger electronics. This
is a problem for the resolution of the PID spectrum that will detailed in Subsec-
tion 3.5.5. Particles in the focal plane are identified by plotting the AE signal from

93

 

6000
5000
E 4000
C
3 3000
c)
2000
1000

 

liillllllllliillillililillllllil

 

-liilllilijiiillililliiiiliiirli

 

 

III-23III-28III-27IIII-25I -25II
E1 Time [ns]

‘1‘,
O
l
N

4

Figure 3.24 — Timing signal for the E1 scintillator.

 

     

 

  

 

 

 

 

 

 

 

 

 

 

-25 :— -25
E E '27 :
-- -26 _— ----- -—- -25_
o _ o _
.§ : .§ :
:1 -27s ~~~~~~ « t- -27_
t F i-
m .( a m T
‘28 31.4%..- mpg I I: _23: l _
a. i REEL“ i .l..rri... .-.
-300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300
CRDC1 X [mm] CRDC1 X [mm]
(a) (b)

Figure 3.25 — The (a) uncorrected and (b) corrected E1 scintillator timing signal as a

function of the dispersive position in the focal plane.
the ionization chamber against the particle’s ToF. The wide and doubled peaked
distribution shown in Figure 3.24 smears out the timing resolution and reduces
the ability to resolve the reaction products. Furthermore, the E1 timing signal also
depends on the dispersive position in the focal plane as shown in Figure 3.253.
The timing signal is improved by empirically correcting the average behavior as a
function of the dispersive position at CRDC 2. The result of the correction is shown

in Figure 3.25b.

94

3.5.2 CRDC Pad Calibration and Corrections

The CRDC pads run vertically along the sides of each CRDC as described in Sub-
section 2.2.4 and determine a particle’s dispersive position in the focal plane through
the induced charge on a distribution of pads. Their position is fixed with a pad
pitch of 2.54 mm. Pedestal values for each channel are typically measured prior to
the experiment with a pulser and are subtracted from the raw channel value.

CRDC pads are readout using the STAR FEE cards discussed in Subsection 2.2.4.
Each chip processes 16 pads. While the gains within a chip are roughly the same,
the gains between chips used in this dissertation were not well matched. Fig-
ure 3.26a shows the total induced charge, summed over a subset of data, as a func-
tion of the pad number (dispersive position). The center of gravity of the pad dist-
ribution is discontinuous at those positions that cross the chip boundaries where
the gains change significantly. Therefore the channels, especially between chips,
must be adequately gain matched. Each channel was individually adjusted manu-
ally to minimize the discontinuity between channels and chips. The results of the
gain matching shown in Figure 3.26b are less than perfect, although of sufficient
accuracy for this dissertation.

For this dissertation, it was only possible to set the global offset for the pad elec-
tronics as opposed to setting the individual offsets for each channel. Because the
hardware gains between chips is poorly matched, this had the unfortunate conse-
quence that some of the chips saturate while others have gains that are too low.
This effect is visible in Figure 3.26a but is more clearly observed in Figure 3.27
where the amplitude for a single pad, when it is the pad with the maximum am-
plitude, is plotted against the AE signal from the ionization chamber. When cal-
culating the center-of-gravity to obtain the dispersive position the saturated pads
flatten the peaks and / or skew the distribution of pad amplitudes when the satu-

ration values of all contributing pads are not the same. To correct for this effect a

95

“halal
8.888

“8’

 

Total Sampled Charge [a.u]

  

.5
O
O

  
   

0 20 40 60 80 10012014016
CRDC1 Pad Number

(a) CRDC 1 summed induced charge signal as a function of pad number without
gain matching or set thresholds.

0180 200 220

 

03501;!
8588

§

 

Total Sampled Charge [a.u.
'2‘

. .. . . _ . : : . - : z |
- ' a
0 20 40 60 80 100 120 140 160 180 200 220
CRDC1 Pad Number

(b) CRDC 1 summed induced charge signal as a function of pad number with gain
matching and set thresholds.

Figure 3.26

96

 

3500
2.450
“9’4400
G

5 350
8 300
3250

Sam
-5 M
01 O
O O
I IIIIIIIIIIII'IIIIIIIIIIII-
i I

 

—l
01°
CO

 

 

 

 

 

 

Maximum

 

O

O FIIIIIIIIIIIIIII

200 400 600 800100012001400160018002000
lon Chamber AE [a.u.]

Figure 3.27 - Saturation of CRDC 2 pad 52.

maximum threshold value was introduced that limits the amplitude of all channels
so that the saturation effect is minimized.

The center-of-gravity calculation is augmented by algorithms to eliminate the
effects of events containing pads that are exterior to the main distribution as well
as pads that are not functioning properly. Ions produced in the CRDC induce a
Gaussian-er distribution on a small number of pads. For noisy events a pad out-
side of this main distribution may also have data. If this is included in the center-
of-gravity calculation it can shift the mean value of the position. An algorithm
removes these pads from the calculation when needed. In addition, a number of
pads for this dissertation were not functioning as expected. The amplitude values
for these pads are set to zero, which means that pad distributions in the neighbor-
hood of such bad pads will be missing information. To correct for this effect an
interpolation is done to estimate the amplitude of these pads before the center-of-

gravity calculation.

97

2000
_2600
O

T: 2400
c 2200

C
“2000

.C
2.1000
0
£1500
|_14W
E1200
51000
300
600
-300 -250 -200 -150 -100 -50 0 50
CRDC1X[mm]

 

100 150 200 250 300

Figure 3.28 — CRDC 1 uncalibrated non-dispersive mask calibration spectrum.

3.5.3 CRDC Mask Calibration and Corrections

While the dispersive calibration is fixed by the pad pitch as discussed in Subsec-
tion 3.5.2, the non-dispersive, or Y-position, is determined by the drift time of the
electrons in the ionized fill gas. A mask containing a hole pattern and a number
of slits is inserted 8 cm in front of either CRDC 1 or CRDC 2. Only those particles
passing through the apertures in the mask are detected and result in a position
spectrum as shown in Figure 3.28. Each hole has a precise position and lies on
a rectangular grid. However, the mask pattern in Figure 3.28 shows an apparent
non—linearity in the y-direction which is clear if one considers the holes along y = 0.
This is directly related either to the physical drift time, the timing of the drift, or
both. The non-linearity depends on the dispersive position in the focal plane as is
shown in Figure 3.29a. The timing signal is corrected by subtracting off the average
dependence on x and the result is shown in Figure 32%. While one may initially
think that the non-linear time dependence is very similar to that discussed in Sub-

section 3.5.1, it should be noted that these times, in principle, are not correlated.

98

2100
'3
a 2000
E
2 1900
2.
E 1800
-,: 1700
=5 1600
a

1500

 

-300 -200 -1 00 0 200 300

0 1 0
CRDC2 X [mm]
(a) CRDC 2 uncorrected drift time signal as a function of dispersive (X) position.

2100
'3'
a 2000
E
E 1900
.2.
E 1 800
-,: 1700
E" 1600
D

1500

 

-300 -200 -100 200 300

0 1 00
CRDC2 x [mm]
(b) CRDC 2 corrected drift time signal as a function of dispersive (X) position.

Figure 3.29

99

The E1 scintillator timing signal is fast, on the order of 10‘9 s, while the drift time
of in the CRDC is a factor of 1000 slower.

A linear fit to the center hole centroid positions is used to convert the raw time
signal from channels to m. For longer drift times the timing signal has an addi-
tional non-linear dependence which will be discussed in the following paragraphs.
Therefore, only the holes located at short drift times were used in the fitting as their
calibration is linear. Each mask is located 8 cm upstream from its CRDC: the cal-
ibration using each mask should take that distance into account. This means that
the angle, or equivalently the position from the opposite CRDC, should be taken
into account. A linear fit to the initial CRDC mask pattern is done to obtain the lst
order calibrations for both CRDCs. Next, the lst order position information is used
to correct for the angle of incidence on the focal plane. The Y-position is given by
the following equation which takes into account the lst and 2nd order mask posi-
tion effect,

Y 2 b1 + (12171 + alaztdrm (3.5)

where b,- and a,- are the lst and 2nd order offsets and slopes from each linear cali-
bration.

A non-linear dependence also exists for long drift times. This is observed in
Figure 3.28 and is clearly visible in a plot of CRDC 1 Y against CRDC 2 Y shown in
Figure 3.30a for reacted beam data. As described in Subsection 2.2.4 the electrons
drift in opposite directions; CRDC 1 drifts from y-min to y-max while CRDC drifts
from y-max to y-min. Therefore, the non-linear drift time affects position tracking
on both the left and right sides of the beam. Consequently, a correction is applied
to y-min for CRDC 1 and y-max for CRDC 2. The correction forces y1 = y2 on the

average and the result is shown in Figure 3.30b.

100

 

 

 

 

 

 

 

C3

 

 

 

 

 

50:

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I 1 I I I 1 ‘ _10 - i 4 i J I I A J r J I I i I I I ‘
'wiioiiIII I50 100 300 -50 0 50 100
CRDC20 Y [mm5]o CRDC2 Y [mm]

(a) (b)

Figure 3.30 — CRDC Y1 / Y2 (a) uncorrected and (b) corrected non—linear timing signal
correction.

3.5.4 Secondary Beam Identification

The secondary beam is identified via a ToF-ToF method involving the timing scin-
tillator at the XFP position of the A1900 and the OB] position at the beginning of

the S800 analysis line. In the non—relativistic limit of Equation 2.6,
A
Bp o< EU (3.6)

where v is the velocity of the beam particle. When filtering neutron deficient beams
the A1900 selects a narrow range of isotones within the chosen momentum accep-
tance and beam optics uncertainties. Typically contaminants in the beam will have
Sirnilar numbers of neutrons. The most likely fragment will differ by at most one
neutron. At fixed Bp a decrease or increase in the A/ Z ratio requires an increase
or decrease in the fragment velocity respectively. Therefore a unique identification

0f the beam components can be made by comparing the ToF between well sepa-

101

 

110......-..--.-.-,.

  

XFPToF[ns] _.
00 (D O
O O 0
III I I I I I III I I I IIIIITTI

\I
O

 

'.._. .llIlIII,.,.II,.|III.1II.I'III'-
100 11 120 130 140
OBJ ToF[ns]

60

Figure 3.31 — Secondary beam PID based on the XFP and OB] ToF signals.

rated plastic scintillators. This is done in Figure 3.31 where the ToF from the XFP to
the E1 scintillator and the OB] to the E1 scintillator are compared. For the reacted
beam the problem with this method is that the ToF of the unreacted beam particles
is folded with the distribution of ToFs of the reaction products, which have large
variations in energy and therefore velocity, traveling from the reaction target to the
focal plane.

An improved identification can be obtained if one removes the folding of the
different fragment flight times from the target to the E1 scintillator. Let the dis-
tances and ToFs be defined according to Figure 3.32. Then, we can find the TOP
from the XFP to the target, Atmget, and from the target to the focal plane, the frag-

102

m9]

Sui

fiec
Inlet:
bee/)2 4

BEAM

XFP OB] Target FP

I d I d I d I

O 1 2

Figure 3.32 — Parameters for the TOP derivation.

ment velocity, Atfragment in terms of the original timing signals,

 

 

 

 

 

 

d1 as was...
At -=t —t -= + =d At 3.7
obj fp obj vbeam vfragment 1 d0 + d} + fragment ( )
do + d1 (12
At = t — t = + =2 At + At . 3.8
xfp fp xfp vbeam ”fragment target fragment . ( )
Subtracting Equation 3.8 from Equation 3.7,
=>At —At --At ————d—1——At (39)
xfp obj —' target d0 + d1 target -
1
Attarget : _d—_ (Atxfp _ Atobj) (3-10)
1 _ 0+ 1
do -i- d1
1‘ do (Atxfp — Atobj) . (3.11)
Upon substitution of the above equations,
—d d +d
:> Atfragment : Atxfp _ Attarget : TafAtxfp + __O_EO—1At0bi. (3.12)

This decouples the fragment velocities from the TOP. The incoming beam is identi-
fied as shown in Figure 3.33. The vertical bands represent each isotope in the beam.
The x-axis is ToF from the XFP to the target and is purely the TOP of the unreacted

beam. These particles are further resolved in the y-axis which is purely the TOP of

103

    

 

 

154;— g
a 152;- —;
£3 150§- g
is 148%- i
l: 146;— -:
g 144;—. —:

1425- a
i? 140§- é
“- 1383a . g

1355‘ 5%; “2.

   

80 385 I 393 395 400 405 410 415
XFP-Target ToF [ns]

365 370 375 3

Figure 3.33 — Components of the secondary beam.

the reacted beam fragments, i.e., the reaction products. Within the secondary beam
there are three main components. They are identified as 71 Br (9.4 %), 7°Se (66.7 %),
and 69A5 (23.9 %).

3.5.5 Particle Identification

Particles that reach the 8800 focal plane are identified with a AE-ToF method with
the AE signal from the ionization chamber and the reaction product particle ToF
given by Atfiagment derived in Subsection 3.5.4. In the previous sections corrections
to the raw detector signals were described. In this section corrections for both the
AE signal of the ionization chamber and the TOP that depend on the trajectory of
the measured particles will be described as well as corrections due to time drifts
of the detector signals. These corrections are required in order to uniquely identify
and resolve particles based on their charge, Z and mass, A.

For example, a particle with a fixed Z, A, and total momentum, entering the
focal plane at an angle of 0° has a shorter flight path through the focal plane de-

tBCtOIs and therefore suffers less energy loss than the same particle with a more

104

divergent trajectory. Similarly, the first particle will also have a shorter ToF com-
pared to the second particle since they both had the same velocity but travel over
different path lengths through the spectrograph. To obtain the PID using the AE-
ToF method both the energy loss and ToF for particles with a given Z and A must
be corrected to remove these effects to allow PID gates that do not depend on the
trajectories of the particles. Consequently, both the AE and TOP signals used for the
PID have linear corrections that depend on the dispersive angle in the focal (AFP)
plane and the X and Y positions in both CRDC 1 and 2.

Calibration parameters are obtained by eliminating the dependence of either
the AE or ToF signal on the AFP and the CRDC X/ Y positions. Since AFP is cou-
pled to the X and Y positions this procedure is carried out iteratively until the de-
pendencies are minimized. Moreover, once a coarse calibration is obtained a gate
is applied to select a single intense isotope in the PID near the reaction products of
interest in order to maximize the resolving effects of the correction for the reaction
products in that region. The procedure is again repeated until the best correction
parameters are found. Figure 3.34 shows the uncorrected and corrected depen-
dencies of the TOP signal on the CRDC 1 X and Y positions (the ion chamber AE
corrections are obtained in the same manner). Similar corrections are obtained for
the dependencies on CRDC 2 and AFP.

The ToF signal depends directly on timing information from both the XFP and
OB] scintillators. Over the course of the experiment their efficiency decreases due
to localized radiation damage caused by the bombardment of the beam. In ad-
dition to reducing the detection efficiency this damage also degrades the timing
signals. To counter these effects the scintillators were periodically adjusted so that
an undamaged region of the scintillator was used or, if an undamaged region did
not exist, the scintillator was replaced. Throughout the experiment these changes

in the scintillators result in unstable shifts which tend to smear out the timing

105

 

ToF [ns]
ToF [ns]

ToF [ns]
ToF [ns]

Y

 

(c) (11)
Figure 3.34 — Uncorrected ToF signal as it depends on CRDCl (a) X and (c) Y com-
pared to the corrected dependence on CRDCl (b) X and (d) Y (gated on 69Se). Similar
corrections are done for ion chamber AE as well as the dependencies on CRDC2 X / Y
and AFP.
signals. To minimized these effects the average shift in the reaction product ToF
signals was determined on a run—by-run basis. The shifts are subtracted from a
fixed reference ToF resulting in an improvement in the PID resolution as shown in
Figure 3.35.

The final corrected 5800 PID is shown in Figure 3.36. The loci of points in the
PID plot represent the different nuclei produced in nuclear reactions with the tar-
get. From calculations using LISE++ as well as the position of the unreacted beams
in this plot we determine the locus of points corresponding to 68Se, the heavy prod—
uct in the decay of 69Br. Additional, the diagonal lines in Figure 3.36 correspond to
isotopes of constant Z. The nearly vertical line on the left of the figure represents

isotopes with N = Z.

106

   

ii

0
C
C
a
.C
0

8‘

l

.0
b
O
o .

Ion Chamber AE [channels]
N
8

lonChamber AE

    

145 1501551000135

0 140 145 150 155
Fragment ToF [ns] Fragment ToF [ns]
(a) (b)

Figure 3.35 - PID of reaction products in the 3800 focal plane for (a) uncorrected and
(b) corrected ToF stabilization.

3.6 MCP 81: S800 Optics
The MCP tracking system and the 5800 provide, to some extent, redundant infor-
mation about the beam and its optical characteristics. The MCP tracking system
provides a measurement of the x — y — 2 interaction position on the target as well
as the dispersive (ATA) and non-dispersive (BTA) angles of the incoming unreacted
beam. Reconstructed events from the 8800 provide a measurement of the Y—position
(YTA) on target as well as the dispersive (ATA) and non-dispersive (BTA) angles
for particles detected at the focal plane. Crosschecks of the calibrations between the
MCP tracking system and the 8800 are done by comparing the Y—position and an-
gles. Consequently, it is found that inconsistencies in the tracking exist and result
in the need for the manual construction of an inverse transfer map instead of using
the 5800 inverse map described in Subsection 2.2.3.

The beam tuning used during the MCP mask calibration described in Subsec-

tion 3.4.1 resulted in an extremely useful optical configuration for investigating the

107

 

Ion Chamber AE [channels]

130

rear--

Ema
IE

 

135 140 145 150 155
Fragment ToF [ns]

Figure 3.36 — S800 particle identification (PID).

108

8800 AFP [mrad]
$800 BFP [mrad]

     

10 20 30[n4'(‘)1]50 10 15[rm2“(:)|
(a) (b)
Figure 3.37 — MCP 1 mask image illustrating the unique correlation between (a) the
X-position and S800 ATA and (b) the Y—position and S800 BTA (b).
particle tracking. During the mask calibration the last superconducting quadru-
pole before the target chamber was turned off. As a result, the beam was defocused
at the target allowing the beam to cover a larger area of the MCP mask. In addi-
tion it is found that the angles of the incoming beam particles are nearly parallel.
This has the fortunate consequence that the X and Y positions on target correspond
to unique dispersive and non-dispersive angles in the focal plane respectively as
shown in Figure 3.37. One then has the ability to select events corresponding to
individual mask holes independently of the MCP detector.

Let’ s first examine the correlation between the Y—position given by the MCP
and that of the 3800. Figure 3.38 shows the Y—position at the target as given by the
$800 (YTA) as a function of the MCP Y-position for a MCP mask calibration us-
ing the secondary beam. The correlation is linear and the two devices are in good
agreement with respect to the Y-position at the reaction target. However, the Y res-
olution of the MCP is slightly better than that of the 5800. The MCP Y—position

resolution is on the average ~ 1.1 mm full width at half maximum (FWHM) ob-

109

N
O

15
"E10
..E. 5
<
t 0
8 -5
Q
m

.L
c

 

-15

'2920-15-10 -5 0__5 10 15 20
MCP1 Y-Posrtlon [mm]

Figure 3.38 — Correlation of the Y—position at the target (YTA) for MCP 1 and the S800.

tained by a Gaussian fit of mask holes resulting from gates placed on positions in
Figure 3.37" whereas the $800 YTA position resolution is ~ 2.3 mm FWI-HVI.

Next the dispersive and non-dispersive angles are compared in Figure 3.39 us-
ing unreacted beam data. While the non-dispersive angles are well correlated there
exits a discrepancy with the dispersive angles. The distribution of dispersive an-
gles given by the MCP tracking system is wider than that of the S800 and the
correlation is not one—to-one. The good agreement between the non-dispersive an-
gles indicates that the problem should lie with the angle given by the 5800 since
there is no difference in the way the MCP tracking system determines the angles.
The validity of the angles measured by the MCP can be verified with the mask

calibration data. Since the apertures in the mask are defined, so too is the angle

 

' Since the apertures in the mask have a finite radius this method of determining the resolution is
only approximately correct since the distribution is not necessarily a perfect Gaussian.

110

    

    

    
  
   

—L

   
   

BTA [mrad]

ATA [mrad]

1001020304050 1001020304050
ATA [mrad] BTA [mrad]

(a) Correlation between the $800 and MCP (b) Correlation between the S800 and MCP
dispersive angles (ATA) at the target loca- non-dispersive angles (BTA) at the target 10-
tion. cation.

Figure 3.39

for a particle passing through any two given holes. Particular dispersive angles
are picked out by gating on their corresponding holes and then compared to the
angles calculated with the inverse map of the 5800. Therefore, an inverse transfer
map for ATA was manually generated using position / angle mapping information
contained in the MCP mask calibration runs. Positions and angles in the S800 fo-
cal plane are mapped to the ATA at the target. The BTA, YTA, and kinetic energy
deviation (DTA) are still calculated using the original 3800 inverse map.

To first order the ATA is a linear function of the AFP as shown in Equation 3.13.
This dependence is expressed in Equation 3.13 where a, and af denote the ATA of
the reaction product and the AFP,

a, = A0 + Alaf I: A0(Xf) + A1(xf)af (3.13)

= [Bo + B1xf] + [C0 + Cle]af (3.14)

111

In principle the coefficients also depend on XFP to higher order. The coefficients in
Equation 3.14 are determined from the dependence of the offsets and slopes of the
dispersive angles measured by the MCP tracking system as a function of XFP. A
narrow range of XFP positions is selected and the corresponding offset and slope of
the correlation between the MCP dispersive angles and the 5800 AFP is produced.
This is illustrated for one of the XFP range selections in Figure 3.40a and a fit of
the centroid positions in Figure 3.40b. The coefficients for the MCP map are taken
from linear fits of both the offsets and slopes over the range of XFP positions and
are shown in Figure 3.40c and Figure 3.40d. From Equation 3.14 Bo and 31 are equal
to the fit parameters in Figure 3.40c while C0 and C1 are given by the parameters
in Figure 3.40d. Applying the MCP inverse transfer map removes the discrepancy

in the dispersive angles as shown in Figure 3.41.

3.7 69Br Proton Emission

In the previous sections the methods of calibrating and correcting data collected
by the MCP tracking system, HiRA, and the S800 spectrograph was described.
Now, in this section, the collected data is processed and physical nuclear structure
information is extracted. Gates are applied to the PID that select events, protons
and 68Se in the case of 693r decay, of a specific reaction as well as gates that exclude
invalid events. Additionally, corrections related to an uncertainty in the total beam
energy and its effects are described. Finally, an initial interpretation of the relative

energy spectrum (proton capture Q-Value) for p+685e events is discussed.

3.7.1 Relative Energy Spectrum Construction

To properly construct a valid proton emission relative energy spectrum with min-
imum background contamination a number of gates are applied to the data. The
relative energy is calculated using Equation 2.2. Consequently, this equation de-

pends on the masses, kinetic energies, and relative momenta of the decay prod-

112

'r"_-".'Y"“DV ‘11‘7-uz—q
l

 

"I:

 

8800 AFP [rad]

(a) Dependence of MCP dispersive angle at
the target (ATA) on the $800 dispersive angle
in the focal plane shown for a one of eight
12.5 mm wide gates on XFP.

ndf
p0

4.55300-04

HM
CO

I
-|
O

MCP ATA/XFP Offsets (x103)
O
O

a:

(c) linear fit to the offsets of the eight linear
fits illustrated in (b). The coefficients of the fit
are used as parameters in the MCP inverse
transfer map.

   

ndf 2.67430-01 /
-7.9032e-04
-1.0071e+00

p0

F
g.
<
i-
<

 

[

(b) Linear fit of the centroid positions of the
mask holes in (3). Again, there are eight such
plots, one for each gate on XFP.

-0.95 9°

-1.00
-1 .05
-1.10

-1.15
-0.

-9.92480-01

MCP AFP/XFP Slopes

 

(d) Linear fit to the slopes of the eight linear
fits illustrated in (b). The coefficients of the fit
are used as parameters in the MCP inverse
transfer map.

Figure 3.40

113

     
   

ATA [mrad]

  

8800 ATA (MCP Map) [mrad]

1001020304050 1001020304050
ATA [mrad] ATA [mrad]

(a) (b)

Figure 3.41 — Correlation between the S800 and MCP dispersive angles (ATA), from

MCP mask calibration data, using the (a) S800 inverse transfer map and using the (b)

manually created MCP inverse transfer map.
ucts. These quantities need to be determined properly as any misidentification or
incorrect assignments will lead to an increased background in the relative energy
spectrum thereby reducing the SNR of our signals. Certain detectors are known to
have regions that do not respond in a predictable or accurate manner with regard
to the detection of particles. Therefore, events occurring in these poorly perform-

ing detector elements are excluded from the analysis. These gates include,

1. The E-front (EF) and E-back (EB) energy signals from the HiRA telescopes

must match to within 500 keV.
2. All malfunctioning strips or CsI(Tl) crystals in HiRA are excluded.

3. Events occurring in the middle DSSD strips (strips 15 and 16) are excluded
since particles in these events may scatter into more than one CsI(Tl) crystal

or miss the crystals completely.

114

 

4. Only events where a single particle is detected in HiRA with no more than
3 DSSD strips firing are included. This accounts for the correctable readout

order problem events.

5. Events that have a dispersive position < —150 mm in the focal plane are ex-
cluded. This is a region in the CRDCs where there is a significant uncertainty
in the calibrations. Additionally, this is the region that is being shadowed by
a blocker that protects the detectors from the secondary beam as well as re-
ducing the number of uninteresting unreacted beam events. It is also a region
that is still intensely bombarded by a fraction of the secondary beam as well

as scattered beam that tends to degrade the detector performance.

The relative energy spectrum is constructed using information from the MCP
tracking system, HiRA, and the 8800. Figure 3.23b shows the position information
of the reacted beam used for correcting the angle of particles detected in HiRA as
discussed in Subsection 2.3.2. In Figure 3.42a the $800 proton coincident yield is
shown. In Figure 3.42b the 68Se coincident particle yield is shown. We find there
are ~ 25 364 events involving 68Se (with the gates described above applied). There

are ~ 12 865 single proton events that are detected in coincidence with 68Se.

3.7.2 Beam Energy and CsI(Tl) Calibration Correction

Before constructing the final relative energy spectrum a correction involving the
total beam energy is needed. In principle, the energy of the secondary beam can
be determined from Equation 2.6 and the magnet settings of the A1900. While the
magnitude of the magnetic field, B, is well known the effective radius, p, is not.
Consequently, it is found that the energy calculated for the secondary beam using
the A1900 magnetic rigidity is higher than that obtained by measurements with
the S800 focal plane.

115

 

   

  
      

 

   

2000 14 -I'- ‘4
'5'
— 1 2 12
5
21500 5 1o 10
o ‘-' j':
m 3 8 I
< I. .
h 0’ I .'
31000 .5 6.
O .. 2 , '-r--
5500- . _ "
....l.. ....Il .._:"'_-..' _' . 0
130 135 140 145 150 155 1 00 20 40 60 80 100120140
Fragment ToF [ns] Csl Energy [MeV]
(a) Reaction products identified in the S800 (b) Single protons in HiRA coincident with
coincident with a single proton in HiRA. 68Se in the 5800.
Figure 3.42

This discrepancy has a direct effect on the measured HiRA particle energies
since the magnetic rigidity of the A1900 is used in Subsection 3.3.4 to determine
the energy of the elastically scattered protons in the CsI(Tl) calibration while the
S800 rigidity is used to determine the recoil energy. However, if the calibrations
are different the decay peak will become unacceptably broad. The discrepancy in
the elastic scattering calibration point means that the calibration was defined to
have a higher energy than it would have been assigned using the S800. However,
by analyzing the relative energy for events where protons are emitted at forward
and backward angles in the COM frame we can correct the CsI(Tl) energy calibra-
tion to make it consistent with the $800. In other words, decay protons emitted in
the forward direction along the beam shall have the same relative energy as those
emitted in the backward direction in the COM. If the CsI(Tl) calibration is incorrect
then any observed decay peaks will have a mean value that depends on the proton
angle of emission in the COM frame. Figure 3.43 demonstrates this effect. In Fig-

ure 3.43a a simulated proton emission from 69Br with a Q-value of 810 keV shows

116

 

 

I l I V V V r l 1 T I

 

 
  

   

 

 

 

 

 

 

 

7000:- I—Seallng=1.000 900— :3: —e=45110°
: E. 5:
00005- """ Scaling=0.990 mg ...... 9:135:100
5000:— _
E g 600;—
E 4000;- 3 500;—
3000:— o 400:—
E 200%-
1000; 1005— :
I. A , . l l E I ‘_. 1 A4 7
3.0 0. 1.5 2.0 3.0 0. 5 2.0

 

 

5 1.0 1.
Q-Value [MeV]

(a) Simulation of proton emission from a (b) Simulated peak gated on forward (solid)
state in 69Br with Q = 810 keV for unscaled and backward (dashed) proton emission an-
(solid) and scaled (dashed) proton energies. gles in the COM frame.

5 1.0
G-Velue [MeV]

Figure 3.43

the change in resolution of the observed relative energy peak when the total proton
kinetic energy is reduced by 1 "/0 of its actual value. However, in Figure 3.43b we
can clearly see the underlying cause of the broader peak. We observe that events at
forward proton emission angles are shifted to lower relative energies while those
at backward angles are shifted to high relative energies.

To account for the known beam energy discrepancy the total proton kinetic
energy is scaled until the best overlap of the low relative energy peak for forward
and backward angles is found. The difference in peak values as a function of the
energy scaling factor is shown in Figure 3.44. A transition crossing through zero
peak difference is observed when the proton energy is reduced by ~ 0.8%. This
value for the difference in A1900 and $800 Bp calibrations is in agreement with
other experiments performed at NSCL where kinematic information was used to
find the scale factor. Consequently, the total energy of particles detected in HiRA
is reduced by ~ 0.8 % for all further analysis of the relative decay energy.

117

P

   
    
  
     
  

Peak Centrold

 

P
o
a:

 
 

0.04 Peak Gausslan Flt

0.02

 
 
  
  
 

-0.02
-0.04
-0.06

Ion Difference [MeV]

 
  

Peak Poslt

 

-0.10

0.980 0.985 0.990 0.995 1 .000
Kinetic Energy Scale Factor

Figure 3.44 — Difference between the peak position for forward and backward proton
emission angles (in the COM frame) for the low p+6SSe relative energy peak as a func-
tion of scaled total proton kinetic energy. The forward and backward peaks overlap
when the energy is reduced by ~ 0.8 %.

3.7.3 Interpretation and Discussion

The final corrected relative energy spectrum for 693r proton emission is shown in
Figure 3.45. Only events corresponding to the 7OSe incoming beam are gated to
produce the spectrum. There are two main features contained in the spectrum: A
continuous distribution of proton emission events at high (Eml ,2 1.4 MeV) relative
energies and a peak at low relative energies. These are all decays from quasista-
tionary states formed mostly by the combined Coulomb and centrifugal barrier
potentials discussed in Section 1.2.

Events at higher relative energies result from decays of many overlapping and
unresolvable resonances. The production of 69Br in its ground state is not a direct
process in our experimental method. We rely on a highly energetic and / or multi-
step process through reactions of the secondary 705a beam and the target nuclei. In

the simplest picture, we must pickup a proton and remove two neutrons in order

118

 

 

 

 

 

102

   
   
   
    

 

 

 

 

Counts

 

 

l:' p+683e

D p+°°Se (Background)

I llllIIl

 

 

 

 

 

 

012345678910
Q-Value [MeV]

 

Figure 3.45 — Relative energy (Q—Value) spectrum for coincident p+685e events.

to reach 69Br. As a result the 69Br nuclei are left in excited configurations which
undergo particle decay. However, the density of states (p(Ex) oc ebVE—I in the Fermi
gas model) is increasing for states with excitation energies, Ex, sufficiently above
the ground state. Additionally, the width of the individual resonances, given by
T = h/ T, is also increasing due to the rapidly decreasing lifetime, T, that results
from the larger Coulomb penetrabilities at larger excitation energies. Due to the
increasing density of states and the increasing resonance widths it is not possible
to resolve and identify contributions from individual states. The continuum of rel-
ative energies in Figure 3.45 is thus understood to be highly energetic (hot), short
lived decays from a statistical distribution of resonances. The distribution rapidly
falls to zero for the lowest relative energies. Here, the density of states is lower and
proton emission rate is reduced due to the greater width of the barrier.

In these regards, the 69Br nucleus is unusual due to its strong affinity for proton

decay from all levels. One finds that, for all energy levels in 69 Br, the penetrabilities

119

are large due to the narrowing width of the Coulomb barrier with increasingly un-
bound energies. The 7-ray widths are not as large in neighboring particle stable nu-
clei because these nuclei have much lower ground state energies and the 'y-decay
rate increases strongly with the 'y-ray energy, which increases as the ground state
energy decreases. The high unbound ground state energy of 69Br allows the proton
decay branch to compete, and indeed dominate the '7-decay branch since I‘p > 1‘7.
This is not the case, however, for less proton rich nuclei with ground states that are
either bound or have proton separation energies that are more positive than 69Br.
For the low-lying levels in these nuclei the ’y-ray decay rates increase significantly
while the penetrabilities and proton decay rates of a proton with fixed outgoing en-
ergy (i.e. Q-value) remain the same. In these cases proton emission from the lowest
excited states is greatly inhibited, since I‘p(Ex) < I' 7(13x).

At the lowest relative energies, proton emission from individual states may be
resolved. Here the density of states is low and proton emission from the ground
state as well as low-lying excited states can be isolated. These states have signifi-
cantly longer life-times compared to those in the continuous relative energy region
due to the increased width of the barrier which is sensitive to the excitation energy
as well as the l-value of the state. Furthermore, as just discussed, proton emis-
sion will dominate over all other decay modes, particularly ry-decay. Again, this
is where 69Br is unique. Proton emission from the ground state is the fastest de-
cay mode as there are no lower energy states to 7—decay into nor is ,B-decay fast
enough to compete. The peak at 812 keV in Figure 3.45 is in the energy domain
dominated by these relatively long-lived decays. The peak lineshape and position
is, we believe, likely the result of emission from the ground state and possibly
nearby low-lying excited state(s) as modified by their lifetimes (see Section 4.3 and
by the detector resolutions. The question as to the contributions of various states

in terms of the observed peak line-shape is addressed in chapter 4.

120

 

In addition, one expects background events at low relative energies to be min-
imized. An advantage of our experimental method is that our background is re-
stricted to charged particle events, specifically, proton emission. However, in prin-
ciple, there can be background at low relative energies coming from proton decays
to excited states in the daughter nucleus 68Se. If some high-lying state decays to
an excited 68Se the excited state decay rate will be lowered by barrier penetration
with respect to decay from the same original state to the ground state of 68Se. But
such decays to excited states will have low penetrabilities when compared to cor-
responding decays to the ground state. If the proton spectroscopic factors of higher
lying states in 698r to the ground state of 68Se are comparable to the decay to the
excited state most of these nuclei will decay directly to the ground state, creating a
large peak at larger relative energies in the spectrum. Such peaks are not observed.
This will be discussed again in Section 4.6.

Strong evidence supporting the above diSCUSSiOIl of proton and ’y-decay branch-
ing ratios can be found in the comparison of the 69Br proton emission spectrum to
those for nuclei with bound states. In Figure 3.46 the p+685e events are compared
to p+X events where X are other selected heavy reaction products detected in the
S800 focal plane. At higher relative energies proton emission can compete with
7-decay due to the reduced barrier width through which the proton must tunnel.
As the relative emission energy is reduced, the barrier width rapidly increases un-
til 7—decay becomes the dominant process for nuclei with bound states. All other
nuclei other than 693r will continue to 'y-decay into bound states and, eventually,
undergo [VF-decay. However, 69Br is unbound and decay by proton emission is the
exclusive decay mode since [3+-decay occurs on a 106 longer timescale and there
are no low-lying bound states to 'y-decay into. Consequently, we observe a low-
lying decay peak in Figure 3.46 only for decays from 69Br where the ground state

is proton unbound.

121

 

IIII'TII‘IIIII'IIII'IIIIIIIIIIIIIIIIIIIIIIIIIIIII

102

    

 

  
 

Counts

 

 

 

 

  
   

  

 

10

   

23 89

4 5 6 7
Q-Value [MeV]

Figure 3.46 — Relative energy (Q—Value) spectrum for proton emission from 6"'Se, 685e,
68As, and 67As normalized to the p+6BSe spectrum from [6, 10] MeV as compared to
the 59Br decay.

122

Chapter 4
69Br Proton Separation Energy and

Consequences for the rp-Process

While chapter 3 discussed the process for producing the relative energy spectrum,
this chapter details the methods to extract the 693r proton separation energy from
the low relative energy proton emission peak and its consequences. A discussion
concerning the possible formation pathways of 693r and a brief analysis of the mo-
mentum distributions of 68Se is given in Section 4.1. Nuclear structure, including
known information about the mirror nucleus 69Se, that affects the interpretation
of the low relative energy 69 Br decay peak is detailed in Section 4.2. In Section 4.3
particle emission from states that have a finite“ lifetime is considered and the effect
on the peak lineshape is analyzed. Section 4.4 expands upon Section 4.3, outlin-
ing the Wentzel-Kramers-Brillouin (WKB) approximation method used to calcu-
late penetration through the barrier in order to obtain estimates for single parti-
cle lifetimes. In Section 4.5 the lifetimes calculated via methods in Section 4.4 are
used in conjunction with a Monte Carlo simulation to extract the 69Br proton sep-
aration energy. Possible uncertainties related to additional detailed nuclear level
structure, deficiencies of the experimental setup, and a general lack of knowledge
about the N = Z ~ 34 region will be addressed in Section 4.6. Finally, using the
measured separation energy, results from a one-zone X-ray burst model and the

consequences for the rp-process are explored in Section 4.7.

 

‘ In this context finite means long enough that the nucleus travels a significant distance past the
target before decaying.

123

4.1 Formation Process

Disentangling the sequence of steps involved in the production of 69Br is a chal-
lenge. Since reactions of the secondary beam with the target must eventually re-
move two neutrons in the case of 71 Br or remove two neutrons and add one proton
in the case of 703e, the process is more complicated than a single neutron knockout
mechanism. While it is not necessary for this dissertation to understand completely
the formation mechanisms nor is there enough information to uniquely identify
them, it is still interesting to make some comparisons of the data to simple pro-
duction mechanisms. Analyzing the momentum distribution of the outgoing 68Se
reaction products can provide insight into possible formation processes.

In Figure 4.1 the 68Se momentum distributions are shown for p+685e events
which are the result of reactions of the 71 Br and 70Se secondary beams with the
target. Figure 4.2 shows the momentum distributions for the region around the low
relative energy proton emission peak, again for both beams. To give some insight
into the formation process, we compare the observed momentum distributions to

three simple limits.
1. Projectile fragmentation of the secondary beam.
2. Complete fusion of a proton with the secondary beam.
3. Transfer reactions of the secondary beam on carbon nuclei in the target.

The results of these models are also shown in Figure 4.1 and Figure 4.2, and will
be explained below.

Projectile fragmentation is the dominant mode for the production of rare iso-
topes at NSCL. It proceeds by rapid violent excitation of the projectile followed,
in many cases, by a slower secondary decay characterized by the emission of neu-

trons, protons, and light particles. This violent excitation is sometimes modeled

124

 

 

    
 
 
  
  
   

 

 

 

 

 

 

- — 708a Beam I I I 1
— 7113: Beam

102 g-u-TOSe Mocko Fit —§

2 ----718rMocko Flt 2

.9 - _

C . _

3 1 0 =— —:

o 5 a

1
24.0 24.5 25.5 26.0

25.0
P [GeV/c]
Figure 4.1 - 68Se momentum distributions associated with the “Br and 7OSe secondary
beams. The peaks are fit using the methods in the fragmentation study of Mocko et al.

[4]. High momentum events for reactions involving the 71 Br beam are clearly missing
due to the acceptance of the S800 spectrograph.

 

 

14 :- - 7OSe Peak
2 - 71 Br Peak
12 .— ‘7050 p Fuslon
1 o :_ -71 Br p Fusion
m : - 7080 Transfer
E _ (EX=0-180 MeV)
3 8 .— - 71 Br Transfer
0 : (Ex=0-180 MeV)
O 6 .—
4 Z—
2 I—
24.0 24.5 25.5 26.0

25.0
P [GeV/c]
Figure 4.2 — 68Se momentum distributions corresponding to the proton emission peak

compared to the momentum expected from the simple proton fusion and transfer
models described in the text.

125

by the ”sudden” approximation in which a few nucleons are knocked out of the
projectile leaving the remaining fragments intact with a momentum equal to the
value it had in the beam nucleus in its ground state. Goldhaber modeled the initial
nucleus by a Fermi gas, and derived an expression for the width of the longitudi-
nal momentum (along the beam axis) distribution about its mean value [76]. In his
original paper, he assumed the remaining fragment to have a Gaussian momen-
tum distribution, exp(f9'2/ (202)), where the width of the longitudinal momentum

distribution in the sudden approximation is given by
02 = (73AM — As/(A — 1). (4.1)

where A is the mass of the projectile, A p is the mass of the fragment, and 00 z
90 MeV/c. In practice, this expression only works well for light nuclei. For heavy
beams, it under predicts the widths of the momentum distributions considerably.
To describe these larger widths, Mocko et al. [4] fit a considerable number of frag-

mentation momentum distributions, do / d pz, by the expression,

d0 _ S-eXPl-(pz-<Pz>)2/(20E)l foerS<pz>, (4.2)

”2 yam—(pl — war/(201%)] form > W

where,

N

= «73.11pm — Ala/(A — 1).

[3

(4.3)

N

(TR = agRAl-“(A — Ap)/(A -- 1).

Using this function, curves for the momentum distributions of 68Se from the frag-
mentation of the 71 Br and 70Se secondary beams are shown in Figure 4.1, where

the widths are estimated from the data of Mocko et al. [4]. The peak momentum

126

distributions shown in Figure 4.2 clearly fall within the estimated fragmentation
momentum distributions.

Complete fusion of a proton with the secondary beam is the second model we
consider. The expected 68Se recoil momenta for fusion involving the 71 Br (red ar-
row) and 70Se (black arrow) beams are denoted in Figure 4.2. This model yields a
value that is within the envelope of the observed momentum distribution, both for
arbitrary proton energies and for the low Q—value gate. However, it is significantly
lower than the peak values, i.e., the momentum of a 68Se recoil produced through
fusion is lower than the center of the decay peak momentum distribution.

As a third model, we also consider the transfer of nucleons between the sec-
ondary beam and the carbon nuclei in the target for carbon excitation energies of
0 and 180 MeV. The range of excitation energy for both the 71 Br (blue) and 70Se
(green) secondary beams is shown in Figure 4.2. This simple transfer model gives
a range of 68Se momenta that, as with the fragmentation model, overlaps well with
the observed momentum distribution. However, a somewhat higher excitation en-
ergy would be required to cover the range of the momenta produced in reactions
with the 71 Br secondary beam.

For these comparisons we conclude that fragmentation, proton fusion, and
transfer can contribute to the 693r production in this dissertation. However, frag-
mentation and transfer both predict the contribution from the 71 Br beam to extend
past P = 25.5 GeV/c. This part of the focal plane was blocked by an absorber that
was inserted to block the unreacted secondary beam. So, a significant part of the
71Br—>69Br reaction was probably lost due to the blocker.

Additionally, Figure 4.1 also highlights a number of analysis issues. In addition
to the beam blocker, cuts were required in the dispersive position of the $800 to
remove data from poorly performing regions in the CRDCs. This caused a reduced

efficiency at the high momentum region of the momentum distribution for 68Se

127

reaction products associated with the 71 Br secondary beam. For both reasons the
relative energy spectrum is probably incomplete at high momentum due to a lack
of acceptance for the 71 Br events.

Finally, there are concerns with 71 Br events that compose the decay peak as is
observed by the distributions that are gated around the Q-value of the low relative
energy peak. The distribution for 7OSe events are relatively narrow and well de-
fined: the peak is at relatively low excitation in the transfer model. In comparison,
the 71 Br decay distribution is much broader and mainly composed of contributions
that would correspond to higher excitation in the transfer process. The lower ex-
citation regions are behind the blocker. Thus, we may have excluded the correct
excitation energy for decay from the low-lying levels in 69Br. This, together with
the overall lower yield for the 71 Br reactions, caused us to focus exclusively on

reactions with the 7'OSe beam.

4.2 Local Structure and the 69Se Mirror Nucleus

In nuclear physics, the principles of charge symmetry and charge independence
play a fundamental role in our understanding and formal treatment of the nu-
cleus. Charge symmetry expresses the equality of the n-n and p-p nuclear interac-
tion while charge independence expresses the equality of the n-p interaction and
reveals that the attractive nuclear force is independent of charge. Charge symme-
try is best illustrated in so called mirror pairs, or nuclei where the number of pro-
tons in one nucleus is equal to the number of neutrons in the other for a fixed A.
More formally, for N = Z the mirror partner of a nucleus with (N, Z + X) is given
by (N + X, Z). The level structure of a given nucleus to the right of the N = Z
line, shown in Figure 1.1, is reflected in its mirror partner on the left side of the
N = Z line. A perfect symmetry would, qualitatively, yield a nuclear landscape
where level structure, drip-lines, masses, etc. were perfectly reflected across the

N = Z line. Consequently, single particle states in one member of the mirror pair

128

915.1

 

 

 

 

 

 

 

(912+) 573.9

’ 128.4

(5/2-) V I I 39,4
(1/2-. 3/2-) 0.0

 

:2Se3.
Figure 4.3 — Level diagram for the low—lying states in the 69Se mirror nucleus.

would be identical to the levels in the other member. Surprisingly to a large extent
the level structure in mirror nuclei are remarkably similar. Charge independence
has led to the neutron and proton being treated as projections of a single spin-like
object, the nucleon, and is expressed within the isospin (isotopic spin) formalism.
However, this symmetry is broken by the Coulomb interaction as well as by small
additional charge symmetry breaking residual interactions. Many of these effects
manifest themselves in the richly complex nuclear landscape found in Figure 1.1.
Despite the existence of charge symmetry breaking effects, mirror symmetry can
be a useful tool to understand the properties of a given nucleus in terms of its
better known mirror partner. In this section we use the structure of 69Se, the mir-
ror nucleus to 69Br, theoretical shell model calculations, and experimental data to
guide our understanding the possible level structure of 69Br.

If isospin were an exact symmetry, one could exactly predict the structure of
693r from the structure of the mirror nucleus 69Se. A diagram of the low-lying
known levels in the 69Se mirror nucleus [77] is shown in Figure 4.3. These are

the only levels of any significance to our current analysis which contribute to the

129

low relative energy part of the spectrum in Figure 3.45. While the energies of a
number of levels are known, the spin assignments are uncertain (as indicated by
the parenthesis). As mentioned in Subsection 1.3.1, missing experimental infor-
mation is fairly typical of nuclei near the proton-drip line. Nevertheless, the in-
formation in Figure 4.3 can still constrain our investigation. To begin, the three
closely spaced low-lying states have spin-parities of (1 / 2",3/ 2"), (5 / 2‘), and
(unassigned). Early measurements of 69Se [78] indicated a preferred ground state
spin-parity assignment of 3 / 2", later studies however found a more probable as-
signment of 1 /2_ [79, 80, 81]. At the highest excitation energies shown there is a
state with a tentative spin-parity assignment of 9/2+, 573.9 keV above the ground
state. Given our experimental resolution and the low statistics in Figure 3.45 we
would not be able to resolve the lowest three states in 69Br if this nucleus has the
same level structure as 69Se and if all three states are populated in the experiment.
It is possible that the low-lying proton emission peak in Figure 3.45 is a convolu-
tion of proton emission from these three lowest lying states. If so, decays from all
three states must be considered when extracting values for the proton separation
energy and its uncertainty.

Alternatively, we could neglect isospin symmetry and look to trends in the
neighboring nuclei in order to predict the structure of 69Br. Nuclei in the region
near N = Z ~ 34 are known to exhibit interesting structural characteristics. De-
formation [82, 83, 84, 85], shape coexistence [86, 87], and possible mirror level inver-
sions [85, 88] are a few of the issues that can distort mirror symmetry while making
this an important and challenging region of study. Small violations of mirror sym-
metry may be sufficient to change the order of the nearly degenerate ground state
and lst excited state in 695e shown in Figure 4.3, when such states appear in 69Br.

Consequently, we should consider that the ground state spin may be inverted

in ‘59 Br with respect to the ordering in 69Se. If this is in fact true then the 69 Br ground

130

“'2‘ V '11.“. z—n-w
\

 

g..-

state would be assigned a single particle orbit of l = 3 (f orbital) as opposed to l =
1 (p orbital). This increases the width of the centrifugal barrier, thereby reducing
the tunneling probability for the proton as discussed in detail in Section 4.3. While
the proximity of the 5/ 2' level to the ground state (AB = 39.4 keV) suggests that
only a slight perturbation would be needed to invert the level ordering, it should
be noted there are no known exceptions of T = 1/ 2 mirror nuclei with inverted
ground state spin orderings. Even if one broadens this to other mirror nuclei, there
are very few exceptions to this rule.

For example, the only known exception for pairs of T = 1 mirror nuclei is the
case of 16N and 16F, which is due to the so-called Thomas-Ehrman shift. While
analog states in mirror nuclei, after accounting for Coulomb energy differences,
are often essentially identical there are isospin non-conserving interactions that re-
sult in displacements of the analog levels. One of the main contributions to the
level displacements was first suggested by Thomas [89] and Ehrman [90] who
studied the levels in 13C and 13N. They found that in the more proton-rich mem-
ber of the analog pair the proton radial wavefunction is distorted with respect to
the neutron wavefunction in the more neutron-rich nucleus. The result is that the
proton wavefunction is more extended and excluded from the nuclear interior,
thereby reducing the Coulomb energy [52]. This is now known as the Thomas-
Ehnnan effect. Furthermore, it is found that the energy shifts are more significant
for weakly or unbound levels than for bound states, due to the lowered Coulomb
barrier, and result in systems that are more bound than they would be when just
taking into account Coulomb displacement energies. The effect is also dependent
on spin, with states of lower orbital angular momentum having larger shifts as
a result of the lowered centrifugal barrier. This is also the case for the low-lying
levels of 16N (2",0",3",1“) and 16F (O‘,1‘,2‘,3") where one finds significant
Thomas-Ehrman shifts [91]. Here, the last proton in 16F is unbound, leading to

131

 

 

 

 

(912+) 71g
(312-) 291 .M
....... m.
.15 -) 1;2,§2
28‘.
1/2- .uflflH" ...£ _
- 0 1 - 0 0
QBru EBru fiBru

Figure 4.4 - Comparison of low-lying states in the 71 Br, 73Br, and 753r isotopes.

more extended s-wave components of the O— and 1‘ levels. The reduction in the
Coulomb energy is significant enough that the 0‘ in 16F is shifted below the 2‘
level to become the ground state, thereby altering the correspondance between the
analog levels in this mirror pair.

Putting this aside for the moment, we note that an assignment of 5/2‘ to the
69Br ground state is also supported by shell model calculations using the GXlA
interaction [92]. In addition, a crude systematic analysis of the odd Br isotopes
near 69Br shown in Figure 4.4 also suggests a ground state assignment of 5/2‘.
50 it is reasonable to explore the possibility of an inversion in the ordering of the
ground and first excited state in these nuclei.

To restrict our interpretation of the low relative energy 69Br peak a set of as-

sumptions will be applied in the analysis that follows.

1. Mirror symmetry is sufficiently obeyed and there is an approximate corre-
spondence between the lowest lying analog states in 69Se and those in 69Br,

although the relative spacing between states and their order may be shifted.

132

1221‘

 

2. The ground state Nilson orbit for 69Se will be taken to be 3 / 2‘ with l = 1
as the dominant component. While recent measurements indicate that the
ground state may be 1 / 2‘ this has little impact on the analysis of this section.

It is more significant that we choose I = 1 for the orbit.

3. The three low-lying excited states in 6gBr will be strongly populated relative
to higher lying excited states, particularly the 9 / 2+ level, and will for sim-

plicity be assigned spectroscopic factors of 1.

4.3 Lifetime Effects

So far a key element of nuclear decay has been ignored in this dissertation: the ef-
fects of finite particle lifetimes. Proton-emitting states in 69 Br are contained mostly
by the Coulomb and centrifugal barriers. The lifetime of these states is dictated by
the transmission through the barrier and observed as resonances in the decay spec-
trum. The lineshape corresponding to these narrow resonances can be described by
a Lorentz distribution, characterized by a width, F. It is well known that the decay
width and the lifetime, 1' of a state are related by,
F = :13. (4.4)
For a fixed orbit with specific I, the lifetime is largely determined by the excita-
tion energy. As the excitation energy is increased the barrier width is reduced,
decreasing the lifetime. However, states with larger orbital momentum have large
centrifugal barriers, making their lifetimes significantly longer.

This is an issue for 69Br since our setup relies on the assumption that the decay
is occurring at the target location and that the nucleus is not stable long enough
to decay at a position between the target and HiRA. If the lifetime of 693r is long

enough, a significant fraction of the decays will occur beyond the target position

133

  
 
 

TAR

Secondary
Beam . (9 + A

 

 
  
  

\
‘
‘._

7‘7 ‘\\. i g
@ 6889

Figure 4.5 — Illustration of finite particle lifetimes on the determination of the emitted

proton angle.
and the inferred relative angle between the proton and 6888 will be reduced as
shown in Figure 4.5. The error in the proton angle assignment due to lifetime will
affect the lineshape of resonances in the relative energy spectrum. For a fixed decay
energy the relative momentum, fip — 56859, will decrease since the relative angle
decreases. The deduced relative energy for these events will therefore be reduced
compared to the true value (see Equation 2.2). In general, the longer the lifetime
the larger the number of decays that will be erroneously calculated with a reduced
relative energy due to the lifetime effect, leading to tails on the decay peaks that
extend toward lower relative energies. This effect is shown in Figure 4.6 where the
proton decay from 69Br for a Q—value of 810 keV is simulated for three different
lifetimes. In addition to the low relative energy tails the peak height as well as its
position is shifted as compared to those decays where 'r = O s.

The low-lying states in the mirror nucleus 695e can influence the lineshape of
the peak in Figure 3.45. The 5 / 2" state, assuming it is a pure f orbit, can have a
lifetime two orders of magnitude longer than those from a p orbit. If the lowest
levels in 6S’Br are all populated then lifetime effects will have an impact on the line-

shape and the determination of the true proton separation energy. For reference,

134

 

q
q
1
d

900’ . . . .
800
700
600
500

 
    

 

Counts

 

300
200
1 00

 

 

Illlllllllllllllllllllllllllllllllllllllllll

 

0.4 0.5 0.6 0.7 0.8 0.9 1.0
Q-Value [MeV]

Figure 4.6 — Simulation of proton emission from states with finite lifetimes in 69Br for
Q = 810 keV.
it should be noted that resolution mainly affects the peak width, as demonstrated
in Figure 4.7 where the CsI(Tl) energy resolution is varied for a fixed decay en-
ergy. This is a minimal effect compared to that of the lifetime; we conclude that the

effects of single particle lifetimes are the largest source of systematic error.

4.4 Barrier Penetration in the WKB Approximation

To properly account for single particle lifetimes, and hence the peak lineshape,
as a function of orbital momentum and excitation energy the Wentzel-Kramers-
Brillouin (WKB) approximation is applied to calculate the transmission through
the barrier. WKB is a well-known semiclassical calculation used to solve the
Schrodinger equation for potentials that are slowly varying over the de Broglie
wavelength, and typically for potentials for which the Schrodinger equation does
not have an exact solution. It has been used successfully in many calculations of

a-decay and typically provides half-lives that are within a factor of ~ 2 of the ac-

135

2500

2000

1500

Counts

1000

500

Figure 4.7 — Line shape dependence on CsI energy resolution. Changes in energy res-
olution effect the width of the peak distribution.
tual experimental measurements. Consequently, it has also been used in numerous
studies of proton radioactivity.

Let us outline the main concepts of this approximation and the procedure for its
application. Let’s consider particle emission from the potential shown in Figure 4.8.
The barrier presented to the proton is a superposition of a Coulomb potential, a nu-
clear potential (which also has a spin—orbit term), and a centrifugal potential. For a
given excitation energy E there are two classical turning points with regard to the
barrier denoted as Rm and Rout. Applying the WKB approximation the penetrabil-

ity, or probability of transmission, for a spherical nucleus is given approximately

by,

 

Csl Resolution 5

 

—o=0MeV _
—0'=1MeV

 

 

 

 

 

 

-i.

—_O=2MeV

llllllllllllll

 

 

 

bllllllllllllllllllllllllll

0.6. I 0.8 1.0
Q-Value [MeV]

1.2 1.4

/Rl:"t ./2mP(V(r) — E)dx]

 

 

 

 

 

Figure 4.8 — Typical potential used for the WKB approximation.

where G is the Gamow factor [93]. The lifetime given the possibility of transmission

through the barrier can be calculated as,

 

12;: . . (4.7)

Here, P is the penetrability, v is the collision frequency, and S is the spectroscopic

factor that accounts for additional nuclear structure effects not accounted for by the

WKB. The frequency with which the proton collides with the barrier is, from [94],
x/27r2h2

1/ = . 4.8

 

where RC is the charge radius of the nucleus.
For the lifetime analysis in this dissertation the real part of the optical model

potential from Perey and Perey [95] is used. The full potential including the cen-

137

'\ ..-“. I'm

 

trifugal term is given by,
V(r) = Re[VC + Vn] + V; (4.9)

2
= Vc — VRf(x0) + (in—:2) V5007 ' l)%;;f(xso) + VI (4-10)

with the Coulomb potential VC, a nuclear central term V", a spin-orbit term, and

centrifugal potential V1. More specifically,

2
%, for r 2 RC
VC = 2 (4.11)
%E (3 _ 12)! for r S RC1 RC : rcA1/3:
c R,
V,(r) = 1(1+ 1)h2/(2mpr2), (4.12)

and f (xi) is a Woods-Saxon potential factor governed by the radius r ~ A1/3
f(x,-) =(1 + e"")“1 where x,- = (r — riA1/3)/a,-. (4.13)

The parameters used in Equation 4.10 are are also taken from those listed for pro-

tons from Percy and Perey but originate from Becchetti and Greenlees [96].

VR =54.0 — 0.325 + 24(N — Z)/A + 0.4(z/A1/3) (4.14)
To =1.17, a0 = 0.75 (4.15)
V50 26.2, 7’50 : 1.01, “so = 0.75 (4.16)

The individual potentials and their superposition for l = 3 are shown in Figure 4.9.

138

 

V [MeV] V [MeV]
40

N '- [fm]

10 20 30

 

 

VNuclear
- 40 _ 10_

 

 

- 20.
(a) (b)

Figure 4.9 — (a) The various components of the optical model + centrifugal potential
used to estimate lifetimes in the WKB approximation and (b) the summation of all
potential components.

4.5 Fitting Methods and the 69Br Proton Separation

Energy

The goal of this section is to obtain a value for the proton separation energy by
fitting the low energy region of the relative energy spectrum with simulated data
that accounts for the peak lineshape in terms of the possible contributions from
the low energy states in 69Br and their lifetimes. First, the procedure used to gen-
erate the simulation data is discussed. This is followed by an analysis of the decay
peak using the latest mass measurement studies, an analysis just using the mir-
ror states, and finally an analysis that leaves the 5/2‘ state from the mirror levels
unconstrained in energy.

The simulation discussed in Section 3.1 is used to generate spectra for a given
decay Q—value and lifetime. To get a sense of the significance of these effects the
simulation was run for a set of Q-values for decay from both I = 1 and l = 3 orbits

within the energy range of the low energy decay peak shown in Figure 3.45. The

139

 

 

 

      
    

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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E . p1 1.0509+00i 3.122903 :
“400.- WWW $10 .="'/-
"' E E E 3
E300: 1’ j" j :09 -.
o a I M. [NH 3 2 3
200: E 0.8_ 7.
s 411.11% Will 5 2
1oo_— 0.7 '2
; l il1”11”1\0 E _
' A I/Iill,\,_.\\\ 0."
3.2 0.41.0 1.2 “075 080 0.95 0.90 11.951.001.05
Q-Value [MeV] Q-Value [MeV]
(c) (11)

Figure 4.10 — Gaussian fits of simulated decay peaks produced over a range of relevant

Q-values for (a) l : 1 and (c) l = 3 orbits. A comparison of the observed to actual

decay Q-value is shown in figures (b) for l = 1 and (d) for I : 3.
peak positions of the simulated decay spectra are fit with Gaussian functions, as
shown in Figure 4.10a and Figure 4.10c, for l = 1 and l = 3 orbits respectively.
Figure 4.10b and Figure 4.10d show the mean peak position from the fit as a func-
tion of the actual simulated Q-Value. The centrifugal barrier for l = 1 does not in-
crease the lifetime such that there is an appreciable effect on the lineshape and the
consequent determination of the separation energy. However, the l = 3 lineshapes

have peak positions that begin to diverge from the actual Q—value. Therefore if an

140

 

 

 

dd

°°'-"‘"..
§§§§§§§§

 

 

I
Counts

 

 

 

 

 

 

 

 

 

 

 

 

0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
O-Vllm (HOV) G-Vduo [HOV]

(a) Simulated decay spectra using SP ob- (b) Normalized simulation spectrum from
tained from mass measurements+Coulomb (a) compared to the experimental data.
displacement and the mirror states in 69Se

populated based on 2] + 1.

0.00.2“

Figure 4.11

l = 3 emission is a large component of the low energy proton decay peak, it will
tend to shift the fit peak position to a value that is lower than the actual Q—value.
In addition, the observed peak position and lineshape will depend on the relative
populations of the lowest states in the mirror nucleus which adds to the uncer-
tainty. In the following we assume that all m—substates of the lowest three levels
are equally populated. This means the levels are in proportion to the total angular
momentum degeneracy, proportional to 2] + 1.

Initially, we will start the analysis by comparing the recent separation energy
obtained from mass measurement together with information on the level scheme
from the mirror nucleus. From Section 1.4 the precise measurements from Schury
[2] and Savory [3] together with Coulomb displacement yield a value of Sp 2
636 keV. This value is taken as the energy of the 693r ground state. The energies
of the first two excited states are set equal to those in the mirror nucleus 695a The
results of the simulated spectra without accounting for background are shown in
Figure 4.11a. The relative background from Figure 3.45 is folded into the simulated

data, normalized to the experimental results, and compared in Figure 4.11b. It is

141

 

clear that the simulated peak position is in poor agreement with the data. More-
over, if the ground state is the only contribution to the peak then the peak position
will be at ~ 636 keV. This clearly does not reproduce the data.

Finding the best-fit of the peak lineshape based on the states of the mirror nu-
cleus is accomplished by exploring the parameter space allowed by our assump-
tions stated in the previous sections. A Kolmogorov-Smirnov test [97], which tests
whether or not two samples come from the same distribution, is applied to find
the data that maximizes the goodness-of—fit probability. The method is explained
in detail in Appendix A. This test has several advantages over a standard xz-test

which include,
1. Advantageous for low statistics analysis.

2. Nonparametric test that is sensitive to the location and shape of the samples

being compared.
3. Can be run on the unbinned data as opposed to fitting a binned histogram.

The next step in the analysis assumes that the calculated Coulomb displace-
ment energy is incorrect but that mirror symmetry is obeyed. A collection of sim-
ulated data is produced with steps in the ground state Q—value of 5 keV while
keeping the relative level spacing the same as in the mirror nucleus. The simulated
unbinned data are compared to the unbinned experimental results and the best-fit
is shown in Figure 4.12a. Figure 4.12b shows the probability values (p-value), with
larger values indicating more statistical significance, for each set of simulated data
as a function of the Q—value. We obtain a proton separation energy from this pro-
cedure of Sp 2 —785f23 keV and a best-fit p-value of 0.86. The uncertainty is taken
from the 95 % confidence level given by the results shown in Figure 4.12b together
with a 30 keV uncertainty related to the HiRA detector positions.

142

 

 

 

 

  

 

 

 

 

 

 

 

 

 

O EXPOI'IMOM 0.9 - l -
l
1 E] Slmulation g 0.8 - -
1 g 0.7 - i -
5 ‘4 n'. 0.5 -
1 5
5 1 a 0.5 ' ‘
a 8' 0.4 - -
E
3 0.3 ' '
4 0.2 - -
2 0.1 -
I I l l n n l
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0. 70 0. 7 2 0. M 0.76 0.78 0.00 0.02 0.
O-Value [MeV] Q-Valuo [MeV]

(a) Best-fit of the experimental data from (b) Probability value distribution for each Q-
a set of simulations with the same level value step in the simulations as a function of
spacing as in 69Se but with 5keV steps in Q—value. The best—fit corresponds to the set
the ground state Q—value. The best—fit to of data with the largest probability value.
the experimental data is chosen using the

Kolmogorov-Smirnov probability test.

Figure 4.12

Next, since the lowest two states provide the dominant contributions to the
peak and the l : 3 orbit contributes mostly to the low energy tail, we allow the
5/2‘ level to be unconstrained in energy with respect to the other mirror lev-
els. The procedure is the same as was performed for the strict mirror symme-
try test except now the simulation also iterates over various 5 / 2‘ level energies.
Interestingly, a best-fit is obtained when the 5 / 2” level is the ground state with
Sp 2 —735 keV i 72 keV and the 3/2‘ with the 3/2‘ placed at an excitation en-
ergy of E x = 805 keV. The best-fit simulated data has a p-value of 0.91 and is shown
compared to the experimental data in Figure 4.13. This result means that the mir-
ror states could actually be in’verted which would be the first such occurrence in a
T = 1 / 2 nucleus (see discussions in Section 4.2), although the possibility of such
a change in level ordering has been argued before [88, 85]. For this result the 5/2’
state would be shifted down relative to the 3 / 2‘ by 109.4 keV.

We must now question the reasonability of such a level inversion, given that

the inversion of T = 1/ 2 mirror levels is unprecedented. There is not much in-

143

 

Counts

 

 

 

 

 

 

 

—L
O
b IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

P.
M

0.4 0.6 0.8 1.0 1.2 1.4
Q-Value [MeV]

Figure 4.13 — Best-fit of the experimental data from a set of simulations with the level
in 69Se but with the 5/2‘ level unconstrained in energy. The best-fit suggests that the
5/2- and the 3/2" are inverted compared to the mirror nucleus.
formation to constrain our thinking but one may get some ideas by looking at the
systematic trends in the region. The systematics of the ordering of Nilson orbits
was already shown in Figure 4.4. A systematic lowering of the 5/ 2 Nilson orbit is
observed as a function of neutron number, which might suggest an inversion of the
mirror levels in 6QBr with the 5/ 2" as the ground state. Figure 4.14 shows another
representation of the systematic trend for the excitation energy of the 5/2— for the
nearby odd A Br isotopes. Extrapolating it to 69Br suggests a 5/2‘ ground state.
Finally, there exists the much simpler possibility that the low relative energy
decay peak is only composed of proton emission from a single state. Therefore, the
same analysis and statistics methods are used to determine the proton separation
energy assuming emission from a pure P1/2, p3/2, and f5/2 orbit. The values found
are —784, —784, and —841 keV respectively.
In summary, it is found that there are five overlapping predictions for the sep-
aration energy dependent upon our initial assumptions. It should be noted that

the peak location is mainly determined by the 3 / 2‘ state since the relative con-

144

x2! ndf 596 I 2
90 -2191i285.6

P1 30.631'3358

 
  

5/2- Energy Relative to 9.9. [keV]
B 8 8 8

71 72 73 74 75 76 77
A

Figure 4.14 - Systematic trends and the predicted level spacing in 69Br based on the
known structure of the nearest Br isotopes.

 

 

I” Ordering Mass Excess [keV] Sp [keV]

 

1 /2—, - , - 4611631 -784_*_‘fi
3/2‘, - , - -46116f§§ 4841:?
5 /2—, - , - «16059ng 541%;
3 /2-,5/2-,1 /2- -46115f%g '785i38

 

Table 4.1 — Summary of the predictions for the 69Br proton separation energy from this
dissertation and their corresponding assumptions.

tribution from the 5/ 2“ state mainly determines the tail at low relative energies.
These results are summarized in Table 4.1. The mass excess is calculated using
Equation 1.5. The uncertainties for the separation energy is assigned based on the
p-values calculated during the fitting procedure (see Figure 4.12b) and added in
quadrature with an uncertainty of 30 keV which accounts for uncertainties associ-
ated with the detector positions. Given that there are no known T = 1/ 2 mirror
nuclei where the ground state and first excited state are inverted we adopt the

value found for the 69Se mirror levels of Sp z —785f23.

145

 

1W (1'. e.

 

1 . . . . . . . . . 1 I Theory
% Q Experiment
' . A Systematics

O This Work

 

 

 

""L:

SPEC:

 

I d—L
a see
@0600

 

 

'!
5
>
Brown
-I-
13; A1150:
0hr-
.- LEBIT

 

 

-1000 _ -

 

 

LEBIT
'0'.

 

 

_ . . . . . . l . . . . l . . 1 l l L
1 500 1 995 2000 2005 201 0

Year

“Br Proton Separation Energy [keV]

Figure 4.15 — Comparison of the 69Br proton separation energies obtained in this dis-
sertation to previous works.

Our suggested value is compared in Figure 4.15 to some of the previous stud-
ies discussed in Section 1.4. Predictions based on pure theoretical calculations are
shown as red squares. Predictions based on experimental measurements of 68Se
and / or 69Se are shown as filled black circles. Both of the Atomic Mass Evaluation
(AME) from 1995 and 2003 are shown as green triangles. Finally, our suggested
value is shown as an open black circle. The proton separation energies found in
this dissertation are in agreement with the lower limit set by Pfaff [43]. Further-
more, the values are in good agreement with those obtained using the latest LEBIT
high precision mass measurements combined with Coulomb displacement energy
calculations, although this dissertation finds 69Br to be slightly more unbound. It
is interesting to note that the timespan over which measurements have occurred
is roughly 20 years. Clearly there is also a wide spread, especially early on, in the
predicted values owing to the fact that this is a difficult region to access. It is also
difficult to properly understand in terms of theory due to the large uncertainties in

the nuclear structure.

146

4.6 Possible Influential Factors on the
Proton Separation Energy

There is a question regarding the physical reason why the proton separation en-
ergy found in this dissertation is higher than what is found when utilizing Coulomb
displacement calculations. The uncertainty associated with the highly precise pen-
ning trap measurements is less than a few keV and the predictions based on Coulomb
displacement calculations are typically good within ~ 100 keV [12, 1]. The proton
separation energy found in Section 4.5 are at least 100 keV higher than those pre-
dicted from the LEBIT mass measurement and Coulomb displacement prediction
of Savory et al. [3]. Additionally, the Thomas-Ehrman effect, which reduces the
Coulomb energy for unbound states, implies that 69Br should be more bound than
what is predicted with Coulomb displacement. Consequently, it is useful to ad-
dress some of the possible factors that may influence predictions of the 69 Br proton
separation energy as well as our measurement. There are a number of possibilities

to consider,
1. The LEBIT mass measurements may have a larger systematic error.

2. There may be an unknown systematic error in our 69Br experiment that has

not been taken into account.

3. The low energy peak observed in Figure 3.45 may not correspond to emission

from the ground state.
4. Deformation and other structure effects can affect the energy levels.

5. The electromagnetic spin-orbit effect may contribute to the Coulomb dis-

placement energy (CDE).

147

Item 1, while possible, seems very unlikely especially on the level of 100 keV that
we are discussing. Item 2 is also difficult to address as it is a complete unknown.
This section will attempt to address the last three of these possible differences.

Thomas-Ehrman shifts, especially in light nuclei, can be quite large (as much as
a few 100 keV) [98]. Since 69Br is unbound it then may be a surprise to some that
this dissertation predicts a less bound ground state as compared to recent predic-
tions involving Coulomb displacement energies, which are the opposite of what
one would expect from Thomas-Ehrman. However, recent Coulomb displacement
energy calculations are constructed to account, although perhaps rather poorly,
for these effects. Results of calculations done by Ormand [52] suggest that near
the proton-drip line Thomas-Ehrman shifts should be contained within the un-
certainty of the theoretical calculation which were estimated to be 100-250 keV by
reference [52]. Similar calculations by Brown [1] are used to determine the sepa-
ration energy given the mass measurements from Schury et al. [2] and Savory et
al. [3]. From these arguments one may conclude that some of the possible Thomas-
Ehrman shifts may be taken into account by the theoretical calculation. Neverthe-
less, it would be interesting to have more detailed theoretical calculations of the
Thomas-Ehrman shift for 69Br.

While a full discussion of the effects of nuclear shapes and their influence on
shifts in mirror levels is beyond the scope of this dissertation, they are still worth
briefly exploring for the region near 69Br. In general the levels in a deformed nu-
cleus can be described within the Nilsson model as well as by more advanced
theories. In general, the Coulomb energy in such systems is sensitive to the over-
all nuclear shape [99]. For example, recent investigations into the mirror nuclei
71Kr and 71 Br by Urkedal and Hamamoto [85] suggested an inversion of ground
state spins based on possible nuclear deformation. Fisher et al. [88] addressed these

ideas with further investigations of the spectroscopy of 71 Br. While an inversion of

148

 

the ground state was not found, evidence for oblate-prolate shape coexistence was
observed. Perhaps more significant is the case of 69Se since it is the mirror partner
of 69Br. Mosna et al. [100] was the first to discover an oblate structure for the 39,2
band in 69Se which was followed by an extended study by Jenkins et al. [84]. In
addition, an oblate ground state band structure for 68Se was found by Fischer et
al. [101]. There is a clear tendency for the isotopes in the region of N z Z w 35
to exhibit a multitude of deformation effects. The uncertain role of such effects
should not be discounted as a possible contribution to the differences that exist in
the separation energies discussed in this dissertation.

The next question that needs to be addressed is whether the observed decay
peak actually corresponds to the true ground state decay. The first concern is that
the decays to 68Se are not ground state to ground state and instead a large num-
ber of decays go to the first excited state in 68Se. However, the first excited state
in 68Se has an energy of 854.2 keV. This relatively large Q-value difference in the
decay of 69Br will most likely leave 68Se in its ground state and should not con-
tribute to a rnismeasurement of the ground state decay. More precisely, if the ob-
served proton decay at Q = 785 keV is to the excited state at Ex 2 854.2 keV, the
Q-value for ground state decay would be about 1.6 MeV. Barring a large spectro-
scopic factor, the relative branching into this excited state can be calculated using
the WKB approximation to be B, = TEX/T83, ~ 10‘4/103 = 10‘7. Thus, compa-
rable spectroscopic factors would dictate the observation of an excited state peak
of 5 x 108 counts in the spectra in Figure 3.45 at 1.6 MeV, given the observed yield
of 50 counts in the low relative energy peak. To be consistent with it being a de-
cay to the 68Se excited state and the observed yield the spectroscopic factor to the
ground state for this level would have to be < 10‘7. This would seem to be rather
small considering that both ground and first excited states of 638e are believed to

be members of the same rotational band [102].

149

The second concern relates to the possibility that the process by which we pro-
duce 69Br results in the population of an isomeric state and that we never actually
populate the ground state. It is well known that low-lying states in this region
have negative parity. However, there is a gg/z intruder state that also appears with
positive parity. Due to the mismatch in angular momentum and parity, 7 tran-
sitions from this 9/2+ state to the ground and low-lying negative parity states
are restricted. In 69Se the state is relatively long lived given its excitation energy
of 573.9 keV with investigations yielding a half-life of 960 ns [81]. Recently, it has
been suggested by Jenkins [103] that the 9/2‘L isomer is responsible for the non-
observation of 69Br in experiments that utilize fusion-evaporation or fragmenta-
tion reactions such as those by Pfaff et al. [43]. The argument is that in these cases
the 9 / 2+ state lies high enough in energy so that it has a lifetime that is short
enough so as to decay by proton emission before it can be detected. Jenkins pro-
posed, using the mirrors states in 695e, taking Op 2 850 keV for the 9 / 2+ so that
it would have an estimated half-life of 3 ns. Given the relative separation of the
mirror states this places the 3 / 2‘ ground state at Qp = 276 keV with an estimated
half-life of 233 ms. In this situation no 693r events would be detected since the pro-
ton emission from the 9 / 2+ state has a sufficiently short half-life and the longer
lived ground state is not populated due to 9 / 2+ isomer. However, this depends
critically on the isomeric ratio, or the amount by which the isomeric state is popu-
lated. This ratio is currently not known but would have to be unusually high (near
100 0/o) in order for this argument to be valid. Emission from the isomeric state is
also not supported by a lineshape analysis of the data in this dissertation as shown
in Figure 4.16. Although the statistics are low, the low relative energy peak is not
as wide as what would be expected for proton decay from a 9/2+ nor does the
data indicate a significant tail towards low relative energies as expected from the

simulation. Lastly, if this peak is the isomeric state, given the spacing between the

150

 

22
20
18
16
14
12
10

8

6

 

l 1 I I l I I I I I I I I I I I I

-Q- Experiment

|:] Simulation

 

 

 

Counts

 

 

llllllllIIIIIllIlllllllllllllllllllllllllll

 

+11

0.4
Q-Value6 [MeV]8

 

 

4
2
0 0.2

b.

Figure 4.16 — Comparison of simulated decay from a 9 / 2+ (1 = 4) to the experimental
data where the lifetime has been estimated using the WKB approximation. The tail at
lower Q—values does not match the data indicating that the decay peak is not due to
decays from a long-lived 9/2+ state.
9/ 2+ and the ground state in 69Se of 573.9 keV and assuming mirror symmetry, one
would predict that the energy of the ground state in 69Br would be ~ 238 keV. This
is a 398 keV disagreement with the value predicted by Savory et al. [3] using the
measured 69Se mass and the calculated Coulomb displacement energy. This would
imply an error in the Coulomb displacement calculation of 398 keV, well outside
of the estimated 100 keV uncertainty for such predictions in this mass region.
Finally, there is an additional shift in the Coulomb energy known as the rela-
tivistic electromagnetic spin-orbit interaction [12]. In the atom the magnetic field
seen by the electron in its orbit through the Coulomb field couples to the electron’s
magnetic moment. The electron undergoes what is known as Larmor precession
in addition to a relativistic interaction that results in Thomas precession. These
effects result in the well known spin-orbit interaction in atoms. Analogously, an
uncoupled proton or neutron experiences the same effect in the Coulomb field of

the nucleus with the main difference being a change in sign of both the Larmor

151

 

 

J" Approximate A50 [keV] E [keV] E x [keV]

 

1 /2— +74 -710 0
5 /2‘ +185 -934.4 224.4
3/2' -37 -801.4 91.4

 

Table 4.2 - Estimated electromagnetic spin-orbit shift, level energy, and excitation en-
ergy assuming a (1 /2‘, 5 / 2‘,3 / 2') ordering for the various I” values being consid-
ered. The assumed proton separation energy (636 keV) is predicted using the Schury
[2] and Savory [3] mass measurements + Coulomb displacement energies of refer-
ence [1].

and Thomas interaction terms. While the electromagnetic spin-orbit interaction is
typically a very small correction to the Coulomb displacement energy, in certain

cases its effect can be significant [104]. From Nolen and Schiffer [12] the shift, A50,

in the Coulomb displacement energy (in MeV) can be approximated by,

1 r12 z<e2
A0212 ——— —— —— l- 4.17
. (11p 2 yn>2M%,2( RC.) 17) < >
._._. _ 0.15.3311. (r) (4.18)
RC
where,

l ifj>l
14: (4.19)

—-1—1 ifj<l

In Table 4.2 the value of the electromagnetic spin-orbit interaction for the spin-
parities of the states being considered as possible ground states in 69Br are given.
It is interesting to note that both the 1 /2— and 5 / 2“ shifts are quite large and in a
direction that would shift the results of the LEBIT+Coulomb displacement energy
(CDE) predictions in better agreement with our measured proton separation en-

ergy. Moreover, while the 3/ 2“ state was taken as the ground state spin-parity in

152

 

the mirror state analysis of this dissertation the 1 / 2‘ has recently been proposed as
the actual assignment [81]. Also included in Table 4.2 are level and excitation ener-
gies for an assumed (1 /2_, 5 / 2’, 3/2‘) level ordering given a 1 /2" ground state,
the 69Se mass, plus a proton separation energy of 636 keV. This shows that the elec-
tromagnetic spin-orbit interaction may have an influence on the proton separation

energy and should not be discounted.

4.7 X-Ray Burst Calculations

Investigations into the role that the rp-process plays during a type I X-ray burst
have been conducted using computer models. These models vary in their level
of sophistication but in general allow one to reproduce the light curve, energy
generation, isotopic abundances, as well as other quantities and track them over
the duration of the burst. For this dissertation full network calculations are used to
explore the possible effects of our recently measured 68Se(p, ry)6gBr Q-value. Note,
that in this section our discussion will involve proton capture Q—values as opposed
to the proton separation energy, Sp, where Qpfl 2 SP.

In this section we consider models designed to simulate the conditions of an X-
ray burst occurring on the surface of a neutron star. This scenario (as was discussed
in Section 1.3) occurs when hydrogen and helium rich material is transferred to the
neutron star from its binary companion. As this material accretes onto the neutron
star surface it is compressed and heated until a critical amount of mass builds and
ignites due to a thermal instability. The resulting energy release during the ensuing
thermonuclear burning is observed in the form of a large release of X—rays on top
of the persistent flux originating from the steady accretion. The light curves of the
burst tail are found to be governed by the physics of the rp-process.

In order to describe the full dynamics and microphysics of this complex system
sophisticated simulations have been developed. For example, the one-dimensional

KEPLER code [105] has been used to investigate the explosive burning occurring

153

during X-ray bursts [33], X-ray burst oscillations [106], and other complex neu-
tron star processes. In principle, the overall characteristics of the X-ray burst can
be influenced by the properties of the neutron star at various depths below the
surface. In addition, the accretion rate [26] and composition of the accreted mat-
ter [32] also play a key role. To handle these effects, codes such as KEPLER break
up the surface layers of the neutron star into zones, where the one-dimensional
coordinate is the Lagrangian mass (as opposed to length). Each zone is filled with
a fixed amount of mass with all zones being tracked during the calculation. These
are typically referred to as multi-zone models. However, these models are computa-
tionally intensive and unnecessary for most studies that only desire to understand
relative sensitivities or qualitative effects of the nucleosynthesis. Less complex one-
zone models have been developed that include most of the key physics needed to
test the dependencies and sensitivities of the nuclear physics inputs. These codes
do not require large scale computer hardware and typically require less computing
power compared to codes such as KEPLER.

The one-zone model by Schatz et al. [31] was chosen to investigate, using prop-
erly calibrated initial conditions, a long duration X-ray burst. This burst is capable
of reaching and processing material up to and beyond the 68Se waiting point. The
initial conditions of the burst assume a metallicity of Z 2: 10‘3, an accretion rate
onto the surface of 0.1 of the Eddington limit, and a flux from the crustal interior of
0.15 MeV accreted nucleon. The total amount of accreted material onto the neutron
star surface is 4.7 x 1021 g. In all simulations processing occurs on burst timescales
of the order ~ 100 3. Finally, all reaction rates are taken from the recent JIN A Rea-

clib Database‘ V1.0 [107].

 

‘ http://groups.nsc1.msu.edu/jina/reaclib/db/

154

 

4.7.1 No 2p-Capture (Q(p,’r) = —2000 keV)

First, the 68Se(p, 'y) Q-value is set to —2000 keV and the reverse reaction rate ad-
justed accordingly thereby effectively removing the 68Se(2p, 'y)70Kr reaction from
the rp-process network. Figure 4.17 shows the luminosity, nuclear energy genera—
tion, and selected abundance curves for the duration of the burst. At ignition, the
density is ~ 106 g/cm3, and the ignition of helium drives a rapid increase in the
luminosity with a risetime of ~ 1 s. The burst reaches a peak temperature of 1.9 GK
before it begins to cool. Over the last ~ 200 s the single zone surface layer that was
ignited continues to drive the burst at longer times. This is observed as a tail in
the luminosity curve, reflecting the burning of the heaviest masses as is observed
in the abundance curves. In addition, it is clear that a significant fraction of the
processed material ends up in the waiting point nuclei. The relative abundances of
both 64'Ge and 68Se are large in comparison to the other isotopes that are produced.

Furthermore, as 69Br is highly unbound in this instance (Sp = —2000 keV), there
are virtually no 69 Br nuclei around to undergo proton capture. As a result the abun-
dance of 7°Kr is near zero. In addition, the percentage integrated reaction flow to

70Kr relative to the flow into 683e is found to be only 2 x 10“6 %.

4.7.2 Non-observation Limit (Q(p,’y) = —500 keV)

For the purposes of comparison the simulation was also run for Op” 2 —500 keV
with the results shown in Figure 4.18. This corresponds to the non-observation
limit set by Pfaff et al. [43]. The results are very similar to the previous results dis-
cussed in Subsection 4.7.1. However, now a larger abundance of 69Br is produced
which is observed to increase the amount of 7OKr, reflecting the larger amount
of the reaction flow that bypasses the waiting point via the sequential 2p-capture
through 69Br. In this case, it is found that the reaction flow through 693r to 7OKr
is 23 %, relative to the flow into 68Se. The amount of flow through the 68Se in the

155

 

 

 

 

 

 

 

 

 

 

 

   

 

    

 

 

 

r 1— —1
2 _
x ..
5 4—
a —
.2. -
E- _
3 21—
.E -
E _
a
.1 _
2 E
x -
1n -
as: 10?
... E
> _
9 _
2 -
m 1E—
5 E
2 _
o _
:1
z 1011
1
'3
E 102
.E.
01 .
g 104 _: --- 646e
a ' —65As
'u 10'6 -_ —sase
g _ —69$e
n _8 ' —-698r
< 10 ‘— ——7OBr
-: _70Kl'
10.10 —-71Kr
3001

Time [s]

Figure 4.17 — X-ray luminosity, nuclear energy generation, and abundance versus pro-
cessing time where the 2p-capture on 6’8Se has been effectively removed from the
network calculation. This was accomplished by setting the (p, '7) to a large (Qpln, =
—-2000 keV) value.

156

present calculation is similar to the results found by Schatz et al. [31]. They as-
sumed a 68Se(p, 'y) Q—value of —450 keV and found that the flow to 70Kr due to

2p-capture reactions was > 10 %.

4.7.3 Slightly Unbound (Q(p.'r) = —200 keV)

To exaggerate the influence of 69Br a significantly lower value of Q?” = —200 keV
was also chosen. Even though this value is only lowered by 300 keV relative to
the previous calculation, the effective half-life of 68Se can be drastically altered by
only small changes in Q-value as was demonstrated in Subsection 1.3.1. Indeed,
the changes in the abundances and light curves shown in Figure 4.19 illustrate
this point. The abundance of 69Br as well as 7OKr has increased by an order of
magnitude. This reduces the 68Se abundance through 2p-capture reactions on 69Br,
with 30 "/0 of the reaction flow bypassing the waiting-point to 7°Kr. In addition the

tail in the luminosity curve is shortened by ~ 15 5.

4.7.4 Comparison of Results and Conclusion

In order to investigate the effects of the 69Br proton separation energy found in
this dissertation, the simulation is run for Qpfl =2 —785 keV. The luminosity, nu-
clear energy generation, and abundances are shown in Figure 4.20. The results are
almost identical to that of Subsection 4.7 .1 with the main exception being an in-
crease in the 70Kr abundance indicating the processing through 2p-captures. How-
ever, at QM. = —785 keV, 69Br is still very unbound as reflected by the lack in its
abundance. Furthermore, only 0.16 % of the flow passes through 69 Br to 7°Kr.

For this choice of X-ray burst initial conditions, lower proton capture Q—values
for 68Se tend to reduce the ”cooling time” in the tail of the burst. In Figure 4.21
qualitative changes in the luminosity, nuclear energy generation, and temperature
due to 68Se(p, 7) Q-value are now more apparent. There is a difference of ~ 15 s

between the length of the tail of the light curve for Qpfl = —200 keV and Qpfl =

157

 

 

 

 

 

 

 

I; - _
x "' -
a 4- —
E Z I
Q _ ..
8 2— ._
.E - _
c”0'‘'5'0””100‘UT11'50‘“2150 250 300
102 ~r~~1v~~1~”Irrr-fir'n-H'
*2"
i‘.
g. 10
5
2
III 1
h
a
.0
o
a
z 101
0 50 100 150 200 250 300
1 5.1:.::.'..‘..‘.T.T.f.f_ff . W H ' ' ' H ' ' ' ' "1 —.—-
3, 2L” .......... 5,. ............... a 1 .......... 4H0
— """"" g ................................ t .. _ ----- 12C
2 10' :- . ‘. _: —-60Zn
g 10.4: \p—— I ‘
' "‘ ‘ —65M
3 - «- -=:::
< 10.8? ['7 ': -—7OBr
=- 0% .-....
10-10 ' """ l 1‘ h- A -. —'71Kl'

Figure 4.18 — X-ray luminosity, nuclear energy generation, and abundance versus pro-

 

 

 

 

 

  

 

 

 

 

 

0 50 100 150 200 250 300
Time [s]

cessing time for QM. = —500 keV.

158

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6 rirfi' I 'r I l ' er rr
r _ _
2
1’5
3
.33
E
o
o
.5
E
:1
.1
is?
x
o
g. 10
2'.
E’
2
m 1
3.
o
:1
z 101LAI -. -.. .... 1 -L._.l;...
0 50 100 150 200 250 300
1.1.2.1: .......... ' fi- ..... .
a E" ........... 1:, ......... '1. '2' ---------- 4".
= 2_ """""""" 2 ........ ... _. """ 12c
E 10' ...- . . H.- . _. ___m
"" 04b ..... i "' —g:131
o 1 :- - ------ ‘ ——
g _ —‘~\ /H— _--'“G.
1111 ' .2‘. '-05h
1! 10": / _—6889
5 :- J 1—35?
—I r
2 10"? y, N 1—703r
_. 5“ ——70Kr
- a
10' ------ 011V ______ —-71Kr
1“ 1 50 200 250 300—

Time [s]

Figure 4.19 - X-ray luminosity, nuclear energy generation, and abundance versus pro-
cessing time for Qp/r = —200 keV.

159

 

.1
1

 

 

 

 

.1; _

3 -

a 4‘

m I—

2. _

g _

3 21—

.5 -

E _

3

_l ..

= 1

1o2 = .
10

lrrrmr lllllllll

Nuclear Energy [egsls x 10”]

 

 

 

 

  

 

 

10‘ - 0
1

E .
E 102
E.
g 10“
5
'g 10*3
3 0.. .

10-10 11‘/ _ ‘J\.‘

100 150 200 250 300

 

Time [s]

Figure 4.20 - X-ray luminosity, nuclear energy generation, and abundance versus pro-
cessing time for QM = —-785 keV.

160

—785 keV. Furthermore, the luminosity during the middle of the cooling phase is
boosted compared to that for Q1,” 2 —785 keV. However, the influence of the 2p-
capture branch through 698r on the luminosity rapidly becomes insignificant as
Qpfl becomes more negative since Azp depends exponentially on Qpfl.

Figure 4.23 shows the integrated final abundances for a given mass number at
the end of the burst. The effect of the Q-value on the abundance of nuclei beyond
685e is clearer in Figure 4.23 where the difference between the final abundance
for Qpfl = —785 keV and the final abundance for Op” 2 —500 keV is shown.
Here, the increase in the final abundances for A = 68 and A = 72 masses due
to the 68Se and 72Kr waiting-points is evident. Also, a reduction in the synthesis
of elements beyond mass 90 is observed although the longer processing time for
(2p;y = —785 keV allows the flow to build at A = 106. These differences amount to
corrections to the final abundances at the percent level.

For the initial conditions in this X-ray burst simulation and the proton sepa-
ration energies determined in this dissertation, the sensitivity of the light curves
and the abundance distribution to the uncertainties in proton separation energy in
our measurement are negligible. We therefore conclude, that for all practical pur-
poses, one can neglect the 2p-capture through 69Br in calculating the abundances

and light curves for this type of X-ray burst.

4.8 Extended Duration X-Ray Burst

To further explore the sensitivities of our measurement a more extreme burst, com-
pared to the simulated burst in the last section, is simulated. A key difference in
this X-ray burst is that it occurs over an extended timescale, giving the material
more time to undergo processing. The results are organized in the same manner
as the results of the burst discussed in the previous section. The X-ray burst lumi-
nosity, nuclear energy generation, and abundances are shown for Qpfl = —2000,

—500, —200, and —785 keV in Figure 4.24, Figure 4.26, Figure 4.18, and Figure 4.27

161

 

 

   
  

 

 

 

  

 

 

 

 

 

e_"lfr"I""l""""'l""r""
5: '5 —— 68$e(p,y)=-0.200 MeV i
3; E -— 68$e(p,y)=-0.500 MeV E
a 4L.— 1
3 E — 68$e(p,y)=-0.785 MeV E
E E E
a — -
.3 2g 3
5 5 3
6“0 ”'50“"100"'150'4200 250 300
1m"I"""‘fi1Trf"I""I""I'r'
*3
1-
X
0
E 10
8.
>1
2’
O
C
I." 1 f
3
s
0
3
z

 

1
1" 0 50 100 150 200 250 300

 

I U I r.

Temperature [GK]

 

l I I l l A l A l l

I A I I I

300

'50 100 150”200”2
Time[s]

Figure 4.21 — Comparison of the luminosity, nuclear energy generation, and tempera-
ture for 68Se(p, ’7)693r Q-values of —200, —500, and -785 keV.

162

 

 

 

 

 

 

    
    

 

 

 

 

 

 

 

 

IU IV
'3 E '5':
a >
010° t:>10‘3 a
s - a
0
§1cr4 210‘ ~
«I a
2 : 2
.5 .
3105: 310 I ~
< Z < l
' . I l l ' . . . . .
1°60 20 40 so so 100 1:0 10‘0 20 4o 60 so 100 1:0
Mass Number Mass Number
(a) No 2p-capture, Qpfl = —2000 keV (b) Qpfl = —785 keV
16' 16’

 

 

d
(a
run I II

Abimdanfe [mollg]
a” a

Abundaer [mot/g]
‘1

—L
01
”nu I Illllll v

 

 

 

 

 

 

 

 

 

 

 

 

 

: . I l I l .s' . . LI . . . . .
”on 20 40 so so 100 1:0 10¢ 20 40 so so 100 1:0
Mass Number Mass Number

Figure 4.22 — Final abundances versus mass number for the Q—values used in the one-
zone X—ray burst model. The recommended “Ge(p, 7) Q-value was used in this calcu-
lation.
respectively. Figure 4.28 shows a comparison of the lightcurves for Qpfl =—200,
—500, and —785 keV. Finally, the difference between final abundances for Qpfl =
—500 keV and Qpfl : —785 keV is shown in Figure 4.29.

The burst has many similarities to the first burst we considered. While the burst
continues twice as long (~ 400 s) as the shorter burst of the last section the evolu-
tion of the abundance curves is roughly the same, just carried out for a longer time.
However, the lightcurves are observed to be even less sensitive to changes in the
Q-value compared to the shorter burst. The reaction flows through 69Br to 70Kr for
Qp” =—2000, —500, —200, and —785keV are 8.4 x 10‘5 %, 10%, 33%, and 0.8%

163

 

 

 

 

 

Abundance Difference
O

 

 

 

 

 

60 7O 80 90 1 00 1 10 120
Mass Number
Figure 4.23 — Difference between the final abundances for Qpfl 2: —785 keV and
pr, = —500 keV.
respectively, again mirroring the order of magnitude of the reaction flow values
from the burst in the previous section. Given the similarities, we conclude that the
X-ray burst is again insensitive the 2p-capture branch through 698r for this second

set of conditions.

164

 

     

 

 

 

 

 

 

l- q
if; _ -
x _ -
S 4‘ ‘
D "' -
.2. - .
E - _
3 2— —
.5 - _
E .
3
_l .-

G‘o””166‘“266”soo'5”hoo soo 600

is?
x 102
O
3
9 1o
3 I
a 1’_
C
III
3 mil
3 .
2 1c" -

 

 

 

 

Abundance [mollg]
3:.

 

 

 

 

 

10 ‘
10’ 0

‘iéd’i‘zéd'eéc‘doo 500 600
Time[s]

Figure 4.24 — X-ray luminosity, nuclear energy generation, and abundance versus pro-
cessing time for prr = -2000 keV for the extended duration burst.

165

 

 

l
I14

h
"""'d
Ill

     

N
' I

l

Luminosity [egale x 10"]

l l J I l

 

l I

 

 

 

 

 

Nuclear Energy [age/e x 10"]

 

 

 

 

 

—cos.
—-698r
-—7OBr
—70Kr

—'71Kf

10 ‘ -
1“ o 100 200 300 400 500 600
Time [s]

Abundance [mollg]

 

 

Figure 4.25 - X-ray luminosity, nuclear energy generation, and abundance versus pro-
cessing time for QP/Y = -500 keV for the extended duration burst.

166

 

Luminosity [age/s x 10”]

 

 

 

 

 

 

Nuclear Energy [age/s x 10"]

 

 

 

 

 

 

 

 

 

 

 

 

é”
o
.E.
o
o
I:
G
1:
c
:I
n
< . -_
10'10‘I---I.--.l...-L\ —'71Kl‘
0 100 200 300 400 500
Time[s]

Figure 4.26 - X-ray luminosity, nuclear energy generation, and abundance versus pro-
cessing time for QM, = -200 keV for the extended duration burst.

167

 

Luminosity [egels x 10”]

 

 

 

 

10'1

 

Nuclear Energy [egsls x 10”]

 

-2 _
1° 0 100 200 300 400 500 600

102
10“
1o45
10"

10-10

Abundance [moi/g]

 

Time [s]

Figure 4.27 — X-ray luminosity, nuclear energy generation, and abundance versus pro-
cessing time for Qpa = —785 keV for the extended duration burst.

168

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g: g — 68$e(p,y)=-0.200 MeV i

x 5 —— case(p,y)=-0.5oo MeV E

'33. “-— 1

a a 5

3 2:— ‘3

.E : :

E : :

a _ _

..I : I
0‘0 ”100””200‘ ' ' '300‘ ' ' '400 560 600

a" T T'

2

X

C)

E

.2.

E

0

C

I.“

1'5

0

3

z . I a .

 

 

”200.3604‘400 T500”'600

 

Temperature [GK]

 

 

0'6”"160'"'260”2166“21604”56d”soo
Time[s]

Figure 4.28 -— Comparison of the luminosity, nuclear energy generation, and tempera-
ture for 68Se(p, '7)69Br Q—values of —200, —500, and —785 keV for the extended dura-
tion burst.

169

 

 

 

 

'- "V. '31? -. '5 3%:
C l '
. I‘-

 

 

 

 

 

 

 

x10"6 _
8 4 . . . . r- f T . . r . ”F I
c -
§ .
5F. 2 ‘
a c -

A

8 0 v '1
C
s -2
g . .
.0 - .
< 4- ...L.a...i.

60 70 80 90 100 110 120

Mass Number
Figure 4.29 — Difference between the final abundances for QM = —785 keV and

Qm = —500 keV for the extended duration burst.

 

170

 

Chapter 5

Summary

The need for precise experimental data on nuclei at the proton drip-line is paramount

if one is to understand and model the rp-process and the sites, such as Type I X-ray
bursts, where it is thought to occur. Sparse data exists for many of the nuclei along
the proton drip-line. These nuclei are challenging to measure due to their low pro-
duction cross-sections and short lifetimes. This is especially the case for the proton
unbound nucleus 69 Br as is evident from the numerous previous studies that have
been done over the past 20 years. However, despite the challenges, these studies
have been motivated by the importance of contraining the uncertainties in the rp-
process 68Se waiting-point.

As was shown in chapter 1, it is possible to bypass this waiting-point through
sequential 2p-capture through 69Br to 70Kr. The reaction rate, however, depends
exponentially on the proton separation energy of 69 Br. Prior to this disertation, the
uncertainty is determined almost completely by the theoretical uncertainties in the
Coulomb displacement energy (CDE) of 100 keV.

We performed an experiment to measure directly, via a full kinematic recon-
struction method, the proton separation energy of 69Br in order to reduce the un-
certainty in the rp-process “Se waiting-point. This experiment, described in this
dissertation, is the first to utilize the High Resolution Array (HiRA) as well as our
MCP tracking system. The observed relative energy spectrum shown in Figure 3.45
for 69Br proton decay events shows evidence of a clear decay peak at low relative

energies which come from low-lying states in 69 Br.

171

 

 

 

5.1 Results

A number of 69Br proton separation energies are possible depending on assump-
tions about the level structure. Assuming the structure of 69Br has the same or-
dering of levels in 69Se, we deduce a value of Sp 2 7853: keV for the proton
separation energy. If one allows for other possible orderings of levels, the sepa-
ration energy could differ mainly because of the possible distortion coming from
long lived states. In the other likely scenerio, we obtain Sp z 735:3: keV if one
allows the 5/ 2+ level to be the ground state.

The effects of the new results reported in this dissertation on the rp-process
were investigated using a one-zone X-ray burst code using initial conditions pro-
vided by Schatz et al. The differences between the two assumptions about level
ordering has little effect on the light curves and final abundances produced during
the X-ray burst. Moreover, the differences observed for proton separation energies
less than the non-observation limit, Sp < —500 keV, were not very significant. Ad-
ditionally, the reaction flow through 69Br to 7OKr, which is 23 % at Sp z —500 keV,
decreases exponentially to 0.16 % at Sp 2 —785 keV. In conclusion, bypassing 68Se
with 2p-captures through 693r does not appear to be favorable for the type of X-
ray burst explored in this dissertation, therefore 683e should remain a substantial

waiting point in the rp-process.

5.2 Outlook

We have explored different initial conditions in the one-zone X-ray burst model
to see whether other scenerios may exist where 2p-capture through 69Br might
become important. One possible direction to explore would be to have a succession
of short X-ray bursts where the seed nuclei from the pervious burst plays a more

important role in the energy generation. This may be worth exploring in the future.

172

 

 

 

This dissertation was successful at measuring the proton separation energy for
69Br. If an improved value for the 69Br proton separation energy is needed or if
the present techniques could be useful for other proton unbound nuclei, the statis-
tics and setup could be improved. First of all, the reduced data collection time
contributed to low statistics in the relative energy spectra. In addition, there were
gaps in the angular coverage of HiRA that could be removed by better optimizing
the positions of the detectors. The angular coverage was chosen conservatively to
minimize the possibility of direct beam hitting the HiRA detectors. Later, it became
clear that one could place detectors safely at smaller angles relative to the beam.
If the telescopes could be placed closer to the beam, one would have a higher ef-
ficiency for the lowest energy decay protons that are detected. With both a longer
data collection time and a reconfiguration of the detector positions, one could prob-

ably increase the statistics by a factor of 5-10.

5.2.1 The Influence of the 64Ge Waiting-Point

While this dissertation focused exclusively on the 68Se waiting-point there are
other influential nuclei along the rp-process path. In particular, the 64Ge waiting-
point is also poorly constrained and determines the reaction flow into the 68Se
region. To explore the effects of this waiting-point the (p, 'y) Q-value for the 64Ge
waiting point was varied within its current uncertainty using the first set of initial
conditions from Section 4.7 in order to test its influence on the rp-process within
the model. As before, we only use the Q—value of QP” = -—785 keV found in Sec-
tion 4.5 as the experimental value in this evaluation.

The effects on the X-ray burst are illustrated in Figure 5.1 where the luminos-
ity, nuclear energy generation, and temperature curves are shown for the various
68Se(p, 7) Q-values at two extremes of the 64Ge waiting point proton capture Q-

values. For this choice of X-ray burst initial conditions, lower Q-values for the 64Ge

173

 

I“ "3].—-

“but! .
1
. __.h'_ _ __ ____ __...

 

 

 

 

 

 
 
   
 

 

 

 

   

 

 

  

 

 

     

 

     

      

 

 

5 _- . . . - ' ' —— seem—{H.200 mv I «comma-0.151 MeV
5; E ------- 69de,7)=-0.200 um I MGe(p,y)=-0.526 uev
'- : scammeosoo uov I 6480(p,7)=-0.151 Mov
E, 4 F_ ------- 69de,7)=-0.500 MeV / 64de,7)=-0.526 MeV
2’ E — 698r(p,7)=-0.785 MeV I MGe(p,7)=-0.151 MeV
f; E - - - - - - - 698r(p,7)=-0.785 MeV I 640e(p,7)=-0.526 MeV
'3 2:".— -:-'.'
.5 P; :
E : :
3 E ...-llll"'.. --Iu.!. E
'4-- ...1.L..l....j.. . .
G o 50 100 150 200 250 300
1021'! 'l"‘*l*f'rlfi'
is:
x
a
E 10
.2.
>
E’
O
c 1
It] ....ll=3="'.'
3
0
3
210.1..1. ..1.-..1..
0 50 100 150 200 250 300
2.5 - -

 

2.0

1.5

Temperature [GK]

 

lllll filllllllllllllllll

 

0 50 100 150 200 250 300
Time [s]

Figure 5.1 - Comparison of the luminosity, nuclear energy generation, and tem-

perature for 68Se(p. ’YlégBr Q-values of —200, —500, and —785 keV at high and low
64'Ge(p, 3065 As Q-values corresponding to the current uncertainty in the waiting point.

174

 

 

 

 

 

 

6 - . - fi - . — 698r(p,1)=-0.200 uov I «map-0.151 nov

 

 

 

 

 

 

 

 

 

 

 

d; E ------- 69de,1)=-0.200 mv I «cum-Imam uov
'- : GOBr(pfi)=-0.500 MeV I 5460(9,7)=-0.151 MeV
ff, 4 '-'_ ------- eoe:m,1)=-o.5oo MeV I 646e(p,y)=-0.526 MeV
E E 69de,1)=—0.785 MeV I «camp-0.151 MeV
g: E - - - - - - - 69de,7):0.785 IleV I MGeip,7)=-0.526 Nov
8 2E -?.
.5 : 2
E : :
:I _ _
. e a ”l
G 600 . L "I
102 I ‘1

Nuclear Energy [erg/s x 10“]

 

 

 

 

 

25 I' ' l fiTI‘ff ['fi1v1w r'vwr

E‘ 2.0

9.

a i

5 1.5 .n .3.

E ‘3.

g 1.0 ~:

5

I- 0.5
”'0”100‘T200"500“hod“§064'600

Time [s]

Figure 5.2 — Comparison of the luminosity, nuclear energy generation, and tempera-
ture for 685e(p. ’rl69Br Q-values of —200, —500, and —785 keV for the extended burst.

175

waiting-point tend to reduce the ”cooling time” in the tail of the burst. Indeed, it
is clear from the X-ray burst calculations that one of the major uncertainties in the
rp-process lies with the 64*Ge waiting point. Small variations in the 65As proton
separation energy have pronounced effects of the light curve of the X-ray burst.
The uncertainties in the 65As proton separation energy could be reduced, for in-
stance, by measuring the Q-value for the 66As(p, d) reaction using the known mass
of 66As.

In addition, for the production of masses with A > 73, it may still be insight-
ful to explore the 72Kr waiting point by measuring the proton separation energy
of 73Rb. This could be done using the same techniques as used in this disserta-
tion. Therefore, future experiments devoted to these waiting points should be per—
formed to reduce the overall uncertainty in the rp—process in this region and be-

yond.

176

 

 

 

Appendices

 

177

Chapter A

Kolmogorov-Smirnov Test

The Kolmogorov-Smirnov test (K-S test) is a statistical test that attempts to de-
termine whether a sample comes from a given reference distribution [97]. It is a
nonparametric test, meaning it makes no assumption about the underlying proba-
bility distribution (i.e. whether the data come from a normal distribution, binomial,
log-normal, or etc.). The sample can be compared to either another reference sam-
ple (two-sample test) or to a defined probability distribution (one-sample test). In
this dissertation the data from the Monte Carlo simulations (see Section 3.1 and
Section 4.5) are taken as reference samples. The low relative energy data from Fig-
ure 3.45 is compared to these references. The simulated reference data which yields
the maximum probability value (p-value) for the statistic test is the best-fit to the
data.

The Kolmogorov-Smirnov test is based on the comparison of either the empir-
ical distribution function (EDF) of two datasets or the comparison of the EDF of
data to be tested to the cumulative distribution function (CDF) of the reference

probability distribution. Given a set of data points, X,- the EDF is given by,
1 n
Pn(x) = — E Ixigx (A.1)
n i=1
where I x15 x is the so-called indicator function,

1 If Xi S. x,
1),in = (A2)
0 Otherwise.

178

 

 

The EDF is a function that increases by a step of 1/ n at each data point in the set
since for a given value of x the summation counts the number of data points that

are 3 x. For example, suppose we have a set of 10 unordered numbers,

X,- = {4, —5, 8, 3, —2, 9, —10, 5, 6, 1} (A3)

then the EDF for this set, as shown in Figure Al, is given by,

r
0/1020 forx< —10

1/10=0.1 for —10$x< —5
2/10=O.2 for —5§x< —2

P10(x) = < (A.4)
3/10=O.3 for—2gx<1

 

L10/1021 forx29.

The Kolmogorov-Smirnov goodness-of-fit statistic for a two-sample test is,
Dmm = sup [Pm(x) — Fn (x)| (A.5)
x

where sup denotes the supremum, or maximum value", of the distance between

the two EDF. And similarly, for tests that utilize a CDF, the statistic is,
0m = sup IFm(x) —P<x>| (A6)
x

where F (x) is the CDF.

Figure A.2 demonstrates how the Kolmogorov-Smirnov method works. For

 

‘ This is true for the sets of real number that we consider although for other sets the supremum is
a more general mathematical concept.

179

 

 

 

 

 

P
O)
lllllllllllllllllllll

 

 

1411

llll'lIIllfi’rI—F

 

lllllllllllllllllll

 

 

O

'-5 -1O -5

0 5 10

X

15

Figure A.1 — Empirical distribution function (EDF) for the example dataset in Equa—
tion A3. The EDF increases by 1 /n at each data point in the set.

 

Landau PDF 2

llrvli

20

   

15

Counts

IIII’IIIIIIII

...Jlrrrrlu

 

 

 

-5' 0"”5 "10L '15

(a) Probability density function for a 100 ran-
dom samples of a Landau distribution with
ameanoannda = 1.

1

.°

Landau EDF
Normal Dlstrlbutlon

IE
«I
.a
2
a.
o
.2
E
:5
E
a
O

    

-4-20246 81012
X

(b) Comparison of the random sample EDF

to the CDF for a normal distribution with

mean 0 and 0' = 1. The distance, Dm, is the

test statistic used to quantify if the functions

come from the same distribution.

Figure A.2

180

 

 

this example, 100 random points were sampled from a Landau distribution with
the resulting probability density function shown in Figure A.2a. Let’s suppose we
want to test if this set of points has come from a standard normal distribution. In
this case, the EDF for the randomly sampled points is compared to the CDF of the
normal distribution. The maximum difference, Dm, as shown in Figure A.2b, quan-
tifies their compatibility. Clearly, the two distribution functions deviate from each
other for values greater than zero as the Landau function, qualitatively, is less like
the standard normal distribution for positive values.

For a given set of data compared in a two-sample test (as is done in this dis-
sertation) one can computer the confidence level for the test. Assuming the null
hypothesis, the probability that the Kolmogorov-Smirnov test exceeds the value 2,
defined by,

mn
m+n

 

D m,n (A7)
is,

P(z) = 2 f(—1)i-1e-2i212. (A.8)
(i=1)

181

 

 

Bibliography

182

 

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