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. LIBRARY
Mnchigan State
niversity

This is to certify that the
dissertation entitled

Beta-decay Studies of 78Ni and Other Neutron-rich Nuclei in
the Astrophysical r-Process

presented by

Paul Thomas Hosmer

has been accepted towards fulfillment
of the requirements for the

Doctoral degree in Phjsics

 

 

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3/12105‘

Date

MSU is an Affirmative Action/Equal Opportunity Institution

 

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2/05 p:/C|RC/DateDue.indd-p.1

. BETA-DECAY STUDIES OF 78Ni AND OTHER NEUTRON-RICH
N UCLEI IN THE ASTROPHYSICAL R—PROCESS

By

Paul Thomas Hosmer

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

2005

ABSTRACT

BETA-DECAY STUDIES OF 78Ni AND OTHER NUCLEI IN THE
ASTROPHYSICAL R—PROCESS

By

Paul Thomas Hosmer

The B-decay properties of several neutron-rich nuclei including the doubly-magic
78Ni were studied. A low-energy neutron detector NERO was designed and calibrated
for use in these measurements. fi-decay measurements, especially those that combine
both half-life and neutron-emission probability measurements, can offer first tests
of nuclear theories of neutron-rich nuclei. In addtion, 78Ni is an important waiting-
point in the astrophysical r-process. The results of the measurements are compared

to several nuclear models, and the astrophysical implications are explored.

for my family

iii

ACKNOWLEDGMENTS

First I would like to thank my collaborators at Notre Dame, University of Mainz,
and University of Maryland. Karl-Ludwig Kratz, Bernd Pfeiffer, Bill Walters, Paul
Reeder, and Andreas Woehr have been very helpful and always willing to sit down
and discuss many things.

In particular, I have considered it a privilege to work with Dr. Kratz and his group
at the University of Mainz. I hold the honest sincerety and intenstity with which Dr.
Kratz pursues an understanding of the Universe as a model to be imitated in any
pursuit. Dr. Pfeiffer is a true friend to the student, not just the students of his own
group, but to any with whom he has come in contact. I have enjoyed also his interest
in the historical and philosophical under-pinnings of his profession.

The entire Notre Dame Nuclear Structure Laboratory have been liberal with their
time and assistance. They are both professional and fun. It has truly been an honor
for me to be associated with the NSL and I always look forward to another visit. I
will proudly risk wearing my Notre Dame shirts on MSU campus despite the threats
of bodily injury.

I would like to thank the staff at the N SCL for all of the help and advice. Some of
these people include Len Morris, Jeanine Honke, Dave Sanderson, John Yurkon, Barb
Pollack, Ron Fox, Reg Ronningen. There are many more people I could list here.

The A1900 peOple have always been extremely helpful, both during experiments
and with any other questions and problems. Andreas Stolz, Mathias Steiner, Tom
Ginter do above and beyond their required job to help experiments and experimenters.
I would specifically like to thank Andreas for introducing me to the world of live opera.

I would like to thank the NSCL professors for their advice and help. They have
always had an open door in every instance. I would particulary like to mention Bill
Lynch and Betty Tsang for treating me and the other group members like family. I

would like to thank Paul Mantica in particular. He and his entire group have always

iv

been extremely helpful and a pleasure to work with during experiments. I would
like to thank my committee members for their time and willingness to put up with
meetings and shifting schedules.

Hendrik Schatz, my advisor, is too young for me to consider a father figure, but I
would like to thank him for his advise and help on all matters. Though I could say
many things in regard to Hendrik, one fact in particular sums things up: the fact that
he and his wife purchase soft drinks just for me for our group parties. I understand
how much emotional distress this costs him.

I would like to thank all my group members. About Thom Elliot I will only say
that he knows more about more things than any human being has a right to know.
To Thom Elliot, that tool of the British oligarchy, I leave my second-best snuff box.
Alfredo Estrade: I remember fondly our mate club and I honor the memory of your
ancestors. Fernando Montes: most of things I would like to say cannot be recorded
here. Thanks to you and Monica and your families for taking me in to your home and
country. Colombia for me is a place of beauty and rest (and lots of dancing and good
food. And more dancing.)

I would like to thank my fellow graduate students, including, but not limited to,
Mark Wallace, Michael Crosser, Bill Peters and Michal Mocko. Mark, thanks cooking
through all the hard times. We helped each other make it here. I’m not going to say
who helped who more.

Finally I would like to thank my family. Dad, Mom, Andy, Rona, Anna, Katie,
Tommy, Maria, Austin, Audrey, Grandma, Uncle Tom and Aunt Doreen for their love

and support.

Contents

1 Introduction 1
1.1 Neutron-rich Nuclei and the Doubly-magic 78N i ............ 1
1.2 Astrophysical Significance ........................ 2
1.3 Previous Work .............................. 5

1.3.1 N=82 shell region ......................... 5
1.3.2 N250 shell region ......................... 5
1.4 This Work ................................. 7

2 Neutron Detector NERO 8
2.1 Introduction ................................ 8
2.2 Neutron Detection ............................ 8

2.2.1 Fast and Slow Neutrons ..................... 9
2.2.2 Neutron Moderation ....................... 10
2.2.3 Proportional Counters ...................... 11
2.3 NERO Development ........................... 12
2.3.1 General Design Considerations .................. 12
2.3.2 MCNP Modeling ......................... 14
2.3.3 NERO Design ........................... 18
2.3.4 NERO Electronics ........................ 21
2.3.5 NERO Support Table ....................... 24
2.3.6 NERO Background ........................ 25
2.3.7 Tests with 252Cf .......................... 26

3 NERO Efficiency Calibration 33
3.1 Introduction ................................ 33
3.2 Resonant Reactions ............................ 38

3.2.1 Resonance Analysis ........................ 43
3.2.2 Narrow Resonances ........................ 48
3.2.3 Neutron Energy .......................... 52
3.3 Summary of Resonance Analysis ..................... 52
3.4 Non-resonant cross section: 51V(p,n) reaction .............. 53
3.4.1 Offline Counting Ge Detector Efficiency ............ 57
3.5 Summary of NERO Efficiency Calibration ............... 66

vi

4 Experiment 70

4.1 Introduction ................................ 70
4.2 Experimental Setup ............................ 70
4.2.1 Fragment Production ....................... 70
4.2.2 Fragment Separation and Identification ............. 71
4.2.3 Isomer Identification with SeGA ................. 72
4.2.4 Scaling Bp to the 78Ni setting ................... 75
4.2.5 Implantation ........................... 75
4.2.6 Beta Counting System ...................... 79
4.2.7 NERO ............................... 83
4.2.8 Electronics ............................. 83

5 Analysis 85
5.1 Particle Identificaton ........................... 85
5.1.1 Energy Loss ............................ 85
5.1.2 Time of Flight ........................... 88
5.1.3 Momentum Correction to Time of Flight ............ 89
5.1.4 Possible Contaminants ...................... 90

5.2 Production Cross-section ......................... 93
5.3 Gain-matching .............................. 95
5.4 Thresholds ................................. 95
5.5 Absolute Calibration of DSSD ...................... 96
5.6 Correlations ................................ 96
5.7 Curve Fitting ............................... 100
5.7.1 fl-detection Efficiency from Curve Fits ............. 102

5.8 A Method of Maxiumum Likelihood ................... 102
5.8.1 Probability Density Functions .................. 104
5.8.2 Probability Function for Observation of No Decays ...... 106
5.8.3 Probability Functions for the Observation of at Least One Decay108
5.8.4 The Likelihood Function ..................... 108
5.8.5 Probability Functions Including Possible Pn .......... 108
5.8.6 Inputs into the MLH Calculation ................ 109
5.8.7 Examples of Likelihood Functions ................ 110
5.8.8 Error Contributions in the MLH ................. 115

5.9 Isomerism in the decay chain ....................... 118
5.10 Half-life Results .............................. 119
5.11 Neutron Analysis ............................. 120
5.11.1 Neutron Spectra ......................... 120
5.11.2 Calculating Pn values ....................... 120

5.12 B, Value Results ............................. 128
6 Discussion 134
6.1 QRPA Calculations ............................ 134
6.2 The Case of 78Ni ............................. 137
6.3 Nuclear Shell Model ........................... 139
6.4 The r-Process ............................... 144

vii

6.4.1 Measurements Relevent to the r-Process ............ 144

6.4.2 r-process code ........................... 145
6.5 Effect of 78Ni Half-life .......................... 145
6.6 Summary ................................. 147
Bibliography ................................... 149

viii

List of Figures

1.1

1.2

2.1

2.2

2.3
2.4
2.5

2.6

2.7

2.8

2.9
2.10

The r—process in the waiting-point approximation. The masses (Sn) de-
termine the waiting points and define the r-process path. The half-lives
of the waiting points affect the time-scales and the final abundances.
The Pn values modify the abundances after freeze-out by shifting on
mass unit per neutron emission. (Images in this dissertation are pre-
sented in color.) ..............................
The current situation for fl-decay measurements in the r-process.The
white boxes represent the r—process path. The blue boxes represent
nuclei for which half-lives have been measured. The dark blue boxes
represent the nuclei in the r-process path for which the half—lives have
been measured. .................. . ...........

Finding the correct moderator size and configuration is a balance be-
tween moderation, detection, capture, and loss (Figure based on Figure
15.1 of Reference [34]. ..........................
An optimization of NERO parameters. Rb is the beamline hole radius.
R, the amount of polyethylene moderator along the inside radius of the
ring. R = (R, — r) — Rb where r is the radius of an individual counter,
and R, is the radius to the detector ring, defined as the distance to the
center of any counter in the ring. ....................
A study of the Optimal detector separation ................
A study of the optimal detector number. ................
NERO efficiency vs. neutron energy as calculated in the code MCNP.
The plot includes the total NERO efficiency, as well as the efficiencies
of each of the three rings of proportional tubes. Ring 1 is the inner
ring and is composed of 16 3He detectors. Ring 2 is the middle ring
and is composed of 20 BF3 detectors. Ring 3 is the outer ring and is
composed of 24 BF3 detectors .......................
NERO polyethelene moderating matrix (view looking along beamline
direction. .................................
Close view of NERO with tubes inserted. The hole is the beamline hole
for insertion of beamline and Beta Counting System. .........
Diagram of NERO quadrant and detector labeling. The beam is coming
out of the page. ..............................
Diagram of NERO electronics for one quadrant. ............
High voltage cables coming out of the proportional tubes to the preamp
boxes. ...................................

ix

10

15
16
16

17

20

20

21
22

2.11 Preamp box for one NERO quadrant. ................. 23
2.12 Pico Systems Shaper/Discriminator (Photograph from http://pico—systems.com). 24
2.13 NERO background spectrum in a typical 3He counter. The character-

istic shape for neutron detection is clearly identifiable .......... 25
2.14 Neutron energy spectrum from the spontaneous fission of 252Cf (Figure

2 of Reference [43]) ............................ 26
2.15 Typical NERO 3He neutron spectrum from 252Cf source. ....... 28
2.16 Typical NERO BF3 neutron spectrum from 252Cf source. ....... 29

2.17 Variation of NERO efficiency in the beamline hole as a function of
position along the beamline axis. Zero is the NERO target position.

Larger negative numbers are up the beamline direction ......... 30
2.18 Schematic for NERO neutron moderation time measurement ...... 31
2.19 BaF2 Moderation timing measurement with 252Cf source. The start

and stop for the TAC were inverted .................... 32

3.1 Layout of the Notre Dame Nuclear Structure Laboratory. The protons
or a-particles were accelerated in the KN Van de Graaff accelerator
(13), then were directed into the experimental vault to the location
of the Gamma Table (17) which was replaced by a special stand for

NERO (Image from http://www.nd.edu/~nsl/) ............. 34
3.2 The KN Van de Graaff accelerator at the Notre Dame Nuclear Struc-
ture Laboratory. (Image from http://www.nd.edu/~nsl/) ....... 34

3.3 View of the experimental vault beamline. NERO was located in the
place of the Gamma Table (tOp right), which was removed for the

experiment (Image from http://www.nd.edu/~nsl/). ......... 35
3.4 NERO set up at Notre Dame. View is up the beamline ......... 36
3.5 A close-up of NERO set up at Notre Dame. The 252Cf source stand is

inside the beamline hole, in front of the target holder .......... 37
3.6 Target holder for Notre Dame calibration. ............... 38

3.7 Figure 3 from p. 1358 Blair and Haas, 1973 (Reference [44]) showing
total neutron cross section for 13C. The axis labels have been modified
for clarity. ................................. 39
3.8 Figure 2 from p. 886 of Wang, Vogelaar and Kavanagh, 1991 (Reference
[45]) showing S—factor for 11B(a,n). The axis labels have been modified

for clarity. ................................. 40
3.9 Energy diagram of the 13C(oz,n)160 reaction ............... 41
3.10 Energy diagram of the llB((Ji,n)1“N reaction. .............. 42
3.11 Scanning over the 1.053 MeV resonance in 13C ............. 43
3.12 Scanning over the 1.5857 MeV resonance in 13C ............ 44
3.13 Scanning over the 0.606 MeV resonance in 11B ............. 45

3.14 Linear Background subtraction for the 1.053 MeV resonance in 13C . 46
3.15 Linear Background subtraction for the 1.5857 MeV resonance in 13C . 47
3.16 SRlM-calculated target thicknesses and energy-losses of the 13C and

11B targets in terms of the energy of the a projectile. ......... 50
3.17 Stopping power of a target of thickness Ax in LAB and CM frames. . 51
3.18 Schematic drawing of the offline counting station. ........... 54

3.19 The 51Cr gamma spectra and 320 keV peaks from targets irradiated
by 1.8, 2.14, and 2.27 MeV protons ....................
3.20 Decay diagram for 133Ba. Diagram and numbering convention as found
in Figure 4.25 of Reference [51]. .....................
3.21 Germanium X—ray mass-attenuation coefficient a from Ref. [52]. . . .
3.22 Germanium X-ray mass attenuation coefficient a from Ref. [52], zoomed-
in on region relevent to the calculation .................
3.23 Total Efficiency curve for the Ge with the specific geometry of the
offline counting station ...........................
3.24 Gamma spectrum from the calibration source 133Ba ...........
3.25 Interpolating the 320 keV peak efficiency of 51Cr ............
3.26 Diagram of the reaction 51V(p,n)5lCr ...................
3.27 Experimental data from NERO efficiency calibration plotted with sim-
ulations from MCNP and GEANT. ...................
3.28 Experimental data from NERO efficiency calibration and MCNP cal-
culations plotted by ring ..........................

3.29 Experimental data from NERO efficiency calibration plotted with shifted

MCNP calculated curve. .........................

4.1 The coupled cyclotrons and the A1900 fragment separator. ......
4.2 The A1900 fragment separator. .....................
4.3 Floorplan of the NSCL ...........................
4.4 SeGA arranged in the “betaSeGA” configuration around the variable
degrader, upstream from the BCS-NERO station. ...........
4.5 Online particle identification by AE—TOF using the experimental vault
energy—loss detector. ...........................
4.6 Gamma spectrum from ”M PID gate showing the 183, 448, 970, and
1259 keV gammas associated with 70mNi. ................
4.7 Gamma spectrum from 72Cu PID gate showing the 138 keV gamma
associated with 72!“Cu. ..........................
4.8 Schematic of beta endstation inside NERO. ..............
4.9 Beamline detector setup in the experimental vault. ..........
4.10 The DSSD. ................................
4.11 The DSSD case inside the bottom half of NERO. SEGA detectors in
the background. View is looking up the beam axis. ..........
4.12 View of the experimental vault, looking up the beamline. SeGA is in
the background. In the foreground is the BCS leading into the bottom
half of NERO ................................
4.13 Electronics diagram for NSCL Experiment 02028. ...........

5.1 Uncorrected energy loss vs. time of flight .................
5.2 Bethe corrected energy loss vs. time of flight ...............
5.3 Element identification using energy loss in Pinl vs. Pin2. .......
5.4 Time of flight vs. intermediate image position for Zn, Cu, and Ni iso-
topes. The first column is uncorrected. The second column is momen—
tum corrected ................................

xi

56

58
60

61
62
63
64
65
66

67

74
76
77
78
80
80
81

81

91

5.5
5.6

5.7
5.8
5.9
5.10
5.11
5.12
5.13

5.14

5.15

5.16
5.17
5.18

5.19

5.20

5.21
5.22
5.23
5.24
5.25
5.26

5.27

5.28
6.1

Energy loss vs. Time of flight for a portion of the data. ........ 92
Energy Loss in Pinl vs Pin2 showing the conservative element gates.
The arrows indicate the unidentified particle distributions ....... 92
Energy Loss in Pinl showing the Ni distribution on the left and the
unidentified particle distribution on the right. The line indicates the
position of the Ni element gate. ..................... 93
228Th calibration source spectrum in a typical DSSD high-gain channel. 95
90Sr calibration source spectrum for setting threshold in a typical DSSD

high-gain channel .............................. 96
Threshold settings for DSSD front high-gain strips. .......... 97
Threshold settings for DSSD back high-gain strips. .......... 98
Decay—curve fits for the high-statistics cases of 75’F’BNi, 77'78Cu and
78‘79Zn. The linear background is not shown. .............. 101
Beta detection efficiency based on fitting of decay curves for isotopes
with more than 500 implants. ...................... 103
,B-background as a function of front strip number for a representative
back strip, and fl-background averaged over the DSSD as a function of
run. .................................... 111
6 background by three different methods, shown for cases with high
statistics. ...................... ' ........... 1 12
Likelihood functions for the sum of the 8 78Ni decay chains ....... 113
Likelihood functions for each of the 8 78Ni decay chains ......... 114
MLH analysis output of 100 8-decay-chain sets of Monte Carlo simu-
lated data with input half-life of 0.130 s. ................ 116
A sketch demonstrating how the quoted uncertainties were obtained.
The points and error bars are rough sketches, not actual data. . . . . 117
Monte Carlo distribution of 78Ni half-lives for background varying
within the background uncertainty range ................. 117
half-lives from this experiment and previous work ............ 119
Neutron energy spectra from NERO quadrant A. ........... 121
Neutron energy spectra from NERO quadrant B. ........... 122
Neutron energy spectra from NERO quadrant C. ........... 123
Neutron energy spectra from NERO quadrant D. ........... 124
Neutron time spectra from the three NERO rings. The graphs show
the full 200 as neutron window. ..................... 125
,B-background rate, random fl-n coincidence rate, and number of ran-

dom ,B-n coincidences per fl event as a function of DSSD front strip
number for a representative back strip (strip 20) and for the entire
DSSD as a function of run ......................... 128
P" values from this experiment and previous work. .......... 129

Comparison of half-lives from this experiment to QRPA calculations
with allowed GT transitions and with allowed GT+ first-forbidden (ff)
transitions. ................................ 135

xii

6.2

6.3

6.4

6.5

6.6

6.7
6.8

Comparison of Pa values from this experiment to QRPA calculations
with allowed GT transitions and with allowed GT+ first-forbidden (ff)
transitions. ................................

136

Proton and neutron configuration for 78Ni according to the shell model. 138

Important transitions in the decay of 78Ni according to QRPA calcu-
lations ....................... . .............
Experimental and theoretical halfiives for N =50 isotones. Moeller et
al. 97 [75], shell model of Ref [74], and previous work (NuDat). . . . .
Comparison of half-lives and R, values from this experiment to shell-
model calculations. ............................
R—process waiting points for three different neutron densities [72]. . .
Observed Solar Abundance, abundances using the half-lives according
to Moller, Nix and Kratz 97, and abundances using the same half—lives
except changing only the 78Ni half-life to the new experimental value.

xiii

140
141
143
144

146

List of Tables

2.1
2.2
2.3
2.4
2.5
2.6
2.7

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10

4.1
4.2

5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12

6.1

Renter-Stokes 3He Counter Part Numbers Used in NERO (Part X—#). 18

Mainz 3He Counter Part Numbers Used in NERO ............ 18
Reuter-Stokes BF3 Counter Part Numbers Used in NERO (Part V-#). 19
Proportional Tube Data. ......................... 19
Proportional Counter High-Voltage Requirements ............ 22
252Cf source information ......................... 27
Moderation Time for Neutrons in NERO ................. 31
Stopping Power of Targets ......................... 49
Target thickness compared to resonance widths. ............ 49
Resonance Information Used in Calculations ............... 51
Results of Resonance Analysis ....................... 53
Irradiation of 51V targets. ........................ 55
Offline counting of 51V targets. ..................... 55
Numbering of 133Ba y-rays. ....................... 58
Ge crystal dimensions. .......................... 60
Germanium X-ray mass attenuation coefficients ............. 62
NERO efficiencies for 51V runs ...................... 66
7 lines used to verify particle ID. .................... 75
Bp settings used. ............................. 75
Values Used in Bethe Energy Loss Correction ............. 87
Correction Factors for Linear Energy-loss Correction ......... 88
Implant Criteria .............................. 99
Decay Criteria ............................... 99
Decay Chains for 78Ni .......................... 100
fl-detection Efficiencies for High-Statistics Cases ............ 104
Inputs for MLH Half-life Calculations .................. 130
T1/2 Results from MLH Analysis .................... 131
NERO dedicated Pico Systems CFD Thresholds for this Experiment . 131
NERO Energy Software Cuts ...................... 132
Neutron Energies and Corresponding NERO Efficiencies ....... 132
Pu values ................................. 133
r-process parameters ............................ 146

xiv

Chapter 1

Introduction

1.1 Neutron-rich Nuclei and the Doubly-magic 78Ni

This work studies the fi-decay properties of the neutron-rich nuclei around the doubly-
magic nucleus 78Ni. Doubly-magic nuclei with completely filled proton and neutron
shells are of fundamental interest in nuclear physics. The simplified structure of these
nuclei and their direct neighbors allows one to benchmark key ingredients in nuclear
structure theories such as single—particle energies and effective interactions. Doubly-
magic nuclei also serve as cores for shell model calculations, dramatically truncating
the model space, thus rendering feasible shell model calculations in heavy nuclei. In
this way, neutron-rich doubly-magic nuclei Such as 1”Sn and 78N i serve as “launching
points” to extend shell-model calculations to neutron-rich nuclei [1].

In addition to the magic 78Ni, fl-decay measurements of neutron-rich nuclei in
general can offer first tests of nuclear theories that try to predict the changing nuclear

structure as one moves farther from stability toward the neutron drip-line.

1.2 Astrophysical Significance

Neutron rich nuclei play a central role in the astrOphysical rapid neutron-capture
process (r-process) [2,3]. The r-process is a rapid neutron-capture process that occurs
in an environment of large neutron flux were nuclei can experience neutron captures
faster than the competing fl-decay even for very neutron—rich nuclei. Within an iso-
topic chain, photodisintigration competes against neutron capture and according to
the waiting-point approximation, an (n,7),(*y,n) equillibrium is established. In this
situation, most of the abundance within an isotopic chain is concentrated on one

nucleus. The relative abundances are determined by the Saha Equation:

Y(Z,A+1)_ G(Z,A+l) A+127rh2 3,, 3,.
Y(Z,A) "n" 20(Z,A) ( A mukT) “mid/"l (1'1)

 

 

where Y(Z, A) is the abundance of nucleus with proton number Z and mass number
A, G are the partition functions, T is the temperature, and 8,, is the neutron separa-
tion energy. The process must then wait for this nucleus (called a waiting-point) to
fl-decay to the next isotopic chain, where again the (n,'y),('y,n) equillibrium is estab-
lished, and so the process moves up to heavier elements. This process will continue
until the neutron flux diminishes, at which point the exotic nuclei will decay back to
stability by fl-decay and B—delayed neutron emission. In the waiting-point approxi-
mation, neutron-capture rates and photodisintigration rates are not required. Only
the neutron separatid'fi energies of the isotopic chain, the fi-decay half-lives of the
waiting-point nuclei, and the Pa values of the nuclei between the r—process path and
stability are required to understand the process (see Figure 1.1).

The r-process process produces roughly half the elements heavier than iron, yet
its astrOphysical site is still unknown. A leading candidate for the astrophysical site
is the neutrino-driven wind off a hot, newborn neutron star following core-collapse
supernovae [4]. While this site has the r—process starting around A = 90, with lighter

nuclei being produced as less neutron-rich species in an a-rich freeze-out thereby

 

 

. Delayed Neutron
Masses Half-lives Emission Ratio

[E D : DI mag-TD?
KD:I m
:«U»: 1 D

Waiting Points Abundances Abundances
Timescale

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.1: The r-process in the waiting-point approximation. The masses (Sn) deter-
mine the waiting points and define the r-process path. The half-lives of the waiting
points affect the time-scales and the final abundances. The P" values modify the
abundances after freeze-out by shifting on mass unit per neutron emission. (Images
in this dissertation are presented in color.)

rendering nuclei in the region around 78Ni less significant, the site exhibits several
problems. The a-rich freeze-out fails to accurately reproduce the observed abundances
for nuclei with A = 80—90 [5], and the corresponding r-process itself is unable to
produce sufficient amounts of the heaviest r-process nuclei around A =195 [6].

Several r-process scenarios try to address these problems. Examples of these sce-
narios include models that assume nonstandard neutron star masses [7], or that are
based on a supernova triggered by the collapse of an ONeMg core in an intermediate
mass star [8]. In these scenarios, neutron-capture process begins at lighter nuclei, and
78Ni becomes an important r-process waiting point.

In addition, recent observations of the element abundances produced by single (or
very few) r-process events as preserved in the spectra of old, very metal-poor stars
in the Galactic halo raise several interesting questions concerning the site of the r-
process [9]. The abundances taken from r-process-enhanced, metal-poor stars, such
as CS 22892-052 [10] and CS 31082—001 [11] for example, show agreement with solar

r-process abundances in the range Z =56 and greater, yet for the lighter elements

around Z=40—50, the abundances from these metal-poor stars do not agree as well
with the solar r—process abundance. This result suggests the possibility of two distinct
r-processes producing the light r-process nuclei below Z < 50 [12,13]. Accurate nuclear
data in the light r-process region will be important in disentangling the contribution
of these different neutron—capture processes in different astrophysical sites, and the
properties of nuclei around 78Ni to 80Zn will again play a critical role. These properties
will be useful to interpret the data on neutron-capture elements expected from the
many new metal-poor stars to be identified in ongoing surveys [14].

For the nuclei that participate directly in the r-process, fi-decay half-lives are
of particular importance (see [15]). For example, in the scenarios where the lighter
neutron—rich nuclei participate in the r-process, the half-life of 78Ni becomes a direct
input into r—process calculation and, together with the other already known waiting
points, 79Cu and ”Zn, sets the r—process timescale through the N = 50 bottleneck to-
wards heavier elements, and also determines the formation and shape of the associated
A = 80 abundance peak in the observed r-process element abundances. Figure 1.2

shows the current status of fi—decay measurements in the r-process.

  
 
 

     
   

Known

Bantams“
Half-lives

 

 
    

A~l 30 Bottle Neck
A~80 Bottle Neck

Figure 1.2: The current situation for fi-decay measurements in the r—process.The white
boxes represent the r-process path. The blue boxes represent nuclei for which half-
lives have been measured. The dark blue boxes represent the nuclei in the r-process
path for which the half-lives have been measured.

For the isotopes not directly in the r-process path but that are between the path
and stability, the Pn values are important since they affect the processing after freeze-

out and thereby affect the final abundance pattern.

1.3 Previous Work

The first measurements of nuclear properties in the r-process occured in 1986 at not
one but two bottle-necks: 80Zn and 130Cd [16—18]. These are measurements of the half—
lives of waiting points at closed neutron shells. These nuclei are particularly important
because they are the locations of the bottle necks and so there is strong interest in
these regions. These nuclei are also the most easily accessible to experimenters because
at the closed shells, the r-process comes closest to stability and so are most accessible

to study.

1.3.1 N=82 shell region

The importance of the N=82 magic neutron shell chain to the r-process was already
stated in B2FH [19]. Here, the breakout was predicted at 1311, making the half-life of
130Cd an important bottleneck. The isotope 130Cd was identified at CERN/ISOLDE
in 1986 [16]. Consequently, the properties of other bottleneck nuclei in this chain,

such as 129Ag half-life [15] and 128Pd were measured.

1.3.2 N =50 shell region

Another bottleneck region is the region of 80Zn. The half-life, Q5 and a decay scheme
of 80Zn was first measured in 1986 at TRISTAN [17] and also at OSIRIS [18].
Progress toward the other N=50 bottlenecks, 79Cu and 78N i continued. In 1985-86,
the SOLAR Neutron Counter (SNC) was used to measure the first half-lifes and P"
values of 7"*76Cu at the TRISTAN facililty through delayed-neutron counting tech—

niques [20,21]. 70'74Ni and 74‘77Cu were first produced as extremely light products of

thermal neutron (low energy) fission of 235U at Grenoble, France and separated by
the recoil spectrometer Lohengrin [22]. Though the yield was low, fi-decay half-lives
were later reported for 71“Ni and remeasured for 75Cu and also 74Cu [23], which
had since been produCed and a half-life measured in 1989 by neutron induced fission
of 235U at TRISTAN where the half-life was also measured [24]. The following year
76Cu was produced by the same method at TRISTAN. The half-life was remeasured,
and isomers were found [25]. Meanwhile in 1988 at OSIRIS, 74”76Cu and 78Cu were
observed and half—lives were measured [26].

Finally in 1991, the next N=50 r-process bottleneck, 79Cu, was produced at
CERN-ISOLDE using a proton beam on a 238U-graphite target and a half-life (188 :1:
25ms) and R, (55 :t 17) were measured [27]. The half-life of 80Zn (537 :l: 29ms) was
remeasured. This experiment also remeasured the half-lives of 74’76Cu, 78Cu, 792m,
and provided the first half—lives of 77Cu, 81Zn (290 i 50ms), and first Pn of 798‘ Zn
(1.3 :i: 0.4, 1.0 2’: 0.5 and 7.5 :i: 3.0 respectively).

With 79Cu and 80Zn measured, this left 78Ni as the only nucleus in the N =50
bottleneck region for which no measurements existed.

In 1992, 75'76Ni were produced by projectile fragmentation of a 500 MeV/u 86Kr
beam from the heavy-ion synchrotron SIS on a Be target and separated in the
projectile-fragment separator FRS at GSI [28]. The half-lives of 75Ni and 76Ni were
reported, but with large uncertainties.

In 1995, 12 77Ni and 3 78Ni were produced at GSI by fission of a 238U projectile
on a Be target [29—31]. The isotopes were seperated “in-flight” by the FRS fragment
separator. For these, only the production cross-sections were measured.

Work on fl-decay properties continued in this region. Half-lives were reported in
1998 for 70“Co and 73""‘Ni from measurements of 86Kr fragmentation at GSI [32]. Also
in 1998, proton-induced fission of 238U at LISOL at Leuven produced half-lives and

gamma spectroscopy of 68‘ 74N i [33]. But the question of the half-life of 78Ni remained.

1.4 This Work

This work extends the nuclear physics data to 78Ni and examines the influence of
these new measurements on our understanding of nuclear structure and the r-process
in this mass region.

In order to measure the P" values, a new detector, the low-energy neutron detector
NERO (Neutron Emission Ratio Observer) was developed. The development and
design of NERO are described in Chapter 2. The calibration of NERO is described
in 3. The experiment to measure the tm and B, of nuclei in the vicinity of 78Ni is
described in Chapter 4. The analysis of this experiment is described in Chapter 5.
We will show how this information can help to constrain theories that try to predict
properties of even more exotic nuclei. This is done in Chapter 6. The results are
applied to a model of the astrophysical r-process, and the effects of the new results

on the process are shown. (also in Chapter 6.)

Chapter 2

Neutron Detector NERO

2.1 Introduction

For the purpose of measuring neutron emission probabilities, the neutron detector
NERO (Neutron Emission Ratio Observer) was designed and built at the NSCL at
Michigan State University and calibrated at the Nuclear Structure Laboratory at

Notre Dame University.

2.2 Neutron Detection

Because they are electrically neutral, the detection of neutrons presents special prob-
lems that are not encountered in charged-particle detection. Unlike charged particles,
neutrons are generally not detected by “direct” methods involving coulomb interac-
tions. Rather, most neutron detection methods depend on a two-step process. In the
first step, the neutron interacts with the detector via a nuclear interaction. This in-
teraction initiates a secondary process that involves charged particles, which are then

detected by the standard detection methods utilizing the coulomb force.

2.2.1 Fast and Slow Neutrons

In the context of detection, neutrons are generally classified into two groups based
on their energy: fast and slow. Neutrons with energies above about 0.5 eV (which is
known as the “cadmium cutoff”) are considered “fast,” and those below that energy
are considered “slow.” [34]. (Neutrons of energies around 0.025 eV are considered
“thermalized”.) Different methods are employed in the detection of neutrons from
these two catagories.

For slow neutrons, neutron-induced nuclear reactions which create secondary ra-
diation that is subsequently detected is the primary detection technique. At the slow
neutron energies, elastic scattering on charged particles does not impart enough en-
ergy to the charged particles for this interaction to be useful in detection. The scat-
tering does however serve to reduce, or moderate, the neutrons.

For fast neutrons with energies above around 0.5 MeV, collisions with charged
particles, usually protons, result in high enough proton energies to use proton-recoil
detectors such as plastic scintillators efficiently. Since the resulting spectra of these
protons spans from the complete neutron energy all the way to zero, the efficiency
of these detectors drops off at lower neutron energies usually due to the necessity to
discrimate the low—energy protons from other low-energy signals such as gamma-ray
signals or photomultiplier noise.

For fast neutron energies up to some point, moderating material (material that
reduces a neutron’s energy) can be employed to reduce fast neutrons to slow neutrons
which can then be detected. using the slow neutron methods. Since the process of
moderation essentially loses information on the energy of the neutron, this moderator-
slow-neutron-detector combination would be employed if only the number and not the
energy of the neutrons impinging on the target is desired.

The neutrons emitted by the neutron-rich nuclei around 78N i are predicted to
have energies ranging from about 0.1 to 1 MeV: too slow to be detected efficiently

by plastic scintillators, but too fast for direct slow-neutron techniques. Therefore,

 

moderator

    
 
 
  

captured

detected

escaped

detector

 

 

 

Figure 2.1: Finding the correct moderator size and configuration is a balance between
moderation, detection, capture, and loss (Figure based on Figure 15.1 of Reference
[34].

if high efficiency is required, a moderating system in conjunction with slow—neutron

detection is the only choice.

2.2.2 Neutron Moderation

The best moderating material (the material that reduces the neutron energy in the
most efficient manner) is one which contains hydrogen because of their comparable
size. A neutron loses the most energy in a collision with a proton as they split mo-
mentum almost equally. Detectors with hydrogen-based moderators therefore allow
for compact size, which also means smaller number of counters.

The disadvantage of hydrogen is that it also has a fairly large neutron capture
cross section. The challenge for the design is to balance moderation needed to increase
the detection efficiency with losses due to absorption in the moderator. The maximum
efficiency possible is therefore limited to about 40%. From this point of view, heavy
water or carbon would be better moderators, but would increase the detector size
dramatically. We therefore chose hydrogen for our moderating material.

One cannot generally use a moderator composed completely of hydrogen, since
this would be either a gas, and so not very dense, or would be liquid or solid, and

so have to be maintained at extremely low temperatures. Therefore, one generally

10

uses materials made of compounds which contain a relatively high density of protons,
and at the same time are physically manageable. Some examples are water, paraffin,
and various other types of organic compounds such as plastics. Water is generally
inconvenient to handle, especially around electronics. Paraffin melts easily and is

flammable. Plastics on the other hand are easily fashioned and managed.

2.2.3 Proportional Counters

Proportional counters have been used successfully as high—efficiency slow-neutron de-
tectors. Proportional counters are tubes filled with a gas, with a cathode (anode) wire
running down the middle. The gas is selected for two properties, corresponding to the
two steps involved in neutron detection mentioned above. First, the gas is selected to
have a high cross section for an (n, p) or (n, a) reaction. Second, the gas must serve to
support the cascade of electrons that cause a signal in the cathode (anode). Generally
the gas has a high cross section for slow neutrons, and the efficiency quickly drops off
as a function of neutron energy for the detection of faster neutrons. For fast neutron
detection, therefore, proportional counters are used in conjunction with moderating
material.

Two common proportional counters are the 3He and Boron Triflouride (BF3) de-
tectors. BF3 detectors make use of the 1°B(n,a)7Li reaction. In this reaction, the
Li can be left in the first excited state, which happens about 94% of the time for
thermal neutrons (Q-value = 2.792 MeV to ground state, 2.310 MeV to first excited
state) [34]. The 3He detectors take advantage of the 3He(n,p)3H reaction (Q-value .-_—.
0.764 MeV). In both cases, since the neutron energy is small compared to the Q-value
of the reaction, the charged reaction products essentially split the Q-value of the reac-
tion, and any knowledge of the neutron energy is lost. The charged reaction products
are detected through the cascading gas and record an energy equal to the Q—value
of the respective reaction. By momentum conservation, the charged products split

the energy inversely by mass. If one of the charged particles strikes the wall of the

11

counter, the energy recorded by the detector is smaller by the amount of energy that
particle carried. This result is known as the wall effect and results in the spreading

of the energy spectrum detected below the Q—value of the reaction.

2.3 NERO Development

2.3.1 General Design Considerations

There were several experimental criteria considered in determining the optimal config-
urtaion for NERO. A high efficiency is required since the rates for fl-delayed neutrons
that will be studied with NERO are generally low. The energies of the neutron-rich
nuclei of interest are generally not known, so the efficiency must remain high for a
range of neutron energies. The efficiency curve must also be as flat as possible in order
to minimize the uncertainty in the final result due to uncertainty in neutron energy.
Lastly, the detector must work in conjunction with existing fi—detectors and beamline
requirements.

The NERO design was based on existing detectors, most directly the Mainz neu-
tron detector (References [35] or [36] for example). NERO and the Mainz detector are
of a class of detectors that utilize moderating material in conjunction with a slow-
neutron detector as mentioned previously. Many variations of slow-neutron detector
types, shapes, sizes, as well as moderating matrix type, shape, size and configurations
have been used in the past. Some well-known styles of detectors of this kind are the
spherical dosimeters and the long counters.

Long counters are proportional tubes embedded in a moderating matrix and gen-
erally possess an axial symmetry. The long counters were designed to give a flat
efficiency response as a function of neutron energy. However, one drawback of this
design is that the detector is designed to accept neutrons only at one face. For the
situation for which NERO is to be used— neutron emitters implanted in a target

and emitting isotropically— this design would start with a detection efficiency of less

12

than 50% simply due to geometrical considerations. A design where the target is
surrounded by detecting material is more advantageous from a geometrical efficiency
point of view.

A sort of quasi-long counter which features almost 41r coverage is sometimes refered
to in the literature simply as 47r detectors, or sometimes 47r long counters. These
detectors feature a relatively flat efficiency dependence on the neutron energy, as
with a long counter. They are also generally axially symmetric as the long counters.
However, instead of accepting neutrons impinging on one face, they contain a hole to
allow insertion of a neutron source or implant beam into the center, thus affording
almost 47r coverage. The flat efficiency is then acheived by a creative arrangement of
rings of detectors. The NERO and Mainz detectors are examples of such detectors.
Some other examples are found in References [27, 37-40].

Multiple rings also allow for the possibility of extractingsome energy information,
which may be desirable since otherwise most of the energy information of the neutron
is lost in moderation. (see References [41,42] for example)

The 47r design was adopted for NERO. The configuration allows for a beamline to
pass into the core of the detector where beams of neutron-rich nuclei can be implanted
into a 5 detector system, and the neutron source will therefore have close to 41r
coverage. This design also can afford, with the proper arrangement of moderator and
proportional tubes, a flat efficiency response.

Because of the size of fast-fragment beams and the need for insertion of an entire
segmented implantation detector, the beamline hole for NERO was required to be
larger than is usually encountered with these types of detectors. The minimum clear-
ance for the intended implant target and fi-detection system— specifically the NSCL
Beta Counting System— was about 11 cm. To have such a large beamline hole and
still maintain a high efficiency was a special challenge and one of the primary reasons
why a redesigned detector was required. The larger the beamline hole, the farther

away the tubes are and therefore the less solid-angle coverage the same number of

13

tubes can provide. For comparison, the beamline hole for the Mainz 47r detector is
5.5 cm. Beamline holes for other similar detectors are for example 4.48 cm [41] and
5.1 cm [38]. The detector in Reference [39] had an 11.5 cm x 11.0 cm beam hole, but

reports a maxiumum efficiency of less than 25%.

2.3.2 MCNP Modeling

The code MCNP (Monte Carlo N-Particle) (http: / / laws.lanl.gov/ x5 / MCN P / index.html)
was used to model NERO during the design phase. MCNP has been used in the
past for modelling of 47r neutron detectors (see Reference [39] and references therein,
and Reference [38] for example). MCNP tracks a neutron’s path and interactions
through material. The proportional counters used for NERO are both Boron Tri-
floride gas (BF3) and 3He gas. The moderating matrix choice was polyethelyne. A
general configuration composed of the above counters arranged in concentric circles
in the polyethelyne matrix was the starting point of the design. This configuration,
with an isotropic neutron source, was input into MCNP. Then several parameters
were varied in MCNP: the position and number of proportional tubes, the size and
shape of the matrix, and the central hole size. All of these parameters were tested over
a range of neutron energies from 1 keV to 5 MeV. The parameters were adjusted to
produce the highest efficiency curve with the flatest energy dependence possible. The
constraints were the type of tubes available, and the large minimum beamline hole
diameter required to fit the NSCL Beta Counting System. The effects of variations
in external shielding were also taken into account.

The design is a balance between moderation and absorption. For example, inside
the first ring there needs to be just enough moderator to moderate the lowest energy
neutrons for detection, but not so much that a large fraction are absorbed inside the
moderating material (see Figure 2.2). The same is true for higher-energy neutrons,
which must encounter enough moderating material before and after the inner ring to

be detected in the second ring, but must not encounter too much moderator that they

14

 

Figure 2.2: An optimization of NERO parameters. Rb is the beamline hole radius.
R, the amount of polyethylene moderator along the inside radius of the ring. R =
(R, — r) — Rb where r is the radius of an individual counter, and R, is the radius to
the detector ring, defined as the distance to the center of any counter in the ring.

are captured in the moderator before arriving at the second ring. The same is true for
the third ring. Eventually the efliciency curve must drop off however for higher neutron
energies as more and more moderation is required and so the probability for neutron
capture in the moderator via (n,'y) increases. In addition, spacing between counters in
the same ring must be optimized. If the detectors are too close together, not enough
moderator will be present to get the optimum efficiency. If the detectors are too far
apart, the probability for a moderated neutron to find a counter decreases. A certain
amount of moderating material is also required beyond the last ring since neutrons
can pass the last ring and then diffuse back to the detectors. Without the moderator
beyond the outer ring, all of the neutrons that passed the ring would escape. The
amount of moderating material at the ends of the detectors are important for similar
reasons, and the amount of that material was also optimized.

The MCNP efficiency curve for the final NERO design is shown in Figure 2.5. As
can be seen from the plot, the calculated efficiency is relatively constant at about

45% from 1 keV to 500 keV, dropping off to around 26% by 5 MeV.

15

 

0.45

Eu = 0.5 MeV

 

 

 

 

 

g 0.4

a 0'35 o R = 2.59 cm

E 0.3 I R = 3.8 cm

III 025 . A R = 5.0 cm
0.2

0102030405060
Detector Separation (mm)

 

 

 

Figure 2.3: A study of the optimal detector separation.

 

 

 

 

 

 

0.45
04 En = 0.5 MeV
3‘
5 0.35
'8 o R = 2.59 cm
5 °'3 - R = 3.8 cm
0.25 o A R = 5.0 cm
0.2
0 5 10 15 20 25 30
it of Detectors

 

 

 

Figure 2.4: A study of the optimal detector number.

16

 

 

 

50 I I I I r I rt I I I I ITI r I I I r1 I T I I .
g I T T G—O Total
C; I El—E'l Ring 1
; I e—e Ring 2
40 IT“ :5 A A Ring3
E 0
s
r; 3 ..
5 : II ’
'§ : =2 ‘
a 2
8 20 E-
% E . .\
<f w i\
10 :- “ ‘t
E .. il
a”

 

1 11111111 I J IlllLLI I 1 1111111 I l
(9001 0.01 0.1 l

Neutron Energy (MeV)

Figure 2.5: NERO efficiency vs. neutron energy as calculated in the code MCNP.
The plot includes the total NERO efliciency, as well as the efficiencies of each of the
three rings of proportional tubes. Ring 1 is the inner ring and is composed of 16 3He
detectors. Ring 2 is the middle ring and is composed of 20 BF3 detectors. Ring 3 is
the outer ring and is composed of 24 BF 3 detectors.

17

Table 2.1: Reuter-Stokes 3He Counter Part Numbers Used in NERO (Part X—#).

 

 

5434
5448
5454

 

5458
5459
5462

 

5463
5466
5467

 

5468
5473
5476

 

 

Table 2.2: Mainz 3He Counter Part Numbers Used in NERO.

849
850
851
852
853

 

 

 

 

2.3.3 NERO Design

Based on the MCNP optimization, the details of the final design of NERO are as
follows. The polyethylene moderating matrix is 60 cm by 60 cm by 80 cm, being
longer along the beam axis. The detector contains 60 proportional counters: 16 3He
and 44 BF3 tubes, arranged in three concentric rings. The inner ring has a radius
of 13.6 cm and contains 16 3He tubes. The second ring has a radius of 19.2 cm and
contains 20 BF3 tubes. The outer ring has a radius of 24.8 cm, containing 24 BF3
tubes. The rings are all concentric around the cylindrical beamline hole of radius 11.2
cm running the length of the detector along the beamline direction.

Two models of 3He counters were used in NERO. Twelve of the 3He counters
are Reuter-Stokes model RS-P4-0814-207, on loan to the NSCL from Pacific North-
west National Laboratory. These tubes have two external connectors at the end of
a Cu cap which are connected inside the cap to the anode wire, for the purpose of
“daisy-chaining” the detectors, although this feature was not exploited in NERO.
The connectors are SMC standard. Table 2.1 lists the part numbers of these counters.
The remaining four 3He detectors are models obtained from the University of Mainz,
Germany. Table 2.2 lists the part numbers of these counters. All of the BF3 tubes are
Reuter-Stokes model RS-P1-1620—205, on loan to the NSCL from Pacific Northwest
National Laboratory. They are 100% BF3 gas enriched in 10B to greater than 96%.

18

Table 2.3: Renter-Stokes BF3 Counter Part Numbers Used in NERO (Part V-#).

3988 4021 4056 4079 4102
3989 4029 4062 4080 4107
3992 4030 4063 4081 4111
3994 4032 4069 4082 4112
3995 4034 4070 4084 4113
3996 4043 4072 4086 4116
4004 4046 4073 4091 4117
4007 4048 4074 4092 4118
4010 4050 4076 4096 4119
4013 4052 4078 4097 4120

 

 

 

 

 

 

 

 

Table 2.4: Proportional Tube Data.

 

 

 

Detector Active Length (in) Inactive Length (in) Radius (in) Nominal Pressure (atm)
Mainzj‘fHe 9.84 10.24 0.5 5.732
:PDUVLififlc 14 17 (15 4
PNNL BF3 20 22 1 1.18

 

 

 

 

 

The casing is 304 Stainless Steel. Table 2.3 lists the part numbers of the tubes. The
dimensions and nominal pressures for the various types of proportional counters used
in NERO can be found in Table 2.4.

The moderating polyethelyne block was divided into two halves, upper and lower.
In addition, each half was cut into 6 equal pieces so that the the entire moderating
block can be dissassembled into 12 pieces for transportation. When assembled, the
pieces are held together by 8 stainless steel bolts which run the length of NERO
and which were included in the simulations. During assembly, first the blocks are
arranged, the bolts are inserted, and then the counters are inserted into the counter
holes, which are drilled from the downstream end of NERO, so that they are centered
about the target position.

A boron carbide shield was added around the outer faces of NERO. The boron
carbide shield was fabricated by mixing boron carbide powder in epoxy and pouring
the mix into a frame. Inside the sheet is layed fiberglass ribbons to provide added

support.

19

 

 

Figure 2.6: NERO polyethelene moderating matrix (view looking along beamline di-
rection.

 

Figure 2.7: Close view of NERO with tubes inserted. The hole is the beamline hole
for insertion of beamline and Beta Counting System.

20

 

Figure 2.8: Diagram of NERO quadrant and detector labeling. The beam is coming
out of the page.

2.3.4 NERO Electronics

For the purpose of electronics, NERO was divided into four quadrants, and the detec-
tors were numbered according to quadrant (See Figure 2.8). A diagram of the N ERO

electronics can be found in Figure 2.9.

High Voltage and Preamplification

All counters from a given quadrant are connected via high-voltage cables (Figure
2.10) to one dedicated preamplifier box designed specifically for the NERO detector

(Figure 2.11), which contains 16 individual preamp chips, leaving one spare channel

21

 

 

 

 

 

Xl5 Shapef ADC
—- — Pre-Amp» - ~»—-—~-~4 ~— ”——~

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DISCIIMIHO‘IOI BII R”ISI9I]——~
19R] *
__§caier __ 1
Master Gate
—>
Computer —~
NOT Busy AND Master Gate Live

 

 

 

Figure 2.9: Diagram of NERO electronics for one quadrant.

Table 2.5: Proportional Counter High Voltage Requirements.

 

 

 

 

Detector High Voltage (V)
Mainz 3He ~+1300
PNNL 3He +1050 — +1100
PNNL BF3 ~+2600

 

 

per preamp box. The high-voltage requirements for the counters is given in Table 2.5.
The preamp chips are powered by i9 Volts which comes into the box through one
connector and is split inside the box to each of the chips. The preamp box has two
high-voltage inputs. The first high-voltage input is sent inside the box to the first four
channels, and the second high-voltage input is sent inside the box to the remaining
12 channels, so that the different tubes can be held at different voltages. The pream-
plifer chips inside the preamp box are Cremat CR—101D miniature charge sensitive
preamplifiers designed specifically for nuclear detection instrumentation. These are

mounted on a board designed and fabricated at the NSCL.

Shaping and Discriminating

The signals for a given quadrant are sent out of the preamp box via a 34-wire ribbon
cable to a dedicated double-wide CAMAC 16-channel shaper/discriminator module
designed by Pico Systems (see Figures 2.12). Inside the double module, the signal

goes through the discriminator, and then is split. One signal proceeds on through

22

 

Figure 2.10: High voltage cables coming out of the proportional tubes to the preamp
boxes.

 

Figure 2.11: Preamp box for one NERO quadrant.

23

 

Figure 2.12: Pico Systems Shaper/Discriminator (Photograph from http://pico-
systemscom).

the shaper, while the other goes out of the discriminator to be used for fast timing
purposes. The discriminator thresholds and shaper gains fOr individual channels can

be changed remotely through software.

Timing, 'Ii‘iggering, Digitalization

The discriminator outputs go to a bit register and a scaler. The shaper signal goes to
an ADC for readout of energies. The discriminator also features an OR signal output
of all 16 channels. This signal serves as the master gate/trigger. It is ANDed with
triggering logic for computer NOT busy, and the result is the master gate/ trigger

LIVE. This signal serves as the gate for the ADC and bit register.

2.3.5 NERO Support Table

Because of the weight of NERO when fully assembled, a special support table was
designed to allow relatively easy position adjustment and alignment. The table in—
cludes four screw feet for height adjustment. The table also features a plate which
rides freely on top of large ball bearings. Indvidual screws are adjusted against the

plate resulting in orientation adjustments in the x-y plane.

24

 

14 I T T f r I I

12» «

10— -

 

Counts

 

 

 

0
0 200 400 600 800 1000 1200 1400

Energy (Arbitrary Units)

Figure 2.13: NERO background spectrum in a typical 3He counter. The characteristic
shape for neutron detection is clearly identifiable.

2.3.6 NERO Background

Background simulations were conducted with various shielding configurations and
background measurements were taken with and without shielding. Figure 5.11.2 shows
a common NERO neutron background spectrum. The signature neutron spectrum
can clearly be seen indicating that the background is in fact real neutrons. Real
neutron background can originate from cosmic rays. During the Calibration at the
Notre Dame Nuclear Structure Laboratory, the detector was shielded by water jugs,
and the background rate was around 15—20 counts per second for the entire detector.
Before experiment 02028 at the NSCL experimental vault, the unshielded background
rate was 5 per second for the entire detector. Consequently, water jugs were not used

for shielding during experiment 02028.

25

 

 

 

 

 

 

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1'5
‘3
m t
‘04
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“a
:3 {\I J
'5
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t:
g “‘lt f j
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Z
1+:
o r
1'3 1 \
“g .
z L
E ] - Time of Flight Data
(6
E ]- Plate Data

3L - l + 1 .L. -_.__.1 _____1__.____.

I 2 J 4 5
Energy (MeV)

Figure 2.14: Neutron energy spectrum from the spontaneous fission of 252Cf (Figure
2 of Reference [43])

2.3.7 Tests with 252Cf
Efficiency

252Cf, a spontaneous-fissioning neutron emitter with a half-life of 2.638 years, is a
readily available neutron source that has been used often for calibration of neutron
detectors (see for example References [35,39, 41]). When it fissions, 252Cf emits neu-
trons with a broad range of energies at 0.116 neutrons/s/Bq (Reference [34], p. 20).
The 252Cf neutron energy spectrum is shown in Figure 2.14. The average neutron
energy is 2.35 MeV.

We obtained a 252Cf source at the NSCL. The specific source information is found
in Table 2.6. An uncertainty in the activity at the time of calibration was not given.
One could assume the figure quoted is to the least significant figure, which would

result in an uncertainty 1 pCi or 2%. However, a conservative 5 % uncertainty was

26

Table 2.6: 252Cf source information

 

 

Company Isotope Products Lab, Burbank, CA
Catalogue # FF-252-4

N SCL Source # N-355

Capsule Type FF Holder

Cover 50 pg Au

Active Diameter 5 mm

Activity 50 ,uCi

Calibrated On Nov. 19, 1990

 

 

 

assumed. The current activity was calculated from the known initial activity. This
activity was multiplied by the neutrons/s/Bq from Ref. [34] to obtain a calculated
neutron rate. This was compared to the neutron rate measured by NERO with the

source located at the target position. The efficiency was calculated to be 26.4 :1: 1.5

%.

Peak Efficiency Position

The 252Cf source was also used to locate the axial position within the beamline hole
which has the maximum neutron efliciency. During experiments, this should be con-
sidered the target position. By design, the target position should be at the midpoint
of the beamline hole. This assumption was validated by the 252Cf study (see Figure
2.17). It can also be seen in the figure that the efficiency function along the axial

direction is fairly symmetric for small displacements around the target position.

NERO Neutron Moderation Time Measurements

The NERO neutron moderation time was also studied with the 252Cf source. In the
fission of 252Cf, 7-rays are emitted in coincidence with neutrons. A 252Cf source was
placed on the bottom surface of the NERO beamline hole 3 in. from the end. A
Ban gamma detector was inserted in the NERO beamline hole from the up—beamline
direction.next to the source. The detection of a gamma by the BaF2 was sent to a

TAC with a delay as a start, and the detection of a neutron by NERO served as a

27

 

250 - r

200 - —

150 - ' a

Counts

 

100 - ‘ r

50—

 

 

 

 

0 . l l 1 l 1 L4.._..-..l.._.. .....l.-..
0 200 400 600 800 1000 1200 1400

Energy (Arbitrary Units)

Figure 2.15: Typical NERO 3He neutron spectrum from 252Cf source.

 

28

Counts

 

120 -

100 -

40-

20-

    

 

   

l

0 ‘ ‘ 500 1000 1500
Energy (Arbitrary Units)

Figure 2.16: Typical NERO BF3 neutron spectrum from 252Cf source.

29

 

2000

 

30 1 T

29»— —~
28— —

r- —I
27— —

Efficiency (%)
b.’ '53

l l

l l

E
l
1

22- -—

21- -

.4
f 1 l l

- 10 0 10
Position of Source (cm)

 

 

 

20

Figure 2.17: Variation of NERO efficiency in the beamline hole as a function of po-
sition along the beamline axis. Zero is the NERO target position. Larger negative
numbers are up the beamline direction.

30

Beam Orientation
<]:

 

NERO (Top Wew)

TAC

 

 

 

252 Cf
\\®

 

 

 

 

 

BCIF2 Delay

 

 

 

 

 

 

 

 

 

START

STOP

 

Figure 2.18: Schematic for NERO neutron moderation time measurement.

Table 2.7: Moderation Time for Neutrons in NERO.

stop (see Figure 2.18). The results of this test can be found in Table 2.7 and the

moderation time spectrum can be found in Figure 2.19. Almost all of the detected

 

Time (as)

Percent of Neutrons Moderated

 

 

50
100
150

 

52
80
93

 

 

neutrons are moderated within about 200 MS.

31

 

 

 

 

 

 

i
|

 

 

l l l I 1 l 1

0 ,
0 500 1000 1500 2000 2500 3000 3500 4000
Moderation Time (A.U.)

Figure 2.19: Ban Moderation timing measurement with 252Cf source. The start and
stop for the TAC were inverted.

32

Chapter 3

NERO Efficiency Calibration

3.1 Introduction

To test the theoretical efficiency curve produced by the MCN P code, a calibration
of the NERO detector was carried out at the University of Notre Dame Nuclear
Structure Laboratory.

Using the KN Van de Graaff accelerator to accelerate a and proton beams into
targets in the NERO target position, 13C(cz,n), 11B(a,n), 51V(p,n) reactions were
used to produce neutrons at several well—defined energies. The detected neutron rates
were compared to calculated rates based on known quantities, and the efficiency was
thus calculated at several energies. For 13C and 11B, resonant reactions were used.
For 51V, non-resonant reactions were used.

The NERO efficiency in percent was calculated as follows.

I

N
c = 100 x Ni (3.1)

where N g is the number of neutrons detected by NERO, corrected for background, and
Np is the number of neutrons produced. Np is calculated based on known information

about the reaction.

33

1. SNICSlonSouroe 10. Conference

2. HIS IonSouree 11 Consoles
3.FNVendeGreeflAooeleretor 12. CleSouroeTeetSetup

4. Gemme Spemeoopy Beemline 13. KN Van de Gin-11mm

5. SoedrognphaeemLine 14.JNVendeGreetl

6. R202 Beem Line 1 meeetterlng climber) 15. ORTEC Seeth' Chember
7.Vlbeklnterection Line 0. Gee emetBeem Line
0.RNB BeemLine 17. Germ-Table
[NeuronDetectlonm

 

 

 

Figure 3.1: Layout of the Notre Dame Nuclear Structure Laboratory. The protons
or a-particles were accelerated in the KN Van de Graaff accelerator (13), then were
directed into the experimental vault to the location of the Gamma Table (17) which
was replaced by a special stand for NERO (Image from http://www.nd.edu/~nsl/).

 

Figure 3.2: The KN Van de Graaff accelerator at the Notre Dame Nuclear Structure
Laboratory. (Image from http://www.nd.edu/~nsl/)

34

 

Figure 3.3: View of the experimental vault beamline. NERO was located in the place
of the Gamma Table (top right), which was removed for the experiment (Image from
http://www.nd.edu/~nsl/).

35

 

Figure 3.4: NERO set up at Notre Dame. View is up the beamline.

36

 

Figure 3.5: A close-up of NERO set up at Notre Dame. The 25“Cf source stand is
inside the beamline hole, in front of the target holder.

37

 

Figure 3.6: Target holder for Notre Dame calibration.

3.2 Resonant Reactions

For the 13C(oi,n) and 11B(0z,n) reactions, resonances were used. Setting the beam
energy on resonances is adventageous for several reasons. On the resonance, the pro-
duction of neutrons is dramatically increased, allowing many more counts in a shorter
time, and overcoming background. Also, as long as the thickness of the target is much
greater than the width of the resonance, the thickness of the target does not enter
the calculation of the neutron production, and so the target thickness does not have
to be known to extreme precision.

Two resonances each were chosen for 13C and 11B. The resonance energy partly
defines the resulting neutron energy (see Figures 3.9 and 3.10). The center-of-mass

neutron energy is calculated by:

E3" = E, — 3,. (3.2)

38

ZOOFT—r-trt—r—r—r. 1"": 1 r . v r1 rr

 

 

 

 

 

 

A ’ . V I I I T T Ifi I I I I Tfir TI 1 T I I T_T I I I I I r Y #
.0 L-

. ,- i —
g . i
.5 . .
o 1 j
2 [ X75 -
U)

8 Z 1.:

0 A. - .. A. 4.. .LL 4* ‘1 .
0.5 1.5 2.5 3.5 4.5 5.5

Alpha Energy (MeV)

Figure 3.7: Figure 3 from p. 1358 Blair and Haas, 1973 (Reference [44]) showing total
neutron cross section for 13C. The axis labels have been modified for clarity.

where Ex is the excitation level in the compound nucleus to which the select resonance
energy corresponds, and S,, is the neutron separation energ of the compound nucleus.
The energies of the resonances were selected to provide apprOpriate points in the
efficiency vs. energy graph. The resonances were also desired to be narrow and well-
separated from other resonances in order to simplify the calculations required. For
13C, the resonances at center-of—mass a-energies of 1.0563 MeV and 1.59 MeV were
chosen, and for 11B, the resonances at 0.606 MeV and the 2.063 MeV. (See Figures
3.7 and 3.8). Due to equipment problems during the 2.063 MeV 11B resonance runs,
good data was not collected, and this resonance could not be analyzed.

The above reactions have been studied previously, so the energies, widths, and
strengths of these resonances are known, all of which enter into the calculation of the
neutron production (see Table 3.3).

Targets of 13C were produced of thickness 14 :l: 2 pg/sz. Targets of 11B were
produced of thickness 12:} pg/cmz. The targets were 1.5 in2 squares of 13C and 11B
evaporated on Ta backing. The 13C target was enriched to 99% 13C, and the 11B was
enriched to 99.71% 11B.

The energy of the a beam was adjusted to scan across the resonance in order
to map the resonance and locate the maximum yield. The beam was then set to

the maximum yield for a certain amount of time. The incident beam current was

39

 

  

 

 

 

 

7] l w“ I l l
2'
‘ ‘010 .]
s
109
1.09 7.0 __.
r ”B(a.n)“N “’8 , ‘
I e ,
fa .' 6*400420440450480500
> ' a- E 9.1
o - ‘2' ' f' 51‘s.
.54 l , 3- ' 2.2
V - 1’ _
a... r 5. 2 _
c 1" 9‘
1'5 1' 1‘ f
«3 '08 / r.
LL. _ - ' l
(I) ~ .
I . ' 51+)
l' 2- .
107 r- -' ..:
. l J j l L L1 1 l l L 1 L A A l A A A A [M J A j l ‘
500 750 1000 , . 1250 1500 1750
E..m.(keV)

Figure 3.8: Figure 2 from p. 886 of Wang, Vogelaar and Kavanagh, 1991 (Reference
[45]) showing S-factor for 11B(o:,n). The axis labels have been modified for clarity.

40

13C(Ct’,n)160

First Excited State in I"O

 

cm
E20 7

 

cm
Earl I

A _
13 cm
c + a — Ecm En2
__—__— n]

 

V
IIIIIIIIIIIIIIIIII

a, of ”o "’0 + n
Sn of 17O

 

170

Figure 3.9: Energy diagram of the 13C((3z,n)160 reaction.

41

I3C(a’n)lbo

First Excited State in “O

 

 

Ecm _
2a ' L
Ecm
a] I
IIIIIIIIIIIIIIIIII
cm

13 A —
C + a _ Ecm n2
—— nI

 

III-IIIIII‘IIIIIIII

o, of ”o "‘0 + n
s, of ”o

 

 

170

Figure 3.9: Energy diagram of the 13C(01,n)160 reaction.

41

IIB(a'n)I4N

First Excited State in “N

 

cm
E 2a

 

Ecm = Ecm cm
(H __————__—_ t n1 "2
IIIIIIIIIIIIIIIIII u-n-u-n-un-eee-m

A

"B+a]k E ”N+n

(2,, of 15ll __..—_ Sn of 15til

 

 

15N

Figure 3.10: Energy diagram of the 11B((Jz,n)1“N reaction.

42

 

 

 

 

 

 

 

 

20 I T I l T I I T I
_ o—o Rough Scan _
A—A Fine Scan
0 Resonance Run

15 _ 0 Resonance Run fl
0
50
{a

.c: - -
U
'5

1.. 10 — -
8.
(I)
S

2: ~ 1
:3
0
Z

5 — _

I l r l l l l l L
9000 1020 1040 1060 . 1080 1 100
Alpha Energy (keV)

Figure 3.11: Scanning over the 1.053 MeV resonance in 13C

measured on an isolated plate with electron suppression behind the target, providing

a measurement of the incident rate.

3.2.1 Resonance Analysis

To derive the NERO efficiency, one needs the number Nd of neutrons detected at
the resonance energy, and a calculation of the number of produced neutrons Np. The

background-corrected N; is simply:

M=M—M (M)

where N5 is the number of background neutrons. To find Nb, the resonances were
scanned from well below to well above the resonance peak. Then a linear background

was fit underneath the resonance peak and the background was subtracted from the

43

 

Neutrons per Unit Charge

 

30

 

 

 

 

 

 

 

 

I I I I I I I I
_ 0—0 Rough Scan _
G—Q Fine Scan
9 Resonance Run
_ 0 Resonance Run _
25
20 - —
- 4
15 - fl
1 1 l i l . l l l
9580 1590 1600 1610 1620 1630
Alpha Energy (keV)

Figure 3.12: Scanning over the 1.5857 MeV resonance in 13C

44

 

Neutrons per Unit Charge
O P
w A

.C
N

 

r l

 

 

G-OScanl
l3—El Scan2

O—OScan3
A-AScan4

O Resonance Run

 

 

 
 
 
 
 
   

 

 

0.1 — _
f a
1 l 1 m l
(590 600 610 620
Alpha Energy (keV)

Figure 3.13: Scanning over the 0.606 MeV resonance in 11B

45

630

 

20 I I I I I T I I r

 

o—o Rough Scan

H Fine Scan
9 Resonance Run

 

 

 

 

 

 

 

15 _ O Resonance Run _
0 — Background
g3 — Systematic Uncertainty
6 - — Systematic Uncertainty -
E
1.. 10 — 4
8.
E
b - _
8
Z

5 — _

- -l
. l l l 1 l t l l
9000 1020 1040 1060 1080 1100

Alpha Energy (keV)

Figure 3.14: Linear Background subtraction for the 1.053 MeV resonance in 13C

peak. This fitting removes both background and non—resonance counts, which must
not be included in order to use the resonance peak formalism to calculate the number
of neutrons produced by sitting on a resonance.
The number of produced neutrons, Np, was calculated using the equation (see
Reference [46]):
Np = Nlana = Nlant (3.4)

where N; is the number of incident particles, 0 is the cross-section for the reaction,
na is the areal target density, or number of target nuclei per unit area, n is the target
number density, or number of nuclei per unit volume, and t is the thickness of the
target. 0 depends on the energy of the beam and therefore on depth a; in the target,

since the beam loses energy as it passes through the target. The number of neutrons

46

30 I I I

 

l l l ' l ' ]

 

__ <>—<> Rough Scan
G—O Fine Scan

9 Resonance Run
25 _ 0 Resonance Run
— Background

    
  

 

 

 

Neutrons per Unit Charge

 

 

 

 

— Systematic Uncertainty
- —— Systematic Uncertainty
20 — —
15 P —
1 1 l l l |_ | l l
9580 1590 1600 1610 1620 1630
Alpha Energy (keV)

Figure 3.15: Linear Background subtraction for the 1.5857 MeV resonance in 13C

47

produced at a particular depth at in the target is:
de = N10(E)nd:r (3.5)

where E is the energy at depth 2:. The number of neutrons produced through the

target is:

Np = dep = N1n£x=tdxa(E) (3.6)

=0
This can be expressed as an integration over energy. Changing variables of integration
gives:

N —N /EtdEd—x (E) (37)
p— In dEU .

O

“3:1 is the stopping power of the target material. In the “thin target approxi-

where
mation” [47], the stopping power is essentially constant in E or 2:, and so it can be

pulled out of the integral, leaving the integral:

E:
I = dEa(E) (3.8)
E0

to be calculated.
One must remember to use the stopping power in the appropriate frame (see
Section 3.2.2). Here we chose to calculate in the center-of-mass since the resonance

strength is usually given in center-of-mass.

3.2.2 Narrow Resonances

If the resonance is broad relative to the target thickness, the integral I must be carried
out over the thickness of the target, and the result is then sensitive to the limits of
integration. If the resonance is narrow relative to the target (narrow being defined as

the width of the resonance is much less than the energy loss in the target), then the

48

Table 3.1: Stopping Power of Targets.

 

 

 

 

 

 

Target Em LAB £1,113 %ICM
(MeV) (MeV/mg/cm2) (MeV/mg/cm2)

13C 1.053 1.722 1.318

13C 1.585 1.451 1.110

11B 0.606 2.087 1.531

 

 

Table 3.2: Target thickness compared to resonance widths.

 

 

 

 

 

 

 

 

Target Em lab t tCM I‘cm Narrow
(MeV) (mg/cm2) (keV) (keV) Resonance?
13C 1.053 0.014 18 1.5 4: 0.2 yes
13C 1.585 0.014 16 S 1 yes
11B 0.606 0.012 18 (2.5 d: 0.5) x 10“3 yes

 

 

integral becomes simply (see Ref. [47], p175):

 

 

”2’12
I = 1..) cm 3.9
”EM 7 ( )
Then
N I pN A7r2h2c2wcycm
'(Tx'I-‘C maERcm

To see if the narrow resonance rules apply in our cases, the target thickness in
energy was calculated using the program SRIM 2000, and these values were compared
to the experimentally determined widths of the resonances from the literature. These
values are found in Table 3.3. The SRlM-calculated target thicknesses are shown in
Figure 3.16. The comparison is shown in Table 3.2. As can be seen from the table,
both resonances in 13C and the 0.606 MeV resonance in 11B are narrow relative to
the targets.

The values for the resonance energies and strengths were taken from experimen-
tally derived values from the literature: the resonance energies and strenghts for
13C from [48] and widths from [44], and the energies, strengths and widths for 11B
from [45]. (See Table 3.3).

dB

The stopping power dx

was calculated in SRIM 2000. The stopping power must

49

 

 

e-e Stopping Power
H W31. Uncertol

 

 

 

    
     

 

13c

Target Thickness (keV)
to
o

 

 

 

 

 

 

 

 

 

0 ' 2
Alpha Energy (MeV)
I
e-e Target Thickness
30~ H W51. Uncertain
S‘
.91
gm. .
.9 t
E- .
" i I I i
g»... B i
00 A l

2
Alpha Energy (MeV)

 

 

 

 

 

 

Energy Loss (MeV/ mg/cm2]

 

 

 

00 . 1

2
Alpha Energy (MeV)

Figure 3.16: SRIM-calculated target thicknesses and energy-losses of the 13C and 11B
targets in terms of the energy of the a projectile.

50

Table 3.3: Resonance Information Used in Calculations.

 

 

 

 

 

 

 

 

 

Target Ea lab (keV) Ea cm (keV) F cm (keV) we; cm (ev) En cm (keV)
”C 10581808) 1.5 as. 0.2 11.9(6) 3022.37(83)
13C 1585.7(15) S 1 10.8(5) 3433(2)
11B 606.0 :1: 0.5 444.4 :t 0.4 (2.5 :1: 0.5) x 10‘3 0.175 :1: 0.010 604.3(7)
11B 2063.7 :1: 1.0 1513.5 1: 0.7 39 :f: 4 (7.9 :l: 0.7) x 103 1660(4)

E . E '
.. LAB

at ___>

E 1
CM

 

Figure 3.17: Stopping power of a target of thickness Ax in LAB and CM frames.

be in the center-of-mass frame if the integral is also calculated in center—of—mass. One
does not take the curve from Figure 3.16 and find the stopping power at the center-

of-mass energy of the incident a-particle. Rather, one uses the stopping power at the

lab energy and converts it into a center-of—mass stOpping power. Consider:

and

Since

rig
dz

_d_E
dz:

)CM

1 _ i
ECM _ FELAB

f .
_ ELAB _ ELAB

LAB _ Arr

f .
_____ ECM — E10111!

 

A2:

(3.11)

(3.12)

(3.13)

 

and

35,, = FEgAB (3.14)

then

 

 

dz: CM A2: A1: dz: LAB

where

mt t
F = “’98 (3.16)
mtarget + mprojectile

 

3.2.3 Neutron Energy

The energies produced via the resonance reactions were calculated based on Equation
3.2. The center-of—mass energies were converted to lab frame energies. The central
value was taken to be the lab frame energy at 90" relative to the beam axis. The
uncertainty included the uncertainties in the excitation energy and neutron seperation
energy of the compound nucleus. In the lab frame, the energy of the neutron depends
on the angle at which the neutron is emitted. Since the information on the angle of
emission of the neutrons is lost in NERO, an additional uncertainty in the lab-frame

energy range was taken as the lab frame value from 0° to 180°.

3.3 Summary of Resonance Analysis

Table 3.4 gives the neutron energies and corresponding NERO efficiencies for the
resonance analysis. In the case of the two 13C resonances, more than one measurement

was taken. The result given is the weighted average of the various measurements.

52

Table 3.4: Results of Resonance Analysis.

 

 

Target Resonance (MeV) Neutron Energy (lab) MeV Efficiency ‘70
11B 0.606 0.6 i 0.2 33.2 :t 2.5
13C 1.053 3.0 :1: 0.4 24.4 2}: 1.3
13C) 1.585 3.4 :l: 0.6 27.6 :l: 1.5

 

 

 

 

 

 

3.4 Non-resonant cross section: 51V(p,n) reaction

This method does not depend on a calculation of neutron production from information
about resonances, but rather is a more direct counting method. This method has been
used previously for neutron detector calibrations [49,50].

A proton beam was accelerated at the KN and impinged on the 51V targets at
the target position of NERO. For this reaction, an area of the known cross-section
curve was chosen where there are no resonances. Neutrons produced in the reaction
are counted by NERO.

For every 51V(p,n)51(3r reaction that occurs in the target, a radioactive 51Cr iso-
tOpe is created. Consequently, the number of neutrons produced is equal to the num-
ber of 51Cr produced. 51Cr decays by the emission of gamma rays. Therefore, if the
activity of the target after irradiation is measured, then one can calculate the num—
ber of neutrons that were produced. 51V was specifically chosen because 51Cr has a
relatively long half-life of 27.7025(24) days (NuDat). Once the target was irradiated,
it was removed from NERO and taken to an offline gamma counting station where
the activity was measured. 51Cr decays by electron capture (EC). It emits several
X-rays, and one gamma-ray, at 320.0824(4) keV (NuDat), with a branching to that
gamma-ray of 9.92% (NuDat).

For this calibration, three beam energies were used: 1.8, 2.14, and 2.27 MeV (See
Table 3.10 for the corresponding neutron energies). A new target was used for each
energy.

The offline detector was an HPGe detector. The irradiated target was placed on

a plastic backplate and mounted in front of the Ge detector at a specific distance,

53

Side View

\ Lead Shield

Target Holder
. Liquid N2

 

 

Top View

 
  

 

 

Figure 3.18: Schematic drawing of the offline counting station.

54

Table 3.5: Irradiation of 51V targets.

 

 

 

Target Ep lab (MeV) Irradiation Time (5) Integrated Current (C) Neutrons Detected
1 1.8 30256 6.93 x 10"2 111493686
2 2.14 13546 4.03 x 10-2 154921397
3 2.27 11359 2.56 x 10‘2 266224751

 

 

 

 

 

 

Table 3.6: Offline counting of 51V targets.

 

 

Target Ep lab (MeV) 'y measuring live-time (s) Detected 7's
1 1.8 14892 1028
2 2.14 29224 3138
3 2.27 78586 13712

 

 

 

 

 

 

surrounded by lead shielding (See Figure 3.18). The activity of the target was mea-
sured once for a duration of several hours. Irradiation times, the time between the
end of- the irradiation and the beginning of the off-line counting (less than 4 hours)
and the off-line counting times were short compared to the 51Cr half-life, and any
decay losses can therefore be neglected. The number of neutrons produced, Np, can

then be calculated simply with:

A r
N, = NC. = A: (3.17)

 

where ACT and A0, are the activity and decay constant of 51Cr. The activity is found
by:

P320keV
A ,. = 3.18
C ACrtI.b3201ceV€~1 ( )

 

where szokev and b320kev are the area under, and the branching to the 320 keV 51Cr
gamma peak in the offline counting, and ti, is the live time of the offline counting.
The X-rays from the decay are at too low energies to enter the detector through the

detector end—cap. e, is the efficiency of the gamma detector.

55

 

 

   

 

ALLJ

 

Detected Counts (per 5)

Detected Comts (per 5)

 

 

 

 

 

 

 

 

 

 

Detected Counts (per 5)

 

 

 

 

 

 

 

900 310 36 ‘ 340

320 3
Gamma Energy (keV)

 

 

 

 

 

 

 

 

 

 

 

 

fl ' ' F ‘ ' ' 1— Background
3.1500 A $1500~ — M. Uncertainty
i E
g 1000+ « 1000— , -
U
4 J
Li J 11 l 1
011 500 1000 900 310 320 330 340
Gamma Energy (keV) Gamma Energy (keV)

Figure 3.19: The 51Cr gamma spectra and 320 keV peaks from targets irradiated by
1.8, 2.14, and 2.27 MeV protons.

56

3.4.1 Offline Counting Ge Detector Efficiency

The efficiency of the gamma detector depends both on distance from the source to the
detector, and on the energy of the 'y-ray. We determined the efficiency of the detector
for a 320keV gamma ray at a specific distance by means of a calibation source.

The calibration source used was 133Ba. The activity of this source had been mea-
sured precisely on April 1, 1981, 1200 GMT to be 11.65pCi with a 4.8% uncertainty.

The current activity was found using

A(t) = Aoe‘)“ (3.19)

The calibration source was placed at the same location as the active targets were
placed. The efficiency was measured for several energies (the energies corresponding
to the energies of the 'y-rays of the calibration source). Since 133Ba has gamma en-
ergies just above and below 320keV, the efficiency for 320keV could then be linearly
interpolated between the 302keV and 356keV 'y-rays from 133Ba.

N Detected

 

(3.20)

67 = N
C alculatedf romK nownActivity

Since 1338a has multiple ’y-rays (see Figure 3.20), some in cascades, the effects of
summing had to be quantified.

Summing in a gamma detector occurs when there are cascades of 'y-rays in the
decay of the source. In this case, multiple 'y-rays would be emitted almost simultane-
ously. If the detector detects both of them, it will interpret them as one photon with
an energy equal to the sum of the two photons.

Both the 302 keV and 356 keV gammas are part of cascades so it is necessary to
quantify summing corrections for both. We follow Debertin and Helmer [51] for this
correction. For simplification in notation, we also follow the numbering convention in

that reference (see Table 3.7). Reference [51] derived Cg, the summing correction for

57

 

 

 

76 79 77 75

73

 

 

 

74 72
73

V 7 V

I33cs

Figure 3.20: Decay diagram for 133Ba. Diagram and numbering convention as found
in Figure 4.25 of Reference [51].

 

 

 

7

 

 

 

 

 

Table 3.7: Numbering of 1338a 7-rays.

Number Energy (keV)
53
80
81
161
223
276
303
356
384

 

 

H

COOONICDCfiuBCJJN)

 

 

 

 

73 = 356 keV already. We take their expression, neglecting terms involving detection
of X-rays, since the X-rays do not have enough energy to enter our detector. Our

correction factor C8 is then:

1 Q3

_—[ _

 

 

+
1 x [1+ P6f62€2€6 P1f17€1€7]

3.21
1 + 03 p858 ( )

where a,- is the total internal-conversion coefficient, 6,- is the peak efficiency for the

ith gamma, 6,,- is the total efficiency for the ith gamma, p,- is the gamma emission

58

probability for transition i, and

__ P2
f62 _ p2(1+ a2) + p4(1+ (14) (3°22)

 

and

P7
__ 3.23
f62 1350 l C15) l P70 l 07) I P90 l 09) ( )

 

The factor 0,, the summing correction for 77 (303 keV) was derived based on

similar arguments as those found in Ref. [51] for deriving Cs.

1 171 6:3 P5f52€5€2
—=1——— —————x1+-—-———— 3.24
07 [ p761 H03] 1 p... 1 < >
The total efficiencies 6t were calculated as in [51].
— 1 f (1 ammo (3 25)
6t — 471" .

where p is the attenuation coefficient of the detector material. The integration
is over the solid angle subtended by the detector. In terms of the dimensions of the
setup where R=radius of the crystal, t=thickness of the crystal, and d=distance from

the source to the front face of the crystal:

1 211' 92 1 01 ‘ Ht . 92 F [IR [1d .
ct — [EA /0 dQ]—§[/0 exp [YES—0] Sln 0dB+/9l exp l__sl—n_fl + 0080] S111 Odd]

 

 

(3.26)
where
6 — arctan( R ) (3 27)
1 _ d + t '
and
R
62 = arctan(-J) (3.28)

Essentially, this efficiency is the solid-angle coverage of the detector, minus some

loss due to gamma rays passing completely through the detector. Except for the sec-

59

Table 3.8: Ge crystal dimensions.

 

 

 

 

 

 

 

   
     
  
   

 

 

   

 

Dimension Measurement (mm)

Diameter 55.9 :1: 1

Crystal Length 52.7 :1: 1

Front of Endcap to Crystal 0.3 :i: 1

Source Holder to Endcap 746 d: 2
10,105 I I IIIIIII I llllllll 1 I IIIHII I I llllll] 2;:
1.0’ 0412;. ’3
JE- F 3
.3 ~ -1
E i 0’16 5— .5.
.9 : z
s : :
g i 0 102 E‘ “a
c E :
O : I
8 "' -4

3 . I
8 1.0 10 5' g
E 5 3
10’ 10° l5- 'gi
: 1
: | l l ' . : : : . 3 q’
I "I I I I I l I I I 41 I I I J_I_IJ I I l I I I I I I I I I I I I I
1.0 10
1.0100 1010‘ 1.0102 1.0103 1010‘

Photon Energy (keV)

Figure 3.21: Germanium X-ray mass-attenuation coefficient a from Ref. [52].

0nd part, it is basically a geometrical calculation based on the dimensions of the
detector and the distance to the source. For our energy range and setup, solid angle
was by far the most important contribution. For this geometric calculation we used
crystal dimensions from Table 3.8. The attenuation coefficients were taken from Ref-
erence [52]. The values from the reference were converted to units of cm‘1 using a Ge
density of p = 5.323 g/cm3 and are plotted in Figures 3.21 and 3.22. The values at
specific energies were linearly interpolated (See Table 3.9).

The calculated curve of total efficiency 6; of the Ge as a function of photon energy

60

 

20.0 llITITIIIIIIFIFIIIIIIIIIlllIITTTIIIIII—YITIIITIIIFIIII[IIIII

10.0

Attenuation Coefficient (chi

 

1

0 100.0 150.0 200.0 250.0 300.0 350.0
Photon Energy (keV)

V A
08IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIJLIIIIIIYIIIIIIIII
'0

 

 

 

Figure 3.22: Germanium X—ray mass attenuation coefficient p from Ref. [52], zoomed-
in on region relevent to the calculation

61

Table 3.9: Germanium X-ray mass attenuation coefficients.

 

 

 

 

 

 

 

 

 

 

 

Photon Energy (keV) Attenuation Coefficient p (cm‘r)
80 5.06
161 1.2318
223 0.81914
276 0.66968
303 0.59882
356 0.54264
384 0.51296
3 5 I I I I I I I r I I I I 1*
3 "" c 1 .—
.. l, 1
g; .11..
‘; 251— i.‘ _
o
c e:
.Q _ .. -
o \. u r,
E ‘r :1 4.
L“ l " ::
:3. 2 — l l .9
'9 :D
1.5— -
l I l L I I I l I l l I _L I
0 l 00 200 300 400 500 600 700
Gamma Energy (keV)

Figure 3.23: Total Efficiency curve for the Ge with the specific geometry of the offline
counting station.

for our specific detector geometry is shown in Figure 3.23. The systematic uncertainty
is due to the uncertainty in the crystal dimensions and source-crystal distance. The
contribution to the efficiency of the term containing the mass attenuation coefficient
is only on the order of 1%.

The peak efficiencies were determined experimentally by simply finding the back-

ground corrected counts in the various gamma peaks and comparing them to the

62

 

1e+0

I I Inn”1
11

I

mood

I I IIIIII]
I I IIIIIII

       
 

1000

I IIIIIIII
I I IIIIIII

Counts

 

 

100

 

I IrWIII]
I I IIILIII

 

10

I I TIIIIII

 

 

 

'l l
Gamma Energy (keV)

O

500

Figure 3.24: Gamma spectrum from the calibration source 133Ba.

calculated peak count based on the known activity of the source and the known
branchings.

The resulting summing corrections for the two 1338a calibration peaks were C7 =
1013521200015 and Cs 2 1.0091 21:0.0014. In other words, the summing is a 1% effect.
This level of effect is smaller than the effect due to the uncertainty in the calibration
source activity, which is a 5% effect.

Next, the summing-corrected peak efficiencies for the 133Ba calibration source were
used to interpolate to the peak efficiency of the 320keV 51Cr. The resulting 51Cr peak
efficiency is 0.0076 :l: 0.0004.

Using this efficiency, the activity of each 51Cr target was then calculated, and
the number of neutrons produced in the 51V(p, n)51Cr reaction was calculated using
equation 3.17. The number of neutrons detected was corrected for background using

the background neutron rate measured in a separate run. The background rate was

63

 

0.95—

0.? ~—

0.85-

0.8—

Peak Efficiency (%)

 

 

I

I I

 

 

G—O 13330 _
B—El Summing Corrected 133
O 510

 

 

 

l
300

350 400

Energy of Gamma peak (keV)

Figure 3.25: Interpolating the 320 keV peak efficiency of 51Cr

64

51v(p’ “)51 Cr

First Excited State in 5‘Cr

Ecm

n1

Ecm IIIIIIIIIIIIIIIIII

P “ 5'Cr + n

51V+p

s, of ”or 3.. 01520

 

 

52Cr

Figure 3.26: Diagram of the reaction 51V(p,n)5ICr.

determined to be 16.5i0.3 neutrons per second. The efficiency for neutron energies at
corresponding proton beam energies of 1.8, 2.14 and 2.27 MeV were then calculated
using equation 3.1. The resulting calculated efficiencies can be found in Table 3.10.

The energy of the neutrons produced was calculated as:

E5“ = S, + Eff“ — S" (3.29)

65

Table 3.10: NERO efficiencies for 51V runs.

 

 

 

 

 

 

 

 

Proton Energy (keV) Neutron Energy (MeV) Efficiency (%)
1.8 230 :l: 25 36.1 :1: 2.3
2.14 564 :l: 43 32.2 :1: 1.8
2.27 692 :l: 49 33.7 :1: 1.8
50—_f;I4 LI 2'; _I_IA “wk ~I I I I I III' I I I
§ s

_ \

 

45

 

 

 

 

 

 

 

 

g 40 —
5 MCNP \ I
.5 35‘ — Fit to MCNP 1
g - — - GEANT
m 30_ . 51V
_ o ”B
25_ I 13C ‘
@001 I l I I [116.10] I I I I IIIIlIl' I I I I IIIIJ]_ I I 4

0 1
Neutron Energy (MeV)

Figure 3.27: Experimental data from NERO efficiency calibration plotted with simu-
lations from MCNP and GEANT.

3.5 Summary of NERO Efficiency Calibration

A summary of the NERO efficiency calibration is shown in Figure 3.27. Figure 3.28
gives the MCNP and calibration results ring by ring. The MCNP calculation is sys—
tematically higher than the experimental values. A GEANT4 simulation of NERO
was carried out independently [53], and this simulation also resulted in a systemati-
cally higher efficiency curve. The cause of this difference is not clear. The fact that the

shift applies to all rings argues against a general deterioration of counter gas since all

66

 

 

 

 

 

 

 

 

40 l l l I I l I I' I I I I I I I II I I I I I I‘I II j I
— MCNP Ring 1
~ — MCNP Ring 2-
— MCNP Ring 3
30‘ 0 Data Ring 1
3 _ 0 Data Ring 2
°; 0 Data Ring 3
8 .. _
.9 1.11
.9 '-
E “ r 21' ‘
10— Pa
L 9 PF fl
(9.001 I l IllLl0.101 l llllull I 1[“1111 I II

0.1
Neutron Energy (MeV)

Figure 3.28: Experimental data from NERO efficiency calibration and MCNP calcu-
lations plotted by ring.

67

types of counters, which are of different types and come from various sources, would
have to be deteriorated in a similar way. The density of polyethylene used in the codes
is another possible source for the discrepency. However, the density of polyethylene
used in NERO was well—specified and this value was used in the simulation. The
energies of the neutrons to be studied in the experiment described in this work are
calculated to be within a range of 0.1-1 MeV. Since this energy range is covered by
direct measurements in the calibration, the extrapolation of the efficiency vs. energy
curve will not be critical to the analysis.

In order to provide a fit to the data, the calculated MCN P efficiency curve was

first fit with a second order polynomial. The resulting fit equation is:

Efficiency 2 0.1519(Energy)2 — 4.651(Energy) + 45.82 (3.30)

where the efficiency is in % and neutron energy is in MeV. The curve was then fit to
the data by X2 minimization allowing only the offset to vary. Using this method, an

offset of -8.85895 :E 1.2 was determined, resulting in a final fit curve of:

Efficiency = 0.1519(Ene'rgy)2 —— 4.651(Energy) + 36.96 (3.31)

The uncertainty in the offset is the 10 error determined by finding the offset for
xgeduced + 1. Figure 3.29 shows the calibration again with the shifted calculations

curve.

68

 

 

 

 

 

 

 

 

 

40 I I IIIIIII I I VIIIITI I I IIIIIII I I I
35 —- —
A 30 — ._
Q
s _ 4»
>3 ..
O
c: 25 — , _1
.92. — MCNP Shifted
LE) I' . 51 "
“L13 V
20 — . 11B
- . 13C
15 l_ 252Cf _.
I I I IIIILI I I LJIIIIL I I I IIIIII I I I
1
(9.001 0.01 0.1 1
Neutron Energy (MeV)

Figure 3.29: Experimental data from NERO efficiency calibration plotted with shifted
MCNP calculated curve.

69

Chapter 4

Experiment

4.1 Introduction

The experiment to measure the half-lives and neutron emission probabilities of neutron-
rich isotOpes around 78Ni was run at the Coupled Cyclotron Facility (CCF) of the
National Superconducting Cyclotron Laboratory (NSCL) at Michigan State Univer-

sity, as NSCL experiment number 02028.

4.2 Experimental Setup

4.2.1 Fragment Production

The neutron rich isotopes were produced in the following manner. 86Kr was ac-
celerated in the K500 Cyclotron at the Coupled Cyclotron Facility (CCF) at the
National Superconduction Cyclotron Laboratory (NSCL). After the K500, the 86Kr
beam passed through a thin stripper foil, and then was injected into the larger K1200
Cyclotron and accelerated to approximately 140 MeV/ u. After extraction from the
K1200 Cyclotron, the beam struck a thin Be production target of thickness 376
mg/cmz, producing a secondary beam composed of a mix of neutron-rich isotopes

via fast fragmentation. The average primary beam intensity was 15 pnA.

70

13i

it s: ..

. ,. , I 4

ti .
J [1’ .. .4

I" 7 , 34‘5”]

fl ‘ .3 (Iris-id}; I "v- 2 iv

I .w ‘3' L 4

Figure 4.1: The coupled cyclotrons and the A1900 fragment separator.

4.2.2 Fragment Separation and Identification

The secondary beam of mixed fragments was then directed through the A1900 frag-
ment separator. The A1900 fragment seperator is a series of 4 dipole magnets whose
magnetic rigidity is set to allow to pass only the fragments of interest [54]. During
the 78Ni production runs, the A1900 was operating with full momentum acceptance.
A position sensitve plastic scintillator at the dispersive intermediate focus was used
to determine the momentum of each beam particle at typical rates of 105/3. A 100.9
mg/cm2 achromatic Al equivalent degrader was placed at the intermediate image
to clean the beam and increase transmission. The A1900 was first set to the 72Ni
secondary beam setting (Bp12=4.0611, Bp34=3.9509). Each nucleus in the secondary
beam was individually identified in flight at the A1900 focal plane by energy-loss
and time-of-flight measurements, in conjunction with the momentum measurement
in the scintillator at the A1900 intermediate focus. The time of flight was measured
using two plastic scintillators as start and stop. One of these scintillators was the
scintillator at the intermediate image of the A1900 which was also used for momen-
tum measuremnts, and the second scintillator was located at the focal plane of the
A1900. In addition, isomers of 70Ni were identified by a Ge detector at the focal plane,

confirming the particle identification there.

71

Intermediate
Image Plane

  
 
  

Production

   

... ‘
l
‘4
,.
:1-10
1.1:.
I 1

. .5; ..
) --.r~to_".=_.~~, "n ’1; .
lxtil c Inn . - .. ~.-
5. « - "- .
. .13, 5:,
hm m
{2:327
was»

Figure 4.2: The A1900 fragment separator.

Next the particle identification had to be passed on to the detectors in the exper-
imental vault. Degraded primary beam was sent first to the A1900 focal plane. Then
the detectors at the focal plane of the A1900 were removed from the beamline and the
degraded primary beam was sent to the experimental vault where the first energy-loss
detector in the experimental vault (referred to as Pinl) was roughly calibrated to the
A1900 energy loss detector. This, in conjunction with a time of flight measurement
using the scintillator in the A1900 intermediate focus and a scintillator in the exper-
imental vault, a separation of about 40 m, brings the particle identification to the

vault.

4.2.3 Isomer Identification with SeGA

In order to further verify the particle identification in the experimental vault, the
Segmented Germanium Array (SeGA) at the N SCL [55], an array of 32-fold segmented
Ge detectors, was used to identify 7—peaks from known isomers of the implanted nuclei.
This confirmation exploits the fact that several isotopes in this region are known to

have microsecond isomers. Because of the relatively long lifetimes of these states, the

72

 

 

  

 

SRF CLEAN ROOM
cavocemc PLANT/

/ ,

 

Figure 4.3: Floorplan of the NSCL.

isotopes can reach the experimental vault before they have decayed out of these states.
The gammas from these decays can therefore be used in the experimental vault to
identify some isotopes independent of energy-loss/time—of—flight. These isotopes can
be used to confirm the energy—loss/time—of—flight identification.

For the isomer identification, a variable degrader in the vault upstream from the
final 6 counting/ NERO station was used as a separate implantation target station.
SeGA was arranged around the degrader station in the “betaSeGA” configuration: 12
detectors at a distance of 8.5 cm from the target (see Figure 4.4.) When being used
for this purpose, the variable thickness degrader was adjusted so that the isotopes to
be identified would be fully stopped within the degrader. The electronics allowed for
triggering on SeGA for purposes of calibration. The resolution of SeGA was checked
prior to the isomer identification by placing a calibration “SRM” mixed gamma source
near the detectors and running with the SeGA trigger. SeGA was then calibrated with
a 56C0 source as well as with the SRM source placed in the beamline on the degrader
mount.

The microsecond isomer verification was done at the 72Ni setting of the A1900.
Isomers of 70Ni, and 72Cu were used [56] (See Table 4.1). In this energy range, the
betaSeGA configuration has an efficiency of 14.4% (at 100 keV) to 5.3% (at 1 MeV)

(see http: / / www.nscl.msu.edu / tech / devices / gammarayspectrometer/sld.pdf). The

73

 

Figure 4.4: SeGA arranged in the “betaSeGA” configuration around the variable
degrader, upstream from the BCS—NERO station.

74

Table 4.1: 7 lines used to verify the particle ID.

 

Isotope with psecond isomer
70Ni
72Cu

7 energy (keV)
183,448,970,1259
138

 

 

 

 

 

Table 4.2: Bp setting used.

 

 

 

Centered Fragment B p12 B p34
”Ni 4.06110 3.95090
73Ni 4.11870 4.00860
7" Ni 4.17550 4.06540
75Ni 4.23150 4.12140
76Ni 4.28850 4.17850
77Ni 4.34300 4.23290
78Ni 4.40140 4.29140

 

 

 

 

online particle identification by energy loss and time of flight in the experimental
vault is shown in Figure 4.5. The isotopes 70Ni and 72Cu were identified by calibra-
tion with the A1900 energy-loss detector. Figures 4.6 and 4.7 show the gamma spectra
gated on the isotopes 70Ni and 72Cu respectively as identified in the particle identifi-
caton by calibration with the A1900. The gamma rays associated with the respective

isomeric states are clearly visible, thus confirming the particle identification.

4.2.4 Scaling Bp to the 78Ni setting.

Following the isomer verification of the particle identification at the 72Ni setting, the
fragment separator setting was stepped out to the 78Ni setting using the Bp scaling
technique. The settings were confirmed through the 75Ni setting by scanning Bp for

production rate. Table 4.2 shows the Bp values for each isotope setting.

4.2.5 Implantation

Once at the appropriate fragment setting, the variable degrader in the experimental
vault was adjusted to allow the particles to pass through to the BCS-NERO station.

The degrader then served to modify the secondary beam energy to achieve implan-

75

 

600 - —

550 -

A
01
O

 

 

 

A
O
O
7

l l l l l l l l l l

400 420 440 460 480 500 520 540 560 580

Time of Flight (Arbitrary Units)

Figure 4.5: Online particle identification by AE—TOF using the experimental vault
energy-loss detector.

 

Energy Loss (Arbitrary Units)

76

 

16 I, i i I l I i I I

14i- —

10— ,/ a
6— ] / —

w l
4'— :‘, l

 

 

 

Counts
\

  
  

 

 

 

   

l
] .

u _
2 l I - . .
0 111011 111 | I l

200 400 600 800 10001200140016001800

Energy (keV)

Figure 4.6: Gamma spectrum from 7oNi PID gate showing the 183, 448, 970, and 1259
keV gammas associated with 70mNi.

 

 

 

 

77

40 /

 

35- .1
30- —
25- 4

Counts

 

l

l 1

1 k1 ‘ IMIIIW“ 1W llliil llllilllllllll . II l 1. .1

0 200 400 600 800 1000 1200 1400

 

 

 

 

Energy (keV)

Figure 4.7: Gamma spectrum from 72Cu PID gate showing the 138 keV gamma asso-
ciated with 721““Cu.

78

tation in the implantation detectors. Coarse thickness adjustments were made by
adding thin pieces of Al in a stack. The degrader was mounted on a rod that could
be rotated manually from a handle external to the beamline, so that fine adjustments
to the thickness could be made without requiring to break the vacuum of the line.
After the degrader, the beam encountered another Si detector, refered to as Pin2, for
a second energy-loss measurement, and finally passed through a third Si detector, ref-
ered to as Pin2a, which was part of the Beta Counting System described in the next
section, before finally implanting in the Double-Sided Silicon-strip Detector (DSSD)

of the Beta Counting System. (See Figure 4.9).

4.2.6 Beta Counting System

The Beta Counting System (BCS) [57] consists of a 985 pm double-sided segmented Si
detector in which the beam was implanted. On one side the forty 1mm wide segments
run horizontally, and on the other side forty vertically, resulting in a pixelation of
1600 pixels in a 4 cm x 4 cm area, giving the location of implantation. The beam
was continuously implanted into the DSSD, which registered the time and position
of each ion. The typical total implantation rate for the entire detector was under 0.1
per second.

Using the dual-gain capabilities of the BCS electronics, the DSSD also registered
the time and position of any fl—decays following the implantation of a nucleus. This
allowed the correlation of a decay event with a previously identified implanted nucleus.
Additional Si detectors in front and behind the DSSD were used to veto events from
light particles in the secondary beam that can be similar to fi-decay events. With
this setup, along with appropriate veto gates, the total ,B-type event background rate
associated with an implanted ion was typically less than 3 x 10‘2/s. From the time
differences between implants and a correlated decays, a decay curve could be built
and half-lives could be deduced. The Si detectors of the BCS were calibrated before

and after the experiment with a 90Sr fl-source and a 228Th a-source.

79

     
  

Degrader

 

 

Si detector
(AE)

Figure 4.8: Schematic of beta endstation inside NERO.

PINI Degrader PIN2 PIN2A DSSD SSSDl-b PIN3 PIN4

__. T I, 17-17-? __

         
        

Beam
Direction

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L I_

4741"" 488nm 966nm 985nm 5900um 993nm 998nm

 

__ 1_..__.__.L_

 

Figure 4.9: Beamline detector setup in the experimental vault.

80

 

Figure 4.10: The DSSD.

 

Figure 4.11: The DSSD case inside the bottom half of NERO. SEGA detectors in the
background. View is looking up the beam axis.

81

 

Figure 4.12: View of the experimental vault, looking up the beamline. SeGA is in the
background. In the foreground is the BCS leading into the bottom half of NERO.

82

4.2.7 NERO

NERO was arranged around the BCS so that the DSSD of the BCS was at the
target position of NERO. If the beta-decay resulted in the emission of a neutron, the
neutron could pass into NERO, where it would be moderated and detected in the
proportional tubes. The electronics of the BCS were fed out the down-beam end of
the NERO beamline hole.

NERO was triggered on any event in the DSSD high-gain side. When a high-gain
(decay) event occured, the NERO gate was opened for 200 as. The energy from the
proportional counters was recorded. In addition, the time of the neutron event was
recorded by a V767 VME TDC which was added to the NERO electronics for this
experiment. The TDC could record multiple neutron events occuring within the 200

as neutron gate.

4.2.8 Electronics

Figure 4.13 shows a diagram of the electronics for the experiment. The DSSD pro—
vided the master trigger; however, alternate master triggers were available for other
detectors, such as NERO and SEGA in case they were needed. The master trigger
was any implant or decay event. The master live trigger was the AND of the master
trigger and the computer NOT busy according to standard trigger configuration. The
master trigger opened the neutron gate for the NERO electronics with a gate in latch

mode for 200 as.

83

PPAC

N3Sci.

IMIN Sci

IMZS Sci

Pin2a2 -4

Pinl
Pin 111

88801 -6

DSSD
Alternative triggers MG

 

Hi

Master Gate Live
New
time
TDC VME out
NERO

MChero
MGLive 11cm

Figure 4.13: Electronics diagram for NSCL Experiment 02028.

84

Chapter 5

Analysis

5.1 Particle Identificaton

As stated in the Experimental Chapter, the isotopes were identified in-flight by
energy-loss, time-of-flight and momentum measurements. The energy loss, when ve-
locity corrected using the time-of-flight measurements, gives elemental seperation.
For a given element, a time—of-flight measurement, when momentum corrected, gives

isotopic seperation.

5. 1.1 Energy Loss

The energy loss was measured in two Si detectors located in the experimental vault
and seperated by a passive Al degrader. The energy loss of a projectile in a material
is proportional to the square of the nuclear charge of the projectile and inversely
pr0pertional to the square of the velocity. The relationship is given by the Bethe

formula [34]:
dB 47re4Z2

“a; = WNAPBW) (5-1)

which in terms of Z is:

 

 

dE m va
Z = —— ° .
\/ dx 47re4NApB(v) (5 2)

85

where

 

— g) — — (5.3)

v and Z are the velocity and atomic number of the projectile, p, A and z are the mass
density, atomic weight, and atomic number of the absorber, in this case Si. mo and e
are electron mass and charge. N A is Avagadro’s number. I is the average excitation
and ionization of the absorber. For a given velocity then, the energy loss uniquely

defines the atomic number, or element, of a particle.

Time-of-flight Correction to Energy Loss

The projectiles in the experiment arrive at the energy loss detectors with a velocity
distribution. To distinguish them, it is necessary to remove the velocity dependence.
One can remove this dependence by measuring the time of flight of each particle. The
velocity is given simply by:

D
t

’v:

(5.4)

Since the distance D, a particle’s path length through the beamline, is essentially the
same for all particles, a measure of the time of flight is a measure of the velocity, and
the energy loss can be corrected using time of flight. The energy loss vs time of flight
with the energy loss uncorrected is shown in Figure 5.1. The same plot with energy
loss corrected is shown in Figure 5.2. The values used for this correction can be found
in Table 5.1.

In this experiment, two energy-loss detectors were used. The full Bethe energy-
loss correction was performed only on the first energy-loss detector, and confirms
the elemental identification. However, for the analysis, a simple linear correction as a
function of time-of-flight was performed for both energy-loss detectors and used for

the remainder of the analysis. The general equation used was:

dECORRECTED = dERAW — [(114 X TOF) + B] + Y (5.5)

86

Table 5.1: Values Used in Bethe Energy Loss Correction

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 1r e4 N A / mo 0.30707 MeV cm2 / mole
m, 0.511003 MeV/c2
0 2.9979 x 103 m/s
A 28.086 g/mole
Z 14
p 2.3212 g/cm3
I 0.000173 MeV
L 37.3 In
dx 0.0474 cm
73‘ 600 I
g
'5 a
3,
—4 500*- ’ d
.5
Q4
3
i? am...

600
Time of Flight (Arbitrary Units)

Figure 5.1: Uncorrected energy loss vs. time of flight.

(no:
02190:

:1:

Atomic Number (Z)
8 l0 8 (D

 

25

600
Time of Flight (Arbitrary Units)

Figure 5.2: Bethe corrected energy loss vs. time of flight.

87

Table 5.2: Correction Factors for Linear Energy-loss Correction

Pinl Pin2
-0.3682 -1.4125
686.93 1575.2

480 480

 

 

 

 

 

<01:

 

 

 

 

 

at
8

i.

a
8

 

Energy Loss Pin2 (Arbitrary Units)
‘8‘

 

 

P I I l I

300 400 500 600 700
Energy Loss Pinl (Arbitrary Units)

 

Figure 5.3: Element identification using energy loss in Pinl vs. Pin2.

where M is the slope, B is the intercept, and Y is another arbitrary offset used for

convenience. The values used for the correction as shown in Figure 5.3 can be found

in Table 5.2.

5.1.2 Time of Flight

In order to separate individual isotopes from the element distributions, one requires
essentially a measurement of the mass of the particle. A time-of-flight measurement
affords such a mass measurement because the time of flight of the projectile is pro-

portional to the mass of the projectile. In the non-relativistic limit,

U

D m
=—=—— 5.6
£2 p ( )

88

In the experiment, the momentum p is not directly measured but the magnet settings
and slits of the fragment separator define a Bp = ‘3, so that

mD
t—

- 5;; (5.7)

For a time of flight gated on an element using the two energy losses as described in

Section5.1.1 (thereby specifying a q), the time of flight uniquely defines a mass.

5.1.3 Momentum Correction to Time of Flight

However, the particles actually have a distribution in Bp due to the 5% momentum
acceptance of the A1900. Therefore, to distinguish masses, it is still necessary to
corrrect for the Bp distribution. This correction to the time of flight was assumed to
be linear. That this assumption is valid is demonstrated by [the following.

The measured position in the intermediate image is prOportional to Bp = 5, or
for a given particle with charge q, proportional to the momentum p (the following

assumes non—relativistic limit):

 

 

 

 

 

:1: or Ap (5.8)
x 2 GA}? (5.9)
17 = G020 — p) (5-10)
:1: = Gpo — va (5.11)

so that

Gpo —— a:
v — mG (5.12)
since
'1) = g (5.13)
t = map = mGD 1 = m0 1 (5.14)
Gpo—a: Gpo—a: pa 1— 0:5,,

89

SO

 

 

 

mD :1: mD mD
t: 1+ =

+... +—-——:1:+... =M23+B+... 5.15
pa GPO pa 01202 ( )

taking the first two terms demonstates the linear correction to the time of flight to
first order.

Therefore, in a plot of momentum-corrected time of flight vs. intermediate image
position, the isotopes of a given element appear as seperated horizontal lines.

In summary, the elements were selected by a gate in the time-of-flight corrected
two—dimensional energy—loss plot. These element gates were then applied to a position-
corrected time—of—flight vs. momentum plot, where the isotopes were then identified.
In addition, reasonable cuts to exclude events at large A1900 intermediate image
(1M2) positions were made. A particle identification plot is shown in Figure 5.5 to
give an idea of the relative statistics. However, this plot was not directly used for
isotope identification, as described above. Based on the identification, a total of 11

78Ni were identified.

5.1.4 Possible Contaminants

As can be seen in the Pinl Energy Loss vs. Pin2 Energy Loss (Figure 5.6), there are
some particles in the identification which do not lie within an elemental distribution.
These particles were gated on and analysed in the same manner as the identified
particles. Their half-lives were determined and compared to the identified elements,
and the results are most consistent with with the hypothesis that these are not charge
states, but particles which encountered an additional energy loss consistent with a
piece of material of thickness 525 :1: 25pm Al equivalent in the beamline. In order to
achieve the corresponding lengthening flight time that would be consistent with their
measured time of flight, this material would have to be located somewhere after the
focal plane of the A1900 but before the experimental vault. A study of the beamline

does not indicate that there should have been any known material in this section

90

 

[10] PIDJZNTOFNSJZPOS'ZN

 

 

 

 

 

[20] PID.TOFN.VS.IZPOS!ZN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

one a - aoo a —
soo~ - soo- , e
I F I I T _I T I
700 750 800 350 700 750 m ”0
[U] PIDJZNTOFNSJZPCBICU [1.] PID.TOFN.VS.INDU
l l l l l I l I
000 ~ — coo .. -
500 —‘ *— 500 “l .. v *"'
I I I I l I l I
700 750 000 8m TN 750 m .50
[9] PIDJZNTOFNSJZPOSWI [19] PID.TC*N.VS.|2POSINI
l A l l l J l I
000 — _. : - coo —l —
V, .' L‘Q} .
' was. « .
m ——4 >— m —4 " . .. “If-L :1 3' 37?. >—
'.;\ty;.?‘¢f:\\.~.o‘° 3:”: .- ..

 

 

 

 

 

 

 

 

 

 

Figure 5.4: Time of flight vs. intermediate image position for Zn, Cu, and Ni isotOpes.
The first column is uncorrected. The second column is momentum corrected.

91

 

 

 

 

550‘ ‘ A:
'3
.9.
gsom
G
”4501-
78
Nl
400

 

Time of Flight [a.u]

Figure 5.5: Energy loss vs. Time of flight for a portion of the data.

 

Energy Loss Pin2 (Arbitrary Units)

 

 

 

I

420440460480500520540560580
Energy Loss Pinl (Arbitrary Units)

 

Figure 5.6: Energy Loss in Pinl vs Pin2 showing the conservative element gates. The
arrows indicate the unidentified particle distributions

of the beamline during the experiment. In addition, these particles do not exibit any
abnormal position distribution or angle distribution, as one would expect for particles
that might encounter different thicknesses of material along the beamline. Therefore
the origin of these particles is still unclear. The element gates were therefore drawn
conservatively in such a way as to avoid possible contamination from these particles

(see Figures 5.6 and 5.7).

92

 

70 *- NI -

60*- ‘

Counts

20* -:

 

 

10— ~

 

 

I I I I

o 1750 1800 1850 1900 1950 2000 2050
Energy Loss Pin 1 (Arbitrary Units)

Figure 5.7: Energy Loss in Pinl showing the Ni distribution on the left and the
unidentified particle distribution on the right. The line indicates the position of the
Ni element gate.

5.2 Production Cross-section

With a particle identification, one can calculate a production cross-section. The pro-
duction cross-section of 78Ni is of particular interest. It has been calculated and tested
at several laboratories and serves as a marker for the capabilities of next generation
accelerators.

The production cross section was calculated based on the equation:

 

(5.16)

where N is the number of target nuclei shown to the beam per unit area, In is the
incident beam rate, and Rb is the rate of outgoing particles. The rate of outgoing
particles of 78Ni was 11 over a beam time of about 104 hours. Our target was 376
mg/cm2 Be. Using the atomic mass of Be, and Avagodro,s number, we convert this

to target nuclei per unit area. BaF2 detectors were placed at the production target

93

to measure the incident beam rate, Ia. However, the voltage was set so that the rate
resulted in overflow in the detectors, so that the BaF2 detectors were not helpful.
Fortunately, the beam current was also measured with a Faraday cup before and/ or
after most runs. The current during a run was taken to be the average of the current
before and after the run. For runs for which no current measurement was taken, the
current was taken to be the average of the run before and after. The uncertainty in
the Faraday cup measurement is known to be on the order of a few enA.

The final factor in the cross section is the transmission of the beam from the
production location before the A1900 to the detection location in the experimental
vault. The transmission was studied using the code MOCADI [58] as well as through
several measurements.

The transmission through the A1900 depends on the angular and momentum
acceptance. The angular acceptance was calculated to be 80-90 % so a value of 85 :l:
5 % was adopted. The reduction in efficiency due to limited momentum acceptance
depends on the momentum distribution of the beam, and the results of calculations
based on some of these distributions range from 90 to 100 %. A value of 95 i 5 %
was adopted.

The transmission to the N3 vault was measured for several isotopes on different
Bp settings. For 72Ni, the FP-N3 transission was measured with the aid of BaF2
detectors to be 84 :l: 12 %. It must be assumed that the transmission of 78Ni on the
78Ni setting does not deviate within 12 % of the 72Ni setting.

Combining these contributions based on both measurement and simulation, the
adopted value for transmission was 65 :l: 13 %.

The resulting cross section for the production of 78Ni was 0.02(1) pb, much smaller
than the value calculated by EPAX [59] of about 4 pb. The largest uncertainty comes
from the statistical uncertainty due to the extremely low 78N i count. The uncertainty

in the transmission is the next largest contribution to the total error budget.

94

[178] FRONTZHIENERGYD3

 

 

 

 

 

 

105 I f f I I3
10‘ g
:9 .
g 103 » “=
o 3
U

102 - ‘2
, I
10‘ -]

1 I l ! lllll l I
0 100 200 300 400 500

Uncalibrated Energy

Figure 5.8: 228Th calibration source spectrum in a typical DSSD high-gain channel.

5.3 Gain-matching

The high gain of the DSSD strips were gain-matched before and after the experiment
using the alpha source 228Th, which displays several peaks of known energy. The
source was placed in front of the DSSD. See Figure 5.8. The low gains were not gain-

matched. The SSSDs were gain-matched in the same way as the high-gain DSSD.

5.4 Thresholds

The high-gain thresholds for the DSSD were set using the B emitter 90Sr. A typical
threshold setting is shown in Figure 5.9

Upper level thresholds were not used. The SSSD thresholds were set as with the
high-gain DSSD.

95

[138] FRONT.HIECAL.03

 

 

 

  

20° ’ Threshold I I i ‘
.5. . H l
‘3
8 100 — ~
50 F ‘
0 0 20 40 60 80“ 100

 

 

 

Uncalibrated Energy

Figure 5.9: 90Sr calibration source spectrum for setting threshold in a typical DSSD
high-gain channel.

5.5 Absolute Calibration of DSSD

An absolute calibration of the high-gain DSSD energy was done. Though it was not
necessary for the analysis of the present experiment, it is useful for the purpose of
comparing the threshold settings to other experiments which make use of the DSSD.
The calibration was based on the energy of the peaks in the 228Th a spectrum. The

settings can be found in Figures 5.10 and 5.11.

5.6 Correlations

An implant event in the DSSD was essentially defined as a low-gain (high-energy)
signal. The actual implant criteria are in Table 5.3. The position of the implant was
taken to be the pixel in which the maximum energy was deposited. A decay event
was essentially defined as a high-gain event which did not also trigger the other Si
detectors in a specific way so as to be vetoed as a punch-through or other type of

event.

96

Threshold (keV)

 

 

 

 

180 I I I I r I I
L
160
140 —
120 —
100 r
l I l l l l L
10 20 30
Front Strip Number

Figure 5.10: Threshold settings for DSSD front high-gain strips.

97

Thresholds (keV)

 

 

 

 

 

180 f I l l I I I
160 -

140 —

120

100 -

r I . J 1 J i
10 20 30
Back Strip Number

Figure 5.11: Threshold settings for DSSD back high-gain strips.

98

Table 5.3: Implant Criteria

Required logical AND of the following
Hit Pinl
Hit DSSD Front
Hit DSSD Back
NOT Hit SSSDl

 

 

 

 

 

 

 

 

Table 5.4: Decay Criteria

 

Required logical AND of the following
NOT Hit Pinl
NOT Hit Pin2
DSSD Front High Gain Signal
DSSD Back High Gain Signal
NOT a Punch Through
Hit SSSDI OR SSSD2 OR Pin3 OR Pin4

 

 

 

 

 

 

 

 

 

If a decay event fired more than one strip, the position of a decay was taken to
be the strip with maximum energy deposited. A decay was correlated to an implant
if the position of the decay was at the pixel of an implant or within one pixel away.
If the decay event fired more than one strip, the maximum strip was required to be
within one pixel away. The decay also had to come within a specified correlation time
window, which is chosen based on the expected lifetime of the isotopes being studied.
Up to three decays could be correlated to a given implant.

For each decay correlated to an implant, the time difference between implant and
decay was found by simply comparing the times of the two events. This produces
a list of decay times associated with a previously identified isotope, each implant
having a decay chain of up to three decays associated with it. Of the 11 78Ni events
identified, 8 had at least one decay associated with it. Table 5.5 shows the 8 decay

chains associated with78Ni.

99

Table 5.5: Decay Chains for 78Ni

 

 

 

 

 

 

 

 

 

Chain Decay Time 1 (s) Decay Time 2 (s) Decay Time 3 (s)
1 0.328 3.322 0
2 0.749 0 0
3 0.120 1.740 2.280
4 0.884 1.555 0
5 0.031 0 0
6 0.391 0 0
7 0.049 0 0
8 0.804 0 0

 

 

 

 

 

 

5.7 Curve Fitting

For the isotopes with high statistics, it was possible to bin the decay times to form a
decay curve. This is a common analysis of decay data in the case of high statistics.
For this method to be valid, the minimum number of counts in a bin must be around
5 (see Ref. [60], p266). This was done for the isotopes of highest statistics. The decay
times were binned and fit to a curve which included terms for parent, daughter,
granddaughter, and background contributions. The equations used are known as the

Bateman equations (Ref. [46]):

A, = Nchie_’\“ (5.17)
i=1

where A, is the activity of the nth member of the decay chain, No is the initial number
of parent nuclei, A,- is the decay constant of the ith member of the decay chain, and

the coefficients are:

fit-
i=1

fi’()\i _ Am)
i=1

where HI indicates for all z' 54$ m. In this case, three generations (parent, daughter,

 

cm (5.18)

granddaughter) were assumed.

The free parameters were the scaling factor and the parent decay constant. Re-

100

    

i" " 1:. l
I |u

immiilllllllilml'lml

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time (s) Time (s)

Figure 5.12: Decay-curve fits for the high—statistics cases of 75‘76Ni, 77’780u and 78‘79Zn.
The linear background is not shown.

101

quired known inputs were daughter and granddaughter half-lives. The background
was assumed to be constant as a function of time and was allowed to vary as a

parameter in the fitting

5.7 .1 fl-detection Efficiency from Curve Fits

Using the curve fits, the DSSD efficiency for detection of decays was determined in the
following way. The number of implants is known simply from counting implant events
in the DSSD. The fit for that isotOpe is then used to identify the number of parent
decays detected. The efficiency is the number of parent decays detected divided by

the number of parent implants observed:

parent

N
6,, = 100 x IV, (5.19)

 

where N, is the number of implants and N grant is the number of parent decays,
calculated from the fit parameters (A0)” and Am, the fitted decay constant of the
parent:

Ngurent = (311; (5.20)

Am
The efficiencies derived in this way are shown in Figure 5.13. For 75Ni, 76Ni,77Cu and
78On the statistics were sufficient to determine the fi-detection efficiency by comparing
fitted decay curves with the total number of implanted species of that isotope. The
resulting efficiencies agree very well and range from 40% to 43% with no systematic

trends in the deviation. (see Table 5.6).

5.8 A Method of Maxiumum Likelihood

In the case of low statistics, it is not possible to bin the data and then analyze a decay
curve by the method of curve fitting. However a method does exist that is correct

even in the case of low statistics. This method has been used previously to extract

102

 

50 I I I I I I I j T I I I I

G—O Ni Isotopes
[El—El Cu Isotopes
0—0 Zn Isotopes

 

 

 

 

Efficiency(%)
assesses
I'I'I'III'I'III‘W'I'I‘ITI'I'

LllllllllllllllllllllllllllLl

b3
0‘

 

 

I—-
I—
_
h
—
I—
I=:—-
_
h: .
h
.—

DJ
“U1
.5
\I
LII

 

76 77 78 79
Mass Number (A)

00
O
on
7.—

Figure 5.13: Beta detection efficiency based on fitting of decay curves for isotopes
with more than 500 implants.

103

Table 5.6: fi-detection Efficiencies for High-Statistics Cases

Isotop Efficiency (%)
WM 41.3 a: 1.2
76Ni 42.7 i 1
77011 42.95 :t 0.34
78Cu 40.71 :t 0.36
79Cu 41.2 :t 1.1
792m 42.2 a: 0.8
"W’zn 41.2 i 0.4

 

 

 

 

 

 

 

 

 

 

 

 

beta-decay half-lives, even with as low as 6 or 7 events [61-63].

The method, which will be refered to as Maximum Likelihood Method (MLH), is
the basis of most common fitting analysis etc, even the curve fitting described above.
However, the analysis used here might be described as more of a direct MLH method,
in that it avoids the necessity of binning the data and thereby losing time information
as well as sequential decay-chain information. This direct method will be referred to
in the following simply as the MLH method, although it should be remembered that

the idea of maximum likelihood is common in error analysis and fitting.

5.8.1 Probability Density Functions

The method finds the decay constant that maximizes a likelihood function, which is
the product of probability densities for three decay generations as well as background
events, to produce the measured time sequence of decay-type events following the im-
plantation of a beam particle. The calculation requires knowledge of the fi-detection
efficiency, background rate, daughter and granddaughter half-lives, including those
reached by fl-delayed neutron emission, and branchings for fl-delayed neutron emis-
sion (Pn) for all relevant nuclei in the decay chain.

The probability functions from which the likelihood function is constructed rep-
resent the probabilities for a given number of decay events to occur and be observed
at specific times t. (The following description is based on Ref [64]).

The probability density function for one decay governed by a decay constant A1

104

to occur at the exact time t is:
f1(A1, t) = Ale—Alt (5.21)
The probability for a decay to occur within a time t is:
t
F1 =/ f1(A1,t’)dt’ = 1 — eflxlt (5.22)
0

The probability density function for a daughter with decay constant A2, which was

populated by a mother with decay constant A1, to decay at exactly time t is:

A A
f2()\1, Amt) = S-z—L—iqfiz‘m — ea") (5.23)

The probability for a decay within a time t of a daughter with decay constant A2

populated by a mother with decay constant A1 is:

A A 1 1
1 2 —e"\“ — —e_)‘2‘) (5.24)

F A A t=l——
2(1129) Ag—A1(A1 A2

The probability function for the granddauther decay with decay constant A3 is:
f3()\1, A2, 43, t) = K123[(/\3 — A2)?“ - (A3 - A1)e_)‘2t+ (A2 — Ade—Mt] (5.25)

where
A1A2A3
(42 — A1)(/\3 - A093 — A2)

 

K123 1‘ (5.26)

The probability for the granddaughter decay to occur within a time t is:

(43 — A0841: _ (43 — A1)e—,\2t + (42 — A1)

F /\ =1—
3( 1,A2,A3at) K123[ )‘1 A2 A3

e-W] (5.27)

Using Poisson statistics, the probability for observing exactly 7‘ background events

105

within a time window to, given an average background rate of b is

__ (btc)"e‘btc

Br
7'!

(5.28)

5.8.2 Probability Function for Observation of No Decays

To this point we have talked only about the probability for real decay events to occur.
For the MLH analysis, we need expressions concerning the probability for decay events
to be detected. As an example, here is how the probability for no events to be detected
is built up. Take D,- to be the probability that an ith generation decay occurs, 0,- the
probability that it is observed, and e,- the detection efficiency for the ith generation

decay. In addition, is = 1 — a: for all variables.
P0 = (D1 + 01011—22 + D101D202D3 + D101D2020303) X Bo (5.29)

where B0 is the probability for exacty 0 background decays observed within the
observation window according to Equation 5.28. The four terms in Equation 5.29
correspond to the four possible ways of observing no decays, assuming three decay
generations are possible: 1) the parent does not decay, 2) the parent decays but is not
observed and the daughter does not decay, 3) the parent decays but is not observed,
the daughter decays but is not observed, and the granddaughter does not decay, and
4) the parent, daughter, and granddaughter all decay, but none are observed. After
some arithmetic, this situation is expressible using the above probability functions

and the detection efficiencies as:

P0(A1, A2, A3, t) = [1—F1(A1, t)€1—F2(A1, A2, t)€1€2—F3(A1, A2, A3, ”6162631 X Bo (5.30)

106

Obtaining Background Rates from No—Decay Probability Function

If the decay efficiencies and decay constants are known, one can use the expression
for P0 to calculate the average background rate from the number of events where no
decays were observed, relative to the number of events where at least one decay event
was observed. If No is the number of events were no decays were observed, and N123

is the number of events with 1, 2 or 3 correlated decays, then based on the definition

Of P0:
N0 _ P0
N123 1 — P0

 

 

(5.31)

In the experiment, both No and N123 were measured. N0 is simply the number of
implant events to which no decay events are correlated, and N123 is the number of
implant events to which at least one decay event is correlated. From Eqn. 5.28 with

r=0, the average background rate b is:

 

b = 71:13” (5.32)
where B0 is calculated from Eqns. 5.30 and 5.31:
BO 2 —1Y9-—— X (1 — F1E1— F2€1€2 — F3€1€263)_1 (5.33)
N0 + N123

The average background rate was calculated for the high-statistics cases in Ni, Cu,
and Zn, assuming the literature values of the decay constant. The results are shown
in Figure 5.15. The results are consistent with the background rates derived by other
methods such as from the curve fits. For the case of 75Ni, the background rate derived
by this method is larger than that derived by the “blocking window” method as

described later, but is consistent with the background derived from curve-fitting.

107

5.8.3 Probability Functions for the Observation of at Least

One Decay

The probabilities for detecting one, two, and three decays can be constructed in a
similar way to P0. These terms are quite long and will not be given here. Using
arguments similar to those used for finding Po, one finds the probability density

functions p, for i decays being observed.

5.8.4 The Likelihood Function
The likelihood function is the product of the probability density function for every
event with one (nizl), two (n,=2), or three (n,=3) decays:

N123
£12391) = [105(7), —— 1)p1 + 5(7)... — 2))?2 + 5(n. — 3)p3) (5.34)

where the product is over all events with one, two, or three decays, and 6(x)=1 for
x=0, and 6(x)=0 for x 74 0. One then finds the most probable value of A1, which is

the value of A1 that maximizes £123.

5.8.5 Probability Functions Including Possible Pn

For this analysis, the probability for neutron emission could be large enough that this
decay mode cannot be ignored in the likelihood function. Probability functions were
therefore constructed to account for the possibility of neutron emission in the first two

decay generations. As an example, the probability function P0 from Equation 5.30

108

was modified to:

P0(A11 A21A3I A212.) A311: A3nna t) = [1 _ Fl(’\l)€l (535)
—((1 — Pn)F2(A1, A2) (5.36)
+PnF2(A1, A2"))E162 (5.37)

—((1 — Pn)(l — P,,,)F3(A1, A2, A3) (5.38)
+(1 — Pn)P,,,,F3(/\1, A2, A3,) (5.39)
+P,,(1 —— Pngn)F3(/\1, A2", A3,) (5.40)

+PnPn2nF3(/\1, Azm Asnn))5152€3l X 30 (541)

where P“, Pm, and Pug" are the neutron emission probabilities of the parent, daughter,
and the daughter assuming neutron emission of the parent (N-l daughter), and A2",
A3,1 and A3,", are the decay constants for N-l daughter, the granddaughter assuming
the N-l daughter does not emit a neutron (N-l granddaughter), and the granddaugh-

ter assuming the daughter does emit a neutron (N-2 granddaughter).

5.8.6 Inputs into the MLH Calculation
Half-lives and Pns in the Decay Chain

Experimental values for the daughter and granddaughter decay properties were used
whenever available. The experimentally unknown P" values for the Ni isotopes were
taken from detailed spherical quasi-particle random-phase (QRPA) calculations for
pure Gamow-Teller (GT) and GT with first-forbidden decay [65] and a number of
different choices of single—particle potentials and mass model predictions. From a
comparison of the different theoretical R, values, we derive an average uncertainty for
the calculated Pu values of about a factor of two. Table 5.7 gives the decay properties

that were used as inputs in the analysis.

109

Background

The ,6 background was determined in three ways: 1) from fitting decay curves as
discussed in a previous section, 2) from the expression for P0 as discussed above, and 3)
from directly counting uncorrelated ,B-type events. For method 3), the background was
determined for each run (typical duration of lb) and in each detector pixel by counting
all decay events that occur outside of a 100 s time window following an implantation.
A background rate for each isotope was then found by averaging the background
rate over the run-averaged background rate for all pixels in which the isotope was
implanted. Because of the low implantation rate the background is constant over
the 5 s time window used to correlate decays to an implantation. This last method of
determining background rates gives by far the smallest uncertainty of all the methods
since it utilizes much higher statistics than either the fitting method or the P0 method,
and also does not depend on input parameters such as decay constants and efficiencies

as do the other methods.

Efficiencies

The efficiencies for the three decay generations were taken from the curve fits as
discussed in Section 5.7.1 for the high statistics cases (see Table 5.6). For the other
isotopes, an average value of 42 :t 1% was used. In the MLH analysis, the efficiency

of the parent was used for each of the subsequent decay generations.

5.8.7 Examples of Likelihood Functions

Figure 5.16 shows the log of the likelihood function for the sum of all the 8 78N i decay
chains individually as an example. Figure 5.17 shows the log of the likelihood function
for each of the 8 78Ni decay chains.

The results of the MLH calculations can be found in Table 5.8.

110

 

.o
O
.1;

 

.9
O
t»

0.02 3

0.01 3

v v v v I w v v v I v w v v I v v u v ' v v v v ' v v v v I v v r ‘7 vvvvv

 

 

Uncorrelated ,8 rate (per s)

Uncorrelated ,8 rate (per 3)

5”‘10”‘15”‘20”255073520

Front Strip Number

 

0.025; ' * ‘ ‘
0.02}
0.015?
0.01:
0.0053

 

 

 

‘80 ' 100
Run

' 120

Figure 5.14: fl-background as a function of front strip number for a representative
back strip, and fi-background averaged over the DSSD as a function of run.

111

 

0.06 I I I I f r I I

 

 

 

 

 

 

 

 

A Average Over Pixel and Run
. 0 Ni Fit
Cl Cu Fit
0.05 - " 0 Zn Fit
0 Ni MLH
A l- I Cu MLH
1’: 0 Zn MLH
g 0.04 —- O —
a - CD -
a: 1-
11
S 0 03 — -- -— —
£3.
5 r t a 5
m
g 0 02 T Q % —
35 A A. an 1
0.01 r __
- +
0 n 1 . I . L . 1 I I . l I
74 75 76 77 78 79 80 81
Mass (A)

Figure 5.15: 6 background by three different methods, shown for cases with high
statistics.

112

-10 r

 

27.
l
l

 

Log of the Likelihood Function (LHF)
:12 IL)
u. o

 

 

_ . l . 1
300 0.5 1

Half-life (s)

 

Figure 5.16: Likelihood functions for the sum of the 8 78Ni decay chains.

113

Log of Likelihood Function

 

 

 

 

 

 

 

 

1 l I l

 

0.5 l
Half-life (s)

Figure 5.17: Likelihood functions for each of the 8 78Ni decay chains.

114

 

5.8.8 Error Contributions in the MLH
Statistical Error Contributions

The statistical error of the derived decay half-lives is obtained directly from the
maximum likelihood analysis (see Ref [64],Schneider96) and is valid even in the case
of very low statistics. The validity of the statistical error bars were tested with input
data resulting from Monte-Carlo simulation. Decay chains similar to the actual data
were simulated and run through the analysis. A sample of the results for 78Ni-type
simulations are shown in Figure 5.18. Each set analysed consists of only 8 Monte
Carlo simulated decay chains to simulate the real 8 78Ni decay-chain analysis. The
Monte Carlo input data had a half-life of 0.130 seconds. The number of sets for which
this input half-life falls within the error bars of the output half-life is 63%, slightly
smaller than the usual 68% confidence level, but the result confirms the error bars

are reasonable, even in the case of very low statistics.

Systematic Error Contributions

The uncertainties in the input half-lives of the daughter, N—l daughter, granddaughter,
N—l granddaughter, and N-2 granddaughter all result in systematic errors in the MLH
output, as well as the Pn values for the same nuclei, the background, and the beta-
detection efficiency.

These uncertainties were taken into account in the following way. Each of the
above values was varied within it’s respective uncertainties, and all possible permu-
tations of all of these variations of all inputs were calculated. The nominal value was
taken to be the value calculated assuming the nominal value of all the inputs. Sys-
tematic and statistical errors are correlated since the shape of the likelihood function
depends on the analysis parameters. We therefore reran the analysis for all combina-
tions of systematic variations and employed the lower and upper one-sigma limits of

the resulting statistical errors as the total error budget. As a result of this method,

115

 

O
IIIIIIIIIII

I.I‘.I.I.I.1.1.I.

 

 

O
93-h
F

 

MLH Output Half-life (s)

 

 

 

 

 

 

 

 

 

.9
N

 

 

 

 

"_-
"

 

 

 

 

 

.5".

O
I.—

T
I

 

 

 

Set Number

Figure 5.18: MLH analysis output of 100 8-decay-chain sets of Monte Carlo simulated
data with input half-life of 0.130 s.

116

 

 

 

 

IIIIIIIIIII+II IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIII QUOIGd
QulptednStcllfléficol 1.} A Total Uncedolnty
nce on —
QUOted P I I I ITI I I I I I I I I I I I Quota
_>. em 0
Half-life .2 4- I I menoimy
% I I I I I I I I I I I I I ¥I I
:1:
co
:5. IIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIII III
3’ 3:32,?ng Different Permutations of Input Data

 

 

 

 

Figure 5.19: A sketch demonstrating how the quoted uncertainties were obtained. The
points and error bars are rough sketches, not actual data.

800 . ,

 

 

 

 

f r I
g 500 .— _
o
‘6
E 400~ ' ~
2
200» 1
l
0 . 1 i 1 . 1 .
0.1 0.105 0.11 0.115 0.12
Holt-lite (s)

Figure 5.20: Monte Carlo distribution of 78Ni half-lives for background varying within
the background uncertainty range.

the quoted statistical error and the systematic error do not necessarily add up to
the total error (see Figure 5.19). The main contribution to the systematic errors are
uncertainties in the detector efficiency, and uncertainties in the parent Pn values.

In the case of 78Ni, due to the low statistics we also took into account the possibility
that one of the events is misidentified. Given the very low number of events beyond
78Ni in the particle identification, this is a very conservative assumption. Each of
the eight decay chains were successively removed and the half—life was redetermined
for the remaining seven decay chains. The resulting range in half-lives leads to an

additional systematic error for 78Ni of féoms.

117

5.9 Isomerism in the decay chain

In principle the analysis depends somewhat on the unknown feeding and decay branch-
ings of the known isomeric states in several nuclei. The isotopes involved in the
analysis which have known isomeric states are 76Cu, 73Zn,77Zn, 79Ge, 81Ge and 82As
(Nudat). 76C‘u has two isomeric states, one with a half-life of 0.641 s and the other
with a 1.27 s half-life. Both of these states are supposed to decay 100% by fl-. The
relative feeding to these states is not known. Most of the delayed neutrons probably
come from the 0.641 3 state. 73Zn has three isomeric states, with half-lives of 23.5 s,
5.8 s, and 13.0 ms respectively. The first and third decay 100% by negative fl-decay.
The second is not known. 77Zn has two isomeric states with half-lives of 2.08 s and
1.05 s. The first decays 100% by fi-decay. The second decays more than 50% by in-
ternal transitions, and less than 50% by ,B—decay, with the fi-decay branch probably
an order of magnitude smaller. 79Ge has two isomeric states with half—lives of 18.98 s
and 39.0 s. The first decays 100% by H- decay. The second is 96% by 5 and 4% by IT.
81Ge has two isomeric states, both are given as 7.6 s half-life. The first decays 100%
by 5- decay. The second may have a small branch to IT. 82As has two isomeric states
with half-lives of 19.1 s and 13.6 3. Both decay 100% by H- decay.

As an example of how these isomers can affect the half-life results, consider the
following cases. Assuming decay from the isomeric state with a half-life of 1.27 s for
760u would increase the 76Ni half-life by no more than 12 ms and the 77N i half-life by
no more than 5 ms. Assuming population of the 1.05 s isomer for 77Zn could change
the half-life of 77Ni by -8 ms to +13 ms, and the half-life of 78Ni by -10 ms to +15
ms depending on the probability for that state to fl-decay.

The uncertainties resulting from the existance of isomers in the chain are based
on extreme assumptions with no obvious central value. We therefore do not include

them in our systematic error bars.

118

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0' I I I I r f I ' I i
r o This Experiment i {o This Experiment]
0.05% 0 Previous Work _ :1 Previous Work
0.04- £ — A I ~ In —
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6 . ‘5
I I B
0.025 _ i
0.01— - I
I.
4 L 1 1 1 I LL 1 A l j
072 73 i4 7‘5 75 078 79 80 81 82
Co Isotope Zn isotope
1 m T . ' I f F ' I ' l f n f r '
o This Experiment] 1 [o This Emeriment]
08 1:1 PreviousWork r a PreviousWork ,
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205- a :5:
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073 74 75 75 77 7s 79 ‘00 81 82 as
Ni Isotope Go Isotope
w j * fifi T I I ' 1 '
[o This Experiment]
0 Previous Work
0.55 g 7
.2
(“-5 5
I f
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1 l L l I l 1 l L l 1
C75 75 77 7s 79 80 an

Cu isotope

Figure 5.21: half-lives from this experiment and previous work.

5.10 Half-life Results

The final half—life results are shown in Figure 5.21 and compared to previous mea-

surements.

119

5. 11 Neutron Analysis

5.11.1 Neutron Spectra

During the experiment, when any DSSD event on the high-gain side occured, a 200ps
gate was Opened on NERO to allow the observation of neutrons. NERO data was
collected by ADCs which recorded an energy spectrum, and a TDC which recorded
the time from the triggering decay event to any neutron event. When the energy
spectrum is gated to cut out the low energy noise signals, the number of counts in
the energy and time spectra agreed to less than 2%. The TDC registers only events
above threshold, but registers all events within the measuring window, while the
ADC registers counts independent of threshold, but only the first event within the
measuring window. The agreement between these two methods of counting implies
that the software cuts applied to the energy spectra (see Table 5.10) agree with the
set thresholds (see Table 5.9), and also that multiple hits in the counters are rare.
Figures 5.22, 5.23, 5.24, and 5.25 show the ADC energy spectra for this experiment.
The first four spectra for each quadrant are from the 3He counters, while the rest are
from BF3 counters. As mentioned in Chapter 2, the energy in the ADC spectra does
not represent the energy of the neutrons being detected but rather the Q-value of the
neutron-capture reaction in the detector modified by wall effects. The noise that is
visible in counters D7 and D11 was gated out in the analysis. Figure 5.26 shows the

neutron time spectra for each of the three NERO rings.

5.11.2 Calculating Pn values

For a given isotope, the Pn value in % is calculated using the equation:

 

13,, = 100 x (5.42)

120

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

89 89 can no 89 89 com o o 89 89 com no 89 89 8m 00
I _ _ low m Ior T _ F 19.
91.3508: 9 «.0503: 3 5502.: 93.0508:
29 89 com 00 89 89 8m 00 89 89 com oo 99 89 08 no
- I9
10F ,1 10F
_ r t 19
96950.8: : <o<ao::o_ 9 350820 m <o<_no_8__
89 89 o8 oo com o 89 89 com o 8 89 com
l]|
19 i =g 1
I _ H r I _ I. _ _
m 35083 a 81883 c 5.30:3 m «.050 SE
88 89 n 88 89 a on 8 89 n 88 n
o o o o
- 1 i 1 19
9 1 i 19
_ r _ -9
VIE/So a: m|<o<no 8: 81350 E: 3550 E

Figure 5.22: Neutron energy spectra from NERO quadrant A.

121

 

 

 

 

P
o 9:850 .8.
8m

   

f

 

0v

 

 

.
9:850 .8.
o8.

 

q

 

0

 

.
@6930 .8.
89 9 08

 

 

 

. .
VImD<DO .Nm.

0

0m

 

 

 

T

 

000..

.
m .6930 .8.
8m

   

0..

 

 

j

000 .4

.
9:850 .3.
8m

   

0

0..

 

 

 

 

_
3.930 .8.
coo. com

   

4

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0..

 

 

.
«image .5.

 

 

 

 

.
3:850 5..

000? 000

 

 

 

L
9rmo<no .8.

89 _ o8

 

 

 

co

 

 

 

.I

.
@6930 .3.
o8.

  

.

co

 

 

.
«Imago .8.

 

 

 

II 1

 

 

.
«Finn—<30 .3.
89 8

.5

     

 

 

.
8:850 E.
08.

 

 

0_.

 

 

.
mumogo .8.
8m. coo.

l

 

  

0..

 

 

P .
.6930 .8...

Figure 5.23: Neutron energy spectra from NERO quadrant B.

122

000v com

000? com

 

 

 

 

 

 

.
9:850 .8.

 

89 88 .

 

0N

 

L
8:850 .88.

   

I
A

 

0

0w

 

 

W850 .8.

0 w

 

 

 

.
9:850 .8.
8m.

 

L

 

 

 

9:850 .E

 

 

 

 

.
8:850 .8.

 

-

.I

 

000. 000

 

oo

 

 

. .
8:850 .8.

 

 

 

.
3:850 .8.
8m

 

 

0

0r

 

 

.
9:850 .88.

 

 

 

.
0:850 .5.
88.. .89 8

 

 

.

  

0w

 

 

_
8:09.50 .8.

 

 

 

.
9:850 .8.
89

 

 

 

 

 

 

 

.
8:850 .88.
com. coo

«.—

 

 

com

 

.

 

 

_
9:850 .8.

0?

Figure 5.24: Neutron energy spectra from NERO quadrant C.

123

 

 

89 89 08 o n 08
.8 oo o o 08 o o co
1 19 1 1
1 9
.
9 0050 .89. 9 89 0050 .3. e9 0050 .9. 91850.9.
89 com o 8 o 8 08 8 9 08 o
o o o o
: or 1 om :ow : —{ :
989 :_0050.99. 9 0050 .9. 90050.89. 810050.89.
089 89 08 o o o .9 08 o
o o oo o
1 £811 1 1

 

 

w :0050 .89.

 

 

.. :0050 .9_~9.

 

m :0050 .89.

 

(C

 

m :0050 .9.

 

 

89 08 .o 89 oo 89 o o ofipV 08 o
.
1 8
18 1 8 1
. . ,
80050.9. m 0050 :9. «:0050.9. 90050.89.

0N

Figure 5.25: Neutron energy spectra from NERO quadrant D.

124

 

Counts

 

 

 

 

 

Counts

 

 

 

 

Counts

 

 

 

o 1 l l l
0 200 400 600 800 1000

 

Time (Arbitrary Units)

Figure 5.26: Neutron time spectra from the three NERO rings. The graphs show the
full 200 as neutron window.

125

ngarent is the number of parent calculated from:
Nflparent = 1Vimp(1 _ e—Mcorr) (5'43)

where Nimp and A are the number of implants and decay constant of the given isotope.
The )1 used were those derived from the MLH analysis. N fiparent is the actual number
of parent fl-decays within the correlation time tam. after every implant of a given
isotope. The number NB—n is the number of fl-n coincidences detected within tam

corrected for background and detection efficiencies:

Nfi—n = NB—ndetected - Nfi—nbackgrounddetected (5.44)

fig.”

 

Ng_ndetected is the raw number of ,B-n coincidences detected within the correlation
time following each implant. Ng_nbackgmunddetected is detected number of random fl-n
coincidences within the correlation time following each implant (see Section 5.11.2).

("-3 is the product of the neutron detection efficiency and the 5 detection efficiency:

611—6 = Enero€fi (5.45)

were cam, is the neutron-energy-dependent NERO detector efficiency (see Section 5.11.2

and 6g is the ,B-detection efficiency from Section 5.7.1.

Neutron Energies and Detection Efficiency

The neutron energies were taken from shell-model calculations carried out at the
NSCL by A. Lisetskiy [67,68] which will be described in more detail in the next
chapter. For the Ni and Cu isotopes for which calculations were available, the neutron
energy branchings were folded with the NERO efficiency curve to produce a weighted
efficiency. The weighted neutron energies and efficiencies can be found in Table 5.11.

The energy dependence of the fitted NERO efficiency curve in this energy range is

126

fairly flat, ranging just 4% from 36.5% to 32.5% within the energy range of 0.1 MeV
to 1 MeV. The uncertainty in the efficiency therefore has only a small dependence
on the uncertainty in the energy within this range. As discussed in Chapter 3, the 1
a uncertainty in the curve fit was 1.2 %. For this analsys, a conservative uncertainty
for the systematic uncertainty in the curve fit of 2 % was used.

For the isotopes for which the neutron energy calculations were not available, their
average neutron energies were conservatively assumed to be within the range 0.1 to 1
MeV. The central efficiency value of this energy range is 34.5%. This possible energy
range results in a systematic uncertainty of i2%. When added to the additional
systematic uncertainty in the fit curve, the resulting uncertainty in efficiency for

these isotopes is :i:4%.

Neutron Background

From Section 5.11.2, the detected number of ,B-n events was corrected by the detected
number of fi-n background events. The number of fi-n background events for a given

isotope was determined based on the equation:

Nfi—nbackgrounddetected : (RateB—ndetected) X tcorr X Nimp (546)

The rate Rateg_ndetected was determined on a pixel by pixel basis by averaging the
random fl-n coincidence rate for a given pixel over all runs to increase the counting
statistics. For a given isotOpe, the background rate was then assigned based on the
run-averaged rate only in pixels in which that isotope was implanted. Figure 5.27
shows the random fl-n coincidence rate for the entire detector as a function of run.
Figure 5.27 also shows the random fi-n coincidence rate averaged over all runs as a
function of DSSD front strip number for a representative back strip number. It can be
seen that the random ,B-n coincidence rate varies as a function of both strip number

and run. However, since the 6 rate varies in a similar way as a function of both strip

127

 

0.04

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E ”f 0.025: '
O
O
a 0.03» g 0.02: ‘ ,
I! ,0 E
o 50 0.015’
3 0.02I , . O 00.. 3 "\‘\\:‘o W o\
§ ,50’ 0, 5;; 0.01‘\Vo.\ ‘5‘ \
s 1.11» .—. ° «w
8 5’”... Nu“ g 0.005 , 9
5 o A A A A A A A 5 0 . . . . 1
5 10 15 20 25 30 35 40 20 40 60 80 100 120
Front Strip Number Run
’5 0'0” ’3‘ wow . " T 1
g 0.0025: fé 0.0012 1 . . i
8 0.002’ 3 0.001 .Q «5”
o o 0
g o_0015 1 g 2:2 0.0008 ’ ' s .00..“ , 0%..” i. 9‘.
°°~ 0 . . "'90", 00. 0.0006’ 5. o ‘
a .001 ”fl 0 E ‘ o .5 o o .
3 00005: o.“ ""o 8 00004 ’g .“o’
5 ' 0 .0. or” 5...: 3 0.0002 ~ 0 ‘
5 :0 15 20 25 30 35 40 0 20 40 50 8,, 100 120
Front Strip Number Run
- - . - 1-
0.] 0.08 ’
“1 o
“1 . \ ‘ o ’3sz
E 0.08 { a: 0.06’ $15.05“ f
“'1 0.05: g i f . ’ '
a iiillinHH! {Hgfififififl l l; f, g 0.04, g .
13 0.04: l . E 5’5 s, ‘ ‘
. P
5 0.02’ 002
0 . . w . ‘ 1 . 0 - 0 - - . 1
S 10 15 20 25 30 35 40 20 40 60 80 100 120
Front Strip Number Run

Figure 5.27: fl-background rate, random fl-n coincidence rate, and number of ran-
dom fl-n coincidences per 5 event as a function of DSSD front strip number for a
representative back strip (strip 20) and for the entire DSSD as a function of run.

and run the result is that the number of random fl-n coincidences per 5 event is fairly
constant except in several contiguous runs which display systematically lower neutron

counts. (see Figure 5.27). For this analysis, the background was averaged over run.

5.12 B, Value Results

The resulting Pn values and are given in Table 5.12 and plotted in Figure 5.28 along

with values from previous works.

128

 

 

. , .
. | o This Experiment]

 

—

Pn Volue (%)
M (a) b
8 - 8 8

O
i

. i

 

 

on
O

 

1 l 1
73 74 75 76
Co isotope

 

' '7 l ' T ' T

 

\I
O

T ' T
’_ [o This Experiment]

 

PnVque (95)
0 . 8 8

M 0) b
O O
ITIpT

d
O
T i

 

 

@
01>

 

l l l
74 75 7b 7 7 78 79
NI Isotope

 

01:
O
T

 

 

' l ' T
o This Experiment

 

0
8

#
8

PO Value (95)

M
8

 

5

0 Previous Work

9.4—1 L 1 i r l L ‘

 

1 I
76 7 7 78 79 80
Cu isotope

 

 

 

 

 

 

 

 

 

 

 

 

 

60 ' l ' l I
1 o This Experiment] .
50— a Previous Work -
.. 40- -
33. . 1
3 30— «
9 .
mc
20- 7
10:- -*
I
. l l 1 I
078 79 80 a: 82
BI Isotope
4o . , r
o This Experiment]
' 0 Previous Work
30~ 0
g .
9 20
‘>’
0::
lO- 'i
i . 1
‘50 a2 83
Go Isotopes

Figure 5.28: P" values from this experiment and previous work.

129

Table 5.7: Inputs for MLH Half-life Calculation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Isotope t M2 (s) P" (Fraction) Reference
72Ni 1.57 :1: 0.05 0 :66]
73Ni 0.84 i 0.03 0.0026 :66:
74Ni 0.5 :1: 0.2 0.02853 :66:
7I‘E’Ni 0.7 :1: 0.4 0.09127 :66:
71Cu 19.5 :1: 1.6 0 NuDat
72Cu 6.6 :1: 0.1 0 NuDat
73Cu 3.9 :1: 0.3 0.00029 :t 0.00006 :66?
72fCu 1.594 :t 0.01 0.00075 :1: 0.00016 :66:

T75Cu 1.224 :t 0.003 0.026 :1: 0.005 :66:
76Cu 0.641 5: 0.006 0.024 3:: 0.005 :66:
77Cu 0.469 5: 0.008 0.158355 :66:
780:: 0.342 :1: 0.011 0.153;},5 :66:
72Zn 167400 :1: 360 0 NuDat
732m 23.5 :1: 1 0 NuDat
74Zn 95.6 :1: 1.2 0 NuDat
75Zn 10 i: 0.2 0 NuDat
76Zn 5.7 3:: 0.3 O NuDat
77Zn 2.08 :I: 0.05 0 [66]
78Zn 1.47 i 0.15 0 {65

L_;9Zn 0.995 :t 0.019 0.013 5: 0.004 (66:
0Zn 0.545 5: 0.016 0.01 :1: 0.005 {66:
74Ga 487.2 i 7.2 0 NuDat
75Ga 126 :1: 2 0 NuDat
76Ga 32.6 :1: 0.6 0 NuDat
77'Ga 13.2 i: 0.2 0 N uDat
78Ga 5.09 :1: 0.05 0 N uDat
79Ga 2.847 :1: 0.003 0.0008 :1: 0.00014 :66?
W03. 1.697 :1: 0.011 0.0085 :1: 0.0005 :66:
81Ga: 1.217 :1: 0.005 0.121 :1: 0.004 :66:
77Ge 40680 :1: 36 0 NuDat
78Ge 5280 :t 60 0 N uDat
79Ge 18.98 :1: 0.03 0 N uDat
Wee 29.5 a: 0.4 0 NuDat
81Ge 7.6 :t 0.6 0 NuDat
79A3 540.6 :1: 9 0 N uDat
Ws 15.2 i 0.2 0 NuDat
81As 33.3 :1: 0.8 0 NuDat
82As 19.1 :1: 0.5 0 NuDat

 

130

 

Table 5.8: T1/2 Results from MLH Analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Isotope T1/2 (s) Stat (+) Stat (-) Sys (+) Sys (-) Total (+) Total (-)
73cc 0.040988 0.005404 0.004803 0.001001 0.000913 0.006164 0.005613
74Co 0.033977 0.004181 0.003539 0.001791 0.005313 0.006189 0.008676
7500 0.0295 0.007778 0.006914 0.003153 0.004509 0.011152 0.010401
74Ni 0.470765 0.102405 0.084284 0.007557 0.00682 0.110431 0.0908
Ni 0.344347 0.018916 0.017935 0.00729 0.005465 0.026203 0.02313
76Ni 0.237776 0.013584 0.013158 0.005255 0.004087 0.019128 0.01703
77Ni 0.128394 0.024826 0.025495 0.010799 0.006732 0.036416 0.032161
Ni 0.111189 0.077691 0.061169 0.023201 0.009315 0.101954 0.063305
760:: 0.599152 0.095446 0.079477 0.011951 0.01351 0.109094 0.091845
7'7Cu 0.449737 0.012847 0.012444 0.014158 0.008581 0.026894 0.020793
780:: 0.322705 0.011345 0.01103 0.009914 0.008047 0.021232 0.018813
790:: 0.254057 0.021771 0.019848 0.010697 0.009044 0.032778 0.028609
73130:: 0.171988 0.105057 0.048707 0.003871 0.004055 0.111167 0.052218
792:: 0.746214 0.037711 0.036436 0.004891 0.004829 0.043256 0.041029
73821: 0.577882 0.019046 0.018811 0.002492 0.002514 0.021611 0.020785
8rZn 0.474277 0.080764 0.072562 0.01035 0.011421 0.092535 0.08292
810a. 0.9568 0.330593 0.251892 0.030856 0.034619 0.366263 0.285397
82G15. 0.609823 0.071687 0.062034 0.010426 0.010826 0.083221 0.072349

 

 

Table 5.9: NERO dedicated Pico Systems CFD Thresholds for this Experiment (On
255 Scale). The corresponding gain settings were 255 for all counters.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Counter Thresh. Counter Thresh. Counter Thresh. Counter Thresh.
A1 55 B1 35 C1 30 D1 25
A2 65 B2 25 C2 40 D2 25
A3 40 B3 30 C3 30 D3 25
A4 40 B4 30 C4 255 D4 30
A5 25 B5 30 C5 20 D5 25
A6 25 B6 35 C6 20 D6 23
A7 25 B7 25 C7 35 D7 20
A8 30 B8 25 C8 33 D8 30
A9 30 B9 25 C9 18 D9 30

A10 25 B10 18 C10 40 D10 25
A11 35 B11 35 C11 20 D11 25
A12 25 B12 25 C12 20 D12 20
A13 35 B13 25 C13 15 D13 25
A14 25 B14 20 C14 25 D14 40
A15 30 B15 20 C15 25 D15 35

 

 

 

131

 

Table 5.10: NERO Energy Software Cuts on 12-bit (4096) scale

Counter Cut Counter Cut Counter Cut Counter Cut
A1 200 B1 117 C1 99 D1 80
A2 186 BZ 100 C2 103 D2 67
A3 179 B3 111 C3 93 D3 76
A4 152 B4 106 C4 76 D4 76
A5 124 B5 110 C5 72 D5 69
A6 108 B6 100 C6 66 D6 67
A7 123 B7 97 C7 97 D7 81
A8 150 B8 123 C8 88 D8 59
A9 126 B9 96 C9 76 D9 71

A10 123 B10 115 C10 99 D10 56
A11 165 811 122 C11 72 D11 84
A12 130 B12 151 C12 62 D12 66
A13 163 B13 110 C13 59 D13 67
A14 114 814 162 C14 68 D14 79
A15 143 B15 170 C15 77 D15 87

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5.11: Neutron Energies and Corresponding NERO Efficiencies

 

 

 

 

 

 

 

 

Isotope Neutron Energy (MeV) NERO Efficiency (%)
74Ni 0.877 33 i 2

75Ni 0.998 33 :t 2

76Ni 1.06 35 :l: 2

78Cu 1.10 32 i 2

79Cu 1.20 32 :t 2

All Other Isotopes From 0.1 to 1 34.5 d: 4

 

 

 

132

 

Table 5.12: Pn values

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Isotope Raw Neutron Count P" from this Work (%) Previous Measurements (%)
Co 4 less than 9

74CO 16 31 :l: 11

75Co 1 less than 16

74Ni 3 16 :t 12

75N i 43 13 :1: 5

76Ni 43 17 i 5

77Ni 13 54 :l: 18

7“’Cu 3 less than 9 2.4 :l: 0.5 [21], [69], [66]

77Cu 348 314: 6 15 i 10 :69], :66]

78Cu 310 47 :l: 6 15 i 10 69], :66}

79Cu 81 78 :1: 12 55 2t 17 [27]

79211 19 2 :t 5 1.3 :l: 0.4 [27]

”“211 45 1 :1: 6 1 :t 0.5 [27]

81Zn 14 62 :l: 22 7.5 a: 0.3 [27]

81Ga 1 12 d: 18 12.1 i 0.4 [70], [66]

8261a 21 32 a: 12 22.3 d: 0.22 [70], [66]

 

133

 

Chapter 6

Discussion

6. 1 QRPA Calculations

Global calculations such as QRPA are employed often in r—process model calculations
because they offer nuclear physics inputs for the wide range of nuclei required for
these studies. The experimental values are compared to QRPA calculations in this
mass region [71,72] (see Figures 6.1 and 6.2). These calculations assumed no defor-
mation and used a Folded-Yukawa potential and Lipkin-Nogami pairing, and take
into account only allowed Gamow-Teller (GT) transitions. The masses were taken
from G. Audi et al. 03 [73]. These calculations differ from those found in Ref. [71] in
the daughter deformations. In addition, they do not include a “smearing-out” of the
levels above around 2 MeV, as does Ref. [71].

The QRPA calculation assuming only allowed GT transitions tends to over-predict
the half-lives of the nuclei in this region, but reproduces well the experimentally
derived P" values. There are several possible explanations for the over-prediction of
the half-lives. First, the calculation takes into account only allowed transitions. If these
transitions feed high-lying states, the higher half-lives will still result (because due
to the energy dependence, there will be less energy to drive the transition). However,

if there exist first-forbidden branches to low-lying states, lower half-lives will result.

134

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 6.1: Comparison of half—lives from this experiment to QRPA calculations with
allowed GT transitions and with allowed GT+ first-forbidden (ff) transitions.

135

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Co Zn
80 r 1 ' 1 ' 1 r 1 ' 1 r 4 v y r
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707 “.91sz - LAQRPA ,I’ ‘
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+ A I 1 l 1 I 1
95 76 77C 78 79 80

Figure 6.2: Comparison of Pn values from this experiment to QRPA calculations with
allowed GT transitions and with allowed GT+ first-forbidden (ff) transitions.

136

Since the P" values probe the transitions to higher-lying states, this is an indication
that these calculations reproduce well the transitions to higher-lying states.

First-forbidden transitions were added heuristically to the QRPA calculations [71,
72]. As can be seen in the Figures, the resulting half-lives in general are shorter and
are more in agreement with the experimental values. The P” values also shift. When
the first-forbidden transitions are added, the P" values get smaller and consequently
agree less with the experimental values, indicating too much strength is added below
the neutron separation energy.

Another possible explanation for the longer half-lives in the calculation which
only includes allowed transitions is that the predicted Q5 values may be too small.
Due to the energy to the fifth power dependence of intensity (I o< (QB — E$)5), the
uncertanties in Q3 can be decisive. A smaller 62;; would result in a higher half-life,
and a higher Q5 value would result in lower half-lives.

In conclusion there are several factors in the model calculation that affect the
half-lives and P" values. To answer which of these factors are mostly responsible
for discrepencies between measurements and calculations may require detailed spec-
troscopy. However, here we showed that first-forbidden strength improves the half-life,
but not the R, values, thus suggesting that the lack of first-forbidden transitions does
not seem to answer the problem of the discrepency between these calculations and
the experimental half-lives. With just a measured half-life and without the measured
Pn value, this result would be unnoticed. This example demonstrates that the com-
binded measurements of half-life and Pn values can be a powerful tool to study nuclear

structure questions in exotic nuclei even with relatively low statistics.

6.2 The Case of 78Ni

To examine these effects in more detail, consider the case of 78N i. Figure 6.3 shows

the 78Ni proton and neutron shell model configurations with the classic shell-model

137

Neutrons Protons

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ih I ”1 I 12 82
3s‘IZ 381': 2 70
28,2 2d1,2 4 68
2:15,, 2d,” 6 64
1g7l2 1g7/2 8 58
19m 19m 10 50
2 33
5/2 5/2

2016 2pm a 4 32
11,,, If,” 8 28
1d,, I lds/z 4 20
281,2 G G 25172 = : 2 16
18,, id.” 6 14
Ip,,2 : = lpm 4 = 2 8
1pm 1pm 4 6
151/2 G c 151/2 = = 2 2

Figure 6.3: Proton and neutron configuration for 78Ni according to the shell model.

gaps. Figure 6.4 shows the important transitions in the decay of 78Ni to 78Cu from
the QRPA calculation. The up1/2/7rp3/2 transition dominates below the neutron sep—
aration energy. The 1199/2 /7rgg/2 transition is the main transition above the neutron
separation energy. The grey region in the middle of the scheme represents the uncer—
tainty in S". The V f5 /2 / 7r f7 /2 transitions lie in this region. There are several consider—
ations which effect the half-life. Assume the calculated half-life is too high. A general
shifting of any of the levels upward will decrease the calculated half-life due to the
energy dependence of the transition intensities. However, raising the 1471/2 /7rp3/2 or
1199/2 / 7rgg/2 states, being the dominant states would have the greatest effect. One of
the problems with comparing the half-lives is that raising one of the states could be

compensated for by lowering the other state. Perhaps the Vp1/2/7rp3/2 is too high, but

138

the 1199/2 /7rg9/2 is too low, and the result is that this effect is cancelled out and the
half-life is insensitive to the position of these levels.

The Pn value measurement, if it were available for 78Ni, would offer additional
insight. The Pn value is sensitive to the states above Sn. Here there is one dominant
transition, the 1199/2 /7rgg/2, according to this calculation. In this case, without con-
sidering the possibility of an incorrect Q3 or Sn, a calculated Pn value that was high
relative to measured value would most likely indicate that this level is too low. An-
other possibility is that one or more of the states in the vicinity of Sn slips below Sn.
In this way, the P" value can be sensitive to states within the vicinity of Sn. Finally ,
the B, value is sensitive to the Sn. A too-high Pn value might indicate that S, is too
low and has slipped under the levels in the vicinity of 8,, in the calculation, when it
actually is above these levels.

This case along with the preceding discussion on first-forbidden transitions demon-
strates how half-life and Pn value measurements, especially when both are available,
can indeed offer some indications of the structure and first tests of theories. These
tests can reveal discrepencies between theory and measurement and indicate where
more detailed data such as mass measurements to determine Q3 and 5,, values and / or

spectroscopy to determine level structure will be needed.

6.3 Nuclear Shell Model

In order to better understand the nuclear structure in this mass region and to bench-
mark global models beyond the range of experimental data it is important to test
the more sophisticated microscopic calculations, which have been performed for a
limited set of singly— and doubly-magic heavy nuclei. The shell-model results of Ref-
erence [74] for 78Ni are in good agreement with experimental data (see Fig. 6.5). Of
course this does not necessarily mean that the shell-model description of this mass

region is entirely correct. For example, as discussed in the previous section, deviations

139

Folded - Yukawa
0+ 159 ms Lipkin - Nogami
78Ni

28 50

 

QB: 10.45 11.17 MeV
(Audi '03)

L4
" 9.6% 3g 1+ strg ‘8 “sz

J)

 

 

6.93

45.7% 3.5 , 1+ V99/2 ‘8 11399/2 5 46

 

- 4.81

6.6% 4.3 1" Vf5/2 ‘8 1tfm 4 23 8,, = 4.2412057 MeV
0 1+ Vf ® th '
5.46 5.0 5/2 7/2 3 95

 

 

3.67

 

0 1+ V ® TC
32.3/0 4.6 p1/2 p3/2 2.76

 

V9972 ‘8’ 1:93/2
78
2901149

 

0

Figure 6.4: Important transitions in the decay of 78Ni according to QRPA calculations.

140

 

 

 

 

1 . 1 . I r I 1 '6 1
"' ’l” ‘\“\“ O "
1E- III, e ‘5
: [I O :
: [I ““““““ ’ C? :
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E E 3
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I ' ”g' --- Moelleretol. 97 ‘
0.01:— a" 0 Shell Model 3
5 0 Experimental 5
i O 0 Present Work 3
C9 1
0.001 1 l 4 I 1 l 1 l
24 26 28 30 32

Atomic Number (2)

Figure 6.5: Experimental and theoretical halflives for N =50 isotones. Moeller et al.
97 [75], shell model of Ref [74], and previous work (NuDat).

in excitation energies, transition strengths, and decay Q-value can in principle com-
pensate each other. The shell-model of Reference [74] did not include the proton or
neutron 99/2 orbitals, which for example carries a significant amount of strength for
78Ni (see Fig. 6.4). Shell-model calculations which include these orbitals in the model
space were carried out in this mass region at the NSCL by A. Lisetskiy [67,68]. To
model this mass range, one would like to assume an inert 40Ca core and the full pf
shell, including the intruder 99/2 orbital. However, this makes the dimensions of the
problem too large. Instead, one assumes an inert 56Ni core and includes the smaller
model space of the 173/2, f5/2, 171/2, and 99/2 orbitals.

To calculate fl-decay properties such as tm and Pn values, one needs binding ener—
gies, spectra of the parent and daughter isotopes, and Gamow-Teller matrix elements.

These were calculated using the code OXBASH. An effective interaction recently de-

141

 

rived from realistic G-matrix and adjusted to experimental data in this region was
used [68]. Using the shell-model output, the half-lives and Pn values were calculated.
The results are compared to the experimental results in Figure 6.6.

The good agreement with half-lives and Pn values indicates reasonable single-
particle energies. However, very strong quenching is required to reproudce the half-
lives. Usually for a full major oscillator shell, one requires a quenching of 0.7 to 0.8
for GT matrix elements. In this case, the f7/2 orbital is missing, which is the spin-
orbit partner of the f5/2 orbital and is responsible for a large part of the sum rule for
GT strengths. Furthermore, this configuration space includes the 99/2 orbital but its
partner g7/2 is excluded from the space. This truncation of the configuration space
results in a GT sum rule that is only 50% of the Ikeda sum rule. Consequently, it
requires a considerably smaller quenching factor (0.35), which means more quench-
ing, for GT strengths. This factor was chosen to reproduce the half-lives of 75' 77N i
(Figure 6.6). It can be seen in that figure that this quenching factor works well also
for the Cu isotopes, so it seems to be the proper quenching factor for this mass re-
gion and model space. The good agreement with P... values is an indicator of correct
distribution of higher-lying GT strengths in the daughter nuclei. It also supports the
choice of single—particle energies.

With the interaction and quenching adjusted to fit the present results, these mea-
surements provide an important basislfor nuclear structure calculations in this region
of the nuclear chart. The fact that both the Pn values and half-lives are well repro-
duced by the shell-model calculation which only includes GT transitions casts further

doubt on the relevance of the first-forbidden transitions in these decays.

142

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

& I r 1 ' 1 ' 80 f r , r v 1 , f #
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NI Isotope Nl Isotope
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0.58 - A 60- ,2 ' -
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‘75 76 77 78 79 80 81 ‘75 76 77 78 79 80
Cu Isotope Cu Isotope
I I I ' I ' 60 ' I ' I ' I I
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ooSheIl Model 50_ eoSheli Model 1
0 .-. 40~ _
13‘
1., Q s.—
g i .1 g 30— _
9 a. ‘
2o~ —
1
10» -
1 1 1 I 1 I 1 1 $ 1 i 1 I 1
078 79 80 81 82 ‘78 79 80 81 82
Zn Isotope Zn Isotope

Figure 6.6: Comparison of half-lives and Pn values from this experiment to shell-model
calculations.

143

Neutron Density (per cm3) O Heaviest Isotope with
I 1020

Measured T1,2
I 1023

I 102‘

    

42 44 46 48 52 54 56 SE 60 62 64 66 68 70 72 74 76 78 HO
-

Nfl

Figure 6.7: R—process waiting points for three different neutron densities [72].

6.4 The r-Process

6.4.1 Measurements Relevent to the r-Process

Figure 6.7 shows calculated r-process waiting points for three different neutron den-
sities [72]. The waiting points whose half-lives were measured in this experiment are
7300 and 75Co, 76Ni and 78Ni,79Cu, 80Zn, and 81Ga, with new half-life measurements
for 75Co and 78Ni. According to this calculation, all the PH values measured in this
experiment will be relevant in the r—process freeze-out. The new relevant P" value
measurements from this experiment are 7$75Co and 74'7‘5Ni. (Pn values are not impor—

tant during the r—process as they are reversed by neutron capture.)

144

6.4.2 r-process code

To test the impact of the new measurements a classical r-process code was used (see
for example Ref [15]). Inputs into the code include the astrophysical conditions of
temperature T and neutron density 72", and a time duration 7' for those conditions.
The nuclear structure inputs include the neutron separation energies Sn, decay con-
stants (half-lives) x\, and neutron emission probabilities P". Given a temperature T,
neutron density 71”, and set of neutron separation energies Sn, the code calculates the

relative abundance distribution across an isotopic chain as described in Chapter 1:

Y(Z,A+1) _n G(Z,A+1)(A+1 217-12
Y(Z, A) ‘ " 20(2, A) A mukT

 

 

S
3/2 -—"- 6.1
) exprkT) ( )
where Y(Z, A) is the abundance of nucleus with proton number Z and mass number A
and G are the partition functions, which are set equal to '1. Given the decay constants
for the isotopes in this chain, the code then follows the movement of mass up to higher
mass. Finally, the abundance distribution at the end of time 7' is adjusted to account

for decay processes during freezeout using the input neutron emission probabilities

P".

6.5 Effect of 78Ni Half-life

In order to test the sensitivity of the calculated r-process abundances to the half-life
of 78Ni, the code was run for a given set of measured and theoretically calculated
half-lives, and astrophysical parameters were set to match the calculated abundance
pattern to the solar system r-process pattern. The decay data used was from Méiller et
al 97 [75]. The neutron seperation energies were taken from experimental masses and
the ETFSI—Q mass model where experimental or extrapolated masses were not avail-
able in Ref [73]. The fit to the observed abundance pattern required three weighted

components shown in Table 6.1.

145

Table 6.1: r—process parameters.

CID

 

 

' l ' I ' I

[ — Observed Solor

I
l

 

100 — Moeller, Nix and Kratz 97

- New 78Ni Holt-life

II IIIII]

 

 

 

l lIlllllI

I I
‘
l lIlllllI

\

1 . 71
ii 1...

' T 50 200
Moss (A)

Figure 6.8: Observed Solar Abundance, abundances using the half-lives according to
Moller, Nix and Kratz 97, and abundances using the same half—lives except changing
only the 78Ni half—life to the new experimental value.

Abundance [A.U.)

—l
l l IIIIIII
r
‘—
l l IlllllI

—l

lllll II

 

 

 

 

The half-life of only 78Ni was then changed from the value from Miiller et (1197 [75]
of 477 ms to the new experimental value of 110 ms. Then the r-process calculation was
run again with the same astrophysical parameters as before. The results are shown
in Figure 6.8. One can clearly see that the different 78Ni half-life has affected the
abundance pattern all the way up to the highest r—process peak. At and around the
A = 78 region there is less material, whereas at higher masses there is more material.
Because the half-life of 78Ni is shorter than expected, for the same amount of time

the material has more time to process up to higher masses.

146

The astrophysical parameters now have to be adjusted, so that calculations with
the new experimental data fit the observed abundance curve. For instance, some
component should be shorter in time duration so as not to allow build-up of material
at the higher mass peaks. This in essance means an acceleration of the r-process.
With a shorter half-life, the material can move through the N = 50 bottle-neck
faster. The fact that a change in only 78Ni affects abundance throughout the process
is a reflection of the fact that 78Ni is indeed a bottle neck to the process for the
assumed astrophysical parameters.

It must be stressed that the above discussion assumes that the r-process starts at
Fe or lighter nuclei. This is currently not expected to be the case in some r-process
scenarios as discussed in Chapter 1. However, these scenarios have problems producing
the heaviest r-process nuclei as well as the abundance pattern in the A = 80 — 90
region, where they assume the seed. Models that try to address this problem have
seeds below Fe and are characterized by neutron—capture flow through N = 50. In
addition, in discussion of the possibility of a weak r—process which is responsible for

the lighter r-process abundances this mass region would also play an important role.

6.6 Summary

In summary, we present the first results for the half-life of the r-process bottle neck
78N i as well as half-lives and Pn values for several other r-process waiting points. The
Pu value measurements were made possible by the development of the low-energy
neutron detector NERO. With these results, experimental half-lives are available for
all but one (48Ni) classical doubly-magic nuclei. Also, the half-lives of all important
N = 50 waiting points in the r-process are now known experimentally. This will
make r-process model predictions of the nucleosynthesis more reliable and comparison
with observational data more meaningful. It will also put the overall delay that the

N = 50 mass region imposes on the r-process flow towards heavier elements on

147

a more solid experimental basis. In this respect the half-life of 78Ni is of special
importance as during the initial stages of the r-process when the heavier nuclei are
synthesized the r-process path passes through 78Ni and 79Cu rather than through
the more stable N = 50 nuclei [76]. The delay timescale for the buildup of heavy
elements beyond N = 50 is therefore set by the sum of the lifetimes of 78Ni and 79Cu.
Our experimental data clearly favor the short timescale of 450 ms obtained with the
prediction of Langanke and Martinez-Pinedo [74], or 233 ms predicted by the new
shell-model calculations by Lisetskiy, over the much longer delays of 960 ms predicted
for example by M611er et al. [75] leading to an acceleration of the r-process. This is
in line with recent improvements in theoretical fl-decay half—life predictions along the
entire r-process path that also tend to result in shorter half-lives thereby speeding up
the r-process [71].

In addition to the astrophysical implications, it was shown how these measure-
ments of the gross ,B-decay properties of half-life and Pn value together can serve as
first indicators of nuclear structure. In particular, the results suggest that the lack
of first-forbidden transitions does not seem to answer the problem of the discrepency
between these calculations and the experimental half-lives in this region, since al-
though they improve the half-life results, the Pn results actually get worse, and the
shell-model calculations which only assume allowed GT transitions reproduce well
both half-lives and P" values.

In addition, the measurements of fi-decay properties in this region give shell-model
calculations benchmarks in this neutron-rich region of the nuclear chart against which

to test interactions which will help predict properties of these and other exotic nuclei.

148

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