INDIRECT NEUTRON-CAPTURE CROSS SECTIONS FOR THE

WEAK R-PROCESS

By

Rebecca L. Lewis

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Chemistry — Doctor of Philosophy

2019

INDIRECT NEUTRON-CAPTURE CROSS SECTIONS FOR THE WEAK R-PROCESS

ABSTRACT

By

Rebecca L. Lewis

Understanding the production of the heaviest elements requires a wealth of information on

the nuclear properties of short-lived nuclei. The rapid neutron capture process (r-process) is

responsible for the majority of the production of the heaviest elements. The r-process utilizes

neutron-capture reactions on heavy, neutron-rich nuclei. The nuclei involved in the r-process

are very neutron-rich, short-lived, and very difficult to produce, so little information is known

about them. The lack of directly measured neutron-capture cross sections has led to the

development of indirect techniques that can be used to reduce the uncertainty in the neutron-

capture cross sections, which can vary by orders of magnitude between different calculations.

The β-Oslo method is one indirect technique which aims to reduce the uncertainty in the

two statistical properties of the nucleus that contribute the largest sources of uncertainty

in the r-process calculations: the nuclear level density (NLD) and γ-ray strength function

(γSF). Both are required to calculate a neutron-capture cross section in the Hauser-Feshbach

statistical framework, along with the neutron optical model. The β-Oslo method utilizes β

decay to populate high-energy excited states in the same nucleus that would have been

formed in the neutron-capture reaction of interest. The γ rays from the de-excitation are

observed in the Summing NaI (SuN) detector to determine the total excitation energy of the

nucleus as well as the γ-ray cascade to the ground state. With this information, the NLD and

γSF can be extracted, after normalization to other data or theoretical calculations. With

experimentally constrained NLD and γSF, the overall uncertainty of a neutron-capture cross

section has been showed to be significantly reduced.

The neutron-capture cross sections of four neutron-rich nuclei (73Zn, 70,71,72Ni) were

experimentally constrained using the β-Oslo method. The 73Zn(n, γ)74Zn data was also

used to compare the constrained neutron-capture cross sections obtained from three different

Hauser-Feshbach codes to determine additional sources of systematic uncertainty. The three

Ni reactions were also compared to the 68,69Ni cross sections that were previously constrained

using the β-Oslo method.

To my nuclear family, in every sense of the term. Thank you for everything.

iv

ACKNOWLEDGMENTS

Let’s make this easy—thank you to everyone! It has taken what feels like a million people

to get me to this point, and I really appreciate every one of you.

I have had incredible

friends and mentors everywhere I’ve been, from Northeastern to Michigan State, but also

at Oak Ridge National Laboratory, Massachusetts General Hospital, the Nuclear Chemistry

Summer School, and Los Alamos National Laboratory.

Of course, the mentor who has put up with me the longest is my advisor, Sean Liddick.

Five years is a long time to listen to my terrible jokes and watch me do math wrong every

time I try, and I really appreciate (and admire) your patience. I think I’ve gotten involved

in almost every kind of science that is happening at the lab while working with you, which

really helped me decide what I wanted to do after graduate school. Thank you for helping

me make the time to do the other things I love as well, especially outreach.

Thank you to my committee: Dave Morrissey, Paul Mantica, and Artemis Spyrou.

I

didn’t just see you once a year to update you on my progress—instead, I was able to talk

to any one of you whenever I needed help or advice. I would also like to acknowledge the

wonderful support and approachability of all of the faculty and staff that I’ve reached out to

at the NSCL. I always felt like I could ask anyone a question, and I’ve become more confident

in my ability to solve problems because I could rely on support from the whole lab.

I can’t forget the beta group members, past and present, who helped me learn the ropes

and let me tag along to experiments until I figured out what I was doing. And especially to

Katie Childers, Ben Crider, and Andrea Richard—we had way more fun than we should have,

but I have also learned more than I could ever image from working with you. Thank you

Katie for letting me talk about everything going on. Ben, your support and encouragement

v

got me through some difficult projects. And Andrea, you are always ready to help me solve

problems or just stand behind me while I run codes in a panic.

The other graduate students and the postdocs at the NSCL have been amazing, and I’ve

made some of my closest friends while I’ve been here, especially Krystin Stiefel, Kalee Fenker,

Amy Lovell, Wei Jia Ong, and Stephanie Lyons. I have to thank Amy and Wei Jia for your

support, weekend breaks, knitting parties, and dinner together. I’m always excited to spend

time with both of you! Kalee, thank you for answering questions whenever I had them and

always being ready for a Wine Night or coffee adventure. And Krystin, you survived with

me for over four years in the same office, which is amazing. Thank you for ignoring all the

times I threatened my computer and for helping me turn our office into a safe place to cry,

laugh, and just take a break from everything. Stephanie, I could never thank you enough

for putting up with me while setting up my experiment. I know that I couldn’t have done it

without you, and you haven’t stopped helping me in every way you can since.

The people who have supported me the most (and put up with me for the longest) are

my family. Amanda, it’s a good thing I like you because having my little sister doing the

same science as me, and being better at it, would be terrible otherwise. I’m extraordinarily

proud of you for finding what you love and learning everything about it, and proud of me for

finding it first so I can always say that you followed me. You’ve stepped up to help me more

times than I can remember, and I’ll always be there to help you back. Mom and Dad—I’ve

discovered so many amazing things because you’ve always encouraged me to try new things

and take risks, even when I didn’t want to. Thank you for making me get out of the car over

and over again. I always know that you’re proud of me, and I’m always excited to share my

accomplishments with you because I know you’ll be just as excited. I love you!

vi

TABLE OF CONTENTS

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

ix

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

Chapter 1

1.2.1 Weak r-process

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Production of heavy elements
. . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The r-process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Nuclear physics uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Hauser-Feshbach model of neutron capture . . . . . . . . . . . . . . . . . . .
1.4.1 Optical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 NLD models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.3
γSF models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Indirect techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5
1.6 Dissertation outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Summing NaI (SuN) detector

Chapter 2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 NSCL experiment e14505 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1
. . . . . . . . . . . . . . . . . . . . . .
2.1.2 Double-sided silicon strip detector . . . . . . . . . . . . . . . . . . . .
2.2 NSCL experiment e16505 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1
SuN calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 DSSD gain matching . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .

2.3 Correlation of implants and decays

Chapter 3

β-Oslo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Populating highly excited states through β decay . . . . . . . . . . . . . . .
3.2 Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Extraction of primary γ rays . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Functional forms of the NLD and γSF . . . . . . . . . . . . . . . . . . . . .
3.5 Normalization of NLD and γSF . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 NLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Limited spin population . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.3
γSF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Cross section and reaction rate calculation . . . . . . . . . . . . . . . . . . .

Chapter 4 Code Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Hauser-Feshbach codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Calculation with default settings . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Calculation with experimental data constraints . . . . . . . . . . . . . . . . .
4.4 Final calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

1
1
2
3
6
9
10
11
15
19
20

21
21
21
24
24
27
27
28

36
37
41
42
44
46
47
50
53
55

59
59
61
61
67

5.2

I2 position corrections

71
Chapter 5 Analysis of Co Decays . . . . . . . . . . . . . . . . . . . . . . . . .
71
5.1 Particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
5.1.1
. . . . . . . . . . . . . . . . . . . . . . . . . .
71Co decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
84
5.2.1
β-Oslo matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
5.2.2 NLD normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
5.2.3
γSF normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72Co decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
5.3.1
β-Oslo matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.2 NLD normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.3
γSF normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
73Co decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4.1
β-Oslo matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.4.2 NLD normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.4.3
γSF normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.3

5.4

Chapter 6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.1 TALYS calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Chapter 7 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . 132

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
APPENDIX A Default NLD and γSF tables . . . . . . . . . . . . . . . . . . . . . 135
APPENDIX B Matrices used in the daughter and background subtraction for the

decay of 71,72,73Co . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
APPENDIX C Fits to experimental γSF (upper and lower limits) . . . . . . . . . 176

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

viii

LIST OF TABLES

Table 1.1: GLO and SLO E1 default parameters for 74Zn in TALYS used to generate
. . . . . . . . . . . . . . . . . . . . . . .

the functions shown in Fig. 1.7.

Table 2.1: Final voltages and scaling factors after gain matching the SuN PMTs for
. . . . .

e14505 using the 40K background peak. All voltages are positive.

18

22

Table 2.2: Calibration values for SuN segments in e14505.

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

23

Table 2.3: Scaling factors for gain matching the front and back strips of the DSSD in
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e14505.

Table 2.4: Final voltages and scaling factors after gain matching the SuN PMTs for
. . . . .

e16505 using the 40K background peak. All voltages are positive.

25

26

Table 2.5: γ-rays used for calibrating SuN segments in e16505.

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

27

Table 2.6: Scaling factors for gain matching the DSSD in e16505.

. . . . . . . . . . .

29

Table 3.1: Parameters used in exponential fit of Eq. 3.10 to shifted calculated NLD
. . . . . . . . . . . . . . . . . . .

for 74Zn and the resulting ρ(Sn) values.

49

Table 3.2: GDR parameters from GLO fits to experimental data from Ref. [76]. EE1
is the energy of the giant resonance, ΓE1 is the width, and σE1 is the
strength. A value of 0.7 for Tf in the GLO function was adopted for all
three data sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 3.3: Parameters for the upbend added to the GLO to describe the experimental
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

γSF of 74Zn.

Table 3.4: Subset of NLD and γSF models available in TALYS used to determine the
.

uncertainty in the cross section and reaction rate of neutron-rich nuclei.

Table 4.1: GLO E1 parameters and SLO M1 parameters used to fit the experimental
γSF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 4.2: 73Zn level energies, spins, and parities including the values assigned in
TALYS, CoH, and EMPIRE, as well as the RIPL-3 suggested levels and
the values used in the final comparison.
. . . . . . . . . . . . . . . . . . .

55

56

57

65

69

ix

Table 4.3: 74Zn level energies, spins, and parities including the values assigned in
TALYS, CoH, and EMPIRE, as well as the RIPL-3 suggested levels and
the values used in the final comparison.
. . . . . . . . . . . . . . . . . . .

Table 5.1: Number of ions of each isotope delivered to S2 in e16505. Number was
determined after the PID corrections but before the application of the cor-
relator software.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 5.2: Results of decay curve fit for 71Co decay using a 150 ms correlation time
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(see Fig. 5.8).

Table 5.3: Results of decay curve fit for 71Co decay using a 5 sec correlation time (see
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 5.9).

70

77

80

81

Table 5.4: Parameters used in exponential fit to shifted calculated NLD.

. . . . . . .

87

Table 5.5: Efficiency for detecting the full energy of select γ rays in one segment of
SuN, determined from Geant4 simulations. . . . . . . . . . . . . . . . . .

96

Table 5.6: Results of decay curve fit for 72Co decay using a 150 ms correlation time

(see Fig. 5.26). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Table 5.7: Results of decay curve fit for 72Co decay using a 5 sec correlation time (see

Fig. 5.28).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Table 5.8: Parameters used in exponential fit to shifted calculated NLD for 72Ni.

. . 107

Table 5.9: Lower, middle, and upper values for ρ(Sn) for different spin population
reductions. The full ρ(Sn) was reduced using several assumptions about the
β feeding to the ground state in 72Ni from the low spin isomer: 0% (upper
limit for populating ρ(Sn)), 42% (measured ground state feeding), and
100% (lower limit for populating ρ(Sn), where only the high-spin ground
state of 72Co is responsible for populating levels around Sn).

. . . . . . . 112

Table 5.10: Results of decay curve fit for 73Co decay using a 150 ms correlation time

(see Fig. 5.40). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Table 5.11: Results of decay curve fit for 73Co decay using a 5 sec correlation time (see

Fig. 5.41).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Table 5.12: Parameters used in exponential fit to shifted calculated NLD for 73Ni.

. . 120

Table 6.1: Parameters used to fit the experimental γSF with a scaled HFBCS table
(strength 3 in TALYS) and exponential upbend. Fits are shown in Figs.
6.1, 6.2, and 6.3 for the middle values. . . . . . . . . . . . . . . . . . . . . 127

x

Table 6.2: Range of neutron-capture cross sections and reaction rates (maximum/minimum

at each energy or temperature) for all three reactions. In each case, the
cross sections and reaction rates were reduced to under a factor of 3 (under
a factor of 2 for the 70Ni reaction). . . . . . . . . . . . . . . . . . . . . . . 128

Table A.1: TALYS default NLD for 74Zn including spin-dependent NLD for J=0-4.

An equal parity distribution is assumed. . . . . . . . . . . . . . . . . . . . 136

Table A.2: TALYS default NLD for 74Zn including spin-dependent NLD for J=5-8.

An equal parity distribution is assumed. . . . . . . . . . . . . . . . . . . . 139

Table A.3: CoH default NLD for 74Zn including spin-dependent NLD for J=0-3. An

equal parity distribution is assumed. . . . . . . . . . . . . . . . . . . . . . 141

Table A.4: EMPIRE default NLD for 74Zn including spin-dependent NLD for J=0-5.

An equal parity distribution is assumed. . . . . . . . . . . . . . . . . . . . 155

Table A.5: EMPIRE default NLD for 74Zn including spin-dependent NLD for J=6-10.

An equal parity distribution is assumed. . . . . . . . . . . . . . . . . . . . 159

Table A.6: TALYS default γSF for 74Zn. . . . . . . . . . . . . . . . . . . . . . . . . . 163

Table A.7: CoH default γSF for 74Zn.

. . . . . . . . . . . . . . . . . . . . . . . . . . 164

Table A.8: EMPIRE default γSF for 74Zn. . . . . . . . . . . . . . . . . . . . . . . . . 169

xi

LIST OF FIGURES

Figure 1.1: Section of the nuclear chart in the Ni region with the known s-process
pathway [1] in the upper left, near stability. A representative r-process
pathway has been added to the very neutron-rich region, though the exact
pathway is unknown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.2:

(a) Solar residual r-process abundance pattern (blue lines, shifted ver-
tically for clarity) compared to observed r-process abundances in six r-
process-rich stars (also shifted for clarity).
(b) Difference between ob-
served abundance and solar r-process abundance for each star. (c) Differ-
ence between average of all six stars and the solar r-process abundance.
Republished with permission of Annual Reviews from [2]; permission con-
veyed through Copyright Clearance Center, Inc. . . . . . . . . . . . . . .

Figure 1.3: Solar r-process abundance pattern (black dots) compared to r-process
abundance pattern calculated using three different mass models (model
indicated in each panel). The lighter bands indicate the uncertainty in
the calculated abundances with the rms error of the mass model com-
pared to known masses. The darker bands indicate the uncertainty when
the rms error is reduced to 100 keV. Reprinted from [13] with permission
from Elsevier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.4:

(a) Uncertainty in calculated abundance pattern for three different mass
models (model indicated in panel, same as in Fig. 1.3) when consider-
ing the uncertainty in β-decay half-lives. (b) Same as (a) but consider-
ing the uncertainty in neutron-capture rates instead of β-decay half-lives.
. . . . . . . . . . . .
Reprinted from [13] with permission from Elsevier.

Figure 1.5: Sensitivity study from Ref. [14] of the impact of uncertain neutron cap-
ture rates on the calculated abundances for a weak r-process. Used in
accordance with the Creative Commons Attribution (CC BY) license. . .

Figure 1.6: Spin distributions for different excitation energies from Eq. 1.3 using
values for 74Zn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.7: Comparison of the shape of the SLO and GLO models used to describe
the γSF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.1: Calibration for each SuN segment in e16505 using the γ-rays listed in
Table 2.5. Each panel is labeled with the segment number. . . . . . . . .

2

5

7

7

8

12

18

28

xii

Figure 2.2: Gain matching the front (top) and back (bottom) of the DSSD high gain
setting in e16505. The strip number is shown versus the channel number,
and the five alpha peaks from a 228Th source can be seen. A single
scaling factor was obtained for each strip to align the peak energies. For
both the front and back, the left panel shows the strip responses before
gain matching, while the right panel shows the strip responses after gain
matching with the five peaks seen in the same channels for each strip. . .

Figure 2.3: Gain matching the front (top) and back (bottom) of the DSSD low gain
setting in e16505. The strip number is shown versus the channel number,
as in Fig. 2.2. A source could not be used due to the gain range, so
gain matching was performed using the maximum energy peak from ions
during the experiment. The last strip on the front of the DSSD (strip 15)
was not working during the experiment. As in Fig. 2.2, the left panels
show the strip responses before gain matching, while the left panels show
the strip responses after gain matching, with the maximum energy peak
occuring in the same channels for all strips.
. . . . . . . . . . . . . . . .

Figure 2.4: Model of a 5x5 DSSD, which can be read as 25 pixels. In this example,
the decay (the black circle) was detected in the central pixel (the highest
energy deposition was in the center strips on both the front and back).
Two correlation pixel fields are possible for this decay. The first is the
same pixel, shown here as the light green box where the decay is located.
The second is a 3x3 field surrounding the decay pixel, shown here by the
dark green box (and including the light green box). The white boxes are
the remaining pixels that would not be considered in either correlation.

30

31

32

Figure 2.5: Organization of correlation logic (see text for details). . . . . . . . . . . .

33

Figure 3.1: Flowchart showing the steps of the Oslo Method.

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

38

Figure 3.2: Schematic of the population of excited states in the same compound nu-
cleus through both β decay and neutron capture for the example of using
74Cu β decay to populate the 74Zn nucleus that would be formed in a
neutron-capture reaction on 73Zn. The relative energies of each ground
state are to scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.3: SuN spectra showing the γ-ray energies, Eγ (top), and excitation energies,
. . . . . . . . . . . . . . . . . . .

Ex (bottom), from the decay of 74Cu.

Figure 3.4: Raw Ex vs. Eγ matrix for the β decay of 74Cu used to create the projec-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

tions in Fig. 3.3.

39

40

41

Figure 3.5: Unfolded Ex vs. Eγ matrix for the β decay of 74Cu.

. . . . . . . . . . .

43

xiii

Figure 3.6: Primary Ex vs. Eγ matrix for the β decay of 74Cu.

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

44

Figure 3.7: Calculated cumulative levels compared to known 74Zn levels. . . . . . . .

48

Figure 3.8: χ2 value versus shift value for the shifting of 74Zn theoretical cumula-
tive levels from Ref. [30]. The calculated cumulative levels are shifted in
excitation energy to match the known cumulative levels.
. . . . . . . . .

Figure 3.9: Goriely level densities (from Ref. [30] shifted in excitation energy according
. . . . . . . . . . . .

to the best shift value found, as shown in Fig. 3.1.

Figure 3.10: Nuclear level density for 74Zn showing the experimental data (black cir-
cles) as well as upper and lower limits (red squares, blue triangles), known
levels from NNDC (solid black line), and level density calculated in Ref.
[30] (solid blue line). Dashed blue lines indicate uncertainties on the shift
of the calculated level density. . . . . . . . . . . . . . . . . . . . . . . . .

48

49

51

Figure 3.11: Distribution of spins for the levels in 74Zn around the neutron separation
energy based on tabulated spin- and parity-dependent NLD from Ref. [30].
Spins highlighted in blue are populated following an allowed β decay of
74Cu and one dipole photon transition. The ground state of 74Cu is 2− [75]. 52

Figure 3.12: Gamma strength function for 74Zn showing the experimental data (black
circles), experimental data for 70Zn and 74,76Ge from Ref. [76] (blue
squares, triangles, and diamonds), and the GLO fit to that data and
extrapolation to lower energies (blue solid, dashed, and dot-dashed lines).
The last 15 points of the experimental γSF were used to minimize the dis-
tance between the experimental γSF and the extrapolations of the (γ,n)
data sets. The green band indicates the combined statistical and system-
. . . . . . . . . . . . . . . . . . . . . .
atic uncertainty of the SuN data.

Figure 3.13: (Top) Cross section for the 73Zn(n,γ)74Zn reaction calculated in TALYS.
The lighter band shows the variation in the cross section resulting from
combinations of the available NLD and γSF options in TALYS. The darker
band shows the uncertainty in the cross section when using the experi-
mental NLD and γSF. (Bottom) Astrophysical reaction rate calculated
by TALYS. The lighter and darker bands are the same as for the cross
section calculation.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.1:

(Top) Default NLD for 74Zn in TALYS, CoH, and EMPIRE compared
to the experimental NLD obtained using the β-Oslo method. (Bottom)
Default γSF for 74Zn in TALYS, CoH, and EMPIRE compared to the
. . . . . . . . . . .
experimental γSF obtained using the β-Oslo method.

54

58

62

xiv

Figure 4.2: Neutron-capture cross section calculated using the default inputs and set-
. . . . . . . . . . . . . . . . . . . . . .

tings for each of the three codes.

Figure 4.3: Experimental γSF for 74Zn fit with an E1 GLO function plus an M1 SLO
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

upbend.

Figure 4.4:

(Top) TALYS, EMPIRE, and CoH 73Zn(n,γ)74Zn cross sections using
experimentally obtained NLD and γSF. All other aspects of the codes
were left to default conditions. (Bottom) Percent deviation of the CoH
and EMPIRE cross sections compared to the TALYS cross section after
including the experimental NLD and γSF. See text for discussion of the
kink at En ∼200 keV.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.5: Neutron-capture cross section calculated after accounting for differences
in the nuclear physics inputs between the codes. . . . . . . . . . . . . . .

Figure 5.1: PID with uncorrected PIN energy versus uncorrected time-of-flight (de-
termined between the I2 scintillator and a PIN detector). . . . . . . . . .

Figure 5.2: PID with uncorrected, summed PIN energy (energy deposited in both PIN
detectors summed together) versus uncorrected TOF. . . . . . . . . . . .

Figure 5.3: Uncorrected PIN energy versus I2 position (determined by the time differ-
ence between signals from the north and south PMTs on the I2 scintillator)
for all data within the gates shown in Fig. 5.2. . . . . . . . . . . . . . . .

Figure 5.4:

(Top) Uncorrected TOF versus I2 position for all Co isotopes. (Bottom)
Corrected TOF versus I2 position for all Co isotopes, with the PIN energy
versus I2 position gate shown in Fig. 5.3 applied.
. . . . . . . . . . . . .

Figure 5.5:

(Top) Uncorrected PIN energy versus I2 position for all Co isotopes. (Bot-
tom) Corrected PIN energy versus I2 position, with the PIN energy versus
. . . . . . . . . . . . . . . . .
I2 position gate shown in Fig. 5.3 applied.

Figure 5.6: Final decay PID, with corrected PIN energy versus corrected TOF and
all element gates (Fig. 5.2) as well as I2 position gate (Fig. 5.3) applied.

Figure 5.7: Known level scheme for the β decay of 71Co. All γ-ray intensities are
relative to the 566.8 keV transition. . . . . . . . . . . . . . . . . . . . . .

63

64

66

68

72

73

73

75

76

77

78

xv

Figure 5.8: Full decay curve fit for the decay of 71Co including the parent contribu-
tion (red dot-dash line), daughter contribution (green dotted line), and
background contribution (gold dot-dash line). The black histogram is the
full decay curve from the data, with the total fit (combination of parent,
daughter, and background) shown with the black solid line. The shape
of the background contribution was determined using a correlation back-
wards in time, shown as the blue histogram. The blue dashed line fit to
the backwards correlation set the background contribution shape, and the
. . .
magnitude was allowed to vary to determine the blue dot-dash line.

Figure 5.9: Long correlation time decay curve fit for the decay of 71Co. The green
band shows the time region used to remove the daughter contribution to
the SuN spectra. The parent and daughter decay constants were set from
the fit shown in Fig. 5.8. The background component was determined the
same way as in Fig. 5.8.
. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.10: (Top) 71Co SuN γ-ray spectrum showing the raw spectrum (black), daugh-
ter decay contribution (green), background contribution (blue), and par-
ent decay contribution (red). The labeled peaks are strong transitions,
and are described in the text. (Bottom) TAS spectrum for the same de-
cay, with strongly fed levels labeled and described in the text.
. . . . . .

Figure 5.11: Raw 2D Oslo matrix for the decay of 71Co into excited states of 71Ni.
The γ-ray energies obtained from the segments of SuN are plotted on the
x-axis, while the excitation energy of the daughter nucleus, obtained from
. . . . . . . . .
the total energy in the detector, is plotted on the y-axis.

Figure 5.12: Unfolded 2D matrix for 71Ni with 600 keV binning on both axis. . . . . .

80

81

83

85

86

Figure 5.13: Primary 2D matrix for 71Ni with 600 keV binning on both axis. The

extraction region used for the NLD and γSF is outlined by the black lines. 86

Figure 5.14: χ2 values for different Ex shifts of the calculated cumulative levels com-
pared to the known cumulative levels for 71Ni. . . . . . . . . . . . . . . .

88

Figure 5.15: Unshifted (red line) and shifted calculated cumulative levels (blue and
green lines) compared to the known cumulative levels (black line). The
best shift value of 0.25 MeV with an error of 0.25 MeV led to only two
shifts needed, as the lower limit shift is 0 MeV.
. . . . . . . . . . . . . .

Figure 5.16: Shifted calculated level densities (upper, mid, and lower) near Sn used to
. . . . . . . . . . . .

determine ρ(Sn) values for the NLD normalization.

88

89

xvi

Figure 5.17: Distribution of spins for the levels in 71Ni around the neutron separation
energy based on tabulated spin- and parity-dependent NLD from Ref. [30].
Spins highlighted in blue are populated following an allowed β decay of
71Co and one dipole photon transition. The ground state of 71Co has
been tentatively assigned a value of (7/2−).
. . . . . . . . . . . . . . . .

Figure 5.18: Normalized NLD for 71Ni, with the known levels and Goriely calculated
. . . . . . . . . . . . .

NLD (shifts of 0 MeV, 0.25 MeV, and 0.5 MeV).

Figure 5.19: Normalized γSF for 71Ni (black dots, uncertainty indicated by grey band)
compared to γSF data on 69,70Ni from the β-Oslo method, as well as
higher-energy Coulomb dissociation data for 68,70Ni.
. . . . . . . . . . .

Figure 5.20: Simplified level scheme for the β decay of the high spin state in 72Co. Only
the four strongest transitions, originating from the strongly populated
3586.0 keV level, are shown for clarity and account for 70% of the β-decay
feeding intensity.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.21: Known level scheme for the β decay of the low spin state in 72Co. All
. . . . . . . . . . . . . . . . . . . . . . . .

known transitions are shown.

Figure 5.22: Geant4 simulation of the decay of the 72Co high spin isomer, with the
. . . . . . . . .

fit used to extract the efficiency of the 1194.2 keV γ ray.

90

91

92

94

95

97

Figure 5.23: Geant4 simulation of the decay of the 72Co low spin isomer at high γ

energies, with the fit used to extract the efficiency of the 3383.4 keV γ ray. 97

Figure 5.24: Low energy raw SuN spectrum with the fit used to extract the number of
. . . . . . . . . . . . . . . . .

1194.2 keV counts seen in the experiment.

Figure 5.25: High energy raw SuN spectrum with the fit used to extract the number
of 3383.4 keV counts seen in the experiment. . . . . . . . . . . . . . . . .

98

99

Figure 5.26: Full decay curve fit for the decay of 72Co.

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

99

Figure 5.27: Low energy GEANT4 simulation with 60% high spin and 40% low spin
decays compared to the SuN spectrum. The simulation has been scaled
to match the SuN data between 4 and 6 MeV. . . . . . . . . . . . . . . . 100

Figure 5.28: Long correlation time decay curve fit for the decay of 72Co. The green
band shows the time region used to remove the daughter contribution to
the SuN spectra.

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

xvii

Figure 5.29: 72Co SuN spectra showing the raw spectrum, daughter decay contribution,
background contribution, and final γ-ray (top) and TAS (bottom) spectra
for the de-excitation of 72Ni. As with Fig. 5.10, the labeled peaks note
strong γ-ray transitions and strongly fed levels, and are described in the
text.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Figure 5.30: Raw 2D Oslo matrix for the decay of 72Co into excited states of 72Ni.
The γ-ray energies obtained from the segments of SuN are plotted on the
x-axis, while the excitation energy of the daughter nucleus, obtained from
the total energy in the detector, is plotted on the y-axis.

. . . . . . . . . 105

Figure 5.31: Unfolded 2D matrix for 72Ni with 120 keV binning on both axis. . . . . . 105

Figure 5.32: Primary 2D matrix for 72Ni with 120 keV binning on both axis. The

extraction region used for the NLD and γSF is outlined by the black lines. 106

Figure 5.33: χ2 values for different Ex shifts of the calculated cumulative levels com-

pared to the known cumulative levels for 72Ni. . . . . . . . . . . . . . . . 106

Figure 5.34: Shifted calculated cumulative levels compared to the known cumulative

levels.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure 5.35: Shifted calculated level densities (upper, mid, and lower) near Sn used to

determine ρ(Sn) values for the NLD normalization.

. . . . . . . . . . . . 108

Figure 5.36: Distribution of spins for the levels in 72Ni around the neutron separation
energy based on tabulated spin- and parity-dependent NLD from Ref. [30].
The ground state of 72Co has been tentatively assigned a value of (6−,7−).
Spins highlighted in blue are populated following an allowed β decay of
72Co from a 6− ground state and one dipole photon transition, while spins
highlighted in green are populated following an allowed β decay from a
7− ground state and one dipole transition.

. . . . . . . . . . . . . . . . . 110

Figure 5.37: Same as in Fig. 5.36, including the spins populated in an allowed β decay
from a 1+ isomeric state and one dipole transition in addition to the
ground state decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure 5.38: Normalized NLD for 72Ni, with the known levels and Goriely calculated

NLD (shifts of 0.05 MeV, 0.25 MeV, and 0.45 MeV).

. . . . . . . . . . . 112

Figure 5.39: Normalized γSF for 72Ni for both spin possibilities for the ground state of
72Co compared to γSF data on 69,70Ni from the β-Oslo method, as well
as higher-energy Coulomb dissociation data for 68,70Ni. . . . . . . . . . . 113

Figure 5.40: Full decay curve fit for the decay of 73Co.

. . . . . . . . . . . . . . . . . 114

xviii

Figure 5.41: Long correlation time decay curve fit for the decay of 73Co. The green
band shows the time region used to remove the daughter contribution to
the SuN spectra.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Figure 5.42: 73Co SuN spectra showing the raw spectrum, daughter decay contribu-
tion, background contribution, and final γ-ray (top) and TAS (bottom)
spectra for the de-excitation of 73Ni. As with Figs. 5.10 and 5.29, the
labeled peaks note strong γ-ray transitions and strongly fed levels, and
are described in the text. . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Figure 5.43: Known level scheme for the β decay of 73Co. . . . . . . . . . . . . . . . . 117

Figure 5.44: Raw 2D Oslo matrix for the decay of 73Co into excited states of 73Ni.
The γ-ray energies obtained from the segments of SuN are plotted on the
x-axis, while the excitation energy of the daughter nucleus, obtained from
the total energy in the detector, is plotted on the y-axis.

. . . . . . . . . 118

Figure 5.45: Unfolded 2D matrix for 73Ni with 120 keV binning on both axis. . . . . . 119

Figure 5.46: Primary 2D matrix for 73Ni with 120 keV binning on both axis. The

extraction region used for the NLD and γSF is outlined by the black lines. 119

Figure 5.47: χ2 values for different Ex shifts of the calculated cumulative levels com-

pared to the known cumulative levels for 73Ni. . . . . . . . . . . . . . . . 120

Figure 5.48: Shifted calculated cumulative levels compared to the known cumulative

levels.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Figure 5.49: Shifted calculated level densities (upper, mid, and lower) near Sn used to

determine ρ(Sn) values for the NLD normalization.

. . . . . . . . . . . . 121

Figure 5.50: Distribution of spins for the levels in 73Ni around the neutron separation
energy based on tabulated spin- and parity-dependent NLD from Ref. [30].
Spins highlighted in blue are populated following an allowed β decay of
73Co and one dipole photon transition. The ground state of 73Co has
been tentatively assigned a value of (7/2−).

. . . . . . . . . . . . . . . . 122

Figure 5.51: Normalized NLD for 73Ni, with the known levels and Goriely calculated

NLD (shifts of 0 MeV, 0.25 MeV, and 0.5 MeV).

. . . . . . . . . . . . . 123

Figure 5.52: Normalized γSF for 73Ni (black dots) compared to γSF data on 69,70Ni
from the β-Oslo method, as well as higher-energy Coulomb dissociation
data for 68,70Ni. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

xix

Figure 6.1: Fit to experimental γSF for 71Ni using the HFBCS model (strength 3 in

TALYS) and an exponential upbend.

. . . . . . . . . . . . . . . . . . . . 126

Figure 6.2: Fit to experimental γSF for 72Ni using the HFBCS model (strength 3 in
TALYS) and an exponential upbend. The γSF obtained from a 6− 72Co
parent is on the left, while the γSF obtained from a 7− parent is on the
right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Figure 6.3: Fit to experimental γSF for 73Ni using the HFBCS model (strength 3 in

TALYS) and an exponential upbend.

. . . . . . . . . . . . . . . . . . . . 127

Figure 6.4:

(Left) TALYS cross section calculations (reactions are labeled). The light
band is the uncertainty in the cross section when considering all combina-
tions of the NLD and γSF models available (excluding the temperature-
dependent HFB NLD and SLO γSF). The darker band is the uncertainty
when including the experimentally constrained NLD and γSF, along with
their associated uncertainties. (Right) TALYS reaction rate calculations
(reactions are labeled). The light and dark bands are the same as for the
cross section, while the blue dashed line is the JINA REACLIB rate for
the reaction (also calculated in TALYS) [15]. . . . . . . . . . . . . . . . . 129

Figure 6.5: Comparison of the five Ni cross sections calculated in TALYS.

. . . . . . 130

Figure 6.6: Experimentally constrained γSF for 71,72,73Ni. . . . . . . . . . . . . . . . 131

Figure B.1: (Top Left) Starting 2D matrix for the analysis of the β decay of 71Co us-
ing the β-Oslo method (includes daughter decay and random correlation,
or background, contributions). (Top Right) Matrix with daughter decay
component that was subtracted from the starting matrix. (Bottom) Ma-
trix with the background component from random correlations that was
subtracted from the starting matrix.

. . . . . . . . . . . . . . . . . . . . 173

Figure B.2: (Top Left) Starting 2D matrix for the analysis of the β decay of 72Co us-
ing the β-Oslo method (includes daughter decay and random correlation,
or background, contributions). (Top Right) Matrix with daughter decay
component that was subtracted from the starting matrix. (Bottom) Ma-
trix with the background component from random correlations that was
subtracted from the starting matrix.

. . . . . . . . . . . . . . . . . . . . 174

Figure B.3: (Top Left) Starting 2D matrix for the analysis of the β decay of 73Co us-
ing the β-Oslo method (includes daughter decay and random correlation,
or background, contributions). (Top Right) Matrix with daughter decay
component that was subtracted from the starting matrix. (Bottom) Ma-
trix with the background component from random correlations that was
subtracted from the starting matrix.

. . . . . . . . . . . . . . . . . . . . 175

xx

Figure C.1: Fit to experimental γSFs for 71Ni using the HFBCS model (strength 3 in
TALYS) and an exponential upbend. The lower limit data set is on the
right, while the upper limit data set is on the left. . . . . . . . . . . . . . 177

Figure C.2: Fit to experimental γSFs for 72Ni, (6− ground state of 72Co) using the
HFBCS model (strength 3 in TALYS) and an exponential upbend. The
lower limit data set is on the right, while the upper limit data set is on
the left.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Figure C.3: Fit to experimental γSFs for 72Ni (7− ground state of 72Co) using the
HFBCS model (strength 3 in TALYS) and an exponential upbend. The
lower limit data set is on the right, while the upper limit data set is on
the left.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Figure C.4: Fit to experimental γSFs for 73Ni using the HFBCS model (strength 3 in
TALYS) and an exponential upbend. The lower limit data set is on the
right, while the upper limit data set is on the left. . . . . . . . . . . . . . 178

xxi

Chapter 1

Introduction

1.1 Production of heavy elements

There are many pathways to the creation of the elements that we see in the universe. Fusion

of light nuclei can explain how everything up to iron is produced, but that process stalls for

heavier elements as fusion is no longer energetically favorable. To move beyond iron there

needs to be another pathway, one that isn’t hindered by the large Coulomb barrier that

exists between charged particles. Neutron capture processes are the solution. The addition

of a neutron to a heavy nucleus is generally easier than adding a charged particle, so the

production of the majority of the elements above iron proceeds by neutron capture reactions.

There are two main processes for neutron capture in the universe–the slow neutron capture

process (s-process), and the rapid neutron capture process (r-process). As the names imply,

the difference between the two is the timescale on which neutrons are captured by the heavy

nuclei. In the s-process, the neutron density is low and the average time between neutron

captures is longer than the β-decay half-life of the nuclei involved, so they will undergo β

decay before capturing another neutron. This keeps the isotopes produced by the s-process

close to stability. In the r-process the neutron density is much higher which leads to a higher

rate of neutron captures. Nuclei will therefore capture many neutrons before β decaying,

leading to the production of isotopes very far from stability. When the neutron density

1

Figure 1.1: Section of the nuclear chart in the Ni region with the known s-process pathway [1]
in the upper left, near stability. A representative r-process pathway has been added to the
very neutron-rich region, though the exact pathway is unknown.

drops, the very neutron-rich nuclei will β decay back to stability. The relative locations of

the s-process and r-process in the Ni region can be seen in Fig. 1.1. The r-process path is

only approximate due to the uncertainty of the properties of these very exotic nuclei and the

uncertainty in the astrophysical conditions in which the process could occur.

1.2 The r-process

Most of the observed solar abundances of nuclei are thought to be produced in a combination

of both the s-process and the r-process. The s-process is easier to model, as the stability or

near-stability of the nuclei involved means that there are many direct measurements of the

nuclear properties required for the models, such as masses, β-decay half-lives, and neutron-

capture cross sections. The astrophysical conditions are also generally known. The solar

r-process abundance pattern can be deduced by subtracting the s-process contribution from

the total observed abundance pattern. The resulting r-process residual abundance pattern

has three peaks around A=80, 130, and 195, which correspond to the neutron shell closures

encountered by the very neutron-rich nuclei involved in the r-process.

2

Neutron Number (N)304050Proton Number (Z)28302632343638424446485254UnstableStableNeutron CapturePhotodisintegration-b Decay+b DecayThe astrophysical location of the r-process is of great interest because it helps define

astrophysical conditions. Many locations have been proposed, with supernova and neutron

star mergers emerging as the leading candidates (e.g. see reviews [2, 3]). The rate of oc-

currence of supernova events in the universe seems to be consistent with the abundance of

r-process nuclei observed, but modeling such events in multiple dimensions is difficult and

does not always result in the ejection of products into the universe [3]. Neutron star mergers,

which would supply the high density of neutrons needed for an r-process, were until recently

considered less likely than supernova due to their expected low rate of events and longer

evolution time.

The recent observation of the neutron star merger GW170718 [4] was the first confirma-

tion of an r-process location. The light curves detected from the kilonova after the merger

were consistent with the production of lanthanide elements [5,6], indicating that an r-process

had taken place in the merger as the light curves matched those predicted in an event in

which lanthanides would be produced [7]. This exciting observation has not solved the whole

mystery of the r-process, however. There is still much to learn about the astrophysical con-

ditions that do (or do not) support an r-process, and the situation is made more complicated

when the large mass range of nuclei produced is considered. Observations of a number of

r-process-rich stars show a difference between heavy and light r-process elements [2], which

has led to the development of the weak r-process to describe the production of the lighter

r-process elements.

1.2.1 Weak r-process

The stellar observations shown in Fig. 1.2 highlight the difference between light and heavy

r-process abundances. In panel (a), the residual solar s-process elemental abundance pattern,

3

represented by the blue lines, is compared to observations from different stars (the lines and

data sets have been offset for clarity) [2]. The difference between each data set and the solar

r-process residual abundance pattern is plotted in panel (b). The scatter in the difference

is large for the lightest elements (Z<50) but not for the heavier elements. The scatter is

evident for the lighter elements even when all of the data sets are averaged together, as can

be seen in panel (c) with the difference between the average of the observational data sets

and the solar system residual r-process abundance pattern. This indicates that there is a

separate process responsible for at least some of the production of these lighter elements,

which has been investigated as a result of high and low frequency supernovae events (e.g.

Refs. [8–11]), as well as in site-independent scenarios [12]. The best way to narrow down

the set of likely astrophysical conditions to determine the exact set required to produce

the observed abundance pattern would be to model many different conditions and compare

the calculated abundances to the observed abundances. That process is made extremely

difficult due to the large uncertainties in the nuclear physics inputs that are needed for the

calculations, such as masses, β-decay half-lives, and neutron capture rates.

The neutron capture rates do not have a large impact on the final abundances when the

temperature is high because the neutron capture is in equilibrium with photodisintigration.

When the temperature decreases, or if it never gets high enough, that equilibrium is not

reached and the capture rates become very important for understanding the final abundance

pattern.

4

Figure 1.2: (a) Solar residual r-process abundance pattern (blue lines, shifted vertically for
clarity) compared to observed r-process abundances in six r-process-rich stars (also shifted
for clarity). (b) Difference between observed abundance and solar r-process abundance for
each star. (c) Difference between average of all six stars and the solar r-process abundance.
Republished with permission of Annual Reviews from [2]; permission conveyed through Copy-
right Clearance Center, Inc.

5

1.3 Nuclear physics uncertainties

The impact of uncertainties in nuclear physics inputs on calculated abundance patterns has

been studied in detail for the heavy (main) r-process elements using Monte Carlo simula-

tions [13]. The masses, β-decay half-lives, and neutron capture cross sections over a large

mass range were varied using a probability distribution based on estimates of their theoret-

ical uncertainties, with a new r-process abundance pattern generated each time a value was

changed. The uncertainty in the abundance pattern calculated using three different mass

models (Fig. 1.3) can be very large, especially when considering the current experimental

uncertainty of approximately 500 keV rms compared to known masses (light band). Even

when artificially reducing the rms error to 100 keV (dark band), the uncertainty in the cal-

culated abundance pattern remains large in areas, making it difficult to determine which

mass model best fits the solar abundance pattern. The situation is similar when considering
the current uncertainties in β decay half-lives (estimated to be a factor of ∼10) and neutron
capture rates (estimated to be a factor of ∼1000), which can be seen in Fig. 1.4. Reduc-

ing the uncertainties in the nuclear physics inputs is the only way to differentiate between

calculations run with different astrophysical conditions.

For weak r-process nuclei, the only detailed study on the impact of uncertain nuclear

physics data is a recent sensitivity study focusing on neutron capture rates [14]. The study

considered a number of astrophysical conditions that produced a weak r-process. The first

set of mass fractions, calculated using reaction rate values from JINA REACLIB v1.0 [15],
were set as the baseline [Xbaseline(A)]. Then the neutron-capture rates of ≈300 nuclei were

varied, individually, by a factor of 100. The resulting mass fractions [X(A)] were compared

6

Figure 1.3: Solar r-process abundance pattern (black dots) compared to r-process abundance
pattern calculated using three different mass models (model indicated in each panel). The
lighter bands indicate the uncertainty in the calculated abundances with the rms error of the
mass model compared to known masses. The darker bands indicate the uncertainty when
the rms error is reduced to 100 keV. Reprinted from [13] with permission from Elsevier.

Figure 1.4: (a) Uncertainty in calculated abundance pattern for three different mass models
(model indicated in panel, same as in Fig. 1.3) when considering the uncertainty in β-decay
half-lives. (b) Same as (a) but considering the uncertainty in neutron-capture rates instead
of β-decay half-lives. Reprinted from [13] with permission from Elsevier.

7

Figure 1.5: Sensitivity study from Ref. [14] of the impact of uncertain neutron capture rates
on the calculated abundances for a weak r-process. Used in accordance with the Creative
Commons Attribution (CC BY) license.

to their corresponding baseline values, and a sensitivity factor F was calculated, where

F = 100 ×(cid:88)

A

|X(A) − Xbaseline(A)|.

(1.1)

The maximum F value over 55 sets of astrophysical conditions is shown in Fig. 1.5. The color

gradient indicates the value of F , with white boxes indicating nuclei that did not have an F

value greater than 0.5 for more than one set of conditions. Many nuclei have large values of

F , confirming that large uncertainties in neutron capture rates also effects the abundances

calculated for weak r-process nuclei, as was seen as in the heavier r-process nuclei. Reducing

the uncertainties of nuclei with large F values in Fig. 1.5 is a good first step to determine

what astrophysical conditions are needed to produce a weak r-process. The nuclei in this

work have various F factors: 73Zn has a value of 2, while 70,71,72Ni have values of 9, 10, and

8, respectively.

The most straightforward way to reduce the uncertainty in a neutron capture rate is to

directly measure the cross section. To do so generally requires a target of the nucleus of

8

interest, which is not possible when considering the very short half-lives of nuclei involved

in the weak r-process (seconds or less). Similarly, the short half-life of the neutron makes

a neutron target extremely challenging. Therefore, indirect methods are required to place

experimental constraints on the neutron-capture cross sections (for a review of the recent

developments in indirect methods for neutron-capture cross sections, see Ref. [16]). Many of

these methods rely on the Hauser-Feshbach model of neutron capture to calculate the cross

section and reaction rate using statistical information about the nuclei involved, which can

be constrained using experimental information.

1.4 Hauser-Feshbach model of neutron capture

When directly measuring a neutron-capture cross section is not possible, calculations are

used. The Hauser-Feshbach model of neutron capture utilizes information about the reac-

tion between the target nucleus and neutron (contained in the neutron optical model) and

statistical information about the nucleus formed after the reaction between the target nu-

cleus and the neutron–the nuclear level density (NLD) and γ-ray strength function (γSF).

Hauser-Feshbach calculations provide a straightfoward way to determine the cross section

for large numbers of neutron-rich nuclei. The required statistical information, however, can

have large uncertainties, which can lead to large uncertainties in the calculated cross sections.

When possible, it is important to determine the NLD and γSF using experimental methods

to constrain the needed inputs. Unfortunately, placing experimental constraints on the NLD

and γSF is currently possible only for select regions of the r-process and weak r-process due

to the difficulty in producing the desired nuclei at experimental facilities. For the majority

of the nuclei involved in both processes, theoretical models of the NLD and γSF are the only

9

viable method for calculating neutron-capture cross sections, so the large uncertainties away

from stability are unavoidable. As more experimental information becomes available, even if

it is just only a small subset of nuclei, both the NLD and γSF modeling can be improved to

better represent these properties in regions where experimental data is not available, which

will reduce uncertainties over the whole region involved.

1.4.1 Optical model

The neutron optical model describes the interaction between the target nucleus and the

incoming neutron and has a long history. The target nucleus is assumed to be a uniform black

body and the interaction between the target and neutron is modelled with a single interaction

potential. In general, a spherical optical model potential (OMP) is used for r-process nuclei.

The impact of including deformation has been found to have an minor impact, on the order

of 10%, which is smaller than the other sources of uncertainty when calculating a neutron-

capture cross section [17]. The standard OMP is that of Koning and Delaroche [18], where

the parameters are determined through experimental scattering data when it is available.

When not available, a global paramaterization is used. A semi-microscopic optical model, the

Jeukenne-Lejeune-Mahaux (JLM) model [19] is also commonly used, and generally results

in a neutron-capture cross section that is within 20% of that obtained with the Koning-

Delaroche model. For the nuclei in this work, the Koning and Delaroche OMP was used

with global parameterizations. When considering nuclei far from the neutron drip line, the

uncertainty in the neutron OMP is the smallest source of overall uncertainty in a Hauser-

Feshbach calculation. Instead, the NLD and γSF provide the majority of the uncertainty in

the final cross section calculation.

10

1.4.2 NLD models

The NLD also has a long history. The NLD function, ρ, represents the number of levels

per unit energy, and can be described as a function of excitation energy (Ex), spin (J), and

parity (π):

ρ(Ex, J, π) = N (Ex, J, π)/∆Ex,

(1.2)

where N is the number of levels of the specified spin and parity within the energy range

∆Ex. A total NLD can be produced by a summation over all spins and both parities, but

converting from a spin- and parity-dependent NLD to a total NLD requires information about

the distributions of both spin and parity in a given nucleus. This is particularly important

when an experiment only populates a subset of levels and thus needs to be corrected to

obtain a total NLD. An equal parity distribution is usually assumed, which has been shown

to be valid [20], especially for heavy nuclei. The parity distribution of lighter nuclei, and

those around shell closures, is less certain. The spin distribution is more complicated, as it

is dependent on both the spin and excitation energy [21]. An average overall distribution

function for the dependence of nuclear spin on excitation energy has been written as:

s(Ex, J) (cid:39) 2J + 1
2σ2(Ex)

− (J+1/2)2
2σ2(Ex) .

e

(1.3)

where σ2(Ex) is the so-called spin cut-off parameter. The above approximation is good for J

below 30 [20]. By fitting a set of 310 nuclei and including only levels with experimental spin

assignments, von Egidy and Bucurescu determined a structure-independent paramaterization

11

Figure 1.6: Spin distributions for different excitation energies from Eq. 1.3 using values for
74Zn.

of σ2 [22]:

σ2(Ex) = 0.391A0.675(E − 0.5P a(cid:48))0.312,

(1.4)

where P a(cid:48) is the deuteron pairing energy, which can be calculated using mass excess values

M (A, Z) for a given nucleus with Z,A as:

P a(cid:48) =

1
2

[M (A + 2, Z + 1) − 2M (A, Z) + M (A − 2, Z − 1)].

(1.5)

The nuclei used in the fit were either stable or very close to stability. An example of the

difference in the spin distribution as the excitation energy changes can be seen in Fig. 1.6.

At lower excitation energies the distribution strongly favors low spins, as is usually seen

in experimentally determined spins at low energy. As the excitation energy increases the

distribution shifts to higher spins. While this general trend is likely to hold, the shape of

the spin distribution is not well known far from stability.

12

Spin0s(E,J)x00.10.20.3Spin Distribution at E = 2 MeVx12345678910Spin Distribution at E = 4 MeVxSpin Distribution at E = 6 MeVxSpin Distribution at E = 8 MeVxThe Fermi Gas (FG) model is a well-known model for the NLD. Nucleons, which are

fermions, must obey the Pauli exclusion principle, which requires each nucleon to have a

unique set of quantum numbers. In the lowest energy configuration, the ground state, the

nucleons fill up the lowest energy single-particle states. As excitation energy is added,

nucleons are promoted to higher single-particle states, which determine the excited states

available to the nucleus. With only a small amount of excess energy, there are very few ways

to promote the nucleons, and therefore very few levels per unit energy. With increasing

energy added to the system, there are more configurations available and the density of levels

per unit energy increases. This simple description was utilized by Bethe in 1937 to obtain

an energy-dependent function for the level density [23]:

ρ(Ex) =

√

aEx

πe2
5/4
12a1/2E
x

,

(1.6)

where Ex is the excitation energy of the nucleus and a is the level density parameter. a can

be calculated using the spacing between the single particle states for protons and neutrons

but is normally determined from experimental NLD information when it is available. Global

systematics are used to determine values of a when it can’t be derived from a known NLD.

More recent determinations of a have included an energy dependence that account for the

energy-dependent shell effects that are not assumed in the simple description outlined above

[24].

The assumption that nucleons do not interact within a nucleus is not correct, which

has led to a modification of the FG model. The Back-shifted Fermi Gas (BSFG) model

incorporates the effect of nucleon interactions with a shift parameter ∆, which takes into

account the separation energy of a pair of nucleons that must be overcome before one can

13

be promoted individually [25, 26]. The simple incorporation of ∆ does not significantly alter

the FG level density formula:

ρ(Ex) =

√
a(Ex−∆)

πe2

12a1/2(Ex − ∆)5/4

.

(1.7)

While ∆ can be calculated as the pairing energy for neutrons and protons [27], both it and

a can also be used as adjustable parameters to reproduce an observed NLD [24].

The FG and BSFG models do not reproduce the NLD at low excitation energies as well as

they do at high excitation energies (above 5-10 MeV) [27]. On the other hand, the Constant

Temperature (CT) model [21] describes the known low energy NLD for many nuclei, with

the simple equation

ρ(Ex) =

e(Ex−E0)/T ,

1
T

(1.8)

where E0 and T are free parameters found through fitting experimental data. It has become

common to use the CT model at lower excitation energies and connect it to the BSFG model

to describe higher excitation energies (this is one of the methods available for the NLD in the

RIPL-3 database [28], for example). The two models are connected at a matching energy,

which is usually between 10-15 MeV for nuclei near stability [24]. For nuclei with incomplete

low-energy level schemes, the matching energy can be set to 0 MeV and only the BSFG

model is used to describe the NLD [24].

The models described above fit well to experimental data, but they are not based on

detailed structural information that would allow extrapolation far from stability where there

is no experimental data. Microscopic level densities provide the best predictive power, but

the computational challenges that arise when calculating mid- to large-mass nuclei have

limited their application at present. The RIPL-3 database contains level densities calcu-

14

lated by Goriely et al. on a Hartree-Fock (HF) basis [29] for energies up to 150 MeV

and spin values up to J=30. More recently, a combined Hartree-Fock-Bogolyubov (HFB)

and combinatorial method [30] provides both spin- and parity-dependent level densities. A

temperature-dependent version has also been published [31]. The fit to experimental data

far from stability is hard to determine, due to the lack of data to compare to.

1.4.3 γSF models

The γ-ray transmission coefficient, T (Eγ), represents the average probability of a γ-ray

escaping the volume of the nucleus, and is related to the γSF, f (Eγ) through the expression

TXL(Eγ) = 2πE

(2L+1)
γ

fXL(Eγ),

(1.9)

where X is the electromagnetic character (electric E, or magnetic, M ) and L is the multi-
polarity. Both T (Eγ) and f (Eγ) describe the average properties of excited states, and are

related as well to the reverse photoabsorption process. The photoabsorption strength can
be written as the average photoabsorption cross section (cid:104)σXL(Eγ)(cid:105):

−→
f XL(Ef , Jf , πf , Eγ) =

1

(cid:104)σXL(Ef , Jf , πf , Eγ)(cid:105)

(2L + 1)(π¯hc)2

(2L+1)
γ

E

,

(1.10)

where Ef is the final energy after the absorption and Jf and πf are the spin and parity

of the excited states at that energy. The shape of the photoabsorption cross section can

be assumed, through the generalized Brink hypothesis [32, 33], to be independent of the

energy at which the system starts, meaning the shape of the photoabsorption cross section

on an excited state is the same as on the ground state. The “upward” strength function

15

−→
f XL(Ef , Jf , πf , Eγ), can be used to describe the “downward” strength function as well

according to the principles of detailed balance. The γSF can be defined in a general way
with the average partial radiative widths (cid:104)ΓXL(Ei, Ji, πi, Eγ)(cid:105) [34],

←−
f XL(Ei, Ji, πi, Eγ) =

(cid:104)ΓXL(Ei, Ji, πi, Eγ)(cid:105)ρ(Ei, Ji, πi)

(2L+1)
E
γ

(1.11)

where Ei is the initial excitation energy bin of levels with spin Ji and parity πi, and a level

density of ρ(Ei, Ji, πi). The connection between the γSF and the photoabsorption cross

section has allowed the γSF to be described as a low-energy extension of the Giant Dipole

Resonance (GDR), a well-studied feature of the photoabsorption cross section of stable nuclei

seen at high excitation energies (around 15-20 MeV). There is generally more data on the

GDR shape than on the low-energy γSF shape, so models of the γSF have utilized the

connection. This relationship also allows for a connection between the γSF and the lifetime

of a state to be made–a small γSF value has a small partial width, which indicates a longer

lifetime for that state, and vice versa.

The Standard Lorentzian (SLO) shape fits the GDR very well, so it has been used to

represent the γSF in many cases. The SLO function was developed by Brink and Axel [32,33]

and is characterized by the strength (σXL), energy (EXL), and width (ΓXL) of the giant

resonance:

fXL(Eγ) = KXL

where the constant KXL is:

(E2

σXLEγΓ2

γ − E2

XL
XL)2 + E2

γΓ2

XL

,

(1.12)

KXL =

1

(2L + 1)π2¯h2c2

.

(1.13)

16

This shape has been used extensively for E1 radiation as well as M1 and E2, and even higher

multipolarities when needed. E1 radiation is by far the most commonly used for the γSF

due to the prevalence of the GDR across the nuclear chart. Currently, the SLO function is

usually reserved for M1 and E2 radiation, as the Generalized Lorentzian (GLO) shape has

been found to better represent the E1 shape [35].

The GLO function is based on the SLO function, but with a temperature-dependent limit

that is non-zero for the lowest γ-ray energies. It was developed by Kopecky and Uhl [35]

in response to the realization that the low-energy shape of the γSF can impact a neutron-

capture cross section calculation (e.g. see Ref. [36]). The GLO form differs most significantly

at low γ-ray energies (shown in Fig. 1.7, parameters detailed in Table 1.1), where data is

more limited, but the change in shape was enough to bring calculated neutron-capture cross

sections into agreement with measured values. The GLO is also described by the strength

(σE1), energy (EE1), and width (ΓE1) of the giant resonance, and has the form:

(cid:16)

fE1(Eγ, T ) = KE1

where:

(E2

γ − E2

Eγ ˜ΓE1(Eγ)
E1)2 + E2
γ

˜ΓE1(Eγ)2

(cid:17)

+

0.7ΓE14π2T 2

E3
E3

σE1ΓE1,

(1.14)

˜ΓE1(Eγ) = ΓE1

E2

γ + 4π2T 2

E2
E1

,

(1.15)

and T was originally meant to represent the Fermi Gas nuclear temperature, approximated

by T ≈(cid:113)

Ex/a. As with the BSFG and CT models, where ∆, a, E0, and T are parameters

that can be adjusted to match a known NLD, T in the GLO function is often used as a free

parameter when fitting measured γ, n data [24].

As with the NLD, microscopic models are desired for predicting the shape of the γSF

far from stability. The quasi-particle random-phase approximation (QRPA) model has been

17

Figure 1.7: Comparison of the shape of the SLO and GLO models used to describe the γSF.

Table 1.1: GLO and SLO E1 default parameters for 74Zn in TALYS used to generate the
functions shown in Fig. 1.7.

EE1 (MeV)

σE1 (mb)

ΓE1 (MeV)

T (GLO only)

17.485

133.069

6.144

0.7

18

-3f (E) (MeV)g-910-810-710-610g-ray energy (MeV)0520251015 Generalized Lorentzian Standard Lorentzianincorporated into both HF [37] and HFB [38] models to build excited states. Hauser-Feshbach

codes such as TALYS [39, 40] will often provide tabulated values from these microscopic

calculations as another option for the γSF.

In the last 15 years, experimental data at low γ-ray energies have shown an “upbend”,

where the strength increases as the γ-ray energy decreases, with a minimum usually around

2-4 MeV. Seen first in Fe isotopes [41], it has also been observed in many other nuclei

(e.g. [42–48]). It is unclear if the strength is of magnetic or electric type, though current

efforts to incorporate it into neutron-capture cross section calculations have used an M1
description. A recent Compton-polarization experiment of the 56Fe(p, p(cid:48)) reaction using

GRETINA [49] indicated the upbend may have a small bias towards magnetic transitions [50].

1.5

Indirect techniques

Indirect methods to constrain neutron-capture cross sections of short-lived nuclei rely on

constraining at least one of the two major contributors to the uncertainty in a Hauser-

Feshbach calculation–the NLD and γSF. There are four major indirect techniques currently

being used: the Oslo method [51–54], the β-Oslo method [55], the surrogate method [56],

and the γSF method [57, 58]. The Oslo and surrogate methods both utilize charged particle

reactions to populate the same compound nucleus that would be formed in the neutron-

capture reaction of interest, followed by observing the decay. This limits both methods to

nuclei near stability due to the high beam rates needed for such experiments. The γSF

method relies on measuring (γ, n) reactions to determine the inverse (n, γ) cross section,

which requires stable targets and again limits the method to nuclei very close to stability. The

β-Oslo method utilizes the β decay of neutron-rich nuclei to populate the nucleus that would

19

be formed in a neutron capture reaction, which allows for its application much further from

stability. It is still limited by the statistical framework of the Hauser-Feshbach calculation,

however, and cannot be applied to nuclei with low NLD (less than 10 levels per excitation

energy bin at the neutron separation energy, Sn) or small Qβ values (below 3 MeV in the
A∼70 region in order to populate a high enough NLD).

1.6 Dissertation outline

The results for experimentally constrained neutron-capture cross sections and reaction rates

for four neutron-rich nuclei are presented. In Chapter 2 the details of two experiments carried

out at the National Superconducting Cyclotron Laboratory (NSCL) are described, along with

information about the detectors that were used. The β-Oslo method is described in Chapter

3 using the extraction of the NLD and γSF for 74Zn as an example. The calculation of

the neutron-capture cross section and reaction rate for the 73Zn(n,γ)74Zn reaction using the

experimentally-constrained NLD and γSF is also included. Chapter 4 contains a comparison

of different Hauser-Feshbach codes, again using the 73Zn(n,γ)74Zn reaction as an example.

The step-by-step extraction of the NLD and γSF for 71,72,73Ni using the β-Oslo method is

described in Chapter 5. The subsequent calculation of the cross section and reaction rates

for the 70,71,72Ni(n,γ)71,72,73Ni reactions, as well as a comparison of the NLD, γSF, and

cross sections with lighter Ni isotopes can be found in Chapter 6. Finally, conclusions are

presented in Chapter 7 and an outlook of future work is provided.

20

Chapter 2

Experimental Setup

2.1 NSCL experiment e14505

The first experiment, number e14505, was carried out in February 2014 at the NSCL. A

primary beam of 86Kr was accelerated to 140 MeV/u through the Coupled Cyclotron Facility

and impinged on a 376 mg/cm2 thick Be target. The fragments were separated in the A1900
fragment separator [59] and ∼10 isotopes were delivered to the end station in the S2 vault,

centered on 71Co. A 60 mg/cm2 Al wedge was used in the Image 2 (I2) position, with a

0.5% momentum acceptance. The experimental setup consisted of the Summing NaI (SuN)

detector [60] to detect β-delayed γ rays, with a Si double-sided strip detector (DSSD) in

the center of SuN for ion implantation. A Si surface barrier detector was placed behind the

DSSD for veto events, and two Si PIN detectors were placed upstream of SuN. The ions were

identified using the energy loss in the PIN detectors and the time-of-flight (TOF) between

a thin scintillator at the focal plane of the A1900 and the PIN detectors. A total of 557,331

ions of 74Cu were delivered to the setup.

2.1.1 Summing NaI (SuN) detector

SuN consists of 8 optically-isolated segments of NaI surrounding a small (1.8 in) borehole.

It is 16 inches in diameter and 16 inches long. Each segment is read out by three PMTs, and

21

Table 2.1: Final voltages and scaling factors after gain matching the SuN PMTs for e14505
using the 40K background peak. All voltages are positive.

PMT
Number

0

1

2

3

4

5

6

7

8

9

10

11

Voltage

(V)

730

740

780

774

771

764

794

803

812

838

824

848

Scaling
Factor

PMT

Number

1.0920

1.0000

1.1099

1.1302

1.0000

1.1195

1.1148

1.0000

1.1316

1.0949

1.0000

1.0993

12

13

14

15

16

17

18

19

20

21

22

23

Voltage

(V)

835

820

821

831

865

824

889

853

831

909

930

892

Scaling
Factor

1.0866

1.0000

1.0995

1.0959

1.0000

1.1033

1.1467

1.0000

1.1131

1.0796

1.0000

1.1026

the signals of all three PMTs are added together to get the total signal in a segment. SuN

is used for total absorption spectroscopy (TAS) due to its large volume and high efficiency

(85(2)% for the 662 keV transitions in the decay of 137Cs, for example). The total signal

from all eight segments can be summed to determine the full energy deposited in the detector

from all the γ rays in a cascade that occur within 200 ns, while an individual segment can

be used to determine the energy of individual γ ray in the cascade. The sum peak in SuN is

a measure of the excitation energy of the daughter nucleus after β decay.

The 24 PMTs needed to be gain matched, which was done in two steps. First, the voltages

of the PMTs were adjusted until the 1460 keV peak from the decay of naturally occurring

22

Table 2.2: Calibration values for SuN segments in e14505.

Segment Number

Calibration Scale

Calibration Intercept

0

1

2

3

4

5

6

7

0.4193

0.4195

0.4113

0.4260

0.4191

0.4216

0.4046

0.4172

-16.02

-15.95

-14.95

-16.50

-16.41

-17.93

-16.20

- 14.74

40K was roughly in the same channel number in the software across all the PMTs. The

second step was done in software, where a scaling factor was applied so that the 1460 keV

peak was centered at exactly the same channel number. The 40K background peak was used

because the γ rays were external to the detector. The PMT signals in a single segment will

be different depending on where in the segment the γ ray is detected–the largest signal will

be from the PMT closest to the interaction. The final PMT voltages and scaling factors are

given in Table 2.1. Once the PMTs were gain matched, the three PMTs in a single segment

could be summed together. The segments were then energy calibrated using a 60Co source

and a 137Cs source. The resulting calibration factors are contained in Table 2.2. For this

experiment a linear calibration was used. The excitation energy was obtained by summing

the calibrated segments.

23

2.1.2 Double-sided silicon strip detector

The central implantation detector was a small, 2.54 x 2.54 cm2, 1 mm-thick DSSD. The

DSSD consisted of two sets of 16 strips, one on each side of the detector, and perpendicular

to each other. The location of an event was defined by the intersection of the strips on the

front and back of the detector that recorded the highest energy depostion. Two gain ranges

were used to differentiate between the implantation of an ion, which deposited 1000s of MeV

in the DSSD, and β-decay electrons, which deposited tens of keV.

The DSSD strips were gain matched in both gain ranges. The high gain (used for detect-

ing β-decay electrons) was gain matched using the 5.423 MeV particles from a 228Th source.

The response of each strip was scaled so that the peak was centered in the same channel.

The low gain (used for detecting implanted ions) could not be gain matched until after the

experiment started because standard sources do not produce α radition with high enough

energies for the low gain range (in the thousands of MeV). The maximum energy peak from

ion deposition in the DSSD was used, and was scaled for each strip so that the peak was

centered in the same channel. The high gain and low gain scaling factors for each strip are

given in Table 2.3, and are very similar as expected.

2.2 NSCL experiment e16505

A second experiment, number e16505, was carried out in September 2017 at the NSCL to

expand on the data collected in experiment e14505, with an emphasis on the β decay of

more neutron-rich Co isotopes. A primary beam of 45pnA of 82Se was accelerated to 140

MeV/u through the Coupled Cyclotron Facility and impinged on a 470 mg/cm2 thick Be

target. The fragments were separated in the A1900 fragment separator [59] and a cocktail

24

Table 2.3: Scaling factors for gain matching the front and back strips of the DSSD in e14505.

Front Strip
Number

Low Gain

High Gain

Scaling
Factor

Scaling
Factor

Back Strip

Number

Low Gain

High Gain

Scaling
Factor

Scaling
Factor

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1.102

0.962

0.952

0.978

0.986

1.087

1.000

0.933

0.973

1.025

0.965

1.008

1.007

0.966

0.996

0.973

1.191

1.099

1.054

1.089

1.125

1.092

1.152

1.094

1.083

1.139

1.092

1.102

1.132

1.104

1.149

1.135

0.752

0.818

0.762

0.863

0.786

0.773

0.823

0.758

0.742

0.765

0.772

0.781

0.774

0.804

0.564

0.814

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1.035

1.067

1.044

0.998

0.955

0.997

1.015

0.993

0.972

0.923

1.027

0.981

0.964

0.992

0.932

0.981

25

Table 2.4: Final voltages and scaling factors after gain matching the SuN PMTs for e16505
using the 40K background peak. All voltages are positive.

PMT
Number

0

1

2

3

4

5

6

7

8

9

10

11

Voltage

(V)

736

745

793

781

776

766

802

807

816

843

825

851

Scaling
Factor

PMT

Number

0.9685

0.9873

1.0391

1.0354

0.9648

1.0052

0.9993

1.0082

1.0364

1.0444

1.0186

1.0613

12

13

14

15

16

17

18

19

20

21

22

23

Voltage

(V)

839

821

836

833

869

828

893

852

833

908

929

891

Scaling
Factor

0.9866

0.9779

0.9403

0.9354

0.9900

0.9612

1.0010

0.9458

0.9294

0.9321

0.9762

0.9332

beam of ∼35 isotopes was delivered to the end station in the S2 vault, centered on 71Fe. A

20 mg/cm2 kapton wedge was used in the I2 position, with a full 5% momentum acceptance.

The experimental setup was the same as for e14505, except that the TOF was determined

between a position-sensitive scintillator in the I2 position and the PIN detectors upstream

of SuN. The more neutron-rich beam was able to produce more exotic fragments for the

measurement.

26

Table 2.5: γ-rays used for calibrating SuN segments in e16505.

Energy (keV)

59.5409(1) [61]

569.698(2) [62]

661.657(3) [63]

1063.656(3) [62]

1173.228(3) [64]

1332.492(4) [64]

2614.511(10) [65]

Calibration Source

241Am

207Bi

137Cs

207Bi

60Co

60Co

208Tl (228Th source)

2.2.1 SuN calibration

The voltages for each PMT used in e16505, as well as the scaling factors needed for the

gain matching, are shown in Table 2.4. The segments were then energy calibrated using the

γ-rays listed in Table 2.5. A linear calibration fit was found to represent the data as well

as a second-order polynomial, and can be seen in Fig. 2.1 for each segment. The calibrated

segment energies were added together to get the TAS energy with no additional calibration

required.

2.2.2 DSSD gain matching

The DSSD high gain was gain matched using four 228Th peaks (5.423, 5.685, 6.288, 6.778

MeV) and a 241Am peak (5.486 MeV). Each peak was scaled to match the channel number

on strip 7 for both the front and the back sets. The average scaling factor from the five

peaks was used. The signals of low gain were gain matched after the experiment started by

applying a scaling factor to each stip so the maximum energy peak was located in the same

27

Figure 2.1: Calibration for each SuN segment in e16505 using the γ-rays listed in Table 2.5.
Each panel is labeled with the segment number.

channel number of the peak of strip 7 on the front and back. The high gain and low gain

scaling factors for each strip are detailed in Table 2.6. The results of the gain matching for

the high gain (decays) can be seen in Fig. 2.2, while the results of the gain matching for the

low gain (ions) can be seen in Fig. 2.3.

2.3 Correlation of implants and decays

The separated ions of interest were delivered to the experimental station and came to rest

inside the DSSD. A short time later a given ion would undergo β decay. The signal from the

β-decay electron was correlated with the previously implanted ion based on both time and

the position within the detector by requiring that the ion and the decay were detected in

either the same pixel or a 3x3 pixel window surrounding the decay (see Fig. 2.4). The choice

of pixel field has to be chosen carefully based on the arrival rate of ions in the experiment.

The higher the rate, the more difficult it becomes to accurately correlate ions and decays due

28

200040006000100020003000Channel Number100020003000Known Energy (keV)200020002000400040004000600060006000y = 0.3791x - 7.671y = 0.3883x - 11.247y = 0.3842x - 11.726y = 0.3804x - 0.587y = 0.3844x - 10.102y = 0.3930x - 12.568y = 0.3907x - 12.094y = 0.3901x - 1.820Segment 0Segment 1Segment 2Segment 3Segment 7Segment 6Segment 5Segment 4Table 2.6: Scaling factors for gain matching the DSSD in e16505.

Front Strip
Number

Low Gain

High Gain

Scaling
Factor

Scaling
Factor

Back Strip

Number

Low Gain

High Gain

Scaling
Factor

Scaling
Factor

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1.067

1.025

1.007

1.004

1.057

1.030

1.074

1.000

1.017

1.050

1.011

1.050

1.058

1.035

1.066

1.018

1.176

0.998

0.947

1.185

1.031

1.045

1.100

1.000

1.085

1.094

1.043

1.066

1.141

1.067

1.113

1.046

1.104

0.969

0.932

1.162

1.081

1.023

1.980

1.000

0.997

1.001

1.292

1.151

1.087

0.956

1.008

1.000

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1.002

1.002

1.041

0.994

0.982

0.974

0.999

1.000

1.010

0.975

1.037

0.979

1.058

0.937

1.132

0.899

29

Figure 2.2: Gain matching the front (top) and back (bottom) of the DSSD high gain setting
in e16505. The strip number is shown versus the channel number, and the five alpha peaks
from a 228Th source can be seen. A single scaling factor was obtained for each strip to align
the peak energies. For both the front and back, the left panel shows the strip responses
before gain matching, while the right panel shows the strip responses after gain matching
with the five peaks seen in the same channels for each strip.

30

160000246810121416110210180002000022000240002600028000Channel NumberFront Strip Number160000246810121416180002000022000240002600028000Channel NumberFront Strip Number110210024681012141611021012000140001600018000200002200024000Channel NumberBack Strip Number024681012141612000140001600018000200002200024000Channel NumberBack Strip Number110210Figure 2.3: Gain matching the front (top) and back (bottom) of the DSSD low gain setting
in e16505. The strip number is shown versus the channel number, as in Fig. 2.2. A source
could not be used due to the gain range, so gain matching was performed using the maximum
energy peak from ions during the experiment. The last strip on the front of the DSSD (strip
15) was not working during the experiment. As in Fig. 2.2, the left panels show the strip
responses before gain matching, while the left panels show the strip responses after gain
matching, with the maximum energy peak occuring in the same channels for all strips.

31

160000246810121416110210310180002000022000240002600028000Channel NumberFront Strip NumberChannel NumberFront Strip Number160001800020000220002400026000280000246810121416110210310160000246810121416110210310180002000022000240002600028000Channel NumberBack Strip Number024681012141616000180002000022000240002600028000Channel NumberBack Strip Number110210310Figure 2.4: Model of a 5x5 DSSD, which can be read as 25 pixels. In this example, the
decay (the black circle) was detected in the central pixel (the highest energy deposition was
in the center strips on both the front and back). Two correlation pixel fields are possible for
this decay. The first is the same pixel, shown here as the light green box where the decay
is located. The second is a 3x3 field surrounding the decay pixel, shown here by the dark
green box (and including the light green box). The white boxes are the remaining pixels
that would not be considered in either correlation.

to random coincidences, so a single pixel correlation is preferred. For low rate experiments
(∼50 particles per second or less when using the small DSSD in SuN), the time between ion

implantations in a single pixel can become long enough that using a 3x3 pixel field becomes

more useful. In experiment number e16505, for example, the average rate of ions per pixel

was 0.1/second, while the half-lives of the isotopes of interest were in the tens of ms. This

allowed for a 3x3 pixel field to be used, as the average rate of ions within that field was still

less than 1/second.

The correlation time window that can be used depends on the half-life of the nucleus of

interest and the implantation rate on the detector (which was kept to below 100 pps in both

experiments). The window needs to be long enough that the chance of seeing the decay is

high, but not so long that the chance of another ion arriving within the pixel window is high.

A good rule of thumb is to use a correlation window that is 2-3 times the half-life of the

32

Figure 2.5: Organization of correlation logic (see text for details).

nucleus of interest with the low implantation rate used. With longer correlation windows the

rate of random correlations increases. For 74Cu, which has a half-life of 1.63(5) seconds [66],

a correlation time of 5 seconds was used. A 150 ms correlation time was used for the three

Co isotopes due to their shorter half-lives: 80(3) ms [67] for 71Co, 59.9(17) ms [68] for 72Co,

and 42(3) ms [69] for 73Co.

Figure 2.5 will be used to describe the correlation logic. In this example it is assumed that

the ions and their decays are located in the same pixel in the detector. Ions are represented

by squares, while decays are represented by diamonds. In panel (a), an ion A is detected

in the DSSD, followed some time later by a decay A1 and then another decay A2. The

33

A2A1ATimeA2A1B1ATimeB(a)(b)A2A1B1ATimeB(c)CA2A1B1ATimeB(d)Canalysis of event proceeds forward in time, so the ion, along with the location and time of

its detection, are saved. When the analysis reaches decay A1, a correlation is searched for.

A correlation window (shown as the light blue bar) is opened to look backwards in time for

an ion that arrived in that pixel that could be the source of the decay. Ion A, which falls

within the correlation window, is then correlated to decay A1. The same procedure occurs

when the analysis reaches decay A2, and is shown with the dark blue bar. Therefore, ion A

has two decays correlated to it, which could correspond to the parent and daughter decay.

In panel (b), the situation is made more complicated with the addition of another ion, B,

that is implanted before ion A, along with its decay B1. When the analysis reaches decay

B1, the correlation window (the lightest blue bar) is long enough that ion B is correlated

to it. This correlation does not affect the correlation of ion A to decays A1 and A2, which

proceeds as described in panel (a). Panel (c) adds another layer of complexity with the

detection of ion C immediately after ion B. The decay from ion C does not happen to be

detected. In this scenario, both ions B and C are saved, and when the correlation window is

opened by the decay B1, both ions are within the window. The correlation is done between

the decay and the ion closest in time to it, so decay B1 would be correlated to ion C, which

would be incorrect. To help prevent these types of miscorrelations, a minimum time window

between ions is enforced in the correlator. This concept can be seen in panel (d), which

has the same ion and decay scheme as panel (c). The correlation of ion A, which was not

affected by ion C in panel (c), now has an extra step to complete before the correlation is

finalized. Decay A1 is correlated to ion A due to the correlation window, but then another

window is opened, which starts with the detection of ion A and is the same length as the

correlator window. This window, shown as the dark green bar, does not encounter another

ion, so the correlation between ion A and decay A1 can proceed, as well as between ion A

34

and decay A2. The correlation of decay B1 does not proceed the same way. Decay B1 is

correlated to ion C as in panel (c), but when the new window is opened from ion C (the light

green bar), ion B is within the window. That means that decay B1 could be from ion B or

ion C, so the correlation is halted and decay B1 is not correlated to an ion. To obtain the

random correlation background, the correlation procedure is done backwards in time. For

this procedure, the exact same correlation as in Fig. 2.5 is performed, but the time arrow

is reversed [70]. The backwards in time procedure should take into account truly random

correlations, including decays from longer-lived isotopes in the DSSD.

The window that opens to prevent a decay from being correlated to an ion that is too close

in time to another ion is referred to as the “minimum implantation window”. The minimum

implantation window is set to be the same length as the correlation window to ensure there

is only one ion present in the correlation window. The longer the correlation window, the

longer the minimum implantation window and the higher the chance of there being another

ion in the window, which lowers the number of successful correlations. Therefore, shorter

correlation windows are preferred. There are less correlations in the first 150 ms of a 5 sec

correlation than there are in the full 150 ms of a 150 ms correlation due to the minimum

implantation window, as the number of decays that are not correlated to ions increases (see

Chapter 5 for values for the decay of 71,72,73Co).

35

Chapter 3

β-Oslo Method

The β-Oslo method [55] builds on the established Oslo method [51–54] for extracting the

NLD and γSF of a nucleus by populating highly excited states and detecting the subsequent

γ-ray emission. The main difference to the Oslo method is that β decay is used to populate

highly excited states instead of charged particle reactions. Populating the nucleus of interest

through β decay allows for experimental information about the NLD and γSF to be extracted

further from stability than other indirect methods, but is limited by the β-decay selection

rules and Q values. The γ-rays that are detected are used to experimentally constrain those

statistical properties so that they can be used to infer a neutron-capture cross section. The

method is generally restricted to nuclei that have large β-decay Q values and a high NLD

around Sn (see Introduction for general limits). The details of the β-Oslo method will be

explained in detail using the β decay of 74Cu, which was used to extract the NLD and γSF

of 74Zn in order to reduce the uncertainty in the 73Zn(n,γ)74Zn reaction cross section. The

analysis contains four main steps:

1. Unfolding of the raw 2D matrix of γ-rays observed in SuN for a given ion.

2. Extraction of the primary γ-ray matrix. These are the first γ rays to be emitted from

a level in a cascade to the ground state.

36

3. Simultaneous extraction of the functional forms of the NLD and T (Eγ) (see eq. 1.9

for translation of T (Eγ) to γSF).

4. Normalization of NLD and γSF.

Each step will be described in detail below. Fig. 3.1 is a flow chart that indicates the steps

required for the analysis, including the physics information required. The MAMA code [71]

handles the unfolding and primary extraction, which requires information about the response

of the γ-ray detector. The other codes are responsible for the NLD and γSF normalization,

and information such as the level density at the neutron separation energy [ρ(Sn)], the low-

energy levels, and the spin of the target nucleus in the neutron-capture reaction of interest

are all required.

3.1 Populating highly excited states through β decay

The β-Oslo method utilizes β decay to populate highly excited states of the nucleus of interest

(the neutron-capture product, 74Zn in this example) as indicated schematically in Fig. 3.2.

Not every β-decaying nucleus is amenable to the β-Oslo method. The most important

consideration is that the Q-value of the decay is large enough to produce statistical γ-ray

decay in the daughter. Generally, Q-values of at least 4 MeV are preferred, with larger

values providing a larger probability that there will be decays going through the statistical

region (roughly above 2-3 MeV [72]). While not necessary, it is preferred that the Q-value is

close to or even slightly above the neutron separation energy of the daughter nucleus so that

the full excitation energy range can be accessed by β decay and γ-ray transitions. It is also

assumed that only Gamow-Teller transitions are observed, as they will dominate and Fermi

37

Figure 3.1: Flowchart showing the steps of the Oslo Method.

38

Root HistogramMAMA MatrixUnfold Raw MatrixGenerate ResponseFunctionMAMAExtract PrimaryTransitionsFill and RemoveNegative CountsFill and RemoveNegative CountsExtract Level Density andGamma TransmissionCoefficient RhosigchiExperimental lower    threshold Spin Cutoff Parameter Fermi Gas model parameters (a and E1) Constant Temperature model parameter (T) Robin Normalize Level Density(and obtain slope fortransmission coefficient) Counting Known low-energy levelsMass number and protonnumber Average s-wave levelspacing at neutronseparation energy  D0Convert TransmissionCoefficient to GammaStrength Function andNormalize  Normalization Neutron separation energy Neutron separation energyAverage s-wave levelspacing at neutronseparation energy  D0Average total radiativeresonance width   ΓγSpin of target nucleusStarting value for level density parameter a γ     lower limitEγEx      upper and lowerlimitsLevel Density at Neutron Separation Energy   D2rho ρ()SnFigure 3.2: Schematic of the population of excited states in the same compound nucleus
through both β decay and neutron capture for the example of using 74Cu β decay to populate
the 74Zn nucleus that would be formed in a neutron-capture reaction on 73Zn. The relative
energies of each ground state are to scale.

transitions will populate isobaric analog states that would not be accessible by a neutron

capture experiment.

The γ-ray energy (Eγ) and excitation energy (Ex) spectra in SuN for the β decay of

74Cu are shown in Fig. 3.3. The level most strongly fed by β decay, at 605.9 keV (Iβ =

30(3)% [66]) is clear, as is a set of levels between 2800-3000 keV that are also strongly fed
(combined Iβ ≈ 31% [66]). The strongest γ-ray transition of 605.9 keV is clear as well.
Both the Eγ and Ex spectra are consistent with the literature on the β decay of 74Cu. The

Q-value of the β decay of 74Cu is 9.751 MeV, while 74Zn has a Sn of 8.235 MeV. The raw

Ex versus Eγ matrix for the decay of 74Cu is shown in Fig. 3.4. This is the starting point

for the β-Oslo analysis.

39

74Cu73Zn74Znnβ-Figure 3.3: SuN spectra showing the γ-ray energies, Eγ (top), and excitation energies, Ex
(bottom), from the decay of 74Cu.

40

 Gamma Energy (keV)0Counts per 5 keV02004006008001000120014001600 10002000300040005000600070008000050010001500200025003000  Gamma Energy (keV)010002000300040005000600070008000Counts per 5 keVFigure 3.4: Raw Ex vs. Eγ matrix for the β decay of 74Cu used to create the projections in
Fig. 3.3.

3.2 Unfolding

The γ-ray energies in the raw matrix were obtained from individual segments in SuN. While

the efficiency of detecting the total energy of a γ ray in the full volume of SuN is high (over

80% for a 1 MeV γ ray), the efficiency of detecting the full energy in just one segment is

lower, at around 40% for a 1 MeV γ ray. To account for this, the Eγ spectrum has to be

unfolded. The response function of the detector, which is a measure of the response to γ rays

of varying energies, was constructed using the Geant4 simulation code [73]. An iterative

unfolding procedure was then used to determine the full γ-ray energies from the raw data

collected, as described in Ref. [51].

The iterative method relies on folding trial γ-ray spectra with the response matrix and

altering the trial spectrum until the folded spectrum matches the experimental data. Letting

f represent the folded spectrum, u represent the trial spectrum, and R the response function

41

012345678910110012345678910210310E (MeV)gE (MeV)xmatrix (the full energy of the γ ray as a function of the energy deposited in the detector),

the folding procedure can be represented as [51]:

f = Ru,

(3.1)

which is compared to the observed spectrum r.

The observed spectrum is taken to be u0, the first trial function. The first folded spectrum

f 0 is calculated using Eq. 3.1 and compared to the observed spectrum. The next trial

function becomes the sum of the original trial function and the difference between the first

folded spectrum and the observed spectrum [51]:

u1 = u0 + (r − f 0).

(3.2)

This procedure is repeated, generating new trial functions at each step, until the folded

spectrum f n matches the observed spectrum within the experimental uncertainties, based

on a χ2 test.

Only the four central segments of SuN were unfolded due to the large volume of the

detector and the observation that very few γ rays deposit energy in the outer four segments.

The unfolding procedure described resulted in the unfolded matrix shown in Fig. 3.5 for

74Zn.

3.3 Extraction of primary γ rays

Primary γ rays are those that are emitted first in a cascade from any excited state. For

this analysis, the primary matrix should contain only these γ rays. To achieve this, the

42

Figure 3.5: Unfolded Ex vs. Eγ matrix for the β decay of 74Cu.

γ rays that follow the first in a cascade must be subtracted. The procedure, as described

in Ref. [52], is based on the assumption that the γ-ray emission probability from a given

excited state is the same if the level is populated directly by β decay or by a γ transition

from a higher excited state. Therefore, the unfolded spectra fi are composed of all the

possible γ rays decaying from excited states within the excitation energy bin i. The spectra

fj<i contain the same γ-ray transitions except for the first γ-rays emitted from bin i, so the

primary γ-ray distribution hi for each bin i is estimated by

h = fi − gi,

(3.3)

where gi is the sum of all spectra, weighted by wij, which represents the probability of the

decay from bin i to states in bin j (normalized so that (cid:80)

j wij = 1)

(cid:88)

j

gi =

nijwijfj

43

(3.4)

E (MeV)g1345678E (MeV)x12345678110210310200410Figure 3.6: Primary Ex vs. Eγ matrix for the β decay of 74Cu.

and requires information about the average γ-ray multiplicity (cid:104)Mi(cid:105) and the number of counts

in spectrum fi, A(fi), so that

nij =

(cid:104)Mj(cid:105)A(fi)
(cid:104)Mi(cid:105)A(fj)

.

(3.5)

g can be thought of as the probability distribution [P (Ex, Eγ)] that describes the probability

that a γ-ray of a given energy will be emitted from a given excited state. The γ-ray spectra

at lower excitation energy bins are subtracted from the bin of interest, leaving only the

primary γ-rays. This is done at each excitation energy. The primary matrix obtained for

74Zn is shown in Fig. 3.6.

3.4 Functional forms of the NLD and γSF

The NLD and γ-ray transmission coefficient [T (Eγ)] are extracted simultaneously from the

primary matrix. The probability that a γ ray of a given energy will be emitted from a

44

E (MeV)g1345678E (MeV)x123456781102103102given excited state can be related to the NLD and T (Eγ), ignoring the nuclear spin for the

moment, as:

P (E, Eγ) ∝ ρ(E − Eγ)T (Eγ)

where T (Eγ) can be converted to the γSF using the equation

γSF =

T (Eγ)
E3
γ

,

1
2π

(3.6)

(3.7)

which is the same as Eq. 1.9 for the specific case of a dipole transition. This relationship
assumes that the NLD and T are independent functions. The other major assumption at
this stage is that T is independent of the excitation energy at which is it extracted, which

has been shown to be valid in 238Np [72].

The primary matrix needs to be normalized so that the γ-ray energies in each excitation
energy bin sum to 1 for it to represent a normalized probability. The NLD and T (Eγ)

extracted from the primary matrix are functional forms which satisfy the following equations

[53]:

ρ(E − Eγ) = Aeα(E−Eγ ),

T (Eγ) = BeαEγ ,

(3.8)

(3.9)

where the A, B, and α parameters are determined in the normalization procedure. The

NLD (determined at the excitation energy of the nucleus after emission of a γ ray of energy
Eγ) and T (Eγ) are extracted simultaneously from a region of the Ex, Eγ matrix that is

45

statistical. The region is chosen to exclude strong transitions (such as from the first excited

state to the ground state) and low excitation energies, so that the γ emission proceeds

through statistical rules instead of being dominated by strong transitions. The Ex upper

limit of the range accounts for the energy of the first excited state in the β-delayed neutron

daughter, so that γ-rays from that nucleus are not included. The extraction region for 74Zn

is indicated by the black outline in the primary matrix in Fig. 3.6.

3.5 Normalization of NLD and γSF

The functional forms of the NLD and γSF need to be normalized to determine A, B, and α.

Three pieces of information are needed for the normalization. Typically, the known levels

at low excitation energies and the level density at the neutron separation energy [ρ(Sn)]

are used to determine A and α. B is usually determined using information from the GDR.

Nuclei accessible in β-decay experiments have at least some known low-energy levels, but

for short-lived nuclei there is little experimental information to determine ρ(Sn) and the

absolute γSF. Instead, they need to be obtained through systematics from nearby nuclei or

theoretical calculations.

In the traditional Oslo method, ρ(Sn) is calculated from the average s-wave level spacing

at the neutron separation energy (D0). D0 is the inverse of the NLD at ρ(Sn) for levels that
would be populated in neutron capture–that is, levels that have ±1/2 spin compared to the

ground state of the capturing nucleus. This value can be obtained using neutron capture

experiments on the nucleus of interest, which is again not possible for short-lived nuclei. The

value of B, the magnitude of the γSF, is calculated using the average radiative width at the

neutron separation energy, Γγ. Γγ can also be determined in neutron capture experiments

46

and suffers from the same restrictions. Theoretical calculations or systematics need to be

used when D0 and Γγ values are not available. In the β-Oslo method, the ρ(Sn) value is

obtained from theoretical NLD calculations, while the magnitude of the γSF is determined

using high-energy γSF information from nearby nuclei.

3.5.1 NLD

For the NLD normalization performed in this work all of the known low-energy levels in

74Zn were used, and the ρ(Sn) value was determined from theoretical calculations. The

procedure for relating the calculated NLD to experimental information was described in

Ref. [30], and involved using the cumulative levels calculated from the theoretical NLD.

They were compared to the known cumulative levels, and the calculated levels were shifted

in excitation energy to match the known levels. The known cumulative levels can be seen
compared to the calculated cumulative levels in Fig. 3.7. The best Ex shift value of 0.4 ±

0.2 MeV was determined from a χ2 minimization between the known levels and calculated

levels in the 2 to 3.25 MeV range. The results of the χ2 distribution can be seen in Fig. 3.8.

Once the excitation energy shifts was determined, it was also applied to the theoretical
level density. With a shift of 0.4 ± 0.2 MeV the level density calculated at 3 MeV would

need to be shifted to 3.4 MeV for the middle value, 3.2 MeV for the upper value, and 3.6

MeV for the lower value. The lower and upper designations refer to the new ρ(Sn) value

compared to the middle value–a larger shift moves a lower level density value to a higher

excitation energy, therefore producing a lower ρ(Sn) value. At higher excitation energies the

NLD has an exponential increase, which should be the same for all three shifted data sets.

Using a simple exponential fit of the form

47

Figure 3.7: Calculated cumulative levels compared to known 74Zn levels.

Figure 3.8: χ2 value versus shift value for the shifting of 74Zn theoretical cumulative levels
from Ref. [30]. The calculated cumulative levels are shifted in excitation energy to match
the known cumulative levels.

48

Excitation Energy Ex (MeV)0Cumulative Levels11021074Known Zn Cumulative LevelsGoriely Cumulative Levels (no shift)Shift = 0.2 MeVShift = 0.4 MeVShift = 0.6 MeV 1234290295300305310315320325330LD shift (MeV)-0.500.512 c value1.5Figure 3.9: Goriely level densities (from Ref. [30] shifted in excitation energy according to
the best shift value found, as shown in Fig. 3.1.

Table 3.1: Parameters used in exponential fit of Eq. 3.10 to shifted calculated NLD for 74Zn
and the resulting ρ(Sn) values.

Shift Value

Constant (a)

Slope (b)

0.2 MeV

0.4 MeV

0.6 MeV

1.7(2)

1.4(2)

1.1(2)

1.00(2)

1.00(2)

1.00(2)

ρ(Sn)

6360(130)

5200(120)

4230(100)

y = aebx,

(3.10)

where a is the constant and b is the slope, the shifted theoretical NLD values produced ρ(Sn)
values of 4230 MeV−1, 5200 MeV−1, and 6360 MeV−1 at the Sn of 8.235(3) MeV [66]. The

parameters are detailed in Table 3.1 and the fits are shown in Fig. 3.9.

49

Shift = 0.2 MeVShift = 0.4 MeVShift = 0.6 MeV Exponential fit to 0.2 MeV shiftExponential fit to 0.4 MeV shiftExponential fit to 0.6 MeV shift74Zn S = 8.235 MeVn210310410510Excitation Energy E (MeV)x6789-1Level Density (MeV)10A number of assumptions are contained within the NLD normalization. The parity

distribution is assumed to be roughly equal at all excitation energies and spins, which is

likely valid for heavy nuclei but may be less valid for lighter nuclei or those near closed

shells. It is also assumed that the populated spin distribution from β decay is the same at

all excitation energies, and the distribution at Sn is used from theory calculations, which

are also assumed to be correct. Finally, the calculated NLD from theory is assumed to have

the correct shape, as only the Ex dependence is altered to match the known levels, but the

slope is not.

With both the known low-energy levels and ρ(Sn), the NLD could be normalized. This

was done through a simultaneous fit of the experimental NLD to the low-energy levels and

to a CT model extrapolated from the ρ(Sn) value. The parameters for the Constant Tem-

perature model were determined through the fit. This provided both the A and α values in

the NLD functional form, as well as α in the functional form of the γSF (see eq. 3.8 and

3.9). The normalized NLD is shown in Fig. 3.10, with the known levels and shifted Goriely

NLD that were used for the normalization.

3.5.2 Limited spin population

The NLD is also a function of angular momentum, or nuclear spin. A limited range of spins

is populated by the β-decay process, which needs to be taken into account in this analysis.
The ground state of 74Cu is 2− [74], which would populate spins of 1−, 2−, and 3− in an

allowed β decay. After one dipole transition, the spins populated would be in the range of

0 to 4, of both parities. The primary γ rays observed in a β-Oslo experiment are restricted

to that spin range, which impacts the normalization of the γSF. Because α was determined

in the NLD normalization, the ρ(Sn) value and the known levels have to be reduced based

50

Figure 3.10: Nuclear level density for 74Zn showing the experimental data (black circles)
as well as upper and lower limits (red squares, blue triangles), known levels from NNDC
(solid black line), and level density calculated in Ref. [30] (solid blue line). Dashed blue lines
indicate uncertainties on the shift of the calculated level density.

51

    74Zn S = 8.245 MeVn SuN data, middle  SuN data, lower limit SuN data, upper limit Known Levels  r from Goriely et al.-1Level density r(E) (MeV) x1-110210310410510Excitation energy E (MeV)x012345678Figure 3.11: Distribution of spins for the levels in 74Zn around the neutron separation energy
based on tabulated spin- and parity-dependent NLD from Ref. [30]. Spins highlighted in blue
are populated following an allowed β decay of 74Cu and one dipole photon transition. The
ground state of 74Cu is 2− [75].

on the expected spin population to determine α for the γSF normalization. To determine

the reduction, the spin- and parity-dependent theoretical NLD from Goriely [30] was once

again used. The percentage of the total NLD around the neutron separation energy for each

spin was calculated (see Fig. 3.11), and the percentage that fell within the spin range of

interest, highlighted in blue in the figure, was determined. For 74Zn, 48% of the NLD fell
within the spin range 0-4, leading to reduced ρ(Sn) values of 2040 MeV−1, 2510 MeV−1,
and 3070 MeV−1. The known levels at low Ex used in the normalization with the reduced

ρ(Sn) were also reduced to include only levels are assigned spins that fall within the spin

range of interest, which resulted in a reduction of 20%. The normalization parameters were

similar between the full and reduced NLD, which was expected.

52

Spin02468101214Percent of Total NLD (%)0246810121416Spin Distribution Spins Populated3.5.3 γSF

With the α value set by the NLD normalization (using the reduced normalization values),

only the value of B was unknown. The γSF of nearby nuclei at high energies was used for

the γSF normalization. For 74Zn, photoabsorption data for 70Zn and 74,76Ge was used [76].

The γ, n cross section can be converted into a γSF using the equation

γSF (M eV −3) =

σ2
γ

(3π¯h)2 ,

(3.11)

where σγ is the photoabsorption cross section of the nucleus of interest.

The photoabsorption cross section is generally measured above the neutron separation

energy of the nucleus, so it must be fit and extrapolated to lower energies to be used for

normalization of the experimental γSF, which does not go above Sn. A GLO function

[35] describes the shape of the γSF at high excitation energies very well, and has been

traditionally used to estimate the low-energy shape of the γSF (see Section 1.4.3). Each

available γ, n data set was fit with a GLO function, and the resulting average function

was extrapolated to lower excitation energies where it overlapped with the experimental

γSF data. The parameters for the GLO functions (one for each data set) are detailed in

Table 3.2, along with the average values. A χ2 minimization was performed to match the

experimental γSF to the average from the GDR fits from 4 to 7 MeV to determine B. The

normalized γSF, along with the γ, n data and GLO function extrapolations, are shown in

Fig. 3.12. The green band in the figure indicates the uncertainty in the SuN data.

53

Figure 3.12: Gamma strength function for 74Zn showing the experimental data (black cir-
cles), experimental data for 70Zn and 74,76Ge from Ref. [76] (blue squares, triangles, and
diamonds), and the GLO fit to that data and extrapolation to lower energies (blue solid,
dashed, and dot-dashed lines). The last 15 points of the experimental γSF were used to
minimize the distance between the experimental γSF and the extrapolations of the (γ,n)
data sets. The green band indicates the combined statistical and systematic uncertainty of
the SuN data.

54

E (MeV)g0-3f(E) (MeV)g-91074 Zn SuN data74 Zn SuN data, upper/lower limits70 Zn(g,n) data, Goryachev et al. 74 Ge(g,n) data, Goryachev et al. 76 Ge(g,n) data, Goryachev et al. 70 Extrapolation of Zn data74 Extrapolation of Ge data76 Extrapolation of Ge data Average fit to GDR data 246810121416-810-710-610-510-410Table 3.2: GDR parameters from GLO fits to experimental data from Ref. [76]. EE1 is the
energy of the giant resonance, ΓE1 is the width, and σE1 is the strength. A value of 0.7 for
Tf in the GLO function was adopted for all three data sets.

Nucleus

70Zn

74Ge

76Ge
Average

EE1 (MeV)

σE1 (mb)

ΓE1 (MeV)

17.64(6)

17.86(10)

17.64(9)

17.71(7)

97(1)

95(1)

101(1)

98(1)

9.9(2)

12.4(4)

11.2(4)

11.2(3)

3.6 Cross section and reaction rate calculation

The NLD and γSF obtained using the β-Oslo method technique were input into a Hauser-

Feshbach reaction code to obtain the neutron-capture cross section. Previous β-Oslo results

have been based on the TALYS reaction code [39, 40], and for consistency this choice was

retained for the 73Zn(n, γ)74Zn reaction, as well as the Ni isotopes that form the basis of

this work. TALYS v. 1.6 was used in all cases. A discussion on the differences among a

select set of Hauser-Feshbach codes can be found in Chapter 4.

TALYS offers a lot of flexibility for describing both a NLD and γSF, which makes it easy

to ensure the NLD and γSF that are used in the calculation represent the experimental data

well. The NLD was input in a tabular form generated from a CT model fit to the experimental

data, which assumed an equal parity distribution. The γSF was represented as an E1 GLO

combined with an exponential function for the upbend. The GDR parameters used in the

GLO+exponential fit for the 74Zn data were the average values from the parameters in Table

3.2, which were used to normalize the γSF. The parameters for the upbend were allowed to

vary to best fit the upper, middle, and lower γSFs, and the results are detailed in Table 3.3.

55

Table 3.3: Parameters for the upbend added to the GLO to describe the experimental γSF
of 74Zn.

Experimental data set

Lower limit

Middle

Upper limit

Exponential

Exponential

constant

slope

1E-7

1E-7

1E-7

-1.4

-1.6

-1.9

The GDR parameters were added to the input file for the calculation, but the exponential

upbend was added directly to the source code.

The resulting 73Zn(n, γ)74Zn neutron-capture cross section and reaction rate are shown

in Fig. 3.13. For both, the light band is the range in values due to all combinations of NLD

and γSF models shown in Table 3.4, which is a subset of the NLD and γSF models available

in TALYS, using default parameters. In v. 1.6 there are six NLD models and five γSF models

available. One of the NLD models (temperature-dependent Hartree-Fock-Bogolyubov using

the Gogny force [31]) and one of the γSF models (SLO [32,33]) were not used in this work due

to systematic disagreements with known data (see Ref. [77]), leaving five NLD and models

and four γSF models. The neutron energy range chosen for the cross section (10 keV to 1

MeV) corresponds to likely weak r-process temperatures [14]. The temperature range shown

in the reaction rate figure, however, is set by TALYS and can not be changed. The range
(0.1 to 10 GK) corresponds to higher neutron energies of ∼4-40 MeV (these are the most

probable energies in the Maxwell-Boltzman distribution). The dark band is the range in

values with the inclusion of the experimentally-constrained NLD and γSF functions. The

uncertainty in the neutron-capture cross section was reduced from a factor of 5 (maximum)

56

Table 3.4: Subset of NLD and γSF models available in TALYS used to determine the un-
certainty in the cross section and reaction rate of neutron-rich nuclei.

NLD models

CT+BSFG [21]

BSFG [21, 78]

Generalized super fluid model [79]

γSF models

Kopecky-Uhl GLO [35]

Hartree-Fock BCS + QRPA [37]

Hartree-Fock-Bogolyubov +

QRPA [38]

Hartree Fock using Skyrme force [29]

Modified Lorentzian [80]

Hartree-Fock-Bogoliubov (Skyrme force) + combina-
torial method [30]

to less than a factor of 2, while the uncertainty in the reaction rate was reduced from a factor

of 11 (maximum) to less than a factor of 2.

57

Figure 3.13: (Top) Cross section for the 73Zn(n,γ)74Zn reaction calculated in TALYS. The
lighter band shows the variation in the cross section resulting from combinations of the
available NLD and γSF options in TALYS. The darker band shows the uncertainty in the
cross section when using the experimental NLD and γSF. (Bottom) Astrophysical reaction
rate calculated by TALYS. The lighter and darker bands are the same as for the cross section
calculation.

58

Neutron Energy (MeV)-210-1101Cross Section (mb)-110110210TALYS Upper/Lower LimitsSuN Upper/Lower LimitsSuN Middle ValueT(GK)-1101103-1-1Reaction Rate (cmsmol)510610710TALYS Upper/Lower LimitsSuN Upper/Lower LimitsSuN Middle ValueChapter 4

Code Comparison

4.1 Hauser-Feshbach codes

There are many codes available to perform Hauser-Feshbach neutron-capture calculations.

Some of the most commonly used codes for astrophysical calculations are TALYS [39, 40],

EMPIRE [81], NON-SMOKER [82, 83], and CoH [84]. These codes utilize various forms of

the NLD and γSF of short-lived, neutron-rich nuclei, which can lead to differences in how

the NLD and γSF are represented in the codes. The uncertainty in both the NLD and γSF

increase when moving away from stability [85, 86] for reasons discussed in the last chapter

that is reflected in model differences for short-lived, neutron-rich nuclei, leading to large

uncertainties in the calculated neutron-capture cross section even within one code (such as

the large uncertainties in TALYS described in Chapters 3 and 6). In addition, the agree-

ment between codes is not guaranteed. There have been previous attempts to determine the

discrepancy between cross sections calculated by different codes for both stable nuclei [87]

and fissionable nuclei [88]. One study with stable nuclei compared the neutron-capture rates

calculated using four Hauser-Feshbach codes – TALYS, NON-SMOKER, CIGAR, and SAP-

PHIRE [89] – and found that variations in the model parameters among the codes resulted in

factors of 2-3 difference at 30 keV even with the same model parameters [87]. Another study

that focused on fissionable nuclei (238U and 239Pu) compared TALYS, EMPIRE, CoH, and

59

CCONE [90] (CCONE was developed specifically for actinides). By requiring all the param-

eters to be the same across the four codes, the authors were able to obtain neutron-induced

fission cross sections and neutron inelastic cross sections for both nuclei that matched within

10%. This result is very promising, but does point to the amount of work that is required

to make sure all of the parameters are consistent. Both studies used nuclei with well-known

nuclear data, so here a new comparison of Hauser-Feshbach codes was performed to de-

termine the uncertainty in the neutron-capture cross section calculated for a short-lived,

neutron-rich, and only partially-studied nucleus, 73Zn due to code differences.

Understanding the scale of the uncertainty inherent in the choice of Hauser-Feshbach

code is particularly important when utilizing indirect methods to obtain experimentally-

constrained NLD and γSFs. The shape of each function, especially the γSF, may not conform

exactly to the model that is used in a particular code (the NLD is usually described by the

CT or BSFG models and is less likely to vary strongly between codes). Learning how to

run a Hauser-Feshbach code with experimental data involves determining what models are

available, learning how to adjust the parameters, and understanding how the experimental

NLD or γSF is manipulated between when it it included and when it is used in the neutron

capture calculation. Checking model predictions between different codes is cumbersome

and thus unlikely to be performed for every nucleus with an experimentally-constrained

NLD and γSF. However, the potential variation among codes results in an additional source

of uncertainty in the neutron-capture cross sections obtained using indirect methods that

should be acknowledged. For the 73Zn(n, γ)74Zn reaction, the neutron-capture cross sections

calculated by different codes differed by almost an order of magnitude,and could be reduced

to a difference of about 10% only after requiring that the NLD, γSF, and level information

were exactly the same.

60

4.2 Calculation with default settings

First, the neutron-capture cross section was calculated using the default settings for each

code in a “black box” calculation. This involved running the Hauser-Feshbach neutron-

capture calculation with only the minimum of inputs, such as the target nucleus (73Zn)

and neutron energies (0.01 MeV to 1 MeV). The three codes have different models of the

NLD and γSF as the default. The TALYS default for the NLD is a CT+FG model [21]

with a matching energy of 0 due to the small number of known levels in 74Zn. CoH uses

the BSFG model for the NLD, while EMPIRE has employed a generalized superfluid model

(GSM) [79] that has been renormalized to discrete levels and Sn information specifically for

the EMPIRE code. For the γSF, TALYS uses a GLO function for E1 radiation and SLO

functions for all other multipolarities. CoH does the same, but restricts γ-ray emission to L

= 1 transitions. EMPIRE uses a modified Lorentzian function (MLO), where the width of

the GDR is determined using a semi-empirical expression [91]. The default NLD and γSF

assumptions used in each code can be seen compared to the experimental values in Fig. 4.1.

For tables of the default NLD and γSF, see Appendix A.

The resulting cross sections, shown in Fig. 4.2, show how different the results can be.

Different models for the NLD and γSF affect both the shape and magnitude of the neutron-

capture cross section as a function of neutron energy, and variations among models can be

an order of magnitude.

4.3 Calculation with experimental data constraints

Tests of the impact of using the same NLD and γSF in each code were performed utilizing the

experimentally-constrained NLD and γSF described in Chapter 3 for 74Zn. The NLD was

61

Figure 4.1: (Top) Default NLD for 74Zn in TALYS, CoH, and EMPIRE compared to the
experimental NLD obtained using the β-Oslo method. (Bottom) Default γSF for 74Zn in
TALYS, CoH, and EMPIRE compared to the experimental γSF obtained using the β-Oslo
method.

62

Excitation Energy (MeV)1-1Level Density (MeV)-110110210310410 TALYS default NLD CoH default NLD EMPIRE default NLD NLD from SuN data 02345678910Gamma Energy (MeV)-3gSF (MeV)-1010-910-810-710 1 TALYS default gSF CoH default gSF EMPIRE default gSF gSF from SuN data02345678910Figure 4.2: Neutron-capture cross section calculated using the default inputs and settings
for each of the three codes.

63

 Cross Section (mb)110210Neutron Energy (MeV)1 TALYS default CoH default EMPIRE default-110-110-210Figure 4.3: Experimental γSF for 74Zn fit with an E1 GLO function plus an M1 SLO upbend.

fit with the CT model described in Chapter 3 to generate a table in the format appropriate

for each code. In all cases, an equal parity distribution was assumed. The γSF had more

limitations, particularly in CoH. The only model available for E1 radiation in CoH is a GLO

function, and an M1 SLO function can be added to represent the upbend component. Due to

this limitation, the experimental γSF was fit with a combination of an E1 GLO and an M1

SLO function. When incorporating the experimental γSF into TALYS for the calculation in

Chapter 3, an exponential function was used to represent the low-energy upbend, which was

incorporated directly into the source code. Direct modification of the source code for CoH

and EMPIRE to incorporate the shape of the experimental γSF was more complicated and

not pursued. The parameters used in the GLO+SLO fit are given in Table 4.1, while the fit

to the experimental γSF is shown in Fig. 4.3.

With the addition of the experimental NLD and γSF, the results from the three cal-

culations were closer, as shown in the top panel of Fig. 4.4. The major difference among
them was the shape as a function of neutron energy–at ∼200 keV the TALYS calculation

64

 E (MeV)g012345678-3SF (MeV)g-810Total SF (E1+M1)E1 contributionM1 contribution-710Table 4.1: GLO E1 parameters and SLO M1 parameters used to fit the experimental γSF.

EE1 (MeV)

σE1 (mb)

ΓE1 (MeV)

EM 1 (MeV)

σM 1 (mb)

ΓM 1 (MeV)

17.7(1)

98(2)

11.2(6)

4.63 x 10−7(500)

39(9)

0.096(88)

decreased, while the EMPIRE and CoH calculations did not. The scale of these differences

can also be seen in the bottom panel of Fig. 4.4, where the percentage deviation of EMPIRE

and CoH from TALYS is shown. At low neutron energies, the CoH calculation was very
close to TALYS, and even the EMPIRE calculation differed by less than 50%. At ∼200

keV, however, the deviation jumped to almost 200% for both. The TALYS cross section was
chosen as the comparison model due to its unique shape at this step. The deviation at ∼200

keV can be explained by the first excited state of 73Zn at 195.5(2) keV [92]. If the level

was used in the code for neutron inelastic scattering on 73Zn then the neutron-capture cross

section would decrease at 195.5 keV. The decrease in the cross section calculated in TALYS

indicated that inelastic scattering was present. In both CoH and EMPIRE, however, the

level was not contributing to inelastic scattering. An investigation of the 73Zn levels being

in each code found that EMPIRE does not assign the 195.5 keV level a spin or parity, while

CoH does but considers it a poorly known level, so it is not used in the calculation (see Table

4.2).

It is important to note that while the NLD is the same as used in the TALYS calculation

in Chapter 3, the γSF is represented differently due to code restrictions. Therefore, the

neutron-capture cross sections from TALYS in Fig. 3.13 and Fig. 4.4 are not comparable.

65

Figure 4.4: (Top) TALYS, EMPIRE, and CoH 73Zn(n,γ)74Zn cross sections using experimen-
tally obtained NLD and γSF. All other aspects of the codes were left to default conditions.
(Bottom) Percent deviation of the CoH and EMPIRE cross sections compared to the TALYS
cross section after including the experimental NLD and γSF. See text for discussion of the
kink at En ∼200 keV.

66

Cross Section (mb)-110110210 TALYS experiment input only CoH experiment input only EMPIRE experiment input only Neutron Energy (MeV)1050100150 CoH percent deviation EMPIRE percent deviation -210-110% Deviation from TALYS Cross Section4.4 Final calculation

The details of the level energies and spin/parity assignments used in each code, as well as

the suggested values in RIPL-3, are detailed in Tables 4.2 and 4.3. For consistency, most

levels were given the spin/parity assignments used TALYS, which had the most complete

assignments. When there is no suggested spin/parity assignment in RIPL-3, TALYS assigns

a spin and parity based on statistical rules. Two assignments were changed from the original

TALYS assignment–the 3+ for the 1418.56 keV level was changed to 4+ due to an updated

ENSDF evaluation in 2017 that suggested a 4+ assignment from Coulomb excitation [93],
while the 5− for the 2148.2 keV level was changed to 2+ due to the suggested values of (1,

2+) in RIPL-3. CoH in particular needed to have levels “turned on” for use. The results

for the cross section calculations after the level assignments were adjusted are shown in

Fig. 4.5. At this point the results from the three codes agreed very well, with EMPIRE

about 10% above the TALYS and CoH calculations. This small discrepancy was due to

the different methods for describing the width-fluctuation corrections (WFC). The WFC

accounts for the correlation between the incident and exit channels in elastic scattering,

and affects the neutron-capture cross section through the elastic scattering component of

the neutron-nucleus interaction. CoH uses a WFC described in [94] based on the Moldauer

approach [95] that is used in TALYS, so they are very similar. EMPIRE uses the HRTW

(Hofmann, Richert, Teppel, and Weidenm¨oller) approach, which has been shown to produce

different neutron-capture cross sections than the Moldauer formulation at the 10% level

[96, 97].

In summary, it is possible to obtain similar neutron-capture cross sections for a neutron-

rich nucleus with different Hauser-Fesbach codes when the differences in input and model

67

Figure 4.5: Neutron-capture cross section calculated after accounting for differences in the
nuclear physics inputs between the codes.

68

  TALYS final comparison CoH final comparison EMPIRE final comparisonCross Section (mb)110210Neutron Energy (MeV)1-110-110-210Table 4.2: 73Zn level energies, spins, and parities including the values assigned in TALYS,
CoH, and EMPIRE, as well as the RIPL-3 suggested levels and the values used in the
final comparison.

73Zn level

energy (keV)

0

195.5 ab

307.2 ab

337 ab

449.6 ab

502.2 ab

1124 ab

2008.9 ab

Suggested
spin/parity
(RIPL-3)
(1/2−)
(5/2+)

(5/2)

none
(3/2−)
(5/2)

(5/2)

(5/2)

a Level not used by CoH.
b Level not used by EMPIRE.

Final

spin/parity

used
1/2−
5/2+

5/2+

3/2+
3/2−
5/2−
5/2−
5/2−

TALYS

CoH

spin/parity

spin/parity

EMPIRE
spin/parity

1/2−
5/2+

5/2+

3/2+
3/2−
5/2−
5/2−
5/2−

1/2−
3/2+

none
3/2−
none

none

none

none

1/2−
none

none

none

none

none

none

none

assumptions are removed. The difficulty in verifying that all the inputs, and the NLD and

γSF models, are the same is large, however, and the situation is made even more complicated

by any limitations in structure information for such short-lived nuclei. The calculated cross

sections are sensitive to the spins and parities of excited states in both the neutron-capture

compound nucleus and the target nucleus. If those values are not known, they need to either

be determined from theory or the level is disregarded completely (which is not physical),

changing the resulting cross section calculation. The overall uncertainty in a neutron-capture

cross section, even when constrained using experimental data from an indirect method, is

therefore larger by some amount due to the choice of Hauser-Feshbach code used. For this

case, the “black box” calculations deviated by up to 80%, which is not an insignificant source

of uncertainty.

69

Table 4.3: 74Zn level energies, spins, and parities including the values assigned in TALYS,
CoH, and EMPIRE, as well as the RIPL-3 suggested levels and the values used in the
final comparison.

74Zn level

energy (keV)

Suggested
spin/parity
(RIPL-3)

0

605.9

0+

2+

1418.56 a

(0+, 4+)

1670.25

1788.9 a

2099.23 a

2148.2 a

2353.6 a

2551.88 ab

2657.6 ab

2698 ab

2809.04 ab

2904.73 ab

2969.3 ab

2985.9 ab

3063.9 ab

3067 ab

3571 ab

4562.4 ab

4861.8 ab

4896.8 ab

5628 ab

(2+)

none

none

(1, 2+)

none

none

none

none

none

none

none

none

none

none

none

none

none

none

none

Final

spin/parity

used
0+

2+

4+

2+

1+
4−
2+

3+

1+
6−
1+
2−
3−
1−
7+
2−
5+
3−
4+
1−
2+
0−

a Level not used by CoH.
b Level not used by EMPIRE.

70

TALYS

CoH

spin/parity

spin/parity

EMPIRE
spin/parity

0+

2+

3+

2+

1+
4−
5−
3+

1+
6−
4−
2−
3−
1−
7+
2−
5+
3−
4+
1−
2+
0−

0+

2+

none

2+

none

none

none

none

none

none

none

none

none

none

none

none

none

none

none

none

none

none

0+

2+

0+

2+

0+

0+

0+

0+

none

none

none

none

none

none

none

none

none

none

none

none

none

none

Chapter 5

Analysis of Co Decays

The β decay of three neutron-rich Co isotopes (71,72,73) was studied using the β-Oslo

method to extract the NLD and γSF of the corresponding daughter isotopes. Details of the

analysis, including the method for obtaining the particle identification as well as the β-Oslo

analysis is presented.

5.1 Particle identification

The uncorrected particle identification plot (PID) is shown in Fig. 5.1. The energy loss

was measured in an upstream PIN detector, while the time-of-flight (TOF) was measured

between the I2 scintillator and the PIN detector. The momentum acceptance of the A1900

was set to 5%, which led to the broad distributions in TOF for each isotope. A second,

smaller distribution was present at smaller TOF (approximately 2 ns) for each isotope. The

smaller distribution was present in all experimentally recorded TOF signals, and was likely

due to a trigger issue with the I2 scintillator used for the TOF. The identity of the isotopes

with the shifted TOF were verified using known γ rays, which confirmed that each isotope

delivered was observed at two separate TOF. A 2D gate was placed around each elemental

band in an uncorrected PID that used the sum of the energy deposition in both PIN detectors

(PIN1 + PIN2) instead of dE in a single PIN detector. The increased separation between

the distributions when using the summed PIN energy can be seen in Fig. 5.2, which also

71

Figure 5.1: PID with uncorrected PIN energy versus uncorrected time-of-flight (determined
between the I2 scintillator and a PIN detector).

contains the gates that were used to select only the major distribution. Approximately 10%

of the data fell outside of the gates shown.

The remaining analysis utilized only the data within the gates shown in Fig. 5.2. Even

after taking a cleaner cut of data, there were still multiple distributions as a function of I2

scintillator position, which can be seen as “wings” around the main distribution in Fig. 5.3.

The position of the ion in the I2 scintillator was determined by taking the time difference

between the signals from the two PMTs on either side of the scintillator. Only about 10% of

the data was located outside of the main distribution, so a cut on the I2 position was used

to remove the extra events. The location of the main distribution in the I2 position was

slightly different for each element band, so a 2D gate was placed on the PIN energy versus

I2 position spectrum (also shown in Fig. 5.3).

72

11500600070008000900010000110001200013000110210310410Uncorrected TOF (arb. units)Uncorrected PIN Energy (arb. units)1200012500130001350014000145001500015500Figure 5.2: PID with uncorrected, summed PIN energy (energy deposited in both PIN
detectors summed together) versus uncorrected TOF.

Figure 5.3: Uncorrected PIN energy versus I2 position (determined by the time difference
between signals from the north and south PMTs on the I2 scintillator) for all data within
the gates shown in Fig. 5.2.

73

1400016000180002000022000240002600011021031011500Uncorrected TOF (arb. units)1200012500130001350014000145001500015500Uncorrected Summed PIN Energy (arb. units)600070008000900010000110001200013000Uncorrected PIN Energy (arb. units)I2 Position (arb. units)60006500700075008000850090001102103104105.1.1 I2 position corrections

The fragment beam is dispersed according to momentum at I2 and the TOF is correlated

with position. When the slits are open to a momentum acceptance of 5%, the TOF of the

ions needs to be corrected based on the location of the ion in the I2 scintillator in order to

improve the PID because an ion that hits one side of the I2 scintillator has a lower velocity

through the A1900 than if the same ion hit the opposite side. A correction to the TOF was

applied so that the TOF of each isotope was independent of the position in the I2 scintillator.

The difference between the uncorrected and corrected TOF for the Co isotopes can be seen

in Fig. 5.4. In each figure, the TOF is plotted against the position in the I2 scintillator. The

uncorrected TOF figure (top) also shows multiple distributions in the I2 position, while the

corrected TOF figure (bottom) has the I2 position gate from Fig. 5.3 applied, so only the

main distribution is present. The bands retain a slight curvature but the major dependence

was removed.

The TOF was not the only parameter that needed to be corrected to improve the PID.

The energy deposited in the PIN detectors was also dependent on the I2 position, which can

be seen for the Co isotopes in the top panel of Fig. 5.5. The corrected dE of the Co isotopes

for PIN1, plotted against the I2 position, is shown in the bottom panel of Fig. 5.5, with the

I2 position gate applied. Figure 5.6 shows the final PID used in the analysis, and also has

the 71,72,73Co isotopes used in this work highlighted. The number of ions of each nucleus

delivered to the end station is given in Table 5.1.

74

Figure 5.4: (Top) Uncorrected TOF versus I2 position for all Co isotopes. (Bottom) Cor-
rected TOF versus I2 position for all Co isotopes, with the PIN energy versus I2 position
gate shown in Fig. 5.3 applied.

75

12000125001300013500140001450015000Uncorrected TOF (arb. units)I2 Position (arb. units)6000650070007500800085009000110210310410Corrected TOF (arb. units)2700028000290003000031000I2 Position (arb. units)260006000650070007500800085009000110210310410Figure 5.5: (Top) Uncorrected PIN energy versus I2 position for all Co isotopes. (Bottom)
Corrected PIN energy versus I2 position, with the PIN energy versus I2 position gate shown
in Fig. 5.3 applied.

76

850090009500100001050011000I2 Position (arb. units)6000Uncorrected PIN Energy (arb. units)650070007500800085009000110210310410I2 Position (arb. units)6000Corrected PIN Energy (arb. units)4500500055006000650070007500650070007500800085009000110210310410Figure 5.6: Final decay PID, with corrected PIN energy versus corrected TOF and all element
gates (Fig. 5.2) as well as I2 position gate (Fig. 5.3) applied.

Table 5.1: Number of ions of each isotope delivered to S2 in e16505. Number was determined
after the PID corrections but before the application of the correlator software.

Isotope

Number of Ions

Isotope Number of Ions

Isotope Number of Ions

64Cr

65Cr

66Cr

67Cr

65Mn

66Mn

67Mn

68Mn

69Mn

70Mn

68Fe

69Fe

154

1463

3371

474

176

2074

41383

33136

8555

526

13999

203581

70Fe

71Fe

72Fe

73Fe

70Co

71Co

72Co

73Co

74Co

75Co

72Ni

73Ni

203990

36073

3579

88

13930

605035

633027

247223

18051

827

295

98246

77

74Ni

75Ni

76Ni

77Ni

75Cu

76Cu

77Cu

78Cu

79Cu

78Zn

79Zn

80Zn

697393

326142

28828

1396

1587

277236

707004

33693

2558

637

18799

934

Corrected TOF (arb. units)27000Corrected PIN Energy (arb. units)3000400050006000700080009000110210310410275002800028500290003000029500Figure 5.7: Known level scheme for the β decay of 71Co. All γ-ray intensities are relative to
the 566.8 keV transition.

5.2

71Co decay

The half-life of 71Co is known to be 80(3) ms [67], so a correlation time of 150 ms was

used. The decay curve for 71Co was obtained from the time difference between correlated

ions and decays, and includes contributions from the parent (71Co) decay, daughter (71Ni)

decay (t1/2=2.56 s [67]), and random correlations. The SuN spectra (both γ rays and

TAS) contained all of these components, and the contribution from the daughter decays and

random correlations needed to be removed to leave only γ rays from the decay of the parent.

By fitting the full decay curve with a combination of all of the components, the number of

daughter decays and random correlations was determined and could be removed, which is

described in detail in this section.

The apparent half-life of the daughter 71Ni was calculated because of a long-lived isomeric

state at 499 keV. The isomer half-life, 2.3(3) s [98], is the same as the ground state half-life of

2.56(3) s [67] within uncertainties. Decays from both states were expected in the experiment,

78

1273.41065.2813.0499280.50-(5/2)-(5/2)+(5/2)-(1/2)+(7/2)+(9/2)774.4  35566.8  100252.2  13813.0  16280.5  2271Co-(7/2)0.080 ms 3-%b = 100.02.3 s 32.56 s 371Nias both the 1065 keV level and a corresponding level at 566 keV (detected when the 1095 keV

level de-excited to the 499 keV β-decaying isomeric state) were observed (see level scheme

in Fig.5.7). By fitting the TAS peaks at 1065 keV and 566 keV it was determined that

19(1)% of the 71Ni decays were from the ground state, leading to an effective 71Ni half-

life of 2.3(4) seconds. The daughter half-life was fixed in the fitting procedure using the

calculated value, as was the decay constant of the exponential background. The shape of the

background was obtained from the backwards correlation by fitting the decay curve with a

simple exponential function to extract the decay constant, which was used to fix the decay

constant of the background component in the forward correlation. The half-life of the parent

as well as the magnitude of the exponential background were left as free parameters in the

fit.

The measured decay curve is shown in Fig. 5.8 as the black histogram, while the blue

histogram represents the decay curve from the backwards correlation. The blue dotted

line is the fit to the backwards correlator decay curve, which was used to set the decay

constant of the background. The black line describes the combined fit to the decay curve,

including the parent decay (red dot-dash line), the daughter decay (green dash line), and the

background component (gold dot-dash line). From this fit, the parent half-life was extracted

and compared to the known half-life. For 71Co, the extracted half-life of 84(7) ms matched

the known half-life of 80(3) ms [67]. The number of parent decays, daughter decays, and

background counts (random correlations) in the 150 ms correlation window could also be

obtained. These values are important for understanding how much of the daughter and

background was contained in the raw SuN spectra, and therefore how much needed to be

removed. The relevant values, including the number of counts in the decay curve from the

backwards correlation, are given in Table 5.2.

79

Figure 5.8: Full decay curve fit for the decay of 71Co including the parent contribution (red
dot-dash line), daughter contribution (green dotted line), and background contribution (gold
dot-dash line). The black histogram is the full decay curve from the data, with the total
fit (combination of parent, daughter, and background) shown with the black solid line. The
shape of the background contribution was determined using a correlation backwards in time,
shown as the blue histogram. The blue dashed line fit to the backwards correlation set the
background contribution shape, and the magnitude was allowed to vary to determine the
blue dot-dash line.

Table 5.2: Results of decay curve fit for 71Co decay using a 150 ms correlation time (see Fig.
5.8).

Number of parent decays

Number of daughter decays

Number of random correlations

Number of events in backwards correlation

157210(920)

3954(18)

171070(150)

221190(36)

80

Time (ms)0Counts050010001500200025003000350020406080100120140Total fitParent contributionDaughter contributionBackground contributionBackwards correlation fitFigure 5.9: Long correlation time decay curve fit for the decay of 71Co. The green band
shows the time region used to remove the daughter contribution to the SuN spectra. The
parent and daughter decay constants were set from the fit shown in Fig. 5.8. The background
component was determined the same way as in Fig. 5.8.

Table 5.3: Results of decay curve fit for 71Co decay using a 5 sec correlation time (see Fig.
5.9).

Number of daughter decays in subtraction region

Number of random correlations in subtraction region

3960(170)

50954(99)

81

040008000120001600020000Time (ms)010002000300040005000Counts per 50 msTotal fitParent contributionDaughter contributionBackground contributionBackwards correlation fitDaughter subtraction regionA representative spectrum including the daughter and background γ-ray events was re-

moved from the SuN spectra (segments and TAS) based on spectra from a time window

where only daughter decays were occurring. To find such a time window, a longer correla-

tion time was used–5 seconds instead of 150 ms. At long decay times the 71Ni decays are

expected to dominate the spectra. The decay curve from the 5 sec correlator, including all

the components, can be seen in Fig. 5.9. The same fitting procedure was used for the longer

correlator, with the daughter half-life set to the known value, the parent half-life set to the

value obtained using the 150 ms correlator, and the background decay constant set by fitting

the backwards in time correlation in the 5 sec correlator. Between 1000 ms and 1484 ms

the same number of 71Ni decays, 3960(170), occurred as with the 150 ms correlation time.

A much longer time was needed to see the same number of decays because of the longer

minimum implantation time, which resulted in a lower correlation efficiency (see Section

2.3). There was also background in that time window due to random correlations (see Ta-

ble 5.3). After removing the daughter decays, 120100(100) background counts were left to

be removed in the 150 ms correlation. The reverse time correlation was used to represent

that background, scaled to the total number of counts that needed to be removed. The

reverse time correlation had 221190(36) counts, while only 120100(100) counts needed to be

removed. The backwards correlation was scaled appropriately to remove the correct amount

of background remaining in the spectra.

The segments and TAS spectra for 71Co are shown in Fig. 5.10.

In each, the black

histogram shows the raw SuN spectrum, the blue shows the scaled SuN spectrum from the

backwards correlation, and the green shows the daughter contribution from the later time

window. The red is the parent contribution, obtained by subtracting the blue and green

spectra from the raw (black line) spectrum.

82

Figure 5.10: (Top) 71Co SuN γ-ray spectrum showing the raw spectrum (black), daughter
decay contribution (green), background contribution (blue), and parent decay contribution
(red). The labeled peaks are strong transitions, and are described in the text. (Bottom)
TAS spectrum for the same decay, with strongly fed levels labeled and described in the text.

83

Gamma energy (keV)0Counts per 10 keV0100020003000400050006000700080009000Raw SuN spectrumDaughter contributionBackground contributionParent contribution50010001500200025003000ABCDExcitation energy (keV)0Counts per 10 keV5001000150020002500300005001000150020002500400030003500Raw SuN spectrumDaughter contributionBackground contributionParent contributionEFGHThe strongest β-delayed γ-ray transition following the decay of 71Co into 71Ni is known

to be 566.8 keV [A], with a relative intensity of 100%. That peak was clearly observed in the

parent segments spectrum, followed by the 774.4 keV transition [B] (Iγ = 35%) and the 280.5

keV transition [C] (Iγ = 22%). Another γ ray was seen at 1273 keV [D], which corresponds

to the de-excitation of the 1273.4 keV level directly to the ground state, and has not been

seen in the literature. The β-decay feedings for the decay of 71Co are not well known, but

the 1065.4 keV level [E] is the most populated. It de-excites to the long-lived isomer at 499

keV, as well as through a weaker branch that bypasses the isomer, so peaks at both 1065

keV and 566 keV [F] are seen in the TAS spectrum. The 1273.4 keV level [G], along with

the 774 keV peak arising from transitions to the isomeric state [H] were clearly seen as well.

5.2.1 β-Oslo matrices

The β-Oslo matrix, with the total excitation energy, Ex, on the y-axis and the energy of

a single γ ray, Eγ, on the x-axis, was obtained by taking the experimental spectrum and

subtracting the daughter and background contributions (the starting matrix, as well as those

with the daughter component and background component can be seen in Appendix B). The

raw 2D matrix was then unfolded to remove the detector response and the primary γ spectra

were obtained following the procedure described in Chapter 3. The raw matrix can be seen in

Fig. 5.11, with 200-keV wide bins on both axes. The matrix was rebinned to 600 keV before

unfolding in an attempt to mitigate the impact of the isomeric state in 71Ni by combining

each set of levels offset by 499 keV. The unfolded matrix can be seen in Fig. 5.12. The

region of the primary matrix used to extract the NLD and γSF is highlighted in Fig. 5.13,
and was restricted to Eγ > 1000 keV and Ex ∈ (2400, 4800) keV. The upper Ex limit was

set above the ρ(Sn) of 71Ni, which is 4.264(3) MeV [67]. The first excited state of 70Ni has

84

Figure 5.11: Raw 2D Oslo matrix for the decay of 71Co into excited states of 71Ni. The γ-ray
energies obtained from the segments of SuN are plotted on the x-axis, while the excitation
energy of the daughter nucleus, obtained from the total energy in the detector, is plotted on
the y-axis.

an energy of 1259.55(5) keV [99], which allowed for the upper Ex limit to be increased to

slightly above ρ(Sn) without the possibility of contamination of γ rays from the β-delayed

neutron daughter.

5.2.2 NLD normalization

As described in Chapter 3, the ρ(Sn) value was determined using cumulative levels calculated

by Goriely [30] and shifted in excitation energy to match the known low energy levels. There

are 5 excited states known in 71Co, all below 1.3 MeV. The known levels are all from β-

decay experiments, so the calculated cumulative level distribution was reduced to include

85

Gamma energy (keV)1000Excitation energy (keV)020004000600080001000011021031002000300040005000600070008000900010000Figure 5.12: Unfolded 2D matrix for 71Ni with 600 keV binning on both axis.

Figure 5.13: Primary 2D matrix for 71Ni with 600 keV binning on both axis. The extraction
region used for the NLD and γSF is outlined by the black lines.

86

010002000300040005000110210310410 Gamma energy (keV)Excitation energy (keV)010002000300040005000010002000300040005000110210310010002000300040005000Gamma energy (keV)Excitation energy (keV)Table 5.4: Parameters used in exponential fit to shifted calculated NLD.

Shift Value

Constant

0 MeV

0.25 MeV

0.5 MeV

3.8(14)

3.0(12)

2.3(9)

Slope

1.02(7)

1.02(7)

1.02(7)

ρ(Sn) (MeV−1)

300(150)

230(120)

178(92)

only those with spins populated following an allowed β decay from the tentatively assigned
(7/2−) ground state of 71Co and one dipole transition, leading to a range of spins from 3/2

to 11/2. The χ2 minimization result for the shifting of the reduced calculated cumulative

levels is shown in Fig. 5.14. The second-order polynomial fit resulted in a best shift value
of 0.25 ± 0.25 MeV. The reduced theoretical cumulative level distribution corresponding

to the best shift, as well as the upper and lower limit shifts of 0 MeV and 0.50 MeV are

shown in Fig. 5.15, compared to the known cumulative levels. The large uncertainty was

due to the small number of known levels in 71Ni. The shifted NLD around Sn was fit with

an exponential function to determine the value of ρ(Sn). The shifted calculated NLD are

shown in Fig. 5.16, with the Sn of 71Ni (4.264 MeV) shown in comparison to the energy

range used in the fit to extract the ρ(Sn) values. Due to the low Sn of 71Ni, the calculated

NLD was fit mostly above Sn, where it was more exponential in shape. The fit results are

detailed in Table 5.4, and resulted in lower, middle, and upper values of ρ(Sn) of 178(92),
230(120), and 300(150) MeV−1, respectively.

The only information known about 71Ni comes from β-decay experiments, so a full NLD

could not be obtained due to the lack of known levels at low energies. Instead, the known

levels at low energies from β decay and the reduced ρ(Sn) value were needed to normalize

the experimental NLD. The reduced ρ(Sn) was determined using the same method as for the

87

Figure 5.14: χ2 values for different Ex shifts of the calculated cumulative levels compared
to the known cumulative levels for 71Ni.

Figure 5.15: Unshifted (red line) and shifted calculated cumulative levels (blue and green
lines) compared to the known cumulative levels (black line). The best shift value of 0.25
MeV with an error of 0.25 MeV led to only two shifts needed, as the lower limit shift is 0
MeV.

88

681012141618LD shift (MeV)-0.4-0.200.20.40.60.812 c value Cumulative Levels110Excitation Energy E (MeV)x00.20.40.60.811.21.41.61.8271Known Ni Cumulative LevelsGoriely Cumulative Levels (Shift = 0 MeV)Shift = 0.25 MeVShift = 0.50 MeVFigure 5.16: Shifted calculated level densities (upper, mid, and lower) near Sn used to
determine ρ(Sn) values for the NLD normalization.

74Zn data. The percentage of the total NLD at the neutron separation energy as a function

of spin is shown in Fig. 5.17. The indicated spins comprise 50.7(5)% of the total NLD, which
led to reduced ρ(Sn) values of 90(46), 116(58), and 150(73) MeV−1.

With the two normalization points (the known low-energy levels and the reduced ρ(Sn)),

the experimental NLD was normalized to match both. The normalization was performed

three times, with the upper and lower limits from the shift uncertainty as well as the central

value. The upper, lower, and middle normalized NLD are shown in Fig. 5.18, along with

the three shifted Goriely calculated NLDs, which were reduced to include only spins in the

range of interest.

89

Excitation Energy E (MeV)x3-1Level Density (MeV)210310Shift = 0 MeVShift = 0.25 MeVShift = 0.5 MeVExponential fit to 0 MeV shiftExponential fit to 0.25 MeV shiftExponential fit to 0.5 MeV shift71Ni S = 4.264 MeVn 4567810Figure 5.17: Distribution of spins for the levels in 71Ni around the neutron separation energy
based on tabulated spin- and parity-dependent NLD from Ref. [30]. Spins highlighted in blue
are populated following an allowed β decay of 71Co and one dipole photon transition. The
ground state of 71Co has been tentatively assigned a value of (7/2−).

5.2.3 γSF normalization

For the value of B, previous β-Oslo data on 69,70Ni was used. The 70Ni γSF was previously

normalized to Coulomb dissociation data for 68Ni [100], and then the 69Ni γSF was normal-

ized to the 70Ni data. For the new 71Ni data, the average of the two data sets was used

for normalization along the entire energy range where 71Ni data was available (1-4.5 MeV).

The normalized 71Ni γSF was also compared to the 68Ni Coulomb dissociation data, as well

as more recent data on the γSF of 70Ni [101]. The normalized γSF for 71Ni, along with the

γSFs obtained for 69,70Ni using the β-Oslo method and the Coulomb dissociation data for

68,70Ni is shown in Fig. 5.19.

90

SpinPercent of Total NLD (%)02468101214Spin Distribution Spins Populated 02468101412161820Figure 5.18: Normalized NLD for 71Ni, with the known levels and Goriely calculated NLD
(shifts of 0 MeV, 0.25 MeV, and 0.5 MeV).

91

 -1Level density r(E) (MeV) x1-1102103101071Ni S = 4.264 MeVn SuN data, middle  SuN data, lower limit SuN data, upper limit Known Levels  r from Goriely et al.Excitation energy E (MeV)x01234Figure 5.19: Normalized γSF for 71Ni (black dots, uncertainty indicated by grey band)
compared to γSF data on 69,70Ni from the β-Oslo method, as well as higher-energy Coulomb
dissociation data for 68,70Ni.

92

 E (MeV)g02468101214-3f(E) (MeV)g-910-810-710-61071 Ni SuN data - present work69 Ni SuN data, Spyrou et al.70 Ni SuN data, Liddick et al.68 Ni data, Rossi et al. 70 Ni data, Wieland et al. 71 Ni Sun upper/lower limits5.3

72Co decay

From previous studies, it has been shown that when 72Co is produced by fragmentation,

both the ground state and a low-energy isomeric state are produced [102]. The energy

of the isomeric state is unknown, but both states β decay to excited states in 72Ni. The

measured half-lives of the two states are very similar: 51.5(3) ms and 47.8(5) ms [103].

However, the spins of the two states are very different, with a high-spin state tentatively
assigned a spin and parity of (6−, 7−) and a low-spin state with a tentative spin and parity

of (0+, 1+) [103]. The high-spin state assignment is based on systematics of even-even Co

isotopes [99, 104], while the low spin-state was suggested due to known long-lived isomers in

lighter Co isotopes [104] as well as observed β feeding to levels with low spins in 72Ni [103].

Characteristic γ-rays from the decay of both states were observed in the present ex-

periment. The population ratio between the high-spin and low-spin β-decaying states was

determined using the characteristic γ-rays and their respective absolute intensities as re-

ported in Ref. [103]. For the high-spin ground state, the 1194.2(12) keV transition was the

best separated characteristic γ ray (see Fig. 5.20 for a simplified level scheme of the high-spin

decay). For the low-spin isomer, the 3039.6(19) keV and 3383.4(18) keV γ rays were used

(see Fig. 5.21 for the low-spin decay scheme). These γ rays were fit in the experimental

segments spectrum following the decay of 72Co, but needed to be corrected using the effi-

ciency of SuN. The known low-spin and high-spin decay schemes were used to model the

Geant4 response of SuN and to determine the detection efficiency for the 1194 keV, 3039

keV, and 3383 keV transitions, see Table 5.5. The results of the simulation of the response

to the high spin ground state can be seen in Fig. 5.22, along with the fit to the simulated

data that was used to determine the efficiency of the 1194 keV γ ray based on the number

93

Figure 5.20: Simplified level scheme for the β decay of the high spin state in 72Co. Only
the four strongest transitions, originating from the strongly populated 3586.0 keV level, are
shown for clarity and account for 70% of the β-decay feeding intensity.

94

1094.801094.8  10172Co--(6,7)0+x51.5 ms 3-%b = 100.072Ni+0+(4)1.587 s 931937.6+(2)842.7  95454.3  621194.2  5070-Ib2391.83586.0Figure 5.21: Known level scheme for the β decay of the low spin state in 72Co. All known
transitions are shown.

95

47581094.801094.8  4872Co++(0,1)0+y47.8 ms 5-%b = 100.072Ni4.6-Ib3909.22455.0+0+(4)+(0,1,2)1.587 s 933997.41937.62220.22827.13307.84134.84478.35105.3+(2)+(2)+(2)+(0,1,2)+(0,1,2)+(0,1,2)+(0,1,2)+(0,1,2)+(0,1,2)+(2)842.7  1.31125.0  7.52220.0  3.71359.8  7.92455.2  3.51732.1  6.5852.9  1.91086.8  2.22212.9  1.21688.9  1.46892060  1.33997.5  0.91680  1.93039.6  6.3481  2.12023.0  4.43383.4  5.42538  1.611082650  2.92885.0  1.71.6128.2<0.41.45.36.5<1.04.4213425.2Table 5.5: Efficiency for detecting the full energy of select γ rays in one segment of SuN,
determined from Geant4 simulations.

γ-ray energy (keV)

Efficiency (%)

1194.2

3039.6

3383.4

16(1)

24(4)

22(4)

of counts compared to the number of β decays simulated. Three main peaks were fit–842.7

keV (A), 1094.8 keV (B), and 1194.2 keV (C). The 1194 keV γ ray is actually a shoulder

on the strong 1095 keV transition from the first excited state to the ground state in 72Ni,

but it was the only γ ray from the high-spin decay that was well separated, which was why

multiple peaks were fitted simultaneously. The results of the simulation of the response to

the low spin isomer can be seen in Fig. 5.23. This figure focuses on the high-energy γ rays;

the fit to the 3040 keV γ ray (D), the 3383 keV γ ray (E), and the surrounding γ rays is

shown. The 3383 keV γ ray had smaller fitting uncertainties, so it was used for the isomer

ratio determination.

The experimental data for the same energy ranges can be seen in Fig. 5.24 (1194 keV,

characteristic high-spin decay) and Fig. 5.25 (3383 keV, characteristic low-spin decay). The

same peripheral peaks were fit in the experimental data as in the Geant4 simulation (when

possible) to help determine the number of counts in the peaks of interest. By correcting for

the efficiency and the absolute intensity of each γ-ray, the number of decays of the high-spin

ground state was calculated to be 164000(21000), while the number of decays of the low-spin

isomer was calculated to be 104000(27000). Adding these values together gives the total

number of 72Co decays to be 268000(34000), which matched within error to the number

extracted from the decay curve fit shown in Fig. 5.26 (and described below). Therefore,

96

Figure 5.22: Geant4 simulation of the decay of the 72Co high spin isomer, with the fit used
to extract the efficiency of the 1194.2 keV γ ray.

Figure 5.23: Geant4 simulation of the decay of the 72Co low spin isomer at high γ energies,
with the fit used to extract the efficiency of the 3383.4 keV γ ray.

97

002000400060008000100001200014000160001800020000220005001000150020002500Gamma energy (keV)Counts per 10 keVABC6007008009001000110012001300260028003000320034003600Gamma energy (keV)38004000Counts per 10 keVDEFigure 5.24: Low energy raw SuN spectrum with the fit used to extract the number of 1194.2
keV counts seen in the experiment.

60(20)% of the decays were from the high-spin state, while 40(20)% of the decays were from

the low-spin state.

The ratio was tested with a Geant4 simulation of a mixed decay scheme, shown in Fig.

5.27. The differences between the data and the simulation at low energies indicates that the

β-decay feeding intensities to highly excited states (e.g. the 70% feeding at 3.586 MeV) is

too large, which is commonly seen when the intensities were determined using low-efficiency

high-purity Ge detectors [105, 106]. It is likely that some of the feeding intensity attributed

to these levels is actually going to higher-lying, unknown excited states, as the highest

known level in 72Ni is just above 5 MeV but the neutron separation energy is 6.891 MeV.

To investigate the impact of feeding to high excited states, two new levels were added in the

simulation: a hypothetical level at 5.085 MeV that was assumed to de-excite by a 1.5 MeV γ

ray to the 3.856 MeV level, and another hypothetical level at 5.978 MeV that also de-excited

by a 1.5 MeV γ ray, but to the 4.478 MeV level. To test the impact of moving β-feeding

98

10002000300040005000600070008000900005001000150020002500Gamma energy (keV)Counts per 10 keVABCFigure 5.25: High energy raw SuN spectrum with the fit used to extract the number of
3383.4 keV counts seen in the experiment.

Figure 5.26: Full decay curve fit for the decay of 72Co.

99

4005006007008009001000260028003000320034003600Gamma energy (keV)38004000Counts per 10 keVDETime (ms)020406080100120140Counts100020003000400050000Total fitParent contributionDaughter contributionBackground contributionBackwards correlation fitFigure 5.27: Low energy GEANT4 simulation with 60% high spin and 40% low spin decays
compared to the SuN spectrum. The simulation has been scaled to match the SuN data
between 4 and 6 MeV.

strength to higher excitation energies, an arbitrary amount (25%) of the β-decay feeding to

the levels being populated by the new γ rays was removed and attributed to the new levels.

For the new 5.086 MeV level, a β-decay feeding intensity of 17.5% was assigned (this was

25% of the 70% β-feeding intensity assigned to the 3.586 MeV level), while a β-decay feeding

intensity of 3% was assigned to the new 5.978 MeV level (25% of the 12% β-decay feeding

intensity assigned to the 4.478 MeV level). This is the simplest case, where the β feeding is

going to just one highly excited state instead of being spread out among many states. With

the new levels, the efficiency of detecting the γ-rays of interest (for determining the ratio of

high-spin ground state to low-spin isomer populated in fragmentation) decreased due to the

higher γ-ray multiplicity. The efficiency of detecting the 1194.2 keV γ ray in a single segment

of SuN decreased from 16(1)% to 15(1)%, while the efficiency of detecting the 3383.4 keV γ

ray in a single segment decreased from 22(4)% to 14(3)%. A smaller decrease in the efficiency

100

010002000300040005000600070008000100020003000400050005001500250035004500g-ray Energy (keV)Counts per 10 keVSuN dataGEANT4 simulationTable 5.6: Results of decay curve fit for 72Co decay using a 150 ms correlation time (see Fig.
5.26).

Number of parent decays

Number of daughter decays

Number of random correlations

Number of events in backwards correlation

252670(570)

10566(25)

189650(40)

228329(36)

Table 5.7: Results of decay curve fit for 72Co decay using a 5 sec correlation time (see Fig.
5.28).

Number of daughter decays in subtraction region

Number of random correlations in subtraction region

10560(270)

99280(240)

of the 1194.2 keV γ ray compared to the 3383.4 keV γ ray was expected, as the 1194.2 keV

γ ray is in a multiplicity four (M=4) cascade, while the 3383.4 keV γ ray is in a multiplicity

two (M=2) cascade. The decrease in efficiency between M=4 and M=5 is small, while the

decrease in efficiency between M=2 and M=3 is larger [60], so adding a single γ ray to each

cascade affected the efficiency as expected. The change in efficiency had a small impact

on the calculated amounts of each β-decaying state populated in fragmentation, within the

uncertainty, so the 60% high spin and 40% low spin population was used.

With the relative amounts of each β-decay state determined, the effective half-life of 72Co

was calculated to be 50.1(79) ms. The decay curve fit, following the procedure described

for 71Co, is shown in Fig. 5.26. The extracted half-life of 52(1) ms agreed well with the

expected effective half-life of the mixed ground state/isomer decay.

The number of parent decays, daughter decays, background counts, and counts in the

backwards correlator for the 150 ms correlation are detailed in Table 5.6. As with 71Co, these

values were used to perform an appropriate subtraction of the daughter and background

101

Figure 5.28: Long correlation time decay curve fit for the decay of 72Co. The green band
shows the time region used to remove the daughter contribution to the SuN spectra.

from the raw SuN spectra. In the 5 second correlation window, a time window from 1000

ms to 1841 ms yielded 10560(270) daughter decays, matching the 10566(25) in the 150

ms correlator, with 99280(240) random correlations in that time window (see Table 5.7).

Subtracting the spectra obtained from this time window left 90370(240) background counts

to be removed in the 150 ms correlation. The backwards correlation was scaled appropriately

to remove the correct amount of background remaining in the spectra.

The strongest transitions in 72Ni were described above (see Figs. 5.20 and 5.21), and

were clearly observed in the parent contribution spectrum in Fig. 5.29. The 1094.8 keV peak

[A], with an absolute intensity of 101% for the high-spin decay and 48% for the low-spin

decay, is by far the strongest transition. The other strong transitions at 842.7 keV [B] (Iγ

= 95% high spin, 1.3% low spin) and 454.3 keV [C] (Iγ = 62% high spin) are also clearly

102

05000100001500020000250003000035000Time (ms)010002000300040005000Counts per 50 msTotal fitParent contributionDaughter contributionBackground contributionBackwards correlation fitDaughter subtraction regionpresent. There is a 70% β-decay feeding to the 3586.0 keV level [D] in the high spin decay,

which can be best seen in the TAS spectrum, and there are no other strongly fed levels.

5.3.1 β-Oslo matrices

As with the 71Co decay, the raw 2D Oslo matrix was constructed using the daughter- and

background-subtracted SuN spectra, which can be seen in Appendix B. The raw matrix can

be seen in Fig. 5.30, with 10 keV wide bins on both axis. The unfolded matrix, in Fig. 5.31,

has 120 keV wide bins to reflect the resolution of SuN, as does the primary matrix (Fig.

5.32). The region of the primary matrix used to extract the NLD and γSF is highlighted
in Fig. 5.32, and was restricted to Eγ > 3000 keV and Ex ∈ (3000, 7000) keV. The upper

Ex limit was chosen to be very close to the ρ(Sn) of 72Ni of 6.891(3) MeV [107]. The first

excited state of 71Ni is at 280.5(2) keV [67], which allowed for the upper Ex limit to be
increased to 7 MeV (∼100 keV above Sn) without the possibility of contamination from the

β-delayed neutron daughter.

5.3.2 NLD normalization

The NLD normalization followed the same procedure as for 71Ni, with the spin-reduced

calculated cumulative levels shifted in excitation energy to match the known levels. The χ2
minimization, shown in Fig. 5.33, resulted in shift values of 0.25 ± 0.2 MeV. The shifted

calculated cumulative levels can be seen compared to the known levels in Fig. 5.34. The

shifts were then applied to the calculated NLD around Sn, which is shown in Fig. 5.35,

along with the exponential fits to each shift. The results for the fitted parameters are given
in Table 5.8 and resulted in ρ(Sn) values of 1055(85), 1300(100), and 1600(120) MeV−1.

103

Figure 5.29: 72Co SuN spectra showing the raw spectrum, daughter decay contribution, back-
ground contribution, and final γ-ray (top) and TAS (bottom) spectra for the de-excitation
of 72Ni. As with Fig. 5.10, the labeled peaks note strong γ-ray transitions and strongly fed
levels, and are described in the text.

104

100020003000400050006000700080009000Gamma energy (keV)0500100015002000250030003500Counts per 10 keVRaw SuN spectrumDaughter contributionBackground contributionParent contribution0ABC0200400600800100012001400Excitation energy (keV)0500100015002000250040003000350045005000Counts per 10 keVRaw SuN spectrumDaughter contributionBackground contributionParent contributionDFigure 5.30: Raw 2D Oslo matrix for the decay of 72Co into excited states of 72Ni. The γ-ray
energies obtained from the segments of SuN are plotted on the x-axis, while the excitation
energy of the daughter nucleus, obtained from the total energy in the detector, is plotted on
the y-axis.

Figure 5.31: Unfolded 2D matrix for 72Ni with 120 keV binning on both axis.

105

02000400060008000100001200014000110210310Gamma energy (keV)100002000300040005000600070008000900010000Excitation energy (keV)11021031041001000200030004000500060007000Excitation energy (keV)10002000300040005000600070000Gamma energy (keV)Figure 5.32: Primary 2D matrix for 72Ni with 120 keV binning on both axis. The extraction
region used for the NLD and γSF is outlined by the black lines.

Figure 5.33: χ2 values for different Ex shifts of the calculated cumulative levels compared
to the known cumulative levels for 72Ni.

106

0100020003000400050006000700011021031041010002000300040005000600070000Gamma energy (keV)Excitation energy (keV)106108110112114116118120122124LD shift (MeV)-0.4-0.200.20.40.60.812 c valueFigure 5.34: Shifted calculated cumulative levels compared to the known cumulative levels.

Table 5.8: Parameters used in exponential fit to shifted calculated NLD for 72Ni.
ρ(Sn) (MeV−1)

Constant

Shift Value

Slope

0.05 MeV

0.25 MeV

0.45 MeV

1.29(7)

1.05(6)

0.85(5)

1.034(8)

1.034(8)

1.034(8)

1600(120)

1300(100)

1055(84)

107

 Cumulative Levels110210Excitation Energy E (MeV)x123472Known Ni Cumulative LevelsGoriely Cumulative Levels (no shift)Shift = 0.05 MeVShift = 0.25 MeVShift = 0.45 MeVFigure 5.35: Shifted calculated level densities (upper, mid, and lower) near Sn used to
determine ρ(Sn) values for the NLD normalization.

108

 -1Level Density (MeV)21031041010Excitation Energy E (MeV)x456789Shift = 0.05 MeVShift = 0.25 MeVShift = 0.45 MeVExponential fit to 0.05 MeV shiftExponential fit to 0.25 MeV shiftExponential fit to 0.45 MeV shift72Ni S = 6.891 MeVnOnce again, the NLD needed to be reduced due to the lack of non-β decay data. The two
possibilities for the ground state spin, 6− or 7−, account for different percentages of ρ(Sn)
due to the different spin ranges they cover: 4 to 8 (both parities) from a 6− state, and 5 to
9 (both parities) from a 7− state. The population of the NLD around Sn as a function of
the spin is shown in Fig. 5.36 for both cases. The case of a 6− ground state would populate
56% of the full ρ(Sn), while the case of a 7− ground state would populate 46%.

The high-spin ground state was found to be only 60% of the decays, however, so the low-

spin isomer decay also needed to be considered. The suggested spins are (0+, 1+), but lighter

Co isotopes have suggested 1+ isomers, so only a spin of 1+ was considered. The percentage

of ρ(Sn) populated by the low-spin decay was found to be 33%, covering spins of 0 to 3,

both parities. The spin range covered by the mixed high spin and low spin decay is shown
in Fig. 5.37 for both high spin options. For a 6− ground state with a 1+ isomeric state,
spins of 0 to 8, both parities, are covered. For a 7− ground state with a 1+ isomeric state,

spins of 0 to 3 and 5 to 9, both parities, are covered. The percentage of ρ(Sn) populated by

the combined ground state and isomeric state decay (for each ground state spin case) was

calculated by combining the percentage of ρ(Sn) populated due to the combined spin range

and the ratio of the ground state to isomeric state produced in fragmentation. Assuming

that the β-decay branching ratio to high excitation energies is the same for both β-decaying
states, a 6− ground state populated 60% of the time in fragmentation combined with a 1+

isomeric state populated 40% of the time in fragmentation would populate 76(11)% of ρ(Sn),
while a 7− ground state with a 1+ isomeric state would populate 67(10)%. That resulted in
lower, middle, and upper reduced ρ(Sn) values of 810(130), 990(160) and 1220(200) MeV−1
for the case of a 6− ground state, and 710(120), 870(140), and 1070(170) MeV−1 for the
case of a 7− ground state.

109

Figure 5.36: Distribution of spins for the levels in 72Ni around the neutron separation energy
based on tabulated spin- and parity-dependent NLD from Ref. [30]. The ground state of 72Co
has been tentatively assigned a value of (6−,7−). Spins highlighted in blue are populated
following an allowed β decay of 72Co from a 6− ground state and one dipole photon transition,
while spins highlighted in green are populated following an allowed β decay from a 7− ground
state and one dipole transition.

Figure 5.37: Same as in Fig. 5.36, including the spins populated in an allowed β decay from
a 1+ isomeric state and one dipole transition in addition to the ground state decay.

110

Spin Distribution- Spins Populated by 6 g.s.- Spins Populated by 7 g.s.0246810121416SpinPercent of Total NLD (%)024681014121618200246810121416 SpinPercent of Total NLD (%)02468101412161820Spin Distribution-Spins Populated by 6 g.s. +and 1 isomeric state-Spins Populated by 7 g.s. +and 1 isomeric stateThe reduced ρ(Sn) values are modified if the low-spin and high-spin decays do not equally

feed the states around Sn. The low-spin isomer has a reported ground-state β-decay branch

of 42(13)% [103]. Accounting for the direct ground state decay, 68(10)% of ρ(Sn) would be
populated for the case of a 6− ground state populated 60% of the time in fragmentation

combined with a 1+ isomer populated 40% of the time in fragmentation, while 58(9)%
would be populated for the case of a 7− ground state combined with a 1+ isomer. The new
reduced ρ(Sn) values would therefore be 720(130), 880(160), and 1080(190) MeV−1 for a 6−
ground state and 620(110), 760(140), and 930(170) MeV−1 for a 7− ground state. The other

extreme, where 100% of the low-spin decay goes to the ground state, would result in 56%
of ρ(Sn) for a 6− ground state and 46% for a 7− ground state (the same values as above,

before accounting for the fact that a β-decaying isomer was produced). With those values,
the reduced ρ(Sn) values were found to be 588(47), 724(57), and 890(69) MeV−1 for a 6−
ground state, and 490(140), 600(170), and 740(200) MeV−1 for a 7− ground state. The

ρ(Sn) values for each case are detailed in Table 5.9.

The case of 0% β-decay feeding to the ground state from the 1+ isomer results in the

largest reduced ρ(Sn) values, so this case was used as an upper limit for the normalization.

The lower, middle, and upper normalized NLD for 72Ni are shown in Fig. 5.38 for both

high-spin cases. The shifted calculated NLD, which were reduced to contain only the spins

in the ranges of interest, are included in the figure as well.

5.3.3 γSF normalization

The two ground state spin possibilities led to two different ρ(Sn) reductions, so the γSF was
normalized twice. The resulting γSF for both a 6− and 7− ground state are shown in Fig.

5.39.

111

Table 5.9: Lower, middle, and upper values for ρ(Sn) for different spin population reductions.
The full ρ(Sn) was reduced using several assumptions about the β feeding to the ground state
in 72Ni from the low spin isomer: 0% (upper limit for populating ρ(Sn)), 42% (measured
ground state feeding), and 100% (lower limit for populating ρ(Sn), where only the high-spin
ground state of 72Co is responsible for populating levels around Sn).

Low spin isomer
ground state Iβ

0%

0%

42%

42%

100%

100%

High spin

ground state J π

6−
7−
6−
7−
6−
7−

Lower ρ(Sn)
(MeV−1)
810(130)

Middle ρ(Sn)
(MeV−1)
990(160)

Upper ρ(Sn)
(MeV−1)
1220(200)

710(120)

870(140)

1070(170)

720(130)

880(160)

1080(190)

620(110)

760(140)

930(170)

588(47)

724(57)

890(69)

490(140)

600(170)

740(210)

Figure 5.38: Normalized NLD for 72Ni, with the known levels and Goriely calculated NLD
(shifts of 0.05 MeV, 0.25 MeV, and 0.45 MeV).

112

Excitation energy E (MeV)x0-1Level density r(E) (MeV) x11234-1102103105672Ni S = 6.891 MeVn SuN data, lower limit SuN data, upper limit Known Levels  r from Goriely et al.10- SuN data, middle (6 g.s.) Excitation energy E (MeV)x0123456772Ni S = 6.891 MeVn- SuN data, middle (7 g.s.)  SuN data, lower limit SuN data, upper limit Known Levels  r from Goriely et al.Figure 5.39: Normalized γSF for 72Ni for both spin possibilities for the ground state of 72Co
compared to γSF data on 69,70Ni from the β-Oslo method, as well as higher-energy Coulomb
dissociation data for 68,70Ni.

5.4

73Co decay

The decay of 73Co is free of any known isomers, which made it the simplest case for fitting

the decay curve. The known half-life of 73Co is 40.7(13) ms [66], while the known half-life

of 73Ni is 840(30) ms [66]. As with the other Co isotopes, the decay curve was fit with

a combination of parent decays, daughter decays with a fixed half-life, and a background

component with a decay constant fixed by the backwards correlator decay curve. This fit is

shown in Fig. 5.40. The half-life of 73Co extracted from the fit was 41(1) ms, which matches

the known half-life well.

The same procedure as described for 71,72Co was used to remove the daughter and back-

ground contributions to the SuN spectra. Table 5.10 details the number of parent decays,

daughter decays, and background counts from the decay curve fit.

113

E (MeV)g02468101214-3f(E) (MeV)g-910-810-710-61072- Ni SuN data (g.s. 6) - present work69 Ni SuN data, Spyrou et al.70 Ni SuN data, Liddick et al.68 Ni data, Rossi et al. 70 Ni data, Wieland et al. 72- Ni Sun upper/lower limits (g.s. 6)E (MeV)g0246810121472- Ni SuN data (g.s. 7) - present work69 Ni SuN data, Spyrou et al.70 Ni SuN data, Liddick et al.68 Ni data, Rossi et al. 70 Ni data, Wieland et al. 72- Ni Sun upper/lower limits (g.s. 7)Figure 5.40: Full decay curve fit for the decay of 73Co.

Table 5.10: Results of decay curve fit for 73Co decay using a 150 ms correlation time (see
Fig. 5.40).

Number of parent decays

Number of daughter decays

Number of random correlations

Number of events in backwards correlation

97980(350)

7966(17)

69383(30)

80511(28)

Table 5.11: Results of decay curve fit for 73Co decay using a 5 sec correlation time (see Fig.
5.41).

Number of daughter decays in subtraction region

Number of random correlations in subtraction region

7970(120)

57100(100)

114

Time (ms)020406080100120140Counts010002000800600400200120014001600180022002400Total fitParent contributionDaughter contributionBackground contributionBackwards correlation fitFigure 5.41: Long correlation time decay curve fit for the decay of 73Co. The green band
shows the time region used to remove the daughter contribution to the SuN spectra.

From the 5 second correlator, a time window of 500 ms to 1523 ms was found to have

the appropriate number of daughter decays, 7970(120), to match the number of daughter

decays in the 150 ms correlator. This time window contained 57100(100) background counts

(see Table 5.11), leaving 12290(100) background counts left in the 150 ms correlator after

removing the daughter spectrum. The backwards correlation was scaled appropriately to

remove the correct amount of background remaining in the spectra.

The SuN spectra for the β decay of 73Co can be seen in Fig. 5.42, and the known level

scheme can be seen in Fig. 5.43. The strongest transition in 73Ni, with an absolute intensity
of ∼70%, is at 239.2 keV, which was clearly apparent in the parent component of the γ-ray
spectrum. There are only three more known transitions, at 284.8 keV (Iγ ∼ 34%), 524.6 keV
(Iγ ∼ 18%), and 774.7 keV (Iγ ∼ 53%). There are two strongly fed levels, at 1299.0 keV

and 239.2 keV, which were clearly seen in the TAS spectrum.

115

0200040006000800010000120001400016000Time (ms)010002000300040005000Counts per 50 msTotal fitParent contributionDaughter contributionBackground contributionBackwards correlation fitDaughter subtraction regionFigure 5.42: 73Co SuN spectra showing the raw spectrum, daughter decay contribution, back-
ground contribution, and final γ-ray (top) and TAS (bottom) spectra for the de-excitation
of 73Ni. As with Figs. 5.10 and 5.29, the labeled peaks note strong γ-ray transitions and
strongly fed levels, and are described in the text.

116

01000200030004000500060007000Gamma energy (keV)050010001500200025003000Counts per 10 keVRaw SuN spectrumDaughter contributionBackground contributionParent contributionABCDA+BB+D0100200300400500600700800Excitation energy (keV)05001000150020002500400030003500Raw SuN spectrumDaughter contributionBackground contributionParent contributionCounts per 10 keVEFigure 5.43: Known level scheme for the β decay of 73Co.

5.4.1 β-Oslo matrices

The raw 2D Oslo matrix for the β decay of 73Co is shown in Fig. 5.44 with 10 keV wide bins,

while the starting matrix, daughter component matrix, and background component matrix

can be found in Appendix B. The unfolded matrix is shown in Fig. 5.45, with 120 kev

binning, and the primary matrix is shown in Fig. 5.46. The extraction range for the NLD
and γSF was Eγ > 1700 keV, Ex ∈ (2800, 4000) keV. Even though the first excited state of

the β-delayed neutron daughter, 72Ni, is relatively high in energy (1.0950(9) MeV [68]), the

upper Ex limit was not raised further above Sn due to a lack of statistics.

5.4.2 NLD normalization

The NLD normalization procedure followed those described for 71,72Ni. The χ2 minimization

to determine the shift value for the calculated cumulative levels (once again restricted to levels

that fall within the spin range populated in β decay) is shown in Fig. 5.47, and resulted

117

S(n)+x1299.0524.3239.20-(5/2)+(5/2)+(7/2)+(9/2)774.7  ~53524.6  ~18284.8  ~34239.2  ~7073Co-(7/2)0.040.7 ms 13-%b = 100.00.84 s 373Ni<42<30<36-IbFigure 5.44: Raw 2D Oslo matrix for the decay of 73Co into excited states of 73Ni. The γ-ray
energies obtained from the segments of SuN are plotted on the x-axis, while the excitation
energy of the daughter nucleus, obtained from the total energy in the detector, is plotted on
the y-axis.

118

020004000600080001000012000110210310Gamma energy (keV)100002000300040005000600070008000900010000Excitation energy (keV)Figure 5.45: Unfolded 2D matrix for 73Ni with 120 keV binning on both axis.

Figure 5.46: Primary 2D matrix for 73Ni with 120 keV binning on both axis. The extraction
region used for the NLD and γSF is outlined by the black lines.

119

010002000300040005000 110210310410010002000300040005000Excitation energy (keV)Gamma energy (keV) 010002000300040005000110210310010002000300040005000Excitation energy (keV)Gamma energy (keV)Figure 5.47: χ2 values for different Ex shifts of the calculated cumulative levels compared
to the known cumulative levels for 73Ni.

Table 5.12: Parameters used in exponential fit to shifted calculated NLD for 73Ni.
ρ(Sn) (MeV−1)

Constant

Shift Value

Slope

0 MeV

0.25 MeV

0.5 MeV

1.7(1)

1.3(1)

0.99(9)

1.06(1)

1.06(1)

1.06(1)

161(17)

124(14)

95(11)

in shifts of 0.25 ± 0.25 MeV. The resulting shifted calculated NLD are shown compared to

the known levels in Fig. 5.48, and the shifted calculated NLD around Sn is shown in Fig.

5.49. The low Sn value (3.953(3) MeV [107]) was less of an issue for this isotope than for

71Ni, as the calculated NLD had a more exponential shape at low energies. The exponential

fits to the shifted calculated NLD are shown in Fig. 5.49, while the parameters for the fits

are detailed in Table 5.12. The fits resulted in ρ(Sn) values of 95(11), 124(14), and 161(17)
MeV−1.

120

68101214161820LD shift (MeV)-0.4-0.200.20.40.60.812 c valueFigure 5.48: Shifted calculated cumulative levels compared to the known cumulative levels.

Figure 5.49: Shifted calculated level densities (upper, mid, and lower) near Sn used to
determine ρ(Sn) values for the NLD normalization.

121

 Cumulative Levels110Excitation Energy E (MeV)x0120.20.40.60.81.21.41.61.873Known Ni Cumulative LevelsGoriely Cumulative Levels (Shift = 0 MeV)Shift = 0.25 MeVShift = 0.50 MeV -1Level Density (MeV)210310Excitation Energy E (MeV)x2345610Shift = 0 MeVShift = 0.25 MeVShift = 0.50 MeVExponential fit to 0 MeV shiftExponential fit to 0.25 MeV shiftExponential fit to 0.50 MeV shift73Ni S = 3.953 MeVnFigure 5.50: Distribution of spins for the levels in 73Ni around the neutron separation energy
based on tabulated spin- and parity-dependent NLD from Ref. [30]. Spins highlighted in blue
are populated following an allowed β decay of 73Co and one dipole photon transition. The
ground state of 73Co has been tentatively assigned a value of (7/2−).

The NLD reduction due to the limited experimental information was necessary for 73Ni

as well. The spin distribution around Sn, with the populated spins of 3/2 to 11/2 (both

parities) highlighted is shown in Fig. 5.50. This represented 60.8(6)% of the total NLD,
leading to reduced ρ(Sn) values of 58(7), 75(8), and 98(11) MeV−1. The upper, middle, and

lower normalized NLD is shown in Fig. 5.51, along with the three shifted Goriely calculated

NLDs, reduced to only the spin range of interest.

5.4.3 γSF normalization

As with the other two Ni isotopes, the 73Ni γSF was normalized using data from 68,69,70Ni.

The normalized γSF is shown in Fig. 5.52.

122

 Spin Distribution Spins Populated0246810121416SpinPercent of Total NLD (%)02468101412161820Figure 5.51: Normalized NLD for 73Ni, with the known levels and Goriely calculated NLD
(shifts of 0 MeV, 0.25 MeV, and 0.5 MeV).

123

 -1Level density r(E) (MeV) x1-11021010Excitation energy E (MeV)x0123473Ni S = 3.953 MeVn SuN data, middle  SuN data, lower limit SuN data, upper limit Known Levels  r from Goriely et al.Figure 5.52: Normalized γSF for 73Ni (black dots) compared to γSF data on 69,70Ni from
the β-Oslo method, as well as higher-energy Coulomb dissociation data for 68,70Ni.

124

 E (MeV)g02468101214-3f(E) (MeV)g-910-810-710-61073 Ni SuN data - present work69 Ni SuN data, Spyrou et al.70 Ni SuN data, Liddick et al.68 Ni data, Rossi et al. 70 Ni data, Wieland et al. 73 Ni Sun upper/lower limitsChapter 6

Results and Discussion

6.1 TALYS calculations

The γSF data for each isotope was fitted with a combination of a Hartree-Fock BCS model

(“strength 3” option in TALYS) and an exponential upbend. The strength 3 table was

chosen because it represented the γSF of all three isotopes well at higher energies (above

2 MeV) and was easy to shift in magnitude in the code. The upbend needed to be added

directly to the source code. The shift value and the parameters for the exponential upbend

were determined by a combined fit to the experimental data. The best results can be seen in
Figs. 6.1, 6.2 (fitted for both the 6− and 7− 72Co parent spin possibilities), and 6.3. Only

the middle values are shown in this section, but the lower limit and upper limit for each

isotope were also obtained and incorporated into the TALYS calculation as well. All of the

results from this procedure are provided in Appendix C. The fitted parameters are given in

Table 6.1.

The neutron-capture cross sections and reaction rates for the 70Ni(n, γ)71Ni, 71Ni(n, γ)72Ni,

and 72Ni(n, γ)73Ni reactions were then calculated in TALYS. All combinations of the NLD

and γSF models in Table 3.4 were first used to determine the model uncertainty, which can be

seen in Fig. 6.4 as the light grey band. The procedure described above was used to incorpo-

rate the experimental γSF, while the experimental NLD was converted to a spin-dependent

125

Figure 6.1: Fit to experimental γSF for 71Ni using the HFBCS model (strength 3 in TALYS)
and an exponential upbend.

Figure 6.2: Fit to experimental γSF for 72Ni using the HFBCS model (strength 3 in TALYS)
and an exponential upbend. The γSF obtained from a 6− 72Co parent is on the left, while
the γSF obtained from a 7− parent is on the right.

126

 E (MeV)g0-3gSF (MeV)-910 Experimental gSF TALYS shifted strength3 + exponential upbend71Ni S = 4.264 MeVn -810-710123456 E (MeV)g0123456 E (MeV)g0-3gSF (MeV)-910 Experimental gSF TALYS shifted strength3 + exponential upbend72Ni S = 6.891 MeVn-810-71012345-6 g.s.-7 g.s.6778Figure 6.3: Fit to experimental γSF for 73Ni using the HFBCS model (strength 3 in TALYS)
and an exponential upbend.

Table 6.1: Parameters used to fit the experimental γSF with a scaled HFBCS table (strength
3 in TALYS) and exponential upbend. Fits are shown in Figs. 6.1, 6.2, and 6.3 for the middle
values.

Isotope

71Ni lower limit

71Ni middle

71Ni upper limit
72Ni (6− g.s.) lower limit
72Ni (6− g.s.) middle
72Ni (6− g.s.) upper limit
72Ni (7− g.s.) lower limit
72Ni (7− g.s.) middle
72Ni (7− g.s.) upper limit
73Ni lower limit

73Ni middle

73Ni upper limit

Strength 3

Exponential

Exponential

scaling factor

constant

slope

3E-8

3E-8

3E-8

4E-8

5E-8

2E-8

3E-8

6E-8

5E-8

3E-8

3E-8

4E-8

-1.2

-1.5

-1.8

-0.7

-0.9

-1.1

-0.5

-0.9

-1.2

-0.8

-0.9

-1.2

1.4

1.6

1.8

0.8

1.2

1.7

0.8

1.1

1.6

1.0

1.3

1.8

127

 E (MeV)g0-3gSF (MeV)-910-810-71012345 Experimental gSF TALYS shifted strength3 + exponential upbend73Ni S = 3.953 MeVnTable 6.2: Range of neutron-capture cross sections and reaction rates (maximum/minimum
at each energy or temperature) for all three reactions. In each case, the cross sections and
reaction rates were reduced to under a factor of 3 (under a factor of 2 for the 70Ni reaction).

Reaction

Input

70Ni(n, γ)

TALYS NLD and γSF models

experimental NLD and γSF

71Ni(n, γ)

TALYS NLD and γSF models

experimental NLD and γSF

72Ni(n, γ)

TALYS NLD and γSF models

experimental NLD and γSF

Cross section

Reaction rate

range

(max/min)

range

(max/min)

28

1.8

30

2.9

90

2.9

52

1.8

28

2.4

77

2.4

table as described in Chapter 3. All combinations of experimental NLD and γSF were run

through TALYS to determine the experimentally-constrained uncertainty. The results for

each isotope can be seen in Fig. 6.4 (for the 71Ni(n, γ)72Ni reaction, the uncertainty from

both potential 72Co ground state spins are combined) as the dark grey band. In all three

reactions, the uncertainties were dramatically decreased when the experimental NLD and

γSF were incorporated (see Table 6.2).

The 71,72,73Ni neutron-capture cross sections were also compared to the 68,69Ni neutron-

capture cross sections previously constrained using the β-Oslo method [77, 108]. The full

ranges for all five nuclei can be seen in Fig. 6.5. The three cross sections for even mass

isotopes (68,70,72Ni) are very similar, while the cross sections for odd mass isotopes (69,71Ni)

are higher. The γSF of 72Ni, which is the result of the 71Ni(n, γ) reaction, is larger at lower

γ-ray energies than 71,73Ni (see Fig. 6.6), which may explain the difference between the even-

mass and odd-mass cross sections. Other potential causes have not yet been investigated,

including the nuclear structure information that was used for each reaction. The increase in

128

Figure 6.4: (Left) TALYS cross section calculations (reactions are labeled). The light band
is the uncertainty in the cross section when considering all combinations of the NLD and
γSF models available (excluding the temperature-dependent HFB NLD and SLO γSF). The
darker band is the uncertainty when including the experimentally constrained NLD and
γSF, along with their associated uncertainties. (Right) TALYS reaction rate calculations
(reactions are labeled). The light and dark bands are the same as for the cross section,
while the blue dashed line is the JINA REACLIB rate for the reaction (also calculated in
TALYS) [15].

129

Cross Section (mb)110-110-210210Neutron Energy (MeV)-2101-110 SuN middle value SuN upper/lower limits TALYS upper/lower limits7071 Ni(n,g)Ni3-1-1Reaction Rate (cmsmol)510610710T (GK)-110110410 SuN middle value  SuN upper/lower limits TALYS upper/lower limits REACLIB rate7071 Ni(n,g)NiCross Section (mb)110-110-210210Neutron Energy (MeV)-2101-110- SuN middle value (6 gs)- SuN middle value (7 gs)- SuN upper/lower limits (6 gs)- SuN upper/lower limits (7 gs) TALYS upper/lower limits7172 Ni(n,g)Ni- SuN middle value (6 gs)- SuN middle value (7 gs)- SuN upper/lower limits (6 gs)- SuN upper/lower limits (7 gs) TALYS upper/lower limits REACLIB rate3-1-1Reaction Rate (cmsmol)510610710T (GK)-1101104107172 Ni(n,g)NiCross Section (mb)110-110-210210-2101-110Neutron Energy (MeV)7273 Ni(n,g)Ni SuN middle value SuN upper/lower limits TALYS upper/lower limits3-1-1Reaction Rate (cmsmol)510610710T (GK)-1101104107273 Ni(n,g)Ni SuN middle value  SuN upper/lower limits TALYS upper/lower limits REACLIB rateFigure 6.5: Comparison of the five Ni cross sections calculated in TALYS.

the cross sections of the even isotopes is interesting, as in general the neutron-capture cross

section decreases as a function of increasing neutron energy past the resonance region. The

reason for the increase at higher neutron energies for all three even-mass reactions is under

discussion.

130

7273Ni(n,g)Ni rangeCross Section (mb)110-110-210210Neutron Energy (MeV)-2101-1107172Ni(n,g)Ni range7071Ni(n,g)Ni range6970Ni(n,g)Ni range (Liddick et al.)6869Ni(n,g)Ni range (Spyrou et al.)Figure 6.6: Experimentally constrained γSF for 71,72,73Ni.

131

71 Ni experimental range72 Ni experimental range73 Ni experimental range g-ray Energy E (MeV)g02468101214-3f(E) (MeV)g-910-810-710-61069 Ni SuN data, Spyrou et al.70 Ni SuN data, Liddick et al.68 Ni data, Rossi et al. 70 Ni data, Wieland et al. Chapter 7

Conclusions and Outlook

A more complete understanding of the astrophysical location of the r-process, and in partic-

ular the weak r-process, relies on detailed information about the nuclei that are involved in

the process. In particular, neutron-capture cross sections are important but can have large

uncertainties due to the lack of direct experimental data at the present time. For the very

neutron-rich nuclei involved in the r-process, indirect methods such as the β-Oslo method

are the only way to constrain neutron-capture cross section calculations using experimental

data. By extracting the NLD and γSF of the nucleus formed in a neutron-capture reaction

from β-decay experimental data the uncertainty in a Hauser-Feshbach calculation of the

neutron-capture cross section can be reduced significantly, as these properties are the main

sources of uncertainty in such calculations. Smaller uncertainties for neutron-capture cross

sections propagate through astrophysics models of the r-process and result in reduced un-

certainties on the predicted abundance patterns, which allows for a more direct comparison

between modeled and observed abundances.

The choice of a Hauser-Feshbach model code can also contribute to the overall uncertainty

in the calculated cross sections. The assumptions and choices made to describe the nuclear

physics within each code, including the NLD, γSF, and known levels, can influence the cross

section. When different codes start from different assumptions the resulting cross sections

can very very different. Comparing the neutron-capture cross sections from multiple codes

132

for every nucleus involved in the r-process is not feasible, but the discrepancies between

them can be reduced with a better understanding of the shape of the NLD and γSF far from

stability, as well as more information about the structure of neutron-rich nuclei.

Experiments to obtain information about the NLD and γSF, even those that utilize

indirect methods, are possible only in select regions of the nuclear chart. That means that

our reliance on models to describe both properties for all of the other nuclei involved in the

r-process remains, but the models can be improved using the select data that is available.

When models of the NLD and γSF are better able to describe the neutron-rich nuclei that

are possible to study, such as the Ni isotopes presented in this work, then there is less

uncertainty in how to describe the NLD and γSF of even more neutron-rich nuclei. As

more β-Oslo experiments are performed, larger-scale systematic studies of the NLD and

γSF as a function of both the proton number and neutron number will be possible and will

also contribute to an increased understanding of both properties. Some theoretical work to

understand the dependence of the γSF as a function of neutron number has begun, but with

more data the theory can be improved [109].

The reduced uncertainties in the neutron-capture cross sections of all five Ni isotopes (70-

74) can now be used to investigate the impact on the overall uncertainty in calculated abun-

dance patterns in weak r-process models. The reduced uncertainty in just the 69Ni(n, γ)70Ni

reaction was previously shown to reduce the uncertainty in abundances in the mass 70 region

as well as up to mass 130, so incorporating the reduced uncertainties of four more reactions

should have a larger impact.

133

APPENDICES

134

APPENDIX A

Default NLD and γSF tables

135

Table A.1: TALYS default NLD for 74Zn including spin-dependent NLD for J=0-4. An equal parity distribution is assumed.

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

J=4

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.50

2.93E-01

3.98E-01

5.41E-01

7.36E-01

1.00E+00

1.36E+00

1.85E+00

2.51E+00

3.41E+00

4.64E+00

6.30E+00

8.57E+00

1.17E+01

1.58E+01

2.15E+01

2.92E+01

3.97E+01

5.40E+01

7.34E+01

9.98E+01

1.84E+02

2.15E-02

2.82E-02

3.71E-02

4.89E-02

6.45E-02

8.50E-02

1.12E-01

1.48E-01

1.96E-01

2.60E-01

3.44E-01

5.55E-02

7.33E-02

9.69E-02

1.28E-01

1.70E-01

2.25E-01

2.98E-01

3.95E-01

5.24E-01

6.95E-01

6.86E-02

9.15E-02

1.22E-01

1.63E-01

2.18E-01

2.90E-01

3.88E-01

5.18E-01

6.91E-01

9.24E-01

6.14E-02

8.31E-02

1.13E-01

1.52E-01

2.06E-01

2.78E-01

3.75E-01

5.06E-01

6.82E-01

9.20E-01

4.34E-02

6.00E-02

8.27E-02

1.14E-01

1.57E-01

2.15E-01

2.94E-01

4.02E-01

5.50E-01

7.51E-01

9.24E-01

1.23E+00

1.24E+00

1.02E+00

4.56E-01

1.23E+00

1.65E+00

1.67E+00

1.40E+00

6.04E-01

1.63E+00

2.20E+00

2.25E+00

1.90E+00

8.02E-01

2.17E+00

2.95E+00

3.03E+00

2.59E+00

1.07E+00

2.89E+00

3.94E+00

4.08E+00

3.52E+00

1.41E+00

3.85E+00

5.27E+00

5.50E+00

4.78E+00

1.88E+00

5.12E+00

7.05E+00

7.41E+00

6.49E+00

2.50E+00

6.83E+00

9.44E+00

9.98E+00

8.82E+00

3.32E+00

9.10E+00

1.26E+01

1.34E+01

1.20E+01

4.42E+00

1.21E+01

1.69E+01

1.81E+01

1.62E+01

7.85E+00

2.16E+01

3.03E+01

3.28E+01

2.99E+01
Continued on next page

136

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

J=4

Table A.1 (cont’d) TALYS default NLD

6.00

6.50

7.00

7.50

8.00

8.50

9.00

9.50

10.0

11.0

12.0

13.0

14.0

15.0

16.0

17.0

18.0

19.0

20.0

22.5

25.0

30.0

3.41E+02

6.29E+02

1.16E+03

2.15E+03

3.91E+03

6.95E+03

1.21E+04

2.06E+04

3.46E+04

9.25E+04

2.34E+05

5.67E+05

1.32E+06

2.95E+06

6.42E+06

1.36E+07

2.80E+07

5.64E+07

1.11E+08

5.65E+08

2.60E+09

4.42E+10

1.39E+01

3.85E+01

5.44E+01

5.94E+01

5.49E+01

2.48E+01

6.87E+01

9.76E+01

1.08E+02

1.01E+02

4.42E+01

1.23E+02

1.75E+02

1.95E+02

1.85E+02

7.88E+01

2.19E+02

3.15E+02

3.54E+02

3.38E+02

1.37E+02

3.82E+02

5.53E+02

6.27E+02

6.08E+02

2.33E+02

6.53E+02

9.51E+02

1.09E+03

1.07E+03

3.89E+02

1.09E+03

1.60E+03

1.85E+03

1.83E+03

6.40E+02

1.80E+03

2.65E+03

3.08E+03

3.08E+03

1.04E+03

2.93E+03

4.32E+03

5.05E+03

5.10E+03

2.61E+03

7.39E+03

1.10E+04

1.30E+04

1.33E+04

6.26E+03

1.78E+04

2.66E+04

3.17E+04

3.29E+04

1.44E+04

4.11E+04

6.19E+04

7.43E+04

7.78E+04

3.21E+04

9.16E+04

1.39E+05

1.67E+05

1.77E+05

6.91E+04

1.98E+05

3.00E+05

3.65E+05

3.89E+05

1.45E+05

4.15E+05

6.32E+05

7.72E+05

8.28E+05

2.96E+05

8.49E+05

1.30E+06

1.59E+06

1.72E+06

5.91E+05

1.70E+06

2.60E+06

3.21E+06

3.48E+06

1.16E+06

3.33E+06

5.11E+06

6.32E+06

6.89E+06

2.22E+06

6.40E+06

9.85E+06

1.22E+07

1.34E+07

1.06E+07

3.05E+07

4.72E+07

5.90E+07

6.53E+07

4.61E+07

1.33E+08

2.07E+08

2.61E+08

2.91E+08

7.11E+08

2.07E+09

3.23E+09

4.10E+09

4.63E+09
Continued on next page

137

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

J=4

Table A.1 (cont’d) TALYS default NLD

40.0

50.0

60.0

70.0

80.0

90.0

100

110

120

130

140

150

160

170

180

190

200

6.69E+12

5.66E+14

3.19E+16

1.32E+18

4.28E+19

1.14E+21

2.55E+22

4.94E+23

8.45E+24

1.29E+26

1.79E+27

2.27E+28

2.66E+29

2.89E+30

2.94E+31

2.82E+32

2.55E+33

9.31E+10

2.72E+11

4.28E+11

5.51E+11

6.34E+11

7.03E+12

2.06E+13

3.26E+13

4.24E+13

4.93E+13

3.61E+14

1.06E+15

1.69E+15

2.21E+15

2.59E+15

1.39E+16

4.07E+16

6.50E+16

8.54E+16

1.01E+17

4.20E+17

1.24E+18

1.98E+18

2.61E+18

3.11E+18

1.05E+19

3.10E+19

4.97E+19

6.58E+19

7.86E+19

2.24E+20

6.59E+20

1.06E+21

1.41E+21

1.69E+21

4.13E+21

1.22E+22

1.96E+22

2.62E+22

3.14E+22

6.76E+22

2.00E+23

3.22E+23

4.30E+23

5.18E+23

9.93E+23

2.94E+24

4.74E+24

6.34E+24

7.66E+24

1.33E+25

3.92E+25

6.34E+25

8.49E+25

1.03E+26

1.63E+26

4.81E+26

7.78E+26

1.04E+27

1.27E+27

1.84E+27

5.45E+27

8.83E+27

1.19E+28

1.44E+28

1.94E+28

5.75E+28

9.33E+28

1.26E+29

1.53E+29

1.92E+29

5.69E+29

9.24E+29

1.24E+30

1.52E+30

1.79E+30

5.30E+30

8.62E+30

1.16E+31

1.42E+31

1.58E+31

4.68E+31

7.60E+31

1.03E+32

1.25E+32

138

Table A.2: TALYS default NLD for 74Zn including spin-dependent NLD for J=5-8. An
equal parity distribution is assumed.

Ex (MeV)

Total NLD (MeV−1)

J=5

J=6

J=7

J=8

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.50

6.00

6.50

7.00

7.50

8.00

8.50

9.00

9.50

10.0

2.93E-01

3.98E-01

5.41E-01

7.36E-01

1.00E+00

1.36E+00

1.85E+00

2.51E+00

3.41E+00

4.64E+00

6.30E+00

8.57E+00

1.17E+01

1.58E+01

2.15E+01

2.92E+01

3.97E+01

5.40E+01

7.34E+01

9.98E+01

1.84E+02

3.41E+02

6.29E+02

1.16E+03

2.15E+03

3.91E+03

6.95E+03

1.21E+04

2.06E+04

3.46E+04

2.51E-02

3.56E-02

5.03E-02

7.08E-02

9.93E-02

1.39E-01

1.94E-01

2.70E-01

3.75E-01

5.20E-01

7.20E-01

9.95E-01

1.21E-02

1.77E-02

2.57E-02

3.72E-02

5.35E-02

7.66E-02

1.09E-01

1.55E-01

2.20E-01

3.11E-01

4.38E-01

6.16E-01

1.37E+00

8.63E-01

4.92E-03

7.44E-03

1.12E-02

1.67E-02

2.47E-02

3.63E-02

5.31E-02

7.74E-02

1.12E-01

1.62E-01

2.33E-01

3.34E-01

4.77E-01

1.89E+00

1.21E+00

6.79E-01

2.60E+00

1.69E+00

9.65E-01

1.69E-03

2.66E-03

4.14E-03

6.40E-03

9.80E-03

1.49E-02

2.24E-02

3.36E-02

5.00E-02

7.40E-02

1.09E-01

1.60E-01

2.33E-01

3.39E-01

4.91E-01

3.58E+00

2.35E+00

1.37E+00

7.08E-01

4.92E+00

3.27E+00

1.93E+00

1.02E+00

6.75E+00

4.55E+00

2.73E+00

1.46E+00

9.25E+00

6.31E+00

3.84E+00

2.09E+00

1.27E+01

8.75E+00

5.39E+00

2.98E+00

2.37E+01

1.67E+01

1.06E+01

6.02E+00

4.43E+01

3.19E+01

2.06E+01

1.21E+01

8.26E+01

6.06E+01

4.00E+01

2.40E+01

1.54E+02

1.15E+02

7.72E+01

4.74E+01

2.85E+02

2.16E+02

1.49E+02

9.31E+01

5.22E+02

4.04E+02

2.85E+02

1.83E+02

9.30E+02

7.33E+02

5.27E+02

3.48E+02

1.62E+03

1.30E+03

9.49E+02

6.40E+02

2.76E+03

2.24E+03

1.67E+03

1.15E+03

4.60E+03

3.79E+03

2.86E+03

2.00E+03
Continued on next page

139

Table A.2 (cont’d) TALYS default NLD

Ex (MeV)

Total NLD (MeV−1)

J=5

J=6

J=7

J=8

11.0

12.0

13.0

14.0

15.0

16.0

17.0

18.0

19.0

20.0

22.5

25.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100

110

120

130

140

150

160

170

180

190

200

9.25E+04

2.34E+05

5.67E+05

1.32E+06

2.95E+06

6.42E+06

1.36E+07

2.80E+07

5.64E+07

1.11E+08

5.65E+08

2.60E+09

4.42E+10

6.69E+12

5.66E+14

3.19E+16

1.32E+18

4.28E+19

1.14E+21

2.55E+22

4.94E+23

8.45E+24

1.29E+26

1.79E+27

2.27E+28

2.66E+29

2.89E+30

2.94E+31

2.82E+32

2.55E+33

1.22E+04

1.03E+04

7.98E+03

5.74E+03

3.07E+04

2.63E+04

2.08E+04

1.54E+04

7.36E+04

6.40E+04

5.16E+04

3.88E+04

1.69E+05

1.49E+05

1.22E+05

9.34E+04

3.75E+05

3.34E+05

2.78E+05

2.16E+05

8.07E+05

7.26E+05

6.10E+05

4.81E+05

1.69E+06

1.53E+06

1.30E+06

1.04E+06

3.44E+06

3.15E+06

2.70E+06

2.18E+06

6.85E+06

6.33E+06

5.47E+06

4.46E+06

1.34E+07

1.24E+07

1.08E+07

8.92E+06

6.61E+07

6.24E+07

5.53E+07

4.64E+07

2.97E+08

2.84E+08

2.55E+08

2.18E+08

4.82E+09

4.69E+09

4.31E+09

3.77E+09

6.74E+11

6.73E+11

6.39E+11

5.79E+11

5.32E+13

5.42E+13

5.25E+13

4.87E+13

2.83E+15

2.91E+15

2.87E+15

2.71E+15

1.11E+17

1.16E+17

1.15E+17

1.10E+17

3.44E+18

3.61E+18

3.63E+18

3.52E+18

8.76E+19

9.26E+19

9.38E+19

9.17E+19

1.89E+21

2.01E+21

2.05E+21

2.02E+21

3.53E+22

3.78E+22

3.88E+22

3.84E+22

5.85E+23

6.28E+23

6.47E+23

6.45E+23

8.67E+24

9.34E+24

9.68E+24

9.70E+24

1.17E+26

1.26E+26

1.31E+26

1.32E+26

1.44E+27

1.56E+27

1.63E+27

1.65E+27

1.64E+28

1.79E+28

1.87E+28

1.90E+28

1.75E+29

1.90E+29

2.00E+29

2.03E+29

1.74E+30

1.90E+30

2.00E+30

2.04E+30

1.63E+31

1.78E+31

1.88E+31

1.92E+31

1.44E+32

1.58E+32

1.67E+32

1.72E+32

140

Table A.3: CoH default NLD for 74Zn including spin-dependent NLD for J=0-3. An equal
parity distribution is assumed.

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

2.46E-02

4.46E-02

6.46E-02

8.46E-02

1.05E-01

1.25E-01

1.45E-01

1.65E-01

1.85E-01

2.05E-01

2.25E-01

2.45E-01

2.65E-01

2.85E-01

3.05E-01

3.25E-01

3.45E-01

3.65E-01

3.85E-01

4.05E-01

4.25E-01

4.45E-01

4.65E-01

4.85E-01

5.05E-01

5.25E-01

5.45E-01

5.65E-01

5.85E-01

6.05E-01

5.61E-01

5.72E-01

5.83E-01

5.95E-01

6.06E-01

6.18E-01

6.30E-01

6.42E-01

6.54E-01

6.67E-01

6.80E-01

6.93E-01

7.07E-01

7.20E-01

7.34E-01

7.48E-01

7.63E-01

7.78E-01

7.93E-01

8.08E-01

8.24E-01

8.40E-01

8.56E-01

8.73E-01

8.89E-01

9.07E-01

9.24E-01

9.42E-01

9.60E-01

9.79E-01

1.40E-01

1.43E-01

1.46E-01

1.49E-01

1.51E-01

1.54E-01

1.57E-01

1.60E-01

1.64E-01

1.67E-01

1.70E-01

1.73E-01

1.77E-01

1.80E-01

1.83E-01

1.87E-01

1.91E-01

1.94E-01

1.98E-01

2.02E-01

2.06E-01

2.10E-01

2.14E-01

2.18E-01

2.22E-01

2.26E-01

2.31E-01

2.35E-01

2.40E-01

2.45E-01

1.85E-01

1.89E-01

1.93E-01

1.96E-01

2.00E-01

2.04E-01

2.08E-01

2.12E-01

2.16E-01

2.20E-01

2.25E-01

2.29E-01

2.33E-01

2.38E-01

2.42E-01

2.47E-01

2.52E-01

2.57E-01

2.62E-01

2.67E-01

2.72E-01

2.77E-01

2.83E-01

2.88E-01

2.94E-01

2.99E-01

3.05E-01

3.11E-01

3.17E-01

1.83E-01

1.87E-01

1.90E-01

1.94E-01

1.98E-01

2.02E-01

2.06E-01

2.10E-01

2.14E-01

2.18E-01

2.22E-01

2.26E-01

2.31E-01

2.35E-01

2.40E-01

2.44E-01

2.49E-01

2.54E-01

2.59E-01

2.64E-01

2.69E-01

2.74E-01

2.79E-01

2.85E-01

2.90E-01

2.96E-01

3.02E-01

3.08E-01

3.14E-01

3.23E-01

3.20E-01
Continued on next page

5.25E-02

5.35E-02

5.46E-02

5.56E-02

5.67E-02

5.78E-02

5.89E-02

6.00E-02

6.12E-02

6.24E-02

6.36E-02

6.48E-02

6.61E-02

6.74E-02

6.87E-02

7.00E-02

7.13E-02

7.27E-02

7.41E-02

7.56E-02

7.70E-02

7.85E-02

8.00E-02

8.16E-02

8.32E-02

8.48E-02

8.64E-02

8.81E-02

8.98E-02

9.15E-02

141

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

6.25E-01

6.45E-01

6.65E-01

6.85E-01

7.05E-01

7.25E-01

7.45E-01

7.65E-01

7.85E-01

8.05E-01

8.25E-01

8.45E-01

8.65E-01

8.85E-01

9.05E-01

9.25E-01

9.45E-01

9.65E-01

9.85E-01

1.01E+00

1.03E+00

1.05E+00

1.07E+00

1.09E+00

1.11E+00

1.13E+00

1.15E+00

1.17E+00

1.19E+00

1.21E+00

1.23E+00

9.98E-01

1.02E+00

1.04E+00

1.06E+00

1.08E+00

1.10E+00

1.12E+00

1.14E+00

1.16E+00

1.19E+00

1.21E+00

1.23E+00

1.26E+00

1.28E+00

1.31E+00

1.33E+00

1.36E+00

1.38E+00

1.41E+00

1.44E+00

1.46E+00

1.49E+00

1.52E+00

1.55E+00

1.58E+00

1.61E+00

1.64E+00

1.67E+00

1.71E+00

1.74E+00

1.77E+00

2.49E-01

2.54E-01

2.59E-01

2.64E-01

2.69E-01

2.74E-01

2.80E-01

2.85E-01

2.91E-01

2.96E-01

3.02E-01

3.08E-01

3.14E-01

3.20E-01

3.26E-01

3.32E-01

3.39E-01

3.45E-01

3.52E-01

3.59E-01

3.66E-01

3.73E-01

3.80E-01

3.87E-01

3.95E-01

4.03E-01

4.10E-01

4.18E-01

4.26E-01

4.35E-01

4.43E-01

3.29E-01

3.36E-01

3.42E-01

3.49E-01

3.56E-01

3.63E-01

3.70E-01

3.77E-01

3.84E-01

3.92E-01

3.99E-01

4.07E-01

4.15E-01

4.23E-01

4.31E-01

4.39E-01

4.48E-01

4.56E-01

4.65E-01

4.74E-01

4.83E-01

4.93E-01

5.02E-01

5.12E-01

5.22E-01

5.32E-01

5.42E-01

5.53E-01

5.64E-01

5.74E-01

3.26E-01

3.32E-01

3.38E-01

3.45E-01

3.52E-01

3.59E-01

3.65E-01

3.73E-01

3.80E-01

3.87E-01

3.95E-01

4.02E-01

4.10E-01

4.18E-01

4.26E-01

4.34E-01

4.43E-01

4.51E-01

4.60E-01

4.69E-01

4.78E-01

4.87E-01

4.97E-01

5.06E-01

5.16E-01

5.26E-01

5.36E-01

5.47E-01

5.57E-01

5.68E-01

5.86E-01

5.79E-01
Continued on next page

9.33E-02

9.51E-02

9.70E-02

9.88E-02

1.01E-01

1.03E-01

1.05E-01

1.07E-01

1.09E-01

1.11E-01

1.13E-01

1.15E-01

1.17E-01

1.20E-01

1.22E-01

1.24E-01

1.27E-01

1.29E-01

1.32E-01

1.34E-01

1.37E-01

1.40E-01

1.42E-01

1.45E-01

1.48E-01

1.51E-01

1.54E-01

1.57E-01

1.60E-01

1.63E-01

1.66E-01

142

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

1.25E+00

1.27E+00

1.29E+00

1.31E+00

1.33E+00

1.35E+00

1.37E+00

1.39E+00

1.41E+00

1.43E+00

1.45E+00

1.47E+00

1.49E+00

1.51E+00

1.53E+00

1.55E+00

1.57E+00

1.59E+00

1.61E+00

1.63E+00

1.65E+00

1.67E+00

1.69E+00

1.71E+00

1.73E+00

1.75E+00

1.77E+00

1.79E+00

1.81E+00

1.83E+00

1.85E+00

1.81E+00

1.84E+00

1.88E+00

1.91E+00

1.95E+00

1.99E+00

2.03E+00

2.07E+00

2.11E+00

2.15E+00

2.19E+00

2.23E+00

2.28E+00

2.32E+00

2.36E+00

2.41E+00

2.46E+00

2.50E+00

2.55E+00

2.60E+00

2.65E+00

2.70E+00

2.76E+00

2.81E+00

2.86E+00

2.92E+00

2.98E+00

3.03E+00

3.09E+00

3.15E+00

3.21E+00

4.52E-01

4.60E-01

4.69E-01

4.78E-01

4.88E-01

4.97E-01

5.07E-01

5.16E-01

5.26E-01

5.37E-01

5.47E-01

5.58E-01

5.68E-01

5.79E-01

5.91E-01

6.02E-01

6.14E-01

6.26E-01

6.38E-01

6.50E-01

6.63E-01

6.76E-01

6.89E-01

7.02E-01

7.15E-01

7.29E-01

7.43E-01

5.97E-01

6.08E-01

6.20E-01

6.32E-01

6.45E-01

6.57E-01

6.70E-01

6.83E-01

6.96E-01

7.09E-01

7.23E-01

7.37E-01

7.51E-01

7.66E-01

7.81E-01

7.96E-01

8.11E-01

8.27E-01

8.43E-01

8.59E-01

8.76E-01

8.93E-01

9.10E-01

9.28E-01

9.46E-01

9.64E-01

9.83E-01

5.90E-01

6.02E-01

6.13E-01

6.25E-01

6.37E-01

6.50E-01

6.62E-01

6.75E-01

6.88E-01

7.01E-01

7.15E-01

7.29E-01

7.43E-01

7.57E-01

7.72E-01

7.87E-01

8.02E-01

8.18E-01

8.33E-01

8.50E-01

8.66E-01

8.83E-01

9.00E-01

9.17E-01

9.35E-01

9.53E-01

9.72E-01

7.58E-01

1.00E+00

9.90E-01

7.73E-01

1.02E+00

1.01E+00

7.87E-01

1.04E+00

1.03E+00

8.03E-01

1.06E+00

1.05E+00
Continued on next page

1.69E-01

1.72E-01

1.76E-01

1.79E-01

1.83E-01

1.86E-01

1.90E-01

1.93E-01

1.97E-01

2.01E-01

2.05E-01

2.09E-01

2.13E-01

2.17E-01

2.21E-01

2.25E-01

2.30E-01

2.34E-01

2.39E-01

2.43E-01

2.48E-01

2.53E-01

2.58E-01

2.63E-01

2.68E-01

2.73E-01

2.78E-01

2.84E-01

2.89E-01

2.95E-01

3.00E-01

143

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

1.87E+00

1.89E+00

1.91E+00

1.93E+00

1.95E+00

1.97E+00

1.99E+00

2.01E+00

2.03E+00

2.05E+00

2.07E+00

2.09E+00

2.11E+00

2.13E+00

2.15E+00

2.17E+00

2.19E+00

2.21E+00

2.23E+00

2.25E+00

2.27E+00

2.29E+00

2.31E+00

2.33E+00

2.35E+00

2.37E+00

2.39E+00

2.41E+00

2.43E+00

2.45E+00

2.47E+00

3.28E+00

3.34E+00

3.40E+00

3.47E+00

3.54E+00

3.60E+00

3.67E+00

3.75E+00

3.82E+00

3.89E+00

3.97E+00

4.04E+00

4.12E+00

4.20E+00

4.28E+00

4.37E+00

4.45E+00

4.54E+00

4.63E+00

4.71E+00

4.81E+00

4.90E+00

4.99E+00

5.09E+00

5.19E+00

5.29E+00

5.39E+00

5.50E+00

5.60E+00

5.71E+00

5.82E+00

3.06E-01

3.12E-01

3.18E-01

3.24E-01

3.31E-01

3.37E-01

3.44E-01

3.50E-01

3.57E-01

3.64E-01

3.71E-01

8.18E-01

1.08E+00

1.07E+00

8.34E-01

1.10E+00

1.09E+00

8.50E-01

1.12E+00

1.11E+00

8.67E-01

1.15E+00

1.13E+00

8.83E-01

1.17E+00

1.15E+00

9.01E-01

1.19E+00

1.18E+00

9.18E-01

1.21E+00

1.20E+00

9.36E-01

1.24E+00

1.22E+00

9.54E-01

1.26E+00

1.25E+00

9.72E-01

1.29E+00

1.27E+00

9.91E-01

1.31E+00

1.30E+00

3.78E-01

1.01E+00

1.34E+00

1.32E+00

3.86E-01

1.03E+00

1.36E+00

1.35E+00

3.93E-01

1.05E+00

1.39E+00

1.37E+00

4.01E-01

1.07E+00

1.41E+00

1.40E+00

4.08E-01

1.09E+00

1.44E+00

1.43E+00

4.16E-01

1.11E+00

1.47E+00

1.45E+00

4.24E-01

1.13E+00

1.50E+00

1.48E+00

4.32E-01

1.16E+00

1.53E+00

1.51E+00

4.41E-01

1.18E+00

1.56E+00

1.54E+00

4.49E-01

1.20E+00

1.59E+00

1.57E+00

4.58E-01

1.22E+00

1.62E+00

1.60E+00

4.67E-01

1.25E+00

1.65E+00

1.63E+00

4.76E-01

1.27E+00

1.68E+00

1.66E+00

4.85E-01

1.30E+00

1.71E+00

1.69E+00

4.95E-01

1.32E+00

1.75E+00

1.73E+00

5.04E-01

1.35E+00

1.78E+00

1.76E+00

5.14E-01

1.37E+00

1.81E+00

1.79E+00

5.24E-01

1.40E+00

1.85E+00

1.83E+00

5.34E-01

1.43E+00

1.89E+00

1.86E+00

5.44E-01

1.45E+00

1.92E+00

1.90E+00
Continued on next page

144

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

2.49E+00

2.51E+00

2.53E+00

2.55E+00

2.57E+00

2.59E+00

2.61E+00

2.63E+00

2.65E+00

2.67E+00

2.69E+00

2.71E+00

2.73E+00

2.75E+00

2.77E+00

2.79E+00

2.81E+00

2.83E+00

2.85E+00

2.87E+00

2.89E+00

2.91E+00

2.93E+00

2.95E+00

2.97E+00

2.99E+00

3.01E+00

3.03E+00

3.05E+00

3.07E+00

3.09E+00

5.93E+00

6.05E+00

6.17E+00

6.29E+00

6.41E+00

6.53E+00

6.66E+00

6.79E+00

6.92E+00

7.05E+00

7.19E+00

7.33E+00

7.47E+00

7.61E+00

7.76E+00

7.91E+00

8.06E+00

8.22E+00

8.38E+00

8.54E+00

8.71E+00

8.88E+00

9.05E+00

9.22E+00

9.40E+00

9.58E+00

9.77E+00

9.96E+00

1.02E+01

1.03E+01

1.05E+01

J=0

J=1

J=2

J=3

5.55E-01

1.48E+00

1.96E+00

1.94E+00

5.66E-01

1.51E+00

2.00E+00

1.97E+00

5.77E-01

1.54E+00

2.04E+00

2.01E+00

5.88E-01

1.57E+00

2.08E+00

2.05E+00

5.99E-01

1.60E+00

2.12E+00

2.09E+00

6.11E-01

1.63E+00

2.16E+00

2.13E+00

6.23E-01

1.66E+00

2.20E+00

2.17E+00

6.35E-01

1.70E+00

2.24E+00

2.22E+00

6.47E-01

1.73E+00

2.28E+00

2.26E+00

6.59E-01

1.76E+00

2.33E+00

2.30E+00

6.72E-01

1.80E+00

2.37E+00

2.35E+00

6.85E-01

1.83E+00

2.42E+00

2.39E+00

6.98E-01

1.87E+00

2.47E+00

2.44E+00

7.12E-01

1.90E+00

2.51E+00

2.49E+00

7.26E-01

1.94E+00

2.56E+00

2.53E+00

7.40E-01

1.98E+00

2.61E+00

2.58E+00

7.54E-01

2.01E+00

2.66E+00

2.63E+00

7.69E-01

2.05E+00

2.71E+00

2.68E+00

7.84E-01

2.09E+00

2.77E+00

2.74E+00

7.99E-01

2.13E+00

2.82E+00

2.79E+00

8.14E-01

2.18E+00

2.88E+00

2.84E+00

8.30E-01

2.22E+00

2.93E+00

2.90E+00

8.46E-01

2.26E+00

2.99E+00

2.95E+00

8.62E-01

2.30E+00

3.05E+00

3.01E+00

8.79E-01

2.35E+00

3.10E+00

3.07E+00

8.96E-01

2.39E+00

3.16E+00

3.13E+00

9.13E-01

2.44E+00

3.23E+00

3.19E+00

9.31E-01

2.49E+00

3.29E+00

3.25E+00

9.49E-01

2.54E+00

3.35E+00

3.31E+00

9.68E-01

2.58E+00

3.42E+00

3.38E+00

9.86E-01

2.63E+00

3.48E+00

3.44E+00
Continued on next page

145

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

3.11E+00

3.13E+00

3.15E+00

3.17E+00

3.19E+00

3.21E+00

3.23E+00

3.25E+00

3.27E+00

3.29E+00

3.31E+00

3.33E+00

3.35E+00

3.37E+00

3.39E+00

3.41E+00

3.43E+00

3.45E+00

3.47E+00

3.49E+00

3.51E+00

3.53E+00

3.55E+00

3.57E+00

3.59E+00

3.61E+00

3.63E+00

3.65E+00

3.67E+00

3.69E+00

3.71E+00

1.08E+01

1.10E+01

1.12E+01

1.14E+01

1.16E+01

1.18E+01

1.21E+01

1.23E+01

1.25E+01

1.28E+01

1.30E+01

1.33E+01

1.35E+01

1.38E+01

1.41E+01

1.43E+01

1.46E+01

1.49E+01

1.52E+01

1.55E+01

1.58E+01

1.61E+01

1.64E+01

1.67E+01

1.70E+01

1.74E+01

1.77E+01

1.80E+01

1.84E+01

1.87E+01

1.91E+01

1.01E+00

2.69E+00

3.55E+00

3.51E+00

1.02E+00

2.74E+00

3.62E+00

3.58E+00

1.04E+00

2.79E+00

3.69E+00

3.65E+00

1.06E+00

2.84E+00

3.76E+00

3.72E+00

1.09E+00

2.90E+00

3.83E+00

3.79E+00

1.11E+00

2.96E+00

3.91E+00

3.86E+00

1.13E+00

3.01E+00

3.98E+00

3.94E+00

1.15E+00

3.07E+00

4.06E+00

4.01E+00

1.17E+00

3.13E+00

4.14E+00

4.09E+00

1.19E+00

3.19E+00

4.22E+00

4.17E+00

1.22E+00

3.25E+00

4.30E+00

4.25E+00

1.24E+00

3.32E+00

4.38E+00

4.33E+00

1.27E+00

3.38E+00

4.47E+00

4.42E+00

1.29E+00

3.45E+00

4.55E+00

4.50E+00

1.31E+00

3.51E+00

4.64E+00

4.59E+00

1.34E+00

3.58E+00

4.73E+00

4.68E+00

1.37E+00

3.65E+00

4.82E+00

4.77E+00

1.39E+00

3.72E+00

4.92E+00

4.86E+00

1.42E+00

3.79E+00

5.01E+00

4.96E+00

1.45E+00

3.87E+00

5.11E+00

5.05E+00

1.48E+00

3.94E+00

5.21E+00

5.15E+00

1.50E+00

4.02E+00

5.31E+00

5.25E+00

1.53E+00

4.09E+00

5.41E+00

5.35E+00

1.56E+00

4.17E+00

5.52E+00

5.45E+00

1.59E+00

4.25E+00

5.62E+00

5.56E+00

1.62E+00

4.34E+00

5.73E+00

5.67E+00

1.65E+00

4.42E+00

5.84E+00

5.78E+00

1.69E+00

4.51E+00

5.96E+00

5.89E+00

1.72E+00

4.59E+00

6.07E+00

6.00E+00

1.75E+00

4.68E+00

6.19E+00

6.12E+00

1.79E+00

4.77E+00

6.31E+00

6.24E+00
Continued on next page

146

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

3.73E+00

3.75E+00

3.77E+00

3.79E+00

3.81E+00

3.83E+00

3.85E+00

3.87E+00

3.89E+00

3.91E+00

3.93E+00

3.95E+00

3.97E+00

3.99E+00

4.01E+00

4.03E+00

4.05E+00

4.07E+00

4.09E+00

4.11E+00

4.13E+00

4.15E+00

4.17E+00

4.19E+00

4.21E+00

4.23E+00

4.25E+00

4.27E+00

4.29E+00

4.31E+00

4.33E+00

1.95E+01

1.99E+01

2.02E+01

2.06E+01

2.10E+01

2.14E+01

2.19E+01

2.23E+01

2.27E+01

2.31E+01

2.36E+01

2.41E+01

2.45E+01

2.50E+01

2.55E+01

2.60E+01

2.65E+01

2.70E+01

2.75E+01

2.80E+01

2.86E+01

2.91E+01

2.97E+01

3.03E+01

3.09E+01

3.15E+01

3.21E+01

3.27E+01

3.33E+01

3.40E+01

3.46E+01

1.82E+00

4.87E+00

6.43E+00

6.36E+00

1.86E+00

4.96E+00

6.56E+00

6.48E+00

1.89E+00

5.06E+00

6.68E+00

6.61E+00

1.93E+00

5.15E+00

6.81E+00

6.74E+00

1.97E+00

5.25E+00

6.94E+00

6.87E+00

2.00E+00

5.36E+00

7.08E+00

7.00E+00

2.04E+00

5.46E+00

7.22E+00

7.13E+00

2.08E+00

5.56E+00

7.36E+00

7.27E+00

2.12E+00

5.67E+00

7.50E+00

7.41E+00

2.16E+00

5.78E+00

7.64E+00

7.56E+00

2.21E+00

5.89E+00

7.79E+00

7.70E+00

2.25E+00

6.01E+00

7.94E+00

7.85E+00

2.29E+00

6.12E+00

8.10E+00

8.00E+00

2.34E+00

6.24E+00

8.25E+00

8.16E+00

2.38E+00

6.36E+00

8.41E+00

8.32E+00

2.43E+00

6.49E+00

8.57E+00

8.48E+00

2.48E+00

6.61E+00

8.74E+00

8.64E+00

2.52E+00

6.74E+00

8.91E+00

8.81E+00

2.57E+00

6.87E+00

9.08E+00

8.98E+00

2.62E+00

7.00E+00

9.26E+00

9.15E+00

2.67E+00

7.14E+00

9.44E+00

9.33E+00

2.72E+00

7.28E+00

9.62E+00

9.51E+00

2.78E+00

7.42E+00

9.81E+00

9.70E+00

2.83E+00

7.56E+00

1.00E+01

9.88E+00

2.89E+00

7.71E+00

1.02E+01

1.01E+01

2.94E+00

7.86E+00

1.04E+01

1.03E+01

3.00E+00

8.01E+00

1.06E+01

1.05E+01

3.06E+00

8.17E+00

1.08E+01

1.07E+01

3.12E+00

8.32E+00

1.10E+01

1.09E+01

3.18E+00

8.48E+00

1.12E+01

1.11E+01

3.24E+00

8.65E+00

1.14E+01

1.13E+01
Continued on next page

147

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

4.35E+00

4.37E+00

4.39E+00

4.41E+00

4.43E+00

4.45E+00

4.47E+00

4.49E+00

4.51E+00

4.53E+00

4.55E+00

4.57E+00

4.59E+00

4.61E+00

4.63E+00

4.65E+00

4.67E+00

4.69E+00

4.71E+00

4.73E+00

4.75E+00

4.77E+00

4.79E+00

4.81E+00

4.83E+00

4.85E+00

4.87E+00

4.89E+00

4.91E+00

4.93E+00

4.95E+00

3.53E+01

3.60E+01

3.67E+01

3.74E+01

3.81E+01

3.88E+01

3.96E+01

4.04E+01

4.11E+01

4.19E+01

4.27E+01

4.36E+01

4.44E+01

4.53E+01

4.62E+01

4.70E+01

4.80E+01

4.89E+01

4.98E+01

5.08E+01

5.18E+01

5.28E+01

5.38E+01

5.48E+01

5.59E+01

5.70E+01

5.81E+01

5.92E+01

6.04E+01

6.15E+01

6.27E+01

3.30E+00

8.82E+00

1.17E+01

1.15E+01

3.36E+00

8.99E+00

1.19E+01

1.17E+01

3.43E+00

9.16E+00

1.21E+01

1.20E+01

3.50E+00

9.34E+00

1.23E+01

1.22E+01

3.56E+00

9.52E+00

1.26E+01

1.24E+01

3.63E+00

9.70E+00

1.28E+01

1.27E+01

3.70E+00

9.89E+00

1.31E+01

1.29E+01

3.77E+00

1.01E+01

1.33E+01

1.32E+01

3.85E+00

1.03E+01

1.36E+01

1.34E+01

3.92E+00

1.05E+01

1.38E+01

1.37E+01

4.00E+00

1.07E+01

1.41E+01

1.40E+01

4.07E+00

1.09E+01

1.44E+01

1.42E+01

4.15E+00

1.11E+01

1.47E+01

1.45E+01

4.23E+00

1.13E+01

1.50E+01

1.48E+01

4.32E+00

1.15E+01

1.52E+01

1.51E+01

4.40E+00

1.18E+01

1.55E+01

1.54E+01

4.48E+00

1.20E+01

1.58E+01

1.57E+01

4.57E+00

1.22E+01

1.61E+01

1.60E+01

4.66E+00

1.24E+01

1.65E+01

1.63E+01

4.75E+00

1.27E+01

1.68E+01

1.66E+01

4.84E+00

1.29E+01

1.71E+01

1.69E+01

4.94E+00

1.32E+01

1.74E+01

1.72E+01

5.03E+00

1.34E+01

1.78E+01

1.76E+01

5.13E+00

1.37E+01

1.81E+01

1.79E+01

5.23E+00

1.40E+01

1.85E+01

1.83E+01

5.33E+00

1.42E+01

1.88E+01

1.86E+01

5.43E+00

1.45E+01

1.92E+01

1.90E+01

5.54E+00

1.48E+01

1.96E+01

1.93E+01

5.64E+00

1.51E+01

1.99E+01

1.97E+01

5.75E+00

1.54E+01

2.03E+01

2.01E+01

5.87E+00

1.57E+01

2.07E+01

2.05E+01
Continued on next page

148

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

4.97E+00

4.99E+00

5.01E+00

5.03E+00

5.05E+00

5.07E+00

5.09E+00

5.11E+00

5.13E+00

5.15E+00

5.17E+00

5.19E+00

5.21E+00

5.23E+00

5.25E+00

5.27E+00

5.29E+00

5.31E+00

5.33E+00

5.35E+00

5.37E+00

5.39E+00

5.41E+00

5.43E+00

5.45E+00

5.47E+00

5.49E+00

5.51E+00

5.53E+00

5.55E+00

5.57E+00

6.39E+01

6.52E+01

6.64E+01

6.77E+01

6.90E+01

7.04E+01

7.17E+01

7.31E+01

7.45E+01

7.60E+01

7.74E+01

7.89E+01

8.05E+01

8.20E+01

8.36E+01

8.52E+01

8.69E+01

8.86E+01

9.03E+01

9.20E+01

9.38E+01

9.56E+01

9.75E+01

9.94E+01

1.01E+02

1.03E+02

1.05E+02

1.07E+02

1.09E+02

1.11E+02

1.14E+02

5.98E+00

1.60E+01

2.11E+01

2.09E+01

6.09E+00

1.63E+01

2.15E+01

2.13E+01

6.21E+00

1.66E+01

2.19E+01

2.17E+01

6.33E+00

1.69E+01

2.24E+01

2.21E+01

6.46E+00

1.72E+01

2.28E+01

2.25E+01

6.58E+00

1.76E+01

2.32E+01

2.30E+01

6.71E+00

1.79E+01

2.37E+01

2.34E+01

6.84E+00

1.83E+01

2.41E+01

2.39E+01

6.97E+00

1.86E+01

2.46E+01

2.43E+01

7.10E+00

1.90E+01

2.51E+01

2.48E+01

7.24E+00

1.93E+01

2.56E+01

2.53E+01

7.38E+00

1.97E+01

2.61E+01

2.58E+01

7.53E+00

2.01E+01

2.66E+01

2.63E+01

7.67E+00

2.05E+01

2.71E+01

2.68E+01

7.82E+00

2.09E+01

2.76E+01

2.73E+01

7.97E+00

2.13E+01

2.81E+01

2.78E+01

8.12E+00

2.17E+01

2.87E+01

2.84E+01

8.28E+00

2.21E+01

2.92E+01

2.89E+01

8.44E+00

2.26E+01

2.98E+01

2.95E+01

8.61E+00

2.30E+01

3.04E+01

3.00E+01

8.77E+00

2.34E+01

3.10E+01

3.06E+01

8.94E+00

2.39E+01

3.16E+01

3.12E+01

9.12E+00

2.44E+01

3.22E+01

3.18E+01

9.29E+00

2.48E+01

3.28E+01

3.24E+01

9.47E+00

2.53E+01

3.34E+01

3.31E+01

9.65E+00

2.58E+01

3.41E+01

3.37E+01

9.84E+00

2.63E+01

3.48E+01

3.44E+01

1.00E+01

2.68E+01

3.54E+01

3.50E+01

1.02E+01

2.73E+01

3.61E+01

3.57E+01

1.04E+01

2.78E+01

3.68E+01

3.64E+01

1.06E+01

2.84E+01

3.75E+01

3.71E+01
Continued on next page

149

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

5.59E+00

5.61E+00

5.63E+00

5.65E+00

5.67E+00

5.69E+00

5.71E+00

5.73E+00

5.75E+00

5.77E+00

5.79E+00

5.81E+00

5.83E+00

5.85E+00

5.87E+00

5.89E+00

5.91E+00

5.93E+00

5.95E+00

5.97E+00

5.99E+00

6.01E+00

6.03E+00

6.05E+00

6.07E+00

6.09E+00

6.11E+00

6.13E+00

6.15E+00

6.17E+00

6.19E+00

1.16E+02

1.18E+02

1.20E+02

1.23E+02

1.25E+02

1.27E+02

1.30E+02

1.32E+02

1.35E+02

1.38E+02

1.40E+02

1.43E+02

1.46E+02

1.49E+02

1.51E+02

1.54E+02

1.57E+02

1.60E+02

1.64E+02

1.67E+02

1.70E+02

1.73E+02

1.77E+02

1.80E+02

1.84E+02

1.87E+02

1.91E+02

1.94E+02

1.98E+02

2.02E+02

2.06E+02

1.08E+01

2.89E+01

3.82E+01

3.78E+01

1.10E+01

2.95E+01

3.90E+01

3.85E+01

1.13E+01

3.01E+01

3.97E+01

3.93E+01

1.15E+01

3.07E+01

4.05E+01

4.01E+01

1.17E+01

3.12E+01

4.13E+01

4.08E+01

1.19E+01

3.18E+01

4.21E+01

4.16E+01

1.22E+01

3.25E+01

4.29E+01

4.24E+01

1.24E+01

3.31E+01

4.37E+01

4.32E+01

1.26E+01

3.37E+01

4.46E+01

4.41E+01

1.29E+01

3.44E+01

4.55E+01

4.49E+01

1.31E+01

3.51E+01

4.63E+01

4.58E+01

1.34E+01

3.57E+01

4.72E+01

4.67E+01

1.36E+01

3.64E+01

4.81E+01

4.76E+01

1.39E+01

3.71E+01

4.91E+01

4.85E+01

1.42E+01

3.78E+01

5.00E+01

4.95E+01

1.44E+01

3.86E+01

5.10E+01

5.04E+01

1.47E+01

3.93E+01

5.20E+01

5.14E+01

1.50E+01

4.01E+01

5.30E+01

5.24E+01

1.53E+01

4.09E+01

5.40E+01

5.34E+01

1.56E+01

4.17E+01

5.51E+01

5.44E+01

1.59E+01

4.25E+01

5.61E+01

5.55E+01

1.62E+01

4.33E+01

5.72E+01

5.66E+01

1.65E+01

4.41E+01

5.83E+01

5.77E+01

1.68E+01

4.50E+01

5.94E+01

5.88E+01

1.72E+01

4.58E+01

6.06E+01

5.99E+01

1.75E+01

4.67E+01

6.18E+01

6.11E+01

1.78E+01

4.76E+01

6.30E+01

6.23E+01

1.82E+01

4.86E+01

6.42E+01

6.35E+01

1.85E+01

4.95E+01

6.54E+01

6.47E+01

1.89E+01

5.05E+01

6.67E+01

6.59E+01

1.93E+01

5.14E+01

6.80E+01

6.72E+01
Continued on next page

150

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

6.21E+00

6.23E+00

6.25E+00

6.27E+00

6.29E+00

6.31E+00

6.33E+00

6.35E+00

6.37E+00

6.39E+00

6.41E+00

6.43E+00

6.45E+00

6.47E+00

6.49E+00

6.51E+00

6.53E+00

6.55E+00

6.57E+00

6.59E+00

6.61E+00

6.63E+00

6.65E+00

6.67E+00

6.69E+00

6.71E+00

6.73E+00

6.75E+00

6.77E+00

6.79E+00

6.81E+00

2.10E+02

2.14E+02

2.18E+02

2.22E+02

2.27E+02

2.31E+02

2.35E+02

2.40E+02

2.45E+02

2.49E+02

2.54E+02

2.59E+02

2.64E+02

2.69E+02

2.74E+02

2.80E+02

2.85E+02

2.91E+02

2.96E+02

3.02E+02

3.08E+02

3.14E+02

3.20E+02

3.26E+02

3.32E+02

3.39E+02

3.45E+02

3.52E+02

3.59E+02

3.66E+02

3.73E+02

1.96E+01

5.24E+01

6.93E+01

6.85E+01

2.00E+01

5.34E+01

7.06E+01

6.98E+01

2.04E+01

5.45E+01

7.20E+01

7.12E+01

2.08E+01

5.55E+01

7.34E+01

7.26E+01

2.12E+01

5.66E+01

7.48E+01

7.40E+01

2.16E+01

5.77E+01

7.63E+01

7.54E+01

2.20E+01

5.88E+01

7.77E+01

7.69E+01

2.24E+01

6.00E+01

7.92E+01

7.84E+01

2.29E+01

6.11E+01

8.08E+01

7.99E+01

2.33E+01

6.23E+01

8.23E+01

8.14E+01

2.38E+01

6.35E+01

8.39E+01

8.30E+01

2.42E+01

6.47E+01

8.56E+01

8.46E+01

2.47E+01

6.60E+01

8.72E+01

8.62E+01

2.52E+01

6.73E+01

8.89E+01

8.79E+01

2.57E+01

6.86E+01

9.06E+01

8.96E+01

2.62E+01

6.99E+01

9.24E+01

9.13E+01

2.67E+01

7.12E+01

9.42E+01

9.31E+01

2.72E+01

7.26E+01

9.60E+01

9.49E+01

2.77E+01

7.40E+01

9.79E+01

9.67E+01

2.82E+01

7.55E+01

9.97E+01

9.86E+01

2.88E+01

7.69E+01

1.02E+02

1.01E+02

2.94E+01

7.84E+01

1.04E+02

1.02E+02

2.99E+01

7.99E+01

1.06E+02

1.04E+02

3.05E+01

8.15E+01

1.08E+02

1.06E+02

3.11E+01

8.31E+01

1.10E+02

1.09E+02

3.17E+01

8.47E+01

1.12E+02

1.11E+02

3.23E+01

8.63E+01

1.14E+02

1.13E+02

3.29E+01

8.80E+01

1.16E+02

1.15E+02

3.36E+01

8.97E+01

1.19E+02

1.17E+02

3.42E+01

9.14E+01

1.21E+02

1.19E+02

3.49E+01

9.32E+01

1.23E+02

1.22E+02
Continued on next page

151

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

6.83E+00

6.85E+00

6.87E+00

6.89E+00

6.91E+00

6.93E+00

6.95E+00

6.97E+00

6.99E+00

7.01E+00

7.03E+00

7.05E+00

7.07E+00

7.09E+00

7.11E+00

7.13E+00

7.15E+00

7.17E+00

7.19E+00

7.21E+00

7.23E+00

7.25E+00

7.27E+00

7.29E+00

7.31E+00

7.33E+00

7.35E+00

7.37E+00

7.39E+00

7.41E+00

7.43E+00

3.80E+02

3.88E+02

3.95E+02

4.03E+02

4.11E+02

4.18E+02

4.27E+02

4.35E+02

4.43E+02

4.52E+02

4.61E+02

4.69E+02

4.79E+02

4.88E+02

4.97E+02

5.07E+02

5.17E+02

5.27E+02

5.37E+02

5.47E+02

5.58E+02

5.69E+02

5.80E+02

5.91E+02

6.02E+02

6.14E+02

6.26E+02

6.38E+02

6.50E+02

6.63E+02

6.76E+02

3.56E+01

9.50E+01

1.26E+02

1.24E+02

3.62E+01

9.68E+01

1.28E+02

1.27E+02

3.69E+01

9.87E+01

1.30E+02

1.29E+02

3.77E+01

1.01E+02

1.33E+02

1.31E+02

3.84E+01

1.03E+02

1.36E+02

1.34E+02

3.91E+01

1.05E+02

1.38E+02

1.37E+02

3.99E+01

1.07E+02

1.41E+02

1.39E+02

4.07E+01

1.09E+02

1.44E+02

1.42E+02

4.14E+01

1.11E+02

1.46E+02

1.45E+02

4.22E+01

1.13E+02

1.49E+02

1.48E+02

4.31E+01

1.15E+02

1.52E+02

1.50E+02

4.39E+01

1.17E+02

1.55E+02

1.53E+02

4.48E+01

1.20E+02

1.58E+02

1.56E+02

4.56E+01

1.22E+02

1.61E+02

1.59E+02

4.65E+01

1.24E+02

1.64E+02

1.62E+02

4.74E+01

1.27E+02

1.67E+02

1.65E+02

4.83E+01

1.29E+02

1.71E+02

1.69E+02

4.93E+01

1.32E+02

1.74E+02

1.72E+02

5.02E+01

1.34E+02

1.77E+02

1.75E+02

5.12E+01

1.37E+02

1.81E+02

1.79E+02

5.22E+01

1.39E+02

1.84E+02

1.82E+02

5.32E+01

1.42E+02

1.88E+02

1.86E+02

5.42E+01

1.45E+02

1.91E+02

1.89E+02

5.53E+01

1.48E+02

1.95E+02

1.93E+02

5.63E+01

1.50E+02

1.99E+02

1.97E+02

5.74E+01

1.53E+02

2.03E+02

2.00E+02

5.85E+01

1.56E+02

2.07E+02

2.04E+02

5.97E+01

1.59E+02

2.11E+02

2.08E+02

6.08E+01

1.62E+02

2.15E+02

2.12E+02

6.20E+01

1.66E+02

2.19E+02

2.16E+02

6.32E+01

1.69E+02

2.23E+02

2.21E+02
Continued on next page

152

Table A.3 (cont’d) CoH default NLD

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

7.45E+00

7.47E+00

7.49E+00

7.51E+00

7.53E+00

7.55E+00

7.57E+00

7.59E+00

7.61E+00

7.63E+00

7.65E+00

7.67E+00

7.69E+00

7.71E+00

7.73E+00

7.75E+00

7.77E+00

7.79E+00

7.81E+00

7.83E+00

7.85E+00

7.87E+00

7.89E+00

7.91E+00

7.93E+00

7.95E+00

7.97E+00

7.99E+00

8.01E+00

8.03E+00

8.05E+00

6.89E+02

7.02E+02

7.16E+02

7.30E+02

7.44E+02

7.58E+02

7.73E+02

7.88E+02

8.03E+02

8.19E+02

8.34E+02

8.51E+02

8.67E+02

8.84E+02

9.01E+02

9.18E+02

9.36E+02

9.54E+02

9.73E+02

9.92E+02

1.01E+03

1.03E+03

1.05E+03

1.07E+03

1.09E+03

1.11E+03

1.13E+03

1.16E+03

1.18E+03

1.20E+03

1.22E+03

6.44E+01

1.72E+02

2.27E+02

2.25E+02

6.57E+01

1.75E+02

2.32E+02

2.29E+02

6.69E+01

1.79E+02

2.36E+02

2.34E+02

6.82E+01

1.82E+02

2.41E+02

2.38E+02

6.95E+01

1.86E+02

2.46E+02

2.43E+02

7.09E+01

1.89E+02

2.50E+02

2.48E+02

7.23E+01

1.93E+02

2.55E+02

2.52E+02

7.37E+01

1.97E+02

2.60E+02

2.57E+02

7.51E+01

2.01E+02

2.65E+02

2.62E+02

7.65E+01

2.04E+02

2.70E+02

2.67E+02

7.80E+01

2.08E+02

2.76E+02

2.72E+02

7.95E+01

2.12E+02

2.81E+02

2.78E+02

8.11E+01

2.17E+02

2.86E+02

2.83E+02

8.26E+01

2.21E+02

2.92E+02

2.89E+02

8.42E+01

2.25E+02

2.97E+02

2.94E+02

8.59E+01

2.29E+02

3.03E+02

3.00E+02

8.75E+01

2.34E+02

3.09E+02

3.06E+02

8.92E+01

2.38E+02

3.15E+02

3.12E+02

9.10E+01

2.43E+02

3.21E+02

3.18E+02

9.27E+01

2.48E+02

3.27E+02

3.24E+02

9.45E+01

2.53E+02

3.34E+02

3.30E+02

9.63E+01

2.57E+02

3.40E+02

3.36E+02

9.82E+01

2.62E+02

3.47E+02

3.43E+02

1.00E+02

2.67E+02

3.54E+02

3.50E+02

1.02E+02

2.73E+02

3.60E+02

3.56E+02

1.04E+02

2.78E+02

3.67E+02

3.63E+02

1.06E+02

2.83E+02

3.74E+02

3.70E+02

1.08E+02

2.89E+02

3.82E+02

3.77E+02

1.10E+02

2.94E+02

3.89E+02

3.85E+02

1.12E+02

3.00E+02

3.97E+02

3.92E+02

1.14E+02

3.06E+02

4.04E+02

4.00E+02
Continued on next page

153

Table A.3 (cont’d) CoH default NLD

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

1.25E+03

1.27E+03

1.30E+03

1.32E+03

1.35E+03

1.37E+03

1.40E+03

1.43E+03

1.45E+03

1.48E+03

1.17E+02

3.12E+02

4.12E+02

4.07E+02

1.19E+02

3.18E+02

4.20E+02

4.15E+02

1.21E+02

3.24E+02

4.28E+02

4.23E+02

1.24E+02

3.30E+02

4.36E+02

4.32E+02

1.26E+02

3.37E+02

4.45E+02

4.40E+02

1.28E+02

3.43E+02

4.54E+02

4.48E+02

1.31E+02

3.50E+02

4.62E+02

4.57E+02

1.33E+02

3.57E+02

4.71E+02

4.66E+02

1.36E+02

3.63E+02

4.80E+02

4.75E+02

1.39E+02

3.70E+02

4.90E+02

4.84E+02

Ex (MeV)

8.07E+00

8.09E+00

8.11E+00

8.13E+00

8.15E+00

8.17E+00

8.19E+00

8.21E+00

8.23E+00

8.25E+00

154

Table A.4: EMPIRE default NLD for 74Zn including spin-dependent NLD for J=0-5. An equal parity distribution is assumed.

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

J=4

J=5

0.000

0.106

0.212

0.318

0.424

0.530

0.637

0.743

0.849

0.955

1.061

1.167

1.273

1.379

1.485

1.591

1.697

1.803

1.909

2.016

2.122

0.00E+00

0.00E+00

0.00E+00

0.00E+00

0.00E+00

0.00E+00

0.00E+00

8.86E-02

9.59E-02

1.16E-01

1.44E-01

1.80E-01

2.27E-01

2.85E-01

3.58E-01

4.49E-01

5.60E-01

6.96E-01

8.63E-01

1.07E+00

1.31E+00

1.61E+00

1.97E+00

2.40E+00

2.93E+00

3.55E+00

4.30E+00

3.73E-02

2.97E-02

2.93E-02

3.13E-02

3.47E-02

3.93E-02

4.51E-02

5.21E-02

6.06E-02

7.06E-02

8.25E-02

9.65E-02

1.13E-01

1.32E-01

1.55E-01

1.81E-01

2.11E-01

2.47E-01

2.88E-01

3.36E-01

4.13E-02

4.44E-02

5.03E-02

5.85E-02

6.89E-02

8.15E-02

9.68E-02

1.15E-01

1.37E-01

1.63E-01

1.93E-01

2.29E-01

2.72E-01

3.22E-01

3.80E-01

4.49E-01

5.29E-01

6.22E-01

7.31E-01

9.39E-03

1.84E-02

2.75E-02

3.80E-02

5.03E-02

6.50E-02

8.27E-02

1.04E-01

1.30E-01

1.60E-01

1.97E-01

2.40E-01

2.92E-01

3.53E-01

4.26E-01

5.12E-01

6.13E-01

7.33E-01

8.73E-01

6.63E-04

3.18E-03

7.25E-03

1.29E-02

2.05E-02

3.02E-02

4.26E-02

5.81E-02

7.75E-02

1.02E-01

1.31E-01

1.67E-01

2.11E-01

2.65E-01

3.29E-01

4.06E-01

4.98E-01

6.09E-01

7.40E-01

1.59E-05

2.52E-04

1.01E-03

2.52E-03

5.06E-03

8.90E-03

1.44E-02

2.20E-02

3.22E-02

4.55E-02

6.28E-02

8.49E-02

1.13E-01

1.48E-01

1.91E-01

2.45E-01

3.11E-01

3.91E-01

4.88E-01

1.35E-07

9.52E-06

7.62E-05

2.93E-04

7.89E-04

1.73E-03

3.32E-03

5.83E-03

9.56E-03

1.49E-02

2.24E-02

3.25E-02

4.60E-02

6.37E-02

8.67E-02

1.16E-01

1.54E-01

2.01E-01

2.59E-01

8.58E-01

1.04E+00

8.97E-01

6.06E-01

3.32E-01
Continued on next page

155

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

J=4

J=5

Table A.4 (cont’d) EMPIRE default NLD

2.228

2.334

2.440

2.546

2.652

2.758

2.864

2.970

3.076

3.182

3.288

3.395

3.501

3.607

3.713

3.819

3.925

4.031

4.137

4.243

4.349

4.455

5.19E+00

6.25E+00

7.51E+00

9.01E+00

1.08E+01

1.29E+01

1.54E+01

1.83E+01

2.17E+01

2.58E+01

3.05E+01

3.61E+01

4.26E+01

5.02E+01

5.91E+01

6.95E+01

8.15E+01

9.56E+01

1.12E+02

1.31E+02

1.53E+02

1.78E+02

3.91E-01

1.01E+00

1.23E+00

1.08E+00

7.49E-01

4.56E-01

1.18E+00

1.45E+00

1.30E+00

9.19E-01

4.22E-01

5.33E-01

5.30E-01

1.38E+00

1.72E+00

1.56E+00

1.12E+00

6.67E-01

6.16E-01

1.61E+00

2.02E+00

1.86E+00

1.37E+00

8.31E-01

7.15E-01

1.87E+00

2.38E+00

2.22E+00

1.66E+00

1.03E+00

8.29E-01

2.18E+00

2.79E+00

2.64E+00

2.00E+00

1.27E+00

9.60E-01

2.54E+00

3.27E+00

3.12E+00

2.41E+00

1.56E+00

1.11E+00

2.95E+00

3.83E+00

3.69E+00

2.89E+00

1.90E+00

1.29E+00

3.42E+00

4.47E+00

4.36E+00

3.46E+00

2.31E+00

1.49E+00

3.96E+00

5.22E+00

5.13E+00

4.12E+00

2.80E+00

1.72E+00

4.59E+00

6.08E+00

6.03E+00

4.91E+00

3.38E+00

1.98E+00

5.31E+00

7.07E+00

7.08E+00

5.82E+00

4.07E+00

2.28E+00

6.13E+00

8.22E+00

8.29E+00

6.89E+00

4.89E+00

2.63E+00

7.08E+00

9.53E+00

9.70E+00

8.14E+00

5.85E+00

3.02E+00

8.17E+00

1.11E+01

1.13E+01

9.60E+00

6.98E+00

3.47E+00

9.41E+00

1.28E+01

1.32E+01

1.13E+01

8.30E+00

3.99E+00

1.08E+01

1.48E+01

1.54E+01

1.33E+01

9.86E+00

4.58E+00

1.25E+01

1.71E+01

1.79E+01

1.56E+01

1.17E+01

5.25E+00

1.43E+01

1.97E+01

2.07E+01

1.82E+01

1.38E+01

6.02E+00

1.64E+01

2.27E+01

2.40E+01

2.13E+01

1.63E+01

6.89E+00

1.89E+01

2.62E+01

2.78E+01

2.48E+01

1.92E+01

7.89E+00

2.16E+01

3.01E+01

3.22E+01

2.89E+01

2.26E+01
Continued on next page

156

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

J=4

J=5

Table A.4 (cont’d) EMPIRE default NLD

4.561

4.668

4.774

4.880

4.986

5.092

5.198

5.304

5.410

5.516

5.622

5.728

5.834

5.940

6.047

6.153

6.259

6.365

6.471

6.577

6.683

6.789

2.08E+02

2.42E+02

2.82E+02

3.27E+02

3.80E+02

4.41E+02

5.10E+02

5.91E+02

6.83E+02

7.90E+02

9.12E+02

1.05E+03

1.21E+03

1.40E+03

1.61E+03

1.85E+03

2.13E+03

2.45E+03

2.79E+03

3.11E+03

3.47E+03

3.85E+03

9.02E+00

2.48E+01

3.46E+01

3.72E+01

3.36E+01

2.65E+01

1.03E+01

2.84E+01

3.98E+01

4.30E+01

3.91E+01

3.10E+01

1.18E+01

3.25E+01

4.56E+01

4.95E+01

4.53E+01

3.63E+01

1.34E+01

3.71E+01

5.23E+01

5.70E+01

5.26E+01

4.24E+01

1.53E+01

4.24E+01

6.00E+01

6.56E+01

6.08E+01

4.94E+01

1.75E+01

4.84E+01

6.86E+01

7.55E+01

7.03E+01

5.75E+01

1.99E+01

5.52E+01

7.85E+01

8.67E+01

8.12E+01

6.69E+01

2.27E+01

6.29E+01

8.98E+01

9.95E+01

9.37E+01

7.76E+01

2.58E+01

7.17E+01

1.03E+02

1.14E+02

1.08E+02

9.01E+01

2.94E+01

8.17E+01

1.17E+02

1.31E+02

1.24E+02

1.04E+02

3.34E+01

9.29E+01

1.34E+02

1.50E+02

1.43E+02

1.21E+02

3.79E+01

1.06E+02

1.52E+02

1.71E+02

1.64E+02

1.40E+02

4.31E+01

1.20E+02

1.74E+02

1.96E+02

1.89E+02

1.61E+02

4.89E+01

1.37E+02

1.98E+02

2.24E+02

2.17E+02

1.86E+02

5.54E+01

1.55E+02

2.25E+02

2.55E+02

2.48E+02

2.14E+02

6.29E+01

1.76E+02

2.56E+02

2.91E+02

2.85E+02

2.47E+02

7.13E+01

2.00E+02

2.91E+02

3.32E+02

3.26E+02

2.84E+02

8.08E+01

2.27E+02

3.30E+02

3.79E+02

3.73E+02

3.26E+02

9.08E+01

2.55E+02

3.73E+02

4.28E+02

4.23E+02

3.72E+02

9.99E+01

2.81E+02

4.11E+02

4.74E+02

4.70E+02

4.15E+02

1.10E+02

3.09E+02

4.53E+02

5.23E+02

5.20E+02

4.62E+02

1.21E+02

3.40E+02

4.98E+02

5.77E+02

5.76E+02

5.12E+02
Continued on next page

157

Ex (MeV)

Total NLD (MeV−1)

J=0

J=1

J=2

J=3

J=4

J=5

Table A.4 (cont’d) EMPIRE default NLD

6.895

7.001

7.107

7.213

7.319

7.426

7.532

7.638

7.744

7.850

7.956

8.062

8.168

8.274

8.380

4.27E+03

4.72E+03

5.22E+03

5.75E+03

6.33E+03

6.96E+03

7.63E+03

8.36E+03

9.14E+03

9.97E+03

1.09E+04

1.18E+04

1.28E+04

1.39E+04

1.50E+04

1.32E+02

3.72E+02

5.47E+02

6.35E+02

6.35E+02

5.68E+02

1.45E+02

4.08E+02

6.00E+02

6.98E+02

7.00E+02

6.28E+02

1.58E+02

4.46E+02

6.57E+02

7.66E+02

7.70E+02

6.93E+02

1.72E+02

4.87E+02

7.18E+02

8.39E+02

8.46E+02

7.64E+02

1.88E+02

5.30E+02

7.84E+02

9.17E+02

9.27E+02

8.40E+02

2.04E+02

5.77E+02

8.54E+02

1.00E+03

1.02E+03

9.22E+02

2.22E+02

6.27E+02

9.29E+02

1.09E+03

1.11E+03

1.01E+03

2.40E+02

6.80E+02

1.01E+03

1.19E+03

1.21E+03

1.11E+03

2.60E+02

7.37E+02

1.09E+03

1.29E+03

1.32E+03

1.21E+03

2.81E+02

7.97E+02

1.19E+03

1.40E+03

1.43E+03

1.32E+03

3.03E+02

8.60E+02

1.28E+03

1.51E+03

1.55E+03

1.43E+03

3.27E+02

9.27E+02

1.38E+03

1.64E+03

1.68E+03

1.55E+03

3.52E+02

9.98E+02

1.49E+03

1.77E+03

1.82E+03

1.68E+03

3.78E+02

1.07E+03

1.60E+03

1.90E+03

1.96E+03

1.82E+03

4.05E+02

1.15E+03

1.72E+03

2.05E+03

2.12E+03

1.97E+03

158

Table A.5: EMPIRE default NLD for 74Zn including spin-dependent NLD for J=6-10. An equal parity distribution is assumed.

Ex (MeV)

Total NLD (MeV−1)

J=6

J=7

J=8

J=9

J=10

0.000

0.106

0.212

0.318

0.424

0.530

0.637

0.743

0.849

0.955

1.061

1.167

1.273

1.379

1.485

1.591

1.697

1.803

1.909

2.016

2.122

0.00E+00

0.00E+00

0.00E+00

0.00E+00

0.00E+00

0.00E+00

8.86E-02

9.59E-02

1.16E-01

1.44E-01

1.80E-01

2.27E-01

2.85E-01

3.58E-01

4.49E-01

5.60E-01

6.96E-01

8.63E-01

1.07E+00

1.31E+00

1.61E+00

1.97E+00

2.40E+00

2.93E+00

3.55E+00

4.30E+00

0.00E+00

0.00E+00

0.00E+00

0.00E+00

0.00E+00

1.74E-07

3.21E-06

2.06E-05

7.90E-05

2.26E-04

5.32E-04

1.10E-03

2.07E-03

3.63E-03

6.02E-03

9.54E-03

1.46E-02

2.16E-02

3.12E-02

4.41E-02

6.13E-02

8.37E-02

1.13E-01

1.50E-01

1.55E-09

0.00E+00

0.00E+00

0.00E+00

7.59E-08

0.00E+00

0.00E+00

0.00E+00

2.34E-08

0.00E+00

0.00E+00

2.18E-07

1.20E-06

4.74E-06

1.49E-05

3.94E-05

9.23E-05

1.96E-04

3.86E-04

7.13E-04

1.25E-03

2.10E-03

3.40E-03

5.34E-03

8.15E-03

1.22E-02

1.78E-02

6.08E-09

0.00E+00

4.97E-08

0.00E+00

2.67E-07

1.07E-06

3.50E-06

9.74E-06

2.40E-05

5.38E-05

1.11E-04

2.16E-04

3.97E-04

6.97E-04

1.18E-03

1.92E-03

3.05E-03

1.07E-08

5.67E-08

2.32E-07

7.85E-07

2.28E-06

5.90E-06

1.39E-05

3.01E-05

6.10E-05

1.17E-04

2.15E-04

3.78E-04

6.42E-04

4.71E-03

1.06E-03
Continued on next page

8.84E-07

5.13E-06

1.99E-05

5.98E-05

1.50E-04

3.32E-04

6.66E-04

1.24E-03

2.17E-03

3.62E-03

5.81E-03

9.01E-03

1.36E-02

2.00E-02

2.87E-02

4.06E-02

5.64E-02

159

Ex (MeV)

Total NLD (MeV−1)

J=6

J=7

J=8

J=9

J=10

Table A.5 (cont’d) EMPIRE default NLD

2.228

2.334

2.440

2.546

2.652

2.758

2.864

2.970

3.076

3.182

3.288

3.395

3.501

3.607

3.713

3.819

3.925

4.031

4.137

4.243

4.349

4.455

5.19E+00

6.25E+00

7.51E+00

9.01E+00

1.08E+01

1.29E+01

1.54E+01

1.83E+01

2.17E+01

2.58E+01

3.05E+01

3.61E+01

4.26E+01

5.02E+01

5.91E+01

6.95E+01

8.15E+01

9.56E+01

1.12E+02

1.31E+02

1.53E+02

1.78E+02

1.97E-01

2.57E-01

3.32E-01

4.25E-01

5.40E-01

6.82E-01

8.55E-01

7.72E-02

1.04E-01

1.40E-01

1.85E-01

2.42E-01

3.14E-01

4.05E-01

1.07E+00

5.18E-01

1.33E+00

6.58E-01

1.64E+00

8.30E-01

2.55E-02

3.60E-02

5.00E-02

6.86E-02

9.30E-02

1.25E-01

1.66E-01

2.18E-01

2.85E-01

3.69E-01

2.01E+00

1.04E+00

4.74E-01

2.46E+00

1.30E+00

6.05E-01

3.00E+00

1.62E+00

7.69E-01

3.65E+00

2.00E+00

9.71E-01

7.12E-03

1.05E-02

1.53E-02

2.19E-02

3.09E-02

4.29E-02

5.90E-02

8.01E-02

1.08E-01

1.44E-01

1.90E-01

2.49E-01

3.23E-01

4.18E-01

4.42E+00

2.47E+00

1.22E+00

5.36E-01

5.34E+00

3.03E+00

1.52E+00

6.84E-01

6.42E+00

3.70E+00

1.90E+00

8.68E-01

1.69E-03

2.64E-03

4.03E-03

6.03E-03

8.87E-03

1.28E-02

1.83E-02

2.58E-02

3.59E-02

4.93E-02

6.71E-02

9.05E-02

1.21E-01

1.60E-01

2.11E-01

2.75E-01

3.57E-01

7.70E+00

4.50E+00

2.35E+00

1.10E+00

4.60E-01

9.22E+00

5.47E+00

2.90E+00

1.38E+00

5.90E-01

1.10E+01

6.61E+00

3.56E+00

1.72E+00

7.51E-01

1.31E+01

7.98E+00

4.36E+00

2.14E+00

9.53E-01

1.56E+01

9.59E+00

5.31E+00

2.66E+00

1.20E+00
Continued on next page

160

Ex (MeV)

Total NLD (MeV−1)

J=6

J=7

J=8

J=9

J=10

Table A.5 (cont’d) EMPIRE default NLD

4.561

4.668

4.774

4.880

4.986

5.092

5.198

5.304

5.410

5.516

5.622

5.728

5.834

5.940

6.047

6.153

6.259

6.365

6.471

6.577

6.683

6.789

2.08E+02

2.42E+02

2.82E+02

3.27E+02

3.80E+02

4.41E+02

5.10E+02

5.91E+02

6.83E+02

7.90E+02

9.12E+02

1.05E+03

1.21E+03

1.40E+03

1.61E+03

1.85E+03

2.13E+03

2.45E+03

2.79E+03

3.11E+03

3.47E+03

3.85E+03

1.85E+01

1.15E+01

6.46E+00

3.28E+00

1.51E+00

2.18E+01

1.38E+01

7.83E+00

4.04E+00

1.89E+00

2.58E+01

1.64E+01

9.47E+00

4.95E+00

2.35E+00

3.04E+01

1.96E+01

1.14E+01

6.05E+00

2.92E+00

3.57E+01

2.33E+01

1.37E+01

7.36E+00

3.61E+00

4.20E+01

2.76E+01

1.65E+01

8.94E+00

4.44E+00

4.92E+01

3.27E+01

1.97E+01

1.08E+01

5.45E+00

5.76E+01

3.86E+01

2.35E+01

1.31E+01

6.67E+00

6.73E+01

4.55E+01

2.80E+01

1.58E+01

8.14E+00

7.85E+01

5.35E+01

3.33E+01

1.89E+01

9.90E+00

9.15E+01

6.29E+01

3.95E+01

2.27E+01

1.20E+01

1.07E+02

7.38E+01

4.67E+01

2.72E+01

1.45E+01

1.24E+02

8.65E+01

5.52E+01

3.24E+01

1.75E+01

1.44E+02

1.01E+02

6.52E+01

3.86E+01

2.11E+01

1.67E+02

1.18E+02

7.68E+01

4.59E+01

2.54E+01

1.93E+02

1.38E+02

9.03E+01

5.45E+01

3.04E+01

2.23E+02

1.61E+02

1.06E+02

6.45E+01

3.64E+01

2.58E+02

1.87E+02

1.24E+02

7.63E+01

4.34E+01

2.97E+02

2.16E+02

1.45E+02

9.00E+01

5.17E+01

3.32E+02

2.44E+02

1.65E+02

1.03E+02

5.95E+01

3.71E+02

2.74E+02

1.86E+02

1.17E+02

6.83E+01

4.14E+02

3.07E+02

2.10E+02

1.33E+02

7.82E+01
Continued on next page

161

Ex (MeV)

Total NLD (MeV−1)

J=6

J=7

J=8

J=9

J=10

Table A.5 (cont’d) EMPIRE default NLD

6.895

7.001

7.107

7.213

7.319

7.426

7.532

7.638

7.744

7.850

7.956

8.062

8.168

8.274

8.380

4.27E+03

4.72E+03

5.22E+03

5.75E+03

6.33E+03

6.96E+03

7.63E+03

8.36E+03

9.14E+03

9.97E+03

1.09E+04

1.18E+04

1.28E+04

1.39E+04

1.50E+04

4.61E+02

3.43E+02

2.36E+02

1.50E+02

8.92E+01

5.12E+02

3.83E+02

2.65E+02

1.70E+02

1.01E+02

5.67E+02

4.27E+02

2.97E+02

1.92E+02

1.15E+02

6.28E+02

4.74E+02

3.32E+02

2.15E+02

1.30E+02

6.93E+02

5.26E+02

3.70E+02

2.41E+02

1.47E+02

7.64E+02

5.82E+02

4.11E+02

2.70E+02

1.65E+02

8.40E+02

6.43E+02

4.56E+02

3.01E+02

1.86E+02

9.22E+02

7.09E+02

5.05E+02

3.35E+02

2.08E+02

1.01E+03

7.79E+02

5.58E+02

3.72E+02

2.32E+02

1.10E+03

8.55E+02

6.15E+02

4.13E+02

2.59E+02

1.21E+03

9.37E+02

6.77E+02

4.56E+02

2.87E+02

1.31E+03

1.03E+03

7.43E+02

5.03E+02

3.19E+02

1.43E+03

1.12E+03

8.15E+02

5.54E+02

3.53E+02

1.55E+03

1.22E+03

8.91E+02

6.09E+02

3.89E+02

1.68E+03

1.33E+03

9.73E+02

6.67E+02

4.29E+02

162

Table A.6: TALYS default γSF for 74Zn.

γ-ray Energy (MeV)

f(M1) (MeV−3)

f(E1) (MeV−3)

0.001

0.002

0.005

0.010

0.020

0.050

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

1.500

1.600

1.700

1.800

1.900

2.000

2.200

2.400

2.600

2.800

3.000

0.000E+00

1.532E-12

3.830E-12

7.660E-12

1.532E-11

3.830E-11

7.661E-11

1.533E-10

2.302E-10

3.073E-10

3.848E-10

4.628E-10

5.413E-10

6.204E-10

7.002E-10

7.809E-10

8.625E-10

9.451E-10

1.029E-09

1.114E-09

1.200E-09

1.288E-09

1.377E-09

1.468E-09

1.561E-09

1.656E-09

1.853E-09

2.059E-09

2.276E-09

2.505E-09

2.749E-09

1.108E-08

1.108E-08

1.108E-08

1.109E-08

1.110E-08

1.112E-08

1.117E-08

1.126E-08

1.135E-08

1.144E-08

1.154E-08

1.163E-08

1.173E-08

1.183E-08

1.193E-08

1.204E-08

1.214E-08

1.226E-08

1.237E-08

1.249E-08

1.262E-08

1.275E-08

1.288E-08

1.302E-08

1.317E-08

1.332E-08

1.365E-08

1.401E-08

1.440E-08

1.483E-08

1.530E-08

γSF (MeV−3)
1.108E-08

1.108E-08

1.109E-08

1.109E-08

1.111E-08

1.116E-08

1.125E-08

1.141E-08

1.158E-08

1.175E-08

1.192E-08

1.210E-08

1.227E-08

1.245E-08

1.263E-08

1.282E-08

1.301E-08

1.320E-08

1.340E-08

1.361E-08

1.382E-08

1.403E-08

1.426E-08

1.449E-08

1.473E-08

1.498E-08

1.550E-08

1.606E-08

1.667E-08

1.733E-08

1.805E-08

Continued on next page

163

Table A.6 (cont’d) TALYS default γSF for 74Zn.

γ-ray Energy (MeV)

f(M1) (MeV−3)

f(E1) (MeV−3)

3.200

3.400

3.600

3.800

4.000

4.500

5.000

5.500

6.000

6.500

7.000

7.500

8.000

8.500

9.000

9.500

3.008E-09

3.286E-09

3.584E-09

3.904E-09

4.251E-09

5.254E-09

6.509E-09

8.110E-09

1.019E-08

1.295E-08

1.662E-08

2.150E-08

2.776E-08

3.503E-08

4.173E-08

4.502E-08

1.582E-08

1.639E-08

1.701E-08

1.769E-08

1.844E-08

2.064E-08

2.338E-08

2.679E-08

3.103E-08

3.628E-08

4.278E-08

5.083E-08

6.083E-08

7.326E-08

8.877E-08

1.082E-07

Table A.7: CoH default γSF for 74Zn.

γ-ray Energy (MeV)

f(M1) (MeV−3)

f(E1) (MeV−3)

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

5.419E-12

1.084E-11

1.626E-11

2.169E-11

2.713E-11

3.257E-11

3.802E-11

4.348E-11

4.896E-11

5.542E-09

5.531E-09

5.519E-09

5.507E-09

5.495E-09

5.483E-09

5.470E-09

5.457E-09

5.444E-09

γSF (MeV−3)
1.883E-08

1.967E-08

2.059E-08

2.160E-08

2.269E-08

2.589E-08

2.989E-08

3.490E-08

4.122E-08

4.922E-08

5.940E-08

7.233E-08

8.858E-08

1.083E-07

1.305E-07

1.532E-07

γSF (MeV−3)
5.548E-09

5.542E-09

5.535E-09

5.529E-09

5.522E-09

5.515E-09

5.508E-09

5.501E-09

5.493E-09

Continued on next page

164

Table A.7 (cont’d) CoH default γSF for 74Zn.

γ-ray Energy (MeV)

f(M1) (MeV−3)

f(E1) (MeV−3)

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

1.65

1.70

1.75

1.80

1.85

1.90

1.95

2.00

5.445E-11

5.995E-11

6.547E-11

7.102E-11

7.658E-11

8.216E-11

8.777E-11

9.341E-11

9.907E-11

1.048E-10

1.105E-10

1.162E-10

1.220E-10

1.279E-10

1.337E-10

1.396E-10

1.456E-10

1.516E-10

1.576E-10

1.637E-10

1.698E-10

1.760E-10

1.822E-10

1.885E-10

1.949E-10

2.013E-10

2.078E-10

2.143E-10

2.209E-10

2.276E-10

2.343E-10

5.431E-09

5.418E-09

5.404E-09

5.391E-09

5.377E-09

5.363E-09

5.349E-09

5.335E-09

5.321E-09

5.307E-09

5.293E-09

5.278E-09

5.264E-09

5.250E-09

5.235E-09

5.221E-09

5.206E-09

5.192E-09

5.178E-09

5.163E-09

5.149E-09

5.135E-09

5.121E-09

5.107E-09

5.093E-09

5.079E-09

5.065E-09

5.052E-09

5.038E-09

5.025E-09

5.012E-09

γSF (MeV−3)
5.485E-09

5.478E-09

5.470E-09

5.462E-09

5.453E-09

5.445E-09

5.437E-09

5.429E-09

5.420E-09

5.412E-09

5.403E-09

5.394E-09

5.386E-09

5.377E-09

5.369E-09

5.360E-09

5.352E-09

5.343E-09

5.335E-09

5.327E-09

5.319E-09

5.311E-09

5.303E-09

5.295E-09

5.288E-09

5.280E-09

5.273E-09

5.266E-09

5.259E-09

5.252E-09

5.246E-09

Continued on next page

165

Table A.7 (cont’d) CoH default γSF for 74Zn.

γ-ray Energy (MeV)

f(M1) (MeV−3)

f(E1) (MeV−3)

2.05

2.10

2.15

2.20

2.25

2.30

2.35

2.40

2.45

2.50

2.55

2.60

2.65

2.70

2.75

2.80

2.85

2.90

2.95

3.00

3.05

3.10

3.15

3.20

3.25

3.30

3.35

3.40

3.45

3.50

3.55

2.412E-10

2.481E-10

2.550E-10

2.621E-10

2.693E-10

2.765E-10

2.838E-10

2.913E-10

2.988E-10

3.064E-10

3.141E-10

3.220E-10

3.299E-10

3.380E-10

3.461E-10

3.544E-10

3.628E-10

3.714E-10

3.801E-10

3.889E-10

3.978E-10

4.069E-10

4.162E-10

4.256E-10

4.352E-10

4.449E-10

4.548E-10

4.649E-10

4.751E-10

4.856E-10

4.962E-10

4.999E-09

4.986E-09

4.974E-09

4.961E-09

4.949E-09

4.938E-09

4.926E-09

4.915E-09

4.904E-09

4.893E-09

4.883E-09

4.872E-09

4.863E-09

4.853E-09

4.844E-09

4.836E-09

4.827E-09

4.820E-09

4.812E-09

4.805E-09

4.799E-09

4.792E-09

4.787E-09

4.782E-09

4.777E-09

4.773E-09

4.770E-09

4.767E-09

4.764E-09

4.763E-09

4.761E-09

γSF (MeV−3)
5.240E-09

5.234E-09

5.229E-09

5.224E-09

5.219E-09

5.214E-09

5.210E-09

5.206E-09

5.202E-09

5.199E-09

5.197E-09

5.194E-09

5.193E-09

5.191E-09

5.190E-09

5.190E-09

5.190E-09

5.191E-09

5.192E-09

5.194E-09

5.196E-09

5.199E-09

5.203E-09

5.207E-09

5.212E-09

5.218E-09

5.224E-09

5.232E-09

5.239E-09

5.248E-09

5.258E-09

Continued on next page

166

Table A.7 (cont’d) CoH default γSF for 74Zn.

γ-ray Energy (MeV)

f(M1) (MeV−3)

f(E1) (MeV−3)

3.60

3.65

3.70

3.75

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

4.25

4.30

4.35

4.40

4.45

4.50

4.55

4.60

4.65

4.70

4.75

4.80

4.85

4.90

4.95

5.00

5.05

5.10

5.070E-10

5.180E-10

5.293E-10

5.407E-10

5.524E-10

5.643E-10

5.764E-10

5.888E-10

6.014E-10

6.143E-10

6.275E-10

6.409E-10

6.546E-10

6.686E-10

6.829E-10

6.975E-10

7.125E-10

7.277E-10

7.433E-10

7.593E-10

7.756E-10

7.923E-10

8.094E-10

8.269E-10

8.448E-10

8.631E-10

8.819E-10

9.012E-10

9.209E-10

9.410E-10

9.617E-10

4.761E-09

4.761E-09

4.762E-09

4.763E-09

4.765E-09

4.768E-09

4.772E-09

4.776E-09

4.782E-09

4.788E-09

4.794E-09

4.802E-09

4.810E-09

4.820E-09

4.830E-09

4.841E-09

4.854E-09

4.867E-09

4.881E-09

4.896E-09

4.912E-09

4.930E-09

4.948E-09

4.967E-09

4.988E-09

5.010E-09

5.033E-09

5.057E-09

5.083E-09

5.110E-09

5.138E-09

γSF (MeV−3)
5.268E-09

5.279E-09

5.291E-09

5.304E-09

5.318E-09

5.333E-09

5.348E-09

5.365E-09

5.383E-09

5.402E-09

5.422E-09

5.443E-09

5.465E-09

5.488E-09

5.513E-09

5.539E-09

5.566E-09

5.594E-09

5.624E-09

5.655E-09

5.688E-09

5.722E-09

5.757E-09

5.794E-09

5.833E-09

5.873E-09

5.915E-09

5.958E-09

6.004E-09

6.051E-09

6.100E-09

Continued on next page

167

Table A.7 (cont’d) CoH default γSF for 74Zn.

γ-ray Energy (MeV)

f(M1) (MeV−3)

f(E1) (MeV−3)

5.15

5.20

5.25

5.30

5.35

5.40

5.45

5.50

5.55

5.60

5.65

5.70

5.75

5.80

5.85

5.90

5.95

6.00

6.05

6.10

6.15

6.20

6.25

6.30

6.35

6.40

6.45

6.50

6.55

6.60

6.65

9.829E-10

1.005E-09

1.027E-09

1.050E-09

1.073E-09

1.097E-09

1.122E-09

1.147E-09

1.174E-09

1.200E-09

1.228E-09

1.256E-09

1.285E-09

1.315E-09

1.345E-09

1.377E-09

1.409E-09

1.442E-09

1.476E-09

1.512E-09

1.548E-09

1.585E-09

1.623E-09

1.662E-09

1.703E-09

1.745E-09

1.788E-09

1.832E-09

1.877E-09

1.924E-09

1.972E-09

5.167E-09

5.198E-09

5.231E-09

5.264E-09

5.300E-09

5.336E-09

5.375E-09

5.414E-09

5.456E-09

5.499E-09

5.544E-09

5.590E-09

5.639E-09

5.689E-09

5.741E-09

5.795E-09

5.851E-09

5.908E-09

5.968E-09

6.030E-09

6.094E-09

6.160E-09

6.229E-09

6.299E-09

6.372E-09

6.448E-09

6.525E-09

6.606E-09

6.688E-09

6.774E-09

6.862E-09

γSF (MeV−3)
6.150E-09

6.203E-09

6.258E-09

6.314E-09

6.373E-09

6.434E-09

6.497E-09

6.562E-09

6.629E-09

6.699E-09

6.771E-09

6.846E-09

6.924E-09

7.004E-09

7.086E-09

7.171E-09

7.260E-09

7.351E-09

7.445E-09

7.542E-09

7.642E-09

7.745E-09

7.852E-09

7.962E-09

8.075E-09

8.192E-09

8.313E-09

8.437E-09

8.566E-09

8.698E-09

8.834E-09

Continued on next page

168

Table A.7 (cont’d) CoH default γSF for 74Zn.

γ-ray Energy (MeV)

f(M1) (MeV−3)

f(E1) (MeV−3)

6.70

6.75

6.80

6.85

2.022E-09

2.073E-09

2.125E-09

2.180E-09

6.953E-09

7.046E-09

7.142E-09

7.242E-09

γSF (MeV−3)
8.974E-09

9.119E-09

9.268E-09

9.421E-09

Table A.8: EMPIRE default γSF for 74Zn.

γ-ray Energy (MeV)

0.106

0.212

0.318

0.424

0.530

0.636

0.743

0.849

0.955

1.061

1.167

1.273

1.379

1.485

1.591

1.697

1.803

1.909

2.016

2.122

2.228

γSF (MeV−3)
3.223E-12

1.290E-11

2.903E-11

5.163E-11

8.073E-11

1.163E-10

1.585E-10

2.073E-10

2.626E-10

3.247E-10

3.935E-10

4.691E-10

5.516E-10

6.410E-10

7.374E-10

8.410E-10

9.517E-10

1.070E-09

1.195E-09

1.328E-09

1.469E-09

γSF (mb/MeV)

3.942E-06

3.154E-05

1.065E-04

2.526E-04

4.936E-04

8.537E-04

1.357E-03

2.028E-03

2.891E-03

3.971E-03

5.294E-03

6.885E-03

8.769E-03

1.097E-02

1.353E-02

1.646E-02

1.979E-02

2.355E-02

2.777E-02

3.249E-02

3.773E-02

Continued on next page

169

Table A.8 (cont’d) EMPIRE default γSF for 74Zn.

γ-ray Energy (MeV)

2.334

2.440

2.546

2.652

2.758

2.864

2.970

3.076

3.182

3.288

3.395

3.501

3.607

3.713

3.819

3.925

4.031

4.137

4.243

4.349

4.455

4.561

4.668

4.774

4.880

4.986

5.092

5.198

5.304

5.410

5.516

γSF (MeV−3)
1.617E-09

1.774E-09

1.938E-09

2.111E-09

2.292E-09

2.482E-09

2.680E-09

2.887E-09

3.104E-09

3.330E-09

3.565E-09

3.810E-09

4.066E-09

4.331E-09

4.607E-09

4.894E-09

5.193E-09

5.502E-09

5.824E-09

6.157E-09

6.503E-09

6.862E-09

7.235E-09

7.620E-09

8.020E-09

8.435E-09

8.864E-09

9.309E-09

9.770E-09

1.025E-08

1.074E-08

γSF (mb/MeV)

4.352E-02

4.989E-02

5.689E-02

6.454E-02

7.288E-02

8.194E-02

9.177E-02

1.024E-01

1.139E-01

1.262E-01

1.395E-01

1.538E-01

1.690E-01

1.854E-01

2.028E-01

2.215E-01

2.413E-01

2.624E-01

2.849E-01

3.087E-01

3.340E-01

3.609E-01

3.893E-01

4.194E-01

4.512E-01

4.848E-01

5.204E-01

5.579E-01

5.974E-01

6.392E-01

6.832E-01

Continued on next page

170

Table A.8 (cont’d) EMPIRE default γSF for 74Zn.

γ-ray Energy (MeV)

5.622

5.728

5.834

5.940

6.047

6.153

6.259

6.365

6.471

6.577

6.683

6.789

6.895

7.001

7.107

7.213

7.319

7.426

7.532

7.638

7.744

7.850

7.956

8.062

8.168

8.274

8.380

γSF (MeV−3)
1.125E-08

1.179E-08

1.234E-08

1.290E-08

1.349E-08

1.410E-08

1.474E-08

1.539E-08

1.607E-08

1.677E-08

1.750E-08

1.826E-08

1.904E-08

1.985E-08

2.069E-08

2.156E-08

2.246E-08

2.340E-08

2.437E-08

2.538E-08

2.642E-08

2.751E-08

2.863E-08

2.980E-08

3.101E-08

3.227E-08

3.358E-08

γSF (mb/MeV)

7.295E-01

7.783E-01

8.297E-01

8.838E-01

9.406E-01

1.000E+00

1.063E+00

1.129E+00

1.199E+00

1.272E+00

1.348E+00

1.429E+00

1.513E+00

1.602E+00

1.695E+00

1.793E+00

1.895E+00

2.003E+00

2.116E+00

2.234E+00

2.359E+00

2.489E+00

2.626E+00

2.770E+00

2.920E+00

3.078E+00

3.244E+00

171

APPENDIX B

Matrices used in the daughter and background subtraction for the decay of 71,72,73Co

172

Figure B.1: (Top Left) Starting 2D matrix for the analysis of the β decay of 71Co using the
β-Oslo method (includes daughter decay and random correlation, or background, contribu-
tions). (Top Right) Matrix with daughter decay component that was subtracted from the
starting matrix. (Bottom) Matrix with the background component from random correlations
that was subtracted from the starting matrix.

173

Gamma energy (keV)Excitation energy (keV)0200040006000800010000110210310410020004000600080001000010003000500070009000Gamma energy (keV)Excitation energy (keV)0200040006000800010000110210310020004000600080001000010003000500070009000Gamma energy (keV)Excitation energy (keV)0200040006000800010000110210310020004000600080001000010003000500070009000Figure B.2: (Top Left) Starting 2D matrix for the analysis of the β decay of 72Co using the
β-Oslo method (includes daughter decay and random correlation, or background, contribu-
tions). (Top Right) Matrix with daughter decay component that was subtracted from the
starting matrix. (Bottom) Matrix with the background component from random correlations
that was subtracted from the starting matrix.

174

Gamma energy (keV)Excitation energy (keV)02000400060008000100001102103100200040006000800010000100030005000700090001200014000Gamma energy (keV)Excitation energy (keV)02000400060008000100001102103100200040006000800010000100030005000700090001200014000Gamma energy (keV)Excitation energy (keV)02000400060008000100001102103100200040006000800010000100030005000700090001200014000Figure B.3: (Top Left) Starting 2D matrix for the analysis of the β decay of 73Co using the
β-Oslo method (includes daughter decay and random correlation, or background, contribu-
tions). (Top Right) Matrix with daughter decay component that was subtracted from the
starting matrix. (Bottom) Matrix with the background component from random correlations
that was subtracted from the starting matrix.

175

Gamma energy (keV)Excitation energy (keV)020004000600080001000011021031002000400060008000100001000300050007000900012000Gamma energy (keV)Excitation energy (keV)020004000600080001000011021031002000400060008000100001000300050007000900012000Gamma energy (keV)Excitation energy (keV)020004000600080001000011021002000400060008000100001000300050007000900012000APPENDIX C

Fits to experimental γSF (upper and lower limits)

176

Figure C.1: Fit to experimental γSFs for 71Ni using the HFBCS model (strength 3 in TALYS)
and an exponential upbend. The lower limit data set is on the right, while the upper limit
data set is on the left.

Figure C.2: Fit to experimental γSFs for 72Ni, (6− ground state of 72Co) using the HFBCS
model (strength 3 in TALYS) and an exponential upbend. The lower limit data set is on the
right, while the upper limit data set is on the left.

177

 E (MeV)g0-3gSF (MeV)-910 Experimental gSF TALYS shifted strength3 + exponential upbend71Ni S = 4.264 MeVn-810-71012345 Lower limit E (MeV)g0123456 Upper limit-3gSF (MeV)-910 Experimental gSF TALYS shifted strength3 + exponential upbend72Ni S = 6.891 MeVn-810-710 E (MeV)g01234567 Lower limit E (MeV)g012345678 Upper limitFigure C.3: Fit to experimental γSFs for 72Ni (7− ground state of 72Co) using the HFBCS
model (strength 3 in TALYS) and an exponential upbend. The lower limit data set is on the
right, while the upper limit data set is on the left.

Figure C.4: Fit to experimental γSFs for 73Ni using the HFBCS model (strength 3 in TALYS)
and an exponential upbend. The lower limit data set is on the right, while the upper limit
data set is on the left.

178

-3gSF (MeV)-910 Experimental gSF TALYS shifted strength3 + exponential upbend72Ni S = 6.891 MeVn-810-710 E (MeV)g01234567 Lower limit E (MeV)g012345678 Upper limit E (MeV)g0-3gSF (MeV)-910-810-7101234 Experimental gSF TALYS shifted strength3 + exponential upbend73Ni S = 3.953 MeVn Lower limit E (MeV)g012345Upper limitBIBLIOGRAPHY

179

BIBLIOGRAPHY

[1] M. Weigand, T. A. Bredeweg, A. Couture, K. G¨obel, T. Heftrich, M. Jandel,
F. K¨appeler, C. Lederer, N. Kivel, G. Korschinek, M. Krtiˇcka, J. M. O’Donnell, J. Os-
term¨oller, R. Plag, R. Reifarth, D. Schumann, J. L. Ullmann, and A. Wallner. Ni 63
(n,γ) cross sections measured with DANCE. Physical Review C - Nuclear Physics,
92(4):045810, 2015.

[2] C. Sneden, J.J. Cowan, and R. Gallino. Neutron-Capture Elements in the Early

Galaxy. Annual Review of Astronomy and Astrophysics, 46:241–288, 9 2008.

[3] M. Arnould, S. Goriely, and K. Takahashi. The r-process of stellar nucleosynthesis:
Astrophysics and nuclear physics achievements and mysteries. Physics Reports, 450:97–
213, 2007.

[4] LIGO Scientific Collaboration and Virgo Collaboration. GW170817: Observation of
Gravitational Waves from a Binary Neutron Star Inspiral. Phys. Rev. Lett., 119(16):30–
33, 2017.

[5] M. R. Drout, A. L. Piro, B. J. Shappee, C. D. Kilpatrick, J. D. Simon, C. Contr-
eras, D. A. Coulter, R. J. Foley, M. R. Siebert, N. Morrell, K. Boutsia, F. Di Mille,
T. W.S. Holoien, D. Kasen, J. A. Kollmeier, B. F. Madore, A. J. Monson, A. Murguia-
Berthier, Y.-C. Pan, J. X. Prochaska, E. Ramirez-Ruiz, A. Rest, C. Adams, K. Alatalo,
E. Ba˜nados, J. Baughman, T. C. Beers, R. A. Bernstein, T. Bitsakis, A. Campil-
lay, T. T. Hansen, C. R. Higgs, A. P. Ji, G. Maravelias, J. L. Marshall, C. Moni
Bidin, J. L. Prieto, K. C. Rasmussen, C. Rojas-Bravo, A. L. Strom, N. Ulloa,
J. Vargas-Gonz´alez, Z. Wan, and D. D. Whitten. Light curves of the neutron
star merger GW170817/SSS17a: Implications for r-process nucleosynthesis. Science,
358(6370):1570–1574, 12 2017.

[6] D. Kasen, B. Metzger, J. Barnes, E. Quataert, and E. Ramirez-Ruiz. Origin of the
heavy elements in binary neutron-star mergers from a gravitational-wave event. Nature,
551(7678):80–84, 2017.

[7] B.D. Metzger, G. Mart´ınez-Pinedo, S. Darbha, E. Quataert, A. Arcones, D. Kasen,
R. Thomas, P. Nugent, I.V. Panov, and N.T. Zinner. Electromagnetic counterparts of
compact object mergers powered by the radioactive decay of r-process nuclei. Monthly
Notices of the Royal Astronomical Society, 406:2650–2662, 2010.

[8] G.J. Wasserburg and Y.-Z. Qian. Prompt iron enrichment, two r-process components,
and abundanced in very metal-poor stars. The Astrophysical Journal, 529:L21, 2000.

180

[9] Y. Z. Qian and G. J. Wasserburg. Stellar abundances in the early galaxy and two

r-process components. Physics Reports, 333-334(4-6):77–108, 2000.

[10] Y Z Qian and G J Wasserburg. A model for abundances in metal-poor stars. The

Astrophysical Journal, 559(2):925–941, 2001.

[11] Y. Z. Qian and G. J. Wasserburg. Determination of Nucleosynthetic Yields of Super-
novae and Very Massive Stars from Abundances in Metal-Poor Stars. The Astrophysical
Journal, 567:515, 2001.

[12] F. Montes, T. C. Beers, J. Cowan, T. Elliot, K. Farouqi, R. Gallino, M. Heil, K.L.
Kratz, B. Pfeiffer, M. Pignatari, and H. Schatz. Nucleosynthesis in the Early Galaxy.
The Astrophysical Journal, 671(2):1685–1695, 2007.

[13] M. R. Mumpower, R. Surman, G. C. McLaughlin, and A. Aprahamian. The impact
of individual nuclear properties on r-process nucleosynthesis. Prog. Part. Nucl. Phys.,
86:86, 2016.

[14] R. Surman, M. Mumpower, R. Sinclair, K. L. Jones, W. R. Hix, and G. C. McLaughlin.
Sensitivity studies for the weak r process: Neutron capture rates. AIP Advances,
4:041008, 2014.

[15] R.H. Cyburt, A. M. Amthor, R. Ferguson, Z. Meisel, K. Smith, S. Warren, A. Heger,
R. D. Hoffman, T. Rauscher, A. Sakharuk, H. Schatz, F. K. Thielemann, and M. Wi-
escher. the Jina Reaclib Database: Its Recent Updates and Impact on Type-I X-Ray
Bursts. The Astrophysical Journal Supplement Series, 189(1):240–252, 2010.

[16] A. C. Larsen, A. Spyrou, S. N. Liddick, M. Guttormsen, V. W. Ingeberg, S. Siem,
M. Wiedeking, B. P. Crider, F. Naqvi, G. Perdikakis, M. R. Mumpower, R. Surman,
G. M. Tveten, D. L. Bleuel, A. Couture, L. Crespo Campo, A. C. Dombos, A. G¨orgen,
R. Lewis, S. M. Mosby, S. Nikas, C. J. Prokop, S. J. Quinn, T. Renstrøm, and B. Ru-
bio. Novel techniques for constraining neutron-capture rates relevant to heavy-element
nucleosynthesis. Progress in Particle and Nuclear Physics, In Press, 2019.

[17] S. M. Grimes. Hauser-Feshbach calculations in deformed nuclei. Phys. Rev. C, 88(2):1–

10, 2013.

[18] A. J. Koning and J. P. Delaroche. Local and global nucleon optical models from 1 keV

to 200 MeV. Nucl. Phys. A, 713:231, 2003.

[19] J.-P. Jeukenne, A. Lejeune, and C. Mahaux. Microscopic calculation of the symmetry
and Coulomb components of the complex optical-model potential. Physical Review,
15:10, 1977.

181

[20] T. Ericson. The statistical model and nuclear level densities. Advances in Physics,

9(36):425–511, 1960.

[21] A. Gilbert and A.G.W. Cameron. A composite nuclear level density formula with shell

corrections. Can. J. Phys., 43:1446, 1965.

[22] T. Von Egidy and D. Bucurescu. Experimental energy-dependent nuclear spin distri-

butions. Phys. Rev. C, 80:054310, 2009.

[23] H.A. Bethe. Nuclear Physics B. Nuclear Dynamics, Theoretical. Rev. Mod. Phys.,

9:69, 1937.

[24] TALYS User Manual (v. 1.6).

[25] T. D. Newton. Shell Effects on the Spacing of Nuclear Levels. Can. J. Phys., 34:804–

829, 1956.

[26] A.G.W. Cameron. Nuclear Level Spacings. Can. J. Phys., 36:1040, 1958.

[27] A. Gilbert, F.S. Chen, and A.G.W Cameron. Level densities in lighter nuclei. Can. J.

Phys., 43(7):1248–1258, 1965.

[28] R. Capote, M. Herman, P. Obloˇzinsk´y, P. G. Young, S. Goriely, T. Belgya, A. V.
Ignatyuk, A. J. Koning, S. Hilaire, V. A. Plujko, M. Avrigeanu, O. Bersillon, M. B.
Chadwick, T. Fukahori, Zhigang Ge, Yinlu Han, S. Kailas, J. Kopecky, V. M. Maslov,
G. Reffo, M. Sin, E. Sh Soukhovitskii, and P. Talou. RIPL - Reference Input Parameter
Library for Calculation of Nuclear Reactions and Nuclear Data Evaluations. Nuclear
Data Sheets, 110(12):3107–3214, 2009.

[29] S. Goriely, F. Tondeur, and J.M. Pearson. A Hartree-Fock Nuclear Mass Table. Atomic

Data and Nuclear Data Tables, 77:311, 2001.

[30] S. Goriely, S. Hilaire, and A. J. Koning.

Improved microscopic nuclear level densi-
ties within the Hartree-Fock-Bogoliubov plus combinatorial method. Phys. Rev. C,
78:064307, 2008.

[31] S. Hilaire, M. Girod, S. Goriely, and A. J. Koning. Temperature-dependent combina-

torial level densities with the D1M Gogny force. Phys. Rev. C, 86:064317, 2012.

[32] D.M. Brink. Individual Particle and Collective Aspects of the Nuclear Photoeffect.

Nuclear Physics, 4:215, 1957.

[33] P. Axel. Electric Dipole Ground-State Transition Width Strength Function and 7-Mev

Photon Interactions. Physical Review, 126(2):671–683, 1962.

182

[34] M. Krtiˇcka and F. Beˇcv´aˇr. What do we really know about photon strength functions?

Journal of Physics G, 35:014025, 2008.

[35] J. Kopecky and M. Uhl. Test of gamma-ray strength functions in nuclear reaction

model calculations. Phys. Rev. C, 41:1941, 1990.

[36] A.C. Larsen and S. Goriely. Impact of a low-energy enhancement in the γ -ray strength

function on the neutron-capture cross section. Phys. Rev. C, 82:014318, 2010.

[37] S. Goriely and E. Khan. Large-scale QRPA calculation of E1-strength and its impact

on the neutron capture cross section. Nuclear Physics A, 706:217–232, 2002.

[38] S. Goriely, E. Khan, and M. Samyn. Microscopic HFB + QRPA predictions of dipole

strength for astrophysics applications. Nuclear Physics A, 739:331–352, 2004.

[39] A. Koning, S. Hilaire, and M.C. Duijvestijn. No Title. In TALYS-1.6: Proceedings of
the International Conference on Nuclear Data for Science and Technology 2007. EDP
Sciences, Nice, France, 2007, 2007.

[40] A. J. Koning and D. Rochman. Modern Nuclear Data Evaluation with the TALYS

Code System. Nuclear Data Sheets, 113:2927, 2012.

[41] A. Voinov, E. Algin, U. Agvaanluvsan, T. Belgya, R. Chankova, M. Guttormsen, G.E.
Mitchell, J. Rekstad, A. Schiller, and S. Siem. Large enhancement of radiative strength
for soft transitions in the quasicontinuum. Phys. Rev. Lett., pages 7–10, 2004.

[42] M. Guttormsen, R. Chankova, U. Agvaanluvsan, E. Algin, L. A. Bernstein, F. Inge-
bretsen, T. L¨onnroth, S. Messelt, G. E. Mitchell, J. Rekstad, A. Schiller, S. Siem, A. C.
Sunde, A. Voinov, and S. Ødeg˚ard. Radiative strength functions in 93-98Mo. Phys.
Rev. C, 71(4):044307, 2005.

[43] A. C. Larsen, M. Guttormsen, R. Chankova, F. Ingebretsen, T. L¨onnroth, S. Messelt,
J. Rekstad, A. Schiller, S. Siem, N. U. H. Syed, and A. Voinov. Nuclear level densities
and γ-ray strength functions in 44,45Sc. Phys. Rev. C, 76(4):044303, 2007.

[44] M. Wiedeking, L.A. Bernstein, M. Krtiˇcka, D.L. Bleuel, J.M. Allmond, M.S. Basunia,
J.T. Burke, P. Fallon, R.B. Firestone, B.L. Goldblum, R. Hatarik, P.T. Lake, I-Y.
Lee, S.R. Lesher, S. Paschalis, M. Petri, L. Phair, and N.D. Scielzo. Low-Energy
Enhancement in the Photon Strength of Mo95. Phys. Rev. Lett., 108(16):162503,
2012.

[45] A. B¨urger, A. C. Larsen, S. Hilaire, M. Guttormsen, S. Harissopulos, M. Kmiecik,
T. Konstantinopoulos, M. Krtiˇcka, A. Lagoyannis, T. L¨onnroth, K. Mazurek, M. Nor-
rby, H. T. Nyhus, G. Perdikakis, S. Siem, A. Spyrou, and N. U.H. Syed. Nuclear level
density and γ-ray strength function of 43Sc. Phys. Rev. C, 85(6):064328, 2012.

183

[46] A. C. Larsen, N. Blasi, A. Bracco, F. Camera, T. K. Eriksen, A. G¨orgen, M. Gut-
tormsen, T. W. Hagen, S. Leoni, B. Million, H. T. Nyhus, T. Renstrøm, S. J. Rose,
I. E. Ruud, S. Siem, T. Tornyi, G. M. Tveten, A. V. Voinov, and M. Wiedeking. Evi-
dence for the dipole nature of the low-energy g enhancement in Fe56. Phys. Rev. Lett.,
111:242504, 2013.

[47] B. V. Kheswa, M. Wiedeking, F. Giacoppo, S. Goriely, M. Guttormsen, A. C. Larsen,
F. L. Bello Garrote, T. K. Eriksen, A. G¨orgen, T. W. Hagen, P. E. Koehler, M. Klinte-
fjord, H. T. Nyhus, P. Papka, T. Renstrøm, S. Rose, E. Sahin, S. Siem, and T. Tornyi.
Galactic production of138La: Impact of138,139La statistical properties. Phys. Lett. B,
744:268–272, 2015.

[48] A. Simon, M. Guttormsen, A. C. Larsen, C. W. Beausang, P. Humby, J. T. Burke, R. J.
Casperson, R. O. Hughes, T. J. Ross, J. M. Allmond, R. Chyzh, M. Dag, J. Koglin,
E. McCleskey, M. McCleskey, S. Ota, and A. Saastamoinen. First observation of low-
energy γ -ray enhancement in the rare-earth region. Phys. Rev. C, 93(3):034303, 2016.

[49] S. Paschalis, I. Y. Lee, A. O. MacChiavelli, C. M. Campbell, M. Cromaz, S. Gros,
J. Pavan, J. Qian, R. M. Clark, H. L. Crawford, D. Doering, P. Fallon, C. Lionberger,
T. Loew, M. Petri, T. Stezelberger, S. Zimmermann, D. C. Radford, K. Lagergren,
D. Weisshaar, R. Winkler, T. Glasmacher, J. T. Anderson, and C. W. Beausang. The
performance of the Gamma-Ray Energy Tracking In-beam Nuclear Array GRETINA.
Nucl. Instr. Meth. Phys. Res. A, 709:44–55, 2013.

[50] M. D. Jones, A. O. MacChiavelli, M. Wiedeking, L. A. Bernstein, H. L. Crawford,
C. M. Campbell, R. M. Clark, M. Cromaz, P. Fallon, I. Y. Lee, M. Salathe, A. Wiens,
A. D. Ayangeakaa, D. L. Bleuel, S. Bottoni, M. P. Carpenter, H. M. Davids, J. Elson,
A. G¨orgen, M. Guttormsen, R. V.F. Janssens, J. E. Kinnison, L. Kirsch, A. C. Larsen,
T. Lauritsen, W. Reviol, D. G. Sarantites, S. Siem, A. V. Voinov, and S. Zhu. Exam-
ination of the low-energy enhancement of the γ -ray strength function of Fe 56. Phys.
Rev. C, 97(2):024327, 2018.

[51] M. Guttormsen, T.S. Tveter, L. Bergholt, F. Ingebretsen, and J. Rekstad. The un-

folding of continuum y-ray spectra. Nucl. Instr. Meth. Phys. Res. A, 374:371, 1996.

[52] M. Guttormsen, T. Ramsøy, and J. Rekstad. The first generation of γ-rays from hot

nuclei. Nucl. Instr. Meth. Phys. Res. A, 255(3):518–523, 4 1987.

[53] A Schiller, L Bergholt, M Guttormsen, E Melby, J Rekstad, and S Siem. Extraction
of level density and γ strength function from primary γ spectra. Nucl. Instr. Meth.
Phys. Res. A, 447(3):498–511, 2000.

[54] A. C. Larsen, M. Guttormsen, M. Krtiˇcka, E. Bˇet´ak, A. B¨urger, A. G¨orgen, H. T.
Nyhus, J. Rekstad, A. Schiller, S. Siem, H. K. Toft, G. M. Tveten, A. V. Voinov, and

184

K. Wikan. Analysis of possible systematic errors in the Oslo method. Phys. Rev. C,
83:034315, 2011.

[55] A Spyrou, S N Liddick, A C Larsen, M Guttormsen, K Cooper, A C Dombos, D J
Morrissey, F Naqvi, G Perdikakis, S J Quinn, T Renstrøm, J A Rodriguez, A Simon,
C S Sumithrarachchi, and R G T Zegers. Novel technique for Constraining r-Process
(n, γ) Reaction Rates. Phys. Rev. Lett., 113:232502, 2014.

[56] J. E. Escher, J. T. Burke, R. O. Hughes, N. D. Scielzo, R. J. Casperson, S. Ota,
H. I. Park, A. Saastamoinen, and T. J. Ross. Constraining Neutron Capture Cross
Sections for Unstable Nuclei with Surrogate Reaction Data and Theory. Phys. Rev.
Lett., 121(5):52501, 2018.

[57] H. Utsunomiya, S. Goriely, H. Akimune, H. Harada, F. Kitatani, S. Goko, H. Toyokawa,
K. Yamada, T. Kondo, O. Itoh, M. Kamata, T. Yamagata, Y.-W. Lui, I. Daoutidis,
D.P. Arteaga, S. Hilaire, and A.J. Koning. γ-ray strength function method and its
application to 107 Pd. Phys. Rev. C, 82:064610, 2010.

[58] H. Utsunomiya, S. Goriely, T. Kondo, C. Iwamoto, H. Akimune, T. Yamagata,
H. Toyokawa, H. Harada, F. Kitatani, Y. W. Lui, A. C. Larsen, M. Guttormsen,
P. E. Koehler, S. Hilaire, S. P´eru, M. Martini, and A. J. Koning. Photoneutron cross
sections for Mo isotopes: A step toward a unified understanding of (γ,n) and (n,γ)
reactions. Phys. Rev. C, 88(1):015805, 2013.

[59] D. J. Morrissey, B. M. Sherrill, M. Steiner, A. Stolz, and I. Wiedenhoever. Commis-
sioning the A1900 projectile fragment separator. Nucl. Instr. Meth. Phys. Res. B,
204:90–96, 2003.

[60] A. Simon, S. J. Quinn, A. Spyrou, A. Battaglia, I. Beskin, A. Best, B. Bucher,
M. Couder, P. A. Deyoung, X. Fang, J. G¨orres, A. Kontos, Q. Li, S. N. Liddick,
A. Long, S. Lyons, K. Padmanabhan, J. Peace, A. Roberts, D. Robertson, K. Smith,
M. K. Smith, E. Stech, B. Stefanek, W. P. Tan, X. D. Tang, and M. Wiescher. SuN:
Summing NaI(Tl) gamma-ray detector for capture reaction measurements. Nucl. Instr.
Meth. Phys. Res. A, 703:16, 2013.

[61] M. S. Basunia. Nuclear Data Sheets for A = 237. Nuclear Data Sheets, 107(8):2323–

2422, 2006.

[62] F. G. Kondev and S. Lalkovski. Nuclear Data Sheets for A = 207. Nuclear Data Sheets,

112(3):707–853, 2011.

[63] E. Browne and J. K. Tuli. Nuclear Data Sheets for A = 137. Nuclear Data Sheets,

108(10):2173–2318, 2007.

185

[64] R.G. Helmer. Nuclear Data Sheets for A = 60. Nuclear Data Sheets, 114(12):51849–

2022, 2013.

[65] M. J. Martin. Nuclear Data Sheets for A = 208. Nuclear Data Sheets, 108(8):1583–

1806, 2007.

[66] B. Singh and A.R. Farhan. Nuclear Data Sheets for A=74. Nuclear Data Sheets,

107(7):1923–2102, 2006.

[67] K. Abusaleem and B. Singh. Nuclear Data Sheets for A=71. Nuclear Data Sheets,

112:113, 2011.

[68] D. Abriola and A.A. Sonzogni. Nuclear Data Sheets for A = 72. Nuclear Data Sheets,

111(1):1–140, 2010.

[69] M. M. Rajabali, R. Grzywacz, S. N. Liddick, C. Mazzocchi, J. C. Batchelder, T. Bau-
mann, C. R. Bingham, I. G. Darby, T. N. Ginter, S. V. Ilyushkin, M. Karny, W. Kr´olas,
P. F. Mantica, K. Miernik, M. Pf¨utzner, K. P. Rykaczewski, D. Weisshaar, and J. A.
Winger. β decay of 71,73Co: Probing single-particle states approaching doubly magic
78Ni. Phys. Rev. C, 85(3):034326, 2012.

[70] T. Kurtukian-Nieto, J. Benlliure, and K. H. Schmidt. A new analysis method to
determine β-decay half-lives in experiments with complex background. Nucl. Instr.
Meth. Phys. Res. A, 589(3):472–483, 2008.

[71] M. Guttormsen. Matrix Manipulation Program (MAMA), Oslo Method v1.1.2, 2018.

[72] M. Guttormsen, A. C. Larsen, A. G¨orgen, T. Renstrøm, S. Siem, T. G. Tornyi, and
G. M. Tveten. Validity of the Generalized Brink-Axel Hypothesis in Np 238. Phys.
Rev. Lett., 116:012502, 2016.

[73] J. Allison, K. Amako, J. Apostolakis, P. Arce, M. Asai, T. Aso, E. Bagli, A. Bag-
ulya, S. Banerjee, G. Barrand, B. R. Beck, A. G. Bogdanov, D. Brandt, J. M.C.
Brown, H. Burkhardt, Ph Canal, D. Cano-Ott, S. Chauvie, K. Cho, G. A.P. Cirrone,
G. Cooperman, M. A. Cort´es-Giraldo, G. Cosmo, G. Cuttone, G. Depaola, L. Des-
orgher, X. Dong, A. Dotti, V. D. Elvira, G. Folger, Z. Francis, A. Galoyan, L. Gar-
nier, M. Gayer, K. L. Genser, V. M. Grichine, S. Guatelli, P. Gu`eye, P. Gumplinger,
A. S. Howard, I. Hˇrivn´aˇcov´a, S. Hwang, S. Incerti, A. Ivanchenko, V. N. Ivanchenko,
F. W. Jones, S. Y. Jun, P. Kaitaniemi, N. Karakatsanis, M. Karamitrosi, M. Kelsey,
A. Kimura, T. Koi, H. Kurashige, A. Lechner, S. B. Lee, F. Longo, M. Maire, D. Man-
cusi, A. Mantero, E. Mendoza, B. Morgan, K. Murakami, T. Nikitina, L. Pandola,
P. Paprocki, J. Perl, I. Petrovi´c, M. G. Pia, W. Pokorski, J. M. Quesada, M. Raine,
M. A. Reis, A. Ribon, A. Risti´c Fira, F. Romano, G. Russo, G. Santin, T. Sasaki,
D. Sawkey, J. I. Shin, I. I. Strakovsky, A. Taborda, S. Tanaka, B. Tom´e, T. Toshito,
H. N. Tran, P. R. Truscott, L. Urban, V. Uzhinsky, J. M. Verbeke, M. Verderi,

186

B. L. Wendt, H. Wenzel, D. H. Wright, D. M. Wright, T. Yamashita, J. Yarba, and
H. Yoshida. Recent developments in GEANT4. Nucl. Instr. Meth. Phys. Res. A,
835:186–225, 2016.

[74] R.P. de Groote, J. Billowes, C. L. Binnersley, S. Franchoo, K. T. Flanagan, S. Rothe,
R. P. de Groote, K. M. Lynch, K. D. A. Wendt, T. Day Goodacre, F. Nowacki,
Y. Tsunoda, A. R. Vernon, T. Otsuka, M. L. Bissell, R. F. Garcia Ruiz, X. F. Yang,
T. E. Cocolios, H. H. Stroke, . Koszor´us, S. G. Wilkins, Z. Y. Xu, D. V. Fedorov,
G. Neyens, and G. J. Farooq-Smith. Dipole and quadrupole moments of Cu7378 as
a test of the robustness of the Z=28 shell closure near Ni78. Physical Review C,
96(4):041302(R), 2017.

[75] K.T. Flanagan, P. Vingerhoets, M.L. Bissell, K. Blaum, B.A. Brown, B. Cheal,
M. De Rydt, D.H. Forest, C. Geppert, M. Honma, M. Kowalska, J. Kr¨amer, A. Krieger,
E. Man´e, R. Neugart, G. Neyens, W. N¨ortersh¨auser, M. Schug, H.H. Stroke, and D.T.
Yordanov. Experimental determination of an I π = 2 ground state in 72,74 Cu. Phys.
Rev. C, 82:041302(R), 2010.

[76] A.M. Goryachev and G.N. Zalesnyy. The studying of the photoneutron reactions cross
sections in the region of the giant dipole resonance in zinc, germanium, selenium, and
strontium isotopes. Voprosy Teoreticheskoy i Yadernoy Fiziki, 8:121, 1982.

[77] S. N. Liddick, A. Spyrou, B. P. Crider, F. Naqvi, A. C. Larsen, M. Guttormsen,
M. Mumpower, R. Surman, G. Perdikakis, D. L. Bleuel, A. Couture, L. Crespo Campo,
A. C. Dombos, R. Lewis, S. Mosby, S. Nikas, C. J. Prokop, T. Renstrom, B. Rubio,
S. Siem, and S. J. Quinn. Experimental Neutron Capture Rate Constraint Far from
Stability. Phys. Rev. Lett., 116:242502, 2016.

[78] W. Dilg, W. Schantl, H. Vonach, and M. Uhl. Level density parameters for the Back-
Shifted Fermi Gas model in the mass range 40¡A¡250. Nuclear Physics, Section A,
217(2):269–298, 1973.

[79] A.V. Ignatyuk, J.L. Weil, S. Raman, and S. Kahane. Density of discrete levels in

116Sn. Phys. Rev. C, 47:1504, 1993.

[80] S. Goriely. Radiative neutron captures by neutron-rich nuclei and the r-process nucle-

osynthesis. Phys. Lett. B, 436:10–18, 1998.

[81] M. Herman, R. Capote, B. V. Carlson, P. Obloˇzinsk´y, M. Sin, A. Trkov, H. Wienke,
and V. Zerkin. EMPIRE: Nuclear Reaction Model Code System for Data Evaluation.
Nuclear Data Sheets, 108:2655, 2007.

[82] T. Rauscher and F.-K. Thielemann. Astrophysical Reaction Rates From Statistical

Model Calculations. At. Data Nucl. Data Tables, 75:1, 2000.

187

[83] T. Rauscher and F.-K. Thielemann. Stellar Evolution, Stellar Explosions, and Galactic

Chemical Evolution. IOP, Bristol, 1998.

[84] T. Kawano, R. Capote, S. Hilaire, and P. Chau Huu-Tai. Statistical Hauser-Feshbach
theory with width-fluctuation correction including direct reaction channels for neutron-
induced reactions at low energies. Phys. Rev. C, 94:014612, 2016.

[85] S. I. Al-Quraishi, S. M. Grimes, T. N. Massey, and D. A. Resler. Are the level densities
for r - and rp -process nuclei different from nearby nuclei in the valley of stability? Phys.
Rev. C, 63(6):065803, 2001.

[86] D. Savran, T. Aumann, and A. Zilges. Experimental studies of the Pygmy Dipole

Resonance. Prog. Part. Nucl. Phys., 70:210, 2013.

[87] M. Beard, E. Uberseder, R. Crowter, and M. Wiescher. Comparison of statistical
model calculations for stable isotope neutron capture. Phys. Rev. C, 90:034619, 2014.

[88] R. Capote, S. Hilaire, O. Iwamoto, T. Kawano, and M. Sin. Inter-comparison of Hauser-
Feshbach model codes toward better actinide evaluations. EPJ Web of Conferences,
146:12034, 2017.

[89] E. Uberseder, T. Adachi, T. Aumann, S. Beceiro-Novo, K. Boretzky, C. Caesar, I. Dill-
mann, O. Ershova, A. Estrade, F. Farinon, J. Hagdahl, T. Heftrich, M. Heil, M. Heine,
M. Holl, A. Ignatov, H. T. Johansson, N. Kalantar, C. Langer, T. Le Bleis, Yu A.
Litvinov, J. Marganiec, A. Movsesyan, M. A. Najafi, T. Nilsson, C. Nociforo, V. Panin,
S. Pietri, R. Plag, A. Prochazka, G. Rastrepina, R. Reifarth, V. Ricciardi, C. Rigollet,
D. M. Rossi, D. Savran, H. Simon, K. Sonnabend, B. Streicher, S. Terashima, R. Thies,
Y. Togano, V. Volkov, F. Wamers, H. Weick, M. Weigand, M. Wiescher, C. Wimmer,
N. Winckler, and P. J. Woods. First experimental constraint on the 59Fe(n,γ)60Fe
reaction cross section at astrophysical energies via the coulomb dissociation of 60Fe.
Phys. Rev. Lett., 112:1211101, 2014.

[90] O. Iwamoto. Development of a Comprehensive Code for Nuclear Data Evaluation,
CCONE, and Validation Using Neutron-Induced Cross Sections for Uranium Isotopes.
J. of Nucl. Science and Tech., 44:687, 2007.

[91] V.A. Plujko, O.M. Gorbachenko, E.V. Kulich, V.M. Bondar, and O.I. Davidovskaya.
Testing simple models of E1 radiative strength functions. In Proceedings of Science,
page PSF07, 2008.

[92] B. Singh. Nuclear Data Sheets for A = 73. Nuclear Data Sheets, 101:193, 2004.

[93] J. Van De Walle, F. Aksouh, T. Behrens, V. Bildstein, A. Blazhev, J. Cederk¨all,
E. Cl´ement, T. E. Cocolios, T. Davinson, P. Delahaye, J. Eberth, A. Ekstr¨om, D. V.
Fedorov, V. N. Fedosseev, L. M. Fraile, S. Franchoo, R. Gernhauser, G. Georgiev,

188

D. Habs, K. Heyde, G. Huber, M. Huyse, F. Ibrahim, O. Ivanov, J. Iwanicki, J. Jolie,
O. Kester, U. K¨oster, T. Kr¨oll, R. Kr¨ucken, M. Lauer, A. F. Lisetskiy, R. Lutter,
B. A. Marsh, P. Mayet, O. Niedermaier, M. Pantea, R. Raabe, P. Reiter, M. Saw-
icka, H. Scheit, G. Schrieder, D. Schwalm, M. D. Seliverstov, T. Sieber, G. Sletten,
N. Smirnova, M. Stanoiu, I. Stefanescu, J. C. Thomas, J. J. Valiente-Dob´on, P. Van
Duppen, D. Verney, D. Voulot, N. Warr, D. Weisshaar, F. Wenander, B. H. Wolf, and
M. Zieli´nska. Low-energy Coulomb excitation of neutron-rich zinc isotopes. Phys. Rev.
C, 79:014309, 2009.

[94] T. Kawano, P. Talou, M.B. Chadwick, and T. Watanabe. Monte Carlo Simulation for
Particle and -Ray Emissions in Statistical Hauser-Feshbach Model. J. of Nucl. Science
and Tech., 47:462, 2010.

[95] P. A. Moldauer. Statistics and the average cross section. Nuclear Physics A, 344:185–

195, 1980.

[96] T. Kawano and P. Talou. Numerical simulations for low energy nuclear reactions to

validate statistical models. Nuclear Data Sheets, 118(1):183–186, 2014.

[97] S. Hilaire, C. Lagrange, and A.J. Koning. Comparisons between various width fluctua-
tion correction factors for compound nucleus reactions. Annals of Physics, 306(2):209–
231, 2003.

[98] I. Stefanescu, D. Pauwels, N. Bree, T. E. Cocolios, J. Diriken, S. Franchoo, M. Huyse,
O. Ivanov, Y. Kudryavtsev, N. Patronis, J. Van De Walle, P. Van Duppen, and W. B.
Walters. Evidence for a β-decaying 1/2- isomer in 71Ni. Phys. Rev. C, 79(4):044325,
2009.

[99] G. G¨urdal and E. A. McCutchan. Nuclear Data Sheets for A=70. Nuclear Data Sheets,

136:1–162, 2016.

[100] D. M. Rossi, P. Adrich, F. Aksouh, H. Alvarez-Pol, T. Aumann, J. Benlliure,
M. B¨ohmer, K. Boretzky, E. Casarejos, M. Chartier, A. Chatillon, D. Cortina-Gil,
U. Datta Pramanik, H. Emling, O. Ershova, B. Fernandez-Dominguez, H. Geis-
sel, M. Gorska, M. Heil, H. T. Johansson, A. Junghans, A. Kelic-Heil, O. Kiselev,
A. Klimkiewicz, J. V. Kratz, R. Kr¨ucken, N. Kurz, M. Labiche, T. Le Bleis, R. Lem-
mon, Yu A. Litvinov, K. Mahata, P. Maierbeck, A. Movsesyan, T. Nilsson, C. No-
ciforo, R. Palit, S. Paschalis, R. Plag, R. Reifarth, D. Savran, H. Scheit, H. Simon,
K. S¨ummerer, A. Wagner, W. Walua, H. Weick, and M. Winkler. Measurement of
the dipole polarizability of the unstable neutron-rich nucleus 68Ni. Phys. Rev. Lett.,
111(24):1–6, 2013.

[101] O. Wieland, A. Bracco, F. Camera, R. Avigo, H. Baba, N. Nakatsuka, T. Aumann,
S. R. Banerjee, G. Benzoni, K. Boretzky, C. Caesar, S. Ceruti, S. Chen, F. C. L. Crespi,
V. Derya, P. Doornenbal, N. Fukuda, A. Giaz, K. Ieki, N. Kobayashi, Y. Kondo,

189

S. Koyama, T. Kubo, M. Matsushita, B. Million, T. Motobayashi, T. Nakamura,
M. Nishimura, H. Otsu, T. Ozaki, A. T. Saito, H. Sakurai, H. Scheit, F. Schindler,
P. Schrock, Y. Shiga, M. Shikata, S. Shimoura, D. Steppenbeck, T. Sumikama,
S. Takeuchi, R. Taniuchi, Y. Togano, J. Tscheuschner, J. Tsubota, H. Wang, K. Wim-
mer, and K. Yoneda. Low-lying dipole response in the unstable 70Ni nucleus. Phys.
Rev. C, 98(6):064313, 2018.

[102] M. M. Rajabali, R. Grzywacz, S. N. Liddick, C. Mazzocchi, J. C. Batchelder, T. Bau-
mann, C. R. Bingham, I. G. Darby, T. N. Ginter, S. V. Ilyushkin, M. Karny, W. Kr´olas,
P. F. Mantica, K. Miernik, M. Pf¨utzner, K. P. Rykaczewski, D. Weisshaar, and J. A.
Winger. β decay of72Co and microsecond isomers in even-mass neutron-rich nickel
isotopes. Journal of Physics G, 41(11), 2014.

[103] A. I. Morales, G. Benzoni, H. Watanabe, S. Nishimura, F. Browne, R. Daido, P. Door-
nenbal, Y. Fang, G. Lorusso, Z. Patel, S. Rice, L. Sinclair, P. A. S¨oderstr¨om,
T. Sumikama, J. Wu, Z. Y. Xu, A. Yagi, R. Yokoyama, H. Baba, R. Avigo, F. L.
Bello Garrote, N. Blasi, A. Bracco, F. Camera, S. Ceruti, F. C.L. Crespi, G. De Angelis,
M. C. Delattre, Zs Dombradi, A. Gottardo, T. Isobe, I. Kojouharov, N. Kurz, I. Kuti,
K. Matsui, B. Melon, D. Mengoni, T. Miyazaki, V. Modamio-Hoyborg, S. Momiyama,
D. R. Napoli, M. Niikura, R. Orlandi, H. Sakurai, E. Sahin, D. Sohler, H. Shaffner,
R. Taniuchi, J. Taprogge, Zs Vajta, J. J. Valiente-Dob´on, O. Wieland, and M. Yal-
cinkaya. Low-lying excitations in Ni 72. Phys. Rev. C, 93:034328, 2016.

[104] E. A. McCutchan. Nuclear Data Sheets for A=68. Nuclear Data Sheets, 113:1735–1870,

2012.

[105] J. C. Hardy, L. C. Carraz, B. Jonson, and P. G. Hansen. The essential decay of
pandemonium: A demonstration of errors in complex beta-decay schemes. Physics
Letters B, 71(2):307–310, 1977.

[106] B. Rubio, W. Gelletly, E. N´acher, A. Algora, J. L. Ta´ın, A. P´erez, and L. Caballero.
Beta decay studies with the total absorption technique: Past, present and future.
Journal of Physics G: Nuclear and Particle Physics, 31(10):S1477, 2005.

[107] M. Wang, G. Audi, F.G. Kondev, W.J. Huang, S. Naimi, and X. Xu. The Ame2016

atomic mass evaluation. Chinese Physics C, 41:030003, 2017.

[108] A. Spyrou, A. C. Larsen, S. N. Liddick, F. Naqvi, B. P. Crider, A. C. Dombos, M. Gut-
tormsen, D. L. Bleuel, A. Couture, L. Crespo Campo, R. Lewis, S. Mosby, M. R.
Mumpower, G. Perdikakis, C. J. Prokop, S. J. Quinn, T. Renstrøm, S. Siem, and
R. Surman. Neutron-capture rates for explosive nucleosynthesis: the case of 68Ni(n,
γ)69Ni. Journal of Physics G, 44:044002, 2017.

[109] R. Schwengner, S. Frauendorf, and B. A. Brown. Low-Energy Magnetic Dipole Radi-

ation in Open-Shell Nuclei. Physical Review Letters, 118(9):092502, 2017.

190