VALIDATION OF THE β-OSLO METHOD; AN INDIRECT METHOD

FOR CONSTRAINING NEUTRON-CAPTURE CROSS SECTIONS

By

Katherine Louise Childers

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Chemistry - Doctor of Philosophy

2021

ABSTRACT

VALIDATION OF THE β-OSLO METHOD; AN INDIRECT METHOD FOR

CONSTRAINING NEUTRON-CAPTURE CROSS SECTIONS

By

Katherine Louise Childers

One of the prevalent questions in nuclear science is the origin of the elements. There

are two stellar nucleosynthesis processes considered to be responsible for the production

of the majority of the abundances of the elements heavier than iron; the slow neutron-

capture process (s-process) and the rapid neutron-capture process (r-process). Both of these

processes are characterized by the successive capture of neutrons on nuclei, with the major

differences between the processes being the timescale over which the processes occur and the

host environment. The s-process occurs in low neutron-density environments, such as low-

to intermediate-mass stars, and proceeds slowly along the valley of stability. Since the nuclei

involved are close to stability, the reactions involved are amenable to direct measurements.

The r-process progresses through an explosive event with high neutron densities which drives

material far from stability. The recent observation of a neutron star merger event by LIGO

and Virgo and the subsequent electromagnetic follow up has demonstrated that an r-process

event can occur in these rare events, but it has not ruled out other potential astrophysical

sites. To better understand and model the r-process, several nuclear properties are needed

for a large number of nuclei, including neutron-capture cross sections. R-process nuclei are

not viable for direct measurement of neutron-capture cross sections since the nuclei involved

are far from stability, and thus have short half-lives. Therefore, several indirect measurement

techniques have been developed to provide experimental constraints on neutron-capture cross

sections. One such method is the β-Oslo method, which uses β decay to populate highly

excited states of a nucleus. The resulting de-excitation via the emission of γ rays is used

to extract statistical nuclear properties of the daughter nucleus. These properties are then

used as input in a reaction model to constrain the neutron-capture cross section. The β-

Oslo method can provide a large number of constrained neutron-capture cross sections far

from stability, but it is necessary to validate the method using a direct neutron capture

measurement. This work will present a validation of the β-Oslo method in the A = 80

mass region with the 82Se(n,γ)83Se reaction. The nuclide 83Se can be accessed through the

β-decay of 83As, which was studied at the National Superconducting Cyclotron Laboratory

with the total absorption spectrometer, SuN. Using the β-Oslo method, the cross section

of the 82Se(n,γ)83Se reaction was constrained. A direct measurement of the 82Se(n,γ)83Se

reaction was performed with the Detector for Advanced Neutron Capture Experiments and

the cross section obtained from the direct measurement is compared to the cross section

determined using the β-Oslo method. The results are in good agreement, validating the

β-Oslo method as a viable method for constraining neutron-capture cross sections.

To Mom and Dad: Jo and Malcolm Childers

iv

ACKNOWLEDGMENTS

It has definitely been a journey to get to this point, and I have met so many amazing people

along the way. It is hard to express in words how much I appreciate all of you, but I will

try!

First off, I would like to thank my advisor, Sean Liddick. Thank you for giving me so

many opportunities to learn, through my research, the many experiments, and all of the

conferences and schools you encouraged me to go to. I appreciate your patience and all of

the knowledge you have passed on. (Also, thanks for all the fajitas.) I would also like to

thank my committee members: Paul Mantica, Dave Morrissey, and Artemis Spyrou. Thank

you all for your guidance and support. I have always felt that I could come talk to any of

you for advice or help.

A huge thank you goes to Aaron Couture. I dont think I would have been able to get

through the selenium analysis without you. Thank you for putting up with me for so long

(probably a little longer than expected...) and thank you for all the support and advice. I

am really lucky to have had the opportunity to work with you, and I have learned so much.

I would also like the thank the rest of the DANCE team: Chris Prokop, Cathleen Fry, Shea

Mosby, and John Ullmann. Being able to run an experiment out at LANL was an awesome

opportunity and I appreciate all of your support so much.

I would be remiss to not give a shout out to the Chemistry and Physics faculty at

Otterbein University, especially Robin Grote, Joan Esson, Carrigan Hayes and Jerry Jenkins.

You guys were supportive throughout undergrad and taught me the skills I needed to be

successful in graduate school and become the scientist I am today. I have many fond memories

of all of you and my time at Otterbein.

v

Graduate school would not be possible without the support and encouragement of friends,

and I have made some wonderful friends during my time here. Becky Lewis, thank you for

welcoming me in when I started grad school and showing me the ropes, and for always

cheering me on, even from afar. Ben Crider, thank you for your help (and infinite patience)

with analysis and coding. I have learned so much from you. Andrea Richard, a simple thank

you isn’t enough. You have been there for me through some tough times, and you always

know what to say to support and encourage me. Thank you for all of your mentorship, and

most of all, your friendship. Thank you to the many other friends I have made: Kyle Brown,

Stephanie Lyons, Mallory Blyth, Caley Harris, Alicia Palmisano, Aaron Chester, and many

more. I appreciate you guys so much and will cherish the many memories.

Lastly, thank you to my family. Aunt Cathy, thank you for always being so excited and

encouraging me to go for what I wanted. The time I have spent with you has been a big part

of my life. Those of you that know me know that I of course need to mention the smallest

member of my family, my guinea pig Revan. You won’t be able to read this but thank you

for being the best little buddy and roommate. Most importantly, thank you to my parents,

Jo and Malcolm Childers. I am where I’m at today because of you. Thank you for your

endless support, for cheering on every accomplishment, no matter how big. I love you both

so much.

vi

TABLE OF CONTENTS

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

ix

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

x

Chapter 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Stellar nucleosynthesis of heavy elements . . . . . . . . . . . . . . . . . . . .
1.2 The rapid neutron-capture process
. . . . . . . . . . . . . . . . . . . . . . .
1.3 Uncertainties of nuclear properties . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Hauser-Feshbach model of neutron capture . . . . . . . . . . . . . . . . . . .
1.4.1 Optical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 Nuclear level density models . . . . . . . . . . . . . . . . . . . . . . .
1.4.3
. . . . . . . . . . . . . . . . . . . . .
1.5
Indirect techniques for constraining (n,γ) cross sections . . . . . . . . . . . .
1.6 Current status of β-Oslo validation . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.7 Dissertation Outline

γ-ray strength function models

Chapter 2

Study of 83As β decay at the NSCL . . . . . . . . . . . . . . . . .
2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 The Summing NaI (SuN) detector . . . . . . . . . . . . . . . . . . . .
2.1.2 Double-sided silicon strip detector . . . . . . . . . . . . . . . . . . . .
Isolation of 83As β decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

Chapter 3

β-Oslo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Population of highly excited states in 83Se . . . . . . . . . . . . . . . . . . .
3.2 Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Extraction of primary γ rays . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Extraction of the functional forms of the NLD and γSF . . . . . . . . . . . .
3.5 Normalization of the NLD and γSF . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 NLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Limited spin population . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.3
γSF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Constraint of 82Se(n,γ)83Se via the β-Oslo Method . . . . . . . . . . . . . .

Chapter 4 Direct Measurement of 82Se(n,γ)83Se . . . . . . . . . . . . . . . .
4.1 DANCE: The Detector for Advanced Neutron Capture Experiments . . . . .
4.2 Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Neutron Fluence Characterization . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Normalization to 197Au . . . . . . . . . . . . . . . . . . . . . . . . .
82Se Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Background Subtraction . . . . . . . . . . . . . . . . . . . . . . . . .

4.5

vii

1
1
3
5
7
8
10
14
17
19
19

21
21
22
26
28

48
49
51
54
55
57
58
59
60
62

66
66
71
72
73
76
79
80

4.5.1.1
Scattering Background . . . . . . . . . . . . . . . . . . . . .
4.5.1.2 Target contaminants . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Efficiency Determination . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Cross Section Results . . . . . . . . . . . . . . . . . . . . . . . . . . .

82
83
87
98

Chapter 5 Results and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 101
5.1 Comparison of β-Oslo Cross Section to Directly Measured Cross Section . . . 101
5.2 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

viii

LIST OF TABLES

Table 2.1: Voltage applied to each PMT and scaling factors used for gain matching
for SuN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

Table 2.2: Scale factor and intercept used for the calibration of SuN’s segments. . . .

27

Table 2.3: Scaling factors used for gain matching the front and back strips of the DSSD. 31

Table 2.4: Half-lives of implanted isotopes and their decay products.

. . . . . . . . .

32

Table 3.1: GDR parameters determined from the fit of a GLO function to photoab-
. . . . . . . . . . . . . . . . . . . . . . . . . .

sorption cross section data.

63

Table 3.2: NLD and γSF models available in TALYS.

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

65

Table 4.1: Composition of the enriched 82Se target and the Q-value of neutron capture
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

on each isotope.

71

Table 4.2: ESum gate used for each isotope identified in the 82Se target data.

. . . .

86

Table 4.3: Efficiencies determined by DICEBOX and GEANT4 simulations (M = [2,5],

2−, 3

2−. 100000 γ-ray cascades

5.0 MeV > ESum > 5.9 MeV) for J π = 1
were simulated for 30 realizations of artificial nuclei.

2+, 1

. . . . . . . . . . . . 100

ix

LIST OF FIGURES

Figure 1.1: A schematic of the paths of both the s-process and r-process and the
. .

subsequent decay modes. From [2], c(cid:13) 2006 John Wiley & Sons, Inc.

Figure 1.2: Calculated residual abundances produced through the r-process, as a func-
tion of mass number. Reprinted from [3], with permission from Elsevier.

Figure 1.3: Residual solar r-process abundance pattern (black dots) compared to mod-
eled r-process abundance patterns using three different mass models. The
lighter bands represent the uncertainty of the calculation with the rms
error compared to known masses. The darker bands represent the uncer-
tainty when the rms error is artificially reduced to 100 keV. Reprinted
from [8], with permission from Elsevier. . . . . . . . . . . . . . . . . . . .

Figure 1.4:

(a) Comparison of the residual solar r-process abundance pattern to abun-
dance patterns modeled for the same three mass models as in Figure 1.3.
Here the uncertainty taken into account is that of the β-decay half-lives.
(b) Same as (a) but with the uncertainty of neutron-capture rates studied
instead of the β-decay half-lives. Reprinted from [8], with permission from
Elsevier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.5: Comparison of the 50Ti(n, γ)51Ti cross section constrained using the β-
Oslo and Oslo methods (grey crosses) to experimentally determined cross
sections (points). Reprinted figure with permission from [68] Copyright
2019 by the American Physical Society. . . . . . . . . . . . . . . . . . . .

Figure 2.1: A representation of the layout of the CCF (comprised of the K500 and
. . . . . . . . . .

K1200 cyclotrons) and the A1900 Fragment Separator.

Figure 2.2: A picture of the e14505 setup in the S2 vault. SuN is shown on the right
in the large blue box, the DSSD and veto and located in the center of
SuN (indicated by the purple box), and the PIN detectors are located
upstream of SuN in the red box. . . . . . . . . . . . . . . . . . . . . . . .

2

4

7

8

20

22

22

Figure 2.3: A schematic of the SuN detector.

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

23

Figure 2.4: An example of TAS for 60Co. On the left is the decay scheme of 60Co. On
the right is a figure from [71], showing the 60Co gamma spectra obtained
with (a) a single segment of SuN, (b) the top half of SuN, and (c) the
total summation of all segments. Reprinted from [71], with permission
from Elsevier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

x

Figure 2.5: A picture of the DSSD used for experiment e14505.

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

28

Figure 2.6: Gain matched energy spectra for the DSSD low gain setting. The front
(top) and back (bottom) strip numbers are shown as a function of channel
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
number.

Figure 2.7: Gain matched energy spectra for the DSSD hi gain setting, using a 228Th
source. The front (top) and back (bottom) strip numbers are shown as a
. . . . . . . . . . . . . . . . . . . . . . . . .
function of channel number.

Figure 2.8: Particle Identification plot. PIN Energy is from the first PIN detector
located upstream of SuN. TOF is determined from the timing between
the PIN detector and the focal plane scintillator located in the A1900
fragment separator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

30

32

Figure 2.9: SuN total absorption spectrum as a function of time.

. . . . . . . . . . .

33

Figure 2.10: (Top) Implantation rate of 83As ions in the DSSD. (Bottom) Implantation
rate of 84Se ions in the DSSD. . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.11: Complete level scheme of the decay of 84Se into 84Br from ENSDF. Ab-
solute γ-ray intensities per 100 decays listed next to γ-ray energies. [73] .

Figure 2.12: (Top) TAS spectrum as a function of time gated on the 408 keV peak
corresponding to 84Br (only first three beam cycles shown) with the de-
cay profile modeled via the Bateman equations overlaid. (Bottom) TAS
spectrum as a function of time gated on the 2053 keV peak that has con-
tributions from the decay chain of 83As → 83Se → 83Br (only first three
beam cycles shown) with the decay profile of each decay, as well as the
. . . . . . . . . . . .
total, modeled via the Bateman equations overlaid.

Figure 2.13: Activity profiles of all decaying species modeled with the Bateman equa-
tions, shown over the full time range. . . . . . . . . . . . . . . . . . . . .

34

35

36

37

Figure 2.14: Regions of production and decay during the pulsed beam setting.

. . . .

38

Figure 2.15: Plot of the long decay period during which the beam was not being deliv-
. . . . . . . . . . . . . . . . . . . .

ered to the experimental end station.

Figure 2.16: Excitation energy (Ex) as a function of γ-ray energy (Eγ), ungated, with
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

all events.

Figure 2.17: Ex, Eγ matrix with 50 keV binning, for a time gate of 26000 seconds to
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

the end of the run.

39

40

40

xi

listed next to γ-ray energies. [74]

Figure 2.18: Decay scheme of 83Br → 83Kr. Absolute γ-ray intensities per 100 decays
. . . . . . . . . . . . . . . . . . . . . .
Figure 2.19: Ex, Eγ matrix with 50 keV binning, for the decay of 83Br → 83Kr simu-
lated in Geant4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figure 2.20: Ex, Eγ matrix with 50 keV binning, for the decay of 83Se → 83Br. . . . .
Figure 2.21: Decay scheme of 83Se → 83Br with selected levels and γ-ray transitions.

41

41

42

Absolute γ-ray intensities per 100 decays listed next to γ-ray energies. [74] 42

Figure 2.22: Ex, Eγ matrix with 50 keV binning, for the decay of 84Se → 84Br simulated
in Geant4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

of 83Se → 83Br and 84Br → 84Kr.

Figure 2.23: Ex, Eγ matrix with 50 keV binning, for the decays of the isomeric state
. . . . . . . . . . . . . . . . . . . . .
Figure 2.24: Decay scheme of the isomeric state of 83Se → 83Br with selected levels and
γ-ray transitions. Absolute γ-ray intensities per 100 decays listed next to
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
γ-ray energies. [74]
Figure 2.25: Decay scheme of 84Br → 84Kr with selected levels and γ-ray transitions.

43

43

44

Absolute γ-ray intensities per 100 decays listed next to γ-ray energies. [73] 45

Figure 2.26: Ex, Eγ matrix with 50 keV binning, for the decay of 83As → 83Se.

. . .

45

trum of 83Se.

Figure 2.27: (Top) γ-ray energy spectrum of 83Se. (Bottom) Excitation energy spec-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figure 2.28: Decay scheme of 83As → 83Se with selected levels and γ-ray transitions.
γ-ray intensities relative to the 734.9 keV transition listed next to γ-ray
energies. [74]
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.1: Flow chart of Oslo method. Bold items are programs used for the respec-
. . . . . . . . . . . . . . .

tive steps in the flow chart. Figure from [75].

Figure 3.2: Schematic of the population of states in 83Se through the β decay of 83As
. . . . . . . . . . . . . . . . . . . . . . . .

and neutron capture on 82Se.

46

47

50

51

Figure 3.3: Unfolded Ex, Eγ matrix for 83Se, with 50 keV binning.

. . . . . . . . . .

54

Figure 3.4: Primary Ex, Eγ matrix for 83Se, with 200 keV binning. . . . . . . . . . .

56

xii

Figure 3.5: Nuclear level density for 83Se, with the experimental data (black circles) as
well as the upper and lower limits (blue band). Known levels are indicated
by the solid black line, the level density at the neutron separation energy,
ρ(Sn), is indicated by the white square, and the Constant Temperature
. . . . . . . . . .
model extrapolation is shown as the dashed black line.

Figure 3.6: Percentage of the total level density of 83Se determined from Ref. [37] as
a function of the spin. Spin range highlighted in blue represents the spin
range populated following an allowed β decay and one dipole transition.

Figure 3.7: Gamma strength function for 83Se (black circles) with the upper and
lower limits based on systematic uncertainty are indicated by the blue
band. Photoabsorption cross section data from [81] (green squares, blue
triangles, purple circles) and the corresponding fit of the GLO function to
the data and an average fit are also shown. . . . . . . . . . . . . . . . . .

Figure 3.8: A plot of χ2 values versus a range of Γγ values, obtained from fitting the
average GDR resonance parameters to the experimental γSF to determine
the best Γγ for the data set. . . . . . . . . . . . . . . . . . . . . . . . . .

60

61

62

63

Figure 3.9: Cross section of the 82Se(n,γ)83Se reaction calculated using TALYS (black).
The upper and lower limits (light blue) are based on the uncertainty of
the experimental NLD and γSF. The grey band shows the range of cross
sections resulting from combinations of all available NLD and γSF models. 64

Figure 4.1: Schematic representation of the DANCE detector geometry, including the
. . . . . . . . . . . . . . . . . . . . . . . . .

beam-line, and LiH sphere.

Figure 4.2: Example of signals from a γ ray and an alpha particle, from a single BaF2
crystal. c(cid:13) 2006 IEEE Reprinted, with permission, from [94]. . . . . . . .

Figure 4.3: Short integral of the detector signal versus the long integral of detector
signal from the data taken with the 82Se target. Gate used to separate
alpha signals shown in red. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.4: Photographs of 82Se target and target holder from a top down view (left)
. . . . . . . . . . . . . . . . . . . . . . . . . . .

and a side view (right).

Figure 4.5:

(Left) Representation of fit used for calibration with a 22Na source. (Right)
Calibrated 22Na spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.6: Alpha decay spectra of one crystal and representation of the fit used for
. . . . . . . . . . . . . . . . . . . . . . . .

crystal-by-crystal calibration.

67

68

69

72

73

74

xiii

Figure 4.7:

(a) Neutron yield measured by the 6Li beam monitor.
(b) ENDF/B-
VII.1 evaluated cross section of 6Li(n, α)3H used in the neutron fluence
determination.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.8:

(a) Neutron yield measured by the gas-filled 235U fission chamber. (b)
ENDF/B-VII.1 evaluated cross section of 235U(n, f ) used in the neutron
fluence determination.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.9: Neutron fluence at the beam monitor position as a function of neutron
energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.10: 2D plot of ESum as a function of En for the 197Au data, over the 4.89 eV
resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.11: Figure depicting the subtraction of a linear background from the time-
of-flight spectrum of neutron capture on 197Au. The blue histogram is
the data pre-subtraction, and the magenta histogram is the data after
subtraction of the linear background, shown in red.
. . . . . . . . . . . .

Figure 4.12: Diagnostic plot showing the ESum projections of the different components
of the background subtraction on the 4.89 eV 197Au resonance. The total
ESum shape (red) corresponds to the data before the background subtrac-
tion was performed. The magenta ESum shape corresponds to the sum of
the background regions on either side of the resonance. The blue ESum
shape is the background subtracted capture ESum.
. . . . . . . . . . . .

Figure 4.13: Cross section of neutron capture on 197Au, in the region of the 4.89 eV
resonance (black squares). The scaled ENDF/B-VII.1 cross section is
shown in red [96]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.14: Counts as a function of the sum of energy deposited in DANCE (ESum)
and neutron energy (En) for the 82Se data. . . . . . . . . . . . . . . . . .

Figure 4.15: Counts as a function of the sum of energy deposited in DANCE (ESum)
and neutron energy (En) for the 208Pb data. . . . . . . . . . . . . . . . .

Figure 4.16: Example scattering background subtraction for a single En bin on a 82Se
resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.17: Counts as a function of the sum of energy deposited in DANCE (ESum)
and neutron energy (En) for the 82Se data, after the scattering background
was subtracted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.18: Yield of neutron capture on 82Se, gated on an ESum range of 5.0 - 5.9
. .

MeV. Contributions of resonances from other Se isotopes are labeled.

75

75

76

78

79

80

81

82

84

84

85

88

xiv

Figure 4.19: ESum projection of (a) 77Se (b) 74Se (c) 78Se and (d) 80Se . . . . . . . .

88

Figure 4.20: Spectra of 74Se (with 77Se contributions removed) gated on an ESum
range of 7.7 - 8.6 MeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.21: Yield of neutron capture on 82Se, gated on an ESum range of 5.0 - 5.9
. . . . . . .

MeV, after the contribution from 74Se has been subtracted.

Figure 4.22: Spectra of 78Se (with 77Se and 74Se contributions removed) gated on an
. . . . . . . . . . . . . . . . . . . . . . . .

ESum range of 6.8 - 7.7 MeV.

Figure 4.23: Yield of neutron capture on 82Se, gated on an ESum range of 5.0 - 5.9
MeV, after the contributions from 74Se and 74Se have been subtracted.
.

Figure 4.24: Spectra of 80Se (with 77Se, 74Se, and 78Se contributions removed) gated
. . . . . . . . . . . . . . . . . . . .

on an ESum range of 6.4 - 6.8 MeV.

89

89

90

90

91

Figure 4.25: Yield of neutron capture on 82Se, gated on an ESum range of 5.0 - 5.9

MeV, after the contributions from 74Se, 78Se and 80Se have been subtracted. 91

Figure 4.26: Energy of individual γ rays, gated on multiplicity 2, for several strong reso-

nances in the 82Se data compared to simulated data for J π = 1
Points correspond to the average across all realizations, while error bars
correspond to the standard deviation of the bin content for each realiza-
tion. The integral of each plot is normalized to unity for a true comparison. 94

2+, 1

2−, 3

2−.

Figure 4.27: Energy of individual γ rays, gated on multiplicity 3, for several strong reso-

nances in the 82Se data compared to simulated data for J π = 1
Points correspond to the average across all realizations, while error bars
correspond to the standard deviation of the bin content for each realiza-
tion. The integral of each plot is normalized to unity for a true comparison. 95

2+, 1

2−, 3

2−.

Figure 4.28: Energy of individual γ rays, gated on multiplicity 4, for several strong reso-

nances in the 82Se data compared to simulated data for J π = 1
Points correspond to the average across all realizations, while error bars
correspond to the standard deviation of the bin content for each realiza-
tion. The integral of each plot is normalized to unity for a true comparison. 96

2+, 1

2−, 3

2−.

Figure 4.29: Energy of individual γ rays, gated on multiplicity 5, for several strong reso-

nances in the 82Se data compared to simulated data for J π = 1
Points correspond to the average across all realizations, while error bars
correspond to the standard deviation of the bin content for each realiza-
tion. The integral of each plot is normalized to unity for a true comparison. 97

2+, 1

2−, 3

2−.

xv

Figure 4.30: Simulation efficiencies and their uncertainties as a function of the lower
ESum gate boundary, for M = [2,5] and an upper ESum gate boundary
of 5.9 MeV.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.31: Cross section of the 82Se(n,γ)83Se reaction measured with DANCE. . . .

98

99

Figure 5.1: Comparison of the directly measured cross section of 82Se(n,γ)83Se (black)
to the neutron capture cross section determined via the β-Oslo method
(black line). The blue lines indicate the upper and lower limits of the cross
section determined via the β-Oslo method through a systematic study of
the uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

xvi

Chapter 1

Introduction

1.1 Stellar nucleosynthesis of heavy elements

The origin of the elements remains one of the mysteries that scientists are still working to

understand today. It is known that the majority of the elements on Earth were not created

terrestrially and instead were present when the Earth was formed. So where did they come

from? The lightest nuclei (hydrogen, helium, and trace amounts of lithium) were created

through primordial nucleosynthesis during the Big Bang. After the Big Bang, as galaxies and

the earliest stars, or protostars, began forming, conditions became right for fusion reactions

to begin, starting a chain of stellar nucleosynthesis pathways. These fusion reactions are
responsible for the production of most of the nuclei up to A ∼ 60. However, around A ∼

60, there is a peak in the nuclear binding energy of nucleons as a function of mass, and

combined with the large Coulomb barrier between charged particles, these fusion reactions

are no longer energetically favored. A reaction that is energetically favorable is neutron

capture, since there is no Coulomb barrier hindering the addition of a neutron to nuclei.

Neutron capture is instead influenced by the free neutron density in the stellar environment.

There are two main neutron capture processes, the slow neutron-capture process (s-process),

and the rapid neutron-capture process (r-process). The s-process is characterized by a low
neutron density (∼ 1010/cm3 ) environment [1], which leads to a relatively long time between

1

neutron captures, hundreds or thousands of years, compared to the relatively quicker β-

decay half lives. This keeps the s-process close to the valley of stability. A schematic of the

s-process pathway is shown in Figure 1.1. Since the nuclei involved in the s-process are close

to stability, many of the properties of these nuclei have been experimentally determined, and

therefore, through the use of astrophysical models, the basic mechanisms and astrophysical

sites of the s-process are fairly well constrained. Currently, theoretical studies support low

to intermediate mass asymptotic giant branch (AGB) stars as one of the sites of the s-

process [1]. Unlike the s-process, there is much that is still unknown about the r-process,

which will be discussed in more detail in the following section.

Figure 1.1: A schematic of the paths of both the s-process and r-process and the subsequent
decay modes. From [2], c(cid:13) 2006 John Wiley & Sons, Inc.

2

1.2 The rapid neutron-capture process

The r-process occurs in stellar environments with a much higher neutron density (∼ 1020/cm3)

than the s-process, and because of this, the rate of neutron capture is also much higher. In

most cases, the time scale of neutron capture reactions will be much less than β-decay

half-lives (on the order of fractions of a second), leading to many rapid, sequential neu-

tron captures before β decaying, creating a zig-zag pattern progressing up the chart of the

nuclides. This drives the r-process farther from stability, as shown in Figure 1.1, to the

neutron-rich region of the chart of the nuclides. Eventually, the neutron density will drop,

neutron-capture reactions will cease, and the neutron-rich nuclei produced will β decay back

to stability, populating the nuclei in between.

The observed solar abundance of heavy nuclei produced is assumed to be a combination

of both the s-process and the r-process. (As a note: The solar abundances are considered

here as the default abundances of elements in the universe, or the cosmic abundances.) Since

the s-process is better understood and easier to model, the solar abundance pattern resulting

from the r-process is determined by subtracting the contribution of the s-process from the

total observed solar abundance. The resulting r-process residual abundance pattern is shown

in Figure 1.2. The three main peaks that are visible in the r-process abundance, at A = 80,

135, and 195, correspond to the shell closures at the magic neutron numbers of 50, 82, and

126 (see Figure 1.1). Nuclei with these magic numbers will have additional stability, and

will therefore accumulate as the reaction flow passes through them, leading to an increase

in their abundance.

Due to the exotic nature of the nuclei produced along the r-process path, there is uncer-

tainty in the properties of many of these nuclei, as well as the general astrophysical conditions

3

Figure 1.2: Calculated residual abundances produced through the r-process, as a function of
mass number. Reprinted from [3], with permission from Elsevier.

that drive the r-process. In order to define the astrophysical conditions of the r-process, the

astrophysical locations must be determined. While there have been many locations proposed,

the most likely candidates are supernovae and neutron star mergers [1, 3]. Unfortunately,

there has been no evidence of r-process nuclei observed in supernova events so far, and even

the most promising models have issues, such as not producing a successful explosion or the

heaviest nuclei, that prevent a conclusive result [1]. Neutron-star mergers were originally put

forth as a potential r-process site, as this site has the high neutron density needed to support

the r-process. However, until recently, a neutron-star merger had never been observed, and

thus were not considered to be as likely as supernova. In August of 2017, the Advanced

LIGO and Advanced Virgo gravitational-wave detectors made the first observation of a neu-

tron star merger, GW170817 [4]. The subsequent transient kilonova event that was observed

had characteristics consistent with what would be expected of an r-process environment and

4

the production of lanthanide elements [5–7], supporting neutron-star mergers as a site of

the r-process. There are still many questions remaining about astrophysical conditions and

other possible astrophysical sites have been hypothesized [8]. Every astrophysical site is

characterized by distinct conditions, including the temperature, neutron density, and initial

composition. These different conditions will produce a unique abundance pattern, which can

be modeled and compared to the observed solar r-process abundance pattern. Comparisons

have proven to be difficult, however, due to the uncertainties the nuclear properties that are

needed for these models, namely, the masses, β-decay half lives, and neutron-capture cross

sections.

1.3 Uncertainties of nuclear properties

In order to determine the impact that the uncertainties of nuclear properties have on mod-

eled abundance patterns, a study employing Monte Carlo simulations was performed by

Mumpower et al. [8]. The masses, β-decay half-lives, and neutron-capture cross sections

over a large mass range were varied using a probability distribution based on the current

uncertainties of each property, and for each set of inputs, a simulated r-process abundance

pattern was generated. Shown in Figure 1.3 are abundance patterns calculated using three

different mass models (HFB-17 [9], DZ [10], and FRDM1995 [11]). Based on a comparison

to measured masses, the uncertainty of the masses calculated via the models was determined

to be 500 keV rms. The uncertainty in the calculated abundance pattern, based on the

propagation of the mass uncertainty, can be large, causing difficulty in comparing to the

known abundance pattern. If an artificial reduction of the uncertainty is performed, to 100

keV rms (indicated by the dark band in Figure 1.3), then the calculated abundance pat-

5

tern become more distinct, but in some areas the uncertainty still remains large. However,

without this reduction, the light band represents the current predictive power of these mass

models. For β-decay half lives, current uncertainties were approximated to be a factor of 10

based on a comparison of known experimental half-lives to a global QRPA calculation of half-

lives [8]. For neutron-capture cross sections, a comparison of experimental values to those

calculated using three different models (TALYS [12], NONSMOKER [13], and CIGAR [14])

led to the determination of a current uncertainty of a factor of 1000. Shown in Figure 1.4

are abundance patterns calculated with the uncertainties associated with β-decay half lives

and neutron-capture rates. Again, these uncertainty bands are large. With the uncertainty

of the masses, β-decay half-lives, and neutron-capture cross sections combined, it becomes

clear that the current theoretical models used to predict these inputs lead to error bars that

are too large to distinguish between different astrophysical models. Therefore, the reduction

of uncertainty introduced into the calculation of abundance patterns from nuclear properties

of heavy nuclei is of great importance. There have been advances in the measurements of

both masses ( see References [15–18] for a selection of recent work) and β-decay half-lives

(see References [19–22]) of nuclei that are critical for r-process simulations. However, the un-

certainty in neutron-capture cross sections for most r-process nuclei remain large due to the

difficulty of directly measuring these reactions. A direct measurement of a neutron-capture

reaction requires a target of the nucleus of interest, which, in the case of r-process nuclei far

from stability, is not feasible due to their short half lives. This has led to the development

of indirect methods of constraining neutron-capture cross sections using experimental infor-

mation [23]. Many of these indirect methods (as well as current theoretical cross-section

calculations) rely on the Hauser-Feshbach statistical model of neutron capture.

6

Figure 1.3: Residual solar r-process abundance pattern (black dots) compared to modeled
r-process abundance patterns using three different mass models. The lighter bands represent
the uncertainty of the calculation with the rms error compared to known masses. The
darker bands represent the uncertainty when the rms error is artificially reduced to 100 keV.
Reprinted from [8], with permission from Elsevier.

1.4 Hauser-Feshbach model of neutron capture

In lieu of directly measuring neutron-capture reactions, the cross section can be calculated

using the Hauser-Feshbach model of neutron capture [24]. The Hauser-Feshbach model

describes neutron capture as a two-step process; first, a compound nucleus is formed, and

second, the compound nucleus decays via the emission of γ rays.

It is assumed that the

second step is independent of the first step [25], and therefore, the subsequent decay of the

compound nucleus is independent of the method through which the nucleus was formed.

Instead, the decay is governed by the statistical properties of the nucleus. The Hauser-

Feshbach model relies on information about the interaction between the neutron and the

target nucleus (optical model potential - discussed in Section 1.4.1), as well as information

7

Figure 1.4: (a) Comparison of the residual solar r-process abundance pattern to abundance
patterns modeled for the same three mass models as in Figure 1.3. Here the uncertainty
taken into account is that of the β-decay half-lives. (b) Same as (a) but with the uncertainty
of neutron-capture rates studied instead of the β-decay half-lives. Reprinted from [8], with
permission from Elsevier.

describing statistical properties of the compound nucleus formed during the reaction (nuclear

level density - Section 1.4.2 and γ-ray strength function - Section 1.4.3).

In many cases,

especially for r-process nuclei, most of this information is not known, so theoretical models

are required to obtain the necessary information. Validating indirect means of inferring

neutron-capture rates, which is the subject of this thesis, is necessary to provide confidence

when extrapolating theoretical models to unknown nuclei.

1.4.1 Optical model

An optical model potential is used to describe the interaction that takes place between the

target nucleus and the incoming neutron. The central assumption of the optical model

8

is that the complicated interaction can be represented by a single mean field potential.

There are two main types of optical model potentials - a phenomenological potential, and a

microscopic potential. The optical model potential most often used for r-process calculations

is that of Koning and Delaroche [26], which is a phenomenological optical model. A suitable

analytical form for the potential is chosen (often the Woods-Saxon potential), and parameters

are determined via fitting to experimental data, where available. If experimental data are

not available, a global parameterization is used. In a microscopic optical model potential,

the strength and shape of the nuclear potential is calculated by folding the nucleon-nucleon

effective interaction with the nuclear density distribution. A semi-microscopic (in between

phenomenological and microscopic) optical model potential that is available and commonly

used is the Jeukenne-Lejeune-Mahaux (JLM) model [27]. This potential usually results in

a calculated neutron-capture cross section that is within 20% of what would be obtained

using the Koning-Delaroche model. The most important quality (particularly for r-process

nuclei) of an optical model potential is that it is able to reliably predict nuclear properties

that are unable to be measured experimentally. Fortunately, for most r-process nuclei, the

uncertainty propagated from the optical model potential is the smallest source of uncertainty

in the calculated cross section. Most of the uncertainty in the results of the Hauser-Feshbach

calculation comes from the models used for calculating the properties that will be discussed

next - the nuclear level density and the γ-ray strength function.

9

1.4.2 Nuclear level density models

The nuclear level density (NLD) is the number of energy levels available at a given excitation

energy (Ex), spin (J), and parity (π). It can be represented by the function:

ρ(Ex, J, π) = ∆N (Ex, J, π)/∆Ex,

(1.1)

where ∆N (Ex, J, π) is the number of levels with the energy bin ∆Ex. A level spacing

parameter, D(Ex, J, π), can be determined as the inverse of the level density,

D(Ex, J, π) = 1/ρ(Ex, J, π).

(1.2)

The total level density within an excitation energy bin can then be calculated by summing

over all spins and parities. In cases where only a subset of levels are populated, it is important

to know the distribution of the spin and parity amongst the states in the nucleus. The spin

and parity distributions are commonly assumed to be uncorrelated. The spin distribution,

s(Ex, J), is dependent on excitation energy and spin, and following Ericson [28], and can be

approximated as:

s(Ex, J) (cid:39) 2J + 1
2σ2(Ex)

− (J+1/2)2
2σ2(Ex) .

e

(1.3)

The σ2 parameter in Eq. 1.3 is called the spin cut-off parameter. This expression is de-

rived assuming that many particles and holes are excited to higher-lying states, and has
been found to be an appropriate approximation for J ≤ 30 [28]. In a study done by von

Egidy and Bucurescu [29], a set of 310 nuclei were fit with Eq. 1.4 to obtain an empirical

10

parameterization of σ2 based on its mass dependence.

σ2(Ex) = p1Ap2(E − 0.5P ´a)p3

(1.4)

From the fit of the above equation, it was determined that p1 = 0.391, p2 = 0.675, and p3 =

0.312. P ´a is the deuteron pairing energy, which can be calculated using mass excess values

M (A, Z) via:

P ´a =

1
2

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

(1.5)

The fit was repeated separately for sets of only the even-even, odd, and odd-odd nuclei

and the parameters determined from the fit were found to be essentially the same as the

parameters listed above, confirming this parameterization to be independent of nuclear shell

structure differences. It is worth noting that the nuclei used in this study were all stable or

close to stability. There is a trend in experimentally determined spin distribution favoring

lower spins at lower excitation energies and the distribution shifting to higher spins as the

excitation energy increases. It is assumed that this trend will hold for nuclei further from

stability, but as of now, the spin distribution is not considered to be well known for nuclei

at the far reaches of the nuclear chart.

The two parities (positive and negative) are usually assumed to be distributed equally

across all nuclear states, regardless of energy. It has been shown through several experimental

and theoretical studies that even if there is a deviation from an equal number of positive and

negative parities, it does not have a large effect of the determination of the level density [23].

11

The first nuclear level density model developed was the Fermi gas (FG) model, which

described the nucleus as a gas of nucleons arranged in single-particle orbits. These nucleons

behave in accordance with the Pauli exclusion principle, which states that they must each

have a unique set of quantum numbers.

In the lowest energy configuration of a nucleus,

the nucleons will fill up the lowest-energy single-particle states. When energy is added

to the nucleus, nucleons are excited to higher energy single particle states. The number

of available configurations and the density of the single particle states will both increase

with an increasing amount of energy available to the system. Using this description, Bethe

determined a level density function [30],

ρ(Ex) =

aEx

√
πe2
5/4
12a1/2E
x

(1.6)

where Ex is the excitation energy, and a is the level density parameter, determined using

the single particle level density parameters of protons (gp) and neutrons (gn),

√

π
6

a =

(gp + gn).

(1.7)

Since nucleons do interact, a modification was made to the FG model, and led to the Back-

shifted Fermi Gas (BSFG) model [31]:

ρ(Ex) =

√
πe2

a(Ex−∆)

12a1/2(Ex − ∆)5/4

.

(1.8)

The BSFG model includes a shift parameter, ∆, which is intended to take into account the

effect of the interactions of nucleons, based on the separation energy the interacting nucleons

must overcome [32,33]. ∆ can be calculated from the pairing energy of protons and neutrons,

12

but along with the level density parameter a, it can be adjusted to match an experimental

nuclear level density [12].

Another commonly used level density model is the Constant Temperature (CT) model

[34], which describes the level density by the function,

ρ(Ex) =

e(Ex−E0)/T

1
T

(1.9)

where Ex is the excitation energy and E0 and T are free parameters that are related to

an energy shift and constant temperature, respectively, that can be found by fitting to

experimental data. The CT model was found to reproduce known nuclear level densities

are lower excitation energies, while the FG and BSFG models were found to reproduce level

densities are higher energies better [34, 35]. For this reason, the CT and BSFG models are

often used together to describe a full range of excitation energy.

While the nuclear level density models described above do a reasonable job at reproducing

experimental data, they are unable to describe some of the finer details in the level density.

When used to extrapolate to nuclei far from the valley of stability, the nuclear level density

models become more unreliable, with no experimental data to help constrain the model,

which leads to a larger uncertainty in the calculated cross section. Ideally, a microscopic

model, based on fundamental interactions and first principles, would be used to calculate level

densities. However, the limits of computational power limit the applicability of microscopic

approaches to determining the nuclear level density. A recently developed approach by

Goriely et al. has been used to calculate level densities for a large range of nuclei (up to 150

MeV and J=30) using a Hartree-Fock basis [36]. Several other versions of this approach have

also been developed; the spin- and parity-dependent combined Hartree-Fock-Bogoliubov and

13

combinatorial method [37], and the temperature-dependent Hartree-Fock-Bogolyubov-plus-

combinatorial method [38]. To date, the efficacy of microscopic methods for level densities of

nuclei far from stability has been difficult to determine due to the scarcity of data available

for comparison.

1.4.3 γ-ray strength function models

The γ-ray transmission coefficient T (Eγ) represents the probability of a γ ray of energy Eγ
being emitted from a nucleus. T (Eγ) is related to the γ-ray strength function (γSF), f (Eγ),

through the expression

TXL(Eγ) = 2πE

(2L+1)
γ

fXL(Eγ),

(1.10)

where X denotes the type of electromagnetic radiation the transition is (E for electric and

M for magnetic), and L denotes the angular momentum. In general, the strength function

can be defined in terms of the average partial radiative width, ΓXL, of a γ ray of energy Eγ

from an initial energy level Ei, with a spin Ji and parity πi, and the level density at that

energy, ρ(Ei, Ji, πi) [39]:

←−
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)

Through the principle of detailed balance, this “downward” strength function (designated

by the left arrow symbol) describing γ decay, can be connected to the “upward” strength

function (designated by the right arrow symbol), which describes the reverse process of

photoabsorption. This “upward” strength function can be described in terms of the average

14

photoabsorption cross section, σ(Eγ) [39]:

−→
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

,

(1.12)

where Ef is the final state after absorption, with a spin Jf and parity πf . One feature of the

photoabsorption cross section that has been observed to be constant throughout the nuclear

chart is a broad E1 resonance, called the Giant Dipole Resonance (GDR). Through the

Brink hypothesis [40,41], which states that the shape of the photoabsorption cross section is

independent of the initial excitation energy of the nucleus, it can be assumed that the shape

of the E1 cross section at an excited state will be the same as at the ground state. Through

this assumption and the connection of the photoabsorption cross section to the γSF, the γSF

can be described using the shape of the lower energy tail of the GDR. Therefore, the GDR

can be used to help constrain models of the γSF, since there is generally more data available

on the GDR than on the γSF.

In order to describe the shape of the GDR, and in turn the γSF, several phenomenological

models have been developed. One of the first functions to be used to fit the GDR is the

Standard Lorentzian (SLO) function, which was developed by Brink and Axel [40, 41]. The

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

the GDR:

fXL(Eγ) = KXL

where KXL is defined as:

(E2

σXLEγΓ2

γ − E2

XL
XL)2 + E2

γΓ2

XL

,

(1.13)

KXL =

1

(2L + 1)π2¯h2c2

.

(1.14)

15

This function was found to fit the GDR well and was thus used to represent the E1 strength,

considered the dominant contribution to the GDR, as well as contributions from M1 and E2

transitions. Kopecky and Uhl introduced a temperature dependence to the SLO, in order

to account for a discrepancy between the SLO function and GDR data at lower energies,

that ultimately, can impact calculations of the neutron-capture cross section [42]. This new

function, the Generalized Lorentzian, is predominantly used to represent the E1 component

of the GDR and is also characterized by the energy (EE1), strength (σE1), and width (ΓE1)

of the GDR:

(cid:32)

fE1(Eγ, T ) = KE1

where

(E2

γ − E2

Eγ ˜ΓE1(Eγ)
E1)2 + E2
γ

˜ΓE1(Eγ)2

(cid:33)

+

0.7ΓE14π2T 2

E3
E1

σE1ΓE1,

(1.15)

The temperature, T , can be approximated by T ≈(cid:112)Ex/a, and is connected to the Fermi

E2
E1

(1.16)

.

˜ΓE1(Eγ) = ΓE1

E2

γ + 4π2T 2

Gas nuclear temperature, but currently it is often used as a free parameter when fitting data.

This function differs from the SLO function most significantly at lower γ-ray energies, but it

has been found to correct discrepancies in cross section calculations using the SLO function.

Recently, a surprising feature of the γSF was discovered - an enhancement in the strength

at low γ-ray energies (below 4 MeV) and high excitation energies. This feature has been

called the “upbend”, and was first seen in Fe isotopes in 2004 [43]. Since then, the upbend

has been observed in many other nuclei, including Mo [44, 45], Sc [46, 47], La [48], and

Sm [49]. One of the Mo studies used a different technique to determine the γSF [45], thus

confirming the upbend as being a feature of the γSF, and not the method used. The upbend

has been found to impact the calculation of neutron-capture cross sections, and therefore,

16

it is important to have a good understanding of the characteristics [50]. In a study of 56Fe,

the upbend was found to be predominantly dipole in nature [51], and while it is not clear

if the upbend is electric or magnetic, it has been shown to have a bias towards a magnetic

character [52], and the nuclear shell model also predicts a magnetic character [53].

Like the NLD, it would be best to use microscopic models of the γSF to determine

information about the finer details of the γSF and to be able to predict the shape of the

γSF for many nuclei, particularly those far from stability. While there has been much

research dedicated to microscopic modeling of the γSF, two publications in particular have

reported the results of large-scale calculations of γSF parameters. One of the publications

used the the quasi-particle random-phase approximation (QRPA) model incorporated into

Hartree-Fock models [54] and the other used the QRPA model incorporated into Hartree-

Fock-Bogoliubov [55] models.

1.5

Indirect techniques for constraining (n,γ) cross sec-

tions

The majority of the uncertainty in Hauser-Feshbach calculations of neutron-capture cross

sections comes from the unreliability of the nuclear level density and γ-ray strength function

models described above. To reduce the uncertainty of these calculations, the nuclear prop-

erties needed for neutron-capture cross section calculations need to be constrained based

on experimental data. Since neutron-capture reactions on nuclei far from stability are un-

able to be measured directly at this time, indirect methods have been developed. Four of

the major indirect techniques being used today are: the surrogate method [56], the γ-ray

strength function method [57, 58], the Oslo method [59–62], and the β-Oslo method [63].

17

The surrogate method utilizes charged particle reactions to populate the compound nucleus

that would be formed in the neutron-capture reaction of interest. The surrogate reactions

can be performed with both traditional stable-beam experiments, or in inverse kinematics

experiments. In normal kinematics, the targets available for measurement are restricted to

those that are stable or near stability. In inverse kinematics, though, the major limitation

is the ability of current facilities to deliver radioactive beams with a sufficient rate for the

measurement of interest. A recent validation of the surrogate method, in inverse kinematics,

for constraining neutron-capture cross sections cites a beam rate of at least 104 particles

per second is needed for successful measurements [64]. The γ-ray strength function method

utilizes photodisintigration reactions (γ, n) to study the γ-ray strength function of the com-

pound nucleus of interest. The goal is to infer the cross section of the inverse (n, γ) reaction.

As with other measurements, the γ-ray strength function method is also limited by the sta-

bility of the target needed for the reaction being studied. The Oslo method also utilizes

charged particle reactions to study the compound nucleus of the neutron-capture reaction of

interest, and is therefore also restricted by the stability of the targets needed. It has been

used extensively for nuclei along the valley of stability to extract nuclear level densities and

γ-ray strength functions, and has been shown to reliably reproduce known cross sections of

neutron-capture reactions. A method based on the Oslo method, the β-Oslo method, has

recently been developed. Instead of charged particle reactions, the β-Oslo method utilizes β

decay to populate the compound nucleus, which gives it the advantage of being applicable

to neutron-rich nuclei that are further from the valley of stability. As the subject of this

work, the β-Oslo method will be covered in more detail in Chapter 3.

18

1.6 Current status of β-Oslo validation

While the traditional Oslo method has been validated extensively [65–67], the β-Oslo method

has not been validated as extensively. To date, there is only one comparison of an (n, γ)

cross section constrained via the β-Oslo method to one determined through a direct mea-

surement [68]. The cross section of 50Ti(n, γ)51Ti was constrained by both the β-Oslo
method (via the measurement of 51Sc→51Ti) and the Oslo method (via the measurement of

50Ti(d, p)51Ti), and these results were then compared to existing data of a direct measure-

ment of 50Ti(n, γ)51Ti, as shown in Figure 1.5. All three cross sections were found to be in

good agreement, and it was concluded that the β-Oslo method is indeed a valid method for

constraining neutron-capture cross sections. However, since 50Ti is a lighter mass nucleus,

it has a lower level density, and it cannot be assumed that neutron capture on 50Ti proceeds

through a compound system. Therefore, a validation needs to be performed in a heavier mass

region, with a nucleus that has a higher level density and is, in principle, a more statistical

system.

1.7 Dissertation Outline

In this dissertation, the process of validating the β-Oslo method in a high mass region is

detailed. Chapter 2 covers the details of the β-decay experiment performed at the Na-

tional Superconducting Cyclotron Laboratory and the steps of the data analysis to isolate

the β decay of 83As. Chapter 3 provides the details of the β-Oslo method, along with the

results of the β-Oslo method applied to the β decay of 83As, to constrain the cross sec-

tion of 82Se(n, γ)83Se. Chapter 4 covers the experimental details of a direct measure of

82Se(n, γ)83Se performed at Los Alamos National Laboratory, along with the subsequent

19

Figure 1.5: Comparison of the 50Ti(n, γ)51Ti cross section constrained using the β-Oslo and
Oslo methods (grey crosses) to experimentally determined cross sections (points). Reprinted
figure with permission from [68] Copyright 2019 by the American Physical Society.

data analysis. Chapter 5 shows a comparison of the directly measure neutron-capture cross

section to the cross section obtain via the β-Oslo method, and provides a final conclusion

and an outlook of future work.

20

Chapter 2

Study of 83As β decay at the NSCL

2.1 Experimental Setup

An experiment measuring the β decay of 83As was performed at the National Superconduct-

ing Cyclotron Laboratory (NSCL) at Michigan State University in East Lansing, Michigan.

A primary beam of 86Kr at 140 MeV/µ was produced by the Coupled Cyclotron Facility

(CCF) and impinged on a 188 mg/cm2 9Be target, producing a cocktail beam with multiple

fragments. A schematic of the front end of the CCF is shown in Fig. 2.1. The fragments

were separated in the A1900 fragment separator [69,70] with a 0.5% momentum acceptance,

producing a beam centered on 83As that was delivered to the end station in the S2 vault. At

the end station, ions were implanted in a Si double sided strip detector (DSSD) located in

the center of the Summing NaI (SuN) detector [71], used to detect β-delayed γ rays. In or-

der to veto light ions, which could increase the background, a Si surface detector was placed

behind the DSSD. Ions were identified on an event-by-event basis based on a measurement

of energy loss in two Si PIN detectors placed upstream of SuN, and the time-of-flight (TOF)

measured between a thin scintillator at the focal plane of the A1900 and one of the PIN

detectors. A picture of the end station setup is shown in Fig. 2.2.

21

Figure 2.1: A representation of the layout of the CCF (comprised of the K500 and K1200
cyclotrons) and the A1900 Fragment Separator.

Figure 2.2: A picture of the e14505 setup in the S2 vault. SuN is shown on the right in the
large blue box, the DSSD and veto and located in the center of SuN (indicated by the purple
box), and the PIN detectors are located upstream of SuN in the red box.

2.1.1 The Summing NaI (SuN) detector

SuN is a total absorption spectrometer (TAS), which employs the γ-summing technique [71].

A cylindrical NaI(Tl) scintillator detector, SuN is 16 inches long and 16 inches in diameter

22

with a 1.8 inch borehole down the center. The SuN detector is depicted in Fig. 2.3. SuN has

eight optically-isolated segments of NaI (separated by aluminum), which are each read out

by three photomultiplier tubes (PMTs). The signals from each of the PMTs in a segment

are added together to obtain the total signal observed in that segment. The total signal from

all of the segments are then summed in order to obtain a summed γ-ray spectrum. SuN has

a high efficiency for detecting γ rays (85(2)% for the 662 keV transition from the decay of

137Cs) and has nearly 4π coverage.

Figure 2.3: A schematic of the SuN detector.

There are several methods through which γ rays can interact with the NaI crystals of

SuN. The three main interactions are photoelectric absorption, Compton scattering, and

pair production. For low energy γ rays (< 1 MeV) the dominant interaction is photoelectric

absorption, in which the γ ray is absorbed by an atom. The absorbing atom will then

emit a photoelectron. The interaction of the photoelectron with the NaI will then create

scintillation light that will be detected by the PMTs. The process of Compton scattering

takes place when an incident γ ray interacts with an electron in the detector material. A

portion of the energy of the γ ray is transferred to the electron (called the recoil electron),

leading to a detection of only the energy transferred to the electron. Compton scattering is

the most likely process for mid-energy γ rays. Pair production is a possible process for γ rays

23

above 1.022 MeV, but will most likely happen above 5 MeV. Pair production is the creation

of a electron-positron pair through the interaction of the incident γ ray with the Coulomb

field of the nucleus. The positron will annihilate, producing two characteristic 511-keV γ

rays. One or both of these γ rays have the possibility of interacting with SuN.

The γ-summing technique is used to determine the excitation energy of a nucleus after β

decay. While SuN can be used in order to obtain the energy of the individual γ rays being

emitted in a cascade, the signals from all eight segments can be summed to obtain the full

energy deposited from all γ rays in a cascade, which corresponds to energy of the excited

state(s) populated through β decay. It is worth noting that there is the chance for multiple

γ rays depositing in a single crystal, leading to additional peaks that could appear in the

single segment spectrum. It is also possible for some γ rays to escape the volume of the

detector, leading to an incomplete recorded energy, which would appear in the spectrum as

peaks below the energy of the excited state fed through β decay.

The γ-summing technique can be illustrated with an example of 60Co, as shown in Figure

2.4. The β decay of 60Co populates a 2505-keV state in 60Ni, which then decays through

two characteristic γ rays (1173 keV and 1332 keV). The γ ray energy spectrum from a single

segment of SuN, shown in panel (a) of Figure 2.4, would exhibit two peaks attributed to

the full energy of the 1173- and 1332-keV γ-ray transitions in 60Ni. There would also be a

small peak at 2505 keV corresponding to the summed energy of the 1173- and 1332-keV γ

rays, from instances where both γ rays are simultaneously deposited in the single segment.

The spectrum of the top half of SuN is shown in panel (b), where again there are two peaks

corresponding to the two γ rays transitions in 60Ni, as well as a larger peak at 2505 keV

(relative to the spectrum of a single segment) since the chance of both γ rays depositing in

the segments comprising the top half of SuN is higher than the chance of both depositing

24

in only a single segment. The spectrum from the total summation of the signal from all

segments (panel (c) of Figure 2.4) shows a “sum peak” at 2505 keV, corresponding to the

2505 keV state populated in the β decay of 60Co.

Figure 2.4: An example of TAS for 60Co. On the left is the decay scheme of 60Co. On
the right is a figure from [71], showing the 60Co gamma spectra obtained with (a) a single
segment of SuN, (b) the top half of SuN, and (c) the total summation of all segments.
Reprinted from [71], with permission from Elsevier.

SuN’s PMTs were gain matched using the 1460.8 keV γ ray from 40K, which is natu-

rally occurring and can be observed in background data. The first step in gain matching

is adjusting the high voltage applied to the PMTs, such that the 40K peak appears in ap-

proximately the same channel for each PMT. The second step involves the application of a

multiplication factor applied in software to precisely center the centroid of the 40K peak in

the same channel number for each PMT. The voltages and multiplication factors are listed

in Table 2.1. After being gain matched, the energy spectrum of each of the three PMTs of

25

a segment can be summed together in software to determine the segment signal. All eight

segments were then calibrated with a linear energy calibration using a 60Co source and a

137Cs source. The parameters determined from the linear calibration are shown in Table

2.2.

Table 2.1: Voltage applied to each PMT and scaling factors used for gain matching for SuN.

PMT
Number

Voltage
(+V)

0

1

2

3

4

5

6

7

8

9

10

11

730

740

780

774

771

764

794

803

812

838

824

848

Gain

Matching

Factor

1.0920

1.0000

1.1099

1.1302

1.0000

1.1195

1.1148

1.0000

1.1316

1.0949

1.0000

1.0993

PMT

Number

Voltage
(+V)

12

13

14

15

16

17

18

19

20

21

22

23

835

820

821

831

865

824

889

853

831

909

930

892

Gain

Matching

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

2.1.2 Double-sided silicon strip detector

The beam, centered on 83As, delivered to the experimental end station was implanted into a

2.54 x 2.54 cm2 and 1 mm thick double sided silicon detector (DSSD) located in the center

of the borehole of SuN. The DSSD consists of 16 electrically-segmented strips on the front,

26

Table 2.2: Scale factor and intercept used for the calibration of SuN’s segments.

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

and another set of 16 perpendicular strips on the back. These strips provide the ability to

define pixels in software. A pixel is defined as the intersection of a front strip and a back

strip. Together, these pixels create a grid-like pattern that allows for the determination of

the location of events. When an event occurs, the location is defined by the pixel with the

highest deposited energy recorded. A picture of the DSSD is shown in Figure 2.5. Two gain

ranges were used to capture the full energy of ion implantations (on the order of 1000s of

MeV) and the energy loss of the β-decay electrons (keV to MeV range). Both gain ranges

needed to be adjusted to ensure that all front and back strips have the same response. The

low gain, used for detecting ion implantations, is gain matched by applying a multiplication

factor in software to shift the centroid of the maximum energy peak of implanted ions of

each strip so the peak was centered in the same channel for all front or back strips. The

low gain matched energy spectrum of both the front strips and the back strips is shown in

Figure 2.6. The high gain, used for detecting β-decay electrons, was gain matched using the

most intense alpha peak from a 228Th source. Similarly to the low gain, a multiplication

27

factor was applied in software to shift the centroid of the peak in each DSSD strip so that it

was centered in the same channel for all strips. The high gain matched energy spectrum of

both the front and back strips is shown in Figure 2.7. All scaling factors used for both the

high gain and low gain matching are given in Table 2.3.

Figure 2.5: A picture of the DSSD used for experiment e14505.

2.2

Isolation of 83As β decay

Ions of 83As, 84Se and 85Se were delivered to the experimental end station. These three

isotopes are labeled in the particle identification (PID) plot, which is a plot of particle time-

of-flight versus energy loss as described in Section 2.1, shown in Figure 2.8. Conventionally,

the β decay of the isotope of interest would be identified by correlating to implanted ions,

which are identified via the PID. In software, a correlation timing window is defined. Once

a decay is observed, the correlation is performed by opening the timing window and looking

backwards in time to identify an ion that arrived within the specified timing window. The

correlated ion must also have arrived in the same DSSD pixel the β decay is observed in.

The correlation timing window is generally chosen based on the half-life of the isotope of

interest, and needs to be long enough that the decay will be seen, but not too long that

there is a chance for another ion to be implanted in the same time window. In the present

28

Figure 2.6: Gain matched energy spectra for the DSSD low gain setting. The front (top)
and back (bottom) strip numbers are shown as a function of channel number.

experiment, the implanted isotopes and their decay products have half-lives on the order

of seconds to hours (summarized in Table 2.4), which would require long correlation time

windows. Along with a high implantation rate, the preferred method of correlation would

be too difficult to successfully identify the decay of 83As. Due to this, another method of

isolating the β decay of 83As needed to be used.

The beam delivered to the experimental end station was pulsed in an eight minutes on,

eight minutes off cycle for seven hours, after which the beam was turned off for eight hours.

The pulsed setting was chosen based on the half-lives of the species involved, to obtain a

29

Figure 2.7: Gain matched energy spectra for the DSSD hi gain setting, using a 228Th source.
The front (top) and back (bottom) strip numbers are shown as a function of channel number.

cleaner spectrum associated with the decay of individual isotopes. Shown in Figure 2.9 is the

total absorption (or summed) spectra corresponding to the decay of all isotopes and their

daughters and granddaughters as a function of time. There are several strongly populated

states in the decay of some of the isotopes that appear here as the horizontal bands. Longer

lived isotopes can be identified based on the bands extending into the long beam-off period

starting around 25000 seconds. The projection of any excitation energy region onto the

x-axis would yield the decay profile of that excitation energy which may have a contribution

from multiple decaying species.

30

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

Front Strip
Number

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Low Gain
Matching

High Gain
Matching

Factor

0.990

Factor

0.680

1.075

0.998

1.130

1.027

1.004

1.203

0.973

0.973

0.998

0.995

1.042

0.990

1.036

0.726

1.054

0.643

0.681

0.698

0.685

0.650

0.658

0.687

0.682

0.654

0.669

0.644

0.658

0.710

0.656

0.642

Back Strip

Number

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Low Gain
Matching

High Gain
Matching

Factor

0.978

Factor

0.639

0.939

0.935

0.953

0.965

1.036

0.974

0.914

0.953

1.005

0.949

0.995

1.010

0.950

0.974

0.939

0.657

0.644

0.670

0.671

0.645

0.680

0.673

0.688

0.657

0.649

0.663

0.678

0.621

0.729

0.674

Using the half-lives and implantation rates of all present species (shown as a function

of time for 83As and 84Se in Figure 2.10), their individual contributions to this total decay

profile were modeled using the Bateman equations, which describe the growth and decay

of activities of a decay chain [72]. The contribution of 85Se to the total decay profile was

determined to be on the order of 1%, and is therefore ignored in the subsequent analysis.
The general solution of the Bateman equations for a decay chain Q1 → Q2 → Q3 → ... →

31

Figure 2.8: Particle Identification plot. PIN Energy is from the first PIN detector located
upstream of SuN. TOF is determined from the timing between the PIN detector and the
focal plane scintillator located in the A1900 fragment separator.

Table 2.4: Half-lives of implanted isotopes and their decay products.

Parent

83As
84Se
85Se

t1/2
13.4 s

3.26 m

32.9 s

Daughter

t1/2

Granddaughter

83Se
84Br
85Br

22.25 m, 70.1 s

31.76 m

2.90 m

83Br
84Kr
85Kr

t1/2

2.374 h

stable

4.480 h

Qn, where there is also an external source of production, Si, is shown in Equation 2.1.

n(cid:88)

i=1

Qn(t) =

n−1(cid:89)

j=i

λj,j+1 × n(cid:88)

j=i

 Qi(0)e
(cid:81)n

p=i
p(cid:54)=j

−λj t
(λp − λj)

(cid:81)n
Si(1 − e
p=i
p(cid:54)=j

−λj t)
(λp − λj)

+

kj




(2.1)

Here, Qn is the number of atoms of a species present at time t, λn is the decay constant for

species n, and λn,n+1 is the partial decay constant, which takes into account the branching

ratio, as shown in Equation 2.2.

λn,n+1 = BRn,n+1 × λn

(2.2)

32

Figure 2.9: SuN total absorption spectrum as a function of time.

To ensure the activity profiles produced using the Bateman equations were accurate

representations of the experimental data, energy cuts were taken for excitation energy peaks

in the 2-dimensional spectrum, shown in Figure 2.9, that could be attributed to the decay of

a single isotope or a decay chain. Each cut was projected onto the x-axis to obtain the decay

profile associated with that isotope or decay chain. This was then compared to the decay

profile produced using the Bateman equations. The first activity profile compared was one

attributed to the 408.2 keV level in 84Br, which is populated through the β decay of 84Se

and decays directly to the ground state. The decay scheme of 84Br is shown in Figure 2.11.

The Bateman equations for the mass 84 chain were scaled according to the efficiency of SuN

(70% at 400 keV) and β-feeding values (100% for the 408.2-keV energy level). The calculated

activity profile was overlaid on the activity profile produced by gating on the 408.2-keV peak

33

Figure 2.10: (Top) Implantation rate of 83As ions in the DSSD. (Bottom) Implantation rate
of 84Se ions in the DSSD.

in the TAS as a function of time spectrum. The result is shown in the top panel of Fig.

2.12. The second activity profile reproduced was one attributed to two decays within the

same decay chain. The peak at approximately 2050 keV in the excitation energy spectrum

has contributions from the β decay of 83As populating a 2076.84-keV level in 83Se and the β

decay of 83Se populating a 2051.45-keV level in 83Br. Due to the poor energy resolution of

SuN, these levels could not be resolved. Both states de-excite via cascades of multiple γ rays

to the ground state. The detector efficiency, β-feeding values, and relative γ-ray intensities

(obtained from ENSDF [73]) of each cascade were used to scale the calculated decay profiles.

34

The calculated decay profiles were compared to the activity profile obtained by gating on

the 2050-keV peak in the TAS as a function of time spectrum. The result is shown in the

bottom panel of Fig. 2.12.

Figure 2.11: Complete level scheme of the decay of 84Se into 84Br from ENSDF. Absolute
γ-ray intensities per 100 decays listed next to γ-ray energies. [73]

Once the calculated decay profiles were confirmed to represent the actual decay profiles,

all decay profiles contributing to the total activity were calculated via the Bateman equa-

tions. All activities over the full time scale are shown in Fig. 2.13. Regions of the pulsed

beam setting and the long decay period are shown in Figures 2.14 and 2.15, respectively.

The decay profiles of individual isotopes were then used to identify time regions in which

selected isotopes could be isolated in order to subtract them from the total activity profile.

The subtractions are done with 2D matrices of the excitation energy (Ex) as a function of

individual γ-ray energies (Eγ), since this is the starting point for the β-Oslo method (which

will be discussed in the next chapter). The total Ex, Eγ matrix is shown in Figure 2.16.

From approximately 26000 seconds to the end of the run, the only activities expected to
be present are from 83Se → 83Br and 83Br → 83Kr, as shown in Figure 2.15. The 2D Ex, Eγ

matrix gated on this time region is shown in Fig. 2.17. Based on the results of the Bateman

equations, there should be more 83Br than 83Se decay at later times. However, only 1.4%

35

Figure 2.12: (Top) TAS spectrum as a function of time gated on the 408 keV peak corre-
sponding to 84Br (only first three beam cycles shown) with the decay profile modeled via
the Bateman equations overlaid. (Bottom) TAS spectrum as a function of time gated on the
2053 keV peak that has contributions from the decay chain of 83As → 83Se → 83Br (only
first three beam cycles shown) with the decay profile of each decay, as well as the total,
modeled via the Bateman equations overlaid.

of the β decays from 83Br into 83Kr populate observable excited states above the threshold

of SuN (see level scheme in Fig. 2.18), leading to a 2D Ex, Eγ matrix that has comparable

contributions from the decays of 83Br and 83Se. In order to independently isolate these two
decays, the decay of 83Br → 83Kr was simulated in Geant4 and is shown in Figure 2.19. The

36

Figure 2.13: Activity profiles of all decaying species modeled with the Bateman equations,
shown over the full time range.

number of decays simulated was determined by integrating the calculated activity profile

from 26000 seconds to the end of the run.

The 83Br → 83Kr matrix was subtracted from the matrix shown in Fig. 2.17 to isolate
a matrix of only 83Se → 83Br, shown in Fig. 2.20. A decay scheme of 83Se → 83Br with

selected levels and γ-ray transitions is shown in Fig. 2.21. Here, the majority of the β

feeding goes to a series of levels between 2600 and 2800 keV and eventually decays through

cascades that have several lower energy, high intensity γ rays. This can be seen in the the

Ex, Eγ matrix as well, providing confirmation that 83Br was isolated. The simple decay of
84Se → 84Br (decay scheme shown in Fig. 2.11), consists of a single excited state fed in β

decay that results in a single γ-ray transition to the ground state. The decay of 84Se was

37

Figure 2.14: Regions of production and decay during the pulsed beam setting.

also simulated using Geant4. The resulting simulated Ex, Eγ matrix is shown in Fig. 2.22.

The two remaining decays, an isomeric state of 83Se (Qβ− = 3673(5) keV) decaying to

83Br and the decay of 84Br (Qβ− = 4660(3) keV) to 84Kr could not be independently isolated

nor could they reliably be simulated, due to their larger Qβ− values. After each beam on

period, 83As (t1/2 = 13.4 s) decayed away, and the Ex, Eγ spectrum from 102 seconds after

the beginning of the beam off period to 19 seconds before the beginning of the next beam on

cycle, was obtained. This time period included contributions from the decay of 83Se, 83mSe,

83Br, 84Se, and 84Br, as can be seen in Figure 2.14. The isolated spectra of the decays of

83Se, 83Br, and 84Se were all scaled and removed, leading to a 2D Ex, Eγ matrix with the

decays of 83mSe and 84Br in a 9 to 1 ratio. This matrix is shown in Fig. 2.23. The decay
schemes of 83mSe → 83Br and 84Br → 84Kr are shown in Figures 2.24 and 2.25. Many of

the strongly fed levels and high intensity γ rays can be observed in the 2D matrix.

38

Figure 2.15: Plot of the long decay period during which the beam was not being delivered
to the experimental end station.

Each of the isolated matrices were then scaled and subtracted from the portion of the

beam-on periods with the same ratio of 83mSe and 84Br decays to obtain the final, isolated
83As → 83Se matrix, shown in Fig. 2.26. This 2D matrix is used as the starting point

for the β-Oslo method, which will discussed in the following chapter. The spectra of γ-ray

energy (Eγ) and excitation energy (Ex) measured in SuN for the β decay of 83As to 83Se

(projections from the Ex, Eγ matrix) are shown in Figure 2.27. A decay scheme with select
levels and transitions of 83As → 83Se is shown in Fig. 2.28. Both spectra are consistent with

literature of known levels and γ-ray transitions of 83Se. In the Eγ spectra, the strongest

γ-ray transition with energy 734.9 keV is evident, as well as the second strongest transition

with energy 1113.4 keV (Iγ = 36.1(11)% relative to the 734.9 keV transition [74]). While

there are no β-feeding intensities reported in literature, a strongly fed level with energy

39

Figure 2.16: Excitation energy (Ex) as a function of γ-ray energy (Eγ), ungated, with all
events.

Figure 2.17: Ex, Eγ matrix with 50 keV binning, for a time gate of 26000 seconds to the end
of the run.

1062.89(7) keV is clear, as well as strongly fed levels in the energy range of approximately

1800 - 2200 keV and 2500 - 3100 keV.

40

 (keV)γE01000200030004000500060007000 (keV)xE01000200030004000500060007000110210310Figure 2.18: Decay scheme of 83Br → 83Kr. Absolute γ-ray intensities per 100 decays listed
next to γ-ray energies. [74]

Figure 2.19: Ex, Eγ matrix with 50 keV binning, for the decay of 83Br → 83Kr simulated in
Geant4.

41

 (keV)γE0100200300400500600700800 (keV)xE0100200300400500600700800110210310410Figure 2.20: Ex, Eγ matrix with 50 keV binning, for the decay of 83Se → 83Br.

Figure 2.21: Decay scheme of 83Se → 83Br with selected levels and γ-ray transitions. Abso-
lute γ-ray intensities per 100 decays listed next to γ-ray energies. [74]

42

 (keV)γE01000200030004000500060007000 (keV)xE01000200030004000500060007000110210310Figure 2.22: Ex, Eγ matrix with 50 keV binning, for the decay of 84Se → 84Br simulated in
Geant4.

Figure 2.23: Ex, Eγ matrix with 50 keV binning, for the decays of the isomeric state of 83Se
→ 83Br and 84Br → 84Kr.

43

 (keV)γE0200400600800100012001400 (keV)xE0200400600800100012001400110210310410 (keV)γE01000200030004000500060007000 (keV)xE01000200030004000500060007000110210310410Figure 2.24: Decay scheme of the isomeric state of 83Se → 83Br with selected levels and
γ-ray transitions. Absolute γ-ray intensities per 100 decays listed next to γ-ray energies. [74]

44

Figure 2.25: Decay scheme of 84Br → 84Kr with selected levels and γ-ray transitions. Ab-
solute γ-ray intensities per 100 decays listed next to γ-ray energies. [73]

Figure 2.26: Ex, Eγ matrix with 50 keV binning, for the decay of 83As → 83Se.

45

 (keV)γE01000200030004000500060007000 (keV)xE01000200030004000500060007000110210310410Figure 2.27: (Top) γ-ray energy spectrum of 83Se. (Bottom) Excitation energy spectrum of
83Se.

46

Figure 2.28: Decay scheme of 83As → 83Se with selected levels and γ-ray transitions. γ-ray
intensities relative to the 734.9 keV transition listed next to γ-ray energies. [74]

47

Chapter 3

β-Oslo Method

The β-Oslo method [63] is based on the established Oslo method [59–62] for extracting the

nuclear level density (NLD) and γ-ray strength function (γSF) of a nucleus. These sta-

tistical properties are extracted from data obtained by populating highly excited states in

the nucleus of interest and observing the subsequent emission of γ rays as the nucleus de-

excites. While the Oslo method uses charged particle reactions to accomplish the population

of highly-excited states in the nucleus, the β-Oslo method utilizes β decay of neutron-rich nu-

clei. The use of β decay gives the β-Oslo method the advantage to experimentally constrain

the NLD and γSF of nuclei further from stability than the Oslo method or other reaction-

based techniques. However, this method has limitations based on β-decay selection rules

and is restricted to nuclei that have large β-decay Q values and a high NLD at the neutron

separation energy (Sn), to ensure that the statistical region of the nucleus is being popu-

lated. The experimental information extracted from the application of the β-Oslo method

is then used to constrain a neutron-capture cross section using the Hauser-Feshbach model

for neutron capture as is explained in the Introduction. The β-Oslo method is comprised of

four main steps:

1. Unfolding the spectra of γ rays observed, for each excitation energy [59].

2. Isolation of the primary γ rays. These are the first γ rays emitted from each excited

state in cascades to the ground state [60].

48

3. Extraction of the functional forms of the NLD and the transmission coefficient (T (Eγ))

(See Section 3.4 for conversion of T (Eγ) to γSF) [61].

4. Normalization of the NLD and γSF [61, 62].

Each of these four steps will be covered in more detail in the following sections, along with

the results of the β-Oslo method being utilized to constrain the 82Se(n,γ)83Se cross section.

The level density and γ-ray strength function of 83Se are determined from the β decay of
83As → 83Se (see Chapter 2 for experimental details). A flow chart of the various steps,

programs, and inputs that are used for a β-Oslo analysis is shown in Figure 3.1. The MAtrix

MAnipulation (MAMA) program [76] is used for the first two steps of the analysis: the

unfolding of the spectra, and the isolation of primary γ rays. A suite of other programs

(shown in bold in Figure 3.1) are used for determination of several input parameters, and

for the remaining steps of the Oslo analysis.

3.1 Population of highly excited states in 83Se

The starting point of the β-Oslo method is a 2D matrix of the excitation levels and γ

rays emitted in the nucleus of interest (the product of the neutron-capture reaction being

constrained). For the case of constraining the cross section of 82Se(n,γ)83Se, the highly

excited states of 83Se were populated via the β decay of 83As. This reaction is shown

schematically, along with the corresponding neutron-capture reaction, in Figure 3.2. To

ensure that the statistical region of the nucleus is being populated, a Qβ− value above 4

MeV is preferred [77]; 83As has a Qβ− value of 5.671 MeV. It is also preferred that the

Qβ− value be close to the neutron separation energy (83Se Sn = 5.818 MeV), to cover the

majority of the energy range of γ rays emitted after neutron capture.

49

Figure 3.1: Flow chart of Oslo method. Bold items are programs used for the respective
steps in the flow chart. Figure from [75].

50

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 states in 83Se through the β decay of 83As and
neutron capture on 82Se.

3.2 Unfolding

As previously discussed in Chapter 2, the spectra of γ-ray energies deposited in SuN is

obtained via the summation of the spectra of each individual segment. While SuN has a

high efficiency for detecting the total energy of a single γ ray within the full detector volume

(above 80% for a 1 MeV γ ray), the efficiency of an individual segment detecting the full

energy of a γ ray is much lower, around 40%. This is mainly due to the various interactions

through which the energy of γ rays is deposited in the segments of SuN. While the full energy

of a γ ray interacting through photoelectric absorption will be deposited in one interaction,

there is a chance that some γ rays will lose energy through pair production or be Compton

scattered to another segment, in which case only part of the full energy would be deposited

in a given segment. These types of γ ray interactions lead to incomplete energy sums in the

γ-ray energy spectra, which is what the method of unfolding addresses.

51

In order to determine the full γ-ray energies expected from the raw data, an iterative

procedure was used to unfold the response function of the detector [59]. This response

function, which represents the response of the detector to a range of γ-ray energies, was

simulated using Geant4 [78]. The goal of this method is to determine a “unfolded” γ-ray

spectrum that, when combined with the response function, will match the experimental data.

The “folded” spectrum f can be represented by:

f = Ru

(3.1)

where f

is the folded spectrum, R is the response function matrix, and u is the unfolded

spectrum. The iteration method is applied as follows:

1. An initial trial unfolded function is defined as:

u0 = r

(3.2)

where r is the observed experimental γ-ray spectra.

2. The first folded spectrum, f 0, is calculated using the response function matrix R and

the first trial unfolded function u0:

f 0 = Ru0

(3.3)

3. The next trial unfolded function, u1, is determined by applying the difference of the

folded spectrum, f 0, and the observed spectrum r to the original trial unfolded function

52

u0 as a correction factor:

u1 = u0 + (r − f 0)

(3.4)

4. The new trial unfolded function is folded to determine the next folded spectrum, f 1,

which is then used to calculate the next trial unfolded function:

f 1 = Ru1

u2 = u1 + (r − f 1)

(3.5)

(3.6)

Step 4 is repeated until the folded spectrum matches the experimental spectrum within
uncertainties (f i ≈ r). Typically, around 30 iterations are performed.

The unfolding procedure used in the traditional Oslo and β-Oslo methods previously

focused only on unfolding the Eγ axis of the 2D matrix shown in Figure 2.26. A recent

development to the β-Oslo method is to also unfold the Ex axis [79]. Since the determination

of the excitation energy is directly linked to the measurement of γ-ray energies, the excitation

energy is also effected by incomplete summing of γ-ray cascades. There is also the chance

of additional background from β-decay electrons also interacting with SuN. The response

function is dependent on the initial excitation energy (Ex), the γ-ray multiplicity (Mγ) at

the excitation energy, and the Qβ value of the decay being measured. Response functions

covering the possible combinations of Ex, Mγ, and Qβ values have been simulated in Geant4.

The rest of the unfolding proceeds in the same method described above. The unfolded 2D

matrix for 83Se obtained by applying this method to both the Eγ and Ex axis of the original

raw 2D matrix for 83Se is shown in Figure 3.3.

53

Figure 3.3: Unfolded Ex, Eγ matrix for 83Se, with 50 keV binning.

3.3 Extraction of primary γ rays

To extract the functional forms of the nuclear level density and γ-ray strength function, the

Ex, Eγ matrix needs to contain only the primary, or first, γ rays emitted in cascades from each

excited state. The first generation method was developed to extract these primary γ rays

for each excitation energy bin [60]. The first generation method is based on the assumption

that the γ-ray emission from any excited state is independent of how that excited state was

populated. For each excitation energy bin i (here, 200 keV wide) of the unfolded matrix,

the γ-ray spectrum, fi, contains γ rays from all cascades that are possible from excited

states within that excitation energy bin. Therefore, γ-ray spectra fj<i, where j represents

excitation energy bins below i, contain the same γ-ray transitions as fi except for the first

γ rays emitted from excited states within bin i. The first generation, or primary γ ray,

54

spectrum hi of excitation energy bin i can then be found by

where gi is a sum of all spectra.

hi = fi − gi

(cid:88)

j

gi =

nijwijfi

(3.7)

(3.8)

gi is weighted by a coefficient wij, which represents the probability of a γ-ray transition

from bin i to excited states in bin j and is normalized so that(cid:80)

j wij = 1. The coefficient

nij accounts for the different probabilities of populating excited states in bin i and the

lower energy states in bin j, and is calculated using information about the average γ-ray
multiplicity (cid:104)M(cid:105) of each bin and the total number of counts in the spectrum fi, A(f ),

nij =

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

.

(3.9)

This procedure of subtracting the γ-ray spectra of lower excitation energy bins from the

higher excitation energy bin of interest is done for each bin in the Ex, Eγ matrix, until only

the primary γ rays remain. The primary matrix obtained for 83Se is shown in Figure 3.4.

3.4 Extraction of the functional forms of the NLD and

γSF

The assumption that the probability of a decay to a specific energy state is independent

of the means of formation has been shown to be valid for compound reactions. Therefore,

the probability P (E, Eγ) of a γ-ray of energy Eγ being emitted from a specific excitation

55

Figure 3.4: Primary Ex, Eγ matrix for 83Se, with 200 keV binning.

energy Ex, is proportional to the level density at the final excitation energy, ρ(Ef ) (where
Ef = Ex − Eγ), and the γ-ray transmission coefficient T (Eγ),

P (E, Eγ) ∝ ρ(E − Eγ)T (Eγ).

(3.10)

Ultimately, T (Eγ) will be converted to the γ-ray strength function (γSF), assuming the

γ-ray transitions are dipoles, via

γSF =

T (Eγ)
E3
γ

1
2π

(3.11)

The relationship in Equation 3.11 relies on the assumption that the γ-ray transmission

coefficient is independent of the excitation energy, which has been shown to be valid in a

study of 238Np [77]. Based on this, the functional forms of the nuclear level density (NLD)

56

and γ-ray transmission coefficient can be simultaneously extracted from the primary Ex,

Eγ matrix [61]. First, though, the primary matrix must be normalized so that for every

excitation energy bin the sum of all γ-ray energies is unity:

γ(cid:88)

Emax

Eγ =Emin

γ

P (E, Eγ) = 1.

(3.12)

The limits of the region of the primary matrix used for the extraction are shown in black in

Figure 3.4. These limits are chosen to ensure that the data are from the statistical energy

region. The lower limit of Eγ is 1275 keV. The lower limit of Ex is 3275 keV, and the upper

limit is 5475 keV. These limits are specified in the rhosigchi program, which performs the
extraction. The extracted NLD and T (Eγ) are functional forms, described by the following

equations:

ρ(E, Eγ) = Aeα(E−Eγ )

T (Eγ) = BeαEγ ,

(3.13)

(3.14)

where α is the slope, and A and B are scaling factors. To determine the physical solutions
of the NLD and T (Eγ), the A, B, and α parameters must be found through normalization,

which will be discussed in the following section.

3.5 Normalization of the NLD and γSF

There are three pieces of information needed to normalize the functional forms of the NLD

and γSF. Parameters A and α from Eq. 3.13 and 3.14 are determined from known discreet

levels at low excitation energies and the level density at the neutron separation energy

57

(ρ(Sn)). Known levels are obtained from β-decay experiments, while ρ(Sn) is calculated

using the average level spacing for s-wave neutrons at the neutron separation energy (D0).

D0 is the inverse of the NLD, for levels that would be populated through a neutron-capture

reaction and can be measured by neutron-capture experiments. Parameter B of Eq. 3.14,

which represents the magnitude of the γSF, is calculated using the average radiative width

at the neutron separation energy, Γγ, which can also be obtained through neutron-capture

experiments.

It is worth noting, much of this experimental information discussed above is limited for

many of the nuclei of interest for r-process calculations, due to short half-lives. Therefore,

theoretical calculations can be used in place of experimentally-determined values, or these

normalization parameters can be determined through extrapolations using information of

nearby nuclei. In this work, the NLD was normalized using known levels in 83Se from β

decay, and a D0 value reported in literature. The γSF was normalized using a Γγ value

determine from a fit to extrapolated GDR data from nearby nuclei, to test the method

generally used when experimental Γγ values are not available. The Γγ value determined

through this method was later compared to one reported in literature from neutron-capture

data, which is currently the best data available for 83Se.

3.5.1 NLD

The nuclear level density of 83Se determined via the β-Oslo method is shown in Figure 3.5.

The known discreet levels shown in this figure were used to normalize the NLD at low en-

ergies, between 675 keV and 1675 keV. The NLD at higher energies was normalized using

ρ(Sn), which was determined using the program D2rho, which calculates the level density at

the neutron separation energy from the average level spacing parameter (D0). A D0 value of

58

5000 ± 2500 eV [80] results in a ρ(Sn) value of 5907 ± 3193 MeV−1. Since the experimental

data does not reach all the way up to the neutron separation energy, the Constant Temper-

ature model is used to determine an extrapolation of the level density between the higher

energy levels of the level density and ρ(Sn). For the CT model, a temperature parameter

of 0.84 was used, as reported by von Egidy and Bucurescu [29]. If using the BSFG model

for the extrapolation of the level density, the level density parameter a, from Equation 1.8,

is reported by von Egidy and Bucurescu to be 9.44 [29]. The normalization was performed

through a simultaneous fit of the experimental data to the low energy known levels and the

CT model extrapolation. The upper and lower limits of the NLD shown in Figure 3.5 were

determined from a systematic study based on the uncertainty of the D0 value used. The
upper value of ρ(Sn) was determined to be 13350 ± 7158 MeV−1, while the lower value
was determined to be 3459 ± 1888 MeV−1. From Equation 3.13, the A parameter was

determined to be 4.51, and the α parameter was determined to be 0.85.

3.5.2 Limited spin population

One thing that needs to be taken into account is the limited range of spins that are populated

based on the restrictions of β decay. The ground state of 83As is 5

2−. By taking into account

one allowed β-decay transition and one γ-ray transition, the range of spins that is expected

to be populated in 83Se is 1

2± to 9

2±. Therefore, the primary γ rays observed in this

experiment are restricted to that spin range. Since the α parameter (of Equations 3.13 and

3.14) determined in the normalization of the NLD is also used for the normalization of the

γSF, the NLD needs to be reduced to account for this restricted spin range. To determine a

reduction factor, a theoretical calculation of the NLD from Goriely [37] was used. For each

spin, the percentage of the total level density was calculated, and is shown in Figure 3.6.

59

Figure 3.5: Nuclear level density for 83Se, with the experimental data (black circles) as well
as the upper and lower limits (blue band). Known levels are indicated by the solid black line,
the level density at the neutron separation energy, ρ(Sn), is indicated by the white square,
and the Constant Temperature model extrapolation is shown as the dashed black line.

2±
For 83Se, it was determined that 52.3 % of the level density fell within the spin range of 1
2±. Using this reduction factor, ρ(Sn) values of 2326.8 MeV−1, 3490.5 MeV−1, and 6982

to 9
MeV−1 were calculated and used to determine the α parameter.

3.5.3 γSF

The normalized γSF of 83Se is shown in Figure 3.7. To determine parameter B of equation

3.14, the average radiative width, Γγ, needs to be calculated. A systematic approach was

used, by studying the γSF of nearby nuclei. Photoabsorption cross section data for 75As,

60

Figure 3.6: Percentage of the total level density of 83Se determined from Ref. [37] as a
function of the spin. Spin range highlighted in blue represents the spin range populated
following an allowed β decay and one dipole transition.

80Se, and 82Se were obtained from [81], and the γ,n cross section, σγ, of each was converted

to a γSF using the equation

γSF (M eV −3) =

σ2
γ

(3π¯h)2 .

(3.15)

These γSFs are also shown in Figure 3.7. Photoabsorption cross sections are usually mea-

sured above the neutron separation energy, while the data obtained from β-Oslo measure-

ments is extracted below the neutron separation energy. Therefore, the γSF of each set of

data must be extrapolated to lower energies. The shape of the γSF is described very well

at higher energies by a Generalized Lorentzian (GLO) function, and the GLO has also been

used to estimate the shape of the γSF at lower energies as well. Each γSF calculated from

γ,n data was fitted to the GLO function, and the average value of each parameter was used

to determine an average GLO function that was extrapolated to lower energies. The average

parameter values are summarized in Table 3.1. A χ2 minimization (shown in Figure 3.8) was

then performed on the fit of the experimental γSF data to the average GDR extrapolation

61

from 3.5 to 5.5 MeV to determine Γγ. For 83Se, Γγ was determined to be 74.09(3.68) meV.

This Γγ does not agree with reported value of 126(15) meV from [82]. It is presently un-

known as to why there is a discrepancy. The upper and lower limits of the γSF, determined

from the uncertainty on Γγ and the NLD, is represented by the blue band in Figure 3.7.

Figure 3.7: Gamma strength function for 83Se (black circles) with the upper and lower limits
based on systematic uncertainty are indicated by the blue band. Photoabsorption cross
section data from [81] (green squares, blue triangles, purple circles) and the corresponding
fit of the GLO function to the data and an average fit are also shown.

3.6 Constraint of 82Se(n,γ)83Se via the β-Oslo Method

The NLD and γSF detailed above were then used as input in a Hauser-Feshbach reaction

code to obtain the neutron-capture cross section. The TALYS reaction code (version 1.95)

was used [12]. The NLD was read in to TALYS in tabular form, which was generated using

62

Table 3.1: GDR parameters determined from the fit of a GLO function to photoabsorption
cross section data.

Nucleus EE1 (MeV) σE1 (mb) ΓE1 (MeV)

75As
80Se
82Se

Average

16.96

16.46

16.20

16.54

127.62

152.55

141.57

140.58

7.86

5.51

5.24

6.20

Figure 3.8: A plot of χ2 values versus a range of Γγ values, obtained from fitting the average
GDR resonance parameters to the experimental γSF to determine the best Γγ for the data
set.

a fit of the CT model to the experimental data. The experimental γSF was fitted with a E1

GLO function combined with an exponential function to represent the upbend. These fits

were used to generate a tabular form of the γSF, which were then be read into TALYS. The

resulting 82Se(n,γ)83Se reaction cross section is shown in Figure. 3.9. The light blue lines

indicate the systematic uncertainty of the cross section calculation, based on the upper and

63

lower limits of the properties constrained in the β-Oslo method. Along with the constrained

cross section, a band representing cross sections calculated with all possible combinations of

the NLD and γSF models available in TALYS version 1.95 (summarized in Table 3.2) is also

shown. Ultimately, this cross section will be compared to a cross section determined in a

direct measurement of the 82Se(n,γ)83Se reaction, which is covered in the next chapter.

Figure 3.9: Cross section of the 82Se(n,γ)83Se reaction calculated using TALYS (black). The
upper and lower limits (light blue) are based on the uncertainty of the experimental NLD
and γSF. The grey band shows the range of cross sections resulting from combinations of all
available NLD and γSF models.

64

Table 3.2: NLD and γSF models available in TALYS.

NLD Models

CT + BSFG [34]

BSFG [31, 34]

γSF Models

Kopecky-Uhl generalized

Lorentzian [42]

Brink-Axel Lorentzian [40, 41]

Generalized superfluid [83]

Hartree-Fock BCS tables [84]

Microscopic level densities
Goriely [36]

(Skyrme force)

from

Microscopic level densities (Skyrme force) from Hi-
laire combinatorial tables [37]

Microscopic level densities (HFB, Gogny force) from
Hilaire combinatorial tables [38]

HFB tables [84]

Goriely’s hybrid model [85]

Goriely T-dependent HFB

T-dependent RMF

Gogny D1M HFB+QRPA

65

Chapter 4

Direct Measurement of 82Se(n,γ)83Se

A direct measurement of neutron capture on 82Se was performed at Los Alamos National

Laboratory in Los Alamos, New Mexico. This experiment was performed with the Detector

for Advanced Neutron Capture Experiments (DANCE) [86–88], which is positioned on a

dedicated neutron flight path at the Lujan Neutron Scattering Center of LANSCE, the Los

Alamos Neutron Science Center. At LANSCE, a linear accelerator produces an 800 MeV

high intensity proton beam that is bunched in pulses that are 250 ns wide at the base of the

pulse shape. This proton beam is impinged onto a tungsten production target, producing a

white neutron source via spallation reactions [89]. The neutrons are then partially moderated

by a room-temperature water moderator surrounding the tungsten target until ultimately a

neutron beam ranging in energy from a few meV to a few MeV travels down flight path 14

to the experimental setup.

4.1 DANCE: The Detector for Advanced Neutron Cap-

ture Experiments

DANCE is a large volume γ-ray calorimeter based on a 162 element close-packed spherical-

shell geometry around the target position [90]. Each BaF2 detector crystal is 734 cm3 in

volume and connected to a photomultiplier tube (PMT). The face of each crystal is located

66

at a distance of approximately 19 cm from the target position. All detector crystals view the

same solid angle, and with all 162 crystals in place, 4π coverage is achieved. However, two

crystals are excluded from the array to account for the neutron beam traveling through the

device. With two crystals removed, the crystals cover a total solid angle of approximately

3.5 π steradians. DANCE has a high efficiency for detecting γ rays, with an efficiency of

approximately 87% for a single 1 MeV γ ray [91]. Inside of DANCE, a 6 cm thick shell of

6LiH surrounds the target position to reduce the background produced by scattered neutrons

capturing in the BaF2 crystals [92]. A schematic of DANCE is shown in Figure 4.1. BaF2 has

Figure 4.1: Schematic representation of the DANCE detector geometry, including the beam-
line, and LiH sphere.

the distinction of being the fastest known inorganic scintillator. There are two components

to its light emission spectrum, a fast component with a 220 nm wavelength and 0.6 ns decay

time, and a slow component with a 310 nm wavelength and a 600 ns decay time [93]. The sub-

nanosecond decay time of the fast component provides the ability for a precise determination

of timing.

67

The fast and slow components are also utilized to differentiate γ-ray signals and signals

originating from α decay which is intrinsic to BaF2 detectors. Barium is chemically analogous

to radium, so it is difficult to produce pure barium without any radium impurities. Therefore,

the BaF2 crystals have some internal background from isotopes along the radium decay

chain. The main decays observed from the radium background are alpha decays from 226Ra

(4.78 MeV), 222Rn (5.49 MeV), 218Po (6.0 MeV), and 214Po (7.69 MeV). The amplitude

of the components of the BaF2 light spectrum depends on the energy, mass, and charge of

the interacting particles and will therefore be different for γ rays and alpha particles. An

example of the signals obtained from the interaction of a γ ray versus an alpha particle is

shown in Figure 4.2. To separate the alpha particles from the spectra, signals are integrated

Figure 4.2: Example of signals from a γ ray and an alpha particle, from a single BaF2 crystal.
c(cid:13) 2006 IEEE Reprinted, with permission, from [94].

with two different integration times (short - first 64 ns and long - next 1 µs) and the plot of

68

the short integral versus the long integral (shown in Figure 4.3) is used to distinguish alpha

particle signals from gamma ray signals. A gate is applied around the signals from alpha

particles in software, as they are used for calibrations that will be discussed in Section 4.3,

and then ignored in the analysis.

Figure 4.3: Short integral of the detector signal versus the long integral of detector signal
from the data taken with the 82Se target. Gate used to separate alpha signals shown in red.

After the alpha signals have been gated out, the remaining signals are used to obtain

calorimetric information about the cascades of γ rays emitted following neutron capture.

Based on the timestamps of signals, an event is created by grouping all signals identified as

γ rays within a 10 ns coincidence window (this is user-selectable and can be optimized during

the analysis). The energy deposited in each crystal, ECr, is determined by subtracting the

short integral of the signal from the long integral. The energy of all γ rays identified within

a particular event are summed and recorded as ESum. The number of crystals (multiplicity)

identified as participating in the event is denoted as MCr. However, there is the possibility

for a single γ ray to Compton scatter and be detected by another crystal. In such a case, the

69

MCr would be recorded as 2 instead of 1. To account for this, a cluster of crystals is defined

by the nearest neighboring crystals to the crystal where the initial photon interaction was

believed to occur. In the case of a γ ray depositing energy into a crystal and then Compton

scattering into a neighboring crystal, the cluster multiplicity, MCl, would be denoted as 1

and MCr would equal n+1. The sum of energy deposited within a cluster is recorded as ECl.

MCl and ECl are a better representation of the true cascade multiplicity and individual

γ-ray energies for typical multiplicities and energies produced in neutron capture due to

the possibility of γ rays scattering and depositing energy in multiple crystals [91]. The

total energy observed by DANCE, ESum, corresponds to the Q-value of the neutron capture

reaction that is occurring, which provides the ability to cleanly identify neutron capture on

different isotopes.

Another important quantity is the neutron energy, which is determined via time-of-

flight measurements. The time-of-flight is measured between the timing of the initial γ-ray

interaction of the event in DANCE and the reference signal of the proton pulse immediately

before it interacts with the tungsten target. The neutron energy is then deduced using

the non-relativistic (since the maximum neutron energy considered here is 1 MeV, which

is approximately 5% of the speed of light) kinematic energy equation (Equation 4.1) using

time-of-flight, tT OF , the length of the flightpath, lF P = 20.25 m, and the neutron mass, mn

= 939.57 M eV
c2 .

En =

1
2

mn

l2
F P
t2
T OF

(4.1)

70

4.2 Targets

An enriched 82Se metal was obtained from Trace Sciences [95] and was pressed into two

pellets that were glued together to form a 176.6 mg, 5 mm target. The target was attached

to an aluminum target holder with kapton tape. Pictures of the target are shown in Figure

4.4. A summary of the isotopic composition of the target is provided in Table 4.1.

In

addition to the 82Se target, several other targets were utilized for this experiment as well.

A measurement of neutron capture on a 4-mm 197Au target was used to determine the

normalization for the neutron fluence measured by the neutron beam monitors downstream

of DANCE (see Section 4.4 for more information). A 97.4-mg 208Pb target, which has a

large neutron scattering cross section relative to the neutron capture cross section, was used

to characterize the background of neutrons scattering off of the target and interacting with

the BaF2 crystals, creating signatures of neutron capture on barium (See Section 4.5.1.1 for

more information). Two γ-ray sources, 88Y and 22Na, were also used for energy calibrations.

Table 4.1: Composition of the enriched 82Se target and the Q-value of neutron capture on
each isotope.

Isotope

Enrichment (%)

(n, γ) Q-value (MeV)

74Se

76Se

77Se

78Se

80Se

82Se

<0.01

<0.01

<0.01

<0.01

3.77

96.20

71

8.03

7.42

10.5

6.96

6.70

5.82

Figure 4.4: Photographs of 82Se target and target holder from a top down view (left) and a
side view (right).

4.3 Calibrations

The response of the BaF2 crystals have been observed to drift over time due to temperature

sensitivity, so the energy calibration of DANCE is performed using a combination of standard

gamma sources to create a calibration template and intrinsic alpha signals to perform a run-

by-run calibration. The initial energy calibration for each crystal was performed using 88Y

and 22Na. An example of the fit to 22Na data and the calibrated energy spectrum for one

crystal are shown in Figure 4.5. This initial calibration is applied to the raw BaF2 spectra

and then saved as a template. Each subsequent data run is then calibrated on a run-by-

run basis using the signals from alpha particles that are intrinsic to the BaF2 crystals as

discussed above. An example of the alpha calibration spectra and fit used to extract the

energy calibration for one crystal is shown in Figure 4.6.

The timing between crystals is also calibrated on a run-by-run basis. This calibration is

performed by utilizing Compton scatter events. For each run, time offsets for pairs of crystals

are adjusted so that Compton scatter events in adjacent crystals have the same timing.

72

Figure 4.5: (Left) Representation of fit used for calibration with a 22Na source. (Right)
Calibrated 22Na spectrum.

4.4 Neutron Fluence Characterization

Another important piece of information for the determination of a cross section is the neutron

fluence, or the number of neutrons per unit of area. The fluence is characterized using a series

of neutron beam monitors located downstream of DANCE. The beam monitors provide a

neutron fluence measurement that is proportional to that at the target position in the center

of DANCE. One of these beam monitors was a silicon detector viewing a 6LiF converter foil

that utilizes the 6Li(n, α)3H reaction. The first beam monitor is located at 22.632 meters

on the flightpath. The second beam monitor used was a gas-filled ion chamber that detects

fragments from neutron-induced fission on a 235U foil. The second beam monitor is located

at 22.794 meters on the flightpath.

The information recorded from each of the two beam monitors is the yield, or the number

of recorded reactions, per neutron energy bin, YBM (En). The fluence, ΦBM , measured at

the beam monitor position, can be deduced from Equation 4.2, where σBM is the known

cross section of the reaction utilized by each beam monitor

ΦBM (En) ∝ YBM (En)
σBM (En)

.

(4.2)

73

Figure 4.6: Alpha decay spectra of one crystal and representation of the fit used for crystal-
by-crystal calibration.

The measured neutron yield from the silicon beam monitor and the cross section of 6Li(n,

α)3H are shown in Figure 4.7. For each neutron energy bin, the yield measured by the

silicon beam monitor was divided by the ENDF/B-VII.1 evaluated 6Li(n, α)3H cross section

to deduce the neutron fluence [96]. The 6Li(n, α)3H cross section is smooth up to a broad,

high energy resonance at approximately 240 keV, which can complicate the fluence charac-

terization in that energy region. Therefore, the neutron fluence deduced from the 6Li beam

monitor was used to define the full neutron fluence from 1 eV to 5 keV.

The measured neutron yield from the 235U beam monitor and the cross section of 235U(n,

f ) are shown in Figure 4.8. For each neutron energy bin, the yield measured by the fission

chamber was divided by the ENDF/B-VII.1 evaluated 235U(n, f ) cross section to deduce

the neutron fluence [96]. Since the 235U(n, f ) cross section is smoother at higher energies,

this calculation was used to define the neutron fluence from 20 keV to 1 MeV. The neutron

74

Figure 4.7: (a) Neutron yield measured by the 6Li beam monitor.
evaluated cross section of 6Li(n, α)3H used in the neutron fluence determination.

(b) ENDF/B-VII.1

fluences deduced from each beam monitor were then combined together to characterize the

neutron fluence over the full energy range. The neutron fluence from the silicon monitor is

scaled to the neutron fluence from the fission chamber in the energy region of 5 keV to 20

keV. The neutron fluence in the region of 5 keV to 20 keV is represented by an average of

the neutron fluence from each monitor. This fluence is shown in Figure 4.9. The dips that

are visible in the neutron fluence are from capture on aluminum and manganese components

in the beam line, both of which have a few strong resonances.

Figure 4.8: (a) Neutron yield measured by the gas-filled 235U fission chamber. (b) ENDF/B-
VII.1 evaluated cross section of 235U(n, f ) used in the neutron fluence determination.

75

Figure 4.9: Neutron fluence at the beam monitor position as a function of neutron energy.

However, the neutron fluence at the beam monitor position is lower than the fluence at

the target positions in the center of DANCE, due to the divergence of the beam. To account

for this, a normalization constant, κ, is introduced. This allows for the determination of

the neutron fluence at the target position, Φ(0), from the beam monitor data, as shown in

Equation 4.3.

Φ0(En) = κ

YBM (En)
σBM (En)

(4.3)

The normalization constant κ is determined from the measurement of neutron capture on

197Au, which will be discussed in the following section.

4.4.1 Normalization to 197Au

The well known neutron-capture cross section of 197Au is utilized to normalize the neutron

fluence at the beam monitor position for the determination of the neutron fluence expected

76

at the target position. The nuclide 197Au has a strong neutron capture resonance at 4.89

eV, with a peak cross section of 27 kilobarns. The ESum vs. En spectrum measured by

DANCE over this energy region is shown in Figure 4.10. The yield of neutron captures on

the 197Au target in a neutron energy bin Y Au

n,γ (En) is related to the 197Au(n, γ) cross section

by:

Y Au
n,γ (En) = Φ(En)NAuσAu

n,γ(En)

(4.4)

where NAu is the number of Au atoms in the target, and Φ(En) is the number of neutrons

per barn for that neutron energy bin. The thickness of the 197Au target was determined via

Rutherford backscattering and used to determined the number of Au atoms in the target,

with a 4% uncertainty. Substituting in Equation 4.3 for Φ(En), and rearranging and solving

for σAu

n,γ, the following equation is obtained,

σAu
n,γ(En) =

1
κ

Y Au
n,γ (En)
NAu

σBM (En)
YBM (En)

.

(4.5)

Ultimately, using the known cross section of 197Au(n, γ) from ENDF/B-VII.1 [96], the nor-

malization constant κ can be extracted. However, the proper subtraction of low energy

background in the 197Au spectra is needed to ensure that the true number of neutron cap-

tures on 197Au is being used.

In the low energy region of the 4.89 eV resonance, not all of the counts are from neutron

capture events. There is some contribution to the background from neutrons scattering off

the 197Au target. The background is mostly suppressed by the LiH sphere between DANCE

and the target position, and thus can be neglected. The dominant background is resulting

mainly from the decay of neutron induced reaction products, random coincidences, and the

ambient neutron background. This background is assumed to be linear in relation to TOF in

77

Figure 4.10: 2D plot of ESum as a function of En for the 197Au data, over the 4.89 eV
resonance.

the region of the 197Au resonance. Therefore, the background in two off-resonance regions on

either side of the resonance were used to determine a linear background, with the slope and

offset parameters left as free parameters. The result of this linear background subtraction is

shown in Figure 4.11. A diagnostic plot of the ESum projections of the background region

and the region over the resonance, as well as the resulting capture ESum shape, are shown

in Figure 4.12. In this diagnostic plot, it is evident that there is some contribution from

neutron capture in the background region, indicated by the small peak around the Q-value

of 197Au. However, the effect of this is negligible. The background subtracted time-of-flight

yield spectrum was then converted into a neutron energy spectrum via Equation 4.1.

With the yield of neutron capture on 197Au determined, the known cross section is scaled

to the experimental cross section, and κNAu = 0.308 is extracted as the scaling factor, as

shown in Figure 4.13. With the number of Au atoms known, the normalization constant κ can

be determined and used in the analysis of the 82Se data. The dominant source of uncertainty

78

in the determination of κNAu is a 4% systematic uncertainty from the number of gold atoms

determined via Rutherford backscattering. Compared to this systematic uncertainty, the

statistical uncertainty of κNAu is negligible.

Figure 4.11: Figure depicting the subtraction of a linear background from the time-of-flight
spectrum of neutron capture on 197Au. The blue histogram is the data pre-subtraction, and
the magenta histogram is the data after subtraction of the linear background, shown in red.

4.5

82Se Data Analysis

The neutron-capture cross section is determined using the following equation:

(cid:19)
(cid:125)

(4.6)

(cid:18) σBM (En)
(cid:123)(cid:122)
(cid:124)

κYBM (En)
(Φ0(En))−1

σnγ(En) =

1

cut

Y 82
n,γ(En)
N82

79

Figure 4.12: Diagnostic plot showing the ESum projections of the different components of
the background subtraction on the 4.89 eV 197Au resonance. The total ESum shape (red)
corresponds to the data before the background subtraction was performed. The magenta
ESum shape corresponds to the sum of the background regions on either side of the resonance.
The blue ESum shape is the background subtracted capture ESum.

where Y82

n,γ(En) is the yield of 82Se neutron-capture events in each neutron energy bin, N82

is the number of atoms of 82Se in the target, 
cut is the efficiency of DANCE in the ESum

and multiplicity cut chosen, and Φ0 is the neutron fluence normalized to the target position.

The determination of the normalized neutron fluence was previously discussed in Section

4.4; this section will discuss the determination of the yield of neutron capture events after

background subtraction (Section 4.5.1) as well as the determination of the efficiency in the

ESum and multiplicity cut (Section 4.5.2).

4.5.1 Background Subtraction

The raw 82Se(n,γ) data are shown in Figure 4.14, with total energy, ESum, plotted on the

y-axis and neutron energy, En, plotted on the x-axis. The z-axis shows the number of counts

80

Figure 4.13: Cross section of neutron capture on 197Au, in the region of the 4.89 eV resonance
(black squares). The scaled ENDF/B-VII.1 cross section is shown in red [96].

for each bin of ESum and En. Resonances expected from neutron capture on 82Se are visible

above 3 keV, with an ESum distribution peaking around 5.8 MeV (82Se (n, γ) Q-value =

5.82 MeV). Due to incomplete summing of all γ rays, the ESum distribution extends to

lower energies. Along with the 82Se resonances, there are other resonances that show up at

ESum values corresponding to the Q-values of other Se isotopes, namely 80Se (Q-value =

6.70 MeV), 78Se (Q-value = 6.96 MeV), 74Se (Q-value = 8.04 MeV), and 77Se (Q-value =

10.5 MeV). There are also several horizontal bands visible in Figure 4.14. These are from

neutron capture induced in the BaF2 crystals of DANCE due to neutrons that scatter off

81

of the target. The neutron capture on BaF2 will appear at ESum values corresponding to

the Q-values of barium isotopes. While the background attributed to scattered neutrons is

greatly reduced by the 6LiH shell, it does not absorb 100% of the scattered neutrons, so the

scattering background needs to be characterized and removed.

Figure 4.14: Counts as a function of the sum of energy deposited in DANCE (ESum) and
neutron energy (En) for the 82Se data.

4.5.1.1 Scattering Background

Neutrons incident on the targets used in this experiment have a probability of scattering

off the target instead of capturing. These scattered neutrons may then capture on the

barium in the DANCE detectors, which leads to signatures corresponding to ESum values

of barium isotopes. This scattering background is characterized using a 208Pb target. The

nuclide 208Pb is used for this characterization due to its relatively low neutron-capture cross

section, relatively high neutron elastic scattering cross section, and low Q-value of 208Pb(n,

γ) (3.94 MeV).

82

The raw data from running with the 208Pb target are shown in Figure 4.15. For each

neutron energy bin, an ESum projection was made for both the Se data and the 208Pb data,

and the 208Pb projection was normalized to the Se data using the normalization factor, αP b.

The normalization parameter is described in Equation 4.7, where C indicates the yield of

the respective isotope.

(cid:82) 9.3M eV
(cid:82) 9.3M eV

8.6M eV CSe(En, ESum)dESum
8.6M eV CP b(En, ESum)dESum

αP b(En) =

(4.7)

The ESum peak at approximately 9 MeV corresponds to neutron capture on 135Ba, and is

used for normalization since this ESum region does not have contributions from other isotopes

present in the Se sample. After normalization, the scattering contribution characterized by

the 208Pb is subtracted from the raw Se data. An example of this subtraction procedure for

a neutron energy bin on a 82Se resonance is shown in Figure 4.16. The full 2D ESum,En plot

after the scattering background has been removed from each neutron energy bin is shown in

Figure 4.17.

4.5.1.2 Target contaminants

One of the key abilities of DANCE is the capability to distinguish events from different

reactions based on the reaction Q-value. The ability to distinguish events is attributed to

the fact that DANCE has a high efficiency for detecting the total energy (ESum) of the

γ-ray cascades released following neutron capture. As discussed previously, there are several

resonances observed that, based on their ESum value, correspond to other stable selenium

isotopes present in the target. To remove these contaminates, a step wise subtraction was

performed.

83

Figure 4.15: Counts as a function of the sum of energy deposited in DANCE (ESum) and
neutron energy (En) for the 208Pb data.

Figure 4.16: Example scattering background subtraction for a single En bin on a 82Se
resonance.

84

Figure 4.17: Counts as a function of the sum of energy deposited in DANCE (ESum) and
neutron energy (En) for the 82Se data, after the scattering background was subtracted.

For each isotope identified in the ESum vs. En spectra, an ESum gate was placed

to obtain the neutron capture yield spectra for that isotope. The range of each gate is

summarized in Table 4.2. Due to incomplete summing of some γ-ray cascades, the ESum

distribution of each isotope will extend to lower energies. Therefore, many of the isotopes

have contributions that appear in the ESum gated spectra of other isotopes. As an example,

the 82Se ESum gated spectrum is shown in Figure 4.18. Observed resonances from other

isotopes are labeled. To characterize this contribution of each isotope to the ESum gated

spectra of the other isotopes, a strong resonance was chosen: 211.7 eV for 77Se, 27.13 eV

for 74Se, 383 eV for 78Se, and 1970 eV for 80Se. Projections were made for each of these

strong resonances and shown in Figure 4.19. From the projection representing each isotope,

integrals were taken over each ESum range to determine the contribution of that isotope

in the spectra of each other isotope. From these integrals, scaling factors were determined

for the subsequent subtractions. The subtractions proceeded in an order beginning with the

85

isotope with the largest Q-value, 77Se. The contribution of 77Se was subtracted from the

spectra of 74Se, 78Se, 80Se, and 82Se. The (now isolated) spectra of 74Se, which has the next

largest Q-value, was then subtracted from each of the following in the same manner. This

step was repeated for each isotope, until all were removed from the spectrum of 82Se.

Table 4.2: ESum gate used for each isotope identified in the 82Se target data.

Isotope ESum Gate (MeV)

77Se
74Se
78Se
80Se
82Se

9.3 - 11.0

7.7 - 8.6

6.8 - 7.7

6.4 - 6.8

5.0 - 5.9

To describe this method in more detail, the subtraction of each isotope from the 82Se

spectrum will be discussed. The subtraction of 77Se from 82Se will not be shown here, as its

contribution is negligible and is not observed in the spectrum of 82Se. To begin with, the

spectrum of 74Se, gated on an ESum range of 7.7 - 8.6 MeV, is shown in Figure 4.20. This

spectrum was scaled by α74(En), as determined by

(cid:82) 5.9M eV
(cid:82) 8.6M eV

α74(En) =

5.0M eV C74(En, ESum)dESum
7.7M eV C74(En, ESum)dESum

,

(4.8)

where the integrals are taken from the 74Se ESum projection shown in panel (b) of Figure

4.19. After being scaled, the 74Se spectrum was subtracted from the 82Se spectrum, to

obtain the spectrum shown in Figure 4.21. The spectrum of the next isotope to be removed,

78Se, is shown in Figure 4.22. The scaling factor was determined in the same manner as

previously described, using the 78Se ESum projection shown in panel (c) of Figure 4.19, and

86

Equation 4.9.

(cid:82) 5.9M eV
(cid:82) 7.7M eV

5.0M eV C78(En, ESum)dESum
6.8M eV C78(En, ESum)dESum

α78(En) =

(4.9)

The scaled 78Se spectrum was then subtracted from the 82Se spectrum to obtain Figure 4.23.

The final isotope, 80Se, was subtracted in the same manner. The spectrum of 80Se is shown

in Figure 4.24, and the ESum projection is shown in panel (d) of Figure 4.19. The scaling

factor was determined via,

α80(En) =

(cid:82) 5.9M eV
(cid:82) 6.8M eV

5.0M eV C80(En, ESum)dESum
6.4M eV C80(En, ESum)dESum

,

(4.10)

and the 82Se spectrum with the scaled 80Se spectrum subtracted (shown in Figure 4.25), is

the final yield of neutron capture on 82Se. There is a slight over-subtraction of the 1970 eV

resonance of 80Se and an under-subtraction of the 1482 eV resonance of 80Se, which could

possibly be due to the scattering cross section of the higher energy resonance, which would

cause the peak to be smaller than predicted by the scaling.

4.5.2 Efficiency Determination

To enhance the signal-to-noise ratio of the data, several gates are made in software. Events

with a multiplicity of 1 are excluded due to an unfavorable signal-to-noise ratio. Events with

a multiplicity of 6 and above are excluded as there are not enough statistics available to

characterize the events. Therefore, for the 82Se data, events with multiplicities from 2 to 5

were used. A gate was also placed on the ESum, as the ESum distribution should only go

up to the Q-value of 82Se (5.818 MeV). For the 82Se data, total energies of 5.0 MeV to 5.9

MeV were used. While these gates enhance the signal-to-noise ratio, it comes at the cost

87

Figure 4.18: Yield of neutron capture on 82Se, gated on an ESum range of 5.0 - 5.9 MeV.
Contributions of resonances from other Se isotopes are labeled.

Figure 4.19: ESum projection of (a) 77Se (b) 74Se (c) 78Se and (d) 80Se

88

Figure 4.20: Spectra of 74Se (with 77Se contributions removed) gated on an ESum range of
7.7 - 8.6 MeV.

Figure 4.21: Yield of neutron capture on 82Se, gated on an ESum range of 5.0 - 5.9 MeV,
after the contribution from 74Se has been subtracted.

89

Figure 4.22: Spectra of 78Se (with 77Se and 74Se contributions removed) gated on an ESum
range of 6.8 - 7.7 MeV.

Figure 4.23: Yield of neutron capture on 82Se, gated on an ESum range of 5.0 - 5.9 MeV,
after the contributions from 74Se and 74Se have been subtracted.

90

Figure 4.24: Spectra of 80Se (with 77Se, 74Se, and 78Se contributions removed) gated on an
ESum range of 6.4 - 6.8 MeV.

Figure 4.25: Yield of neutron capture on 82Se, gated on an ESum range of 5.0 - 5.9 MeV,
after the contributions from 74Se, 78Se and 80Se have been subtracted.

91

of losing valid events. Therefore, an efficiency of these cuts (εcut) is determined to account

for the lost counts by determining the ratio of events counted within these gates to the true

number of neutron captures. The multiplicity and ESum gates were chosen to minimize the

uncertainty on εcut.

Due to a strong dependence on the properties of the γ-ray cascades emitted after neutron

capture, such as the energy and multiplicity distribution, the efficiency was determined

through simulations. Ultimately, the energy and multiplicity distribution depend on the

characteristics of the nucleus formed in neutron capture, in this case, 83Se, and the resonances

populated through neutron capture. The γ-ray cascades also depend strongly on the spin

and parity of the resonances. One of the strongest 83Se resonances observed (at an energy

of 6580 eV) has an assigned spin and parity of 1

2+, while the other two strongest resonances

observed (at energies of 3630 eV and 9508 eV) have tentative negative parity assigned, but

do not have a spin assigned [82]. Based on selection rules, the spin of these two resonances

can be assumed to be either 1
2−, and 3

2−.

1

2 or 3

2. Therefore, simulations were performed for J π = 1

2+,

Cascades of γ rays following neutron capture were simulated using the DICEBOX pro-

gram [97]. Below a certain energy, Ecrit (1.85 MeV for 83Se), the known levels and transitions

are used, as the level scheme is assumed to be complete. Above Ecrit, a statistical model

is used to determine levels and transition probabilities to generate simulated cascades. A

nuclear level density model is chosen and used to generate the levels, while the transition

probabilities are calculated from the partial radiative widths via:

XL(Ei − Ef )2L+1 fXL(Ei − Ef )

y2

ρ(Ei, J π
i )

,

(4.11)

(cid:88)

Γi,f =

XL

92

where fXL is the chosen γ-ray strength function model for the transition type X (electric

E or magnetic M) and multipolarity L, ρ(Ei, J π

i ) is the nuclear level density at the initial

excitation energy Ei, and y2

XL is a random value independent of the normal distribution,

with a zero mean and a unit variance. For 83Se, the Constant Temperature model was chosen

for the nuclear level density, and the generalized Lorentzian model was chosen for the γ-ray

strength function to be consistent with the models utilized in the β-Oslo analysis described

in Chapter 3. Both of these models have previously been described in Chapter 1.

For each spin and parity, 30 simulated systems (referred to here as realizations) with

100,000 cascades each were generated. Each realization is a different system of levels and

decay probabilities. These simulated cascades were then used as input in a Geant4 detector

simulation and then analyzed using the same conditions under which the 82Se data was ana-

lyzed. The total energy, ESum, distribution and the individual γ-ray spectra, or Multi-Step

Cascade (MSC) spectra, were averaged over all 30 simulations and compared to the experi-

mental data to validate the simulations and choice of NLD and γSF models. Comparisons of

MSC spectra from the simulations and from three strong resonances, gated on multiplicities

2, 3, 4 and 5, are shown in Figures 4.26 - 4.29.

As stated before, the uncertainty of the efficiency was taken into account when choosing

the range of the ESum gate. A study of the average efficiency across all 30 realizations and

the standard deviation as a function of the lower boundary of the ESum gate is shown in

Figure 4.30. The lower ESum boundary of 5.0 MeV was chosen to keep the uncertainty of

the efficiency to a relative minimum. Therefore, for < M > = [2,5] and 5.0 MeV > ESum >

5.9 MeV, efficiencies were calculated, and are shown in Table 4.3. A global average was
taken over all simulations to obtain an average efficiency of 0.422 ± 0.038. A global average

is used to represent all contributing neutron capture resonances.

93

Figure 4.26: Energy of individual γ rays, gated on multiplicity 2, for several strong resonances
in the 82Se data compared to simulated data for J π = 1
the average across all realizations, while error bars correspond to the standard deviation of
the bin content for each realization. The integral of each plot is normalized to unity for a
true comparison.

2−. Points correspond to

2+, 1

2−, 3

94

Figure 4.27: Energy of individual γ rays, gated on multiplicity 3, for several strong resonances
in the 82Se data compared to simulated data for J π = 1
the average across all realizations, while error bars correspond to the standard deviation of
the bin content for each realization. The integral of each plot is normalized to unity for a
true comparison.

2−. Points correspond to

2+, 1

2−, 3

95

Figure 4.28: Energy of individual γ rays, gated on multiplicity 4, for several strong resonances
in the 82Se data compared to simulated data for J π = 1
the average across all realizations, while error bars correspond to the standard deviation of
the bin content for each realization. The integral of each plot is normalized to unity for a
true comparison.

2−. Points correspond to

2+, 1

2−, 3

96

Figure 4.29: Energy of individual γ rays, gated on multiplicity 5, for several strong resonances
in the 82Se data compared to simulated data for J π = 1
the average across all realizations, while error bars correspond to the standard deviation of
the bin content for each realization. The integral of each plot is normalized to unity for a
true comparison.

2−. Points correspond to

2+, 1

2−, 3

97

Figure 4.30: Simulation efficiencies and their uncertainties as a function of the lower ESum
gate boundary, for M = [2,5] and an upper ESum gate boundary of 5.9 MeV.

4.5.3 Cross Section Results

With the yield of neutron capture on 82Se determined and the efficiency of γ rays detected

within the ESum and multiplicity cuts calculated, the cross section of 82Se(n,γ)83Se was

determined using Equation 4.6. The results are shown in Figure 4.31. The statistical un-

certainty shown in Figure 4.31 includes the uncertainty of the measured yield of neutron

capture propagated through all background subtractions, as well as the uncertainty of the

beam-monitor yields propagated through the determination of the neutron fluence. In ad-

dition to the statistical uncertainty shown, there is a systematic uncertainty of 4.25%. The

systemic uncertainty includes the 4% uncertainty from the neutron-fluence normalization

and the 0.47% uncertainty from the efficiency, added in quadrature.

The measured cross section was converted to a Maxwellian-Averaged Cross Section

(MACS) using Equation 4.12, where µ is the reduced mass, σ(En) is the cross section at

98

neutron energy En, and δ(En) is the bin width of the bin centered on En. At a temperature
(kT ) of 30 keV the MACS was determined to be 5.67 ± 4.72 mb. The experimentally deter-
mined MACS is in agreement with the recommended theoretical value of 9 ± 8 mb at 30 keV

from the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADoNiS) [98].

σM ACS(kT ) =

2√
π

σ(En)Ene

En
kT δ(En)

(4.12)

(cid:16) µ

(cid:17)2

1M eV(cid:88)

kT

En=10eV

Figure 4.31: Cross section of the 82Se(n,γ)83Se reaction measured with DANCE.

99

Table 4.3: Efficiencies determined by DICEBOX and GEANT4 simulations (M = [2,5], 5.0
MeV > ESum > 5.9 MeV) for J π = 1
30 realizations of artificial nuclei.

2−. 100000 γ-ray cascades were simulated for

2+, 1

2−, 3

Jπ = 1

2− Jπ = 3
2−

0.392

0.389

0.394

0.390

0.391

0.390

0.390

0.389

0.392

0.391

0.390

0.389

0.386

0.390

0.387

0.392

0.389

0.391

0.388

0.395

0.395

0.392

0.391

0.386

0.392

0.393

0.394

0.392

0.394

0.390

Realization

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

2+ Jπ = 1
0.409

0.468

0.413

0.408

0.406

0.406

0.405

0.406

0.408

0.409

0.407

0.410

0.407

0.407

0.408

0.404

0.407

0.405

0.404

0.406

0.409

0.411

0.411

0.411

0.413

0.412

0.406

0.411

0.413

0.408

0.405

0.469

0.466

0.470

0.466

0.467

0.466

0.466

0.468

0.466

0.467

0.466

0.469

0.470

0.467

0.468

0.469

0.465

0.467

0.472

0.467

0.467

0.471

0.465

0.468

0.465

0.467

0.466

0.469

0.466

100

Chapter 5

Results and Conclusion

5.1 Comparison of β-Oslo Cross Section to Directly

Measured Cross Section

The cross section of the 82Se(n,γ)83Se reaction was determined via a direct method and an

indirect method. As discussed in Chapter 3, the β-Oslo method was utilized to determine

the 82Se(n,γ)83Se cross section through a study of 83As β decay. As discussed in Chapter 4,

a direct measurement of neutron capture on 82Se has been measured using the Detector for

Advanced Neutron Capture Experiments, DANCE. These two cross section determinations

were compared to validate the β-Oslo method. The results are shown in Figure 5.1. The β-

Oslo cross section is systematically higher compared to the directly measured cross section.

The discrepancy is likely due to the β-Oslo cross section missing the resonance behavior,

which is not unsurprising, since TALYS calculates an average cross section. There is better

agreement at higher energies (above approximately 40 keV).

5.2 Conclusions and Outlook

The r-process is important to understanding the production of heavy elements, but there is

still a lack of knowledge about the r-process, including the astrophysical sites where it takes

101

Figure 5.1: Comparison of the directly measured cross section of 82Se(n,γ)83Se (black) to the
neutron capture cross section determined via the β-Oslo method (black line). The blue lines
indicate the upper and lower limits of the cross section determined via the β-Oslo method
through a systematic study of the uncertainty.

place. Models of the r-process can be used to produce abundance patterns with the aim of

pinpointing the astrophysical site, but such models require information on nuclear properties

of the nuclei involved, including neutron-capture cross sections. The cross sections of the

neutron-capture reactions that drive the r-process are a critical piece of information, but

presently there is a lack of directly measured neutron-capture cross sections in the neutron-

rich region where the r-process takes place. Results from theoretical models are used for

cases where experimental data does not exist. The lack of knowledge on the accuracy of these

theoretical calculations leads to an inability to reproduce r-process abundance patterns to

the degree of certainty needed for successful comparisons to known solar abundance patterns.

The β-Oslo method has been developed to constrain neutron-capture cross sections for β-

unstable nuclei not amenable to direct measurement, using experimental data from β-decay

102

studies. The nuclear level density and γ-ray strength function can be extracted from the

experimental β-decay data, and used to perform a Hauser-Feschbach calculation of the cross

section.

A previous study showed that the cross section of 50Ti(n, γ)51Ti, obtained via the β-Oslo

method, had excellent agreement with a directly measured cross section of 50Ti(n, γ)51Ti.

Since 51Ti is a relatively low mass nucleus with a low level density, a comparison of a higher

mass nucleus (and therefore a higher level density) is necessary to validate that the efficacy

of the β-Oslo method and the assumptions made in the analysis will hold for higher level

densities. The present work has determined a cross section for 82Se(n, γ)83Se from both a

direct measurement of neutron capture on 82Se, and the application of the β-Oslo method

on the β decay of 83As to 83Se. The two cross sections are in reasonable agreement.

It

is recommended to investigate the slight overestimation of the indirectly determined cross

section in the future to determine whether the overestimation is a systematic deviation or

an artifact of the analysis performed.

It is also recommended to perform a validation in

a heavier mass region for a nucleus with a higher level density than. Both 50Ti and 82Se

are located near shell closures, so it would be advantageous to perform a validation with a

nucleus that somewhere between shell closures. Overall, the β-Oslo method has been shown

to be a viable method for constraining neutron-capture cross sections.

103

BIBLIOGRAPHY

104

BIBLIOGRAPHY

[1] Christopher Sneden, John J Cowan, and Roberto Gallino. Neutron-Capture Elements

in the Early Galaxy.

[2] Walter Loveland, David J. Morriessey, and Glenn T. Seaborg. Modern Nuclear Chem-

istry. John Wiley & Sons, Inc., 2006.

[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] 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(4):2650–2662, 8 2010.

[6] Daniel Kasen, Brian Metzger, Jennifer Barnes, Eliot Quataert, and Enrico Ramirez-
Ruiz. Origin of the heavy elements in binary neutron-star mergers from a gravitational-
wave event. Nature, 551:80–84, 2017.

[7] M R Drout, A L Piro, B J Shappee, C D Kilpatrick, J D Simon, C Contreras, D A
Coulter, R J Foley, M R Siebert, N Morrell, K Boutsia, F Di Mille, 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 Campillay, 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,
358:1570–1574, 2017.

[8] M. R. Mumpower, R. Surman, G. C. McLaughlin, and A. Aprahamian. The impact
of individual nuclear properties on r-process nucleosynthesis. Progress in Particle and
Nuclear Physics, 86:86–126, 2016.

[9] S Goriely, N Chamel, and J M Pearson. Skyrme-Hartree-Fock-Bogoliubov Nuclear Mass
Formulas: Crossing the 0.6 MeV Accuracy Threshold with Microscopically Deduced
Pairing. Phys. Rev. Lett., 102:152503, 2009.

105

[10] J Duflo and A. P. Zuker. Microscopic mass formulas. Phys. Rev. C, 52(1), 1995.

[11] P. Moller, J. R. Nix, W. D. Myers, and W. J. Swiatecki. Nuclear Ground-State Masses

and Deformations. Atomic Data and Nuclear Data Tables, 59:185–381, 1995.

[12] Arjan Koning, Stephane Hilaire, and Stephane Goriely. TALYS User Manual (v. 1.95).

Technical report.

[13] Thomas Rauscher and Friedrich-Karl Thielemann. Astrophysical Reaction Rates From
Statistical Model Calculations. Atomic Data and Nuclear Data Tables, 75(1-2):1–351,
2000.

[14] M. Beard, E. Uberseder, R. Crowter, and M. Wiescher. Comparison of statistical model
calculations for stable isotope neutron capture. Phys. Rev. C, 90:034619–undefined,
2014.

[15] G. Savard, R. C. Pardo, S. Baker, C. N. Davids, A. Levand, D. Peterson, D. G. Phillips,
T. Sun, R. Vondrasek, B. J. Zabransky, and G. P. Zinkann. CARIBU: A new facility
for the study of neutron-rich isotopes. Hyperfine Interactions, 199(1):301–309, 7 2011.

[16] J Van Schelt, D Lascar, G Savard, J A Clark, P F Bertone, S Caldwell, A Chaudhuri,
A F Levand, G Li, G E Morgan, R Orford, R E Segel, K S Sharma, and M G Sternberg.
First Results from the CARIBU Facility: Mass Measurements on the r-Process Path.
Phys. Rev. Lett., 111:–undefined, 2013.

[17] J Hakala, J Dobaczewski, D Gorelov, T Eronen, A Jokinen, A Kankainen, V S Kolhinen,
M Kortelainen, I D Moore, H Penttil¨a, S Rinta-Antila, J Rissanen, A Saastamoinen,
V Sonnenschein, and J A Yst¨o. Precision Mass Measurements beyond 132 Sn: Anoma-
lous Behavior of Odd-Even Staggering of Binding Energies.

[18] M Matoˇs, A Estrade, M Amthor, A Aprahamian, D Bazin, A Becerril, T Elliot,
D Galaviz, A Gade, S Gupta, G Lorusso, F Montes, J Pereira, M Portillo, A M Rogers,
H Schatz, D Shapira, E Smith, A Stolz, and M Wallace. TOF-Bρ mass measurements
of very exotic nuclides for astrophysical calculations at the NSCL. Journal of Physics
G: Nuclear and Particle Physics, 35:6, 2008.

[19] G Lorusso, S Nishimura, Z Y Xu, A Jungclaus, Y Shimizu, G S Simpson, P.-A
S¨oderstr¨om, H Watanabe, F Browne, P Doornenbal, G Gey, H S Jung, B Meyer,
T Sumikama, J Taprogge, Zs Vajta, J Wu, H Baba, G Benzoni, K Y Chae, F C L
Crespi, N Fukuda, R Gernh¨auser, N Inabe, T Isobe, T Kajino, D Kameda, G D Kim,
Y.-K Kim, I Kojouharov, F G Kondev, T Kubo, N Kurz, Y K Kwon, G J Lane, Z Li,
A Montaner-Piz´a, K Moschner, F Naqvi, M Niikura, H Nishibata, A Odahara, R Or-
landi, Z Patel, Zs Podoly´ak, H Sakurai, H Schaffner, P Schury, S Shibagaki, K Steiger,
H Suzuki, H Takeda, A Wendt, A Yagi, and K Yoshinaga. β-Decay Half-Lives of 110

106

Neutron-Rich Nuclei across the N 82 Shell Gap: Implications for the Mechanism and
Universality of the Astrophysical r Process. Phys. Rev. Lett., 114, 2015.

[20] M Quinn, A Aprahamian, J Pereira, R Surman, O Arndt, T Baumann, A Becerril,
T Elliot, A Estrade, D Galaviz, T Ginter, M Hausmann, S Hennrich, R Kessler, K.-L
Kratz, G Lorusso, P F Mantica, M Matos, F Montes, B Pfeiffer, M Portillo, H Schatz,
F Schertz, L Schnorrenberger, E Smith, A Stolz, W B Walters, and A W¨ohr. β decay
of nuclei around 90Se: Search for signatures of a N = 56 subshell closure relevant to the
r process. Phys. Rev. C, 85:35807, 2012.

[21] A I Morales, J Benlliure, T Kurtuki´an-Nieto, K.-H Schmidt, S Verma, P H Regan,
Z Podoly´ak, M G´orska, S Pietri, R Kumar, E Casarejos, N Al-Dahan, A Algora,
N Alkhomashi, H ´Alvarez-Pol, G Benzoni, A Blazhev, P Boutachkov, A M Bruce, L S
C´aceres, I J Cullen, A M Denis Bacelar, P Doornenbal, M E Est´evez-Aguado, G Farrelly,
Y Fujita, A B Garnsworthy, W Gelletly, J Gerl, J Grebosz, R Hoischen, I Kojouharov,
N Kurz, S Lalkovski, Z Liu, C Mihai, F Molina, D M¨ucher, B Rubio, H Shaffner, S J
Steer, A Tamii, S Tashenov, J J Valiente-Dob´on, P M Walker, H J Wollersheim, and P J
Woods. Half-Life Systematics across the N 126 Shell Closure: Role of First-Forbidden
Transitions in the β Decay of Heavy Neutron-Rich Nuclei. Phys. Rev. Lett., 113, 2014.

[22] T. Kurtukian-Nieto, J. Benlliure, K. H. Schmidt, L. Audouin, F. Becker, B. Blank, I. N.
Borzov, E. Casarejos, F. Farget, M. Fern´andez-Ord´o˜nez, J. Giovinazzo, D. Henzlova,
B. Jurado, K. Langanke, G. Mart´ınez-Pinedo, J. Pereira, and O. Yordanov. Beta-decay
half-lives of new neutron-rich isotopes of Re, Os and Ir approaching the r-process path
near N = 126. Eur. Phys. J. A, 50(9):1–8, 2014.

[23] A. C. Larsen, A. Spyrou, S. N. Liddick, and M. Guttormsen. Novel techniques for
constraining neutron-capture rates relevant for r-process heavy-element nucleosynthesis.
Progress in Particle and Nuclear Physics, 2019.

[24] Walter Hauser and Herman Feshbach. The inelastic scattering of neutrons. Physical

Review, 87(2):366–373, 1952.

[25] N Bohr, R Peierls, and G Placzek. Nuclear Reactions in the Continuous Energy Region.

Nature, 144:200–201, 1939.

[26] A J Koning and J P Delaroche. Local and global nucleon optical models from 1 keV to

200 MeV. Nucl. Phys. A, 713:231–310, 2003.

[27] J.-P Jeukenne, A Lejeune, and C Mahaux˜. Microscopic calculation of the symme-
try and Coulomb components of the complex optical-model potential. Phys. Rev. C,
15(1):10–29, 1977.

[28] Torleif Ericson. The statistical model and nuclear level densities. Advances in Physics,

9(36):425–511, 1960.

107

[29] T Von Egidy and D Bucurescu. Experimental energy-dependent nuclear spin distribu-

tions. Phys. Rev. C, 80:54310, 2009.

[30] H. A. Bethe. Nuclear Physics B. Nuclear Dynamics, Theoretical. Rev. Mod. Phys., 9:69,

1937.

[31] 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 A, 217:269–298, 1973.

[32] A. G. W. Cameron. Nuclear Level Spacings. Can. J. Phys., 36:1040–1057, 1958.

[33] T. D. Newton. Shell Effects on the Spacing of Nuclear Levels. Can. J. Phys, 34:804–829,

1956.

[34] A Gilbert and A G W Cameron. A composite nuclear level density formula with shell

corrections. Can. J. Phys., 43:1446, 1965.

[35] A. Gilbert, F. S. Chen, and A. G. W. Cameron. Level Densities in Lighter Nuclei. Can.

J. Phys, 43:1248–1258, 1965.

[36] S. Goriely, F. Tondeur, and J. M. Pearson. a HartreeFock Nuclear Mass Table. Atomic

Data and Nuclear Data Tables, 77(2):311–381, 2001.

[37] S Goriely, S Hilaire, and A J Koning. Improved microscopic nuclear level densities within
the Hartree-Fock-Bogoliubov plus combinatorial method. Phys. Rev. C, 78:64307, 2008.

[38] S Hilaire, M Girod, S Goriely, and A J Koning. Temperature-dependent combinatorial

level densities with the D1M Gogny force. Phys. Rev. C, 86:064317, 2012.

[39] M Krticka and F Bev´a. What do we really know about photon strength functions? Re-
lated content Scissors mode of Gd nuclei measured, with the DANCE detector. Journal
of Physics G, 35:014025, 2007.

[40] D M Brink.

Individual Particle and Collective Aspects of the Nuclear Photoeffect.

Nuclear Physics, 4:215–220, 1957.

[41] Peter Axel. Electric Dipole Ground-State Transition Width Strength Function and

7-Mev Photon Interactions. Phys. Rev., 126(2), 1962.

[42] J Kopecky and M Uhl. Test of gamma-ray strength functions in nuclear reaction model

calculations. Phys. Rev. C, 41(5), 1990.

[43] 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, 93(14), 2004.

108

[44] 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–undefined, 2005.

[45] 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 95Mo. Phys. Rev. Lett., 108:162503, 2012.

[46] 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 Sc44,45. Physical Review C, 76(4):044303, 2007.

[47] 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. Norrby,
H. T. Nyhus, G. Perdikakis, S. Siem, A. Spyrou, and N. U.H. Syed. Nuclear level density
and γ-ray strength function of 43Sc. Physical Review C - Nuclear Physics, 85(6):1–5,
2012.

[48] 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 of 138La: Impact of 138,139La statistical properties. Phys. Lett.
B, 744:268–272, 5 2015.

[49] 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 Mc-
cleskey, 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–undefined, 2016.

[50] A. C. Larsen and S. Goriely. Impact of a low-energy enhancement in the γ-ray strength
function on the neutron-capture cross section. Physical Review C - Nuclear Physics,
82(1):1–7, 2010.

[51] A C Larsen, N Blasi, A Bracco, F Camera, T K Eriksen, A G¨orgen, M Guttormsen,
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. Evidence for the Dipole Nature
of the Low-Energy Enhancement in 56 Fe. Phys. Rev. Lett., 111:242504, 2013.

[52] M D Jones, A O Macchiavelli, M Wiedeking, L A Bernstein, H L Crawford, C M Camp-
bell, 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

109

Sarantites, S Siem, A V Voinov, and S Zhu. Examination of the low-energy enhancement
of the γ-ray strength function of 56Fe. Phys. Rev. C, 97:24327, 2018.

[53] B. Alex Brown and A.C. Larsen. Large Low-Energy M1Strength for Fe-56,57 within

the Nuclear Shell Model. Physical Review Letters, 113(25), 12 2014.

[54] 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.

[55] S. Goriely, E. Khan, and M. Samyn. Microscopic HFB + QRPA predictions of dipole

strength for astrophysics applications. Nuclear Physics A, 739:331–352, 7 2004.

[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., 121:052501, 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 107Pd. Phys. Rev. C, 82:064610–undefined, 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,
88:15805, 2013.

[59] M Guttormsen, T S Tveter, L Bergholt, F Ingebretsen, and J Rekstad. The unfolding
of continuum y-ray spectra. Nuclear Instruments and Methods in Physics Research A,
374:371–376, 1996.

[60] M Guttormsen, T Ramsoy, and J Rekstad. The First Generation γ-rays From Hot

Nuclei. Nuclear Instruments and Methods in Physics Research, 255:518–523, 1987.

[61] 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. Nuclear Instruments
and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment, 447(3):498–511, 2000.

[62] 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
K. Wikan. Analysis of possible systematic errors in the Oslo method. Physical Review
C - Nuclear Physics, 83(3):1–23, 2011.

110

[63] 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. Physical Review Letters, 113(23):232502, 2014.

[64] A Ratkiewicz, J A Cizewski, J E Escher, G Potel, J T Burke, R J Casperson, M Mc-
cleskey, R A E Austin, S Burcher, R O Hughes, B Manning, S D Pain, W A Peters,
S Rice, T J Ross, N D Scielzo, C Shand, and K Smith. Towards Neutron Capture on
Exotic Nuclei: Demonstrating (d,pγ) as a Surrogate Reaction for (n,γ). Phys. Rev.
Lett., 122:052502, 2019.

[65] T A Laplace, F Zeiser, M Guttormsen, A C Larsen, D L Bleuel, L A Bernstein, B L
Goldblum, S Siem, F L Bello Garotte, J A Brown, L Crespo Campo, T K Eriksen,
F Giacoppo, A G¨orgen, K Hadynska, Hadynska-Klek Klek, R A Henderson, M Klinte-
fjord, M Lebois, T Renstrøm, S J Rose, E Sahin, T G Tornyi, G M Tveten, A Voinov,
M Wiedeking, J N Wilson, and W Younes. Statistical properties of 243 Pu, and 242
Pu(n,γ ) cross section calculation. Phys. Rev. C, 93:014323–undefined, 2016.

[66] T. G. Tornyi, M. Guttormsen, T. K. Eriksen, A. G¨orgen, F. Giacoppo, T. W. Hagen,
A. Krasznahorkay, A. C. Larsen, T. Renstrøm, S. J. Rose, S. Siem, and G. M. Tveten.
Level density and γ-ray strength function in the odd-odd Np238 nucleus. Phys. Rev. C,
89:044323–undefined, 2014.

[67] B V Kheswa, M Wiedeking, J A Brown, A C Larsen, S Goriely, M Guttormsen, F L
Bello Garrote, L A Bernstein, D L Bleuel, T K Eriksen, F Giacoppo, A G¨orgen, B L
Goldblum, T W Hagen, P E Koehler, M Klintefjord, K L Malatji, J E Midtbø, H T
Nyhus, P Papka, T Renstrøm, S J Rose, E Sahin, S Siem, and T G Tornyi. 137,138,139
La(n,γ) cross sections constrained with statistical decay properties of 138,139,140 La
nuclei. Phys. Rev. C, 95:045805, 2017.

[68] S N Liddick, A C Larsen, M Guttormsen, A Spyrou, B P Crider, F Naqvi, J E Midtbø,
F L Bello Garrote, D L Bleuel, L Crespo Campo, A Couture, A C Dombos, F Giacoppo,
A G¨orgen, K Hadynska-Klek, T W Hagen, V W Ingeberg, B V Kheswa, R Lewis,
S Mosby, G Perdikakis, C J Prokop, S J Quinn, T Renstrøm, S J Rose, E Sahin,
S Siem, G M Tveten, M Wiedeking, and F Zeiser. Benchmarking the extraction of
statistical neutron capture cross sections on short-lived nuclei for applications using the
beta-Oslo method. Phys. Rev. C, 100:024624, 2019.

[69] D. J. Morrissey, B. M. Sherrill, M. Steiner, A. Stolz, and I. Wiedenhoever. Commis-
sioning the A1900 projectile fragment separator. Nuclear Instruments and Methods in
Physics Research, Section B: Beam Interactions with Materials and Atoms, 204:90–96,
2003.

[70] A. Stolz, T. Baumann, T. N. Ginter, D. J. Morrissey, M. Portillo, B. M. Sherrill,
M. Steiner, and J. W. Stetson. Production of rare isotope beams with the NSCL

111

fragment separator. Nuclear Instruments and Methods in Physics Research, Section B:
Beam Interactions with Materials and Atoms, 241:858–861, 12 2005.

[71] A. Simon, S. J. Quinn, A. Spyrou, A. Battaglia, I. Beskin, A. Best, B. Bucher,
M. Couder, P. A. Deyoung, X. Fang, J. Gorres, 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. Nuclear In-
struments and Methods in Physics Research, Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment, 703:16–21, 2013.

[72] H. Bateman. The solution of a system of differential equations occurring in the theory

of radioactive transformations. Proc. Cambridge Philos. Soc., 15:423–427, 1910.

[73] Daniel Abriola, Melih Bostan, Sefa Erturk, Manssour Fadil, Monica Galan, Sakari Juu-
tinen, Tibor Kib´edi, Filip Kondev, Aurelian Luca, Alexandru Negret, Ninel Nica, Bernd
Pfeiffer, Balraj Singh, Alejandro Sonzogni, Janos Timar, Jagdish Tuli, Tsanka Venkova,
and Kazimierz Zuber. Nuclear Data Sheets for A = 84. Nuclear Data Sheets, 110:2815–
2944, 2009.

[74] E. A. McCutchan. Nuclear data sheets for A = 83. Nuclear Data Sheets, 125:201–394,

2015.

[75] Rebecca L Lewis. Indirect Neutron-capture Cross Sections for the Weak r-process. PhD

thesis, Michigan State University, 2019.

[76] M. Guttormsen. Matrix Manipulation Program (MAMA), 2019.

[77] M. Guttormsen, A. C. Larsen, A. Gorgen, T. Renstrom, S. Siem, T. G. Tornyi, and
G. M. Tveten. Validity of the Generalized Brink-Axel Hypothesis in Np 238. Physical
Review Letters, 116(1):1–5, 2016.

[78] 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. Cooper-
man, M. A. Cort´es-Giraldo, G. Cosmo, G. Cuttone, G. Depaola, L. Desorgher, X. Dong,
A. Dotti, V. D. Elvira, G. Folger, Z. Francis, A. Galoyan, L. Garnier, 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. Mancusi, A. Man-
tero, 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.

112

Truscott, L. Urban, V. Uzhinsky, J. M. Verbeke, M. Verderi, B. L. Wendt, H. Wen-
zel, 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, 11 2016.

[79] M. Guttormsen, A.C. Larsen, A. Spyrou, S.N. Liddick, and F. Zeiser. Unfolding
of excitation-energy spectra from total absorption γ-ray spectroscopy for the β-Oslo
method. In Preparation. 2020.

[80] A.V. Ignatyuk. Contribution to the Second CRP Meeting on RIPL. Technical report,

Vienna, 11 1996.

[81] P. Carlos, H. Beil, R. Bergere, J. Fagot, A. Lepretre, A. Veyssiere, and G. V. Solodukhov.
A Study of the Photoneutron Contribution to the Giant Dipole Resonance of Nuclei in
the 64 ¡ A ¡ 86 Mass Region. Nuclear Physics, 258:365–387, 1976.

[82] S.F. Mughabghab. Atlas of Neutron Resonances: Resonance Parameters and Thermal

Cross Sections Z = 1-100. Elsevier, 5th edition, 2006.

[83] A.V. Ignatyuk, J.L. Well, S. Raman, and S. Kahane. Density of discrete levels in 116Sn.

Phys. Rev. C, 47:1504–undefined, 1993.

[84] 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.

[85] S. Goriely. Radiative neutron captures by neutron-rich nuclei and the r-process nucle-

osynthesis. Phys. Lett. B, 436(1-2):10–18, 1998.

[86] M. Heil, R. Reifarth, M. M. Fowler, R. C. Haight, F. K¨appeler, R. S. Rundberg, E. H.
Seabury, J. L. Ullmann, J. B. Wilhelmy, and K. Wisshak. 4π BaF2 detector for (n,γ)
cross-section measurements at a spallation neutron source. Nuclear Instruments and
Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment, 459:229–246, 2001.

[87] C J Prokop, A Couture, S Jones, S Mosby, G Rusev, J Ullmann, and M Krtiˇcka.
Measurement of the 65Cu(n, γ) cross section using the Detector for Advanced Neutron
Capture Experiments at LANL. Phys. Rev. C, 99, 2019.

[88] S. Mosby, F. Tovesson, A. Couture, D. L. Duke, V. Kleinrath, R. Meharchand, K. Meier-
bachtol, J. M. ODonnell, B. Perdue, D. Richman, and D. Shields. A fission fragment de-
tector for correlated fission output studies. Nuclear Instruments and Methods in Physics

113

Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment,
757:75–81, 9 2014.

[89] P W Lisowski, C D Bowman, G J Russell, and S A Wender. The Los Alamos National
Laboratory Spallation Neutron Sources. Nuclear Science and Engineering, 106(2):208–
218, 10 1990.

[90] D Habs, F S Stephens, and R M Diamond. A Proposal for a Crystal-Ball Detector

System. Technical report, 1979.

[91] M. Jandel, T. A. Bredeweg, A. Couture, M. M. Fowler, E. M. Bond, M. B. Chadwick,
R. R.C. Clement, E. I. Esch, J. M. O’Donnell, R. Reifarth, R. S. Rundberg, J. L.
Ullmann, D. J. Vieira, J. B. Wilhelmy, J. M. Wouters, R. A. Macri, C. Y. Wu, and
J. A. Becker. GEANT4 simulations of the DANCE array. Nuclear Instruments and
Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms,
261(1-2 SPEC. ISS.):1117–1121, 8 2007.

[92] A. Couture and R. Reifarth. Direct measurements of neutron capture on radioactive

isotopes. Atomic Data and Nuclear Data Tables, 2007.

[93] Saint-Gobain Crystals. BaF 2 Barium Fluoride Scintillation Material, 2016.

[94] Jan M. Wouters, Ana Alpizar Vicente, Todd A. Bredeweg, Ernst Esch, Robert C.
Haight, Robert Hatarik, John M. O’Donnell, Rene Reifarth, Robert S. Rundberg,
Jon M. Schwantes, Steven A. Sheets, John L. Ullmann, David J. Vieira, and Jerry B.
Wilhelmy. Acquisition - Analysis system for the DANCE (detector for advanced neutron
capture experiments) BaF 2 gamma-ray calorimeter. IEEE Transactions on Nuclear
Science, 53(3):880–885, 6 2006.

[95] Trace Sciences International. Stable Isotopes Supplier.

[96] M. B. Chadwick, M. Herman, P. Obloˇzinsk´y, M. E. Dunn, Y. Danon, A. C. Kahler, D. L.
Smith, B. Pritychenko, G. Arbanas, R. Arcilla, R. Brewer, D. A. Brown, R. Capote,
A. D. Carlson, Y. S. Cho, H. Derrien, K. Guber, G. M. Hale, S. Hoblit, S. Holloway,
T. D. Johnson, T. Kawano, B. C. Kiedrowski, H. Kim, S. Kunieda, N. M. Larson,
L. Leal, J. P. Lestone, R. C. Little, E. A. McCutchan, R. E. MacFarlane, M. MacInnes,
C. M. Mattoon, R. D. McKnight, S. F. Mughabghab, G. P.A. Nobre, G. Palmiotti,
A. Palumbo, M. T. Pigni, V. G. Pronyaev, R. O. Sayer, A. A. Sonzogni, N. C. Summers,
P. Talou, I. J. Thompson, A. Trkov, R. L. Vogt, S. C. van der Marck, A. Wallner, M. C.
White, D. Wiarda, and P. G. Young. ENDF/B-VII.1 nuclear data for science and
technology: Cross sections, covariances, fission product yields and decay data. Nuclear
Data Sheets, 112(12):2887–2996, 12 2011.

114

[97] F. Becvar. Simulation of gamma cascades in complex nuclei with emphasis on assessment
of uncertainties of cascade-related quantities. Nuclear Instruments and Methods in
Physics Research A, 417:434–449, 1998.

[98] I. Dillmann, R. Plag, F Kappeler, and T. Rauscher. The third update of the ”Karl-
sruhe Astrophysical Database of Nucleosynthesis in Stars”. EFNUDAT Fast Neutrons,
Proceedings of the Scientific Workshop on Neutron Measurements, 2009.

115