EXPERIMENTAL CONSTRAINTS ON NUCLEOSYNTHESIS IN OXYGEN-NEON NOVAE

By

Cathleen Fry

A DISSERTATION

Submitted

to Michigan State University

in partial fulfillment of the requirements

for the degree of

Physics – Doctor of Philosophy

2018

ABSTRACT

EXPERIMENTAL CONSTRAINTS ON NUCLEOSYNTHESIS IN OXYGEN-NEON NOVAE

By

Cathleen Fry

Classical novae occur in close binary systems consisting of a white dwarf and a star with a hydro-

gen rich envelope. The white dwarf accretes hydrogen which ignites in a thermonuclear runaway.

Nucleosynthesis proceeds close to the valley of stability through a series of (p,γ) and (p,α) re-
actions and β + decays. Each of these events ejects 10−7 − 10−3 M(cid:12) of material. Some of this
ejected material condenses into grains, and these grains can be identified in primitive meteorites

by comparing their measured isotopic ratios to those predicted by various stellar models.

The 30P(p,γ)31S reaction rate potentially acts as a bottleneck, controlling nucleosynthetic flow
in the 30 ≤ A ≤ 40 region. Large uncertainties in this rate dominate the uncertainty in expected
silicon isotopic ratios and also certain elemental ratios which have been proposed to help constrain

the peak temperatures reached in classical novae. Resonances expected to contribute to this rate

are known, but the corresponding resonance strengths are not known. As a step towards deter-

mining experimental resonance strengths, we ran an experiment to determine lifetimes of these
states populated via the 32S(3He,α)31S reaction and using the Doppler Shift Lifetime chamber

and GRIFFIN detectors at TRIUMF. Our initial run failed due to a number of issues. Diagnosis

of those issues and improvements informed by this analysis are discussed. Preliminary data from

a second run are included to demonstrate improvements in our setup. Two states in the region of

astrophysical interest have been observed, and we expect to be able to provide constraints on the

lifetimes of these two states as well as a number of bound states.

Similarly, the 34g,mCl(p,γ)35Ar reaction rate impacts predictions of sulfur isotopic ratios.

These ratios were only very recently measured in nova candidate grains, and other measured iso-

topic ratios (C, N, Si) are not currently sufficient to distinguish between classical nova and type II

supernova grain origins. As a first step toward determining this reaction rate, we have performed

an experiment at Maier-Leibniz Laboratorium using the 36Ar(d,t)35Ar reaction to populate the

states of interest and a Q3D magnetic spectrograph to extract excitation energies. 17 new levels

have been discovered, and the uncertainties associated with previously known levels have been

reduced from 10 keV to typically 3 keV.

To perserverance

iv

Copyright by
CATHLEEN FRY
2018

ACKNOWLEDGMENTS

Without my advisor, Chris Wrede, none of this dissertation work would have been possible. Chris

gave me a lot of space and opportunities to grow as a scientist. When something went wrong, he

was always ready with another plan, with something else we could try. If he didn’t have funding

for a summer school, conference, or experiment I wanted to attend, he was always supportive of

me writing small travel grants. While my path through grad school was bumpy and nonlinear, he

and the rest of my committee, Alex Brown, Laura Chomiuk, Wade Fisher, and Artemis Spyrou,

stuck with me through a few project changes.

I’m grateful for the entire Wrede group. David Pérez-Loureiro and Mike Bennett were partic-

ularly helpful as I was getting started in grad school. Brent Glassman and I have been in the group

together for over five years now, and he was always willing to listen to me talk through a problem.

Sarah Schwartz, Jason Surbrook, Tamas Budner, and Moshe Friedman have also provided helpful

input throughout my career. While our group has had many undergraduate students in my time as

a graduate student, I have to give special thanks to Pranjal Tiwari for his patience while I learned

how to be a mentor.

As someone who lead experiments at two different facilities in different countries, I have col-

laborators all over the world to thank for their successes. For my first experiment, in only my

second semester of graduate school, I have to thank Alan Chen and Anuj Parikh, as well as the

local group at MLL. My second experiment ran twice, and there are numerous people to thank for

making that happen. In particular, Barry Davids provided a lot of insight into this project, from

proposal writing to target making to data analysis. Oliver Kirsebom provided me with a lot of tools

he developed for the analysis of another dataset from the DSL setup. Nick Esker was invaluable in

the second run, and I’m glad to leave the remaining data analysis in his hands.

I also have to thank the people that helped me find my love of nuclear physics. Michael Thoen-

nessen provided me with an excellent opportunity to learn about the history of nuclear physics

vi

during my REU with him in 2011 as well as encouraging me to experience an NSCL experiment

during the comissioning of LISA. Umesh Garg provided me the opportunity to travel across the

world to participate in one of my first experiments as an REU student in 2012. Ray Kozub taught

my first nuclear physics course, while I was an undergraduate at TTU, and encouraged me to apply

for REUs, then grad scool. I also have to thank Mr. Foy, my high school physics teacher, who

accidentally assigned me "probably too much for a high schooler" in a presentation preparing for

a field trip to ORNL, where I started to learn what nuclear physics really was.

I’ve also made a number of friends in graduate school that have provided an immense amount

of support through many tough times. There are too many to name here. The Graduate Employees

Union provided connections to graduate students outside the physics department as well as mean-

ingful volunteer work. I was given the chance to grow as a leader and I’ve made friends for life.

The Grand Canonical Ensemble provided a great opportunity to get away from my desk twice a

week to make music with great people. APS Forum on Graduate Student Affairs connected me

with physics students across the country.

Thank you to all of the graduate students across the lab and the physics department for assorted

lunch and hallway discussions. Thanks to everyone who reminded me to eat or sleep when I got so

caught up on something that I would forget. My office mates have put up with so many questions

and listened to me vent about so many things. I’ll miss our nerf fights.

I must also thank my family for their unwavering support. They took my calls at weird hours

when I was freaking out about missing a plane, changing dissertation plans, or any other problems.

I’m especially grateful for my mother, who was always there when I needed her, but her only

requirement when I was busy was that I occasionally text her that I was not dead.

vii

TABLE OF CONTENTS

LIST OF TABLES .

LIST OF FIGURES .

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CHAPTER 1

1.1 Nuclear astrophysics
1.2 Binary star systems .

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1.2.1 Classical novae .
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INTRODUCTION .
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1.3.1 Modeling of grain formation . . . . . . . . . . . . . . . . . . . . . . . . .
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1.4 Presolar grains .

1.3 Stellar dust .

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1
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2.3

Shell Model . .

Indirect measurements

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CHAPTER 2 CLASSICAL NOVA NUCLEOSYNTHESIS . . . . . . . . . . . . . . . . .
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9
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2.1 Reaction rate formalism .
2.2 Methods for determining resonant capture reaction rates . . . . . . . . . . . . . . . 13
2.2.1 Hauser-Feshbach formalism . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2
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2.2.3 Direct measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.4
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30P(p,γ)31S .
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2.3.1 Nucleosynthetic bottleneck . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Nova thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.3
2.3.4 Current experimental information on 30P(p,γ)31S
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34g,mCl(p,γ)35Ar .
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Isomeric state in 34Cl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.1
2.4.2
Sulfur isotopic ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.3 Current experimental information on 34g,mCl(p,γ)35Ar . . . . . . . . . . . 22

Si isotopic ratios

2.4

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3.1 Applicability of DSAM .
3.2 Theory .
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CHAPTER 3 DOPPLER SHIFT ATTENUATION METHOD . . . . . . . . . . . . . . . . 23
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3.3 Lineshape analysis
3.4 Advantages of inverse kinematics . . . . . . . . . . . . . . . . . . . . . . . . . .

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Stopping powers
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3.2.1

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CHAPTER 4

32S(3He,α)31S EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1 Beam delivery .
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4.2 Gold targets implanted with 3He . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Target chamber

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
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4.4 Detectors
4.5 Electronics .
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4.6 Run 2 experimental differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

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CHAPTER 5

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5.1 Calibration .

5.2 Run 1 analysis . .

32S(3He,α)31S ANALYSIS AND DISCUSSION . . . . . . . . . . . . . . . 43
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.1.1
Silicon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.1.2 Germanium Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.1
γ-ray identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2.2
31S first excited state . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 47
5.2.3
32S first excited state . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5.2.4
5.2.5
Fusion evaporation reactions . . . . . . . . . . . . . . . . . . . . . . . .
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5.2.6 Collimator activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
. 53
5.3.1 Background reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3.2 Tentative transition identification . . . . . . . . . . . . . . . . . . . . . . . 55

5.3 Preliminary analysis of Run 2 data . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 6

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Ion-implanted C targets .
2H ion source .
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36Ar(d,t)35Ar EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.1
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6.2
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6.3 Munich M-P tandem Van de Graaff accelerator
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6.4 Target interaction .
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6.5 Q3D magnetic spectrograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 65
6.6 Position sensitive cathode strip detector
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6.7 Data acquisition system (DAQ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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CHAPTER 7

7.1 Particle identification .
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7.2 Background subtraction .
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7.3 Spectrograph plotting .
7.4 Peak fitting . .
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7.5 Calibration .
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7.6 Excitation energies in 35Ar . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7 Level densities .

36Ar(d,t)35Ar ANALYSIS AND DISCUSSION . . . . . . . . . . . . . . . 71
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
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CHAPTER 8 SUMMARY AND OUTLOOK . . . . . . . . . . . . . . . . . . . . . . . . 89

BIBLIOGRAPHY .

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LIST OF TABLES

Table 7.1

35Ar excitation energies measured in each spectrum and the statistical sig-
nificances of the corresponding peaks, expressed as standard deviations (σ).
Uncertainties quoted include systematic uncertainties and statistical uncertain-
ties from individual fits. Two separate measurements were taken at 15◦. The
results from the higher statistics measurements are reported in the left-most
column and shown in the top panel of Figure 7.13.

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. 85

Table 7.2 Previous and present 35Ar excitation energies and corresponding center of

mass (C.M.) resonance energies (keV) from the present work.

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. 86

Table 7.3 Comparison of isotopic abundances in the argon bottle used for implanted

targets and solar isotopic ratios.

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x

LIST OF FIGURES

Figure 1.1 Binding energy per nucleon as a function of mass number, A. Figure from [1].

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Figure 1.2 Diagram of the binary system. Each star, their Roche lobes, and the inner

Lagrangian point are labeled.

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Figure 1.3 Dust mass for grains larger than 10 Å summed over ejecta zones in a type
II supernova as a function of time post explosion. The dotted line shows the
sum of all dust mass formed in the model with a progenitor of 15 M(cid:12). Figure
from [2].

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Figure 1.4 Cartoon of the steps from presolar grain formation through identification.

Figure adapted from [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.5 Measured C and N isotopic ratios for various presolar grains. The dotted

lines are used to show solar isotopic ratios. Figure from [4]. . . . . . . . . . .

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Figure 1.6 Secondary electron micrographs of silicon carbide grains from the Murchi-

son meteorite. Figure from [5].

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1

2

5

6

7

8

Figure 2.1 Classical nova nucleosynthesis path for a 1.35 M(cid:12) ONe nova at peak tem-

perature. Figure from [6].

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Figure 2.2 Graph showing the two components that contribute to the Gamow peak, the

energy distribution, and Coulomb barrier penetrability. Figure from [1].

. . . . 11

Figure 2.3 Diagram of energetics for capture of a proton capture with center of mass

energy Er onto a nucleus with Z protons and A-Z neutrons.

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Figure 2.4 Classical nova nucleosynthesis path, zoomed in around 30P. Figure adapted

from [6].

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Figure 2.5 Elemental ratios proposed as nova thermometers. Figure from [7].

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Figure 2.6 Error bands on predicted elemental ratios. The black line is the post pro-
cessing prediction, and the dotted black lines show the uncertainties in the
ratios. The uncertainties in these ratios are dominated by the uncertainty in
the 30P(p,γ)31S rate. The predictions from full hydrodynamic calculations
are shown in red. Figure from [7].

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Figure 2.7 Measured silicon isotopic ratios in presolar grains. Nova grains are high-

lighted in blue and red. Figure adapted from [8]. . . . . . . . . . . . . . . . . . 18

xi

Figure 2.8 Current partial level scheme for 31S. Data taken from [9].

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Figure 2.9 Lifetime of 34mCl as a function of temperature in an astrophysical plasma.

Figure from [10].

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Figure 2.10 Classical nova nucleosynthesis path, zoomed in around 34Cl. Figure adapted

from [6].

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Figure 2.11 Previous partial level scheme for 35Ar. Highlighted are the regions of interest

for capture onto the 34Cl ground and isomeric state. Data taken from [11].

. . . 22

Figure 3.1 Diagram of a nuclear reaction. See text for details. . . . . . . . . . . . . . . .

. 24

Figure 4.1 Layout of TRIUMF-ISAC facility.

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. 32

Figure 4.2 Schematic of the detector setup at TRIUMF. Detector sizes not to scale.

. . . . 33

Figure 4.3 Graph of temperatures of the target ladder and cold shroud from Run 1, in
2016. Beam tuning on the target ladder began around midnight on May 27,
where the ladder was not in thermal contact with the shroud. Subsequent
temperature spikes correspond to short runs with the target ladder in the low-
est target position, which had poor thermal contact with the shroud, due to
bent BeCu springs. The dewar was last filled June 2, and after the beam was
turned off on June 3, additional LN2 in the dewar was blown out.

. . . . . . . . 34

Figure 4.4 Drawing of the DSL chamber. The target and silicon detectors are located in
the aluminum chamber, and a copper braid provides thermal contact to the
LN2 dewar.

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Figure 4.5 Photo of the target ladder immediately after the Run 1. Target temperature
is monitored with the PT100 thermometer in the bottom left. The target
implanted at McMaster filled the top two target positions, and an old target
from [12] that is known to be dirty was placed in the bottom position.

. . . . . 36

Figure 4.6 Photo of the collimators and cooling mechanism within the target chamber.

The beam direction in this photo is from the top downward.

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Figure 4.7 Photo of the target chamber with the silicon detectors and target ladder in-

stalled. The beam comes from the top right in this photo.

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Figure 4.8 Picture of the detector setup at TRIUMF-ISAC II.

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Figure 4.9 Simulated Ge detector spectrum for a monoenergetic 4000 keV γ-ray. FEP,
SEP, and DEP correspond to the full energy peak, single escape peak, and
double escape peak.

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Figure 4.10 Block diagram of the data acquisition from Run 1. Bold lines signify multiple

connections.

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Figure 5.1 Uncalibrated α energy spectrum taken with a triple-α source at the target
position with the thick silicon detector (thin detector removed). The energies
of the three peaks used for calibration are labeled.

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. 44

Figure 5.2 Particle identification plot for Run 1.

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. 46

Figure 5.3 Left: α-gated γ spectrum zoomed in on the 31S first excited state. Right:
1249 keV γ-ray energy gated α energy spectrum. The background in gray is
taken by applying a gate on background γ rays with slightly lower energies.
Figure 5.4 Data from 32S(3He,3He’)32S∗ in red along with preliminary best fit lineshape
and flat background in blue. The lifetime extracted from this fit, 240(30) fs
agrees with the literature lifetime of 244(15) fs [13].

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. . 48

Figure 5.5 α-gated γ-ray spectrum with peaks from 12C+32S reactions labeled. Peaks

with gray labels correspond to false coincidences with proton events.

. . . . . . 50

Figure 5.6 α-gated γ-ray spectrum with peaks from 63,65Cu+32S reactions labeled in

black and 63,65Cu+p,n,α reactions labeled in gray. . . . . . . . . . . . . . . . . 51

Figure 5.7 α-gated γ-ray spectrum showing continuum background at high energies

from 63,65Cu+32S reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Figure 5.8

γ-ray spectrum showing β -delayed γ rays in the 8 hours immediately after
the beam was turned off. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Figure 5.9 ∆E-E particle identification plot.

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Figure 5.10 γ-ray spectra gated on all α particles, where Run 1 data is scaled based on
the ratio of photopeak counts in the 1249 keV γ-ray, corresponding to depop-
ulation of the 31S first excited state. . . . . . . . . . . . . . . . . . . . . . . . . 54

Figure 5.11 Same as Figure 5.10, zoomed in to show two γ-ray lines from carbon contam-
ination, from 39K at 3597 keV and at 3736 keV from 40Ca, and the reduction
in intensity from Run 1 to Run 2.

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Figure 5.12 Second excited state to ground state transition, gated on α particle energy
47-49 MeV with a simulated lineshape for the literature lifetime of 320 fs
(red) [13].

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Figure 5.13 Third excited state to ground state transition, gated on α particle energy 46-
48 MeV (blue) with a simulated lineshape with arbitrary lifetime of 10 fs
(red). .

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Figure 5.14 4971 keV excited state to ground state transition, gated on α particle energy
42-44 MeV (blue) with a simulated lineshape with arbitrary lifetime of 10 fs
(red).

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.

.

Figure 5.15 5157 keV excited state to ground state transition, gated on α particle energy
42-44 MeV (blue) with a simulated lineshape with arbitrary lifetime of 10 fs
(red). .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

.

.

.

.

.

.

.

.

.

Figure 5.16 6400 or 6392 keV excited state to first excited state transition, gated on α
particle energy 39-41 MeV (blue) with a simulated lineshape with arbitrary
lifetime of 10 fs for the 6400 keV state (red). . . . . . . . . . . . . . . . . . . . 58

Figure 5.17 6400 or 6392 keV excited state to second excited state transition, gated on α
particle energy 39-41 MeV (blue) with a simulated lineshape with arbitrary
lifetime of 10 fs for the 6400 keV state (red). . . . . . . . . . . . . . . . . . . . 59

Figure 5.18 6542 keV excited state to first excited state transition, gated on α particle
energy 39-41 MeV (blue) with a simulated lineshape with arbitrary lifetime
of 10 fs (red).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

.

.

.

.

Figure 6.1 Calculated depth distribution for 24Mg implanted in C foils using the same
methods as the 36Ar target, as discussed in [14]. The black line represents the
total depth distribution, and the grey lines show components from individual
energies.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

.

.

.

.

.

.

.

.

Figure 6.2 Layout of the MLL facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Figure 6.3 Flow chart of the ion source components at MLL . . . . . . . . . . . . . . . . 63

Figure 6.4 Schematic of the Munich target ladder and targets used in the run. Details of
the implanted targets are discussed in the text. 36Ar targets are labeled by the
year of first use.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

. .

.

Figure 6.5 Top down view of the ion optics of the Q3D magnetic spectrograph at MLL.

Figure adapted from [15].

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Figure 6.6 Top down view of the focal plane detector of the Q3D. Figure from [16].

. . . . 67

Figure 6.7 Conceptual diagram of the position reconstruction used in the MLL Q3D

focal plane detector. Figure from [16].

. . . . . . . . . . . . . . . . . . . . . . 68

Figure 6.8 Diagram of the DAQ electronics for the MLL experiment. Figure adapted

from [15].

.

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Figure 7.1 Expected shape and relative separation for stable hydrogen and helium isotopes

72

xiv

Figure 7.2 Particle identification plots, along with triton gates, for the first set of 15◦
data taken on the 36Ar implanted target. The particle group at high ∆E cor-
responds to α particles, and the particle group at low ∆E corresponds to
unresolved protons and deuterons.

. . . . . . . . . . . . . . . . . . . . . . . . 73

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

.

.

13C(d,t)12C data.

Figure 7.3
Figure 7.4 A background subtracted 36Ar(d,t)35Ar spectrum taken at 15◦.
Figure 7.5 A sample SpecPlot output for relevant reactions at 54◦.
Figure 7.6 Data taken at 15◦, showing the 32S(d,t)31S and 36Ar(d,t)35Ar spectra over-
laid by SpecPlot, roughly aligning previously identified peaks. Only previ-
ously known information on 35Ar is included in the SpecPlot input.

. . . . . . . . . . . . . 75

. . . . . . . . . 75

. . . . . . 77

Figure 7.7

32S(d,t)31S spectra used for calibration.

. . . . . . . . . . . . . . . . . . . . . 78

Figure 7.8

28Si(d,t)27Si spectra used for calibration.

. . . . . . . . . . . . . . . . . . . . 79

Figure 7.9 Example of the fit procedure used in the data analysis. Shown is the middle

of the focal plane in the 54◦ 36Ar(d,t)35Ar data.

. . . . . . . . . . . . . . . . 80

Figure 7.10 Fit for the left of edge of the focal plane at 54◦ for 36Ar(d,t)35Ar .
Figure 7.11 SPANC windows for the 15◦ data.
Figure 7.12 15◦ data gated on α particles, which was used to track drifts in the beam

. . . . . . . . . . . . . . . . . . . . . . . . 81

. . . . . . . 80

energy and magnetic fields.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Figure 7.13 Position spectra from 36Ar(d,t)35Ar labeled with excitation energy in keV. . . . 84

Figure 7.14 Experimental level densities of 35Ar and the mirror nucleus 35Cl and calcu-
lated shell model level densities. Experimental level densities for 35Ar with
Ex < 5.9 MeV and 35Cl are taken from [11].

. . . . . . . . . . . . . . . . . . . 88

xv

CHAPTER 1

INTRODUCTION

Where were the elements in the universe synthesized? How were they synthesized? How do we

explain the observed abundance patterns? What drives energy generation in stars? These are some

of the questions nuclear astrophysics seeks to answer.

1.1 Nuclear astrophysics

A star at the beginning of its lifetime is made predominantly of 1H and 4He. Once the core of the
star has reached sufficient temperatures, the 1H can be fused to form 4He and release ≈30 MeV
of energy per 4He. Once this hydrogen is depleted in the core, if the star is massive enough (>0.7
M(cid:12)), gravitational contraction increases the temperature and pressure in the star. The star then
burns 4He to form 12C and 16O, and releases energy. This series of contractions and burning in

sufficiently large stars can liberate energy and synthesize elements up to the iron region, where
56Fe, 58Fe, and 62Ni have the highest binding energy per nucleon, as seen in Figure 1.1.

Figure 1.1 Binding energy per nucleon as a function of mass number, A. Figure from [1].

1

Elements with higher masses are energetically unfavorable to produce, and are not explained by

quiescent burning in stars. These elements are synthesized in more extreme stellar environments.

Due to the high Coulomb barrier, charged particle fusion is hindered, but a series of neutron cap-
tures and β− decays can bypass this issue. In the r-process, neutron captures are rapid, relative to
the β− decay rates. In contrast, the s-process, neutron captures are slow relative to the β− decay
rates, and proceeds much closer to stability. These two processes account for the production of

most nuclei heavier than iron, while another process is needed to produce the p-nuclei, which are

neutron deficient isotopes blocked by other stable isotopes from s- and r-processes.

1.2 Binary star systems

A binary star system consists of two stars orbiting their center of mass., and roughly half of stars

exist in binary systems. If the stars differ in mass, their rate of evolution and orbital speeds will

differ. Each star has a Roche lobe, within which orbiting materials are gravitationally bound to

the star, and if the star extends past its Roche lobe, the extended material can be transferred to the

companion star [1]. At the inner Lagrangian point, the gravitational potentials of the two stars are

equal. A diagram of the binary system can be seen in Figure 1.2.

Figure 1.2 Diagram of the binary system. Each star, their Roche lobes, and the inner Lagrangian
point are labeled.

2

1.2.1 Classical novae

Classical novae occur in close binary systems consisting of a white dwarf and a companion star

with a hydrogen rich envelope. When the material on the surface of the companion star overflows

its Roche lobe, the material can be transferred to the white dwarf. This material collects in an

accretion disk surrounding the white dwarf. Some of this matter accumulates on the surface of the

white dwarf and is heated by the high gravitational potential. This inner shell eventually becomes

degenerate, and hot enough to ignite hydrogen burning, increasing temperature. This does not ex-

pand the degenerate layer, and the temperature continues to increase. This leads to thermonuclear

runaway on the accreted material, eventually causing an explosion.

Nova outbursts eject ≈ 10−7−10−3 M(cid:12) of material at velocities on the order of 106 m/s, reach
peak luminosities of 105 L(cid:12), and reach peak temperatures of 0.1-0.4 GK. These events can recur
on typical time scales of 104-105 years. Approximately 35 occur in the Galaxy per year, of which

5-10 are detected. The other events are obscured by dust in the plane of the galaxy. These events

have been observed throughout the entire electromagnetic spectrum [17].

1.3 Stellar dust

Many stellar events are known to eject matter, including classical novae. While most of this matter

enters the interstellar medium in the form of a gas, some of the ejecta can condense and form dust,

or small grains, typically a few µm or smaller. This dust has been observed through a variety of

observational astronomy techniques and is predicted in theoretical models.

Gas phase material from the bulk of stellar sources are homogenized in the interstellar medium,

creating uniform isotopic ratios in many situations. However, primitive meteorites have been found

to contain small (nm-µm) grains that do not show these uniform isotopic signatures. An explanation

given for this is that these grains were formed in a star, ejecta, or stellar winds and stayed intact

during the homogenization of the interstellar medium and the formation of the solar system.

3

1.3.1 Modeling of grain formation

Some stellar events that return matter to the interstellar medium are dusty, and these stellar sources

will each be discussed in this subsection. This newly made stardust moves away from its stellar

source and travels through the interstellar medium. These grains can collapse together with gas

forming a new star, which is a relatively slow process. Through various processes, the composition

of these grains is altered and only a small fraction of grains maintain their initial composition [18].

In a core collapse supernova model, the core continues contracting after Si burning, as the

Fe-core gains mass until it reaches a Chandrasekhar mass and eventually collapses. After this ex-

plosion occurs, the knowledge of chemical yields is necessary to understand the ejecta. A blast

wave deposits energy as it crosses the ejected materials. Neutrino-driven convection leads to mix-

ing in the core, which occurs over a few hours and leads to a partial fragmentation of the core.

After this mixing, the abundances are assumed to remain constant within each mass zone.

Chemical processes are assumed to not be effective before around day 100, due to the high

temperatures. The temperature evolution within the ejecta is controlled by the deposition of en-

ergy from γ-rays and x-rays, which depend on elemental abundances at a given time. Chemical

processes such as thermomolecular reactions, thermal fragmentation, and radiative association are

then considered and evolved based on the temperature and density profile. A chemical network

is then evolved to determine the formation of molecules which then condense into grains. Nucle-

ation of these molecules into grains is the bottleneck of the grain formation process [2]. The time

evolution of the total mass of several grain types can be seen in Figure 1.3.

Presolar grains from CO novae have not yet been measured in the laboratory, but this absence

of SiC and graphite grains is consistent with condensation calculations for CO nova ejecta, due to

higher abundance of oxygen relative to carbon. This leads carbon to be locked into CO molecules

leaving oxygen to form oxide and silicate grains [4].

Other types of stellar events that produce presolar grains include type Ia supernovae, asymptotic

giant branch (AGB) stars, and Wolf-Rayet stars. The known presolar minerals from giant stars

4

Figure 1.3 Dust mass for grains larger than 10 Å summed over ejecta zones in a type II supernova
as a function of time post explosion. The dotted line shows the sum of all dust mass formed in the
model with a progenitor of 15 M(cid:12). Figure from [2].

include corundum, spinel, hibonite, silicon carbide and silicate grains. Graphite grains with high
12C/13C ratios are also potentially from these sites, as well as potentially some diamonds [19].

1.4 Presolar grains

Dust grains in the solar system that were condensed before the solar system formed are referred

to as presolar grains. Some of these grains can be found within meteorites that have fallen to

earth. They are characterized by isotopic ratios that differ from measured solar isotopic ratios.

These grains can then be identified with sources by comparing measured isotopic ratios to model

predictions for various stellar events outlined in subsection 1.3.1. A cartoon of the steps from grain

formation to identification can be seen in Figure 1.4.

These grains can condense into several different minerals. In this subsection, several of the

currently observed grain types are discussed. Suggested origins for some of these grains are given.

Most of these grains have typical sizes of micrometers, whereas nanodiamonds are a notable ex-

ception, with sizes on the order of nanometers.

5

Figure 1.4 Cartoon of the steps from presolar grain formation through identification. Figure
adapted from [3].

Nanodiamonds (∼2.5 nm diameter) are the most abundant presolar grain, and many are iden-
tified by their Xe and Te isotopic ratios, which suggest type II supernovae origins. Isotopic mea-

surements are limited by the small size and they must be measured in aggregate. C isotopic ratios

are indistinguishable from solar ratios and nitrogen ratios are similar to solar in these grains. It has

been suggested, based on this information, that the majority of nanodiamonds were formed in the

solar system, and that only a small fraction are from supernovae [20].

Silicon carbide grains are the best studied type of grain, and isotopic measurements of single

grains have revealed isotopic anomalies in nearly all measured elements. 90% of these grains have

been identified as part of the “mainstream” population, and the remaining groups are much smaller.

6

One of these remaining groups is classical nova candidate grains. AGB stars are the proposed site

for the formation of mainstream grains [21].

Figure 1.5 Measured C and N isotopic ratios for various presolar grains. The dotted lines are used
to show solar isotopic ratios. Figure from [4].

Presolar graphite is less well understood. Subgrains have been found within these grains, which

likely served as nucleation seeds for the condensation of the graphite. The majority of these grains
are enriched in 12C and have close to solar N ratios. Lower density grains have higher contents of

trace elements and have similar isotopic ratios to those of SiC X-grains, which likely originated in

supernovae. The higher density grains are proposed to have originated from several environments,

including AGB stars, supernovae, and novae [21]. Secondary electron micrographs of two graphite

grains and SiC grain are shown in Figure 1.6.

Unlike other grain types, only ∼200 presolar oxide grains (mostly spinel and corundum) have

7

been identified, and they are expected to make a small contribution to the bulk of the interstellar

dust. These are difficult to locate due to the large background from oxides with solar isotopic ratios.

Most of the oxide grains are believed to have originated from O-rich red giants, and a supernova

origin has been suggested for a few others. There is still no explanation for Group 4 grains, based

on their O isotopic ratios [21].

Figure 1.6 Secondary electron micrographs of silicon carbide grains from the Murchison meteorite.
Figure from [5].

8

CHAPTER 2

CLASSICAL NOVA NUCLEOSYNTHESIS

This chapter discusses nucleosynthesis in classical novae. The study of two particular reactions,
30P(p,γ)31S and 34g,mCl(p,γ)35Ar , is motivated, and an overview of the currently available ex-

perimental information is given for both of these reactions.

Classical novae can be divided into two types, based on the type of underlying white dwarf.
For main sequence stars with masses of 0.5 to 8 M(cid:12), the core will contain carbon and oxygen,
but not reach sufficient temperatures to produce neon. Stars with slightly higher masses, up to
≈ 10 M(cid:12), can reach high enough temperatures to create neon [1]. CO novae are enriched in C,
N, and O. In both cases, sufficient temperatures are not reached for significant breakout from the

CNO hydrogen-burning cycle. ONe novae result in higher peak temperatures and nucleosynthesis

proceeding on Ne and Mg seeds from the underlying white dwarf.

In most ONe classical novae elements as heavy as 40Ca are believed to be synthesized through

(p,γ) and (p,α) reactions and β + decays [1]. In comparison to other sites of explosive nucleosyn-

thesis, the reaction path in novae is relatively localized near the valley of β stability. As a result,

experimental information on the relevant nuclear reactions is abundant and there is a realistic op-

portunity to produce a complete set of experimentally determined reaction rates. The classical

nova nucleosynthesis path can be seen in Figure 2.1.

2.1 Reaction rate formalism

Following the derivation in [1], consider a reaction of the type A(a,b)B, where a and A are both

massive particles (not photons). The rate of this reaction can be described as

raA = NaNAvσ (v)

(2.1)

9

Figure 2.1 Classical nova nucleosynthesis path for a 1.35 M(cid:12) ONe nova at peak temperature.
Figure from [6].

where Na and NA are the number densities of particles a and A, v is the relative velocity, and σ (v)
is the nuclear cross section as a function of velocity. In a stellar plasma in thermodynamic equilib-

rium, the relative velocities are given by a probability distribution, P(v). Given a distribution, the

reaction rate can be written as

raA = NaNA

(cid:90) ∞

0

vP(v)σ (v)dv = NaNA(cid:104)σv(cid:105)aA

(2.2)

where (cid:104)σv(cid:105)aA is the reaction rate per particle pair.
non-relativistically and are not degenerate. Therefore, the velocity distribution is given by the

In a stellar plasma, nuclei typically move

Maxwell-Boltzmann distribution.

P(v) =

(cid:17)3/2

(cid:16) maA

2πkT

e−maAv2/(2kT )4πv2

(2.3)

where k is the Boltzmann constant, T is the temperature, and maA is the reduced mass. The reaction
rate per particle pair can then be written in terms of velocity or kinetic energy, as

(cid:104)σv(cid:105) =

vP(v)σ (v)dv =

1

Eσ (E)e−E/kT dE.

(2.4)

(cid:90) ∞

0

(cid:18) 8

(cid:19)1/2

(cid:90) ∞

πmaA

(kT )3/2

0

10

The energy range where most charged particle nuclear reactions take place is strongly affected

by two factors. The probability of penetrating the Coulomb barrier increases with energy, and
probability to penetrate the Coulomb barrier is given by e−2πη where η is the Sommerfeld pa-
rameter, η = αZaZb
small, in the high energy tail of the Maxwell-Boltzmann distribution. These factors can be seen in

(cid:112)µc2/2E. However, the number of particles that have high energy is quite

Figure 2.2. Combining these two factors leads to the Gamow peak. This range is characterized by

a centroid given by

E0 =

and a 1/e width ∆ given by

Thermonuclear reactions occur mainly in the energy range of E0 − ∆/2 to E0 + ∆/2.

(cid:21)1/3

(cid:17)

(kT )2

(cid:20)(cid:16)π

¯h

Z0Z1e2(cid:17)2(cid:16)maA
(cid:17)2(cid:16)
(cid:112)E0kT

∆ =

2

4√
3

(2.5)

(2.6)

Figure 2.2 Graph showing the two components that contribute to the Gamow peak, the energy
distribution, and Coulomb barrier penetrability. Figure from [1].

This work considers resonant capture reactions, where a particle is captured into an excited state

in the compound nucleus, which enhances the reaction rate. Here, we consider narrow resonances,

where the level density is sufficiently low that resonances have no significant overlap and the partial

width is approximately constant across each resonance (the total width is less than a few keV,
which corresponds to a lifetime ≈ 10−18 s or longer). The cross section for isolated resonances

11

can be described by a Breit-Wigner form given by

σBW (E) =

λ 2
4π

(2J + 1)(1 + δaA)
(2Ja + 1)(2JA + 1)

ΓaΓb

(Er − E)2 + Γ2/4

If we define the following quantities:

ω =

(2J + 1)(1 + δaA)
(2Ja + 1)(2JA + 1)
ΓaΓb
Γ =

BaBb

¯h
τ

γ =

(2.7)

(2.8)

(2.9)

where Γa and Γb are partial widths for exit channels a and b, respectively, τ is the lifetime of the
compound state and Ba and Bb are the branching ratios for exit channels a and b, respectively, then
the reaction rate for a single resonance can be written as:

(cid:19)3/2

(cid:18) 2π

maAkT

(cid:104)σv(cid:105) =

¯h2e−Er/kT ωγ

(2.10)

where ωγ is referred to as the resonance strength and Er is the resonance energy. In cases where

multiple resonances contribute to the reaction rate, these contributions are summed. For the re-

actions relevant to the present work, resonant capture dominates the reaction rates. The relevant

energies can be seen diagrammatically in Figure 2.3.

Figure 2.3 Diagram of energetics for capture of a proton capture with center of mass energy Er
onto a nucleus with Z protons and A-Z neutrons.

12

2.2 Methods for determining resonant capture reaction rates

There are several methods for determining these resonant capture reaction rates. In this section

two theoretical methods and two experimental methods will be outlined below.

2.2.1 Hauser-Feshbach formalism

The derivation for this theoretical mod here follows [22], and is applicable when there are many

resonances that contribute to the overall reaction rate. To obtain an energy averaged cross section

in an interval I, with many narrow resonances, with spacing D, one can write the average cross

section as:

(cid:104)σ (E)(cid:105) =

This expression can be rearranged as follows:

1
I

(cid:90) E+I/2
E−I/2 ∑
(cid:90) ∞

p

σp(E)dE =

σp(E)dE

(cid:90) ∞

0

1
I

I
D

σp(E)dE

Using a Breit Wigner form for each resonance, as in Equation 2.7:

(2.11)

(2.12)

(2.13)

(cid:104)σ (E)(cid:105) =

1
I

∑

p,Ep∈[E± I
2 ]

0

(cid:42)Γα pΓα(cid:48) p

(cid:43)

Γp

(cid:104)σ (E)(cid:105) =

π
k2 gJ

2π
D

=

π
k2 gJ

2π
D

Wαα(cid:48)

(cid:104)Γα p(cid:105)(cid:104)Γα(cid:48) p(cid:105)

(cid:104)Γp(cid:105)

where Wαα(cid:48) is the width fluctuation factor, which accounts differences in the average of the whole
width factor and the average of each individual width and gJ =
(2JA+1)(2Ja+1) is the spin statistical
factor.

2J+1

These average partial widths can be estimated by comparing to S matrix scattering cross sec-

tions, which can be calculated using the optical model. Here:

σα (E) =

π
k2 gJ

2π
D

(cid:104)Γα p(cid:105)

and the S matrix cross section can be written as:

σα (E) =

π
k2 gJ(1−|Sopt

αα|2)

13

(2.14)

(2.15)

Comparing these two equations, one can define a transmission coefficient:

(1−|Sopt

αα|2) =

2π
D

(cid:104)Γα p(cid:105) = Tα

With these transmission coefficients, the averaged cross section can be rewritten as

(cid:104)σ (E)(cid:105) =

π
k2 gJ

2π
D

Wαα(cid:48)

Tα Tα(cid:48)
∑α(cid:48)(cid:48) Tα(cid:48)(cid:48)

(2.16)

(2.17)

When performing this averaging, one commonly used level density is a back-shifted Fermi gas

model. The level density can be written as

ρbsfg(ε) =

(cid:19)

(cid:18)2
√
π
12a1/4 e

√
aU
U5/4

Here, instead of using the unshifted energy, an emprical shift is applied, where

U = ε − ∆bs

(2.18)

(2.19)

This backshift parameter ∆bs is an empirical parameter related to pairing effects, which is used to
replicate known odd-even effects in nuclei.

2.2.2 Shell Model

If the level density is not sufficient for the averaging needed in the Hauser-Feshbach calculations,

another theoretical method for obtaining reaction rates is to calculate individual resonance prop-

erties using the nuclear shell model. Shell model calculations are performed by treating indepen-

dently protons and neutrons in an average potential. This produces a shell structure analagous to

electrons shells in noble gases for separately protons and neutrons. One downfall of this method

is that the excitation energy uncertainties in shell model are often large. Since the reaction rate

depends exponentially on the resonance energy, this translates to large uncertainties in the reaction

rate.

14

2.2.3 Direct measurements

Ideally, the reaction rate can be directly measured experimentally, by measuring the cross section

for the relevant resonance energies. These measurements, however are often not straightforward.

These measurements suffer from low cross sections, which lead to low count rates. Many of the

reactions take place on unstable nuclei. If the heavy nucleus is unstable, the measurement must

then be done in inverse kinematics, and beam production rates tend to be low. A high resolution

mass separator is also then required to separate the reaction products from the unreacted beam,

which are very similar in mass.

2.2.4

Indirect measurements

If a direct measurement of the reaction rate is not feasible, or to guide rate estimates if the direct

measurement is feasible, individual resonance properties can be measured and the reaction rate can

be determined using the formalism outlined in Section 2.1. Unfortunately, indirect determinations

of the reaction rate require many experiments to determine the different resonance properties.

One can also use a combination of experimental and theoretical methods, such as experimentally

determing resonance energies and identifying those resonances with shell model states to determine

the resonance strengths.

2.3

30P(p,γ)31S

This section presents classical nova observables that are impacted by the experimentally unknown
30P(p,γ)31S rate. An overview of the currently available experimental information is also given.
An experimental 30P(p,γ)31S rate is necessary because the level density in the region of interest

for relevant temperatures is not sufficiently high to warrant the use of a statistical model rate.

15

2.3.1 Nucleosynthetic bottleneck

30P(p,γ)31S is potentially a bottleneck to nucleosynthetic flow beyond A = 30. As seen in Figure
2.4, when nucleosynthesis reaches 30P, the available options are to β + decay or proton capture,
as seen in Figure 2.4. The β + decay half life of 30P is long (2.5 min.) relative to the duration of

the peak temperatures in classical nova, effectively closing this path. Therefore, the flow to higher
masses is regulated by the 30P(p,γ)31S rate.

Figure 2.4 Classical nova nucleosynthesis path, zoomed in around 30P. Figure adapted from [6].

2.3.2 Nova thermometers

Certain elemental ratios have been proposed as a way to determine the peak temperature of a

classical nova. These ratios must vary monotonically with peak temperature, and ideally they

would vary steeply with temperature. Downen et al. [7] have considered these ratios and these can
be seen in Figure 2.5. Uncertainty in the 30P(p,γ)31S rate contributes the largest uncertainty in all

of the ratios including S or P. Error bands for these ratios can be seen in Figure 2.6.

2.3.3 Si isotopic ratios

Silicon isotopic ratios have the potential to be used to identify presolar grains from classical novae,
because the 30Si/28Si ratio is sensitive to the 30P(p,γ)31S reaction rate. With a fast 30P(p,γ)31S

16

Figure 2.5 Elemental ratios proposed as nova thermometers. Figure from [7].

rate, little 30P is left to β + decay to 30Si. Qualitatively, high 30Si/28Si ratios are expected, but
an experimental 30P(p,γ)31S reaction rate is needed to quantitatively constrain 30Si production in

novae. Measured Si isotopic ratios can be seen in Figure 2.7.

2.3.4 Current experimental information on 30P(p,γ)31S

Several experiments have already been performed in an attempt to work out the resonance en-
ergies and spins and parities of the relevant resonances, with Ex ≈ 6130 − 6700 keV. Several
techniques have been used to populate 31S excited states. These techniques include single neu-
tron transfer: 32S(p,d)31S [23, 24], 32S(d,t)31S [25, 26], 32S(3He,α)31S [27, 28, 29], in beam
gamma spectroscopy: 12C(20Ne,nγ)31S [30], 28Si(α,nγγ)31S [31], 24Mg(16O,ααnγ)31S [32],
and 16O(16O,nγ)31S [33], other reactions such as 31P(3He,t)31S [34, 35, 36], and 31Cl β + decay

[37, 38, 39].

While it is expected that most if not all of the states in the region of interest have been popu-

17

Figure 2.6 Error bands on predicted elemental ratios. The black line is the post processing predic-
tion, and the dotted black lines show the uncertainties in the ratios. The uncertainties in these ratios
are dominated by the uncertainty in the 30P(p,γ)31S rate. The predictions from full hydrodynamic
calculations are shown in red. Figure from [7].

Figure 2.7 Measured silicon isotopic ratios in presolar grains. Nova grains are highlighted in blue
and red. Figure adapted from [8].

lated, many of them have tentative or discrepant spin parity assignments. A partial level scheme,

showing the region of interest, can be seen in Figure 2.8. None of the states of interest have known

partial or total widths. Therefore, the resonance strengths are not yet known. These resonance
strengths cannot currently be measured directly due to a lack of sufficiently intense 30P beams at

18

the appropriate energy. Therefore, we must pursue indirect techniques. As a step toward determin-

ing these resonance strengths, this work outlines measurements that will constrain total widths of

these resonances.

Figure 2.8 Current partial level scheme for 31S. Data taken from [9].

2.4

34g,mCl(p,γ)35Ar

This section presents the structure of 34Cl and 35Ar and its impact on the 34g,mCl(p,γ)35Ar rate as
well as classical nova 34S/32S ratios, which are impacted by the currently experimentally unknown
34g,mCl(p,γ)35Ar rate. An overview of the currently available experimental information is also
given. An experimental 34g,mCl(p,γ)35Ar rate is necessary because the level density in the region

19

61386160625562806327635763776390, 6392, 6394, 6401654265836636}Region of interest30P+pEx(31S)of interest for relevant temperatures is not sufficiently high to warrant the use of a statistical model

rate.

2.4.1

Isomeric state in 34Cl

34Cl has a low lying isomer (Ex = 146.36(3) keV) with a half life of 32 min. in the laboratory.
The ground state of 34Cl has a shorter half life of 1.5 s, and due to the large angular momentum

difference (3+ for the isomer, and 0+ for the ground state) transitions directly between these two

states are highly suppressed. However, at stellar temperatures, higher lying excited states can

be thermally excited. In particular, there are two 1+ states at Ex=461.00(4) and 665.56(4) keV

that have decay branches to both the ground and isomeric states. This indirectly allows transitions
between the ground state and isomeric state, effectively shortening the lifetime of the 34Cl isomeric
state. This effect on the 34mCl lifetime has been calculated in [10] and can be seen in Figure 2.9.

Figure 2.9 Lifetime of 34mCl as a function of temperature in an astrophysical plasma. Figure from
[10].

However, the lifetimes of the β + decays of the ground state and the isomeric state are both

20

comparable to the proton capture lifetime. Therefore, the 34Cl ground and isomeric states should

potentially be considered separately, rather than as one total rate. Transitions between the ground

and isomeric state also need to be considered.

2.4.2 Sulfur isotopic ratios

Given the current constraints on the relevant reaction rates, the currently measured isotopic ratios

are insufficient to distinguish presolar grains from classical novae and type II supernovae. In both
cases, low 14N/15N and 12C/13C ratios and high 30Si/28Si ratios are expected qualitatively. 34S/32S
ratios have the potential to distinguish grains from these two origins. 32S/33S was proposed to

distinguish grains of these origins, but [40] demonstrated that this ratio would not be distinct from
the expected solar ratio. This same reference predicts a 32S/34S ratio of ≈100, which is distinct
from both solar and type II supernova expected ratios.

However, the 34S/32S ratios are fairly sensitive to the currently experimentally unconstrained
34g,mCl(p,γ)35Ar reaction rate. Once 34Cl is reached in classical novae, it can either proton capture
or β + decay, as seen in Figure 2.10. 34Cl β + decays to 34S, and if the 34g,mCl(p,γ)35Ar reaction
rate is fast, little 34Cl remains, leading to less 34S.

Figure 2.10 Classical nova nucleosynthesis path, zoomed in around 34Cl. Figure adapted from [6].

Work is being done to measure sulfur isotopic ratios in presolar grains [41]. Contamination

from the sulfuric acid used to separate the grains is an issue, but this is being overcome [42].

21

These ratios have not been measured yet in nova candidate grains.

2.4.3 Current experimental information on 34g,mCl(p,γ)35Ar

The Q value of this reaction is known to be 5896.3(8) keV for capture onto the ground state,

and 6042.7(8) keV for capture onto the isomeric state. Prior to the work presented in this thesis,

few levels just above the proton emission threshold were known and the known levels had an

excitation energy uncertainty of 10-20 keV as seen in Figure 2.11. Since the reaction rate depends

exponentially on the resonance energy, this contributes a large uncertainty to the reaction rate.

The first measurements were performed by Kozub [23] and Johnson and Griffiths [43] just above
the proton emission threshold, using the 36Ar(p,d)35Ar reaction, which lead to the discovery of

three new levels with uncertainties of 20 keV. Betts et al. [44] then performed a measurement
using 36Ar(3He,α)35Ar, discovering two new levels and reducing the uncertainty on two of the
known levels to 10 keV. In the thesis of Vouzoukas [45], another 36Ar(3He,α)35Ar was performed,

discovering no new levels, but reducing uncertainties on 4 known levels. However, this work was

never published in a refereed journal. This work presents an effort to search for new resonances

and reduce uncertainties on the energies of known resonances.

Figure 2.11 Previous partial level scheme for 35Ar. Highlighted are the regions of interest for
capture onto the 34Cl ground and isomeric state. Data taken from [11].

22

5911(10)6032(10)6153(10)6258(10)6630(10)gsexregions of interest34Cl+pCHAPTER 3

DOPPLER SHIFT ATTENUATION METHOD

In the Doppler Shift Attenuation Method (DSAM), a nucleus is populated in an excited state with a

nuclear reaction. That excited state then slows down in a continuous medium. The amount of time

that the excited nucleus spends traversing the stopping material before decaying by γ-ray emission

is dependent on the lifetime of the state. Given the beam energy, target nuclei distribution, angular

acceptances, and stopping powers in the medium, one can simulate γ ray energy lineshapes based

on the expected Doppler shift for a range of possible excited state lifetimes. Comparing these

lineshapes to data, excited state lifetimes can be extracted. A deeper discussion of the technique is

given in this chapter.

3.1 Applicability of DSAM

Nuclear lifetimes range many orders of magnitude. Many different techniques are needed to cover

this large range. Electronic timing can measure lifetimes down to nanoseconds, but resolution is

insufficient to measure shorter lifetimes. Lifetimes down to a few picoseconds can be measured

with methods where the recoiling nucleus recoils into vacuum, then into other discrete foils, where

the lifetime is extracted by simulating relative populations of peaks Doppler shifted by different,
discrete amounts. In the range ∼ 3 fs− 10 ps, DSAM can be used to extract lifetimes that are too
short for the recoil to leave a target, but still somewhat comparable to the slowing down time of
the recoil in material. For excited states with lifetimes of ∼10 as-10 fs in states that emit protons,
one can measure characteristic x-rays in coincidence with recoiling protons. One can compare the

number of characteristic x-rays from the nucleus before and after proton emission, and use the ratio

of x-ray integrals along with the characteristic time for x-ray emission of the nucleus to determine

the lifetime of a proton emitting state.

23

3.2 Theory

Figure 3.1 Diagram of a nuclear reaction. See text for details.

Here we consider a reaction A(a,b)B* as in Figure 3.1, where A and a are the projectile and

target and b and B are the ejectile and excited recoil. For B* in vacuum, the speed v of a given

atom is constant, and determined by reaction kinematics. The Doppler shift of the deexcitation

In DSAM, however, B* is created in a target and recoils within a stopping medium, making

Given the ability to calculate speed at a given time, the Doppler shifted γ-rays apparent in the lab

frame are a measure of the decay time. To do this calculation, one needs stopping powers of the

recoil within the stopping medium.

24

γ-ray is then given by the formula:

Eγ = E0
γ

where β = v

c and θ is the angle given by cosθ =

speed a function of time, giving

Eγ = E0
γ

(cid:112)1− β 2

1− β cosθ
˜vr· ˜pγ
vr pγ .

(cid:112)1− β 2(t)

1− β (t)cosθ

(3.1)

(3.2)

Nuclear excited state decays as a function of time follow an exponential decay law. The number

of Doppler shifted γ rays emitted at each speed can be calculated.

N = N0e−t/τ

(3.3)

where N0 is the number of initially populated excited states and τ is the lifetime.

3.2.1 Stopping powers

Ion energy loss in medium depends on the energy of the ion, the characteristic stopping power

of the medium, and the density of the medium. High density solids have characteristic slowing

down times of hundreds of femtoseconds. Targets for DSAM measurements are selected such that

characteristic slowing down times are comparable to the lifetime of the excited state. This allows

for measurements of lifetimes from a few fs to a few ps. If energy loss per distance is known, then

change in velocity as a function of time is given by:

−Mr

dv
dt =

dE
dx

(3.4)

where Mr is the mass of the recoil with speed v at time t, and the stopping power is dE/dx.

Stopping powers are determined by two physical mechanisms, electronic and nuclear stopping.

Electronic stopping is easily measured or calculated, and depends on long range electromagnetic

interactions of electrons of the stopping atom with the moving ion. Nuclear stopping is due to

inelastic collision between the moving ion and stopping atoms, and leads to large energy losses

and large angular scattering, which is hard to measure.

In the low speed regime, β (cid:46) 0.5%, nuclear stopping dominates, so theoretical estimates must
be used, due to difficulty in measurement, which leads to large uncertainties.
In the medium
speed regime, 0.5% (cid:46) β (cid:46) 5%, nuclear and electronic stopping powers are of the same order,
but measurements are feasible. For high speeds, β (cid:38) 5%, electronic stopping powers dominate,
and measurements tend to have lower uncertainties. In this regime, stopping power uncertainties

contribute least to overall lifetime uncertainties.

25

Phenomenologically, as discussed in [46], stopping powers can be fitted with

(cid:16) v

(cid:17)

v0

(cid:16)v0

(cid:17)

v

+ Kn

1
ρ

dE
dx = Ke

(3.5)

near v0 = αc, the Bohr speed, where α is the fine structure constant, e2/¯hc, ρ is the density of the
stopping medium, and Ke and Kn are the electronic and nuclear stopping coefficients. Ke can be

determined experimentally, then Kn is fit to data or calculations at lower speed.

Equations 3.4 and 3.5 can now be solved for v(t). For the sake of simplicity in this derivation,

we assume low recoil speeds, unidirectional recoils, and no large angle scattering. Other effects

are included in the analysis, and will be discussed later in this chapter.

We first combine equations 3.4 and 3.5

dv

dt = − ρ

M

(cid:20)

Ke

(cid:16) v

(cid:17)

v0

(cid:17)(cid:21)

(cid:16)v0

v

+ Kn

and for convenience, we define

ω =

To solve for C, we then impose the initial condition v(t = 0) = vi,

Then, multiplying each side by v/v2
0

d
dt

and making a change of variables:

which gives:

and has the solution:

W (t) =

(cid:35)

Kn
Ke

+

ρKe
Mv0

.

(cid:34)(cid:18) v
(cid:19)2

v0

+

(cid:19)2
(cid:35)

Kn
Ke

.

(cid:18) v

(cid:19)2

v0

W =

= − 2
ω

(cid:34)(cid:18) v

v0

W

(cid:35)

dW

dt = − 2
ω
(cid:34)(cid:18) v
(cid:19)2
(cid:34)(cid:18) vi

(cid:19)2

Kn
Ke

v0

+

C =

+

Kn
Ke

v0

26

= Ce−2t/ω .
(cid:35)

(3.6)

(3.7)

(3.8)

(3.9)

(3.10)

(3.11)

(3.12)

and substitute this in for C, giving

(cid:34)(cid:18) v

(cid:19)2

v0

(cid:35)

=

+

Kn
Ke

(cid:19)2

(cid:35)

+

Kn
Ke

e−2t/ω .

We then make another change of variables, V = v
v0

(cid:20)

V 2 =

V 2
i +

To compute dN/dV , we then need to solve for t and dt in terms of N and dN

(cid:34)(cid:18) vi
(cid:21)

v0

Kn
Ke

(cid:34)

(cid:20)

(cid:19)(cid:21)
(cid:21)

Kn
Ke

.

e−2t/ω − Kn
Ke
(cid:35)

t =

ω
2

ln

V 2 + Kn/Ke
V 2
i + Kn/Ke

(cid:20)

(cid:18)

tc =

ω
2

ln

V 2
i +

Kn
Ke

+ ln

.

(cid:18) Ke

(cid:19)

Kn

This applies until nuclei stop, at tc such that v(tc) = 0

Substituting in gives:

−2
ω
dN/dt is given by an exponential decay law,

V 2 =

d
dt

V 2
i +

e−2t/ωdt

rearranging gives:

and plugging this in gives:

dN =

e−t/τdt

N0
τ

dt =

−ωV
V 2
i + Kn/Ke

e2t/ωdV

(cid:35)ω/2t

V 2 + Kn/Ke
V 2
i + Kn/Ke

ωV

V 2 + Kn/Ke

(cid:34)

dN
dV =

N0
τ

(3.13)

(3.14)

(3.15)

(3.16)

(3.17)

(3.18)

(3.19)

(3.20)

for all nuclei that decay before stopping. To account for the number of nuclei Nc that decay after

tc, a delta function must be added:

(cid:34)

dN
dV =

N0
τ

V 2 + Kn/Ke
V 2
i + Kn/Ke

(cid:35)ω/2t

27

ωV

V 2 + Kn/Ke

+ N(tc)δ (V ).

(3.21)

3.3 Lineshape analysis

While equation 3.21 gives us a lineshape under several simplifying assumptions, real experiments

include broadening by several factors. Major factors are listed in the following paragraphs.

Kinematic broadening occurs due to an initial velocity distribution that will then be broadened

by a range of Doppler shifts as well as a range of recoil angles. One way to reduce this is to limit

the acceptance of the ejectile, which kinematically limits the accepted γ-ray angles.

Aberration occurs due to Doppler boosting. In the rest frame of the recoil, the solid angle

subtended by the detector is larger than that of the lab frame. The relationship between the two

angles is given by:

cosθlab =
which is non-negligible for recoils with β (cid:38) 5%.

cosθcm + β
1 + β cosθcm

(3.22)

At low speeds, dominated by nuclear stopping, ions will have large scattering angles. For

lifetimes sufficiently long to reach these low speeds, there can be a large smearing of the angle of

the recoils, which leads to a large range of Doppler shifts, in turn broadening the lineshape.

So far, we’ve assumed a point detector at 0◦. However, real detectors have finite size, therefore
covering a larger spread in γ-ray angles. This broadening typically dominates the intrinsic detector

resolution. One must also consider the efficiency as a function of angle. While this doesn’t broaden

the distribution, it does affect the lineshape.

γ-ray detectors also have an intrinsic energy resolution and lineshape. Ideal lineshapes must

be convoluted with these intrinsic responses to produce accurate comparisons with experimental

data. This lineshape is determined from fitting γ-ray lines from either radioactive sources or long

lived states that have time to fully stop before decaying. This procedure is done for many γ-rays to

determine the response as a function of energy.

Angular distributions may also be anisotropic, which would affect the lineshape. The recoil

angular distribution will depend on the angular momentum transfer. γ-ray angular distributions are

isotropic for spin 0 or 1/2 levels, but otherwise anisotropic. Both of these angular distributions can

28

be described by a sum of Legendre polynomials.

For low lying states, the excited state of interest can be populated either directly or by higher

lying states. Population via higher lying states can artificially increase the extracted lifetime if not

accounted for. In certain cases, this can be avoided by selecting beam energies such that population

of higher lying states is negligible, or in cases such as this one, looking at states where higher lying

states do not γ-decay, but decay through other channels, such as proton emission.

The discussion so far has assumed a beam without any spatial distribution. However, physical

beams have some spatial extent. A large beam spot leads to a smearing in angle, leading to a

larger range of Doppler shifts. Care should be taken to ensure a small beam spot for DSAM

measurements. For a spot size of a few millimeters, however, the uncertainty due to the distribution

of the beam will be negligible compared to other effects such as uncertainty in the stopping power.

All of these points must be considered, and included if applicable, when simulating lineshapes

to extract lifetimes. For cases where the recoil velocity is sufficiently large to lead to a γ-ray

distribution broader than the detector resolution, then lineshape analysis is appropriate.

3.4 Advantages of inverse kinematics

While DSAM can in principle be done in either normal or inverse kinematics, there are several

advantages to inverse kinematics, where a heavy beam impinges on a light target, including:

• Recoils tend to be in the electronic stopping power regime. Electronic stopping powers are
both more easily measured and have smaller angular scattering, leading to smaller uncertain-

ties in the extracted lifetimes.

• Velocity change can be larger, due to a maximum in stopping powers for typical systems
around recoil energies of tens of MeV for nuclei with mass number A ≈ 20− 40. This is
particularly helpful for extracting finite lifetimes for short lived states.

29

• Higher recoil velocities lead to larger Doppler shifts, making it easier to distinguish unshifted

peaks from shifted peaks, particularly at low energies, where the absolute shift is small.

30

CHAPTER 4

32S(3He,α)31S EXPERIMENT

This chapter discusses the experimental equipment used in 32S(3He,α)31S Doppler Shift Attenua-

tion Method (DSAM) experiments. Two experimental runs were performed at TRIUMF. The first

run suffered from large backgrounds, due largely to a beam delivery issue, caused by a quadrupole

focusing magnet wired to have the wrong polarity by the TRIUMF operations group. Both runs

used the same setup, save a few details discussed below.

4.1 Beam delivery

Before atoms can be accelerated, they need to be ionized. Stable beams at TRIUMF-ISAC are

ionized using the Offline Ion Source (OLIS). OLIS uses multiple types of ionization techniques,

depending on the ion of interest. Sulfur beams are delivered using the Multicharge Ion Source

(MCIS) [47]. A magnet is then used to separate the various isotopes, in this case, selecting mass

32. Ions then enter the Radiofrequency Quadrupole (RFQ), which bunches the beam into packets

separated in time by 85 ns and accelerates the beam.

A thin carbon foil is then used for charge stripping, here to the 7+ charge state. Further

acceleration is then provided by a Drift-Tube Linac (DTL). This stage can accelerate ions from

150 keV/u to 1.9 MeV/u, and is the final acceleration stage for experiments in the ISAC-I hall. For

experiments in the ISAC-II hall, such as this one, ions then enter the superconducting linac, which

allows for beam energies ranging from 150 keV/u to 16.5 MeV/u (for A/q=2). In ISAC-II, typical

beam characteristics include a 0.2% FWHM energy spread and 2 mm beam spot size. The layout

of the lab can be seen in Figure 4.1.

31

Figure 4.1 Layout of TRIUMF-ISAC facility.

4.2 Gold targets implanted with 3He

A 25 µm× 2.5 cm × 2.5 cm Au target foil was implanted over a 2.85 cm2 circular area with
35 keV 3He ions using the ion implanter at McMaster University in Hamilton, ON, Canada for
the first run. A density of 4× 1017 ions/cm2 was implanted into the foil. The foil thickness was
selected to completely stop heavy reaction products and unreacted beam, while allowing for the

light particles to propagate through to the ∆E-E Si telescope.

However, during the run at TRIUMF, this foil was found to be dirty, and the dirt was likely

accumulated during the implantation process. For the second run, an identical gold foil was im-

planted at the University of Montreal, where foils for previous DSAM experiments have been
cleanly implanted with an areal density of 6× 1017 ions/cm2.

32

Figure 4.2 Schematic of the detector setup at TRIUMF. Detector sizes not to scale.

During Run 1, the loss of 3He was monitored via the ratio of the 3He elastic scattering rate to

the beam current. The temperature of the foils is monitored via a PT-100 resistance thermometer.
If these foils are heated, 3He can potentially diffuse out of the foils, so the foils must be cooled.

Temperatures of the target ladder and cold shroud throughout the run can be seen in Figure 4.3.

33

GRIFFINGe detectorcollimator32S beam128 MeVSi detectorstargetGRIFFINGe detectorcollimatorsFigure 4.3 Graph of temperatures of the target ladder and cold shroud from Run 1, in 2016. Beam
tuning on the target ladder began around midnight on May 27, where the ladder was not in thermal
contact with the shroud. Subsequent temperature spikes correspond to short runs with the target
ladder in the lowest target position, which had poor thermal contact with the shroud, due to bent
BeCu springs. The dewar was last filled June 2, and after the beam was turned off on June 3,
additional LN2 in the dewar was blown out.

4.3 Target chamber

The Dopppler Shift Liftetimes (DSL) chamber at TRIUMF has been designed specifically for

DSAM experiments. Drawings of the chamber can be seen in Figure 4.4. To further reduce po-

tential contamination, an additional turbomolecular pump is also employed in the target chamber.

This chamber allows for cooling of the target and a surrounding cold trap. The cold trap surrounds

the beam with an LN2 cooled copper shroud to reduce the condensation of carbon, water, and
other contaminants onto the target. The LN2 dewar used to cool the target was filled every 24
hours. With these measures, typical pressures in the DSL chamber during this experiment were
between 9× 10−8 and 3× 10−7 torr.

Additionally, the target must be kept somewhat cool. However, to keep the target clean, it

should remain warmer than the cold trap, as contaminants preferentially condense on the coldest

surface. The target ladder is cooled via BeCu fingers in contact with a BN plate attached to the

copper shroud. BN is a ceramic that acts as a good electrical insulator, and provides moderate

thermal insulation. This keeps the target cool, but still warmer than the shroud. A photo of the

34

Figure 4.4 Drawing of the DSL chamber. The target and silicon detectors are located in the alu-
minum chamber, and a copper braid provides thermal contact to the LN2 dewar.

ladder with targets from Run 1 can be seen in Figure 4.5.

The DSL chamber also contains two collimators, with diameters of 2.5 and 3.0 mm to ensure

that the beam spot is well defined, as a large beam spot would lead to a large uncertainty in the

reaction position, leading to poor lifetime sensitivity. The smaller collimator is placed further

upstream, and the larger collimator is closer to the target, to clean up beam particles scattered off

the first aperture. In the initial run at TRIUMF, these collimators were composed of copper. In

conjunction with the poor beam tune, this lead to a large background in this run, which will be

discussed further in the following chapter. To mitigate this background in the second run, tantalum

collimators were used.

Electrical beam currents were read from the smaller, upstream collimator and the target ladder.

35

Figure 4.5 Photo of the target ladder immediately after the Run 1. Target temperature is monitored
with the PT100 thermometer in the bottom left. The target implanted at McMaster filled the top
two target positions, and an old target from [12] that is known to be dirty was placed in the bottom
position.

These currents were used as beam tuning diagnostics. During tuning, currents on the collimator are

minimized and currents on the target ladder are maximized. Early in the TRIUMF run, the beam

is tuned with the target ladder in the lowest position, with beam hitting the copper plate. After we

realized that we were activating the copper with the beam, all other tuning was done on the area of

unimplanted gold in the second target position. An image of the collimator readouts and cooling

can be seen in Figure 4.6.

36

Figure 4.6 Photo of the collimators and cooling mechanism within the target chamber. The beam
direction in this photo is from the top downward.

4.4 Detectors

This experiment uses two Ge clover detectors along with two Si detectors, which will be discussed

in the following subsections. Additionally, this experiment used two PT100 thermometers to mon-

itor the temperature of the copper shroud and the target ladder. These thermometers are platinum

wires, and the resistance of these wires increases monotonically with rising temperature.

Both silicon and germanium are semiconductors. In all crystalline materials, the periodic lattice

establishes allowed energy bands.

In the lower band, or valence band, electrons are bound to

37

particular lattice sites. The conduction band is a higher lying band, in which electrons are free to

move within the crystal. The gap between these bands is referred to as the bandgap. Metals are

excellent conductors due to the fact that their valence band is not filled, and electrons can move

within the valence band. For insulators, this bandgap is quite large, typically 5 eV or greater.

Semiconductors are an intermediate case, with a smaller bandgap of roughly 1 eV.

Semiconductor detectors are operated with an applied bias voltage such that no charge is ini-

tially flowing, or "reverse-biased". When ionizing radiation passes through the biased semiconduc-

tor, electron-hole pairs are created and drifted in opposite directions, with the number of electron-

hole pairs being proportional to the energy of the radiation. Without this bias, electron-hole pairs

would equilibrate and recombine. Due to the small amount of energy needed to create an electron-
hole pair (≈3 eV) compared to other types of detectors such as gas filled detectors (≈30 eV) a
relatively better resolution can be obtained.

At 0◦, behind the target, two silicon detectors were placed on an aluminum stand inside the
DSL chamber on a movable plate. This allows for ∆E − E particle identification, which will
be discussed in the following chapter. Both detectors are Ortec B Series silicon surface barrier
detectors with 150 mm2 active area. For Run 1, the thin, or ∆E detector was 500 µm thick, and
the thick, or E detector was 1000 µm thick. The α particles of interest lose roughly 50% of their

energy in the ∆E detector and they are stopped in the E detector. A collimator was placed in front

of the silicon detectors to avoid edge effects. A picture of the silicon detectors in the DSL chamber

can be seen in Figure 4.7.

In both experiments, two high-purity germanium clover detectors were placed near the target,
with one at 0◦, for maximal Doppler shift, and another at 90◦, for reference. Clover detectors
consist of four germanium crystals, packed in a square configuration within a single cryostat. Due

to the low bandgap in germanium, electron hole pairs can be generated thermally, which leads to

leakage current and broadening of energy peaks. To combat this thermal noise, germanium detec-

tors are operated at liquid nitrogen temperatures. The liquid nitrogen dewars in thermal contact are

typically refilled every 8-12 hours. An image of the detector setup at TRIUMF is shown in Figure

38

Figure 4.7 Photo of the target chamber with the silicon detectors and target ladder installed. The
beam comes from the top right in this photo.

4.8.

While incoming charged particles directly create electron-hole pairs in the silicon detectors, γ-
rays in germanium detectors interact in multiple ways. At energies below ∼200 keV, photoelectric
absorption is most likely, where the photon is absorbed by a germanium atom, freeing an atomic
electron. For energies ∼200-1200 keV, Compton scattering dominates, where the photon transfers
some energy to an atomic electron. For energies above 1022 keV, twice the electron mass, pair

production can occur. In pair production, a high energy photon near a nucleus can produce an

electron-positron pair. When the positron annihilates with another electron, two 511 keV photons

are produced.

There are a number of general characteristics in germanium detector response for a single γ-ray

energy. I briefly cover these characteristics here, and more detail can be found in [48]. For high

energy γ-rays, pair production is the most significant mechanism for energy deposition. If either

the positron or electron escapes this leads to a peak at 511 keV below the full energy peak, referred

39

Figure 4.8 Picture of the detector setup at TRIUMF-ISAC II.

to as a single escape peak, and if both the electron and positron escape, this leads to a double escape

peak, 1022 keV below the full energy peak. A broad peak typically exists around 0.2-0.25 MeV,

caused by γ-rays that first Compton scatter on a material surrounding the detector, referred to as a

backscatter peak. The Compton edge corresponds to the maximum amount of energy transferred

in a single Compton scattering event.

4.5 Electronics

An electronics diagram for this experiment can be seen in Figure 4.10. Preamplifiers couple each

detector with a high voltage power supply and readout electronics. The silicon detector preampli-

fiers were attached directly to the feed-through on the DSL chamber flange, to reduce the length

40

Figure 4.9 Simulated Ge detector spectrum for a monoenergetic 4000 keV γ-ray. FEP, SEP, and
DEP correspond to the full energy peak, single escape peak, and double escape peak.

of cable available to pick up noise. To avoid RF noise, the DSL chamber, electronics racks, and

detectors were grounded separately from the beamline.

Preamplifier signals from the two silicon detectors and eight germanium crystals were read into

a single GRIF-16 card. These digitizers are 16-channel, 14-bit analog-to-digital converter (ADC)

with a sampling rate of 100 MHz. The Maximum Integrated Data Acquisition System (MIDAS),

developed at PSI and TRIUMF interfaces with the GRIF-16 digitizer to create a high-throughput

system to write experimental data to disk. More information on the acquisition can be found in

[49]. In the first run, the DAQ required 2 coincident events in the silicon detectors to write data to

disk.

41

-ray energy (keV)γDeposited05001000150020002500300035004000Counts/keV110210310410Backscatter511 keVDEPSEPFEPCompton edgeFigure 4.10 Block diagram of the data acquisition from Run 1. Bold lines signify multiple connec-
tions.

4.6 Run 2 experimental differences

The second run of this experiment was rather similar to the first one with a few small changes.

Due to damage to the 500 µm ∆E detector was replaced with an 87 µm detector, which provides

reasonable particle identification, but comes with the disadvantage of not completely stopping α
particles with energies corresponding to direct population of the first excited state of 31S. The Si

detectors were also placed farther back from the target, decreasing the solid angle coverage, which

improves energy resolution while decreasing count rate. As discussed previously, the upstream

collimators were replaced with tantalum. Current monitors on the collimators were inadvertently

disconnected. A cleaner target was fabricated at University de Montreal, where targets for previous

DSAM experiments were performed. This run also used a triggerless DAQ and wrote all events

above thresholds to disk.

42

Si ESi ΔEpreamplifierpreamplifierpreamplifierHV powerHV powerGRIFFINGRIF-16preamplifiersCHAPTER 5

32S(3He,α)31S ANALYSIS AND DISCUSSION

This chapter outlines the preliminary analysis of a two datasets from TRIUMF. While 31S proton

unbound state lifetimes could not be extracted from Run 1 data, useful insight on an improved

second experiment was provided. Identification of background sources and methods to mitigate

these backgrounds are provided. Reduction of background from Run 1 to Run 2 and tentative

assignments for peaks in Run 2 will be briefly discussed.

5.1 Calibration

This section discusses the calibration of the silicon and germanium detectors both with radioactive

sources and in situ data.

5.1.1 Silicon Detectors

The silicon detectors were calibrated before the run, using a triple-α source containing 239Pu,
241Am, and 244Cm, with the strongest α branches of 5.155 MeV, 5.486 MeV, and 5.805 MeV

respectively. This source was then affixed to the target ladder, without the BN plate or BeCu

springs in place. Each detector was sufficiently thick to stop the α particles, so the thick E detector

was calibrated before the thin ∆E detector was put in place.

An uncalibrated energy spectrum of one of these triple-α source runs can be seen in Figure 5.1.

During these runs, the resolution for each silicon detector was detemerined to be 0.8%. A linear

calibration was applied and used to extrapolate to higher energies. The extrapolation was verified

by comparing beam-on data to SRIM calculations. The calibration of these detectors could then

be used for particle identification and applying particle energy gates, to impose restrictions on the

initial excitation energy in the nucleus of interest.

43

Figure 5.1 Uncalibrated α energy spectrum taken with a triple-α source at the target position
with the thick silicon detector (thin detector removed). The energies of the three peaks used for
calibration are labeled.

5.1.2 Germanium Detectors

Before this experiment, data were taken with a 56Co source, which was used for the initial calibra-

tion. This source provides γ-rays up to 3.6 MeV, and the calibration was linearly extrapolated to
higher energies and confirmed using the 6129 keV γ-ray from 16O background. This calibration
was sufficient for monitoring online data, which was confirmed using stopped γ-ray lines at 547
keV from Coulomb excitation, as well as a number of lines in 39K, including those at 2814 and

3597 keV.

Temperature fluctuations between day and night time lead to daily drifts in the gain corre-

sponding to 4-5 keV near Eγ=3.5 MeV. To correct for this temperature fluctuation, a run-by-run
calibration was performed. The initial calibration was used to identify strong, narrow lines (not

Doppler shifted), which could then be used in the run-by-run calibration. A linear calibration was
applied using a line from 197Au Coulomb excitation at Eγ=279.00(5) keV and a line from 39K pro-
duced in 32S+12C fusion evaporation at Eγ=2814.06(20) keV. This calibration was then confirmed

44

channel number420440460480500520540560580600counts/channel01000200030004000500060005.4865.1555.805at the end of the run using well known lines from 90Nb β -decay from collimator activation.

5.2 Run 1 analysis

This section discusses analysis of Run 1 data, including a discussion of major background sources

and potential methods to mitigate those backgrounds.

5.2.1 Particle identification

Particle identification (PID) was performed by gating on a ∆E − E plot. ∆E was measured by a
silicon detector that is sufficiently thin that the particle deposits some, but not all of its energy,

and then the remaining energy is measured in a thick silicon detector. This energy loss gives

us information about the charge of the incoming nucleus. The stopping power, dE/dx, can be

described using the Bethe formula given below

where

(cid:34)

ln

B ≡ z

−dE

dx =

2mev2

I

4πe4Z2
mev2 NB
(cid:32)
1− v2
c2

− ln

(cid:33)

(cid:35)

− v2
c2

(5.1)

(5.2)

and v, Ze, z, N, and me are the velocity and charge of the incoming charged particle, the atomic

number and number density of the absorber atoms, and the electron mass, respectively.

I is a

parameter related to the mean excitation and ionization potential of the absorber that is typically

determined experimentally. For particles passing through the same amount of silicon, ∆x, the
energy loss is ∆E ∝ Z2

v2 . Multiplying by E = 1

2Mv2, gives

∆E × E ∝ M × Z2

(5.3)

Then a ∆E − E plot should show hyperbolic curves for each particle group corresponding to dif-
ferent values of MZ2. The PID plot for Run 1 can be seen in Figure 5.2.

45

Figure 5.2 Particle identification plot for Run 1.

5.2.2

γ-ray identification

As there were many sources of background in this experiment, many different techniques were

used to try to identify the source of the various γ-rays. Initially, we considered for each transition,

the integral in the α-gated γ spectrum compared the integral in the proton-gated γ spectrum. If a

peak was visible in the α-gated spectrum, but not (or very weakly) in the proton gated spectrum,

we assumed that the event came from a channel that did not produce protons (neutrons could still

be emitted and would not be detected), and occurred at the target position, so that the α particles

could reach the silicon detectors.

If a peak was observed both in the α and proton gated spectra, a ratio of the integrals of these

peaks was taken. Ratios close to 1 correspond to events from reaction channels that emit one proton

and one α-particle. Ratios of less than 0.1 α/proton were attributed to decay channels that did not

produce α-particles, and that the α-gated events were false coincidences. A transition with a ratio

46

of around 0.19 was assigned to events that were false coincidences with other events, as this ratio

corresponds to the ratio of the total number of α particle events over the number of total proton

events.

For events that could not be identified using the technique above, the geometry of this setup
was used to gain position information. Our 0◦ detector was placed at a distance of 7.5 cm from
the target to the face of the detector. Due to space constraints, the 90◦ detector was placed at a
distance of 21 cm. This lead to roughly an order of magnitude difference in geometrical efficiency

for events that occured at the target position. However, the difference in the distance between the

detectors and the upstream collimator was much more similar, leading to a difference in geometric

efficiency of a factor of 2. Therefore, ratios of integrals between the various detectors provided

information about the source position of these radiations. These provided some constraints on what

reaction mechanisms are likely.

5.2.3

31S first excited state

Although this experiment suffered from high background, the first excited state of 31S was clearly

visible above background at 1249 keV. Even though transitions from higher lying states were

obscured by background, we could gate on this γ-ray and look at the α energy spectrum, to get an
idea of what 31S excited states are feeding the first excited state. More energy goes into populating

higher lying excited states, leading to lower α-particle energies. The γ-ray lineshape of the 1st

excited state and 1st excited state gated α energy can be seen in Figure 5.3.

In Figure 5.3, we see the first excited state has a fairly weak direct population, that is well

separated from higher lying excited states, as expected. Fortunately, roughly 50% of the α particles
from 32S(3He,α)31S correspond to feeding of states with Ex =5-7 MeV, corresponding to our states
of interest. This feeding was used to make rate estimates for Run 2.

47

Figure 5.3 Left: α-gated γ spectrum zoomed in on the 31S first excited state. Right: 1249 keV
γ-ray energy gated α energy spectrum. The background in gray is taken by applying a gate on
background γ rays with slightly lower energies.

5.2.4

32S first excited state

3He inelastic scattering, populating the first excited state in 32S provides a fairly high statistics,

low background peak to test the validity of our lineshape simulation code. A fit of

5.2.5 Fusion evaporation reactions

The majority of the background in this experiment came from fusion-evaporation reactions. In

these reactions, heavy nuclei collide, and fuse into a hot compound nucleus. These reactions

tend to populate continuum states which emit, or evaporate, protons, neutrons, and α particles.

All fusion evaporation calculations in this thesis used PACE4 [50], based on a modified JULIAN

fusion evaporation Monte-Carlo code [51] included in the software package LISE++ [52].

This experiment suffered from the build up of a carbon layer on the surface of the target before

or during implantation. The carbon compounds forming this layer turn orange under beam heating

and can be seen in Figure 4.5, with the top two target positions holding the target implanted for

this run, and the bottom position with a target that was cooled improperly in another experiment

[12], which resulted in hydrocarbon condensation on the target.

Reactions on the carbon were particularly problematic: since they were on the surface of the

48

energy (keV)γ12001220124012601280130013201340counts/2 keV1200140016001800200022002400direct populationα34363840424446485052counts/0.2 MeV050100150200250300350400450energy (MeV)backgroundof 1st excited stateEx(31S)=5-7 MeV31S39K42CaFigure 5.4 Data from 32S(3He,3He’)32S∗ in red along with preliminary best fit lineshape and flat
background in blue. The lifetime extracted from this fit, 240(30) fs agrees with the literature
lifetime of 244(15) fs [13].

target, light reaction products could propagate to the silicon telescope, and could not be gated out.

Not only did many channels produce α-particles, but the energy distribution of the α-particles from
the carbon fusion-evaporation reactions was peaked at the region of interest for 32S(3He,α)31S .
An α-gated spectrum with peaks from 12C+32S reactions labeled can be seen in Figure 5.5.

By comparing to cross sections calculated with PACE4, as well as short runs with the dirty
target from [12], we determined the areal density of the carbon to be roughly 3× 1017 atoms/cm2.
This areal density is comparable to that of the implanted 3He. Unfortunately, the cross section for
α-particle producing events from 32S+12C is calculated by PACE4 to be roughly 800 millibarns,
compared to the cross section for 32S(3He,α)31S of only 95 mb calculated by PACE4.

In previous experiments, [53, 54] while some carbon contamination was present, levels of

49

Figure 5.5 α-gated γ-ray spectrum with peaks from 12C+32S reactions labeled. Peaks with gray
labels correspond to false coincidences with proton events.

contamination were 1-2 orders of magnitude lower. This level of carbon contamination would be

manageable, and would not create much background in the region of interest. To mitigate this

problem in Run 2, we have implanted a new foil at University de Montreal, where targets from

previous experiments were successfully implanted.

Due to a poor beam tune, up to 80% of the beam was dumped on our copper collimators early

on in the run, and even after spending extra time on an improved tune, typically half of the beam

was lost on the collimator. The collimator essentially acted as a thick target, which combined with

a cross section of roughly 800 mb at the full energy lead to a very high yield.

These reactions populate nuclei with Z≈39-44 and A≈85-94. These nuclei are sometimes pop-
ulated in excited states, which lead to a few low energy γ-rays, which can be seen in Figure 5.6.

If this were the only background from the copper, it would not have any significant impact on a

successful analysis of this data set, due to the low γ-ray energies, below our region of interest. Un-

fortunately, these reactions also lead to a rather large continuum background. This effect has been
seen before in a very similar system, 35Cl+54Fe at similar beam energy, in [55]. This continuum,

seen in Figure 5.7, obscured the transitions of interest for this analysis.

To mitigate this background in any future experiments, new collimators were fabricated at

TRIUMF for Run 2, using tantalum. Using a higher Z material leads to a larger Coulomb barrier.

50

Energy (keV)05001000150020002500300035004000counts/2 keV31041039K42Ca42Sc36Ar39K39K36Ar39K42Ca39K37Ar42Ca36Ar38Ar36Ar38Ar43Sc39K39K39K40Ca38ArFigure 5.6 α-gated γ-ray spectrum with peaks from 63,65Cu+32S reactions labeled in black and
63,65Cu+p,n,α reactions labeled in gray.

Figure 5.7 α-gated γ-ray spectrum showing continuum background at high energies from
63,65Cu+32S reactions.

Using the same beam energy as Run 1, we were below the Coulomb barrier for Run 2. The fusion

evaporation cross section is then negligible, and the only concerns with tantalum collimators would

then be Coulomb excitation of the tantalum and reactions on any contaminants in the tantalum.

Tantalum Coulomb excitation has been well studied and will only give low energy γ-rays, below the

region of interest. Contamination of the tantalum must be kept to a minimum, but with relatively

51

Energy (keV)05001000150020002500300035004000counts/2 keV31041088Nb90Zr67Ga66Zn66Zn65CuEnergy (keV)40004500500055006000650070007500800085009000Counts/2 keV210310pure tantalum or a good beam tune, background from the collimator should be minimal.

In addition to γ-rays from the fusion-evaporation reactions, these reactions also produced large

numbers of protons, neutrons, and α-particles. These light particles can then undergo reactions on

the copper in the collimator. Photopeaks identified as coming from these reactions can be seen in

Figure 5.6, labeled in gray. Replacing the collimators mitigates this background.

5.2.6 Collimator activation

Some of the isotopes produced by the reactions on the collimator have long half-lives, up to 107
days for 88Y. β -delayed γ-rays were not time-correlated with the beam, and were effectively gated
out of the on-line data. However, after the beam was turned off, these β -delayed γ-rays were

counted for 8 hours, then briefly again after 2.5 days of calibration runs. The first 8 hours of data

can be seen in Figure 5.8.

Figure 5.8 γ-ray spectrum showing β -delayed γ rays in the 8 hours immediately after the beam
was turned off.

In the analysis of this spectrum, initial assignments were made using expected β -decay daugh-

ters of nuclei identified during the experiment, corresponding to fusion evaporation products. Iden-

tifying other lines in the spectrum lead to the realization that light particle induced reactions were

52

Energy (keV)0500100015002000250030003500400045005000Counts/keV1021031041051061066Ga66Ga66Ga89Nb66Ga90Nb90Nb89Nb52Mne+89Nbalso occurring in the collimator.

5.3 Preliminary analysis of Run 2 data

A detailed analysis of Run 2 data is beyond the scope of this dissertation; however, preliminary

results are discussed below. This data was calibrated using the same procedure as discussed

above. Silicon detectors were calibrated with a triple α source, and germanium was calibrated
run by run using the 247 keV γ-ray from 197Au Coulomb excitation and the 2841 keV γ-ray from
32S(12C,pα)39K. Particle identification can be seen in Figure 5.9.

Figure 5.9 ∆E-E particle identification plot.

53

5.3.1 Background reduction

High energy γ-ray background obfuscated peaks of interest in Run 1 data. Figure 5.10 shows the

reduction in background by reducing carbon contamination on the surface of the target as well as

replacing copper collimators with new collimators. The background is reduced by roughly a factor

of three in the region of interest. The major sources of remaining high energy γ-ray background

are likely fusion evaporation reactions on dirt and ice on the surface of the target and fluorine

contamination in the tantalum collimators.

Figure 5.10 γ-ray spectra gated on all α particles, where Run 1 data is scaled based on the ratio
of photopeak counts in the 1249 keV γ-ray, corresponding to depopulation of the 31S first excited
state.

While it was possible to entirely remove copper background from our experiment, carbon con-

tamination at some level will always be present. As seen in Figure 5.11, the intensity of the 3597
keV line (as well as other 39K lines not shown) are reduced by roughly a factor of five, which

suggests the new target is a factor of five cleaner than the old target.

54

0100020003000400050006000700080009000Energy (keV)110210310410Counts/2 keVRun 1Run 2Figure 5.11 Same as Figure 5.10, zoomed in to show two γ-ray lines from carbon contamination,
from 39K at 3597 keV and at 3736 keV from 40Ca, and the reduction in intensity from Run 1 to
Run 2.

5.3.2 Tentative transition identification

While an in depth analysis of this data set has not yet been performed, I outline here tentative

assignments of new peaks seen in this data.

Below, in Figures 5.9-16, α particle energy gated γ-ray spectra are shown for a number of

α-particle energies, along with tentative assignments for various peaks, including two states in the

region of interest for classical nova nucleosynthesis. To guide the eye, lineshape simulations for

these tentative assignments are included, without included background. For states where there is

no experimentally determined lifetime in the literature, a lifetime of 10 fs is assumed. Lifetimes
of 1-30 fs are expected for most of these states, based on comparisons of 31S states to shell model
calculations and the mirror nucleus, 31P. The major difference in lineshapes from 1 fs to 30 fs

lifetimes is the width of the lineshape. Shorter lifetimes correspond to a narrower lineshape, and

55

Energy (keV)34003450350035503600365037003750380038503900counts/2 keV210310longer lifetimes correspond to a broader lineshape.

Figure 5.12 Second excited state to ground state transition, gated on α particle energy 47-49 MeV
with a simulated lineshape for the literature lifetime of 320 fs (red) [13].

The only 31S excited states observed in this run with literature lifetimes are the first and second

excited states. These states can be used to confirm that our lineshape simulation works as expected.

We expect to place constraints on bound states at 3077, 4971, and 5157 keV that currently do not

have experimentally determined lifetimes in the literature. We also expect to be able to place

constraints on lifetimes of two or three states in the region of astrophysical interest, at 6392, 6400,

and 6542 keV. Detailed analysis of this data set is beyond the scope of this work.

56

Energy (keV)20002050210021502200225023002350240024502500Counts/2 keV024681012Figure 5.13 Third excited state to ground state transition, gated on α particle energy 46-48 MeV
(blue) with a simulated lineshape with arbitrary lifetime of 10 fs (red).

Figure 5.14 4971 keV excited state to ground state transition, gated on α particle energy 42-44
MeV (blue) with a simulated lineshape with arbitrary lifetime of 10 fs (red).

57

Energy (keV)30003050310031503200325033003350340034503500Counts/2 keV0246810Energy (keV)50005050510051505200525053005350540054505500Counts/2 keV024681012Figure 5.15 5157 keV excited state to ground state transition, gated on α particle energy 42-44
MeV (blue) with a simulated lineshape with arbitrary lifetime of 10 fs (red).

Figure 5.16 6400 or 6392 keV excited state to first excited state transition, gated on α particle
energy 39-41 MeV (blue) with a simulated lineshape with arbitrary lifetime of 10 fs for the 6400
keV state (red).

58

Energy (keV)52005250530053505400545055005550560056505700Counts/2 keV024681012Figure 5.17 6400 or 6392 keV excited state to second excited state transition, gated on α particle
energy 39-41 MeV (blue) with a simulated lineshape with arbitrary lifetime of 10 fs for the 6400
keV state (red).

Figure 5.18 6542 keV excited state to first excited state transition, gated on α particle energy 39-41
MeV (blue) with a simulated lineshape with arbitrary lifetime of 10 fs (red).

59

CHAPTER 6

36Ar(d,t)35Ar EXPERIMENT

This chapter discusses the method used to search for 35Ar excited states just above the proton

emission threshold. The procedure for making the ion-implanted targets used for this measurement

is briefly discussed and the remaining portion of the chapter discusses measurements performed

at the Maier-Leibnitz Laboratorium (MLL) in Garching, Germany in January 2014. The layout of

the facility can be seen in Figure 6.2.

6.1 Ion-implanted C targets

The 36Ar targets used were fabricated by implanting 3-6 µg/cm2 36Ar into a 30 µg/cm2 natC foil

at the Center for Experimental Nuclear Physics and Astrophysics (CENPA) using several beam

energies (25-70 keV) to provide a more uniform depth distribution than a single beam energy
would permit. This technique was used to fabricate targets of several isotopes, including 36Ar.

A model of the depth distribution is shown in Figure 6.1. Further details of the implantation and

other uses of these targets can be found in [14, 56, 57]. One target used in this run was fabricated

by the authors of [14] and backup targets were fabricated by Ronaldo Ortez and Alejandro Garcia,

coauthors on [58].

32S targets were used for calibration. 10.4 µg/cm2 of 32S ions were implanted into 40 µg/cm2
isotopically enriched 12C foils. This implantation was carried out at the Tandetron Accelerator

Laboratory (TAL) at University of Western Ontario, as described in [59, 25, 26]. This target was
chosen over the 32S target made using the procedure outlined in [14] used for the 36Ar target due
to the higher amount of 32S and lower amount of 13C.

60

Figure 6.1 Calculated depth distribution for 24Mg implanted in C foils using the same methods as
the 36Ar target, as discussed in [14]. The black line represents the total depth distribution, and the
grey lines show components from individual energies.

6.2

2H ion source

This section discusses the ion source used to provide the deuteron beam used for this measurement.

Molecular deuterium (D2) gas is moved into a dissociator by an atomic jet, which is created by
adiabatic expansion [60]. A radiofrequency (RF) field is created in the cold plasma in the dissocia-

tor using a high frequency AC circuit. This causes the electrons in the plasma to oscillate in helical

orbits. These electrons collide with the molecular deuterium, producing neutral atomic deuterium.

This deuterium then enters another pumping stage, which helps to minimize the scattering of the

beam and charge exchange between the atomic and residual molecular deuterium. This provides
intensities on the order of 1016 atoms/s for the Electron Cyclotron Resonance (ECR) ionizer.

The ECR ionizer ionizes the atomic deuterium, producing D+ ions by impacting electrons in a

static magnetic field and an RF field in a plasma. An axial magnetic field is provided by two sets of

coils, which helps to confine the plasma. The 2.45 GHz RF field is applied to the plasma through

a waveguide, insulated by a cylindrical pyrex tube. Radial confinement is provided by a sextupole

field produced by FeNdB magnets. This ionization process has an efficiency of a few percent.

The ion beam is then transported through a system of electrostatic lenses into a cesium vapor

61

Figure 6.2 Layout of the MLL facility

region. The extraction electrodes are placed at a large diameter to allow the atomic beam to leave

the region unhindered to be pumped out. The beam is extracted by a series of electrodes followed

by an Einzel lens, which focuses the beam without changing its energy using electrostatic fields.

The beam is then focused onto a cesium target (which has a low ionization energy), where it
acquires a negative charge (D−). This charge flipping efficiency is approximately 22%. The beam
then leaves this region with an energy of a few hundred keV. A conceptual flow chart of the source

can be found in Figure 6.3.

62

Figure 6.3 Flow chart of the ion source components at MLL

6.3 Munich M-P tandem Van de Graaff accelerator

After leaving the ion source, the deuterons are further accelerated by the MP tandem Van de Graaff

accelerator, downstream of the Cs vapor target. Like most Van de Graaff accelerators, there is an

electrically charged terminal that accelerates the charges through a series of insulated tubes in high

vacuum. However, for this tandem accelerator, there are two sets of accelerating tubes in one

pressure tank. At the junction of these two accelerating tubes is a positive high voltage terminal.

This terminal is kept at a high voltage by delivering charge using three pelletron chains which each

deliver a current of 100 µA [61]. These chains consist of metal pellets charged by induction that

are joined by insulating nylon.

Negative ions coming from the Cs vapor target are accelerated to an energy given by the charge

times the voltage. They are then charge stripped in a carbon foil and accelerated again, this time

with a positive charge. For isotopes of hydrogen, the ions reach an energy of E = 2qeV , where

V is the terminal voltage and qe is the electron charge. After acceleration, the beam is bent by an

analyzing magnet through a set of slits that provides a further cut on beam energy, improving the

resolution. More information on this accelerator can be found in [61].

6.4 Target interaction

The beam is then delivered to the target chamber upstream of the Q3D spectrograph. The target

chamber is a cylindrical metal vacuum chamber and houses the target ladder. Once the target ladder

63

is inserted, the chamber is pumped down to avoid energy loss and background reactions on air in

the chamber. Each target ladder has 6 positions, 5 for targets, and a collimator for beam tuning. A

schematic of the target ladder can be seen in Figure 6.4.

Figure 6.4 Schematic of the Munich target ladder and targets used in the run. Details of the im-
planted targets are discussed in the text. 36Ar targets are labeled by the year of first use.

The target can also be rotated by an angle θ in the plane between the beam and the target.

Increasing the angle θ increases the amount of target nuclei seen by the beam, increasing statistics.

However, increasing this angle also increases the effects of energy loss and straggling within the

target, effectively broadening the peak shape of triton position at the focal plane. The energy loss

of the higher energy deuterons is much less than that of the lower energy tritons, leading to an

asymmetric peak shape.

The amount of charge incident on the target is also a quantity of interest. A Faraday cup is
located behind the target at 0◦ and connected to a current integrator. This determines the amount
of charge that has passed through the target. Since most of the deuterons pass through the target

64

1 2345613C-13.5 μg/cm2  32S-implanted36Ar-implanted (2014)28Si-25 μg/cm2 collimator36Ar-implanted (2009)without undergoing nuclear reactions, this is a good approximation of the total beam current in-

cident on the target. The Faraday cup also provides instantaneous current, which is a useful way

to monitor the stability of beam delivery. During this experiment the beam current was typically

200-700 nA.

6.5 Q3D magnetic spectrograph

For this measurement, a magnetic spectrograph was used to separate the reaction products of in-

terest. The light reaction products traverse a magnetic field and are separated by their momentum

over charge. The momentum can then be calibrated for each particle group from position infor-

mation in the focal plane. Knowing the momentum of the reaction product and the ground state

masses, excitation energies can be determined. The spectrograph focuses light reaction products

onto a position sensitive detector. For the sake of acquiring statistics, a large solid angle acceptance

is also desired.

These requirements, along with kinematic broadening need to be corrected for in the geom-

etry and magnetic field configurations. Spectrographs are typically optimized using computer

simulations and ray tracing. These aspects were considered in the design of the Q3D (quadrupole-

dipole-dipole-dipole) spectrograph. The quadrupole focuses the particles in the vertical direction

and defocuses in the horizontal direction. The first dipole then focuses the particles onto a line in

the horizontal direction. A multipole element then corrects for kinematic broadening in the hori-

zontal direction. The particles then see two more dipoles separated by an electrostatic deflector. A

schematic is shown in in Figure 6.5.

The solid angle acceptance of the Q3D assuming the entrance slits are fully open is 13.9 msr,
which was the case throughout this experiment. The attainable energy resolution ∆E/E = 2×10−4
is similar to that of the tandem accelerator. The operating software takes as inputs the reaction of

interest and the excitation energy and applies settings to place reaction products corresponding to

the state of interest to be at the center of the focal plane detector. Proton NMR is used to monitor

65

Figure 6.5 Top down view of the ion optics of the Q3D magnetic spectrograph at MLL. Figure
adapted from [15].

and stabilize the magnetic field produced by the second dipole.

6.6 Position sensitive cathode strip detector

After the particles have been separated, they are detected at the focal plane by a device with sim-

ilar resolution to the beam energy and the Q3D field configuration to take advantage of this high

resolution setup. In this case, a position sensitive cathode strip detector was designed with these

criteria as well as things such as detector geometry and positioning in mind. A diagram of the

entire detector can be seen in Figure 6.6.

A particle enters the detector by passing through 25 µm Kapton foil into a region filled with

66

Figure 6.6 Top down view of the focal plane detector of the Q3D. Figure from [16].

isobutane gas. The particle then encounters a proportional counter consisting of a cathode foil and

an anode wire. The particle ionizes the gas and creates electron-ion pairs. The particles near the

anode will be accelerated, and then ionize more gas atoms, creating a charge avalanche. The charge

collection at the anode is proportional to the energy loss of the particle from the first ionization.

This energy loss is referred to as ∆E1.

The particle then passes through the cathode foil, a gas filled region, and another cathode foil,

both made of 2.9 µm aluminized mylar [15, 16]. The particle enters another proportional counter

composed of two anode wires. The particle then creates an avalanche of ion-electron pairs. Energy

loss is then measured and called ∆E.

Cathode strips are located after the anode wires. These cathode strips are electrically isolated

and 3.5 mm wide, with a separation distance of 0.5 mm. There are 255 of such strips that cover 890

mm of the Q3D focal plane. Based on the incoming angle, charge is typically induced on about

67

6 strips. The position can then be extracted by fitting the charge distribution with a Gaussian. A

diagram showing this position reconstruction based on the induced charge can be seen in Figure

6.7. The particles then travel through the cathode strips and deposit their residual energy in a

scintillator.

Figure 6.7 Conceptual diagram of the position reconstruction used in the MLL Q3D focal plane
detector. Figure from [16].

While a Gaussian fit provides better position resolution, using this method online is too slow

and would increase the dead time. Instead, the center of gravity method is used to look at online

data. This calculation is similar to finding the center of mass of a system of masses. The calcu-

lation is faster but introduces systematic effects due to the separation of the cathode strip foils.

Periodic minima occur in the position spectra. Gaussian fits can then be performed offline, and

after performing this fit, the position resolution is reported to be less than 0.5 mm FWHM [15].

68

6.7 Data acquisition system (DAQ)

The data acquisition system at MLL is called the Multi-Branch System (MBS) and ROOT based

online/offline utility (MARaBOU). This system controls the conversion of analog signals and pro-

duces digital outputs to be interpreted and manipulated by the acquisition computer. The MBS

developed at GSI in Darmstadt, is used as the front end, which reads out the data, builds the events

and transports the data. The back end provides software libraries for setup, run control, and for

data analysis and storage, using the ROOT analysis software. More details can be found in [62].

The modules used in the data acquisition are connected and operated under the Computer Auto-

mated Measurement and Control (CAMAC) system. The system is set up such that the Application

Specific Integrated Circuit (ASIC) only records good events. For an event to be recorded, it is re-

quired that 3-7 adjacent cathode strips have induced charge above the threshold within a window

of 100 ns. If this event has an invalid multiplicity, then the system is reset, which takes about 4

µs. If an event is good, then the signals are sent to an Analog to Digital Converter (ADC) and the

event is written to disk. A diagram of the electronics can be seen in Figure 6.8.

69

Figure 6.8 Diagram of the DAQ electronics for the MLL experiment. Figure adapted from [15].

70

Control RoomQ3D HallCathode strip detectorScintillator leftPMTrightPMTAnode wires upper wire inv. preamp lower wireinv. preampamplifieramplifier255 Cathodestrips255 preampsASIC255 analog switches255 peak-hold255 discriminators255 shapersdiscr.,  etc   spec. amplifier  fastadderMARaBOUMARaBOUHDD   TimingGeneratorNIMCAMAC8 ADCTransferControlDualInputcounterADC-Gate   DetectorCoincidenceExt. TDTExt. TDTfast resetStart readoutMultiplexing and    control unitCoinc. logicOutputbufferdelaydiscr.discr.delayStartExt.gateData 1Data 2   spec. amplifier   spec. amplifier   spec. amplifier  fastadder    GateGeneratorcounter    GateGenerator    GateGenerator    GateGeneratorCHAPTER 7

36Ar(d,t)35Ar ANALYSIS AND DISCUSSION

This chapter gives an overview of the data analysis and a discussion of the results of the exper-

iment outlined in the previous chapter. Many of the techniques discussed here are applicable to

other transfer reaction studies. Particle identification (PID), spectrograph plotting, calibration tech-

niques, and extracted excitation energies are discussed. A discussion of the measured level density
of 35Ar is also presented.

7.1 Particle identification

Particle identification was performed by gating on a ∆E − E plot. ∆E is measured in a detector
that is sufficiently thin that the charged particle deposits some, but not all of its energy, and then

the remaining energy is measured in another detector. This energy loss gives us information about

the charge of the incoming nucleus. The stopping power, dE/dx, can be described using the Bethe

formula given below

where

(cid:34)

ln

B ≡ z

−dE

dx =

2mev2

I

4πe4Z2
mev2 NB
(cid:32)
1− v2
c2

− ln

(cid:33)

(cid:35)

− v2
c2

(7.1)

(7.2)

and v, Ze, z, N, and me are the velocity and charge of the incoming charged particle, the atomic

number and number density of the absorber atoms, and the electron mass, respectively.

I is a

parameter related to the mean excitation and ionization potential of the absorber that is typically

determined experimentally. For particles passing through the same amount of absorber, ∆x, then
the energy loss, ∆E ∝ Z2

v2 . If we multiply by E = 1

2Mv2, we find that

∆E × E ∝ M × Z2

(7.3)

71

Then a ∆E − E plot should show hyperbolic curves for each particle group corresponding to dif-
ferent values of MZ2, as seen in Figure 7.1.

Figure 7.1 Expected shape and relative separation for stable hydrogen and helium isotopes

In this case, the ∆E detector is a multi-wire proportional counter, and the rest of the energy

(E) is deposited in a plastic scintillator. Due to the geometry of the detection setup (discussed

in Section 6.6) ∆E depends on the incoming angle, which effectively broadens the expected line

width. The total energy is constrained by the Q3D settings, turning the expected bands into more

circular shapes. Similarly, a comparison of the total energy lost in the proportional counter (∆E)
can be compared to the energy lost in a portion of the proportional counter (∆E1) to provide further
constraints on the PID. These plots, including triton gates can be seen in Figure 7.2.

7.2 Background subtraction

In this experiment, the targets used contained 36Ar, 12C, and 13C. Both 12C and 13C have the
potential to introduce background in addition to the peaks of interest from reactions on 36Ar.
For all but the 25◦ data, all peaks from 12C(d,t)11C are excluded from the focal plane by the
kinematics. In the 25◦ data, the first excited state of 11C (Ex=2000.0(4) keV) is populated, but the

72

Figure 7.2 Particle identification plots, along with triton gates, for the first set of 15◦ data taken
on the 36Ar implanted target. The particle group at high ∆E corresponds to α particles, and the
particle group at low ∆E corresponds to unresolved protons and deuterons.

corresponding peak is on the edge of the focal plane. To deal with this, an additional peak was

added to the fit in that region.

13C(d,t)12C produced a broad, defocused peak (Ex=16.1 MeV) in all of the spectra other than
the 54◦. Spectra from these runs can be seen in Figure 7.3. In addition, nearby peaks with large
intrinsic widths of 1.15 and 1.5 MeV produced a relatively flat background. To deal with this
background, runs were taken on an enriched 13C target with a thickness of 13.5 µm/cm2. Then
based on the amount of 13C in each of the targets and the dead time corrected integrated beam
rate, a normalization was applied to the collected 12C spectra. These targets were also different
thicknesses. The differences in energy loss were estimated to be 2 keV at 15◦, 20◦, and 25◦, and 3
keV at 54◦ (due to the increased effective thickness because of the geometry).

For this analysis, spectra were rebinned by a factor of five. Once this was done, a rough
calibration of 1 bin≈0.5 keV was obtained. This was used to determine the shift to apply to the
13C(d,t)12C spectra. After applying these corrections, a bin by bin subtraction was performed.

Poisson statistics were used to estimate the errors in the number of counts in each bin, and these

uncertainties were then combined for the subtracted spectra. These spectra were then used for the

final fitting in the analysis of this data. An example spectrum can be seen in Figure 7.4.

73

Figure 7.3 13C(d,t)12C data.

7.3 Spectrograph plotting

Once the reaction of interest has been identified, known peaks in the position spectrum need to be

identified. For this measurement, it was expected that we would see many previously unidentified
peaks, but the 31S and 27Si peaks need to be identified before they can be used to calibrate the
excitation energies of the 35Ar peaks. For this work, a program called SpecPlot, which is a part of

a larger simulation package Nukesim-classes [63], was used.

SpecPlot calculates the bending radius (ρ) of each of the light reaction products given momen-

tum p and charge q, in a magnetic field B. The momentum can be determined using relativistic

kinematics. If we combine these results we see that for a particle with an energy E, their radius is

74

02040010200204060800204060Position (channels)0500100015002000250010020016106161061610616106Counts/5 channels20°15°15°25°54°Figure 7.4 A background subtracted 36Ar(d,t)35Ar spectrum taken at 15◦.

(cid:115)(cid:18)E

c

given by

ρ =

1
qB

(cid:19)2 − (mc)2

(7.4)

Using the knowledge of the light reaction product and using conservation of energy, one can

determine the mass of the excited state (ground state mass plus excited state energy) of the heavy

recoil nucleus. SpecPlot calculates the focal plane position of the light reaction products given

information on the ground state mass and excitation energy inputs. Light particle energy increases

with increasing ρ, which corresponds to decreasing excitation energy in the target nucleus. Figure

7.5 shows an example of this calculated position spectrum.

Figure 7.5 A sample SpecPlot output for relevant reactions at 54◦.

SpecPlot takes as inputs both nuclear masses and excitation energies for all nuclei involved in

75

05001000150020002500050100150200counts/5 binsposition (channels)the calculation. Mass inputs for this code come from the 2003 Atomic Mass Evaluation (AME)

[64]. This mass database was compiled in 2003, and since then more information has become

available, and further mass evaluations have been performed. However, at this level, the previous

data is sufficient to estimate the peak locations. Input excitation energies were taken from the

Evaluated Nuclear Structure Data File (ENSDF) database [13]. Information on the beam energy

and the reaction products, as well as the spectrograph angles are also required inputs.

To identify peaks, one can compare to previous data or use the Q3D centering settings to

identify a reference state. From there, one can try to line up all other states in SpecPlot to a

corresponding state in the position spectrum. This program is limited by the fact that it assumes

that the particles traverse a constant magnetic field. The field strengths within the Q3D are not

constant, but this provides a useful approximation. The input parameters such as radii and B can

be tuned to attempt to match what is seen on the focal plane. Therefore the states are not expected

to line up exactly. The Q3D dispersion also has a small variation which can add to these effects.
Figure 7.6 shows a SpecPlot window aligned with 31S and 35Ar spectra obtained at 15◦.

SpecPlot can be used as a guide for identification of the states populated from both expected

reactions and potential target contaminants. It is also useful in the planning of these experiments.

Different beam energies and spectrograph angles can be input to optimize these parameters before

the run. These parameters can be selected so that potential contaminant peaks are out of the way
of those peaks of interest. Spectra used for calibration can be seen in Figures 7.7 (31S) and 7.8
(27Si).

7.4 Peak fitting

After the reaction products of interest are selected and calibration peaks are identified, the next

step in this data analysis is to determine the peak centroids, for both calibration peaks and peaks

of interest. This fitting was performed in ROOT [65]. The software that applies the PID gates and

performs the position reconstruction mentioned earlier outputs a ROOT file containing histograms

76

written as:

f (x) = Aexp

σ 2
2τ2 +

x− µ
τ

erfc

(cid:33)

(cid:18) 1√

2

(cid:18)σ

τ

(cid:19)(cid:19)

− x− µ
σ

(cid:32)

Figure 7.6 Data taken at 15◦, showing the 32S(d,t)31S and 36Ar(d,t)35Ar spectra overlaid by
SpecPlot, roughly aligning previously identified peaks. Only previously known information on
35Ar is included in the SpecPlot input.

of the PID plots and the position spectrum.

Due to dissipative effects such as energy straggling in the target, an asymmetric peak shape

was necessary to fit the observed peak shape. An exponentially modified Gaussian, which is the

convolution of a Gaussian and an exponential was chosen for this analysis. This fit function can be

(7.5)

where erfc is the complementary error function, A is related to the height of the peak, τ describes

the asymmetry of the peak, σ is the width of the Gaussian, and µ is the centroid of the Gaussian.

A ROOT macro was written to fit a given number of peaks with this peak shape, as well as

to include a linear background. Since nonlinear fitting is sensitive to the initial guess, fairly good

77

Figure 7.7 32S(d,t)31S spectra used for calibration.

estimates of the fit parameters were needed as inputs. Output parameters for each peak were then

written out to a data file. This fit was performed over various regions of the focal plane, being

sure to select a large enough region to characterize the background. An example fit can be seen in

78

040801200204060020406001020304050Position (channels)5001000150020002500010203040506637658665436395637763576327628062556160663765866543639563776357632762806255616066376586654363956377635767206749683466376586654368706357616063776139632762806255597867206749683420°15°15°25°54°Counts/5 channelsFigure 7.8 28Si(d,t)27Si spectra used for calibration.

Figure 7.9. For these fits, τ was fixed for each spectrograph angle, and σ was fixed based on the

widths of nearby high statistics peaks.

For one case, the left edge of the focal plane in the 54◦ spectrum, the fitting was complicated
by the fact that there were no well isolated peaks in the region. The width for each peak in this fit
was constrained by the widths of other peaks in the 35Ar data at this angle and peaks near the left
edge of the focal plane in the 31S data, accounting for the kinematic broadening. Then, this region
was fit with a flat background and adding peaks until a reasonable value of χ2/ν was achieved.

Based on this procedure, 6 peaks were used in the fit. This fit can be seen in Figure 7.10.

7.5 Calibration

Once peak centroids have been extracted for all of the peaks of interest and calibration peaks,

a calibration can then be applied to extract energies for the peaks of interest. This calibration

was done using a program called SPANC (SPlitpole Analysis Code), which is also a part of the

Nukesim-classes package [63]. Inputs for SPANC include a description of the targets, a list of the

79

02040605001000150020002500020406080position (channels)counts/5 channels44474704447444474704447420°25°Figure 7.9 Example of the fit procedure used in the data analysis. Shown is the middle of the focal
plane in the 54◦ 36Ar(d,t)35Ar data.

Figure 7.10 Fit for the left of edge of the focal plane at 54◦ for 36Ar(d,t)35Ar .

reactions, the beam energy, the projectile’s charge state, the spectrograph angle and B field, and

the energy and position of each calibration peak. To estimate the energy loss in these targets, it is

assumed that the interaction occurs in the center of the target.

This code also requires as input the ground state masses of all nuclei in the reaction, to calculate

80

12013014015016017018019020020406080100120position (channel)counts/10 channelsposition (channel)100200300400500600700800counts/10 channels020406080100the Q values. Incorrect Q value calculations lead to a systematic shift in the extracted energies.

Since SPANC was written, using AME 2003 [64], two new mass evaluations have been released,
and the recommended mass for 31S has changed by ≈1 keV. To properly account for this, mass
values were updated in the code to reflect the then current values in AME 2012 [66].

For the calibration peaks, SPANC then calculates the expected ρ value for each calibration
peak. For this measurement, calibration peaks from 31S were used at all angles, and at 20◦ and
25◦, 27Si peaks were also used. SPANC then fits ρ as a function of channel number. Once this fit
is obtained, this can be applied to the centroids of other peaks to extract excitation energies. Peaks

used for calibration were those that had low uncertainties, did not appear to be part of a doublet,

and were located across but completely on the focal plane. SPANC then outputs the energies of

input peaks, given their centroids. An example of these windows can be seen in Figure 7.11.

Figure 7.11 SPANC windows for the 15◦ data.

81

7.6 Excitation energies in 35Ar

SPANC can take in the centroid of a peak and the uncertainty of that peak and output an excitation

energy and a corresponding statistical uncertainty. In addition to statistical uncertainties, system-

atic effects also need to be considered. When the calibration or the averaging over the values

obtained for different states had a value of(cid:112)χ2/ν greater than unity, the statistical uncertainty

was inflated by that factor. This lead to inflated statistical uncertainties of 1-2 keV.

The fit routines were varied to estimate systematic uncertainties, and these were found to be 1

keV. Potential shifts in beam energy and Q3D magnetic field were tracked using high yield peaks
from 12C(d,α)10B corresponding to the ground and first excited states of 10B. A sample spectrum

can be seen in Figure 7.12.
In addition to these uncertainties, there exist conflicting literature
data on the excitation energies of 31S. This discrepancy is discussed in Section 2.3.4. These
discrepancies span a range of ≈4 keV [9]. Calibration energies were dominated by one of these
two data sets. We then shifted all energies downward by 2 keV to account for these discrepancies

and added a 2 keV uncertainty to cover both possibilities.

Combining all of these systematic uncertainties in quadrature (δ E2

shi f t +
calib) gives an overall systematic uncertainty of 2.4 keV. This systematic uncertainty is then
combined in quadrature with the statistical uncertainty (inflated if the agreement at different an-

δ E2

sys = δ E2

f it + δ E2

gles is poor, as discussed previously), leading to total uncertainties of 3-5 keV, depending on the

level. The extracted energies can be seen in Table ?? and Figure 7.13.

Two criteria were required to claim the discovery of a new level. First, it was required that each

peak be observed in at least two spectrograph angles at the 3σ level, which provided kinematic
confirmation that the peak was in fact from 35Ar. Second, the significance of the peak was also

required to be greater than 5σ total, where significances of peaks at separate angles are added in

quadrature. Applying these criteria, 17 new levels were discovered, and the uncertainties in the
excitation energies of 5 known levels were decreased by a factor of ≈3.

82

Figure 7.12 15◦ data gated on α particles, which was used to track drifts in the beam energy and
magnetic fields.

83

Position (channels)0500100015002000250010210310410510counts/channelFigure 7.13 Position spectra from 36Ar(d,t)35Ar labeled with excitation energy in keV.

84

04080120160200020406080040801201600406080100position (channels)500100015002000250002040200240301050646063456332627362536164599164156076605564396037646063456332627362536164599164156076605564396037667266516617660665856557652364606415634563026273625366446672661766066557652364606439641563456273625366516585664463456332630262736253607660555991591361646037counts/5 channels20°25°15°15°54°15◦
Ex
(keV)

5994(2)
6039(2)
6057(2)
6078(2)
6167(2)
6254(3)
6273(3)

6334(3)
6348(3)
6417(3)
6444(3)
6461(3)

significance

(σ)

13
37
3.1
6.6
3.0
6.8
6.9

7.0
6.2
5.2
2.2
6.4

15◦
Ex
(keV)

5990(2)
6038(2)

6078(2)
6167(2)
6256(3)
6277(3)

6334(3)
6348(3)
6416(3)
6446(3)
6463(3)

54◦
Ex
(keV)
5913(5)
5994(3)
6041(3)
6065(7)
6082(3)
6168(4)
6260(5)
6281(4)
6308(3)
6335(3)
6349(4)

significance

(σ)
2.3
5.1
22
1.1
5.4
2.4
3.6
4.0
5.9
4.2
3.2

significance

(σ)

20◦
Ex
(keV)

significance

(σ)

25◦
Ex
(keV)

significance

(σ)

7.6
22

3.0
4.1
3.1
3.5

4.7
3.9
5.9
2.8
5.9

6256(3)
6276(3)

6345(3)
6413(6)
6437(3)
6456(3)
6525(3)
6559(3)
6586(2)
6608(3)
6618(2)
6647(2)
6654(3)
6674(3)

5.9
3.3

5.9
8.9
3.8
8.4
5.8
5.4
25
5.6
12
4.1
5.1
14

6256(3)
6275(3)
6304(3)

6347(3)
6417(3)

6461(3)
6526(3)
6559(3)
6588(2)
6608(3)
6619(2)
6645(2)
6652(3)
6672(3)

5.8
3.7
8.5

5.6
5.0

3.7
5.3
3.3
18
6.1
15
7.6
3.4
3.7

Table 7.1 35Ar excitation energies measured in each spectrum and the statistical significances of the corresponding peaks, expressed
as standard deviations (σ). Uncertainties quoted include systematic uncertainties and statistical uncertainties from individual fits. Two
separate measurements were taken at 15◦. The results from the higher statistics measurements are reported in the left-most column
and shown in the top panel of Figure 7.13.

85

Ex
NDS
[11]

5911(10)

36Ar(3He,α)35Ar

Ex

[45]1
5916(3)

6032(10)

6036(3)

6153(10)
6258(10)

6162(2)
6267(12)

6630(10)

6614(2)

Ex

36Ar(d,t)35Ar

present
5913(5)2
5991(3)
6037(3)
6055(3)3
6076(3)
6164(3)
6253(3)
6273(3)
6302(3)
6332(3)
6345(3)
6415(2)
6439(4)4
6460(3)
6523(3)
6557(3)
6585(3)
6606(3)
6617(2)
6644(3)
6651(3)
6672(3)

Er (C.M.)
34gCl(p,γ)
present
17(5)
95(3)
140(3)
158(3)
180(3)
268(3)
357(3)
376(3)
406(3)
436(3)
448(3)
518(2)
543(4)
563(3)
627(3)
661(3)
689(3)
710(3)
720(2)
748(3)
755(3)
775(3)

Er (C.M.)
34mCl(p,γ)

present

12(3)
33(3)
122(3)
210(3)
230(3)
259(3)
289(3)
302(3)
372(2)
396(4)
417(3)
480(3)
515(3)
543(3)
563(3)
574(2)
601(3)
608(3)
629(3)

Table 7.2 Previous and present 35Ar excitation energies and corresponding center of mass (C.M.)
resonance energies (keV) from the present work.

7.7 Level densities

35Ar and 35Cl are called a mirror pair. Their structure is expected to be similar because they differ
by only one nucleon, a proton for 35Ar and a neutron for 35Cl. Therefore, the level density of
35Cl should be able to provide some insight for what to expect in 35Ar. However, if one compares

1unpublished
2only observed at 54◦
3tentative
4tentative

86

the measured level density of 35Ar to the level density of the mirror nucleus, 35Cl, in this region
of excitation energy, there are roughyly 10 more levels in 35Ar. This can lead to one of two
conclusions. Either some of the features that have been attributed to 35Ar are from a contaminant,
or some of the 35Cl levels in this region have not yet been discovered. As a first check of potential

contaminants, we looked at the ratio of beam currents for the various isotopes in the argon bottle

used for the target implantation. These values agree well with the solar values, as shown in Table

7.3. Due to magnetic analysis of the ion beam, only mass 36 is delivered to the target.

mass number

beam current

current ratio

solar abundance

A
36
38
40

(nA)
19
4

6000

(%)
0.315
0.066
99.618

(%)
0.334
0.063
99.603

Table 7.3 Comparison of isotopic abundances in the argon bottle used for implanted targets and
solar isotopic ratios.

Based on the focusing settings of the Q3D spectrograph, any triton groups from a reaction
on anything with a different mass would be defocused (for an example, see the 28Si(d,t)27Si

calibration data). Along with these considerations, all levels have been observed in spectra from

at least two spectrograph angles. Due to the kinematics, one would not expect these features to all

move together if they were not from the same nucleus.

Our measured level density is also greater than one would expect from an sd shell model

calculation. However, at these excitation energies, one should also consider excitations of nucleons
into the p f shell. sd − p f shell model calculations including 0, 1, and 2 nucleon excitation from
the sd shell into the p f shell by Alex Brown were compared to data. These level densities agree

quite well, as shown in Figure 7.14. Further details can be found in [58] and references therein.

Based on these calculations and our experimental level density for 35Ar, it is clear that there
are still many undiscovered mirror levels in 35Cl. However, even with the larger 35Ar level density,

this level density is not quite sufficient to rely on Hauser-Feshbach model calculations to produce
the 34g,mCl(p,γ)35Ar reaction rates in this case [67, 68], so detailed properties of individual res-

87

Figure 7.14 Experimental level densities of 35Ar and the mirror nucleus 35Cl and calculated shell
model level densities. Experimental level densities for 35Ar with Ex < 5.9 MeV and 35Cl are taken
from [11].

onances discovered in this work need to be determined. Only resonance energies are insufficient

to constrain the reaction rate, but further information on these resonances could be used to guide

matching of these levels to shell model states to create a hybrid reaction rate.

88

Energy (MeV)01234567Levels/0.4 MeV24681012141618=0wh=1wh=2whExpt (Previous)Expt (Current)Cl Expt35 CHAPTER 8

SUMMARY AND OUTLOOK

This work has presented transfer reaction studies which are steps toward understanding nucleosyn-
thesis in ONe classical novae, in particular, the production of 30Si and 34S. Here I provide a brief

summary of this work and discuss future work to better understand the relevant reaction rates.

The experiment outlined in Chapters 3-5 endeavored to determine total widths of known 31S
resonances using the Doppler Shift Attenuation method, using the 32S(3He,α)31S reaction. The

first run of this experiment failed due to background that can be attributed to carbon on the target,

and beam hitting a copper collimator due to a mis-wired quadrupole magnet. Data from a second

run are still under analysis, but preliminary analysis shows an improvement in signal to noise in

the new run. We expect to be able to set constraints on lifetimes of two relevant resonances.

Before the experiment presented in Chapters 6 and 7, only six levels in the astrophysical region

of interest were known, most without a certain spin assignment, and all with energy uncertainties
of at least 10 keV. In our effort at MLL, using 36Ar(d,t)35Ar, we discovered 17 new levels, and

reduced uncertainties on new levels to typically 3 keV. Discovering most, if not all of the levels

in the region of interest aids planning and analysis of future experiments to constrain the spins,

parities, and partial widths of these resonances.

While these experiments are important steps toward understanding two reaction rates impor-
tant for classical nova nucleosnythesis, 30P(p,γ)31S and 34g,mCl(p,γ)35Ar, further experiments are
needed. Partial widths of 31S resonances need further experimental constraints. To complement
the lifetime measurements presented here, a 31Cl(β p)30P measurement is scheduled in November

2018 at the NSCL to measure proton branching ratios for selected resonances [69]. Another ex-
periment to better understand 34g,mCl(p,γ)35Ar was recently run at the Argonne Tandem Linear
Accelerator System measured γ-ray angular angular distributions for 35Ar resonances populated
via 32S(α,n)35Ar [70], which should lead to Jπ constraints.

89

Further steps are still necessary to understand both of these reaction rates. Discrepancies ex-
ist among different data sets for 31S resonance energies and spin assignments which need to be

resolved with the help of further measurements. Further constraints on the partial widths are also
needed, as some, but not all states were populated in this DSAM measurements. 35Ar experi-

mental data is much more incomplete, and several future experiments will be needed for a fully
experimental 34g,mCl(p,γ)35Ar reaction rate.

These two reaction rates warrant further study to reduce nuclear physics uncertainties in classi-

cal nova models used to understand nucleosynthesis in classical novae, particularly to understand

silicon and sulfur isotopic ratios in presolar grains formed in classical novae.

90

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