MEASURING THE 15O(α, γ)19Ne REACTION IN TYPE I X-RAY BURSTS USING
20Mg β-DECAY

By

Tyler Markham Wheeler

A DISSERTATION

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

Physics—Doctor of Philosophy
Computational Mathematics, Science and Engineering—Dual Major

2024

ABSTRACT

A neutron star can accrete hydrogen-rich material from a low-mass binary companion

star. This can lead to periodic thermonuclear runaways, which manifest as Type I X-ray

bursts detected by space-based telescopes. Sensitivity studies have shown that 15O(α, γ)19Ne

carries one of the most important reaction rate uncertainties affecting the modeling of the

resulting light curve. This reaction is expected to be dominated by a narrow resonance

corresponding to the 4.03 MeV excited state in 19Ne. This state has a well-known lifetime,

so only a finite value for the small alpha-particle branching ratio is needed to determine the

reaction rate. Previous measurements have shown that this state is populated in the decay of

20Mg. 20Mg(βpα)15O events through the key 15O(α, γ)19Ne resonance yield a characteristic

signature: the near simultaneous emission of a proton and alpha particle.

To identify these events of interest the GADGET II TPC was used at the Facility for Rare

Isotope Beams during Experiment 21072. An 36Ar primary beam was impinged on a 12C

target to create a fast beam of 20Mg whose decay fed the 19Ne state of interest. The details

of the development, and testing of the GADGET II system will be discussed along with the

preliminary results from this experiment, which include discussion of the data processing

and analysis methods being used on the newly acquired data.

Moreover, convolutional neural networks (CNNs) are explored for rare event identification

in the TPC data. To leverage the computational advantages of 2D CNNs and the availability

of pre-trained models, early data fusion techniques have been adopted to efficiently convert

the data into 2D formats. Addressing real training data scarcity and simulation discrep-

ancies, parameter variations are incorporated in simulations to enhance model robustness,

making the CNNs ultra-sensitive to subtle event indicators. The resulting ensembles de-

ployed on the experimental data are able to identify >98% of all two-particle-events in the

dataset. The techniques of this ongoing study are detailed, highlighting the promising future

applications of this methodology.

Copyright by
TYLER MARKHAM WHEELER
2024

This thesis is dedicated to my wife, Kari, and to my son, Maxwell.
Together, you are my strength, my bliss, my everything.

v

ACKNOWLEDGMENTS

The journey to completing this thesis has been a remarkable one, filled with challenges and

victories, all made possible by a constellation of incredible individuals whose support and

guidance have been instrumental.

First and foremost, I extend my deepest gratitude to Chris Wrede, my physics advisor

and mentor. Chris’s guidance and mentorship have been the cornerstone of my PhD studies.

His help in navigating the complexities of research and academia, and the wisdom he has

shared with me along the way has been invaluable. Additionally, the opportunity to be part

of his distinguished research group has been a privilege, offering me a wealth of knowledge

and an experience I will forever cherish.

Equally essential to my academic journey has been Sai Ravishankar, my CMSE advisor.

Sai’s expertise in Machine Learning broadened my academic horizons and introduced me to

new and exciting areas of analysis and research. His readiness to explore innovative ideas

and provide thoughtful insights has enriched my studies immeasurably.

I owe a huge thank you to two different post docs that were in our research group. First,

I want to thank Ruchi Mahajan, with whom I was fortunate to work closely with during my

PhD research. Our collaboration in setting up a new experimental detection system was not

just a professional milestone but one of the great joys of my scientific career. Additionally,

I want to thank Lijie Sun for all of his support over the years. Lijie’s dedication to science

and willingness to share his vast knowledge have significantly contributed to my growth as

a scientist.

It is a serious undertaking to run an experiment, and there are a number of collaborators

I would like to thank that were crucial to our success. First, I must extend a heartfelt thank

you to Moshe Friedman. Moshe played a pivotal role in guiding us through building and

vi

diagnosing our detector, and was always generous with his knowledge and time. Special

appreciation goes to Lolly Pollacco, whose exceptional skills in detector design and exper-

imental setup were indispensable to our project. Gratitude is also due to Yassid Ayyad,

whose critical work in event simulation within our detector was foundational. Yassid’s pa-

tience and assistance were deeply appreciated throughout our collaboration. I owe a sincere

thank you to Daniel Bazin as well. Daniel’s contributions before and during our experiment

were monumental. His effort, dedication, and positive spirit made the daunting tasks man-

ageable and the working environment a joyous one. Lastly, I am profoundly thankful for all

the members of our collaboration who played a significant role in our experiment’s success.

Their collective effort and support have been the backbone of our achievements.

Along with my advisors Chris and Sai, I would like to thank my other PhD committee

members; Ed Brown, Darren Grant, and Paul Gueye. They have been pillars of support

throughout this journey. Their insights and encouragement have been fundamental in guiding

my research and academic growth. Thank you all so much.

I also want to thank my family. In both a literal and metaphorical sense, I would not

be here without my parents. Thank you to my mother Vickie and my father Walt. Their

love and support have been a constant source of strength and motivation throughout this

journey. I am eternally grateful for everything they given me. Also, a special thank you

to my brother Justin. The best brother and friend I could ever ask for, and a beacon of

inspiration in my life. His influence was the catalyst for my return to school, a decision that

has profoundly shaped my life.

Finally, thank you to my wife, Kari, the most extraordinary person I’ve ever had the

privilege of having in my life. This journey would not have been possible without her.

Together, we’ve made sacrifices, sharing the weight of this endeavor in equal measure. For

vii

all the late nights and weekends buried in research, Kari was there to fill in the gaps of

our life with grace and unwavering support. In moments of stress and overwhelm, she was

my sanctuary, bringing peace and clarity to a tumultuous path. When doubts clouded my

vision, it was Kari who rekindled my belief in myself. Her love and sacrifice are woven into

the fabric of this work, making her contributions as integral as my own. Words fall short of

capturing the magnitude of my love and appreciation for her.

This acknowledgment, while attempting to encapsulate my gratitude, hardly does justice

to the profound impact each of you has had on my life and work. Thank you all, from the

bottom of my heart.

viii

TABLE OF CONTENTS

INTRODUCTION: OVERVIEW OF RELEVANT PHYSICS . . . . . . . . . . . . . .

1

MOTIVATION FOR MEASURING THE 15O(α, γ)19Ne REACTION . . . . . . . .

18

THE TIME PROJECTION CHAMBER FOR GADGET II

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

34

EXPERIMENT E21072 AT THE FACILITY FOR RARE ISOTOPE BEAMS . . . .

56

PRELIMINARY ANALYSIS OF EXPERIMENTAL DATA FROM E21072 . . . . . .

77

OVERVIEW OF RELEVANT MACHINE LEARNING ALGORITHMS . . . . . . . 104

RARE EVENT SEARCH WITH CONVOLUTIONAL NEURAL NETWORKS . . . 118

SUMMARY AND OUTLOOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

ix

INTRODUCTION: OVERVIEW OF

RELEVANT PHYSICS

1.1

Introduction to Nuclei

The atom, often called the fundamental building block of matter, has been the subject of

scientific curiosity and investigation since the 19th century. However, it was only in the early

20th century that significant breakthroughs in our understanding of its intricate structure

were achieved. Contrary to earlier models that envisioned the atom as a homogenous blend

of positive and negative charges (the so-called ”plum pudding” model [1]), groundbreaking

experiments in the early 1900s unveiled a more complex reality.

In a pivotal experiment, the physicist Ernest Rutherford directed a beam of alpha par-

ticles (helium nuclei) towards a thin sheet of gold. According to the plum pudding model,

the alpha particles should have passed through the gold foil with only slight, infrequent de-

flections. However, the experimental results were surprising and changed our understanding

of the atom. While most of the alpha particles did pass through the gold foil with minimal

deflection, a small number were deflected at very large angles, and some were even scattered

straight back towards the source [2]. This unexpected behavior suggested that the atom’s

positive charge, along with most of its mass, was concentrated in a central region, later

termed the ”nucleus.”

The experimental endeavors following Rutherford’s alpha particle scattering experiment

further enhanced our understanding of atomic structure, particularly with the discovery of

1

the neutron by James Chadwick in 1932 [3]. This discovery was instrumental in refining

the atomic model. It revealed that the nucleus consists of two types of nucleons: protons,

which are positively charged, and neutrons, which are electrically neutral. These nucleons

are bound together by the strong nuclear force, a powerful fundamental interaction that

overcomes the electrostatic repulsion between the positively charged protons.

A nucleus is distinctly defined by its elemental name and mass number, A, where the

mass number represents the sum of protons and neutrons within the nucleus. The elemental

name is determined by the proton count, Z, a feature that forms the basis of the periodic

table. For instance, a magnesium nucleus with 12 protons and 8 neutrons is denoted as

20Mg, where the elemental symbol, Mg, inherently provides the atomic number information.

The atomic landscape showcases a variety of nuclear configurations. Isotopes are one such

variation, characterized by nuclei of the same element (same number of protons) but differing

in their neutron numbers. These differences in the number of neutrons between isotopes do

not alter the chemical properties of the element but do affect the nuclear properties, such as

stability and decay modes (more on decay modes in Section 1.3).

In contrast, isotones are nuclei that share an identical neutron count but differ in their

number of protons, thus they are different elements. Isotones often exhibit different chemical

properties due to their varying atomic numbers but can share some nuclear characteristics

due to having the same number of neutrons. Additionally, the term isobar applies to nuclei

with the same mass number A but different numbers of protons and neutrons.

Isobars,

therefore, belong to different elements and have distinct nuclear properties.

Excited states are another fascinating aspect of nuclear variety. They exist because

nucleons in a nucleus can arrange in different energy configurations. This can mean a nucleon

moving to a higher energy orbital, or adding rotational or vibrational energy to the core of

2

paired nucleons [4] (see the discussion of the shell model in Section 1.2). Some of these

configurations/states can be relatively stable, leading to the existence of metastable states

called isomers that have longer half-lives. A classic example of this is Technetium-99m, a

metastable nuclear isomer used in medical imaging [5]. Many excited states, however, are

extremely unstable and decay rapidly via different decay modes.

The chart of nuclides provides a comprehensive map of all known nuclei, encompassing

both stable and unstable varieties. This chart plots Z vs N, and is an invaluable tool for

understanding the relationships and properties of different nuclear species, including isotopes,

isotones, isomers, and isobars. It serves as a visual representation of the intricate and diverse

world of nuclear physics and can be seen in Figure 1.1.

The nucleus’s unveiling brought forth a myriad of questions, particularly about the origins

of elements. This curiosity birthed the domain of nuclear astrophysics in the mid-20th

century. Pioneering work in this field aimed to discover the origins of the elements. As the

discipline evolved, it grappled with profound questions about stellar energy generation, life

cycles of stars, nucleosynthesis sites, and the stellar events responsible for creating various

isotopes (more on the field of nuclear astrophysics can be found in Section 1.4).

To navigate these cosmic riddles, a deep comprehension of nuclear structure (properties

of stable and unstable nuclei) and nuclear reactions (interactions between nuclei) is crucial.

1.2 Nuclear Shell Model

The nuclear shell model has been critical in improving our understanding of nuclear structure

and behavior, offering profound insights into the internal arrangements and energy states of

a given nucleus. The model draws inspiration from the atomic shell model, where electrons

3

Figure 1.1: The chart of nuclides. On this chart, the y-axis signifies the number of protons
(Z) in the nucleus, while the x-axis indicates the number of neutrons (N). Black boxes on the
chart identify stable nuclei, and boxes in various colors represent various types of unstable
nuclei [6].

4

are organized into discrete (quantized) energy levels called shells. Electrons fill these shells in

order of increasing energy, with the lowest energy levels (closest to the nucleus) being filled

first. As these shells are filled, electrons occupy higher and higher energy shells consistent

with the Pauli exclusion principle. With this approach, we obtain a structure consisting of a

stable core formed by completely filled shells, accompanied by a number of valence electrons.

The model then posits that the fundamental properties of atoms are primarily influenced by

these valence electrons, and this theory has been remarkably successful. Interestingly, proton

and neutron separation energies exhibit patterns and discontinuities at specific nucleon num-

bers, analogous to the changes in atomic properties observed with electron configurations

[4]. This suggested that a similar model could be applied to nuclear structure.

In the nuclear shell model protons and neutrons fill shells independently. Each shell

contains subshells called orbitals, that are determined by the quantum states the nucleons

can occupy. The states are characterized by quantum numbers that include the orbital

angular momentum l, the total angular momentum j, and the principal quantum number n,

which refers to the number of nodes in the corresponding wave function and can be effectively

represented using a harmonic oscillator potential (see Figure 1.2). Note that no 2 protons

or neutrons in a given nucleus can have the exact same quantum numbers, as nucleons are

fermions, which means that they are spin s = 1/2 particles that obey the Pauli Exclusion

Principle. This characteristic inherently limits the capacity of each shell.

Each shell contains specific types of orbitals denoted as s, p, d, f..., where each letter

corresponds to a specific value for the orbital angular momentum (l = 0, 1, 2, 3...). The

degeneracy for each orbital (the number of protons or neutrons in each subshell) is given

by 2l + 1. To get this shell structure to agree with observed data, a critical modification

is needed; spin-orbit coupling. This concept is essential for the correct ordering of nuclear

5

Figure 1.2: Figure illustrates the first five wave functions of a quantum harmonic oscillator.
Vertical lines mark the classical turning points, representing the extremities of motion for a
classical particle with equivalent energy. This depiction shows how, with increasing principal
quantum number, the wave functions transition between even and odd symmetries [7].

6

subshells and the emergence of the magic numbers (2, 8, 20, 28, 50, 82, 126), which represent

the observed number of nucleons needed to fill each successive major shell. From spin-orbit

coupling we derive the expression for the total angular momentum, j = l±1/2, where a larger

j value represents a lower energy state. Then the spacing between levels depends on the

spin-orbit potential. An example of the single-particle energy level scheme for the harmonic

oscillator potential can be seen in Figure 1.3. Note that in this context, the number in front

of the denoted orbital does not represent the principal quantum number but rather serves

as a counter for the number of levels corresponding to a specific l value. This means that

the ’1d’ level refers to the initial (lowest) d state, ’2d’ identifies the subsequent d-state, etc.

Based on the above let’s work through an example using 20Mg. The isotope of 20Mg

contains 12 protons and 8 neutrons. We can see from Figure 1.3 that the 8 neutrons will

completely fill the p-shell. The protons will also fill the p-shell, so the first 8 protons and

neutrons combine to form something like an inert 16O core. Then the remaining protons will

go into the d5/2-shell. From this we can determine the spin and parity, J π, of this nucleus in

the ground state (lowest possible energy configuration). In this case J is the total coupled

angular momentum of the system, and π is the parity, which refers to the symmetry of the

nuclear structure under coordinate inversion, and is given as (-1)l. Of the four protons in

the d5/2-shell, two will be spin-up and two will be spin-down, which leaves us with a total

angular momentum of J = 0. Then the d-shell corresponds to l=2, which gives us positive

parity. Thus, the ground state of 20Mg can be described as J π = 0+.

There are of course other models (liquid drop model, collective model, etc.); however,

the nuclear shell model, with its basis in empirical evidence and its successful predictions,

remains an essential tool in nuclear physics. While simplified, it provides deep insights into

the complex world of nuclear structure and interactions, underscoring the intricacies of the

7

Figure 1.3: Single-particle energy level scheme derived from the harmonic oscillator potential.
The spin-orbit component in the nuclear potential results in the division of these energy
levels, which approximates shell closures and leads to the emergence of the magic numbers
(the boxed integers). Figure Credit: Bakken (GPL).

8

forces at play within the atomic nucleus.

1.3 Nuclear Decay

The chart of nuclides, Figure 1.1, reveals that a majority of nuclei are inherently unstable.

Such nuclei invariably undergo a transformation, or decay, transitioning towards a more

stable state. The degree of instability of a nucleus can often be gauged by its distance from

the line of stability on the chart of nuclides (black boxes in Figure 1.1): the farther it is, the

greater its instability.

Interestingly, the exact moment an unstable nucleus will decay is unknowable, and this

unpredictability is deeply rooted in the principles of quantum mechanics. In quantum me-

chanics, the behavior of particles, including atomic nuclei, is inherently probabilistic. How-

ever, this probabilistic nature means that when we observe a substantial sample of identical

nuclei, their decay behavior adheres to the exponential law of radioactive decay. This can

be mathematically represented as

N (t) = N0e−λt,

(1.1)

where N (t) denotes the number of undecayed nuclei at time t, N0 is the initial number of

nuclei, and λ is the decay constant. Note also that the term τ = λ−1 signifies the mean

lifetime of the nucleus, representing the average time for a nucleus to decay [4]. Thus, the

decay constant (λ) is notably larger for nuclei that are very unstable, when juxtaposed with

nuclei near stability.

Nuclei can undergo decay through various mechanisms. Lighter nuclei predominantly de-

9

cay via mechanisms such as β-decay, γ-decay, and particle emission (like proton, neutron, or

α-particle emission). In contrast, heavier nuclei, while also susceptible to the aforementioned

decay modes, have the added possibility of undergoing spontaneous fission. In this process,

a nucleus splits into two fragments of nearly equal size. Spontaneous fission is a significant

decay mode for superheavy elements (A > 232) and sets a practical limit on the number of

nucleons in heavy elements.

A nucleus may undergo decay through multiple pathways, each known as a decay branch.

These branches represent the nucleus’s potential transitions to different states. The total

lifetime of the parent nucleus τtotal

τtotal =

1
(cid:80)
i λi

,

(1.2)

is a composite measure that intertwines the decay rates of all possible branches. λi represents

the decay constant for each branch and indicates the rate of decay along that specific pathway.

While the total lifetime offers a collective perspective, understanding the individual decay

constants, λi, is crucial. These constants illuminate the branching ratios—the probabilities

of the nucleus decaying via each particular branch. Knowledge of these ratios is fundamental

for accurately predicting nuclear behavior and understanding the stochastic nature of nuclear

decay.

1.3.1 α-Decay

Alpha decay, a process governed by the interaction of the strong nuclear force and the

Coulomb force, serves as a pathway for nuclei to achieve greater stability. It involves the

emission of an alpha particle (helium nucleus), which is comprised of two protons and two

10

neutrons. The alpha particle can be seen as a beacon of stability, having a significantly

higher binding energy than neighboring isotopes, meaning it has a small mass relative to its

separate constituents. Thus, this tightly bound quartet of nucleons is a favored particle to

emit, and once it escapes from a parent nucleus the resulting daughter nucleus will be in a

more stable configuration [4].

For a nucleus represented as A

Z X, alpha decay transforms it into a lighter nucleus A−4
Z−2Y

plus the emitted alpha particle. The process can be expressed as

Z X →A−4
A

Z−2 Y + α.

(1.3)

The energy dynamics of this transformation are encapsulated in the Q-value for alpha decay,

Qα. This value represents the net energy released during the decay process and is the

difference in mass-energy between the initial state (parent nucleus A

Z X) and the final states

(daughter nucleus A−4

Z−2Y and the alpha particle). The Q-value is given by

(cid:104)

Qα =

m(A

Z X) − m(A−4

Z−2Y ) − mα

(cid:105)

c2.

(1.4)

In alpha decay, the Q-value describes the transformation of mass into kinetic energy,

shared between the daughter nucleus and the alpha particle. This energy release is the

driving force of alpha decay.

It propels the alpha particle on its journey away from the

parent nucleus and signifies the shift towards stability.

11

1.3.2 β-Decay

Beta decay is mediated by the weak force and is the process whereby a proton is converted

into neutron or vice versa. This conversion conserves mass number (A = Z +N ), but changes

both the proton number (Z) and the neutron number (N ) by one unit such that Z → Z ± 1,

N → N ∓ 1. Thus, this process is a convenient path for steering nuclei towards stability [4].

Beta-minus decay (β−-decay) occurs in neutron-rich nuclei below the stability line. This

process transforms a neutron into a proton. In the course of the transformation, it emits an

electron (e−) and an electron antineutrino (¯νe),

A
Z X →A

Z+1 Y + e− + ¯νe.

(1.5)

The energy released, denoted by the Qβ−, is the mass-energy difference between the parent

and daughter nuclei, converted into kinetic energy:

Qβ− = [m(A

Z X) − m(A

Z+1Y )]c2.

(1.6)

Beta-plus, or positron decay (β+-decay), is observed in proton-rich nuclei and involves the

conversion of a proton into a neutron, while emitting a positron (e+) and an electron neutrino

(νe). The process is viable only if the transition energy exceeds the combined mass of two

electrons (1.022 MeV). This threshold accounts for the energy required to create the emitted

positron. An expression for this transformation and the corresponding Q-value can be given

as

Z X →A
A

Z−1 Y + e+ + νe

Qβ+ = [m(A

Z X) − m(A

Z−1Y ) − 2me]c2.

12

(1.7)

(1.8)

Electron capture, another decay mode for proton-rich nuclei mediated by the weak inter-

action, involves the nucleus capturing an inner orbital electron to convert a proton into a

neutron:

Z X + e− →A
A

Z−1 Y + νe.

The associated Q-value, QEC , considers the binding energy of the captured electron:

QEC = [m(A

Z X) − m(A

Z−1Y )]c2 − BE(e−).

(1.9)

(1.10)

These processes illustrate the complexity of beta decay, involving continuous energy spectra

for emitted electrons, the introduction of neutrinos, and the nuanced interplay of nuclear

forces, reflecting the intricate nature of atomic transformations.

1.3.3 γ Decay

Following α or β decay it is typical for a nucleus to be left in an excited state, and then

rapidly decay to the ground state via the emission of one or more γ-rays [4]. Gamma-rays

are high-energy (0.1 to 10 MeV) photons that when emitted don’t alter the atomic number

or mass number of the nucleus. The energy of the emitted gamma ray is equal to the energy

difference between the initial and final nuclear states less the kinetic energy of the recoiling

nucleus

∆E = Ei − Ef = Eγ + KErec,

(1.11)

where ∆E is the energy released in the transition, Ei is the energy of the initial state, Ef is

the energy of the final state, Eγ is the energy of the emitted γ-ray, and KErec is the kinetic

energy of the recoiling nucleus, which can be expressed in terms of its momentum using the

13

classical kinetic energy formula for non-relativistic speeds,

KErec =

p2
rec
2Mf

,

(1.12)

where Mf is the mass of the recoiling nucleus and prec its momentum. Additionally, con-

servation of momentum dictates that the momentum of the recoiling nucleus is opposite in

direction to that of the emitted gamma-ray (⃗pγ where pγ = Eγ/c),

⃗pγ = −⃗prec.

(1.13)

Using the above, we find

KErec =

1
2Mf

(cid:18) Eγ
c

(cid:19)2

=

E2
γ
2Mf c2 .

Then the total energy balance of the process is represented by

∆E = Eγ +

E2
γ
2Mf c2 .

(1.14)

(1.15)

The energy of an emitted gamma-ray allows us to deduce the energy of the corresponding

excited state from which it was emitted (assuming we know the final state excitation energy),

and our knowledge of nuclear spectroscopy is tantamount to our knowledge of excited states.

Thus, the study of gamma-ray emission emerges as a gold standard technique in nuclear

spectroscopy [4]. This method, celebrated for its ability to measure gamma-ray energies

with remarkable precision, works to reveal the complex energy levels of excited nuclear states,

thereby enhancing our understanding of nuclear structure and dynamics. Additionally, the

14

study of gamma emission and internal conversion together provides a robust framework for

deducing intrinsic nuclear properties, such as spins and parities of excited states, and offer

a holistic view of nuclear behavior.

1.3.4 Nucleon Emission

Nucleon emission (the emission of a proton or neutron) hinges on the Q-value for the decay

being positive. This process is encapsulated by the neutron separation energy (Sn) and

proton separation energy (Sp), defined as the differences in binding energy when a neutron

or proton, respectively, is removed from a nucleus:

Sn = −Qn = BE(N ; Z) − BE(N − 1; Z)

Sp = −Qp = BE(N ; Z) − BE(N ; Z − 1)

(1.16)

(1.17)

These energies delineate the threshold beyond which nuclei become unstable against nucleon

loss, delineating the so-called nuclear drip-line [4]. Here, nuclei are replete with excess

protons or neutrons, and any attempt to add another nucleon fails, as it ’drips off’ unbound,

signifying the transition from positive to negative separation energies.

Similar to gamma-decay (Section 1.3.3), nucleon emission can occur following beta-decay

(Section 1.3.2), and will be in competition with gamma-decay. This happens if the resulting

nucleus is in a sufficiently excited state (Eexc) such that Eexc > SN (where N = n or p).

This phenomenon is termed beta-delayed nucleon emission, and a schematic of the process

can be seen in Figure 1.4. Additionally, if Eexc is greater than the alpha separation energy,

15

Figure 1.4: Schematic of beta-delayed nucleon emission: The beta decay of the precursor
leads to the population of highly excited states within the emitter. These states are prone
to nucleon emission due to their instability. It is important to recognize that the energy
level of the emitter’s excited state is the sum of the energy of the nucleon emitted, and the
nucleon separation energy between states X’ and X”, and a minor adjustment accounting
for the recoil of the emitting nucleus [4].

Sα, where

Sα = −Qα = BE(N, Z) − BE(N − 2, Z − 2),

then alpha emission can occur as well.

1.4

Introduction to Nuclear Astrophysics

The field of nuclear astrophysics marries the intricate principles of nuclear physics with the

grand tapestry of cosmic phenomena. There are a host of fundamental questions at the

heart of astrophysics, and cosmology that can only be answered if we posses a detailed

understanding of nuclear structure and nuclear reactions, and such is the work of nuclear

astrophysicists.

The field came into prominence in the mid to late 1960s, a pivotal era when the Big Bang

16

theory crystallized as the prevailing narrative of cosmic genesis. However, the Big Bang was

found to produce primarily the lightest elements—hydrogen, helium, and traces of lithium

[8]. This revelation gave rise to a cosmic conundrum:

if the Big Bang birthed only the

lightest elements, how did the rest of the elements form? It was against this backdrop that

the concept of nucleosynthesis, championed by astrophysicist Fred Hoyle, came into favor,

proposing that the synthesis of heavier elements occurs within stars.

Discoveries such as the existence of technetium in red giant stars worked to solidify the

concept of nucleosynthesis. Technetium is a transient element without stable isotopes and a

life-time that is far shorter than the age of the universe [9]. Thus, stars are not just nuclear

furnaces but also cosmic crucibles where the elements of the universe are forged. Over eons

stars transmute the primordial Big Bang elements into a rich array of heavier elements. The

mechanisms of alpha, beta, and gamma decays, detailed in the previous sections, are not

confined to Earthly laboratories but are active participants in the alchemy of stars.

In the realm of nuclear astrophysics, the role of observational astronomy is pivotal in

painting a detailed picture of cosmic processes. This pursuit is complemented by nuclear

experiments probing the properties of atomic nuclei. This interdisciplinary field, thus, seeks

to unravel the origins of the elements, the nature of matter in extreme astrophysical envi-

ronments, the properties of neutron stars, and much more. In the context of this thesis, we

will be exploring the nuclear physics underlying X-ray bursts from neutron stars (see Section

2). And in so doing we will discover how measuring critical nuclear reactions within these

bursts can shed light on the properties of neutron stars including their mass, radius, and

crust elemental composition.

17

MOTIVATION FOR MEASURING

THE 15O(α, γ)19Ne REACTION

2.1 X-ray Bursts from Neutron Stars

Binary star systems, where two stars are gravitationally bound, are common throughout

the cosmos. When a close binary system includes a neutron star and a low-mass stellar

companion, this can lead to phenomena such as Type I X-ray bursts. These bursts are a

result of thermonuclear explosions on the surface of neutron stars and are a topic of active

investigation in the nuclear astrophysics community.

Consider a binary system where a neutron star, typically with a mass of ≳ 1.4M⊙ and

a radius between 10 to 15 km, orbits in tandem with a companion star of mass ≲ 1.5M⊙.

The neutron star, with its extreme density on the order of 1014g/cm3, acts as a gravitational

sink, pulling material from its partner star [8].

The structure of such a system is defined by Roche lobes, which are regions around

each star where their respective gravitational pulls are dominant (see Figure 2.1). Material

transfer occurs when the companion star fills its Roche lobe and matter spills over through

the inner Lagrangian point onto the neutron star. This leads to a series of nuclear reactions

on the neutron star’s surface [10].

As the accreted hydrogen undergoes fusion, it forms helium, which eventually ignites in

a helium flash via the triple-α process, as detailed in Section 2.2.1. This ignition is the

spark that triggers the X-ray burst, a brilliant and rapid increase in X-ray luminosity, which

18

can be observed from Earth through the use of space-based telescopes [11]. The nature of

these emissions can vary depending on the mass of the companion star and the magnetic

field strength of the neutron star, with some systems exhibiting X-ray pulsations due to the

misalignment of the magnetic and rotational axes [8].

For systems that accrete rapidly enough, there is still H present at the time of He ignition.

Following the initial flash, the burning of H continues through the hot Carbon-Nitrogen-

Oxygen (CNO) cycles (detailed in the next section) and the rp-process, which can cause

temperatures to reach upwards of 109 K. Despite this intense nuclear activity, the strong

gravitational field of the neutron star prevents the newly synthesized elements from escaping.

Thus, the bursts exert a negligible influence on the galactic chemical composition. There is

evidence, however, that a small fraction of the envelope can escape via radiation-driven winds

[12]. Regardless, the bursts themselves are invaluable for probing the physical characteristics

of neutron stars, such as their masses, radii, and surface compositions [8].

2.1.1 Hot-CNO cycles and Breakout

The CNO cycle is a cornerstone of stellar nucleosynthesis, particularly in stars with masses

exceeding 1.3M⊙, where it serves as the primary mechanism for energy generation through

the fusion of hydrogen into helium. This process is facilitated by a sequence of proton

captures and β-decays involving CNO isotopes, with the cycle’s rate constrained by the

slower proton capture reactions compared to β-decays [8].

During a Type I X-ray burst, the scenario changes drastically as the thermonuclear

temperatures rise, and accelerate the reaction rates of the CNO cycle. This results in the

Hot CNO (HCNO) cycle, where the proton captures start occurring much more rapidly than

the β-decays, which are temperature independent (Figure 2.2 illustrates these cycles). The

19

Figure 2.1: Illustration of a binary star system comprising a neutron star and a hydrogen-
rich companion, each enclosed by their respective Roche lobes. The inner Lagrangian point,
where gravitational forces and rotational effects equilibrate, facilitates mass transfer from
the companion star to the neutron star. Adapted from [13].

HCNO cycles are particularly dominant in energy generation at temperatures ranging from

0.1 to 0.4 GK in environments rich in CNO nuclei. The rate at which energy is generated

in these cycles is influenced by the concentration of the catalysts, namely the CNOF nuclei,

and is independent of temperature. [8].

The HCNO cycles, such as HCNO1, involve isotopes like 14O and 15O, which have β-decay

half-lives of 70.62 seconds and 122.24 seconds, respectively. These half-lives are significantly

longer than the near-instantaneous proton captures and (p, α) reactions occurring in these

cycles. Consequently, the extended β-decay lifetimes of these isotopes present a barrier to

the synthesis of heavier elements within the duration of a typical Type I X-ray burst.

However, at temperatures exceeding 0.5 GK, novel pathways for element synthesis be-

come accessible, facilitating the creation of elements with atomic mass numbers exceeding

20. Among these, the breakout reaction 15O(α, γ)19Ne(p, γ)20Na plays a pivotal role. The

20

sequence’s initial step, 15O(α, γ)19Ne, stands out as a critical reaction rate for the accurate

modeling of X-ray burst light curves. Its significance stems from its role in initiating the

HCNO cycle breakout at elevated temperatures. Thus, it serves as a critical bottleneck for

the breakout process. The exploration of this reaction is essential for understanding the

intricate processes of nucleosynthesis, and energy generation mechanisms during these Type

I X-ray bursts [14].

2.2 Mathematical Framework of Reaction Rates

Nuclear reactions in stars, particularly those of lower temperatures like our Sun, predom-

inantly involve nuclei in their lowest-energy, stable configurations, known as ground states

(X). The probability of such reactions depends on three fundamental parameters: the abun-

dance of the reacting nuclei; their relative velocity; and the cross-section, σ. The cross-section

quantifies the reaction probability between two nuclei and can be extracted from empirical

data through the observed reaction rate, R, which follows the relationship

R = σIaN,

(2.1)

where Ia denotes the flux of incoming particles and N represents the area density of target

nuclei.

In high-temperature, explosive stellar environments like supernovae or X-ray bursts, nu-

clear reactions are not limited to ground states. Nuclei are often excited to higher energy

levels (X∗), which opens up additional reaction pathways. Excitation can occur through

two primary mechanisms: gamma-ray absorption (X + γ → X∗), where a nucleus absorbs

21

Figure 2.2: Illustration of the three Hot CNO cycles operative during Type I X-ray bursts.
Each cycle effectively fuses four protons into one He nucleus. Stable isotopes are denoted by
gray boxes, while the arrows indicate the flow of reactions and β-decays within the cycles.
Adapted from [8].

22

a high-energy photon, and inelastic scattering (X(a, a′)X∗), a process in which a nucleus

collides with another particle, resulting in energy redistribution.

The role of these excitation mechanisms in stellar nucleosynthesis is profound. They

enable reactions that are otherwise forbidden in ground state nuclei, and therefore alter

the dynamics of nuclear synthesis. In environments typified by rapid, intense thermonuclear

reactions like Type I X-ray bursts, including these additional channels is essential for accurate

astrophysical modeling.

Expanding on the mathematical depiction of reaction rates, we consider

R12 = N1N2⟨vσ⟩,

(2.2)

where N1 and N2 are the number densities of the interacting nuclei, and v is their relative

velocity. The term σ(v) represents the energy-dependent reaction cross-section, with ⟨vσ⟩

indicating an average, given the continuous velocity distribution in stellar contexts.

The reaction cross-section, σ(v), is a function that is characterized by several components:

a geometric term related to the projectile’s de Broglie wavelength (πλ2

p, where λp =

(cid:113) h

2mE ),

the quantum mechanical interaction matrix element (M = ⟨f |H|i⟩, where i and f delineate

the wave functions of the initial and final states), and the penetrability factor (Pl(E), where

E is the energy of the projectile), which assesses the likelihood to penetrate the potential

barrier of the target nucleus, with significant reductions due to the Coulomb and angular

momentum barriers. Incorporating these insights, the cross-section can be formulated as

σ ∝ πλ2

p · |⟨f |H|i⟩|2 · Pl(E).

(2.3)

23

At temperatures relevant to astrophysical phenomena, Pl(E) is dominated by the l = 0

(s-wave) term, and can be expressed as an exponential function dependent only on the

Sommerfeld parameter η, which is a dimensionless quantity encapsulating the essence of the

Coulomb interaction between the colliding nuclei. This is expressed as

Pl(E) ∝ e−2πη, where

η =

Z1Z2e2
ℏ

(cid:114) µ
2E

.

(2.4)

Here, Z1 and Z2 represent the atomic numbers of the target and projectile nuclei, respec-

tively. The symbol e stands for the elementary charge, ℏ is the reduced Planck’s constant,

and µ is the reduced mass of the system.

The astrophysical environments of interest are characterized by non-relativistic veloci-

ties and thermal equilibrium, and as such can be described using the Maxwell-Boltzmann

distribution for velocities,

f (v) = 4π

(cid:17) 3

2 v2e−

µv2
2kT ,

(cid:16) µ

2πkT

(2.5)

where k is the Boltzmann constant, and T is the temperature of the environment. Substi-

tuting this distribution into our reaction rate equation yields

R12 = 4πN1N2

(cid:16) µ

2πkT

(cid:17) 3
2

(cid:90) ∞

v3σ(v)e−

µv2
2kT dv.

0

(2.6)

Transitioning to the center-of-mass energy framework, we can express the average rate per

particle pair as

⟨σv⟩12 =

R12
N1N2

(cid:114) 8
πµ

1

(cid:90) ∞

3
2

(kT )

0

Eσ(E)e− E

kT dE.

(2.7)

The derivation of the reaction rate given above, reveals the distinct contributions of the

24

cross section, σ(E), and the kinetic energy of the particles, E, to the nuclear reaction rate.

In thermonuclear environments, the cross-section for rapid proton capture displays a unique

energy dependency, σ(E) ∝ e

√

E. This highlights the cross-section’s sensitivity to particle

energy, especially at low energies where the Coulomb barrier plays a significant role.

The high energy tail of the Maxwell-Boltzmann distribution suggests that higher energies

are exponentially less probable. The convolution of this distribution with the penetrability

factor is graphically presented in Figure 2.3, delineating the probability of nuclear reactions

as a function of energy. This convolution culminates in the Gamow window—a pronounced

peak in the probability distribution signifying the optimal conditions for charged-particle

reactions and hence, thermonuclear burning. The Gamow window marks the energy range

where a substantial fraction of nuclei have enough energy to overcome the Coulomb barrier,

thereby enabling fusion reactions [15, 14].

For experimental physicists, the Gamow window provides a targeted energy range for

designing nuclear reaction experiments. It’s not the sole factor to consider, however. Reso-

nance reactions, which occur when the kinetic energy of the nuclei aligns with a resonance

state, can also amplify reaction rates substantially, echoing the kinetic energy considerations

seen in the Gamow window. These resonances are pivotal in nuclear astrophysics, as they

can lead to significant enhancements in reaction rates.

2.2.1 Dynamics of Direct and Resonant Nuclear Capture

Direct and resonant nuclear capture are crucial for stellar nucleosynthesis, significantly con-

tributing to the formation of new elements and energy generation in stars. These processes

influence the life cycle and evolution of stars, and play a pivotal role in phenomena like X-ray

bursts.

25

Figure 2.3: The Gamow window, illustrated in red, arises from the convolution of the
Maxwell-Boltzmann distribution (in black) with the penetrability factor Pl(E) (in blue).
For visual clarity, the peak of the Gamow window has been enhanced by a factor of 100.
Adapted from [15].

26

In direct nuclear capture, a charged particle is rapidly absorbed by a nucleus, forming a

new element or isotope. This process adheres to the principle of mass-energy equivalence,

resulting in the release of energy (∆E) in the form of gamma radiation. The energy release

is described by the equation ∆E = (mass of reactants − mass of product nucleus) × c2. A

critical aspect of direct capture is the separation energy, which is the minimum energy

required to remove a particle from a nucleus. The value of this separation energy varies

depending on the type of particle and the specific nucleus involved, influencing the probability

of forming a bound state in different nuclear capture scenarios.

Resonant nuclear capture, in contrast, occurs when the center of mass energy of the

reactants is near one of the excited energy states of the resulting compound nucleus. This

phenomenon is characterized by distinctive peaks in the reaction cross-section at resonant

energies. A well known example of resonant capture is the triple-alpha process, which is

essential for carbon production in stars [16]. In this process, two alpha particles combine

to form unstable 8Be, which can capture another alpha particle to form 12C. This resonant

capture to the Hoyle state, an excited state in 12C at 7.7 MeV, results in the formation of

carbon, bypassing the gap in stability for nuclei with 5 or 8 nucleons. The decay probabilities

of this excited state are related to the partial widths Γγ and Γα, where the total width is Γ

= Γγ + Γα, and the probabilities of gamma decay or alpha particle re-emission are given by

the branching ratios Γγ/Γ and Γα/Γ, respectively.

The resonant capture cross-section σ(E) is described by the Breit-Wigner formula,

σ(E) =

λ2
4π

ωΓ1Γ2

(E − Er)2 + (Γ/2)2 , ω =

2Jr + 1
(2Ja + 1)(2Jb + 1)

,

(2.8)

where λ represents the DeBroglie wavelength of the incoming projectile, Γ1 and Γ2 denote

27

the partial widths corresponding to the two decay modes, E and Er signify the center of

mass energy and the resonance energy, respectively, and Ja, Jb, and Jr are the spin quantum

numbers of the reacting and resultant nuclei.

In the context of the 15O(α, γ)19Ne reaction, the key resonance of interest is narrow and

isolated (Γ ≪ Er). This means that the reaction rate is highly sensitive to the energy of the

incoming alpha particle and happens most effectively when the energy of the alpha closely

matches the resonance energy of the 19N e nucleus. In this case, the resonance reaction rate

simplifies to:

where γ is

⟨σv⟩ =

(cid:19)3/2

(cid:18) 2π
kT µ

ℏ2e−Er/kT ωγ,

γ =

Γ1Γ2
Γ

.

(2.9)

(2.10)

When the resonance energy (Er) and the temperature (T ) are known, all factors in this

equation 2.9 become constants except for the resonance strength ωγ. This simplification

allows experimentalists to measure the branching ratios of specific decay channels from an

astrophysical resonance, in addition to the spins and lifetimes of the relevant states, to

construct the reaction rate. This approach is invaluable, especially when direct measurement

of the cross section of a resonant reaction is challenging or impossible, which is often the

case when one of the reactants is unstable.

2.3 The 15O(α, γ)19Ne Reaction

The shape of the light curve in Type I X-ray bursts from neutron stars can potentially unveil

critical attributes of neutron stars, such as their mass, radius, and crust elemental abundance.

28

To extract this information, it’s imperative to simulate these light curves and juxtapose

them with empirical data. However, the accuracy of these simulations is compromised by

uncertainties in nuclear reaction rates, which can markedly alter the simulated light curve

profiles.

Sensitivity studies underscore the pivotal role of the 15O(α, γ)19Ne reaction, especially

at breakout temperatures of ≈0.5 GK (see Figure 2.4). This reaction emerges as one of

the most important reaction rate uncertainties that needs to be determined to refine the

modeling of X-ray burst light curves. Furthermore, the significance of the 15O(α, γ)19Ne

reaction extends to burst ashes, as it is ranked among the top reactions affecting the ashes

in multi-zone models [14, 17].

Some contemporary models suggest other reactions might hold equal or greater impor-

tance [14], and at least one study found the reaction to have no impact at all [18], however, the

prominence of the 15O reaction remains widely agreed upon. The neutron star’s continuous

fusion of hydrogen into helium culminates in a helium ignition, instigating a thermonuclear

runaway. This explosive burning phase, often termed the helium flash, amplifies hydro-

gen burning, elevating temperatures and accelerating the hydrogen burning rate, thereby

propelling the system into the hot-CNO cycle.

As this beta-limited cycle iterates, temperatures escalate, eventually reaching the thresh-

old ( 0.5 GK) that permits the onset of breakout reactions. At these elevated temperatures,

15O captures an α particle, yielding 19Ne, paving the way for nucleosynthesis that can extend

up to mass number 100 via the rp process [11, 19].

A direct measurement of the 15O(α, γ)19Ne reaction is not currently possible due to the

absence of high-intensity, low energy radioactive 15O beams. Fortunately, the reaction rate

is anticipated to be dominated by a single resonance corresponding to the 4.03 MeV state

29

in 19Ne. With the spin [20] and lifetime [21, 22, 23] of this state already established, the

focus narrows down to determining the α particle branching ratio (Γα/Γ), which represents

the fraction of decays via α particle emission from this state. Acquiring this branching ratio

will unveil the resonance strength, and consequently, the thermonuclear reaction rate.

Figure 2.4: Left: Table ranking the sensitivity of light curve models to each of the relevant
nuclear reaction rates. Right: Simulated plot of light curve intensity as a function of time
using both the upper and lower limit for the 15O(α, γ)19Ne reaction rate [14].

2.3.1 Previous Studies of 15O(α, γ)19Ne

Over the past few decades, accurately measuring the 15O(α, γ)19Ne reaction has become

a focal point in nuclear astrophysics research. Various transfer reaction techniques have

been employed to populate the 4.03 MeV state in 19Ne, aiming to determine the elusive α

branching ratio.

The pioneering transfer reaction p(21Ne, 3H)19Ne∗ utilized inverse kinematics to produce

tritons and 19Ne* [24]. This generated a distinct energy signature when measuring the

30

alpha branch that came from the combination of tritons and the low-energy alphas. Despite

minimal background interference, this experiment could only establish an upper limit for

Γα/Γ at less than 4.3 × 10−4. Following experiments, such as those by Rehm et al. using

3He(20Ne, α)19Ne∗ [25], and Tan et al. with 19F(3He, t)19Ne∗ [26], faced similar challenges.

The latter reported an α branching ratio at 1.8 σ significance, but the results are contentious

due to uncertainties in background modeling, and the lack of statistical significance [18].

Other studies have focused on Ne∗ states above the α separation energy, Sα [27, 28, 29],

but these too struggled to detect the α branch from the 4.03 MeV state. The inherent

challenges of transfer reactions, including the production of a multitude of byproducts and

consequential statistical noise, have consistently impeded the detection of α particles amidst

the background. Complications are further exacerbated by the resonance’s closeness to the α

separation energy and the kinetic energy loss of the α particles, making these measurements

particularly complex. Despite these obstacles, the scientific community has been persistently

investigating this reaction for over twenty years, primarily employing transfer reactions to

probe the 4.03 MeV state in 19Ne. While these methods’ substantial background and limited

statistical precision pose significant challenges for obtaining definitive measurements, they

have been instrumental in establishing a stringent upper limit on the branching ratio, thereby

underscoring the difficulty of accurately measuring this reaction.

2.3.2 Purpose of this Work

Past research by our group led to a significant discovery: the 4.03 MeV state in 19Ne can be

populated through the beta-delayed proton decay of 20Mg. This decay sequence results in a

distinct signature—the near simultaneous emission of a proton and α particle. This process,

as depicted in Figure 2.5, opens a new avenue for accurately measuring the Γα/Γ ratio, and

31

consequently, the 15O(α, γ)19Ne reaction rate [19].

Bolstering this method is our prior determination of the proton energy from the excited

state in 20Na that feeds the 4.03 MeV state in 19Ne. This was achieved by analyzing

the Doppler-broadened 4.03 MeV gamma peak from the recoiling 19Ne nucleus. Through

simulations that aligned with observed data, the proton energy was estimated to be 1.21+0.25
−0.22

MeV [30]. This detailed energy profile allows us to define a precise search region in range

and energy (see Section 5.3.1), which aids in the filtering out of irrelevant data and focusing

on the critical proton-α events.

Employing the GADGET II Time Projection Chamber (TPC) detailed in chapter 3, we

capture these elusive proton-α coincidences. The TPC’s ability to reconstruct 3D decay

events is key to identifying the unique double Bragg peak topology of these proton-α events,

ensuring a nearly background-free measurement.

The detection and analysis of these events are expected to lead to the first definitive

measurement of the alpha branching ratio from the 4.03 MeV state in 19Ne. This advance-

ment will constrain the 15O(α, γ)19Ne reaction rate and enable us to model X-ray burst

light curves from neutron stars far more accurately. Such an achievement would represent

a substantial leap forward in nuclear astrophysics, providing vital insights into neutron star

behavior.

32

Figure 2.5: Decay sequence of 20Mg illustrating the β-delayed proton emission that populates
the 4.03 MeV state in 19Ne. Figure adapted from [19].

33

THE TIME PROJECTION

CHAMBER FOR GADGET II

The GAseous Detector with GErmanium Tagging (GADGET) was built to detect individual

protons emitted after beta decays. However, GADGET is ill-equipped for detecting multiple

particle emissions and distinguishing between them. But as we’ve learned from Chapter 2,

the characteristic signature of our events of interest, 20Mg(βpα), is the near simultaneous

emission of a roton and alpha particle. To achieve the granularity necessary for the identifi-

cation of these multi-particle events, we transformed the GADGET Proton Detector into a

time projection chamber (TPC), which is the key component of the upgraded GADGET II

detection system (the full GADGET II system is described in Section 4.3). This TPC allows

for the reconstruction of 3D images of decay events that occur in the active volume of the

detector.

The subsequent sections are adapted from our previously published work in collaboration

with Mahajan et al. [31]. These adaptations are used with permission and have been modified

to fit the context of this thesis.

3.1 Description of TPC

The GADGET II TPC (see Fig 3.1) is a cylindrical gaseous detector that can be thought of

as having two distinct regions; a drift region, and proportional amplification region (Figure

3.2 shows a simplified schematic of the TPC). The drift region operates by thermalizing

34

Figure 3.1: The GADGET II TPC in a lab space off the beam line.

radioactive ions within its gas volume, facilitating the measurement of their subsequent decay.

The resulting ionization electrons created from the charged decay products are directed to a

readout by a uniform electric field that is tuned to prevent the liberation of any additional

charge.

The proportional amplification region is characterized by a strong electric field that gen-

erates a Townsend avalanche, effectively amplifying event signals (more details in Section

3.1.1). The charge cluster created in this region is collected on a position-sensitive Mi-

croMegas (MM) gaseous amplifier [32]. This MM is notable for its high granularity, featur-

ing 1016 measurement pads, each measuring 2.2 × 2.2 mm², covering an area of 50.24 cm².

This design marks a substantial enhancement over the original GADGET proton detector,

which was equipped with only 5 measurement pads. This high density of pads coupled with

precise timing information from arriving electrons allows the GADGET II TPC to perform

3D reconstructions of charged particle tracks.

The operational efficiency of the GADGET II TPC is highlighted by its ability to function

in distinct modes that correspond to implant-decay cycles with radioactive beams. During

35

Figure 3.2: Simplified schematic of the GADGET II TPC.

’beam off’ periods, charged particles from decays are detected as they are drifted towards

the MM. During ’beam on’ periods, the system employs an electrostatic gating grid [19]

to counteract the intense ionization caused by the beam, which can cause large signals

and distort the electric field, thus ensuring accurate detection while minimizing background

interference.

The GADGET II TPC’s design and functionality enable it to play a crucial role in astro-

physical studies, particularly in the identification and analysis of low-energy β-delayed single-

and multi-particle emissions. Table ?? enumerates some of the TPC’s nominal operating

parameters, and the following subsections delve into the specifics of the TPC’s individual

components.

3.1.1 Resistive MICROMEGAS

The GADGET II readout board is a MM that is uniquely designed with a resistive-anode,

which is a novel application in the field of low-energy nuclear physics [33]. This resistive

MM, which doubles as the detector’s gas volume end cap, is a custom-designed component

36

TPC Parameters
No. of measurement pads
Pad size
Pad plane area
No. of veto pads
Veto pad area
Length of drift region
Amplification gap
Gating Grid Parameters
No. of gold plated copper wires
Diameter
Wire separation
GET Parameters
Electronic sampling frequency
Signal shaping time
Event rate
GET gain
Gas Amplifier Parameters
Typical gas composition
Gas pressure
Gas gain
Drift field
Amplification field
Drift velocity
Temperature
Micromesh Parameters
Resistance
Capacitance (calculated)
Mesh - Anode separation

1016
2.2 × 2.2 mm2
50.24 cm2
8
28.26 cm2
400 mm
128 µm

60
20 µm
2 mm

50 MHz
502 nsec
1 kHz
1 pC

P10 (90% Ar + 10% CH4)
800 Torr
40 for 220Rn α-particles
150 V/cm
30 kV/cm
5.44 ±0.03 cm/µsec
25°C

10 MΩ/square
287 nF
128 µm

Table 3.1: Nominal operating parameters of GADGET II TPC.

manufactured at CERN. It features a resistivity of 10 MΩ per square, which works to safe-

guard the front-end electronics [34] from electrical breakdown caused by sporadic discharges.

Additionally, the MM comprises a stainless steel micromesh characterized by an 18 µm wire

diameter and a 45 µm micromesh opening. The micromesh, following calendaring, attains

a thickness of 30 µm with 45% optical transparency. The micromesh is supported by in-

sulating pillars placed 128 µm above the anode plane and maintained at ground voltage.

The Townsend avalanche of electrons occurs across a 128 µm amplification gap between the

37

micromesh and the resistive anode at an electric field strength of approximately 35 kV/cm.

The resistive MM in GADGET II is further characterized by its high-granularity readout

plane, which includes 1024 square pads, with 1016 measurement pads covering an area of

50.24 cm² and 8 veto pads covering an area of 28.26 cm². The readout plane’s segmentation

ensures effective capture of charged particles, with the veto pads functioning to exclude

particles escaping the active volume. The anode forms a circular area with a diameter of 10

cm on a PCB frame, parallel to the micromesh. The resistive anode is layered atop 50 µm

of Polyimide, which is bonded to the segmented readout plane using a thin layer of glue.

This arrangement forms a two-dimensional RC network, where the resistance is defined by

the surface resistivity, R, of the anode, achieved through a uniform layer of diamond-like

carbon (DLC). The capacitance, C, is determined by the relative permittivity of the glue

and Polyimide. We can model this RC network by utilizing the two dimensional Telegraph

equation [35]:

∂ρ
∂t

= h

(cid:20)∂2ρ
∂r2 +

1
r

∂ρ
∂r

(cid:21)

,

(3.1)

where ρ is the charge density, r is radial position, and h = 1

RC . In the ideal case we take the

resistive anode to have an infinite radius, and at time t = 0 we assume there to be a point

charge at the origin. Then the solution for the charge density is given by

ρ(r, t) =

1
2th

exp

(cid:18) −r2
4th

(cid:19)

.

(3.2)

Using this equation one can find the charge density as a function of radial position for various

R and C values. We can also model the amount of charge that will be deposited on each pad,

38

Qpad [36]. We start by writing the Telegraph equation in terms of Cartesian coordinates

∂ρ
∂t

= h

(cid:20) ∂2ρ
∂x2 +

∂2ρ
∂y2

(cid:21)

.

(3.3)

Then, in order to ensure a closed form solution we assume a delta function point charge is

collected at the origin at t = 0, to get

ρδ(x, y, t) =

(cid:18) 1
√
2

πth

(cid:19)2

(cid:20)

exp

−

x2 + y2
4th

(cid:21)

.

(3.4)

To account for the fact that the actual charge profile is described by a Gaussian, we convolve

the above equation with the Gaussian characterizing the charge cluster

ρ(x, y, t) =

N qe
2π(2ht + w2)

(cid:20)

exp

−

x2 + y2
2(2ht + w2)

(cid:21)

,

(3.5)

where N represents the numbers of electrons, qe is the electron charge, and w is the width of

the Gaussian describing the charge cluster. From here we can integrate the charge density

function over the area of a single pad to get the charge on a pad

Qpad(t) =

(cid:34)

(cid:32)

erf

N qe
4

xhigh√
2σxy

(cid:33)

(cid:32)

− erf

xlow√
2σxy

(cid:33)(cid:35)

(cid:34)

(cid:32)

×

erf

yhigh√
2σxy

(cid:33)

(cid:32)

− erf

ylow√
2σxy

(cid:33)(cid:35)

,

(3.6)

where xhigh, xlow, yhigh, and ylow represent the pad boundaries, and σxy =

√

2th + w2.

This expression for Qpad let’s one calculate the charge on a pad for an event of interest.

For GADGET II R and C were chosen so as to affect minimal charge dispersion, confining

39

Figure 3.3: a) Schematic of the MM board’s front view, illustrating the central region com-
posed of 1016 measurement pads, along with 8 veto pads labeled V1 to V8. b) A view of the
MM board’s rear end cap, showing 8 multi-pin connectors, each with 144 channels, which
are then connected to the T-Zap boards (not depicted).

the charge spread to a single pad covering an area of 4.84 mm², thereby facilitating precise

detection. Figure 3.3 a) and b) show the front and rear view, respectively of the installed

MM at one end of the TPC.

3.1.2 The GET System

To handle the high-density of signals from our MM we utilized the GET (Generic Elec-

tronics for TPCs) system. This system, specifically developed for gas-filled detectors in

nuclear physics, is notable for its scalability and adaptability to various TPC configurations.

The GET system’s architecture is designed around a versatile ASIC (Application Specific

Integrated Circuit), enabling multiple modes of data acquisition tailored for different exper-

imental needs.

Central to the GET system is the AsAd (ASIC and ADC) front-end card, which comprises

40

four AGET chips and ADCs. These chips are responsible for the initial aggregation of data

from 64 input channels to a single analog output, a process critical for handling the large

amount of data generated by the TPC. To facilitate control and monitoring, the system

includes a small Field Programmable Gate Array (FPGA), which oversees the slow control

of the chips, while keeping track of parameters like currents, voltages, and temperature.

The CoBo (Concentration Board) can accommodate up to four AsAd boards, and is

equipped with an FPGA. The CoBo performs several key functions: configuring the AsAd

cards, local calibration, trigger functions, and managing data flow.

It also plays a role

in time-stamping and formatting functions, contributing to efficient data management and

transfer at high speeds. For the GADGET II experiment (E21072) at FRIB (see chapter 4

for more details), a configuration of four CoBos was employed to read out all 1024 channels of

the MM, addressing the challenge of data throughput limitations (see Section 4.3.6.1). While

a single CoBo is capable of handling all 1024 channels, the use of four CoBos enhances the

system’s performance.

The MuTanT (Multiplicity Trigger and Time) module within the GET system provides

the internal clock. This module is also essential for triggering capabilities and offers flexible

triggering options for different experimental scenarios. For our purposes, we have exclusively

used the external trigger functionality. For additional details on the GET system see Ref.

[37]. Figure 3.4 presents a schematic representation of the GET system, illustrating all its

primary components and the specially designed mesh trigger (refer to Section 3.1.4) for the

data acquisition system.

41

Figure 3.4: Simplified schematic of the GET system with a single µTCA (Micro Telecommu-
nications Computing Architecture) chassis, 4 CoBos (Concentration Board) and a MuTanT
(Multiplicity Trigger and Time).

3.1.3 AsAd Box and T-Zap Boards

The integration of front-end electronics with the TPC is achieved through the innovative

design of the AsAd Box and T-Zap boards. The AsAd Box was designed to house the front-

end electronics of the GET system.

It consists of four triangular Printed Circuit Boards

(PCBs), known as T-Zap boards. These boards were custom designed and fabricated at

CERN, and connect directly to the MM (see Figure 3.5). This connection is crucial as it

enables the transmission of signals from the TPC to the AsAds (ASIC and ADC) boards.

Each T-Zap board is designed to interface with the AsAd boards, with the layout allowing

each AsAd board to handle a total of 256 signals originating from the MM pads. This design

ensures that the signal transmission from the TPC to the AsAds is both efficient and reliable.

To optimize this configuration, the AsAd boards are positioned perpendicularly to the

T-Zap boards. This arrangement places the AsAd boards as close as possible to the MM to

42

Figure 3.5: Left: Image of the 4 triangluar T-Zaps attached to the MM. Right: Image of the
completed AsAd box.

minimize signal loss and ensure the integrity of the data being transmitted. An additional

design consideration is the electromagnetic shielding of these components. The entire assem-

bly, including the T-Zap and AsAd boards, is housed within a box constructed from copper

plates. These plates serve as a Faraday cage to reduce the pickup of external electromagnetic

noise. This shielding is vital in maintaining the quality of the signal and preventing inter-

ference that could compromise the quality of the data collected by the TPC. The assembled

AsAd Box configuration, including the T-Zaps, is depicted Figure 3.5.

3.1.4 Mesh Trigger

To trigger the DAQ a mesh trigger was designed to signal the arrival of charge at the MM

mesh (see Figure 3.4). The operational principle of the mesh trigger revolves around the

movement of ionization electrons towards the MM mesh. As these electrons traverse the mesh

and enter the gap between the mesh and the resistive anode, they instigate an avalanche

43

of charges. This avalanche results in electrons moving towards the resistive anode and ions

towards the mesh, generating detectable signals on both the resistive anode and the mesh.

Notably, these signals exhibit identical pulse heights but opposite polarities: negative on the

resistive anode and positive on the mesh.

By grounding the mesh through a low impedance charge amplifier (a modified Canberra

model 2006), a trigger logic signal is generated. This is achieved using a fast amplifier and

leading-edge discriminator, ensuring that all particle tracks above a set threshold entering the

active volume generate a mesh trigger. The signal-to-noise ratio (S/N) for the mesh signals,

specifically using an α-particle source (see Section 7.10 for more details), was measured to be

16. Additionally, Section 4.3.6.1 describes an anti-coincidence circuit that was introduced to

reduce the mesh trigger rate using the veto pad signals.

3.2 Performance Evaluation of GADGET II TPC

3.2.1 α-Particle Source Test

The initial performance assessment of the GADGET II TPC involved an α-particle source

test, utilizing a 228Th source (1µCi) which was installed in the TPC’s gas handling system.

The detector volume was filled with a P10 (90% Argon, 10% Methane) gas mixture at 800

Torr. The 228Th undergoes decay to 220Rn gas (half-life of 55.4 seconds), which, due to

recoil from alpha emission, occasionally escapes the source’s thin window, mixes with the

P10 gas in the inlet line, and then flows into the detector. The decay of 220Rn to 216Po

emits α-particles with an energy of 6.288 MeV and a branching ratio of 99.886% [38]. The

subsequent decay of 216Po emits a 6.778 MeV α-particle with a 99.9981% branching ratio

[39].

44

For effective track analysis, signals on pads outside the main track’s locality in a given

event were removed to eliminate noise. This was achieved by implementing two different

outlier detection algorithms, Hotelling and Squared Prediction Error (SPE), in sequence

[40]. The Hotelling algorithm computes distances between data points and their mean based

on variance, identifying potential outliers as points significantly distant from the mean. The

SPE algorithm, on the other hand, calculates squared prediction errors for each data point

using a statistical model, flagging points with high SPE values as outliers. Charge collection

on a pad (point) is considered an outlier only if both algorithms concur on this assessment.

Figures 3.6 and 3.7 illustrate the projected 2D images of the 220Rn alpha tracks on the

pad plane, both before and after the elimination of outliers, respectively. Figure 3.8 presents

a 3D reconstruction of an alpha track within the TPC. Principal Component Analysis (PCA)

was employed to fit tracks by identifying lines and planes that best approximate the data via

least squares optimization [41]. In this analysis, the first and second principal components

correspond to the length and width of a track, respectively. The length of a track is extracted

and then the charge is integrated over all pads and converted to energy. The resulting

energy spectrum for 220Rn and 216Po alphas is depicted in Figure 3.9. The 6.778 MeV α-

peak appears weaker in comparison to the 6.288 MeV α-peak, likely because the positively

charged 216Po drifts towards the cathode. As a result, α-particles emitted into the inactive

cathode from 216Po decay are not detected.

After calibrating the MM pads using signals induced from pulses on the mesh, an energy

resolution of 5.4% was achieved for events with an angular range of 0° to 70° relative to the

pad plane. This level of resolution aligns with that of other TPC energy resolutions cited in

the literature [42, 43, 44, 45]. However, it is important to note that the energy resolution of

TPCs can vary depending on various factors such as gain matching procedures and operating

45

Figure 3.6: Label a)-d): 2D track projections on the MM pad plane in GADGET II TPC,
showcasing tracks from 220Rn alpha particles. The pads that are diffusely illuminated rep-
resent the points identified as outliers.

46

Figure 3.7: Label a)-d): 2D track projections on the MM pad plane in GADGET II TPC,
showcasing tracks from 220Rn alpha particles after outlier removal.

47

Figure 3.8: a) Illustrates a 3D hit pattern of a 220Rn alpha track within the GADGET II
TPC. b) Provides a zoomed-in image of the 220Rn alpha track in the same TPC. For this
representation, the z-coordinate is assigned an arbitrary value since the precise z position of
the decay event within the TPC is not known. The numbers (11, -11, 45, and -6) displayed
on the axis labels correspond to the lengths of the X, Y, and Z axes, respectively, measured
in centimeters.

48

parameters (e.g., type of gas, pressure, drift voltage) [43, 44]. Also, reference [43] mentions

a smaller angular range relative to the pad plane, which can improve energy resolution at

the expense of reduced statistics.

A range versus energy plot was generated for an ensemble of events, as shown in Figure

3.10. This plot is essential for particle identification, revealing two predominant features.

The dense region where the 6.288 MeV and 6.778 MeV α-particles are found is marked as

Region 1. Most events in Region 1 indicate α-particles depositing their full energy in the

active volume, with expected ranges for the 6.288 MeV and 6.778 MeV α-particles. Events

in Region 2 represent “wall effect,” occurring when decays happen near the TPC’s anode

or cathode, resulting in α-particle tracks terminating on a solid surface after partial energy

deposition in the active gaseous region. Events with tracks crossing the volume projected

by the veto pads have been eliminated using an anti-coincidence condition, as discussed in

Section 4.3.6.1.

3.2.2 Cosmic-ray Muon Events

The GADGET II TPC’s proficiency in detection extends to cosmic-ray muon measurements.

This testing avenue focused on detecting low-ionizing cosmic-ray muons streaming through

the active volume of the TPC. Given the average energy of a cosmic-ray muon at Earth’s

surface, ≈27 electron-ion pairs are formed per pad along the particles track in the drift zone,

as is inferred from the cosmic-ray muon stopping power in P10 gas [46]. Thus, detecting

these low-ionizing cosmic-ray muons demonstrates the superb sensitivity of the detector and

the very good signal-to-noise ratio on the pads.

To accurately detect these muons, a setup using two plastic scintillators (BC408), each

connected to a photomultiplier tube (PMT), was employed. These scintillators, measuring

49

Figure 3.9: Energy spectrum for 220Rn (shown in blue), featuring a fitted curve (in red) that
indicates an energy resolution of 5.4% at 6.288 MeV. The peak at the higher energy level
corresponds to the 6.778 MeV α-particle from 216Po.

50

Figure 3.10: Aggregate histogram depicting range versus energy for 220Rn and 216Po α-
particles, encompassing events with angular orientations ranging from 0° to 70° relative to
the pad plane.

51

Figure 3.11: Label a)-b): Examples of cosmic-ray muon tracks detected in the GADGET II
TPC.

2.5 cm in width, 40 cm in length, and 2 mm in thickness, were strategically positioned

above and below the TPC’s drift chamber. The PMT signals were used to generate a

coincidence signal whenever a cosmic muon passed through both scintillators simultaneously.

This coincidence signal served as a trigger for the data acquisition system instead of the mesh

trigger detailed in Section 3.1.4. For these specific measurements, the amplification field was

increased to 44 kV/cm to ensure adequate gain. A few example tracks captured using this

method can be seen in Figure 3.11.

These cosmic-ray muon measurements provide valuable insights into the diffusion effects

of ionization electrons within the gas volume. For beam-line experiments there is no global

external trigger, so the absolute z-position (distance from the MM) is not known. However,

by measuring the width of cosmic muon tracks as a function of distance from the MM, we

can calibrate the absolute position of charged particle events (alphas and protons) relative

to their track width. To this end, the entire drift length of the detector was scanned in 5

cm increments to determine the cosmic-ray muon track widths as a function of distance.

52

The width W of these tracks as a function of drift length is mathematically described by the

function W = A−BCx [47], where A represents the limiting value of the track width at large

distances, B controls the scale of change in the track width, C is directly correlated to the

rate of diffusion, meaning the rate at which the impact of diffusion on track width diminishes

with increasing drift distance, and x is the drift distance in the gas. Consequently, tracks

closer to the upstream end (cathode) appear broader than those nearer to the downstream

end (anode), as illustrated in Figure 3.12.

Additionally, the drift velocity of these events was ascertained from the timing distri-

bution of the cosmic-ray muon events. The value was determined by fitting the drift time

versus distance from the MM data with a linear model as seen in Figure 3.13. The drift

velocity was found to be 5.44 ± 0.03 cm/µsec. In a 40-cm drift region, the maximum drift

time for primary ionization electrons is thus calculated to be 7.352 ± 0.041 µsec. These

findings align with previous measurements conducted with the original GADGET detection

system using a particle-gamma coincidence method [48].

53

Figure 3.12: Average width of cosmic-ray muon tracks as a function of distance from the
MM pad plane.

54

Figure 3.13: Average width of cosmic-ray muon tracks as a function of distance from the
MM pad plane.

55

EXPERIMENT E21072 AT THE

FACILITY FOR RARE ISOTOPE

BEAMS

Experiment E21072 was conducted at the Facility for Rare Isotope Beam (FRIB) at Michigan

State University in November 2022. The experimental campaign lasted just over one week

starting on November 19th and concluding on November 28th. During the experiment, a

beam of 20Mg was delivered to the GADGET II TPC. This chapter will cover the purpose of

the experiment, how the 20Mg beam was produced, and detail the experimental setup and

procedure.

4.1 Purpose

Sensitivity studies indicate that the 15O(α, γ)19Ne reaction is among the most important

reaction rate uncertainties affecting the modeling of Type I X-ray burst light curves (see

Chap. 2). The rate of this reaction is anticipated to be dominated by the 4.03 MeV excited

state in 19Ne. Given the established lifetime of this state, determining the reaction rate

requires only a finite value for the minor alpha-particle branching ratio, Γα/Γ. Past mea-

surements have documented that this particular state is populated in the decay sequence

of 20Mg, with 20Mg(βpα)15O transitions occurring through the critical 15O(α, γ)19Ne res-

onance. This process is marked by the distinct emission of a proton and an alpha particle.

56

In order to detect these near simultaneous emissions, the GADGET II detection system (see

Section 4.3) was employed at the Facility for Rare Isotope Beams.

4.2 Beam Production

The production of the rare isotope beam at FRIB began with a stable isotope that was ionized

using an electron cyclotron resonance ion source. The resulting ions were then injected into

the FRIB superconducting RF heavy-ion linear accelerator (linac). This accelerator uses

superconducting radio frequency (SRF) cavities to accelerate ions to high kinetic energies.

A 3D rendering and schematic of the superconducting RF linac can be see in Figure 4.1.

The primary beam for experiment E21072 was 36Ar, which was accelerated using the linac

to an energy of ∼ 200 MeV/u.

The 36Ar primary beam was then focused to a 1mm spot and impinged on a multi-slice

carbon target rotating at 5000 rpm. When the beam struck this target it generated a nuclear

fragmentation process, which produced a cascade of different isotopes including 20Mg, the

isotope required for the experiment.

Following fragmentation, the resulting cocktail beam passed through the Advanced Rare

Isotope Separator (ARIS). ARIS is a sophisticated three-stage fragment separator, aimed

at the efficient refinement of rare isotope beams (see Figure 4.2) [49]. The first stage is

the vertically-oriented preseparator, complete with a beam dump. In the preseparator the

secondary beam undergoes coarse initial selection of the desired isotopes. This is accom-

plished using the preseparator’s magnetic dipoles that work much like prisms, bending and

spreading the beam such that only the desired isotopes make the turn to the next section.

This process allows for the categorization and isolation of fragments, and is described by the

57

Lorentz force, expressed as mv/q = Bρ. Here, m represents the ion’s mass, v denotes its

velocity, q is the nucleus’s charge, and Bρ symbolizes the magnetic rigidity. This configu-

ration is meticulously calibrated to ensure that 20Mg ions maintain their trajectory at the

beam-line’s core. Consequently, ions exhibiting particular magnetic rigidities follow distinct

trajectories with differing radii, thereby facilitating their separation from the primary beam.

Nonetheless, ions with different masses can exhibit similar magnetic rigidities to that of

the desired 20Mg ions. To address this, a wedge energy degrader was employed between the

preseparator dipoles. This wedge operates by decelerating ions in a manner proportional to

the square of their mass (A2), effectively altering the magnetic rigidity of these non-target

ions. The preseparator then delivered the beam to the ground level separator (stage 2 and

3) which consists of additional dipole and quadrupole magnets for further isotope refinement

and beam focusing, respectively. When the 20Mg beam exited ARIS it was incident on a

focal plane with collimating slits, and was then delivered to our experimental setup, which

was located in the transfer hall at FRIB. Additionally, the beam was delivered in cycles.

Each cycle was comprised of two phases: initially, the beam was delivered for a period of 110

milliseconds, immediately after which the beam was stopped. Subsequently, a decay counting

phase would occur, spanning an identical duration of 110 milliseconds. This pattern ensured a

clear separation between delivery and measurement intervals. The main beam contaminants

included 18Ne, 17F, and 16O, however, none of these contaminants create a background of

any concern as they are not beta-delayed particle emitters. However, there was some 21Mg

contamination, which is definitely a concern given that it is a beta-delayed particle emitter,

and even has a strong p − α channel (this is discussed in more depth in Section 4.4).

58

Figure 4.1: Top) Scale 3D rendering of the superconducting radio-frequency driver linear
accelerator at FRIB. Bottom) Schematic layout of the FRIB driver linac [50].

59

Figure 4.2: This ARIS diagram illustrates the driver linac’s primary beam approaching the
production target from the lower left.
Isotope beams travel through the three stages of
the fragment separator (preseparator, stage 2, and stage 3) before being channeled towards
experimental setups [49].

4.3 Experimental Setup

The GADGET II detection system as configured for E21072 consists of a diverse assembly of

detection technologies, encompassing four primary detector types: A compact TPC with a

resistive MicroMegas, the Decay Germanium Array initiator (DEGAi), Lanthanum Bromide

(LaBr3) detectors, and a silicon PIN (positive-intrinsic-negative) detector.

Other ancillary components are integral to the successful operation of these detectors,

such as an energy degrader, and various Data Acquisition Systems (DAQs), which play

pivotal roles in the seamless operation and data handling of the detection array. Discussions

on both the primary detectors and these essential supporting elements are presented in the

ensuing sections and subsections.

60

4.3.1 TPC

The TPC was operated with P10 gas (90% Argon 10% Methane) at ∼ 800 Torr. This pressure

was chosen as it yields optimal track lengths, and ensures that any small leaks would cause

gas to flow out of the TPC thereby mitigating air contamination. The pressure was regulated

and monitored continuously using the MKS πPC PC99 pressure controller with mass flow

meter. To maintain a comprehensive record of the operational environment, the temperature

of the TPC was also recorded throughout the experiment via a thermocouple attached to

the outside of the drift chamber.

The resistive MicroMegas of the TPC was biased at +440V. Additionally, the gating grid

was switched between −225V (transparent mode, used during decay counting phase) and

+150V (opaque mode, used during beam implantation) to correspond to the beam pulsing.

The gating grid timing also needed a 5ms buffer period after the beam had stopped and

before beam turned back on to ensure implantation ionization was not captured. The timing

for the gating was provided from the accelerator as an on/off signal (square wave) that was

5 ms wider on both sides to account for the desired buffer period. This signal was then

used with a CGC Instruments NIM-AMX500-3 switch which alternated the transparent and

opaque voltages.

Biasing for both the MicroMegas and the gating grid was done using a Mesytec MHV-4

module, a 4-channel high precision bias supply. Furthermore, to establish a drift field of 150

V/cm, the field cage was biased at −6 kV via a N1470B programmable high voltage power

supply from CAEN. Additional details of the TPC, including default operating parameters

used during the experiment, are covered in Section 3.

61

4.3.2 DEGAi

DEGAi is part of the FRIB Decay Station initiator (FDSi), which is generally maintained/serviced

by Oak Ridge National Laboratory (ORNL) and the University of Tennessee at Knoxville.

DEGAi consists of 11 high-purity germanium (HPGe) clover detectors that are used for the

detection of prompt gamma-rays. This works because when gamma-rays interact with the

crystal lattice of the Ge, it leads to the formation of electron-hole pairs. When a reverse

bias is applied, this triggers a current pulse to propagate through the Ge. The magnitude

of the current pulse is proportional to the number of electron-hole pairs generated, which

in turn is proportional to the energy of the absorbed gamma ray. By measuring this pulse,

the energy of the incident gamma ray can be accurately determined. Being able to detect

gamma-rays in this fashion gives us a detailed way to identify beam contaminants, and acts

as a beam diagnostic. It also allows us to clarify the decay scheme of 20Mg. Using a single

CLARION1, spherically symmetric hemisphere that covers a 2π solid angle we obtain an

efficiency of 6.0(12)% at 1 MeV [51]. A schematic of DEGAi coupled with the TPC and

AsAd box can be seen in Figure 4.3.

A significant amount of development work was needed to integrate the TPC with DEGAi.

This included designing and building a new TPC support structure, a new gas manifold, and

an additional support structure to house LaBr3 detectors. A schematic showing these new

design elements can be seen in Figure 4.4, and an image of the full experimental setup can

be seen in Figure 4.5.

62

Figure 4.3: Schematic representation of the FRIB Decay Station’s DEGAi, featuring the
TPC and AsAd box at the core. A red arrow illustrates the entry path of a 20Mg beam
into the TPC, and DEGAi is used to measure gamma-rays emitted from the TPC following
nuclear decay.

4.3.3 LaBr3 Detectors

Three 2” LaBr3 detectors were tested as a beam ranging diagnostic tool. The central LaBr3

detector was positioned so as to align with the central beam implantation location. Then

the relative gamma counts in each detector could provide a coarse method for ensuring

that the beam was being deposited in the center of the detector. LaBr3 detectors work by

utilizing the scintillation process to detect gamma rays. When a gamma ray enters the LaBr3

crystal, it interacts with the crystal lattice, producing high-energy electrons that excite the

atoms in the crystal. These excited atoms then emit visible light as they return to their

ground state. The emitted light is collected by a photomultiplier, which converts it into an

electrical signal proportional to the energy of the incoming gamma ray. Despite an efficiency

of approximately 0.27% at 1 MeV—considerably lower than the efficiency of DEGAi’s HPGe

63

Figure 4.4: Schematic of the TPC with the new design elements needed for the integration
of the detector with FDSi. These new elements include: a new TPC support structure,
a new gas manifold, an additional support structure to house LaBr3 detectors, a preamp
support and cable feedthrough assembly. Detector dimensions are detailed in Chapter 3.
For reference, when on the support structure the center of the detector is 50.75” off the
ground, and the base of the support structure is 29” x 29”.

detectors—LaBr3 detectors offer superior response times and the convenience of operation

at ambient temperatures.

4.3.4 PIN Detector

A Silicon MX100 PIN detector was housed in a diagnostics box approximately 1m upstream

from the Kapton window of the TPC, and was positioned in the beam path to measure

energy loss (∆ E). A PIN semiconductor diode consists of three main layers: the intrinsic (i-

type) layer (in this case Si), which is sandwiched between p-type, and n-type layers. When

particles from the beam pass through the PIN detector, they lose energy in the intrinsic

layer, which is measured. The PIN detector operates in tandem with a scintillator in ARIS

to generate a timing signal that corresponds directly to the time of flight (ToF) between the

64

Figure 4.5: Image of the experimental GADGET II setup. The TPC and AsAd box are
positioned at the center of the CLARION1 array by a newly built support structure that
includes a new gas manifold and three LaBr3 detectors. Surrounding the TPC on one side
is DEGAi.

65

two detectors. The scintillator is located at the DB3 position in ARIS. By integrating the

energy output from the PIN detector with the ARIS timing signal, a particle identification

(PID) plot can be constructed (see Figure 4.6). Note that the PIN detector cannot be

used with full beam intensity without risking radiation damage, thus, a 100x attenuated,

continuous beam was used during periodic PID runs. The PIN detector was moved in and

out of the beam path via manual actuators.

4.3.5 Beam Energy Degrader

An aluminum degrader with a thickness of 3.227 mm was also housed in the diagnostics

box with the PIN detector. This high purity aluminium plate is placed in the beam path to

degrade the energy of the incoming ions. Simulations were done to ensure optimal energy loss

and beam ranging with the degrader at 30°. Then the degrader can be rotated to increase

or decreased the amount of energy loss. In this case 0°(perpendicular to the beam) reduces

the effective thickness of the degrader, and thus reduces energy loss. Conversely, an angle of

>30°increases the effective thickness and therefore increases energy loss. The degrader was

attached to a stepper motor that could be controlled remotely, so that the ideal degrader

angle needed to ensure beam implantation in the center of the TPC could be found while

beam was being delivered.

4.3.6 Data Acquisition

The GADGET II TPC utilizes the GET (Generic Electronics for TPCs) data acquisition

system (see Section 3.1.2 for a full description of the GET system). The experimental setup

for the GET system includes 4 AsAd boards (one board for each quadrant of the MM), 4

66

Figure 4.6: PID plot generated using the ΔE-TOF technique for precise particle differenti-
ation. The plots shows that 20Mg was in the beam, along with some other contaminants.

CoBos, 1 MuTanT module, 1 MCH module, a Micro-TCA chassis, a 1 GB/10 GB network

switch, 4 Mac-mini computers (one for each CoBo), and 4 20 TB external hard-drives (data

storage for each CoBo).

The germanium array of DEGAi uses the Digital Data Acquisition System (DDAS) [52].

This system utilizes the 250 MHz XIA Pixie-16 module, which can handle signals from an

array of different detectors. Each module is equipped with 16 channels and is installed in

a computing crate. This setup allows for the interconnection of several modules within the

same framework.

Ideally, each channel from the detectors in DEGAi and from the MM pads in the TPC,

would yield consistent outputs for a specific energy input. Yet, output values can vary

slightly over time, a phenomenon referred to as gain drift. To mitigate the effects of gain

67

drift, data from the GET electronics for the TPC and DDAS for DEGAi were taken in 1 hour

long runs, where the start and stop of each run for both systems was synchronized. This

strategy ensures that any variations in output due to gain drift are consistently adjusted for

during energy calibration. Additionally, by frequently starting new data runs, the potential

loss of data resulting from DAQ malfunctions is significantly reduced.

To ensure precise synchronization for gamma-particle coincident measurements, a clock

signal was sent between DDAS and GET at 50 MHz. Both systems would reset clocks at

the start of each run. Additionally, the mesh trigger signal (see Section 3.1.4) was split and

sent to both DAQs and recorded for the duration of each run. This unique signal can then

be matched in both systems ensuring proper synchronization.

4.3.6.1 Data Throughput Optimization in TPC

The data acquisition capabilities of the GET system (Section 3.1.2), crucial for the GADGET

II TPC’s operational efficacy, are notably constrained by data throughput limitations. These

limitations directly influence the TPC’s rate capability. In the context of our experiment,

we needed to be able to record events at the scale of thousands of decays per second in order

to have enough statistics to measure the rare 20Mg(βpα)15O events. However, this target

event rate far exceeded the handling capacity of the existing GET system, which posed a

substantial challenge to the feasibility of our experiment.

The live time of the GET system, as depicted in Figure 4.7, illustrates the system’s

performance as a function of channels read for a single AGET chip. These AGET chips, being

fundamental to the GET system’s operation, represent a critical bottleneck. As evidenced

in the plot, at an event rate of 2 kHz, even with a single pad firing, the system fails to

process approximately 10% of triggers. This inefficiency escalates dramatically with increased

68

Figure 4.7: Live time of the GET system as a function of channels read for one AGET chip.
The plot illustrates the system’s performance degradation with increasing event rates and
channel activity.

channel activity, and renders the system incapable of supporting the desired event rates for

our experiment. To address this significant bottleneck, a multifaceted approach was adopted.

This first step in tackling this problem involved expanding the array of Concentration

Boards (CoBos) and optimizing parameter settings. The CoBos are responsible for data

aggregation and transfer to the computing system. Our initial setup was designed for use

at the NSCL facility, for which beam intensities were limited, and only called for a single

CoBo to be used, but this leads to substantial dead time for anticipated FRIB event rates

surpassing 1 kHz. A series of tests investigating this issue, involving a random pulse generator

and the analysis of α-decay events from 220Rn, led to a crucial finding: the data throughput

of the system increases approximately linearly with additional CoBos [37]. A particularly

effective configuration that emerged from these trials involved the use of a four-CoBo setup

(one CoBo per AsAd board) [31].

69

In addition to increasing the number of CoBos, fine-tuning parameter settings, such as

channel hit readouts and threshold adjustments, was identified as a pivotal factor in enhanc-

ing data throughput. A significant breakthrough was achieved by reducing the number of

time bins per trace. Specifically, decreasing the default readout depth from 512 to just 64

time bins resulted in a notable increase in throughput. This optimization and its consequen-

tial impact on data handling capabilities are depicted in Figure 4.8, which illustrates the data

throughput as a function of event rate under various time binnings and CoBo configurations.

Figure 4.8: Data throughput as a function of event rate for various time binnings and CoBo
configurations [31].

The next method we used to improve the system throughput was the introduction of a

front-end veto condition, which emerged as the most impactful solution. If any energy is

detected on the veto pads of the pad plane (see Figure 4.9), the event trigger is discarded,

70

ensuring that only events with energy concentrated on the main part of the pad plane are

acquired. This is achieved by soldering lemo connections to the capacitor pads on the zap

boards that are linked to each veto pad. With this we established a direct signal connection

from the veto pads, which were connected to a mesytec MSCF-16-F; a shaping/timing filter

amplifier with constant fraction discriminator and multiplicity trigger. The resulting output

from this amplifier is then placed in anticoincidence with our mesh trigger (see Section

3.1.4 for details on the mesh trigger) through an OR gate, allowing for the preemptive

exclusion of veto events from processing. This front-end veto condition reduced our trigger

rate by an order of magnitude, effectively mitigating the event rate issue and aligning the

system’s capabilities with the requirements of our high-event-rate experiment. Images of the

construction/setup of the front-end veto condition can be seen in Figure 4.10.

4.4 Procedure

During the experiment, data was collected in hour long runs to guarantee uniform readings

across our array of detectors. Moreover, supplementary runs were taken prior to and subse-

quent to the experimental phase to facilitate calibration of the TPC. These calibration runs

were done using 220Rn and 216Po alpha-particles from a 228Th source installed in the gas

handling system of the TPC (see Chapter 3 for additional details on source tests). Calibra-

tion runs were also done for DEGAi using 152Eu and 60Co sources that were taped outside

the center of the TPC chamber.

At the commencement of our experimental campaign, diagnostic tests were performed to

verify the accuracy of the beam’s composition and its precise implantation within the TPC.

To tune the beam ranging, we took a pulsed beam at full intensity and observed the LaBr3

71

Figure 4.9: Schematic diagram of the front-end trigger veto condition showing the pad
plane, connections to the veto pads (marked V1-V8), and the module used to create an
output trigger if any signal arrives at the veto pads. The output trigger from the MSCF-16
F module is then placed in anticoincidence with the mesh event trigger.

72

Figure 4.10: Images showing the construction of the front-end veto condition. Left) Image
of the soldered lemo connections on the capacitor pads of the zap boards that correspond
to each veto pad. Middle) Veto connections integrated into single input for a preamplifier,
and AsAd boards are connected with copper shielding. Right) Full AsAd box setup with
front-end veto condition fully implemented.

detectors to make coarse degrader angle adjustments, aiming for a uniform distribution of

gamma counts among them. However, using DEGAi proved to be the most reliable method

for adjusting the beam implantation depth, due to it’s superior resolution. By analyzing the

distribution of mesh trigger-to-gamma times, gated on energies indicative of specific nuclear

transitions in the decay of 20Mg 5.4, we finely tuned the degrader angle. We determined that

an angle of ∼25 degrees was optimal for stopping the beam in the center of the TPC. To

ensure that the beam was centered on the pad plane, we took data with the TPC and then

summed all pad hits across all events. This effectively generates a heatmap that establishes

the xy position of the beam, which showed that the beam spot was indeed centered on the

pad plane (see an example in Figure 4.11).

To verify that a beam of 20Mg was being delivered, we inserted the Si PIN detector

into the beam line and took a continuous beam at 100x rate attenuation. The initial PID

plots generated showed significant 21Mg contamination (∼10% the intensity of 20Mg). This

73

Figure 4.11: Example heatmap used during experiment E21072 to establish the xy position
of the beam. The plot is generated with data from the TPC where all pad hits are summed
across all events.

was a worrisome contaminant, as it also has a p-α channel at a nearby energy to that of our

events-of-interest (20Mg(βpa)), but with a significantly higher branching ratio (∼0.03% of all

21Mg events). However, this proved to be beneficial, effectively serving as a commissioning

beam for the detector. It allowed us find p-α events in the data, and show that they had

the signature we were expecting. Figure 4.12 shows what is likely a 21Mg p-α found during

this commissioning phase. The image shows a clear double peak structure in both the 2D

projected track and the time projection, thus demonstrating that the GADGET II TPC is

indeed capable of identifying our events-of-interest.

During this beam sampling, we also encountered an unexpected low beam intensity.

Per our proposal, we required ∼29,000 particles per second (pps) of 20Mg deposited in the

active region of the TPC during each implantation phase. From the Experiment Service

74

Figure 4.12: The upper panel illustrates the energy deposition in the x-y plane of the GAD-
GET II TPC, highlighting the distinct Bragg peaks indicative of simultaneous proton-alpha
particle emission. The lower panel shows the time projection (energy deposition along z),
reinforcing the identification of the dual Bragg peaks. These observations strongly suggest
the event originates from the beta decay of 21Mg, characterized by a significant 21Mg(βpa)
decay pathway.

Description, we were expecting to have at least ∼8000 20Mg particles per second (pps).

However, integrating the 20Mg peak on our PID plots showed we were only getting ∼700

pps. After a few days of additional beam tuning efforts, a more isotopically pure beam with

enhanced intensity was received. The reduction of the 21Mg was corroborated by PID plots,

but still showed the contamination was ∼1% the intensity of 20Mg. This cleaned up 20Mg

beam was depositing ∼1,800 pps of 20Mg to the PID, and our experiment was extended by

two days due to the time spent with impure beam, and the insufficient rate.

While the beam rate was greatly improved, given that we are searching for extraordinar-

ily rare events, the reduction in statistics from what we were expecting will likely hinder our

75

ability to make a finite measurement of the 19Ne alpha branching ratio. Had we received the

beam intensity we anticipated, we would have expected 5-50 events-of-interest. Now, consid-

ering a rough estimate of the integrated beam at this reduced rate, our detector efficiency,

and the established upper limit of the branching ratio, we will likely see no more than 3

events-of-interest under the most optimistic scenarios, and 0.3 based on the lowest estimate

of the branching ratio. However, the astrophysical problem at hand can be effectively ad-

dressed with a branching ratio uncertainty of ∼70% or less on a finite value, equating to us

finding roughly 2 events-of-interest (assuming a background free measurement).

With the beam optimized, we focused on calibrating the TPC, experimenting with various

voltages applied to the MM DLC to refine the clarity of TPC tracks and enhance the signal-

to-noise ratio. Starting with an initial voltage of +380 V, we incrementally increased it by

10 V steps, identifying +440 V as the optimal setting for maximizing gain while minimizing

sparking events and noise (see 4.3.1 for additional setup details). Production runs then

commenced with minimal interruption except due to periodic PID runs (see 4.3.4), pauses

for the liquid nitrogen filling of DEGAi, and occasional beam maintenance.

76

PRELIMINARY ANALYSIS OF

EXPERIMENTAL DATA FROM

E21072

5.1 Data Processing

For every decay event that occurs in the GADGET II TPC each CoBo sends a single data

frame of pad traces per AsAd (see Section 3.1.2 for details of the GET system). We operated

in partial readout mode, so only those pads that are hit have traces that are recorded. Figure

5.1 shows the traces on one AGET chip from a typical TPC event. Each trace spans 512, 10

ns time bins and the integral of each trace is proportional to the energy deposited on each

pad; thus, the abscissa of each peak indicates the time of arrival for the charge on that pad.

The trace data from each AsAd is output as a separate raw data file, and these files

are subsequently merged and converted to HDF5 files for analysis [53]. During this data

transformation channel signals are mapped to the pad plane layout. Additionally, a peak

detection algorithm finds the time bucket in which each channel peak is located, then the

drift time of the detector is used to extract the z-coordinate for that charge deposition. Once

the merge is complete, the resulting HDF5 file contains the x,y,z hit pattern, the max charge

per pad, the time of the pad hit, and the summed trace data as an array with 512 elements

(one value per time bucket).

These HDF5 files can then be used for several different types of analysis/visualization.

77

One can use the x,y hit data to construct 2D projection images of particle tracks representing

the components transverse to the beam axis. Additionally, by normalizing the charge per

event, the relative charge density along the track can be seen. This allows us to see clear

Bragg peaks for each event regardless of the total energy of that event (see Figure 3.7).

The reconstruction of the z-coordinate during merging also allows for the visualization of

a 3D dimensional point-cloud for the event as can be seen in Figure 3.8. With the point-cloud

generated we can then apply outlier removal algorithms to clean up the event tracks. As is

detailed in Section 3.2.1, noise reduction was achieved by removing points in the point-cloud

from the main track cluster using Hotelling’s T-squared and Squared Prediction Error (SPE)

algorithms sequentially. The Hotelling method identifies outliers by their significant distance

from the mean considering variance, while SPE flags points with high prediction errors. A

point in the cloud is considered an outlier only if both methods agree, ensuring accurate

elimination of noise, and/or beta particle ionization in the data.

The data can be further cleaned by instituting veto conditions. There are 8 veto pads

that surround our main detection pads, and these veto pads are essential for improving data

quality. They enable the rejection of events that fall outside the main detection area, ensuring

that only events that deposit all of their energy in the main area of the pad plane are analyzed.

Throughout the experimental campaign, a front-end veto condition was applied (detailed in

Section 4.3.6.1) to preclude numerous events that fell outside this detection area. Despite

this measure, some events could still bypass the initial filter, necessitating the exclusion of

any event with veto pad signals surpassing a set threshold via software. Additional unwanted

events are removed by implementing integrated charge, and track length thresholds, above

which the events are removed. This event selection works to eliminate nonphysical events

caused by detector noise, such as sparks.

78

Figure 5.1: Traces on a single AGET chip for a typical TPC event. Each trace represents
the signal from one pad. Each trace spans 512, 10 ns time bins and the integral of each trace
corresponds to the energy collected.

79

5.1.1 Improved Point-cloud Reconstruction

The process delineated above constructs the 3D point clouds for our events by creating a

point based on the max charge per pad. This means that events that are very perpendicular

relative to the pad plane would have very sparse point clouds, which can affect the fitting of

their range.

To fix this issue we improved the reconstruction of the z-coordinate by leveraging and

modifying software originally developed by the ATTPC group at Michigan State Univer-

sity. This adapted software utilizes a Gaussian Mixture Modeling approach to enhance the

z-coordinate reconstructions. This statistical model fits multiple Gaussian distributions to

the signal data, and effectively captures the nuances of charge distribution over time. Each

Gaussian component can represent a localized charge deposition, with its mean correspond-

ing to the time bucket of peak charge and its variance indicating the spread of the charge

distribution. By ensuring the integrated charge of all Gaussians matches the total observed

charge, this method not only preserves the total charge information but also enhances the

spatial resolution of the reconstructed tracks. We introduced additional routines for inter-

polating between points on a trace-by-trace basis. This modification significantly improved

the reconstruction quality, allowing for the accurate depiction of tracks even for events per-

pendicular to the pad plane. Figure 5.2 shows a few events that are almost completely

perpendicular to the pad plane, and what the point clouds look like before and after this

method is applied.

80

Figure 5.2: Point-cloud representations of particle events in the GADGET II TPC that
occurred perpendicular relative to the pad plane (xy-plane). Left) Sparse point-clouds gen-
erated using only the max charge per pad. Right) Dense point-clouds generated using a
combination of Gaussian Mixture Modeling transforms and additional interpolation rou-
tines.

81

5.2 Energy Spectrum

Among the first data we looked at from the experiment were energy spectra from the TPC.

These spectra are generated by integrating the charge from all pads and across all good

events (all veto conditions mentioned above were applied). The main normalization peak in

these spectra is the salient ∼800 keV peak. This peak is a beta-delayed proton from 20Mg

(see Figure 5.3), it has a well known branching ratio, and we have a near 100% efficiency for

detecting them. Integrating this peak for a later experimental run with the more iostopically

pure beam and improved intensity (Section 4.4), and using the well known branching ratio,

shows that a typical run contains ∼500,000 20Mg decays. From this we can estimate that

around 80 x 106 20Mg decay events were recorded in the TPC, with about half of this having

been searched for rare events, so far (see Chapter 7). While a precise normalization won’t

be completed until we finish our rare event search of the data, we can still use this peak to

calibrate the energy spectrum.

A calibrated energy spectrum from the TPC can be seen in Figure 5.4. The peaks in

the spectrum were modeled using exponentially modified Gaussian functions, and the figure

shows a composite function of those fits. This energy spectrum reveals several notable

peaks and features that merit discussion. Some of these characteristics are currently under

investigation, highlighting the ongoing exploration and analysis efforts in understanding the

underlying phenomena. For example, the small shoulder at 0.31 MeV could in part be due

to wall-effect, where decays take place close to the TPC’s anode or cathode, causing particle

tracks to end prematurely, and thus only deposit part of their energy in the active region.

Then the event trigger energy threshold causes the shoulder to terminate slightly above zero

MeV. But this part of the spectrum requires careful consideration to differentiate between

82

Figure 5.3: Simplified decay scheme showing 797 keV beta-delayed proton from 20Mg, which
serves as the main normalization peak in our energy spectrum. Figure adapted from [54].

83

Figure 5.4: Energy spectrum from the TPC representing one hour worth of data taken during
experiment E21072. Peaks were fit using exponentially modified Gaussian functions, and the
orange dashed line is a composite function of those fits displayed to highlight key features
in the spectrum.

signal and potential background effects.

The peak at 0.43 MeV is attributed with high confidence to the 537 keV 16O recoil,

stemming from the Ecm = 2.69 MeV beta-delayed alpha emission from 20Na decay [55].

This can occur when neutralization is not fully achieved, and atoms carrying a positive

charge drift towards, and decay on, the detector’s cathode.

In these instances, only the

energy from either the emitted alpha, or the 16O recoil will deposit energy in the active

volume of the TPC (as the decay is back to back). The observed discrepancy in energy can

be ascribed to a significant pulse-height defect, which is exacerbated given that these events

always drift the full length of the detector. The pulse height defect in gaseous detectors refers

to the lower-than-expected electrical signal produced when ionizing radiation is detected, due

84

to energy losses from recombination, attachment, diffusion, excitation of gas molecules, and

the presence of quenching gases. These factors prevent some of the energy deposited by

ionizing particles from being fully converted into measurable ionization signals, affecting the

accuracy of energy measurement and particle identification in radiation detection systems

[56]. At the relevant energies there appears to be a ∼100 keV shift down in an energy for

heavy recoils, and ∼70 keV shift down for alphas due this effect.

The feature at 1.01 MeV could be a confluence of several phenomena, including the 1056

keV beta-delayed proton from 20Mg and the 1108 keV 16O recoil. The latter originating from

the Ecm = 5540 keV alpha emission from 20Ne. The slightly lower observed measurement

can once again be ascribed to the pulse height defect.

The peak at 1.68 MeV is identified as the well known beta-delayed proton from 20Mg.

At 2.08 MeV, the spectrum shows what is likely a single alpha particle resulting from the

Ecm = 2.69 MeV alpha decay on the cathode. Once again considering the impact of the

pulse height defect on the observed energy.

Finally, the feature at 2.44 MeV appears to encapsulate the combined energies of the

0.43 MeV and 2.08 MeV peaks. This suggests it could represent the Ecm = 2.69 MeV peak

inclusive of both particles—minus the pulse height defect—for 20Na decay occurring within

the bulk volume. This interpretation implies a complex interplay of emissions and detector

effects that are crucial for understanding the decay mechanisms at play.

This analysis is ongoing, and the hypotheses outlined above will undergo further exami-

nation. This will involve applying gates on protons and alphas within the two-dimensional

histograms of range versus energy, as detailed in the subsequent section. Moreover, we

will leverage the comprehensive functionalities of the GADGET II system to explore these

hypotheses, particularly through the analysis of particle-gamma coincidences. This dual

85

approach aims to provide a thorough investigation of the phenomena under study.

5.2.1 Energy Sharing

A critical aspect of the E21072 analysis involves determining the energy sharing in two-

particle events, which is key to identifying the specific type of two-body decay that has

occurred. For instance, while p-α decays from 20Mg and 21Mg may occur at similar energies,

the energy sharing between the decay particles is markedly different. To glean a preliminary

understanding of the energy distribution, one can extract the total energy of an event, fit a

3D point cloud of the event’s trajectory, and project the track’s energy onto this line. The

projection is done with a kernel density estimator with Gaussian kernels. Analysis of the

resulting curve yields insight into the energy distribution along the track, shedding light on

the energy sharing dynamics in multi-particle events. An illustrative example of this method

applied to a 21Mg p-α candidate event from the dataset is depicted in Figure 5.5.

It should be noted, however, that this approach is part of a broader analytical framework.

A more detailed analysis, which will utilize the full spectrum of raw data to provide a

nuanced quantitative assessment of an event’s characteristics, is currently in development.

Such comprehensive analysis will be reserved for a select subset of particularly significant

events due to its data-intensive nature, while the point-cloud methodology offers efficiency

when dealing with larger datasets.

5.3 Range vs Energy Histogram

As is discussed in Section 3.2.1, Principal Component Analysis (PCA) was utilized to model

tracks by determining lines and planes that optimally represent the data through least

86

Figure 5.5: Probability density histogram displaying the energy projection onto the point-
cloud fit line for a 21Mg p-α candidate, with a total energy of ∼1.78 MeV. The energy
contributions of particle 1 (∼860 keV) and particle 2 (∼920 keV) are represented by the
blue and orange dotted lines, respectively. The composite fit of the energy distribution is
indicated by the red dashed line. Below the main panel are the residuals of the fit.

87

Figure 5.6: Range vs Energy Plot for Experiment 21072 (1 hr run) in linear scale. A few key
peaks are highlighted via red arrows, and the distinct proton and alpha bands are marked-
out with purple lines.

squares optimization. Within this framework, the primary and secondary principal compo-

nents represent the track’s length and width, respectively. The track length is determined,

followed by the aggregation of charge across all pads, which is subsequently converted into

energy. With the range and energy of each event determined we can generate a range vs

energy histogram from the experimental data.

Figure 5.6 represents such a plot, derived from a single, 1 hour run from experiment

E21072. This plot illustrates how decay events manifest as densely populated clusters in

both range and energy. As a result, range vs. energy plots serve as a potent tool for gating

88

on specific decay events. Additionally, protons and alphas form distinctive bands on these

plots, reflecting their unique interactions with the gaseous medium based on differences in

mass and charge. Importantly, this characteristic separation gives us a powerful method for

defining a search region to find our events-of-interest that must lie between these bands.

This capability is further explored in the following subsection (Section 5.3.1).

Additionally, comparative analyses of range versus energy histograms, as a function of

the event angle relative to the pad plane, provide significant insights. Figure 5.7 exhibits

a sequence of range-energy histograms from a single experimental run. Each histogram

represents a distinct angular segment, demarcated by 10° intervals, with the complete series

spanning from 0° to 90°. These histograms illustrate that events with higher energies, which

correspond to elongated particle trajectories, are predominantly observed at more acute

angles. This observation is due to the increasing likelihood for longer tracks to be vetoed the

more parallel they are with respect to the pad plane. Consequently, events of higher energies

tend to exhibit diminished range resolution. This effect arises because the resolution in the

xy-plane surpasses that of the z-axis, the latter of which relies on the reconstruction of the

z-coordinate. This effect causes the range distribution to be more smeared out for longer

tracks as can be seen in Figure 5.8.

5.3.1 Search Region

The ultimate goal of experiment E21072 is to measure 20Mg(βpα)15O events, through the

key 15O(α, γ)19Ne resonance. This process is marked by the near-simultaneous emission

of a proton and an alpha particle (Ch. 2). The proton energy in this coincidence event

is expected to be 1.21+0.25

−0.22 MeV [30]. This was determined previously by analyzing the

Doppler-broadened 4.03 MeV gamma peak from the recoiling 19Ne nucleus. By simulating

89

Figure 5.7: Range vs energy histograms for event tracks oriented between 0° to 90° with
respect to the pad plane by applying angular cuts of 10°. Note that longer range events are
more prevalent at higher angles as they are less likely to be vetoed when more perpendicular
to the pad plane.

90

Figure 5.8: Composite of range histograms from a single experimental run, organized into a
grid. Each histogram corresponds to a different 10° angular segment relative to the pad plane,
ranging from 0° to 90°. The figure demonstrates a more confined range distribution for events
occurring parallel to the pad plane, as their range is determined predominantly from the xy-
plane measurements.
In contrast, events at steeper angles exhibit broader distributions,
indicative of longer tracks that necessitate substantial z-coordinate reconstruction, leading
to a spread or smearing effect in the observed range.

91

this broadened gamma peak and adjusting the proton energy in the simulations to match the

observed data, the energy of the emitted proton from 20Na could be inferred (see Figure 5.9).

These protons will have a range in 800 Torr P10 gas of 2-3 cm. The alpha particles in the

coincidence event, along with the corresponding 15O recoils, will deposit a total energy 506

keV over a extremely short range (<4mm). Given the energies and ranges of the particles, an

identifying feature of the events-of-interest is the ratio of the track length to the total energy

deposited, which is distinct from single-proton (cid:0)20Mg(βp)(cid:1) and single-alpha (cid:0)20Mg(βα)(cid:1)

events. Thus, these p−α events occupy a specific region on the range vs. energy plot,

nestled between the distinctly separate proton and alpha bands as illustrated in Figure 5.6.

As such, we can apply a well defined search region to the range vs energy histogram based on

this ratio and the expected total energy of 1.7 MeV. Only searching for our events-of-interest

in this region eliminates the vast majority of background events (>95%). Figure 5.10 shows

such a search region that extends 2 standard deviations in both range and energy.

Even though defining this search region markedly narrows down the volume of data

we must sift through to isolate the p-α events, the remaining dataset is still substantial,

demanding significant human effort for manual examination. This challenge presents an

ideal opportunity to employ machine learning techniques to streamline our search process.

The application of machine learning algorithms in enhancing our search efficiency is explored

in depth in the subsequent chapter (Ch. 7).

5.4 Gamma Spectrum

The experimental setup for E21072 utilized the GADGET II TPC (with a mesh trigger),

surrounded by DEGAi for gamma-ray detection. The calibration of the germanium detector

92

Figure 5.9: Upper panel: A 4.03 MeV Doppler-broadened gamma peak fit with the 1.21
MeV CoM energy. Lower panel: Displays residuals from subtracting the fit function from
the data. Figure from [30].

array was accomplished using 152Eu and 60Co sources, which were affixed to the exterior of

the central region of the TPC chamber.

A calibrated gamma spectrum from 1 run (1 hour worth of data) can be seen in Figure

5.11. A few key peaks from 20Mg decay are labeled in the spectrum, including the prominent

984 keV gamma from 20Na, and a known peak from 20Ne that occurs following the beta-plus

decay of 20Na.

To ensure that the 20Mg beam used during the experiment was in fact being deposited

in the center of the active volume, we can view the mesh trigger - gamma time distribution,

as can be seen in Figure 5.12. This time distribution was recorded in 100 ns intervals. The

resulting dataset was categorized into three subsets: the total count spectrum (red), events

gated on the 511 keV gamma peak indicative of positron annihilation (blue), and events

93

Figure 5.10: Range vs. Energy Plot for Experiment 21072 (1-hour run) displayed on a linear
scale. The plot illustrates the designated search region, encompassing 2 standard deviations
in both range and energy dimensions. This search region is targeted for isolating p-α events
of interest within the dataset.

94

Figure 5.11: Calibrated gamma spectrum taken with DEGAi over 1 run. Prominent peaks
associated with the decay of 20Mg are identified and annotated.

gated on the combined energies of 238, 275, and 1298 keV gamma rays (green), which are

characteristic of specific nuclear transitions in the decay of 20Mg. The time calibration was

centered at channel 400, designated as ”zero,” which means the TPC cathode signal would

occur at 7.2 microseconds (the drift time of the detector), equivalent to channel 472. The

centered distribution of the gates at 3.6 microseconds suggests that there was optimal ion

placement within the center of TPC.

All the gamma spectra from the experiment are in the process of being sorted, calibrated,

and analyzed. Part of this analysis will include looking at particle-gamma coincidences by

gating on certain energies. For example, we plan to gate on the 4.03 MeV characteristic

gamma from 19Ne. Looking at the proton spectrum in coincidence with this prompt-gamma

should allow for a more direct and precise measurement of the 20Na proton energy feeding

this astrophysically important state.

95

Figure 5.12: Mesh trigger - gamma time distribution from experimental Runs 85-86 using
the DEGAi setup. The data, binned at 100 ns per channel is shown with the total event
count (red), events gated on 511 keV gamma rays (blue), and events gated on the sum of
238, 275, and 1298 keV gamma rays (green). Channel 400 represents the zero-time reference
point, and the TPC’s ion centering is evidenced by distribution peaks at 3.6 microseconds.

5.5 Development of Analysis Software

To enhance the efficiency of analyzing TPC data, we developed a software analysis tool.

Figure 5.13 showcases the main interface of this analysis framework. The interface is or-

ganized with the primary analysis categories on the left in what we will refer to as the

navigation column, and corresponding sub-options emerge on the right upon selection of a

main category (see Figure 5.14). The tool offers flexibility in data handling, allowing for

individual run analysis or aggregate analysis through the “Sum Runs” feature located at the

base of the navigation column. After inputting a run number(s), the “Create New Files”

radio button is enabled, facilitating the pre-processing of the data via the application of

length and integrated charge vetoes, pad and point cloud thresholds, and outlier parameter

adjustments. The pre-processed files are organized and saved in a directory reflecting the

selected parameters. Once these files are generated, choosing the ”Use Existing Files” option

96

Figure 5.13: Main view of the GADGET II TPC analysis interface. Individual runs can be
analyzed (as is the case for run 273 in the image), or runs can be compiled via the “Sum
Runs” button at the bottom of the navigation column. Each option in the navigation column
opens up additional analysis features in that context on the righ-side of the interface (see
Figure 5.14).

enables the selection of a directory containing pre-processed data. This action unlocks the

full suite of functionalities available in the navigation column, with further details provided

below:

Energy Spectrum: The “Energy Spectrum” feature offers a user-friendly interface

for generating energy histograms. Users can specify the desired number of bins for the

histogram and initiate the generation process by clicking “Generate Spectrum.” Additional

customization includes setting lower and upper threshold values, which are visualized on the

97

Figure 5.14: An example of sub-options that are available when selecting a main option from
the navigation column. In this case “Range vs Energy” is selected allowing for the creation
of a range vs energy plot, plotting a point on that plot, applying a polygon or static cut
on the plot, viewing previous cuts, or projecting cuts to an axis for fitting and resolution
determination.

98

plot as two vertical lines, alongside a count of the data points within the selected range.

For peak analysis, the “Quick Gaussian Fit” option provides an expedited method to

fit a Gaussian to any peak within the selected range. For a more detailed analysis, the

“Initial Guesses for Multi-peak Fit” feature enables users to engage directly with the plot.

By actively clicking on the plot, users can set initial guesses for the peak parameters, such

as peak amplitude and standard deviation. This interactive method significantly enhances

the fitting process by allowing precise and intuitive placement of initial guesses. The chosen

fitting functions and the user-defined initial parameters facilitate a tailored fitting experience.

The output is a plot with all identified peaks clearly labeled, and the corresponding fit

parameters are exported to a separate file for in-depth analysis. The output fit parameter

file can be re-imported to refine fits or adjust parameters, with the option to fix specific

parameters by marking them with an asterisk. These features ensure a comprehensive and

flexible approach to spectrum analysis, catering to both quick assessments and detailed

multi-peak fitting.

Range vs Energy: The “Range vs Energy” feature provides a dynamic interface for

creating two-dimensional histograms of range versus energy. Users can define the desired

number of bins for this histogram and then generate the visualization by clicking the “Plot

Range vs Energy” button. A notable feature allows for the input of specific event number(s),

which are then highlighted on the histogram, aiding in the identification of their positions

within the 2D plot.

A particularly versatile functionality is the “Polygon Cut” option. Activating this feature

opens the range vs energy plot, where users can interactively draw a polygon directly on the

plot to define a custom selection region. Only data within this polygonal boundary will be

selected for further analysis. The software then proceeds to generate data-fused images for

99

the selected events (detailed in Section 7.6), which are displayed in an intuitive viewer. This

viewer displays both individual images and grid views of the images, and allows you to flag

and store any interesting events, enhancing the examination process.

Moreover, the interface includes predefined “1 Std. Cut” and “2 Std. Cut” buttons for

quickly applying standard deviation-based selection criteria, aligning with the search regions

discussed in Section 5.3.1. Users have the flexibility to navigate through previously applied

cuts, revisiting selected events or projecting the cut data onto the x or y axis for detailed

fitting analysis. This capability not only streamlines the identification of relevant data points

but also facilitates the derivation of resolutions from the processed data.

3D Event Plot: The “3D Event” feature offers a way to explore individual events

within the dataset through 3D visualization. Upon specifying an event number, users can

generate and view the event’s 3D point cloud representation. Two visualization options are

available to cater to different analysis needs. The “Original 3D Point Cloud” option presents

the event’s point cloud as reconstructed from the HDF5 file, offering a direct view of the

spatial distribution captured during the experiment (refer to Section 5.1.1 for details on

point cloud reconstruction). Whereas the “Enhanced 3D Point Cloud” option offers a more

refined visualization, as it applies additional interpolation techniques to the original point

cloud data. The result is a denser and smoother point cloud that outlines the event’s tracks

with greater continuity and clarity.

Figure 5.15 illustrates a comparison between these two point cloud visualizations for a

proton track event. This capability not only enhances the visual examination of the data

but also aids in the qualitative assessment of event characteristics.

Track with Trace: The “Track with Trace” feature enables users to delve into the

analysis of specific events by generating data-fused images, as detailed in Section 7.6. This

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Figure 5.15: 3D point clouds for a typical proton track from experiment E21072. Left)
Original point cloud from HDF5 file generated after point cloud reconstruction. Right)
Dense point cloud that implements additional interpolation to improve 3D visualization.

tool not only visualizes the event but also offers advanced functionality for analyzing the

temporal dynamics of particle tracks.

Upon selecting an event, users can engage in interactive analysis by fitting the trace, or

time projection, of the event. This is accomplished by clicking directly on the histogram,

allowing for the intuitive placement of initial guesses for the fit parameters. This hands-on

approach facilitates a preliminary understanding of the event’s structure and dynamics.

Moreover, the feature extends to fitting the particle track itself, enabling the projection

of the track’s energy onto the fitted line. Analyzing the resultant curve provides insights

into the energy distribution along the track, which is particularly useful for understanding

energy sharing between two particles in events involving multiple particle emissions.

Track Angles: The “Track Angles” feature enables the examination of energy spec-

tra and range versus energy plots through the lens of angular distribution. Users have

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the flexibility to either define a specific angular range for detailed analysis or to explore a

comprehensive overview of the data across varying angles via a systematic grid of images.

This function allows for the investigation of how events vary as a function of angle with

respect to the pad plane, providing insights into the directional dependence of these events.

For instance, users can generate and compare histograms for different angular segments,

offering a visual representation of the angular dependence of range and energy. As an

illustrative example, Figure 5.7 presents range versus energy histograms from a single run,

where each plot is segmented into 10° angular intervals ranging from 0° to 90° relative to the

pad plane.

ConvNet Track ID: The “ConvNet Track ID” feature introduces a powerful applica-

tion of machine learning to the analysis process, specifically utilizing Convolutional Neural

Networks (CNNs) for event classification. Upon selecting a subset of the data via previously

established cuts, users have the option to employ either a single CNN model or an ensem-

ble of CNNs, detailed in Section 6, to automatically process and classify data-fused images

associated with the subset (refer to Section 7.6). This process is fully automated, with the

CNNs evaluating each image to determine its likelihood of belonging to predefined classes.

Following the classification process, the interface dynamically updates to present a series

of buttons, each representing a different event class as determined by the CNN model(s).

Users can then interact with these buttons to filter and visually inspect all images predicted

to belong to a particular class, facilitating an efficient review and further analysis of the

data.

This integration of ConvNet technology with the analysis software streamlines the clas-

sification and review process, significantly enhancing the ability to quickly identify and

categorize complex event patterns within the data. This method not only accelerates the

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analysis but also improves the accuracy of event classification, leveraging the sophisticated

pattern recognition capabilities of CNNs.

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OVERVIEW OF RELEVANT

MACHINE LEARNING

ALGORITHMS

6.1 Convolutional Neural Networks

Machine learning (ML) represents a significant stride in the field of artificial intelligence,

and offers the ability to automate the extraction of knowledge from data. Among its many

applications, ML excels in pattern recognition and predictive analytics. The essence of

machine learning lies in its capability to learn and improve from experience without being

explicitly programmed for specific tasks. This adaptability makes it a powerful tool across

a wide array of domains.

In recent years, the focus has shifted towards deep learning, a subset of ML, which

employs neural networks with multiple layers. These multilayered structures, known as

deep neural networks, are adept at handling vast amounts of data and extracting complex

patterns. Convolutional Neural Networks (CNNs), a class of deep neural networks, have

gained prominence, particularly in the realm of image processing and classification [57].

In the context of this thesis, the focus on CNNs is particularly pertinent due to the nature

of the experimental data gathered. The data for this thesis experiment was obtained using a

Time Projection Chamber (TPC) (see Chap. 3 for details on TPCs). TPC data can be visu-

alized as 2D images, as illustrated in Figure 3.7. This representation aligns perfectly with the

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capabilities of CNNs, making them the most appropriate choice for analyzing and extracting

valuable insights from the dataset [58]. By employing CNNs, we can harness the computa-

tional efficiency and superior performance of these networks, particularly in image-related

tasks. Furthermore, the availability of a wide range of pre-trained models allows for lever-

aging and fine-tuning these models to suit our specific dataset and tasks, thereby enhancing

the model’s performance and reducing the need for extensive computational resources.

In the following sections, we delve into the fundamental components and strategies in-

volved in optimizing CNNs, ensuring that they are well-equipped to handle the intricacies

of the dataset in question.

The subsequent sections/subsections are adapted from our other work that is currently

in preparation [59]. These adaptations are used with permission and have been modified to

fit the context of this thesis.

6.1.1 CNN Building Blocks

Convolutional Layers: The convolutional layer stands as the core component of a CNN,

and it is primarily responsible for feature extraction from images. An image input to this

layer is typically has dimensions n×n×nc, where n represents the image’s width and height,

and nc denotes the channel count (for instance, nc = 3 in RGB images).

Within a convolutional layer, several filters (or kernels) are present, each possessing

adjustable parameters. These filters are characterized by dimensions f × f × nc, with f

being smaller than n. Common values for f include 3, 5, or 7. These smaller sizes allow the

filters to have a compact receptive field, and provide computational efficiency. Additionally,

odd-sized filters have a central pixel, allowing for symmetric operations around the pixel

being processed, thus ensuring a uniform application of the filters across the input data.

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Figure 6.1: An illustration of the convolution process. The input is a 7 x 7 image with a 3
x 3 filter. The output feature map has dimensions 5 x 5 [60].

The application of these filters across the entire image facilitates the extraction of a diverse

set of features, with each filter targeting different characteristics of the image.

The essence of the convolution operation lies in a sliding dot product mechanism. As the

filter traverses the input image, a dot product computation occurs, treating both the filter

and the covered image region as vectors. This process is visually illustrated in Figure 6.1,

showcasing the convolution operation on a simplified, single-channel input. The resultant

feature map post-convolution possesses a depth equal to the number of filters utilized and

dimensions given by (n − f + 1) × (n − f + 1).

Activation Layers: The role of an activation layer is to introduce non-linear capabilities

into the Convolutional Neural Network (CNN). It receives the output from a convolutional

layer and applies a non-linear function to these inputs. This non-linearity is crucial as it

allows the CNN to capture complex patterns and relationships in the data that go beyond

what linear operations can achieve.

Among the various activation functions, two are particularly prevalent. The first is the

sigmoid function, σ(z) =

1

1+e−z . This function maps any input to a value between 0 and

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Figure 6.2: Illustration of reducing the dimensions of a feature map using 2 x 2 max pooling
[63].

1, making it especially useful for models where output interpretation as a probability is

beneficial. The second is the Rectified Linear Unit (ReLU) function, R(z) = max(0, z).

ReLU has gained popularity due to its computational efficiency and the ability to mitigate

the vanishing gradient problem often encountered in deep networks [61].

Pooling Layers: Pooling layers are integrated into CNNs following the convolutional

and activation layers. The purpose of these layers is to infuse the network with robustness to

minor positional changes and variations within the input. This is achieved by downsampling

the output feature maps from preceding layers, which fosters local translation invariance and

concurrently diminishes the computational demand for the layers that follow.

Max pooling stands out as a commonly used pooling technique. In this approach, the

principal idea is to traverse the feature map with a defined window and stride, and at each

step, select the maximum value within the window. This process effectively distills the most

salient feature within the observed region of the feature map, thereby capturing the most

critical aspects and discarding the rest. The operation of max pooling is visually depicted

in Figure 6.2, providing a clear example of how this technique condenses the information in

the feature map while maintaining the most prominent features [62].

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Fully Connected Layers: The Fully Connected (FC) or dense layers come into play

after the convolutional and pooling layers have completed the feature extraction phase. These

layers are instrumental in interpreting the features extracted previously and mapping them

to specific categories in the context of the classification task [62]. The data flowing from

the preceding convolutional or pooling layer is transformed into a one-dimensional array

and forms the input for the FC layers. Within these layers, a comprehensive network of

connections is established, wherein each neuron (or activation unit) is linked to every neuron

in the layer that follows, creating a densely interconnected structure. The culmination of

these layers is typically marked by an FC layer that contains a number of neurons equivalent

to the number of classes in the classification problem at hand. Subsequently, a softmax

activation function is applied,

SoftMax(zi) =

ezi
j ezj

(cid:80)

,

(6.1)

where zi represents the input to the softmax function for class i, and the denominator is

the sum of the exponentials of all the class inputs, ensuring normalization. This function

converts the raw output scores from the network into output values in the range (0, 1),

making them interpretable as probabilities. These probabilities signify the likelihood of the

input being categorized into each class, as illustrated in Figure 6.3.

6.1.2 The VGG16

The VGG16, a distinctive CNN architecture, has demonstrated its prowess in handling

TPC data [58]. This robust neural network boasts an extensive array of over 130 million

parameters. Its capabilities were recognized globally when it clinched victory in the ImageNet

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Figure 6.3: Representation of fully connected layers [64]. The input, after being flattened,
passes through 3 FC layers. The final layer utilizes a softmax activation function to yield
probabilities for each class.

competition in 2014, cementing its status as a premier choice for image classification tasks.

Figure 6.4 provides a schematic representation of the VGG16 structure. The architecture

encompasses 16 weighted layers: 13 of these are convolutional layers, while the remaining

3 are fully connected layers. In the convolutional segments, ReLU activations are utilized.

This strategic choice is inspired by ReLU’s effectiveness in mitigating the vanishing gradient

dilemma, a prevalent issue with other activation functions, such as the sigmoid. The VGG16

is designed to handle 224 x 224 x 3 dimension RGB images. It introduces a padding of one

pixel preceding each convolutional layer, a design nuance that not only preserves the spatial

dimensions of the image post-convolution — thereby facilitating the construction of a deeper

network — but also boosts the network’s efficacy by ensuring comprehensive weighting of

the image borders. The network’s architecture proceeds with the integration of max pooling

layers, strategically placed to downsample the feature maps obtained from convolutional and

activation stages. The culmination of the VGG16’s architecture is marked by a trio of fully

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Figure 6.4: A depiction of the VGG16 architecture, illustrating the orderly sequence of layers
from the initial input to the final output [65]. The upper segment of the Figure elucidates
the journey from the raw input through a series of convolutional and pooling layers. The
lower segment visualizes the transformation of an input image as it traverses through the
network, delineating the evolution in dimensions and depth of the feature maps at various
junctures.

connected layers, with the final layer employing a softmax activation function, which allows

the network to perform classification tasks [57].

6.1.3 Fine-Tuning

The technique of fine-tuning is employed to harness and augment the capabilities inherent

in the VGG16 architecture. Fine-tuning is a form of transfer learning that involves adapting

a pre-trained model to undertake a new, albeit related, task [66].

In executing this strategy, we begin by retaining the weights of the initial layers from the

pre-trained model. This leverages the network’s established expertise in feature extraction,

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preserving the core insights embedded in the network’s architecture. Following this, we

incorporate a custom classifier tailored to our specific dataset. This classifier is structured

with three fully connected layers, each initialized with random weights, and culminates in

a final layer that contains a number of nodes equivalent to the distinct categories in our

classification task. During the phases of training and validation, the focus is on adjusting

only the weights associated with this newly introduced classifier. It’s noteworthy that our

experimental findings revealed that retraining the entirety of the network’s weights did not

lead to a marked enhancement in performance. Instead, it incurred a significant escalation

in the duration of the training process. This observation further reinforces the practicality

and efficacy of the fine-tuning methodology.

6.2 Strategies for Optimal Model Training

Mastering the art of CNN-based detection in extensive datasets, particularly when dealing

with the challenge of identifying rare events, necessitates a nuanced and precise approach.

The realm of TPC data perfectly encapsulates this challenge, presenting a highly imbalanced

dataset where events of interest can be notably scarce (see Chap. 7 for more details).

Attaining peak performance from a model in such conditions is contingent upon various

critical factors. Paramount among these is the careful selection of hyperparameters, which

profoundly impact the model’s performance. This is especially true given the vulnerability

of CNNs to overfitting, a risk that becomes markedly acute when dealing with sparsely

occurring target events. In such cases, the model might exhibit remarkable accuracy on the

training data but falter in its ability to generalize to new, unseen datasets.

To deal with these complexities, adopting a comprehensive approach to model training is

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indispensable. This involves meticulous efforts in data preparation, strategic data splitting,

the deployment of regularization strategies, and the careful choice of a loss function. Par-

ticularly in the context of the significant imbalance characteristic of TPC data, employing

strategies such as class reweighting, oversampling, and undersampling is not merely bene-

ficial but imperative. These methods are instrumental in ensuring that the model retains

its sensitivity towards sought after rare events while bolstering its resilience against false

positives. Additionally, the incorporation of advanced methodologies, like active learning,

serves to further refine the model. Through an iterative process, active learning progressively

enriches the training dataset, guaranteeing the thorough capture and precise classification

of each rare event. This section delves into these methodologies and sheds light on how

each methodology significantly contributes to the ultimate goal of accurately detecting rare

events.

6.2.1 Training, Validation, and Testing Splits

To effectively train a CNN model, one must first hand-label a substantial number of images.

This carefully annotated dataset can then be strategically segmented into three distinct

subsets: training, validation, and testing. Such segmentation is a cornerstone in the edifice

of robust model development. The Training Set will typically encompass 80% of the labeled

dataset, and serves as the primary learning source for the model. Through iterative exposure

to this dataset, the model fine-tunes its internal parameters, like weights and biases, aiming

to diminish the disparity between its predictions and the actual labels.

The Validation Set, typically representing 10% of the data, functions as a pivotal

checkpoint within the training regime. Subsequent to each training epoch (an entire cycle

through the training data) the model’s performance is assessed against this validation set.

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This phase is crucial, not for further training of the model, but to evaluate its efficacy on

unseen data. Insights gleaned from the validation set performance are instrumental in fine-

tuning the model’s hyperparameters. In essence, while the training set enables the model to

learn, the validation set serves as a check of the model’s capabilities, guiding us in optimizing

its configuration.

Finally, the Testing Set, often comprising 10% of the data, is safeguarded for the final

phase of the training process. This subset provides an unbiased assessment, offering a genuine

metric of the model’s potential performance in real-world settings. The employment of this

tripartite data split orchestrates a holistic training approach, delicately balancing the model’s

learning phase with the imperative need for thorough evaluation and fine-tuning.

6.2.2 Loss Function

Central to the evaluation of a model’s predictive accuracy is the loss function, also known as

the cost or objective function. This function measures the discrepancy between the model’s

predictions and the actual observations, quantifying the error in terms of a positive value.

The objective is to minimize this value, where a lower loss function value indicates a stronger

alignment between the model’s predictions and the true labels, reflecting higher accuracy.

In the context of our classification challenge, Cross-Entropy Loss emerges as the pre-

ferred metric. Its suitability for classification scenarios, particularly binary classification, is

well-documented [67]. In binary classification, where the true label y can assume values of 0

or 1 and the predicted probability by the model is p, the Cross-Entropy Loss is defined as

L(y, p) = −y log(p) − (1 − y) log(1 − p).

(6.2)

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This formulation encapsulates the penalty for the divergence between the predicted prob-

abilities and the actual labels, effectively guiding the model towards minimizing prediction

errors.

For scenarios encompassing multi-class classification, the expression for cross-entropy loss

evolves to accommodate multiple classes, as illustrated by

L(y, p) = −

C
(cid:88)

i=1

yi log(pi).

(6.3)

Here, C symbolizes the total number of classes, yi denotes the actual label for class i, and

pi signifies the predicted probability that a given sample falls within class i.

The guiding aim during the model’s training phase is the minimization of this loss func-

tion. Achieving a lower value for the loss function is tantamount to ensuring that the model’s

predictions are in closer harmony with the true labels, thus enhancing the model’s predictive

precision.

6.2.3 Optimization and Learning Rate

The optimization process serves as the navigator of the model’s training journey, guiding

the model toward the apex of performance amidst a complex terrain of potential outcomes.

This journey involves the methodical refinement of the model’s parameters to curtail the loss

function. In this pursuit, we use the Stochastic Gradient Descent (SGD) optimizer [68].

SGD updates the model’s weights incrementally, utilizing subsets of data, thereby enhancing

the efficiency of the optimization process. It computes the gradient of the loss function in

relation to each parameter and nudges the weights towards a direction that diminishes the

loss. The extent of these parameter updates is modulated by the learning rate, a pivotal

114

hyperparameter that dictates the step size in the optimization journey.

To amplify the effectiveness of SGD, the process can be infused with momentum. Mo-

mentum serves as a strategic tool, enabling the optimizer to deftly traverse local minima

and sidestep potential stagnation points by factoring in past gradients. It introduces a ve-

locity component, bolstering the optimizer’s descent in directions of sustained gradient and

mitigating the propensity for oscillatory movements.

Moreover, to ascertain that the learning rate is consistently fine-tuned throughout the

training voyage, one can deploy a learning rate scheduler equipped with a patience parameter.

The patience parameter here denotes the count of epochs the scheduler observes before

adjusting the learning rate. This is contingent on the absence of performance enhancement

(as depicted in Figure 6.5). This dynamic adaptation of the learning rate, orchestrated by the

scheduler, strikes a balance between expedited convergence and the stability of the training

dynamics. It ensures that the model adeptly navigates through the data’s intricacies and

converges on an optimal solution.

6.2.4 Regularization

When training deep neural networks, one prevalent challenge is overfitting. This phenomenon

occurs when a model excels in its performance on the training data but fails to replicate

this success on new, unseen data, indicating that the model is memorizing rather than

generalizing. To address this issue, we integrate regularization techniques into our training

methodology.

Our current approach harnesses the strengths of L2 regularization [69], a strategy de-

signed to prevent the model from becoming overly complex, which is a common precursor to

overfitting. L2 regularization introduces a penalty term to the original loss function. This

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Figure 6.5: Depiction of the learning curve, illustrating the evolution of the model’s loss on
the training set (in blue) and the validation set (in red) across epochs. The epochs where
the learning rate underwent a decrement by an order of magnitude are marked by the yellow
dashed lines.

term is directly proportional to the sum of the squares of the model’s weights, and inherently

promotes smaller weight values. The mathematical representation of the L2 regularization

term is given as

L2 = λ

(cid:88)

w2
i .

i

(6.4)

In this expression, λ symbolizes the regularization strength, a hyperparameter that can be

fine-tuned, while wi denotes the individual weights of the model. By judiciously adjusting λ,

we are able to navigate the balance between fitting the training data closely and maintaining

modest weight values to enhance the model’s ability to generalize effectively.

In subsequent studies, we aim to explore various techniques for combating overfitting.

Among these techniques, the use of sparse neural networks stands out. This approach is

inspired by the lottery ticket hypothesis, which suggests that within a dense neural net-

work, there exist smaller, sparsely connected subnetworks (referred to as ”winning tickets”)

116

that can achieve comparable or even superior performance to the original network when

trained from the beginning. The exploration of sparse neural networks, as encouraged by

this hypothesis, holds the promise of enhancing model efficiency and mitigating overfitting

by reducing the complexity of the model without significantly compromising its predictive

accuracy [70].

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RARE EVENT SEARCH WITH

CONVOLUTIONAL NEURAL

NETWORKS

One of the main goals of experiment E21072 is detecting rare two-particle events, namely,

20Mg(βpα)15O events. In the following sections a novel approach for finding these rare events

will be described. This includes methods for leveraging Convolutional Neural Networks

(CNNs) alongside various data processing techniques (for details on how CNNs work see Ch.

6). Our approach employs early data fusion strategies to take advantage of the different TPC

data modalities, converting 3D TPC tracks into 2D representations that still capture all the

relevant features of the 3D topology. This adaptation facilitates the use of computationally

efficient 2D CNNs while also allowing us to leverage an extensive collection of pre-trained

models.

Recognizing the limitations posed by the rare nature of the events under investigation

and the risk of discrepancies arising from heavy reliance on simulated data, our methodology

incorporates a layered approach. To enrich our training dataset we utilize techniques such

as active learning and iterative reinforcement. Additionally, to maximize the utility of each

genuine two-particle event within our training data, we apply custom data augmentation

techniques.

In order to effectively use simulations in the training data, we introduce perturbations

into our simulations to account for physics parameter and detector response uncertainties,

118

thereby enhancing the model’s adaptability to differences between simulated and real-world

data. In parallel, we refine our training methodologies to produce CNNs that act as highly

discerning filters for our events-of-interest. This includes training with data that, while not

directly representing our target events, exhibits characteristics suggestive of such events,

ensuring that even the most subtly indicative events are captured for detailed interrogation

by humans. As a result, we develop models that excel in identifying rare two-particle events.

The subsequent sections/subsections are adapted from our other work that is currently

in preparation [59]. These adaptations are used with permission and have been modified to

fit the context of this thesis.

7.1 Addressing Class Imbalance

Within our TPC data, the rare two-particle events we seek are vastly outnumbered by more

common occurrences. This imbalance presents a significant hurdle, as models trained on

such skewed datasets can become biased toward the more prevalent class, thereby neglecting

the less common but critically important events. To counteract this, we implement two main

approaches: class reweighting and selective data sampling.

Class Reweighting: Given the paramount importance of accurately identifying rare

events, we can significantly enhance the impact of these occurrences within our model’s

learning process by applying a disproportionately high weight factor to the minority class

[71]. This strategic reweighting serves to intensify the consequences of incorrectly classifying

these pivotal events. By imposing a substantial penalty for each misclassification of rare

events, we effectively compel the model to allocate more focus and resources towards under-

standing the unique characteristics and subtle indicators of these events. Such a deliberate

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Figure 7.1: A figure showing the balancing of a training dataset through oversampling of the
minority class (rare events) and undersampling the majority class.

adjustment in the learning dynamics is instrumental in guiding the model to achieve a deeper

comprehension of the rare event features, thereby enhancing its overall detection capability.

Balancing Through Sampling: We adopt a dual approach of oversampling the minor-

ity class and undersampling the majority class to cultivate a balanced training environment.

Augmenting the minority class through oversampling ensures that the dataset is replete with

examples of the events-of-interest for the model to learn from. However, it is important to

note that excessive oversampling will lead to overfitting, where the model performs well on

the training data but poorly on new, unseen data [71]. Thus, finding the optimal amount of

oversampling is a delicate process that requires meticulous experimentation and validation.

Simultaneously, reducing the prevalence of the majority class via undersampling helps in

diminishing its overwhelming influence on model training. The undersampling is done by

taking random subsets of the majority class such that the total data across all subsets is

equal to the amount of data in the over sampled minority class. This balanced approach is

depicted in Figure 7.1, showcasing how oversampling and undersampling are used to create

a balanced dataset which mitigates the issues of imbalanced classes.

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7.2 Active Learning

Active learning emerges as a pivotal strategy once a model demonstrates a basic proficiency

in making predictions, serving to further enhance its accuracy. This technique empowers the

model to sift through a reservoir of unlabeled data and earmark instances its uncertain about

for closer scrutiny. Concentrating on these ambiguous events allows for targeted improve-

ments in areas where the model stands to gain the most from additional information. This

approach is exceptionally beneficial in scenarios where acquiring labeled data is a challenge,

either due to scarcity or the high cost of labeling, by ensuring that the labeling efforts are

directed towards the most impactful samples [72].

Upon identification, these instances are subjected to expert review for correct labeling,

embedding human expertise into the loop to resolve the model’s uncertainties. This inte-

gration of newly labeled data back into the training corpus enables the model to evolve,

learning from its prior uncertainties to enhance its comprehension iteratively. This process,

as illustrated in Figure 7.2, not only enriches the pool of labeled data but also methodically

fine-tunes the model’s performance by continuously adapting and refining its predictions.

7.3 Ensemble Method

Ensemble techniques stand out in the realm of machine learning for their capacity to amalga-

mate the unique capabilities of various models, thereby surpassing the performance that any

individual model could achieve on its own [74]. For our problem, the strategy involves the

parallel training of several models, each on a distinct partition (different random subsets) of

the majority class alongside the complete set of the minority class, as illustrated in Figure

7.3. The essence of an ensemble’s advantage lies in the diversity it brings into play: disparate

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Figure 7.2: Illustration of the Active Learning Process. This figure demonstrates the cyclic
nature of active learning: beginning with the model’s application to unlabeled data, identi-
fying uncertain instances, which are then evaluated and labeled by specialists. This freshly
labeled data is reincorporated into the training dataset, enabling the model to refine its
predictions through successive training cycles. Figure adapted from [73].

models can elucidate different facets of the dataset, and when their predictions are pooled,

the outcome tends to be more comprehensive and precise. Additionally, because prediction

is aggregated across models, this method works to eliminate individual model bias.

Although ensemble methods necessitate additional computational resources, the improve-

ment in detection accuracy they facilitate is frequently a worthwhile trade-off, especially in

scenarios where achieving a high detection rate is crucial.

7.4 Simulating Events

To augment our training dataset and bolster the accuracy of our CNNs, we integrate sim-

ulated events into the data pool. These simulations, crafted to closely emulate real decay

events observed in the GADGET II TPC, are generated with the ATTPCROOTv2 analysis

framework. This framework was developed by the ATTPC group at MSU, and is built atop

the foundations provided by the FairSoft and FairRoot suites, drawing upon established nu-

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Figure 7.3: The ensemble method visualized. Here, multiple models (m1-mn) are each
trained on unique combinations of the majority class and the entire minority class. These
models then collectively influence the final decision on test samples, employing a majority
vote system.

clear physics libraries and an array of physics generators to simulate decay events with high

fidelity.

ATTPCROOTv2 equips users with the versatility to create a custom environment that

includes detector specifications, and generates event-by-event simulations via a virtual Monte

Carlo package. It enables the simulation of particular decay pathways, including 20Mg(βpα)15O

and 220Rn α-decay, as depicted in Figure 7.4. One of the standout features of ATTPC-

ROOTv2 is it produces simulated outputs in a format that mirrors real data from our data

acquisition system, facilitating a seamless transition to analysis phases.

Upon the creation of these simulated datasets, pulse shape analysis is performed on the

simulated signals from the pad plane. Employing sophisticated pattern recognition algo-

rithms, the system assesses each event and determines the particle paths within the detec-

tor’s active volume. These Monte Carlo simulations utilize the Geant4 toolkit for physics

processes, while data structuring is managed using the HDF5 library. For further insights

into the simulation framework and the digitization methodology, the reader is directed to

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Figure 7.4: Visual representations from ATTPCROOTv2 simulations for the GADGET II
TPC: (a) and (b) show the simulation for the 20Mg(βpα)15O decay process, illustrating both
the three-dimensional rendering and two-dimensional projection. Panels (c) and (d) exhibit
the 220Rn α-decay simulation in analogous representations.

124

Ref.[75].

7.5

Issues with 2D Projections

The rare proton-alpha coincidence events under investigation possess a distinct 3D topology.

However, their uniqueness in 2D projections is preserved only when the event trajectory is

almost parallel to the projection plane, which is an issue if we want to use 2D CNNs for

event classification.

To elaborate, let’s consider two classes of events that a CNN could confuse if one used

only 2D projections: the proton-alpha coincidence event and a lone proton event. When

these events occur parallel to the pad plane, distinguishing a proton-alpha coincidence is

feasible due to the significant energy deposition observed at both extremities of the track,

as depicted in Figure 7.5a-b. This is characterized by the proton’s Bragg peak at one end

and the alpha’s point-like energy deposition at the other. In contrast, when these events

are perpendicular to the pad plane, they resemble nondescript blobs, making differentiation

challenging (see Figure 7.5c-d).

This observation highlights that the likelihood of a CNN misidentifying these events

increases as their orientation with respect to the pad plane becomes more perpendicular.

Nonetheless, a contrasting feature is notable in the time projection of these events, which

aggregates the track’s charge over time. Here, while parallel-oriented events appear indistin-

guishable, perpendicular alpha-proton coincidence events reveal a distinct dual-peak profile,

as shown in Figure 7.6c. This characteristic underscores the utility of merging these two data

representations for improved event classification, a topic we will delve into in the sections

that follow.

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Figure 7.5: Illustrative comparison of 2D event projections on the pad plane: (a) A proton-
alpha coincidence event aligned parallel, showing clear energy deposition at both ends. (b) A
single proton event parallel to the plane. (c) A proton-alpha coincidence event perpendicular
to the plane. (d) A lone proton event also perpendicular.

126

Figure 7.6: Time projection views for the described particle events: (a) The development over
time of a parallel proton-alpha coincidence event. (b) Time projection for a lone proton event
parallel to the pad plane. (c) The unique double-peak feature of a perpendicular proton-
alpha coincidence event. (d) Time projection for a lone proton event occurring perpendicular
to the pad plane.

127

7.6 Early Data Fusion

In confronting the issues arising from the reduction of event data to 2D projections, our

strategy employs early data fusion, or data-level fusion [76].

In our case, this technique

entails appending the feature space of our 2D images with different data modalities. The

types of data we integrate are as follows:

• 2D Particle Track Projections: These provide a spatial visualization of the par-

ticle’s path, projected onto the pad plane. This projection emphasizes the relative

distribution of charge along the particle’s trajectory.

• 1D Time Projections: Also referred to as the trace signal, this dimension aggregates

the charge collected over time from all pads for each event, offering insight into the

temporal evolution of the particle track within the active volume of the detector.

• Scalar Energy: Visually represented through what we refer to as the ”energy bar,”

this metric quantifies the total energy deposited in the event.

This multi-faceted data is synthesized into a unified composite image, herein referred to

as a data-fused image (depicted in Figure 7.7). This fusion process ensures that the CNN is

furnished with a holistic view, encompassing all critical information that mirrors the unique

3D structure of the events under scrutiny. Such a data representation not only facilitates

the precise categorization of these events but also enhances the CNN’s learning efficacy by

providing a richer dataset for both training and inference phases.

It should be noted that alternative strategies exist for merging these data sources. For

instance, one could use a late fusion technique, and deploy a 2D CNN to analyze the 2D track

projection and a separate 1D CNN for the time projection histogram data, subsequently

128

Figure 7.7: Illustration of a data-fused image, incorporating the three principal data modal-
ities: the 2D particle track projection, the 1D time projection (trace signal), and the scalar
event energy depicted through the ”energy bar”.

integrating the outputs using an aggregation function for final predictions. Nevertheless,

we discovered that generating a unified, data-fused image—where all pertinent information

undergoes convolution and interpretation by a singular CNN—not only yields computational

efficiency but also enhances the clarity of events of interest for manual labeling.

7.7 Robustification through Parameter Variation

The challenge of aligning network training with simulations to the complex realities of ac-

tual data lies in the inherent differences between simulated environments and real-world

conditions. These differences can lead to a shift in data distribution, potentially reduc-

ing the effectiveness of the model. A strategic approach to mitigate this issue involves the

concept of robustification, inspired by strategies developed to counter adversarial perturba-

129

Figure 7.8: An example of adversarial perturbation leading to misclassification. The original
image is recognized as a 5, but after perturbation, it is misclassified as an 8.

tions. Such perturbations are minor modifications to input data designed to deceive machine

learning models, as depicted in Figure 7.8 with a handwritten digit being misclassified due

to intentional noise.

To bolster our network against the discrepancies between simulated and real datasets,

we engage in a process similar to adversarial training. This process introduces intentional

variations or perturbations into our simulation parameters, thereby preparing the model to

withstand real-world data variations. For example, variations in the transverse diffusion

coefficient within our simulations could result in inaccuracies in event representation, such

as the number of detector pads activated, leading to potential misclassifications.

Our approach to minimizing simulation-real data discrepancies involves a dual-phase

strategy. Initially, we calibrate our simulations to more accurately reflect observed real data

by adjusting simulation parameters based on actual decay events. This calibration involves a

specialized algorithm that dynamically modifies simulation parameters, seeking to minimize

the difference between simulated outcomes and real event characteristics.

Upon refining our simulation parameters, we introduce a phase of parameter variation.

Here, we establish Gaussian distributions centered around each optimized parameter value

(gas gain, gas pressure, transverse and longitudinal diffusion, charge dispersion, etc), allow-

ing for random selection of specific parameters for each simulated event. This approach,

130

Figure 7.9: Illustration of simulated proton-alpha events with variable physics parameters
and their time projections: (a) shows the standard simulation, (b) introduces increased
transverse diffusion, and (c) demonstrates adjustments in gain and pad threshold settings.

visualized in Figure 7.9, diversifies the possible event representations in the training dataset,

thereby providing the model with a broad spectrum of data scenarios to learn from. Such a

varied training set aids the model in identifying more consistent and robust features across

a range of real-world events, significantly improving its classification accuracy.

7.8 Filter Method

Our CNN ensembles are engineered to serve as highly sensitive filters, designed to identify

any events bearing even a slight resemblance to two-particle events. The preparatory step in

this process involves the creation of data-fused images derived from our experimental data.

A meticulous hand-labeling effort follows, where tens-of-thousands of images are classified.

Most of the classes are straightforward, for example, a 1.6 MeV proton event gets labeled

as a proton event. However, for the two-particle event class we cast a very wide net. Any

event that is either a different two-particle event than the one we are looking for (recall we

131

are specifically interested in 20Mg p-alphas), or even shares any common features with our

events-of-interest is used for training.

For instance, early in our experiment we took a 21Mg beam rather than 20Mg. 21Mg

also has a p-alpha branch, but with a significantly (orders of magnitude) higher branching

ratio compared to 20Mg, providing a rich source of training data. Additionally, we iden-

tified ”pseudo-events-of-interest” which, while not actual two-particle events, exhibit key

characteristics of interest. Examples include tracks mimicking a double Bragg peak caused

by random ionization fluctuations, or the ionization from a recoiling daughter nucleus. The

rationale behind integrating pseudo-two-particle events lies in their ability to enhance the

dataset, compensating for the rarity of actual two-particle events. This method ensures that

our CNNs are exposed to a wide range of pertinent features, some of which might only subtly

suggest the presence of the events we seek.

Training our models on this diversified dataset, which also includes parameter varied

simulated images (Section 7.7), yields CNNs that function as ultra-sensitive filters. Given

our emphasis on sensitivity, the CNNs exhibit a high detection rate for our target events, but

this comes at the cost of a large number of false positives. This balance between detection

rate and false positive rate is deemed acceptable due to the infrequency of the events under

investigation.

Employing CNNs as filters in this manner offers significant advantages for our research.

The scarcity of the target events necessitates a method that leaves no stone unturned, yet

manually reviewing the entire dataset is untenable. By leveraging our CNNs, we drastically

streamline the data review process, achieving a substantial reduction in the dataset volume

that requires expert analysis. This approach not only ensures that no potential event is

overlooked but also enhances the efficiency and manageability of the data review process.

132

Figure 7.10: Illustration of data augmentation on a real two-particle event from experimental
data. This figure showcases the transformation of a singular event into multiple augmented
versions, employing techniques such as track rotations, translations, noise addition, ran-
dom pad activations, scaling, and blurring for spatial adjustments, alongside trace scaling,
shifting, mirroring, and energy scaling for temporal/energy modifications. Each augmented
image represents a potential variation in training data, enabling the convolutional neural
network (CNN) to more robustly learn and identify the key features of two-particle events,
thereby enhancing model generalization and precision.

7.9 Data Augmentation

As more and more real two-particle events are found in the experimental data via the fil-

tering technique (Section 7.8), data augmentation emerges as the best strategic method to

substantially enhance our training dataset. Given the scarcity of two-particle events, each

instance is exceedingly precious. Yet, the specialized nature of our data imposes limita-

tions on the applicability of standard augmentation techniques, such as cropping or random

rotations applied to whole images.

To adapt to our unique dataset, we concentrate on manipulating the 2D projections

133

of particle tracks on the pad plane. By selectively applying our augmentation features

(track rotations, translations, track and edge noise, random pad fires, track scaling, and

track blurring) to this aspect of the data, we enable the CNN to recognize and learn the

fundamental characteristics of real two-particle events.

Beyond spatial modifications, we also apply augmentation features to the time projection

component of our data through the addition of trace scaling, trace shifting, and trace mir-

roring. Additionally, we also apply energy scaling as an augmentation feature. Figure 7.10

shows an example of a real two-particle event and how we can create an arbitrary number

of augmented images from it by applying our augmentation features.

Employing this strategy, we can transform a solitary two-particle event into a plethora

of varied training examples. This approach not only enriches the model’s exposure to the

minority class but also significantly broadens its capability to generalize from even a single

occurrence of an event-of-interest. Given this, we can train new models that are far more

precise than the initial filtering ensembles. These new models still have a high detection rate

for our target events, along with a reduction in the number of false positives.

7.10 Performance Metrics

As is common when evaluating CNN performance, we will use the metrics precision, recall,

and F1 score [77, 58]. To lay the groundwork for understanding these evaluation metrics

we will look to the confusion matrix. When dealing with a binary classification problem,

confusion matrices work by categorizing model predictions into four distinct outcomes: true

positives (TP ), false positives (FP ), true negatives (TN ), and false negatives (FN ) (see

Figure 7.11).

134

Precision measures the model’s accuracy in predicting two-particle events. Specifically,

it answers the question: ”Of all the events predicted to be two-particle events, how many

were actually two-particle events?” A higher precision score indicates a model that is more

accurate in its positive predictions, minimizing the risk of false positives. The metric is

defined as the ratio of true positives to the sum of true positives and false positives:

Precision =

T P
T P + F P

(7.1)

Recall evaluates the model’s ability to identify all actual two-particle events. It addresses

the question: ”Of all the actual two-particle events, how many did the model successfully

identify?” This metric is essential in scenarios where missing an actual two-particle event (a

false negative) could lead to significant oversight or loss of crucial information. Thus, a high

recall score signifies that the model is proficient at detecting two-particle events, ensuring

minimal loss of vital events-of-interest. As such, it is this metric that we are most concerned

with, and it is calculated as the ratio of true positives to the sum of true positives and false

negatives:

Recall =

T P
T P + F N

(7.2)

F1 score harmonizes the balance between precision and recall, offering a single metric

that encapsulates both the model’s accuracy and its completeness in identifying two-particle

events. It is particularly useful when you need to compare models that might have a trade-

off between precision and recall, allowing for a balanced assessment of model performance.

The harmonic mean is used because it is more sensitive to low values, ensuring that models

can only achieve a high F1 score by performing well in both precision and recall. A high

F1 score indicates a model that is both accurate and comprehensive in its identification of

135

Figure 7.11: Depiction of a confusion matrix in binary classification. Rows illustrate predic-
tions made by the classifier, and columns indicate actual class labels. The left matrix defines
the terminology for each component of the matrix, while the right matrix demonstrates how
these terms are utilized in the context of the GADGET II TPC rare event search. In an
ideal scenario, the classifier would produce a confusion matrix with all values concentrated
along the diagonal, showcasing perfect predictive accuracy (adapted from [58]).

two-particle events, striking a desirable balance where both false positives and false negatives

are minimized.:

F1 = 2 ×

Precision × Recall
Precision + Recall

(7.3)

Employing precision, recall, and the F1 score provides a nuanced understanding of model

performance in the GADGET II TPC data. These metrics, ranging from 0 to 1, allow for a

detailed evaluation of models’ abilities to correctly identify two-particle events.

7.11 Results

The filter method (Section 7.8) necessitated the training of a large number of models. The

5 best performing models were selected to operate as an ensemble (Section 7.3).

In this

case, the performance metric we were most concerned about was recall (Section 7.10), as we

136

Figure 7.12: Depiction of the learning curve for Model A, illustrating the evolution of the
model’s loss on the training set (in blue) and the validation set (in red) across epochs.

wanted to ensure that few events of interest were missed, even at the cost of false positives.

Model

Precision Recall

F1

Model A
Model B
Model C
Model D
Model E
Ensemble

0.85
0.73
0.74
0.82
0.71
0.75

0.96
0.96
0.97
0.95
0.97
0.98

0.90
0.83
0.84
0.88
0.82
0.85

Table 7.1: Performance metrics for models A-E, and the corresponding ensemble. Models in
the ensemble were chosen to favor recall for the two-particle class. The models were trained
on a combination of parameter varied simulated data, and experimental data using the filter
method (Section 7.8).

The selected models shared common training characteristics: they leveraged the pre-

trained VGG16 architecture which was fine-tuned with a custom classifier (Section 6.1.2).

The training employed cross-entropy loss and utilized an SGD optimizer with a momentum

setting of 0.9. To adjust the learning rate, we applied a ReduceLROnPlateau scheduler,

initialized with a learning rate of 0.001 and a patience interval of four epochs (Section 6.2.3).

To counteract data imbalance, we implemented sampling strategies to ensure a balanced

137

training dataset (Section 7.1), with a batch size set to four. Additionally, the training

protocol augmented the class weight for the minority class, which pertains to the two-particle

events-of-interest, amplifying the loss impact from errors in this category by a factor of ten

(Section 7.1). The training duration spanned 100 epochs, and Figure 7.12 shows an example

of a learning curve (loss vs epochs) plot for Model A. Performance metrics for individual

models and the ensemble are presented in Table 7.1, showcasing that the ensemble is able

to successfully identify >98% of two-particle events within the dataset.

Refined Model Precision Recall

F1

Model F
Model G
Model H

0.78
0.79
0.87

0.98
0.98
0.98

0.87
0.87
0.92

Table 7.2: Performance metrics for refined models F-H. The models were trained on ad-
ditional augmented images of real events found during the ensemble filter process. Note
that each model performs better than the ensemble from Table 7.1, and the models are get
progressively better as additional augmented images are added.

This ensemble was applied to well-defined search regions on runs of experimental data

(Section 5.3.1). These search regions typically have tens-of-thousands of events in them, thus

our week long experimental campaign would require the manual examination of millions

of images. After applying the ensemble filter the dataset is reduced by over an order of

magnitude, making the total amount of data requiring human review closer to hundreds of

thousands of images. While still sizable, this is a massive reduction in the person-power

required for event classification.

As the ensemble filter is applied and new two-particle-events are found, we then use the

data augmentation software (Section 7.9) to turn those events into a much larger training

pool. Then new, more precise models are trained that still have a high recall, but also

improved precision leading to a reduced number of false positives. Table 7.2 highlights the

138

performance of three such refined models, each outperforming the initial ensemble. Notably,

the models improve sequentially, with each subsequent model benefiting from an increased

number of augmented images found with the ensemble filter. As of writing this thesis, the

process of training refined models from events found via the ensemble filter is still on going.

Once enough refined models are trained, a more precise ensemble will be deployed on the

remaining data to find all outstanding two-particle events.

139

SUMMARY AND OUTLOOK

The 15O(α, γ)19Ne reaction rate is a critical uncertainty in the modeling of X-ray bursts

emanating from neutron stars. The essence of determining this reaction rate lies in the

precise measurement of the small alpha-particle branching ratio from the 4.03 MeV state in

19Ne. This state is populated in the decay of 20Mg, with 20Mg(βpα) events offering a unique

p-α signature that can be used to measure the key alpha branching ratio.

To capture these elusive events the GADGET II TPC was built, and tested. The tests

were performed using 220Rn and 216Po and revealed the TPC’s proficiency in detecting and

identifying charged particles, alongside measuring their trajectory, range, and energy with

notable precision. Utilizing P10 gas, the GADGET II TPC showed an energy resolution of

≈5.4% at 6.288 MeV, which was achieved through detailed charge integration methods. The

sensitivity of the TPC was also established from its ability to detect low-ionizing cosmic-ray

muons. This also allowed for the determination of the drift velocity under normal operating

conditions. Notably, the GADGET II TPC is among the first micro pattern gaseous detectors

to utilize a resistive anode in the realm of low-energy nuclear physics. Additionally, it’s the

first TPC to be surrounded by an array of HPGe detectors for the measurement of gamma-

rays [31].

Extensive development work was done to couple this new TPC to DEGAi, the HPGe

array, which is part of FRIB Decay Station initiator. This coupled system forms the full

GADGET II experimental setup employed in E21072. Experiment E21072, conducted at the

FRIB, utilized the newly upgraded GADGET II detection system. Early in the experiment

we received a beam of 21Mg, which we used to commission the detector, and successfully

140

measured p-α events that closely mirror our primary events-of-interest. Subsequent to that,

we received an isotopically pure beam of 20Mg, albeit at a substantially lower intensity

than initially anticipated. Owing to this, our projections have been cautiously adjusted to

anticipate the identification of no more than 3 events-of-interest under the most optimistic

scenarios, and 0.3 based on the lowest estimate of the branching ratio. The astrophysical

problem in question can be satisfactorily resolved by achieving a branching ratio uncertainty

of ∼70% or less on a finite value, equating to us finding roughly 2 events-of-interest (assuming

a background free measurement). Therefore, there is a strong possibility that a subsequent

experimental campaign will be needed to collect a sufficient amount of statistics to determine

the branching ratio with an acceptable level of uncertainty.

In our pursuit to find these events-of-interest in the data, a search region was applied

to range vs energy histograms, on which the p-α events will occupy a specific region. This

approach enables a more efficient and targeted analysis. The sophistication of this search is

significantly enhanced through the integration of machine learning algorithms, particularly

CNNs. Our methodology utilizes early data fusion techniques to leverage the different TPC

data modalities, transforming 3D TPC tracks into 2D representations that retain essential

3D topological information. This approach takes advantage of the computational efficiency

of 2D CNNs, and a wealth of pre-trained models.

In light of the challenges presented by the scarcity of the events under investigation and

the potential inaccuracies stemming from the significant use of simulated data, our approach

adopts a comprehensive strategy. We enhance our training dataset through the adoption

of active learning and iterative reinforcement techniques, and fully leverage each authentic

two-particle event in our dataset through the implementation of custom data augmentation

methods. Additionally, to ensure the effective incorporation of simulations into our training

141

dataset, we integrate perturbations that reflect physics parameter and detector response

uncertainties. This significantly improves the model’s ability to bridge the gap between

simulated and real data. Concurrently, we refine our training protocols to cultivate CNNs

that operate as extremely sensitive filters for our specified events-of-interest, and deploy

them as ensembles to reduce individual model bias. The resulting ensembles applied to the

experimental data are able to identify >98% of all two-particle events in the dataset [59].

Approximately half of the experimental dataset has been meticulously searched for rare

events-of-interest, with models undergoing refinement based on two-particle events detected

by the ensemble filter. This process is enhancing both the accuracy and precision of the

models, consequently accelerating the search for rare events.

Looking forward, we will continue to diligently analyze the dataset in search of events-

of-interest. Upon identification, such events will undergo a thorough validation process to

confirm their derivation from the anticipated state in 19Ne, with a special focus on the

detailed examination of the p-α energy distribution. This scrutiny is essential for accurately

distinguishing between various decay mechanisms. In the event that 20Mg(βpα) occurrences

are detected within our data, thus allowing for a finite measurement of the 19Ne alpha

branching ratio, our next steps will involve calculating the 15O(α, γ)19Ne reaction rate.

Achieving this milestone will not only advance our comprehension of the fundamental nuclear

reactions involved but also facilitate the precise modeling of Type I X-ray burst light curves

from neutron stars.

Additionally, we have a PAC 2 approved FRIB experiment to measure the next two

critical reactions in Type I X-ray bursts. This experiment will also utilize the GADGET

II system, and will investigate 56Ni(α, p)59Cu and 59Cu(p, γ)60Zn using the beta decay

of 60Ga. The primary objective of this study is to identify and characterize resonances,

142

alongside quantifying branching ratios for proton, alpha, and gamma emissions.

143

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