PRODUCTION OF NEUTRON-RICH RARE ISOTOPES NEAR N = 126 VIA MEDIUM
ENERGY FRAGMENTATION

By

Kenneth Taylor Haak

A DISSERTATION

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

Physics - Doctor of Philosophy

2024

ABSTRACT

The production of neutron-rich rare isotopes near 𝑁 = 126 seeks to elucidate the limit of

existence for nuclear matter and explain the origin of heavy elements. In the most recent develop-

ment, eight new isotopes, 182,183Tm, 186,187Yb, 189,190Lu, and 191,192Hf, were discovered in medium

energy fragmentation and are presented here. This work marks the first time a 198Pt primary beam

was used to produce neutron-rich heavy isotopes near 𝑁 = 126. Two primary beam energies were

explored, 85 MeV/u and 186 MeV/u. A total of 60 production cross sections were measured in the

85 MeV/u 198Pt + 9Be reaction, and 50 production cross sections were measured in the 85 MeV/u

198Pt + Ni reaction. The 198Pt + 9Be cross sections were compared to EPAX3 , COFRA , ABRABLA07 ,

and LISEAA , showing the most consistent agreement with LISEAA . The Ni target cross sections

were systematically greater than the Be target cross sections by roughly an order of magnitude. This

result suggests that heavy neutron-rich targets may aid in production of neutron-rich isotopes for

medium energy fragmentation. Several pick-up reactions between 198Pt and three separate targets

(Be, Ni, C) were observed for the first time at intermediate energies. Nuclei up to two neutrons

greater than the primary beam were observed. This work also led to the development of a novel

charge state analysis for cross section calculations. The probability distribution for the charge state

of the projectile residue immediately after reaction is generated from Monte Carlo calculations

and optimization to experimental data. By using this new method, it was observed that not all

primary beam electrons are stripped from the projectile residue during a fragmentation reaction.

The number of electrons which remain on the projectile residue immediately after reaction (named

𝑁e𝑅 ) were observed to be inversely proportional to the number of protons removed in reaction.

Copyright by
KENNETH TAYLOR HAAK
2024

I dedicate this work to my family.
I hope I have brought a sense of pride, how ever small, to each of your lives.

iv

ACKNOWLEDGMENTS

I would like to first and foremost acknowledge my advisor, Brad Sherrill. Thank you for your

guidance, patience, and knowledge. While there is always more to learn, I have gained a great

deal of understanding about what it means to be a nuclear physicist from the fruitful mentorship

I have received over the past several years.

I am obliged to acknowledge my scientific mentor,

Oleg Tarasov. This work would not have been possible without his contributions. Funding was

provided by the NSF and DOE under the following grants: PHY-15-6554, 20-12040, 23-10078,

and DE-SC0023633.

I also extend my gratitude to the fragment separator group, ARIS, for allowing me to participate

in RI beam preparation during many nights and weekends. Thank you for letting me be a part of

your daily work. I would also like to thank Mallory Smith for teaching me everything I know about

electronics. Working with you was an absolute pleasure, and I felt very supported and encouraged

to learn new things with out fear of making mistakes. Thank you so much for your patience and

support. The fellow students within my research group have also been an immeasurable blessing.

Thank you for providing much-needed solidarity. We have walked the same path in this research

group, through thick and thin. To Isaiah, thank you for your kindness and patience with me, I feel

blessed to have been treated so kind. To Shane, thank you for the countless long conversations

about practically any topic, it is such a pleasure to listen to your stories and have you share your

knowledge.

Finally, I am honored to acknowledge all others who supported me emotionally throughout the

pandemic and my entire graduate school journey. I would like to choose three words that come to

mind for each individual, and then provide a couple sentences of gratitude.

Nick - Caring, Supportive, Hilarious. Thank you so much for helping me come out of my

shell with your energetic humor. We persevered through our mutual feelings of homesickness and

dreamed of traveling to far-off places, anywhere but here. You were there to support me when I

needed it, and I am deeply grateful for everything.

Nico - Integrity, Strength, Discipline. You provided me with a cathartic and safe place to share

v

both professional and personal concerns. You are a true ally, always willing to defend me and

support me in any situation. Also, thank you for your studious documentation of very iconic quotes

heard within the confines of the office.

Evan - Reliable, Forgiving, Steady. In the darkest moments, quite literally in the dead of night,

you were always there for me. You served as an absolute lightning rod for my chaotic personality,

and no amount of panic or instability could shake your steady demeanor. Thank you Saam.

Ricky - Enthusiastic, Positive, Charismatic. You helped me find my passion for programming,

which most likely led to my future career decision. I am so excited to see what you do next, and

hopefully I get the absolute pleasure of working together with you someday. Thank you for being a

true friend for life, and making an effort to preserve this friendship from halfway around the world.

Mom - Patient, Kind, Gentle. From a psychological perspective, I believe we lead similar lives,

filled to the brim with endless tasks that always inevitably require a meticulous attention to detail.

Knowing this, I have learned from you how to cope with adversity and proceed through life. Thank

you for telling me that when life becomes overwhelming, it is best to just take things one step at a

time.

Dad - Hardworking, Easy-Going, Resilient. Sometimes I just need to calm down, and it always

feels particularly salient hearing that from you. From observing you, I have learned how to tune

out catastrophe and stay positive. Thank you for telling me to relax, it is so desperately needed,

much more than you may ever know.

Nathan - Mature, Productive, Confident. You have consistently assisted and guided me in both

personal and professional reflection.

I am delightfully certain that our many life conversations

have significantly shaped the individual I have become. Thank you for taking such an integral and

critical role in my life. I am endlessly and forever grateful.

Yuki - Considerate, Persevering, Bright. Bright is truly the best word to describe you. You have

been my bright light in the darkest of times, a beacon of hope, like a lighthouse that guides me to

safe shores in the midst of stormy seas. Thank you for giving me hope, happiness, and excitement

for the future.

vi

TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION ................................................................................................
1.1 Background ...................................................................................................................
1.2 Motivation .....................................................................................................................
1.3 Prior Work.....................................................................................................................

1
1
6
9

CHAPTER 2: EXPERIMENTAL CONFIGURATION .............................................................. 15
2.1 Fragmentation at NSCL ................................................................................................ 15
2.2 Fragmentation at FRIB.................................................................................................. 18

CHAPTER 3: DATA ANALYSIS................................................................................................ 20
3.1 Particle Identification .................................................................................................... 20
3.2 Cross Section Calculation ............................................................................................. 24
3.3 Asymmetric Error ......................................................................................................... 29
3.4 Charge States................................................................................................................. 36

CHAPTER 4: RESULTS ............................................................................................................. 45
4.1 Particle Identification and New Isotope Discovery....................................................... 45
4.2 Cross Sections ............................................................................................................... 49
4.3 Evidence of Residual Electrons .................................................................................... 53

CHAPTER 5: DISCUSSION ...................................................................................................... 55
5.1 Uses for New Isotopes................................................................................................... 55
Interpretation of Cross Section Results......................................................................... 57
5.2
5.3 Motivations and Limits of the Novel Charge Analysis ................................................. 65

CHAPTER 6: CONCLUSION .................................................................................................... 74
6.1 Summary ....................................................................................................................... 74
6.2 Outlook.......................................................................................................................... 76
6.3 Perspectives................................................................................................................... 80

REFERENCES ............................................................................................................................ 82

APPENDIX.................................................................................................................................. 90

vii

CHAPTER 1: INTRODUCTION
Terra incognita is Latin for unexplored territory. This phrase was first used in Ptolemy’s Geography

around the year 150 AD and was later reintroduced during the Age of Exploration in the 15th century.

Unexplored territory was often either costly or challenging to reach. It required a great deal of

resources and ingenuity to make it through rough waters, thick jungles, and over steep mountains.

Likewise, the Chart of Nuclides (see Figure 1.1), in the context of nuclear physics, contains several

regions which are difficult to access. These areas draw a parallel to the unexplored territory on old

maps of Earth, due to cost and technological constraints of discovering a new nuclide. Therefore,

the unexplored area of the Chart of Nuclides has been aptly named Terra Incognita [1].

Since the discovery of the first unbound nuclei [2], there has been a continuous effort to define the

limits of existence for nuclear matter by charting the unexplored territory of what would eventually

be represented as the Chart of Nuclides. Currently, the neutron-rich region near neutron number

𝑁 = 126 is the new world, ripe for discovery. This region is relatively unexplored compared to

other areas in the Chart of Nuclides. The nuclei in this region also hold the answers to the creation

of the heaviest elements found in nature [3]. The latest discoveries of neutron-rich rare isotopes

near 𝑁 = 126 are over a decade old and were produced by high energy fragmentation of heavy

elements, such as lead and uranium [4, 5]. The next step toward pushing the boundary of discovery

was carried out with medium energy fragmentation of 198Pt and is described in this work.

1.1 Background

A nuclide is often addressed with the misnomer “isotope." Isotopes are atoms of the same element

that differ by the number of neutrons contained in the nucleus. A nuclide is a distinct nucleus of

an atom, characterized by a specific number of protons and neutrons. In this thesis, the common

practice of using the term isotope synonymously with nuclide is adopted. There are roughly 280

isotopes found naturally on Earth [8], which is a small subset of the 3373 isotopes that have

been discovered in the course of human history [9]. Most natural elements contain multiple

isotopes in varying abundances. For example, platinum occurs naturally in six different isotopes

190,192,194,195,196,198Pt, which occur at abundances 0.01%, 0.8%, 32.9%, 33.8%, 25.2%, and 7.4%,

1

respectively [10].

Atomic nuclei have varying degrees of radioactive stability. Radioactivity is observed when a

nucleus spontaneously emits energy as a particle or a wave. Commonly emitted particles include

𝛼, 𝛽−, or 𝛽+ particles, which are more easily understood as a helium nucleus, an electron, and

a positron, respectively. These processes change of the number of neutrons and protons of the

nucleus and thus the identity of the nuclide. Certain nuclides are sufficiently stable that an emission

of one of these particles has never been observed, and these are considered “stable." Stable nuclei

comprise the majority of matter we see in our everyday life, whether it is the atomic nuclei of 12C

in the soil, 14N in the air, or 16O in water. The Chart of Nuclides helps visualize stable nuclides

with a line that runs through the middle of the chart (shown in light grey in Figure 1.1)

Figure 1.1: The Chart of Nuclides was generated in LISE++ using the UNDEF1 mass model [6, 7].
The magic numbers 𝑁 = 126, 82, and 50 are denoted with a dashed black line. The region of interest
for this work is denoted by the ellipse drawn with a solid black line. The orange circle slightly to the
left of 𝑁 = 126 denotes 198Pt, the primary beam used in both fragmentation experiments presented
in this thesis. The different colors on the chart indicate different types of radioactive decay. Red is
decay, and yellow is 𝛼 decay. Stable nuclei are shown in light grey, and terra
𝛽
incognita is shown in dark grey.

decay, blue is 𝛽

−

+

2

Nuclei can also be bound or unbound. Certain combinations of protons and neutrons do not

stick together and exist for incredibly short times, which are shorter than the time for a neutron or

proton to cross the nucleus. This may occur if protons are added to an already proton-rich nucleus

or neutrons are added to an already neutron-rich nucleus. For example, if one neutron is added

to 12Be to create 13Be, the extra neutron simply “drips" out of the nucleus within an incredibly

short time interval. This perspective of the atomic nucleus gives rise to the term “dripline." The

dripline is the boundary of the Chart of Nuclides, and it defines the limits of existence for nuclear

matter. Quantitatively, an unbound nuclide beyond the neutron dripline can be defined by its neutron

separation energy, 𝑆𝑛. If 𝑆𝑛 is negative, the nuclide is unbound. For instance, measurements have

shown that 13Be has 𝑆𝑛 =

−

510 keV, indicating it is unbound [11].

A relatively small portion of the Chart of Nuclides has been explored to the dripline. For each

element, the proton dripline is defined by the lightest bound isotope, while the neutron dripline is

defined by the heaviest bound isotope. The proton dripline has been established up to 26P and the

neutron dripline has been established up to 39Na [9, 12]. While these nuclides are the complete

extent of the dripline from hydrogen, there are several scattered observations of unbound nuclides

beyond these limits, such as 54Cu which demonstrates the proton dripline for copper. The dark

grey region in Figure 1.1 shows how far the dripline could possibly extend away from stability as

nuclides increase in mass. However, this region is only a theoretical prediction. The true extent of

the Chart of Nuclides is uncertain and better constrained with new discoveries of nuclides at the

dripline.

New isotope discoveries and the exploration of the Chart of Nuclides has progressed in several

waves, with each wave being the result of a new technology (see Figure 1.2). The discovery of

nuclides technically began with radioactivity at the beginning of the 20th century, but the first notable

wave of discoveries happened in the 1920s with the advent of mass spectroscopy. It was at this time

the majority of naturally occurring nuclides were discovered, as each element was systematically

studied with mass spectroscopy and their relative isotopic abundances were documented. Shortly

after, the first accelerators were constructed, and it became possible to experimentally study the

3

Figure 1.2: The discovery of isotopes is separated by historical breakthroughs in technology.
The colors indicate the transition from one main method of discovery to the next. From left to
right, the colors purple, dark blue, light blue, blue-green, green-yellow, orange, and red represent
radioactivity, mass spectroscopy, the first accelerators, reactors, fusion evaporation, early projectile
fragmentation plus in-flight fission, and next generation facilities, respectively.

collision of atomic nuclei at energies high enough to induce nuclear reactions. After a short pause

on discoveries during the early 1940s, consistent progress has been made toward filling in the Chart

of Nuclides. Nuclear reactors became a widely studied technology in the 1950s leading to another

spike in new isotope discoveries. Fusion evaporation was the next step in history and became the

main nuclear reaction mechanism for rare isotope production for the next couple decades. Most

recently, projectile fragmentation and in-flight fission saw widespread use in the production of

exotic nuclides, starting in the 1990s.

Projectile fragmentation is a nuclear reaction mechanism in which a fast heavy-ion collides with

a stationary target atom and fragments into lighter nuclei. This reaction is commonly viewed in a two

step process called abrasion-ablation, and is depicted with a simple cartoon in Figure 1.3. Initially,

the projectile collides with the target, losing several nucleons and becomes energetically excited.

Next, the excited pre-fragment quickly emits protons and neutrons, releasing excitation energy in

the process. Projectile fragmentation is fundamentally characterized by a fast heavy projectile and

4

<HDU,VRWRSHV'LVFRYHUHGa light target atom. It is an advantageous means of production because the prefragment is moving at

close to the initial beam velocity, and the product can exit the target to be analyzed at a later stage.

This is different than slower or smaller projectiles, which create reaction products that remain in

the target and require chemical separation to be extracted.

Figure 1.3: A cartoon depiction of projectile fragmentation is illustrated in the two-step abrasion-
ablation process. The heavy projectile participates in a grazing collision with the target atom where
a number of nucleons are quickly removed (abrasion). The pre-fragment then evaporates neutrons
and protons until reaching a bound state (ablation).

The fragmentation of heavy nuclei produces an enormous variety of products that must be

separated in order to study a given exotic nuclide. Figure 1.4 demonstrates the wide range of

particles that can be produced in the fragmentation of a single nuclide, 208Pb. This reaction will

produce fragments that are only a single proton or neutron lighter than lead, as well as the lightest

nuclides. The separation and selection of a given nuclide from the vast sea of fragmentation products

is performed with a fragment separator. A fragment separator uses magnetic fields to guide the

collection of fragmentation products through a series of separation and selection steps [13, 14].

The detailed setup of each fragment separator used in this work is provided in Chapter 2.

The use of fragment separators to deliver rare isotope (RI) beams from projectile fragmentation

is a flexible and widespread method for creating exotic nuclides. This work presents the medium-

energy fragmentation of a 198Pt beam, and the separation and identification of its resulting products.

Motivation for the production of neutron-rich rare isotopes near 𝑁 = 126 is described in the

following section, and a summary of previous work carried out in this region is given in Section 1.3.

5

Figure 1.4: The production rate of each fragment for 400 kW of 208Pb at 212 MeV/u on a carbon
target is shown. The EPAX3 parametrization was used for the cross sections [15], and the plot was
generated in LISE++ version 16.0.3 [16]. Projectile fragments span the majority of the chart. The
rate is shown in log scale and the highest intensity rates occur down and to the left of the primary
beam.

1.2 Motivation

Research in the production of neutron-rich rare-isotopes near 𝑁 = 126 is motivated by the impor-

tance of these isotopes to nuclear astrophysics and nuclear structure studies. Many nuclear science

facilities around the world are focused on this region [17]. Given the importance of nuclei in this

region, it becomes equally important to explore how to make these nuclides. This exploration

will ultimately lead to filling in uncharted nuclear territory on the Chart of Nuclides and thereby

answering important questions about the universe, such as the origin of heavy elements [3]. De-

spite the interest, producing these isotopes has been difficult. Today, the neutron-rich region near

𝑁 = 126 is relatively unexplored compared to other neutron-rich areas of the Chart of Nuclides,

leaving plenty of room for discovery. As the region is uncovered, each new isotope can be used

for nuclear physics studies and may also lead to applications outside the field of nuclear physics.

6

An important goal is to reach the isotopes that play a fundamental role in understanding the origin

of heavy elements, such as platinum and uranium [3]. New isotope discoveries not only make a

wide variety of nuclear experiments possible, but they also hold the potential for new applications

in material science, medicine, and industry. For example, precise measurements of isotopic mass

and charge radii help refine our models of atomic structure and contribute to the standards used in

precision instruments [18, 19]. The half-life of an isotope is also useful, as it informs us about its

stability and potential uses in radiometric dating or medical diagnostics [20].

A vast number of unique nuclei are naturally created by nucleosynthesis, the cosmic formation of

nuclei more complex than a free proton or neutron, which mostly occurs in stellar environments [22].

However, due to the fact that the half-lives for most nuclei are short on the time scale of the Earth [8],

a small subset of nuclei are naturally available for nuclear astrophysics and nuclear structure studies.

Therefore, studies involving how to make rare isotopes in laboratory conditions become necessary.

The astrophysical phenomenon of nucleosynthesis occurs in a variety of cosmological conditions,

Figure 1.5: The Chart of Nuclides organized by nucleosynthesis processes [21]. The same color
scheme for decay is used as in Figure 1.1. The rp-process, s-process, and r-process are represented
by the blue, black, and green arrow, respectively.

7

such as in the core of the sun, in supernovae explosions, and in neutron star merger processes [22].

While nucleosynthesis processes such as the pp-chain and CNO cycle have explained the origin of

lighter elements in our universe [22], it is still not well understood how heavier elements are formed.

Several notable candidates have been proposed such as the rp-process (rapid proton capture), the

s-process (slow neutron capture), and the r-process (rapid neutron capture). The general pathways

of these three processes through the Chart of Nuclides are shown in Figure 1.5. The rp-process is

characterized by a rapid capture of protons and then a 𝛽-decay back to stability [22]. This process

occurs in supernovae and x-ray bursts, and it is capable of producing nuclei up to the masses of

Sn isotopes [21]. The s-process is a relatively slow nucleosynthesis process that climbs along the

valley of stability in the Chart of Nuclides (see Figure 1.5), and it is predicted to occur mostly in

asymptotic giant branch stars [22]. While the s-process is capable of producing stable nuclei up to

208Pb, it cannot reproduce the peak in natural isotopic abundances near mass number 𝐴

195 [3].

≈

The r-process is the missing puzzle piece that completes the picture of nucleosynthesis, offering an

explanation for the 𝐴

≈

195 mass peak and the origin of super-heavy elements, such as uranium [22].

Neutron-rich nuclei near 𝑁 = 126 contain vital astrophysical information that can help develop

our understanding of the r-process. The r-process is theorized to occur at incredibly high neutron

densities, conditions which are present in neutron star mergers and supernova explosions [22]. In

these conditions, it is possible for a series of rapid neutron captures to out-compete the relatively

long beta-decay half-lives near stability [22]. Consequently, the r-process pathway is predicted to

lie considerably far away from stability, as shown in Figure 1.5. The pathway also passes directly

through the neutron-rich region near 𝑁 = 126 and is theorized to “hit a wall" at the 𝑁 = 126

shell closure. This “wall" in the r-process pathway is directly tied to the isotopic abundance peak

at 𝐴

≈

195, and it can be studied by producing new isotopes in this region. Once produced, the

neutron separation energies and beta-decay half-lives of these rare isotopes can be measured and

used to develop our understanding of the r-process.

The neutron-rich region south of lead has not been well studied because of the difficulty

in making these isotopes. For example, only 10 neutron rich isotopes have been discovered

8

beyond the heaviest stable platinum isotope (𝑍 = 78), whereas 25 neutron rich isotopes have been

discovered beyond the heaviest stable rhodium isotope (𝑍 = 45) [9]. There are many approaches

to creating rare isotopes through nuclear reactions, and various reaction models can be categorized

into low and high energy mechanisms. Fusion-fission and multi-nucleon transfer (MNT) are low

energy reaction models, which occur at energies near the Coulomb barrier of the two participating

nuclei [23, 24]. On the other hand, projectile fragmentation and in-flight fission occur at higher

energies, such as hundreds of MeV/u [17]. It is necessary to experimentally test these reaction

models to develop a more complete understanding of how to produce rare isotopes in this region.

The main contributing factors to the relative difficulty of producing isotopes by fragmentation in

this region are the presence of multiple charge states in heavy ions and the exponentially decreasing

cross sections of successive proton removal from neutron-rich nuclei [25]. However, the 400 kW

upgrade at FRIB [26] will allow researchers to explore reactions that occur at very small cross

sections and lead to the discovery and production of many rare isotopes.

1.3 Prior Work

The production of neutron-rich rare isotopes has been recently dominated by projectile fragmen-

tation and in-flight fission. In the past four decades, over 80% of new isotope discoveries in the

neutron-rich region between 104

𝑁

≤

≤

131 have been created by fragmentation or fission (see

Figure 1.6). However, the discovery of new isotopes with fragmentation has slowed down as

exponentially shrinking cross sections have prevented further progress. In an attempt to explore a

new pathway, there has been a great deal of focus placed on lower energy reactions just above the

Coulomb barrier. Recently, one of the low energy reaction models with the most attention is MNT.

Despite the fact that renewed interest in MNT began over a decade ago, there have been no direct

measurements of new neutron-rich isotopes produced by MNT since 2010 [27] (limited to the scope

of Figure 1.6). Fusion-fission also deserves recognition as a viable production mechanism for new

isotopes in this region of interest [23]. Both projectile fragmentation and MNT will be covered in

this section, and key work will be highlighted.

Before the widespread use of projectile fragmentation at the turn of the century, the majority

9

131, organized by production methods
Figure 1.6: The neutron-rich region between 104
that led to the first discovery of a given nuclide. Elements between promethium and bismuth are
shown (61
83). The proton-rich side of the chart has been grayed out, the stable isotopes
are shown in black, and neutron-rich isotopes discovered before 1980 are shown in blue. All low
energy experiments are shown in red, neutron beam experiments are shown in light purple, and
every other listed experiment was carried out using projectile fragmentation or in-flight fission.

≤

≤

≤

≤

𝑍

𝑁

of new isotopes were being discovered by fusion-evaporation reactions. These are inherently low

energy collisions that aim to fuse the participating nuclei rather than break them apart. These

reactions required the use of on-line isotope separator devices to extract the products made in the

target. Limiting the scope to neutron-rich isotopes between 104

𝑁

≤

≤

131, these low energy

heavy-ion collisions were responsible for almost every new isotope discovery in the 1980’s [9] (see

Fig. 1.6). The only exception was the discovery of 207Hg by irradiating lead and bismuth targets

10

with neutrons [9]. Low energy heavy-ion collisions were often carried out at low beam energies

near the Coulomb barrier of the two participant nuclei. Several examples include beams of 136Xe,

186W, and 238U, all under 15 MeV/u, irradiated on tungsten-tantalum sandwich targets [28].

Eventually it was realized that the vast collection of fragments created in the collision of

relativistic heavy-ions could be utilized with a fragment separator. A couple examples of early

fragment separators include the A1200 at NSCL, RIPS at RIKEN, and LISE3 at GANIL [14, 29, 30].

These devices were able to capitalize on the relatively small emittance of the fragmentation products,

which had similar momentum distributions to the primary beam. Production of new isotopes in

the neutron-rich region near 𝑁 = 126 with fragmentation began at GSI with a 238U primary

beam at 1 GeV/u [31]. This experiment focused on reactions involving the removal of over 40

nucleons, a relatively energetic process compared to previous low energy heavy-ion experiments.

The fragmentation of 197Au was also carried out at GSI [32]. However, this time the focus was

on fragments much closer to the primary beam, and the newly discovered isotopes were the result

of removing only a few nucleons from the projectile. Therefore, while the projectile was still at a

relatively high energy, the reactions that produced the fragments of interests were hypothesized to

come from low excitation energies of the projectile residual. In contrast to the uranium beam, it was

observed that the experimental data from the gold beam did not agree with EPAX , an experimental

parametrization of cross section data [33]. This led to the development of an analytical code named

Cold Fragmentation (COFRA ) [32]. COFRA was based on a simplified version of the abrasion-

ablation model, only considering the 1n decay channel in the de-excitation step. COFRA was able to

reproduce the experimental cross sections for fragments created by the removal of a few nucleons

relatively well.

Next generation facilities continued to push the limits of fragmentation, leading to the discovery

of many new isotopes. Upgrades such as the coupling of cyclotrons at the NSCL [34], and

incremental upgrades to the RIBF accelerator at RIKEN [35] led to the increase of beam intensity

by multiple orders of magnitude. With massively increased beam intensity, a landslide of new

discoveries were made across the Chart of Nuclides [36, 37, 38, 39, 40]. While the aforementioned

11

238U fragmentation experiment was carried out in 1998 at GSI, with a primary beam intensity of

5e6 pps [31], the results of an experiment with 8e8 pps of 238U was published in 2012 [5]. For

perspective, FRIB recently produced a 177 MeV/u 238U beam with a rate of roughly 1.5e12 pps [41].

The 2012 GSI experiment led to the discovery of 60 isotopes, the majority of which are shown in

Figure 1.6. It was reported that fragmentation plays the dominant role in creating elements above

𝑍 = 72 whereas fission becomes the dominant reaction below 𝑍 = 69. The fragmentation of 1

GeV/u 208Pb also led to the discovery of over 20 new neutron-rich isotopes near 𝑁 = 126 [42, 43,

44, 45]. Cross sections were measured and compared to an updated experimental parametrization

(EPAX3 [15]), COFRA, and a Monte Carlo abrasion-ablation code called ABRABLA07 [46]. Both

238U and 208Pb fragmentation studies concluded that EPAX3 underpredicts cross sections in this

region, and that COFRA and ABRABLA07 reproduce experimental data relatively well [5, 47]. In-

flight fission experiments performed at RIKEN using a 345 MeV/u 238U beam led to the discovery

of 29 new isotopes, shown in Figure 1.6. Within the scope of neutron-rich isotopes between

104

𝑁

≤

≤

131, 99 new isotopes were produced from projectile fragmentation or in-flight fission

experiments since the turn of the century.

In the same two decades, only one new neutron-rich nuclide between 104

𝑁

≤

≤

131 was

discovered by MNT in 2010 [27]. Several explorations into the viability of MNT were also

carried out. The main motivation for the renewal of interest in MNT compared to fragmentation

was the difference in cross section. Fragmentation had shown to exhibit exponentially shrinking

cross sections upon subsequent proton removal [47], whereas theoretical predictions for the cross

sections of MNT reactions remained considerably higher [48]. Initially, mass spectra of fragments

produced in the <7.5 MeV/u 136Xe + 208Pb reaction was deduced and found to be even higher than

the previous theoretical predictions [49]. Later, the reactions of 5 MeV/u 64Ni + 207,208Pb were also

explored and found to have higher production cross sections than fragmentation for the most exotic

fragments [50]. However, due to the relatively thin target and lack of a contribution from multi-step

reactions, the production rates for MNT were below fragmentation. Another study of 136Xe +

208Pb was performed, this time at 3.3 MeV/u, and the identity of the products were determined

12

from 𝛾-ray spectra of well known isomers [51]. These results were two orders of magnitude

lower than the theoretical predictions for cross sections of 𝑁 = 126 isotones. The 136Xe + 198Pt

reaction at 8 MeV/u was also executed, and the production cross section for a target-like fragment

resembling 200W, a new 𝑁 = 126 isotone, was extracted from the cross sections of projectile-like

fragments [52].

Turning to the past five years, the interest in MNT reactions has continued to gain momentum.

Several large scale projects have begun to focus on making neutron-rich isotopes near 𝑁 = 126,

such as the N=126 Factory at ANL [53] and the NEXT project [54]. The NEXT project will use a

large solenoid that encloses the production target so that the wide angular distribution of products

can be captured and focused into a beam. Fusion-fission reactions also exhibit large angular

distributions and could benefit from the NEXT project [23]. Some of the latest experimental

results for MNT include the 238U + 198Pt reaction at 10.75 MeV/u, which led to the discovery of

241U [55]. Additionally the 5.60 MeV/u 204Hg + 208Pb reaction was carried out, and it was reported

that experimental cross sections were multiple orders of magnitude greater than leading MNT

models [56], such as the di-nunclear system model (DNS), which originally came from JINR [57].

During that time, the fragmentation of a 198Pt beam led to the most recent discovery of new

isotopes in this region (see Fig. 1.6) and is the focus of this thesis. Eight new isotopes were

discovered using medium energy projectile fragmentation of the neutron-rich 198Pt isotope. First,

the experimental configuration for both the fragmentation of 85 MeV/u 198Pt at NSCL and the

fragmentation of 186 MeV/u 198Pt at FRIB will be presented. Next, the methodology behind

the particle identification of projectile fragments and the measurement of their production cross

sections will be described. A systematic procedure for dealing with asymmetric error will also

be provided.

In addition, a novel charge state analysis will be explained, which was especially

developed to correct large systematic errors in cross section measurements due to ion charge states.

The results will then be presented in three main sections: (i) the discovery of new isotopes, (ii)

cross section measurements, and (iii) the evidence of residual electrons on the projectile fragment.

Each section will be discussed in depth in the discussion chapter, where possible uses for the new

13

isotopes are suggested along with a comparison of cross section results to several models. The

final section of the discussion will provide a detailed motivation for the development of a new

methodology to calculate charge state fractions of heavy ions. Finally, the conclusion will be

presented with a summary of this work, an outlook on the next steps that should be taken, and a

long term perspective of fragmentation’s role in the production of rare isotopes.

14

CHAPTER 2: EXPERIMENTAL CONFIGURATION
Two separate platinum beam fragmentation experiments were performed, one at the NSCL and

one at FRIB. Compared to the NSCL experiment, the FRIB experiment was performed with over

double the primary beam energy and an increase in power of over two orders of magnitude. This

advancement in acceleration capability allowed for the use of a considerably thicker production

target to facilitate an increase in the production rate of rare isotopes. This chapter will first

provide details of configuration for the NSCL experiment and then for the FRIB experiment. The

experimental setups for the NSCL and FRIB experiments are presented here in a form closely

following their descriptions in the 2023 Physical Review C publication [25] and the 2024 Physical

Review Letters publication [58], respectively.

2.1 Fragmentation at NSCL
A 198Pt61

+ beam was accelerated by the Coupled Cyclotron Facility (CCF) at the National Super-

conducting Cyclotron Laboratory (NSCL) at Michigan State University to an energy of 85 MeV/u

and an intensity of 0.3 pnA. The corresponding beam power was 5.05 W. A combination of the

A1900 fragment separator [59] and the S800 analysis beam-line [60] was used to separate and

identify rare isotopes produced from fragmentation of the 198Pt beam. Both nickel and beryllium

targets of varying thickness were utilized at the target position of the A1900.

The experimental setup is shown in Figure 2.1. This two-stage separation system was similar to

a previous NSCL experiment with a 82Se beam [39], which allowed for a high degree of rejection

of unwanted reaction products. However, in this work the S800 beam-line optics were modified to

produce a 50 mm/% dispersion at the target location of the S800 spectrometer. This modification

made it possible to measure momentum without making additional position measurements in

the beam-line, thereby better preserving initial charge state distributions of fragments exiting

the production target. Depending on the presence of an achromatic energy degrader (wedge),

momentum selection slits were present at both Image 1 (I1) and Image 2 (I2) of the A1900

(Figure 2.1). The magnetic rigidity of the system was adjusted depending on the fragment of

interest, but varied between a minimum of 3.2063 𝑇 𝑚 and a maximum of 3.5420 𝑇 𝑚. A 22.7

15

Figure 2.1: Sketch of the experimental setup used in the 198Pt fragmentation experiment performed
at NSCL, as presented in Haak et al. [25]. A 198Pt beam was produced by the NSCL coupled
cyclotrons and fragmented on a production target at the start of the A1900 fragment separator.
Fragments were transported to the target location of the S800 spectrometer and stopped in a silicon
telescope surrounded by GRETINA [61]. Image 1 (I1) of the A1900 was located between D2 and
D3. I1 contained momentum selection slits and an achromatic degrader (wedge). Image 2 (I2) was
located at the focal plane of the A1900, labeled “FP", and it contained another set of slits and a
timing scintillator.

mg/cm2 Kapton wedge was used to increase purity for certain data sets. A summary of experimental

runs and further details can be found in Table 2.1.

At the end of the S800 analysis beam-line, the particles of interest were stopped in a PIN

diode telescope consisting of five stacked silicon detectors (50

50 mm2), with thicknesses of

×

140 𝜇m, 140 𝜇m, 500 𝜇m, 1000 𝜇m, and 1000 𝜇m, respectively [62]. The third silicon detector

in the stack was a segmented silicon strip detector (SSSD). A timing scintillator (150 𝜇m) was

placed at the focal plane (FP) of the A1900 fragment separator, as shown in Figure 2.1. The signals

produced in the silicon stack were used to measure energy loss (Δ𝐸) and total kinetic energy (TKE).

The SSSD was also used to measure position in the dispersive plane and therefore reconstruct an

event-by-event momentum to be used for particle identification (PID). The HPGe detector array,

16

Table 2.1: Experimental Settings.

Data Fragment Magnetic rigidity, 𝐵𝜌
set
D2

3.5150 3.5150

of interest 𝐷1𝐷2 𝐷3𝐷4 𝐷5𝐷6𝐷7 𝑚𝑔

197Ir

𝑇 𝑚

3.4390 Be 23

/

(

)

𝑐𝑚2 𝑚𝑔

/

𝑐𝑚2 𝑚𝑔
-

𝑐𝑚2
/
-

Target Stripper Wedge Δ𝑝

/

𝑝 Time Beam
(%) ℎ𝑜𝑢𝑟 𝑠 particles
0.2

5.9

Part

4.93e12 Isomer tagging

D3a
D3b
D4a
D4b
D5

D6a
D6b
D7a
D7b

186Hf
186Hf
186Hf
186Hf
186Hf

189Hf
189Hf
192Hf
192Hf

3.5127 3.5127
3.5127 3.5127
3.4928 3.4928
3.4928 3.3912
3.3948 3.2875

-
3.4425 Be 23
3.4425 Be 23
-
3.4204 Ni 17 Be 9
3.3147 Ni 17 Be 9
-
3.2063 Be 47

3.4440 3.4440
3.5420 3.5420
3.4910 3.4910
3.4910 3.4910

-
3.3638 Be 47
3.3680 Ni 17 Be 9
-
3.4141 Be 47
-
3.4141 Be 47

-
-
-
22.7
22.7

-
-
-
-

0.1
0.9
0.2
0.8
0.7

0.5
0.9
0.7
0.9

0.4
7.57e11
6.3
4.36e11
7.18e13
3.2
15.4 1.58e14
18.6 2.07e14

22.8 1.72e14
14.4 2.68e14
21.9 6.23e14
13.8 3.00e14

Isomer study

Production
of new
isotopes

GRETINA [61], surrounded the telescope at the end of the S800 analysis beam line, and it was used

to measure gamma rays for high confidence PID via isomer tagging. The delayed timing signal

from the scintillator was used as the stop signal for the time of flight (ToF). The timing signal from

the first pin in the silicon stack was used as the event trigger and ToF start signal.

A concern to be addressed in experiments at intermediate or low energies is the multiple charge

states of ions exiting the production target. In inverse-kinematics experiments, various methods

are employed to prevent primary beam charge states from reaching the detectors. One approach

involves inclining the primary beam on the target, as demonstrated in the case of a 238U beam at

24 MeV/u on light targets at GANIL using the LISE3 fragment separator [23]. Alternatively, thick

targets can be utilized to shift the primary beam charge states to a lower magnetic rigidity relative

to the fragments of interest. This method has been demonstrated by the BigRIPS separator group

in RIKEN experiments [63, 64] with a 238U beam at 345 MeV/u. However, with a 198Pt beam at 85

MeV/u using the A1900 separator, neither of these methods could be applied, necessitating the use

of a thin target to select fragments at rigidities between the primary beam charge states. Each time

a target was replaced, the charge state distribution of the primary beam was mapped out by varying

the magnetic rigidity (𝐵𝜌) of the first two dipoles of the fragment separator (𝐷1, 𝐷2). Therefore,

the central 𝐵𝜌 could be set to a value between charge states of the primary beam.

This experiment was comprised of three parts, as listed in Table 2.1. The three objectives were:

17

(i) isomer tagging for PID, (ii) conducting an isomer study, and (iii) the production of new isotopes.

For the majority of the data sets, the only material present after the target was a scintillator at I2

of the A1900, with the exception of D4b and D5 (see Table 2.1), which contained a wedge at I1

(Figure 2.1). Three separate target configurations were used: thin beryllium (23 mg/cm2), thick

beryllium (47 mg/cm2), and a nickel target (17 mg/cm2) with a beryllium stripper (9 mg/cm2).

For new isotope production, the separator was tuned on more exotic hafnium fragments, namely

189Hf and 192Hf. The wedge was not used at these settings due to the already low rate of exotic

fragments. It was a priority to maintain a high momentum acceptance while striking a balance

between increasing the statistics of reaction products and minimizing detector damage caused by

the edge of the primary beam.

2.2 Fragmentation at FRIB
A beam of 198Pt nuclei was accelerated to 186 MeV/u with the FRIB linear accelerator [26, 65], and

then directed onto a 3.54 mm thick carbon target rotating at 500 rpm with a density of 1.89 g/cm3. All

of the data collection in this experiment was performed with the Advanced Rare Isotope Separator

(ARIS)[66, 67]. The accelerator delivered three charge states to the ARIS target (198Pt66
+

,67

+

,68

+)

enhancing beam intensity by over double compared to using a single charge state [68]. A different

beam dump strategy was utilized at FRIB compared to the previous 198Pt fragmentation at NSCL.

A thicker target was used, resulting in a considerable difference in energy loss of the primary beam

compared to the fragments. This target thickness accounted for 70% of the primary beam’s range,

shifting the unreacted primary-beam ions to a low-𝐵𝜌 region, which could be separated without a

significant loss in the fragments of interest.

In this work, the ARIS ion optics, typically set for momentum compression [66], were adapted

to a non-compression dispersive mode to facilitate the production of a wider array of neutron-rich

isotopes. A 50 𝜇m Al-degrader was placed strategically in the dispersive plane of the preseparator

to block lighter particles using acceptance slits at the DB1 position. The setup is detailed in

Figure 2.2. The C-Bend section of ARIS, from DB1 to DB5, operated as a high-resolution analysis

stage with a horizontal dispersion of 67.4 mm/% at DB3, effectively separating high-𝑍 particles.

18

Figure 2.2: Sketch of the experimental setup used in fragmentation experiment performed at FRIB
as presented in Tarasov et al. [58]. A 198Pt beam was produced by the FRIB linear accelerator and
fragmented on a production target at the start of the pre-separator. Fragments were transported to
the fifth diagnostic box (DB5) where they were stopped in silicon to measure TKE and ToF.

The secondary cocktail beam was stopped at the DB5 station in a silicon PIN diode telescope

comprised of six detectors, each measuring 50x50 mm2, with thicknesses 505, 307, 496, and

998 𝜇m for the final three detectors [69]. These thicknesses were chosen to stop the fragments

of interest in the 4th silicon detector, and the remaining detectors were used to veto reactions

that happened in previous detectors. Trajectory details were deduced from measurements taken at

the DB1, DB3, and DB5 focal points using delay-line position-sensitive parallel plate avalanche

counters (PPACs). The positioning of these instruments is shown schematically in Figure 2.2. A

germanium 𝛾-ray detector was placed at DB5, and aided in PID by detecting the isomeric decay of

188Ta [70], described in the following chapter.

Optimization of the separator to enhance the production of the 190

72 Hf70

+ ion was based on

predictions from the LISE++𝑐𝑢𝑡𝑒 software [6]. The identification of each fragment was performed by

analyzing 𝐵𝜌, ToF, Δ𝐸, and TKE. The detailed methodology will be provided in the following

chapter.

19

CHAPTER 3: DATA ANALYSIS
An event-by-event identification of charged particles passing through the separator and the calcu-

lation of production cross sections for each species of nuclide was performed in this work. This

chapter will begin with a discussion of each method and then continue with a description of the

treatment used to propagate asymmetric error. Finally, a novel Monte Carlo analysis of charge state

fractions will be explained in detail.

3.1 Particle Identification
Particle Identification (PID) was performed with the Δ𝐸-TKE-ToF-𝐵𝜌 method [38] through a series
of three steps:

1. Initial detector calibration using primary beam,

2. Final detector calibration using several fragments of interest,

3. Calibration verification with isomer tagging.

In the first step, a very low rate of primary beam was delivered to the experimental setup

where every detector was triggered. The program LISE++ [16] was used to predict energy loss

(Δ𝐸), time of flight (ToF), and dispersive position of the primary beam and calibrate each detector.

These calibrated measurements were then utilized in the following expressions to calculate nucleon

number (𝐴), proton number (𝑍), and electric charge (𝑞) of the primary beam.

√︄

𝑍

∝

(cid:20)

ln

Δ𝐸
𝛽2

1

(cid:21) −

,

5930𝛽2
𝛽2
1

−

𝐴
𝑞

=

𝐵𝜌
𝛽𝛾

𝑒
𝑢𝑐

,

𝑞 =

𝑢

𝛾

(

𝑇 𝐾 𝐸
1

) (

−

,

𝐴

𝑞

)

/

(3.1)

(3.2)

(3.3)

Equation 3.1 is a simplified version of the Bethe-Bloche formula and the numerical value is

calculated from the mean excitation energy of a silicon medium [71]. All other quantities are

defined as follows:

20

Δ𝐸: Energy loss in material,
𝛽: Relativistic velocity,
𝛾: Lorentz factor,
𝐵𝜌: Magnetic rigidity,
𝑒: Electron charge,
𝑢: Atomic mass unit.

After the initial application of Equations 3.1, 3.2, and 3.3, the centroids of each particle group

on the PID spectra did not line up on the integer axes of 𝑍, 𝐴, or 𝑞. To fix this discrepancy, the

calculated value of each PID variable was linearly calibrated to be equal to the know value of that

variable. This linear calibration was particularly useful for 𝑍 because the simplified Bethe-Bloche

in Eq. 3.1 is only a proportionality. The original Bethe-Bloche formula involves many constants,

but, in this PID code, the constants were replaced by a slope and an intercept.

After the initial calibration, the secondary cocktail beam was delivered to the experimental

setup and the PID was confirmed via isomeric tagging of the well known 188Ta and 190W isomers

(Figure 3.1) [70, 72]. The same isomers were used in both experiments. To perform isomer

tagging, the gamma rays were first detected with either GRETINA at the target position of the S800

spectrograph, in the case of the NSCL experiment, or a smaller HPGe detector located at DB5, in

the case of the FRIB experiment. The gamma ray spectra recorded with these devices were then

gated on peaks whose energy corresponded to a known isomeric decay. These gates were placed

on PID plots to confirm the location of the known isomer (Figure 3.2). In this way, the PID was

able to be confirmed with high confidence.

21

Figure 3.1: A 𝛾-ray spectrum of events in GRETINA recorded up to 800 𝜇s after events identified
as 190W, modified from Haak et al. [25]. This data was recorded during the Be target settings of
the NSCL experiment (see Table 2.1). The energies of the observed peaks correspond to gamma
transitions from the 166 𝜇s isomeric state of 190W [72], confirming particle identification.

𝑞 = 2 gated on specific gamma ray energies from
Figure 3.2: PID spectra of charge state 𝑍
Figure 3.1. The plot on the left hand side shows the PID after placing a single gamma gate from
the 484 keV peak. The plot on the right hand side shows the PID after placing an AND-gate of
both the 484 keV and 694 keV peak. The remaining counts are located at position 𝑍 = 74 and
𝐴

26, or 𝐴 = 190, confirming the identity of 190W72

3𝑞 =

−

+.

−

−

The final detector calibration was performed by collecting raw channel data of each detector

for several particle groups in the confirmed PID and incorporating those measurements into a

large scale optimization process. This process was essentially a multi-dimensional linear fit that

22

010020030040050060070080090010000100020003000400050006000singlesEntries  19716Mean    216.4Integral  3.249e+05Core_Charge calib in kev vs timeE𝛄 (keV)Counts per keV206358484592694W x-raysΔt = 5 𝞵s - 2msFigure 3.3: Calculation procedure for PID calibration. Detectors are as defined from Section 2.1.
A key is included to explain the color scheme. The Bethe-Bloch Log Component is the natural log
term from Eq. 3.1 and the Bethe-Bloch SQRT Component is the entire square root term from Eq. 3.1.
𝑍0 is the initial calculation of the proton number (𝑍) before momentum dispersion corrections.
“Momentum Dispersion From Z" is related to the dispersive position dependence on 𝑍, and it was
only present in data sets with a wedge setting.

23

minimized global error [O. Tarasov, Private Communications]. The global error was defined as the

difference in the calibrated value of each measurement and the predicted value in LISE++ [73, 16].

The optimization for the NSCL data included a linear fit for each Δ𝐸 measurement (four total),

each ToF measurement (two total), and a final linear fit for each PID variable, 𝐴, 𝑍, and 𝑞. The

Δ𝐸 measurement used to calculate 𝑍 was not entirely in the linear region of the Bragg curve, and,

therefore an exponential fit was also applied to 𝑍, specifically to the logarithmic component of the

Bethe-Bloche formula. A detailed flow chart of this procedure can be seen in Figure 3.3.

The FRIB PID followed a similar procedure as the NSCL PID. The main difference was the use

of multiple PPACs, rather than a single SSSD, to reconstruct the trajectories of particles passing

through the fragment separator. This resulted in more accurate calculations of momentum disper-

sion and 𝐵𝜌. The resulting PID spectra from each experiment, demonstrating charge separation,

can be found in Section 4.1.

3.2 Cross Section Calculation

The cross section for production of a given rare isotope is determined from the number of observed

ions of that isotope compared to the expected number for a given reaction. Cross sections were

only calculated for data collected in the NSCL experiment. During the FRIB experiment, the

transmission through the pre-separator was determined to be considerably lower than what was

planned, and it was concluded that the error on those calculations would be too large to provide

meaningful results. The production cross section for individual fragments was calculated using the

following expressions:

𝜎 =

𝑁 𝑓

𝑁𝑏 𝑁𝑡 𝑇 ×

1027

𝑚𝑏

,

]

[

𝑁𝑡 =

𝑡 𝐴𝑣
𝜌𝑡

.

(3.4)

(3.5)

Where 𝑁 𝑓 is the number of a given fragment detected at the end of the fragment separator (or

yield), 𝑁𝑏 is the number of total incoming beam particles, 𝑇 is the fraction of all ions produced at

24

the target and transmitted through the separator, and 𝑁𝑡 is the number of target atoms per unit area.

The number of beam particles, 𝑁𝑏, is the integrated beam current divided by the charge state and the

charge of a proton. The value of 𝑁𝑏 was determined from integrating beam current over the course

of the run. The current was determined from scaler values that are linearly correlated to the beam

current. 𝑁𝑡 was derived via Equation 3.5, where 𝑡 is target thickness, 𝐴𝑣 is Avogadro’s number, and

𝜌𝑡 is the density of the target material. The fraction of transmitted fragments, 𝑇, depends on several

factors including the momentum and angular distribution of fragments produced in the reaction,

the momentum and angular acceptance of the beams lines, and the charge states populated in the

reaction. At the time of this analyis, 𝑇 was calculated using versions 16 and 17 of LISE++𝑐𝑢𝑡𝑒 [16, 6].

The yield of each fragmentation product was obtained by the integration of all counts present

in a given particle group. To avoid undercounting, PID spectra were fit with integer-spaced fixed-

width Gaussian functions. The integer spacing was due to the integer nature of charge and nucleon

number. The fixed width was assigned due to the assumption that experimental resolution was

consistent across all isotopes.

Figure 3.4: Procedure for counting isotopes in one-dimensional spectra while minimizing losses in
event gates. The assumptions for parameter resolution and range are given in green. Spectra are
shown in varying shades of grey, primary gates are shown in blue, and secondary gates are shown
in orange. The convolution of three primary gates with six secondary gates leads to a total of 18
AND-gates. This example is visualized in Figure 3.5.

25

Figure 3.5: A visual example of the gating procedure from Figure 3.4. The data shown is from the
D4a data set (see Table 2.1). The 𝑞 vs mass (𝐴
3𝑞) spectrum is shown with three mass gates on
the left, and 𝑞 vs charge state (𝑍

𝑞) spectrum is shown with six charge gates on the right.

−

−

The integration of integer-spaced fixed-width Gaussian functions was performed on one-

dimensional spectra (Figure 3.6). Due to the fact that three parameters are required to uniquely

identify ions (𝑍, 𝑞, and 𝐴 or 𝐴

−

3𝑞), the reduction of PID spectra to a single dimension required

two series of gates. The first series of gates were drawn about integer values of the best resolution

parameter, which varied between data sets. This series of gates was then applied to two-dimensional

spectra of the remaining two parameters. The second series of gates was drawn within these two-

dimensional spectra around integer values of the second best resolution parameter. The first two

series of gates were then combined into a third series of AND-gates and applied to one dimensional

spectra of the lowest resolution parameter. This process is depicted in Figure 3.4 and 3.5, and

guarantees the lowest resolution parameter was “saved for last". Therefore, the integration of the

fixed-width integer-spaced Gaussian peaks accounted for the most possible overlap of particle group

distributions. A visualization of overlapping edges of Gaussian peaks can be seen in Figure 3.6.

The experimental yield was modified for settings that included a Ni target plus a Be stripper

foil (see Table 2.1). First, cross sections were calculated for the 198Pt + 9Be reaction by using the

26

Figure 3.6: One dimensional fixed-width integer-spaced Gaussian peaks fitted to experimental data
from Figure 3.5. Raw Spectra (blue) is the one dimensional 𝑍 histogram of data from the 𝑞 = 73
3𝑞 = 25 gate. Gaussian Fit (red) shows each individual Gaussian function fitted to their
AND 𝐴
corresponding particle group. Gaussian Sum shows the summed profile of all individual peaks
added together.

−

target-only 9Be runs. Next, the yield of fragments produced in the 9Be foil was estimated using

those cross sections. Finally, the predicted yields of the stripper foil were subtracted from the total

experimental yields to produce a value that corresponded to production in the Ni target.

The next term calculated from Equation 3.4 was the total number of beam particles which hit

the target, 𝑁𝑏. During this experiment we did not have a direct measurement of the beam current

on target at all times. Therefore another quantity, which scales linearly with the beam current, was

chosen as the live measurement which can be recorded at all times. It was necessary to perform

a measurement of both the beam current on target, for example using a Faraday cup at the target

position, and the beam scalar for each given configuration of experimental settings. This ensures

a proper linear calibration of beam scaler to beam current can be performed. In this experiment,

the scaler counts on the scintillator at the extended focal plane of the A1900 separator was used for

27

beam integration. Primary beam current was measured before the attenuator with a Faraday cup

and after the attenuator with a non-intercepting probe. A charge to scaler ratio was calculated for

every measurement of beam current and beam scaler rate taken during the experiment. An average

of this ratio was taken for multiple measurements within a given experimental configuration and

Figure 3.7: A flow chart of the cross section calculation procedure. 𝑇 is the fraction of a given
nuclide that transmits from the target to the end of the fragment separator. The different subscripts of
𝑇, such as targmax, is the value of 𝑇 for a given experimental parameter shift. AEWA (Asymmetric
Error Weighted Average) is an error weighted average that accounts for asymmetric error bars and
is defined by Equation 3.8. Steps 8, 9, 12, 13 utilize the AEWA and are shown in red. Steps 4, 7,
10, 11 constitute the novel charge state analysis developed in this work and are shown in green. The
remaining steps, shown in orange, describe how 𝑇 was calculated and condensed from LISE++ .

28

Step1Identifyexperimentalpa-rametersthatmostsignif-icantlyimpact𝑇(ie.slitwidth,targetthickness,etc.)Step2UsingLISE++,varyeachparameteruntiltheexper-imentalparticleyieldsareroughlyreproducedbyLISE++predictions(defining𝑇𝑚𝑒𝑎𝑛)Step3UsingLISE++,calculate𝑇forthemaximumandminimumvalueofeachparameterchosentovary(ie.𝑇𝑚𝑒𝑎𝑛,𝑇𝑡𝑎𝑟𝑔𝑚𝑎𝑥,𝑇𝑡𝑎𝑟𝑔𝑚𝑖𝑛,𝑇𝑠𝑙𝑖𝑡𝑚𝑎𝑥,𝑇𝑠𝑙𝑖𝑡𝑚𝑖𝑛,etc.)Step4RemovechargestatemodelfactorsfromalltransmissionsStep5Condensealltransmissionsgeneratedfromparametervariationintoasinglemean,max,andminforeachionStep6CalculatecrosssectionswiththemodifiedtransmissionsStep7Duplicatethedataintosev-eralpossibleinstancesof𝑁𝑒𝑅andapplyMonteCarlogeneratedchargestatefractionsforeach𝑁𝑒𝑅Step8GenerateathinandthicktargetdatasetwithineachpossibilityviaAEWAThinTargetSet(D2andD3)ThickTargetSet(D6aandD7)Step9PerformanotherAEWAtocondensechargestates(ions→isotopes)Step12TakeanAEWAofallpos-sibilitiesusingthePDFforweightsforboththinandthicktargetdatasetsStep11Constructadiscreteprobabilitydistributionfunction(PDF)fromthediagnosticfactorsStep10Generatethethreediagnosticfactorstoquantifythelikeli-hoodofeachpossibilityof𝑁𝑒𝑅Normalizationfactor(N)Functionalconsistencyfactor(C)Chargestateoverlapfactor(E)Step13CalculatethefinalcrosssectionmeasurementviaAEWAofthickandthintargetdatasets1used to calculate a total integrated beam current for a given data set. This total charge was then

simply divided by the individual charge of the primary beam, 198Pt61

+, to result in the total number

of beam particles incident on the target.

The transmission value, 𝑇, is defined as the fraction of a given nuclide that transmits from the

point of creation in the target to the point of detection at the end of the fragment separator. This

value represents all of the particles lost at each slit, in each material, around the bend of each dipole,

and through each quadrupole. It is a value that depends not only on the momentum and angular

distribution of the fragments themselves, but also the momentum and angular acceptance of the

beam lines. A final, yet crucial, consideration is the charge states of each nuclide. These charge

state distributions are populated in the production target and change in each subsequent material

down the beam line.

An accurate estimate of 𝑇, along with quantification of its error, is arguably the most complex

aspect of cross section determination due to the multitude of factors which can significantly impact

𝑇. A list of cross section calculations steps involving 𝑇 are depicted in Figure 3.7. These steps will

be referred to by their number for the rest of the chapter. Systematic errors in the cross section are

captured by the estimation of errors in 𝑇. This is a complex process that will be described in detail

in the following section.

3.3 Asymmetric Error

The errors associated with exponential distributions are inherently asymmetric. If an ion distribution

sits on the edge of a slit, closing the slit by a small amount could cause complete loss of transmission.

Opening the slit by a small amount will increase the transmission by several orders of magnitude.

Therefore, it was necessary to formulate a methodology to perform calculations with asymmetric

error and accurately propagate this error to the final calculation. The procedure of the cross section

calculations performed in this work are listed in 13 steps in Figure 3.7. The majority of this

procedure will be described here with the exception of steps 4, 7, 10, and 11, which are related to

a novel method of charge state analysis that is described in the final section of this chapter.

Starting with step 1 (Fig. 3.7), the major sources of systematic error were identified as the energy

29

loss model, the momentum distribution model, the charge state model, and the ion optics setting of

the fragment separator. The ATIMA energy loss model [74] (Option 2 in LISE++ ) and the Universal

Parameterization momentum distribution model [75] (Option 4 in LISE++ ) were chosen for this

analysis. The uncertainty in the energy loss model was probed by variation in material thicknesses,

specifically materials that come before momentum selection slits, such as the production target

and wedge. The uncertainty of the momentum distribution model was explored by variation of

underlying 𝜎 and coeff parameters [75]. The uncertainty of the charge state model was investigated

by questioning certain underlying physical assumptions of the fragmentation process, and it will

be discussed in detail in the next section. The uncertainty of the ion optics setting was examined

by a left-right variation of the I1 slits (see Fig. 2.1). Other quantities that required adjustment

from nominally quoted values during experiment, but were not varied for error estimation, were

the thickness of the focal plane scintillator and the initial energy of the primary beam.

In the next step, the mean value of each target thickness was determined via a global optimization

process involving energy loss of the primary beam. The energy of each primary beam charge

state which reached the I2 thick scintillator (see Fig. 2.1) was experimentally calculated using its

dispersive position at Image 2 and the magnetic rigidity of the separator. This experimental energy

was compared to the difference of the primary beam initial energy and the predicted energy loss in

each target or stripper material using LISE++ . The He-parameterization [76] and ATIMA , options 0

and 2 in LISE++ , were explored in this experiment. The parameters varied during this optimization

included a position calibration at Image 2, the I2 dispersion, all material thicknesses, and primary

beam energy. The most optimal global fit was achieved using the ATIMA energy loss model.

The mean value of slits and momentum distribution assumptions were selected via a manual

optimization process where the yield patterns of experiment were compared to predicted yield

patterns in the LISE++ program. An adequate comparison can be performed by normalizing the

LISE++ beam rate in particles per second to the total number of beam particles detected for a

given data set. An example of this manual optimization process is depicted in Figure 3.8. A final

configuration is shown in Figure 3.9. The goal was to get the overall shape of each ion curve

30

Figure 3.8: Plots of experimental yields vs LISE++ predictions. The comparison of these plots was
used to deduce the optimal wedge thickness for data set D4b (see Table 2.1). The isotopic chain
for tungsten (𝑍 = 74 and 184
196) is shown for varying wedge thicknesses. A total of five
𝑞.
4) are shown from left to right in decreasing order of 𝑍
𝑍
different charge states (0
Thicknesses 20.32, 21.06, 21.81, 22.55, 23.3, 24.05, and 24.8 mg/cm2 are shown in (a) through (g),
respectively. Based on this comparison an optimal wedge thickness of 22.55 mg/cm2 was deduced.

≤
−

≤
≤

𝐴
𝑞

≤

−

to match. Once that configuration is reached, the mean value for each parameter has been set.

This procedure was also applied to the thicknesses of the Ni target and the Kapton wedge when

analyzing the Ni target data in order to further improve upon the aforementioned global energy loss

calibration.

It is important to note that exact agreement is not expected in these comparisons. This is due

to the fact that the yield patterns predicted by LISE++ are produced with cross sections calculated

from a model. Therefore, instead of looking for an exact match, we aimed to match global trends.

Once the mean value of each parameter is set, they must be systematically varied to capture

the error in the transmission (step 3 in Figure 3.7). There is no predefined range to this variation

and therefore an understanding of the underlying models is necessary to stay within physically

reasonable bounds. For example, when comparing the LISE++ yields to the experimental yields

and varying the wedge thickness parameter, one can observe a breakdown of the yield pattern as

31

Figure 3.9: Optimized LISE++ parameters matching experimental results from data set D4a (see
Table 2.1). Counts of each ion are on the y-axis and mass number is on the x-axis. A total of
six elements, with between two and three charge states per element, are shown. The charge states
present in each plot are indicated by the legend and are listed in order from left to right (L to R).
The experimental data is shown in red and the LISE++ predictions are shown in orange.

shown in Figure 3.8. It is clear that the optimal wedge thickness is somewhere in the investigated

range and that the extremes on either end (

10%) are not physically possible. The acceptable range

±

of variation was selected to be between sub figure (c) and (e), a variation of

3%. The range of

±

variation for each parameter selected is shown in Tables 3.1 and 3.2 for the beryllium and nickel

target data, respectively.

The pattern change due to varying the slit width parameter is slightly different than the one for

material thickness. The transmission of ion distributions that sit past the edge of the slit, and only

have an exponential tail within the range of acceptance, will vary wildly with a change in slit width.

32

This contributes to our estimation of the total error. The variation of momentum distribution model

parameters also results in a similar behavior of transmission values. Ion groups that sit outside the

momentum acceptance of the separator in narrow momentum distribution settings may have small

but significant transmissions when the momentum distributions are widened. This is a result of the

exponential tails of momentum distributions.

Table 3.1: Experimental parameters that were varied to asses the uncertainty in the transmission
of fragments produced during runs using a beryllium target. The most probable value for each
parameter in each data set is listed. The amount varied is consistent for each data set and is shown
in the final column. The target thicknesses listed here are not the physically measured values,
which were reported in Table 2.1. This adjustment was made to ensure the best match between
experimental transmissions and the given setup in the LISE++ code.

Parameter
Beryllium Target (mg/cm2)

D2

21.80

D3

21.80

D6a

50.15

D7

50.15

Image-1 Momentum Slits (mm)

-2.2 : +2.5

-15.7 : +11.0

-7.7 : +8.0

-10.6 : +10.0

Momentum Distribution [75] Width

(Separation Energy Model 2)

Coef

125

0.8

125

0.8

125

0.8

125

0.8

Variation

2%

±
20%

±
+25

+0.2, -0.3

Table 3.2: Experimental parameters that were varied to assess the uncertainty in the transmission of
fragments produced during runs using a nickel target. The most probable value for each parameter
in each data set is listed. The amount varied is consistent for each data set and is shown in the final
column.

Parameter
Nickel Target (mg/cm2)
Kapton Wedge (mg/cm2)

D4a

17.75

D4b

17.75

22.5

Image-1 Momentum Slits (mm)

-2.1 : +2.1

-12.4 : +12.4

Momentum Distribution [75] Coef

1.0

1.0

Variation

4%

±

3%

±
20%

±

0.2

±

By step 5 (see Figure 3.7), each ion had roughly seven to nine possible transmission values

predicted by the parameter variation listed in Tables 3.1 and 3.2. The transmission from the

optimized LISE++ configuration file, 𝑇𝑚𝑒𝑎𝑛, was used for 𝑇 in Equation 3.4. The positive and

negative error of the transmission were defined as 𝛿𝑇
+

= 𝑇𝑚𝑎𝑥

𝑇𝑚𝑒𝑎𝑛 and 𝛿𝑇
−

−

= 𝑇𝑚𝑒𝑎𝑛

𝑇𝑚𝑖𝑛,

−

respectively. 𝑇𝑚𝑎𝑥 and 𝑇𝑚𝑖𝑛 are the maximum and minimum transmission values of the seven to

33

nine possibilities predicted in parameter variation. This method ensured the most conservative

approach to preserving the estimated error from the previous steps.

The propagation of the transmission error, 𝛿𝑇
±

, to the cross section error, 𝜎
±

, was performed

via direct calculation as shown in Equation 3.6. Next, 𝜎
±

was adjusted, using Equation 3.7, to

include the uncertainty of the fragment yield, 𝛿𝑁 𝑓 . The propagation of error from 𝑇 and 𝑁 𝑓 was

performed in two steps, instead of a single step with the error propagation formula, because 𝛿𝑁 𝑓

was symmetric and 𝛿𝑇
±

was asymmetric.

=

𝜎
±

𝜎

∓

±

𝑁𝑏 𝑁𝑡

𝑁 𝑓
𝑇

(

𝛿𝑇

∓)

∓

𝜎∗
±

= 𝜎
±

√︄(cid:18) 𝛿𝑁 𝑓
𝑁 𝑓

(cid:19) 2

𝑇
𝛿𝑇
∓

1

+

(3.6)

(3.7)

To conclude that exactly 68% or 95% of the probability is encapsulated in the cross section

error bars would be incorrect. However, it is acceptable to say the true value does lie within the

limits selected and that the error bars are a reasonable estimation of systematic errors. In fact, this

method can be considered more conservative than the standard partial derivative method of error

propagation, which is not suitable for use here because there is asymmetric error. Additionally, the

cross section function has a strictly positive domain which requires corrections to error analysis

methods that result in negative error bars greater than the mean value. The limited sampling of

the parameter space also led to an issue where 𝑇𝑚𝑒𝑎𝑛 could equal the minimum or maximum of the

sample. These issues led to two corrections for the lower error bar:

(i) if 𝜎∗
−
(ii) if 𝜎∗
−

> 𝜎 then 𝜎∗
−
= 0 then 𝜎∗
−

= 0.9𝜎
=

𝛿𝑁 𝑓

(

0.1𝜎
−

+
𝑁 𝑓

/

𝜎

)

[correction of non-physical case],
[correction when 𝑇𝑚𝑒𝑎𝑛 = 𝑇𝑚𝑎𝑥],

and one correction for the upper error bar:

(i) if 𝜎∗
+

= 0 then 𝛿𝑇
−

= 0.1𝑇𝑚𝑒𝑎𝑛

[correction when 𝑇𝑚𝑒𝑎𝑛 = 𝑇𝑚𝑖𝑛].

The Asymmetric Error Weighted Average (AEWA) mentioned in steps 8, 9, 12, 13 of Figure 3.7

was performed next. Due to the exponential nature of the data, both the cross section values and

34

their error bars were transformed to log scale before the AEWA operation. Then the mean result

of the AEWA ( ¯𝑐) was calculated via a simple weighted average. The weight of each cross section

(𝑤𝑖) was chosen to be inversely proportional to its underlying transmission (absolute inverse log).

The error bars were calculated via the following analytic function:

(cid:118)(cid:117)(cid:117)(cid:117)(cid:117)(cid:117)(cid:116)

=

𝑆

±

¯𝐴

+

𝜎±𝑖

𝑛
∑︁

𝑖=1

,

𝑉
±𝑛
∑︁

𝑤𝑖

𝑖=1

(3.8)

where 𝑆

±

is the negative and positive error of the final result, 𝜎± is the negative and positive

error for each input data point, ¯𝐴 is a weighted error amplitude shown in Equation 3.9, and 𝑉
±

is a

conditional weighted sum of variances (Eq. 3.10 and 3.11).

¯𝐴 =

1
𝑛√2𝜋

𝑛
∑︁

𝑖=1

(

𝜎±𝑖 𝑤𝑖
𝜎+𝑖 )
𝜎−𝑖 +

2

= 2

𝑉
+

= 2

𝑉
−

𝑛
∑︁

𝑖=1

𝑛
∑︁

𝑖=1

¯𝑐

(

¯𝑐

(

−

0

−

0









2𝑤𝑖

𝑐𝑖

)

if ¯𝑐 < 𝑐𝑖,

otherwise

2𝑤𝑖

𝑐𝑖

)

if ¯𝑐 > 𝑐𝑖,

otherwise

(3.9)

(3.10)

(3.11)

A graphical representation in the difference between this method and the standard method when

dealing with symmetric errors can be seen in Figure 3.10. The mean value of the symmetric error

propagation is miscalculated and is greater than both mean values of the input data points.

In

comparison, the mean value of the asymmetric case lies between the two input data points which

is expected for the average of two values.

35

Figure 3.10: Probability distributions of two arbitrary data points with asymmetric error, Data1 and
Data2. The standard symmetric average of these measurements and the specialized asymmetric
average used in this work (AEWA) are shown. Data1 and Data2 are equally weighted in both
averages shown here. The y-axis is probability as a fraction of unity, and the x axis is arbitrary
units of the independent variable. The symmetric and asymmetric distributions have yet to be
normalized.

3.4 Charge States

Ions passing through material can pickup or lose electrons. In this analysis, the final charge state was

modeled by GLOBAL [77]. The systematic error associated with GLOBAL was large and motivated the

creation of a novel method of analysis. The implementation is described here, while the motivation

is explored in Section 5.3. The number of electrons on the projectile fragment residue, 𝑁e𝑅 , was

selected as a physically significant quantity to consider when calculating charge state fractions from

a Monte Carlo approach. This method of analysis included the removal of charge fractions from

LISE++ output files (step 4 of Figure 3.7), the calculation of new charge state fractions for several

possibilities of the 𝑁e𝑅 parameter (step 7), the formulation of three optimization parameters to

quantify the probabilistic likelihood of each 𝑁e𝑅 (step 10), and the construction of a discrete PDF

using those three parameters (step 11).

Starting with step 4, the underlying charge state fractions calculated by GLOBAL were removed

36

from LISE++ transmission values. This was performed by using the result file provided by the

“Transmission A,Z,q-last" option in LISE++ (extension res4). Inside this result file are two columns

of interest:

the “Trans, %" column and the “q_All-trans%" column. To remove the underlying

charge state fractions, the former was simply divided by the latter. The transmission values were

then considered ‘raw’, or without reduction due to charge state factors.

In step 7 of Figure 3.7, the charge-related transmission fractions were calculated for several

possibilities of the 𝑁e𝑅 parameter. A charge state fraction was calculated for every material in

the beam path using a Monte Carlo simulation in LISE++ . The total charge-related transmission

factor for a given element was simply the product of each material’s individual charge state fraction

for that element. Only one nuclide of the isotopic chain was considered for each element, as the

charge state fractions did not vary significantly with changing neutron number. Also, due to the

small momentum acceptance of the beam lines, only ions which remained in the same charge state

throughout the entire separator, from production target to implant, were considered in this analysis.

The actual execution of Monte Carlo simulations in LISE++ was performed as follows:

1. The LISE++ calculation assumed no slits for each data set (thick and thin target) so that a

measure of solely charge state effects on transmission could be performed.

2. 𝑁e𝑅 was set via: Physics Models →Production Mechanism →Charge States →Charge state

after reaction.

3. Navigated to: Calculations →Monte carlo calculation of transmission →Target.

4. Selected “One FRAGMENT of interest" and set the fragment to be an isotope of the desired

element.

5. Material was selected from drop down menu of “X-coordinate."

6. The “q (ion charge)" option was selected in the “Ion parameter (M, Z, q...) box.

Two separate charge state distributions were calculated for each element: (i) ions exiting the

target and (ii) ions exiting the scintillator. Figure 3.11 shows a two-dimensional Monte Carlo plot

from LISE++ comparing these two distributions for a given isotope. It was assumed that the only

ions reaching the end of the separator were those that did not undergo electron pickup or ionization

in the scintillator. These events are represented by the ion groups on the X=Y line of Figure 3.11

(each group is denoted by a red square contour). To calculate the charge-related transmission factor

37

Figure 3.11: The dependence of the final charge state distribution on 𝑁e𝑅 is illustrated. Two-
dimensional charge state distributions of 196Os for 𝑁e𝑅 = 7 and 𝑁e𝑅 = 0 are on the left and right,
respectively. Generated via a Monte Carlo simulation in LISE++ , each figure shows the charge state
distribution of the isotope exiting the target on the x-axis and the charge state distribution exiting
the scintillator on the y-axis. The particle groups enclosed in red boxes represent the ions which
did not change charge state in the scintillator and were consequently transmitted through the S800
analysis line to the detector setup.

for a given ion of a given element, the number of events of for that X=Y ion group was divided by the

total number of events created in the simulation. Table A.3, in the appendix, lists the charge-related

transmission factors for all ions detected in the thin Be target settings (see Table 2.1).

In some cases with small transmissions, such as 𝑇 < 10−

6, the Monte Carlo calculation did not

produce events, even after extensive run time. This often occurred when 𝑍

𝑞 values were high and

−

𝑁e𝑅 values were low, such as 𝑍

−

𝑞 = 5 and 𝑁e𝑅 = 0 (see Figure 3.12, on the left). To address this

issue, the program ETACHA4.v3 [78, 6] was used to calculate the charge state distribution of ions

exiting the scintillator. These calculations provided a relatively accurate estimate of the charge state

fraction for very low transmission ions (see Figure 3.12, on the right). This charge state fraction

was then used to extrapolate the Monte Carlo results, which had too few statistics, by multiplying

the ETACHA fraction calculated for the scintillator by the Monte Carlo fraction calculated for the

target.

The bounds of 𝑁e𝑅 exploration were set using the following considerations. Although 𝑁e𝑅

38

Figure 3.12: A LISE++ Monte Carlo calculation of 196Os charge states using GLOBAL is compared
with an ETACHA4.v3 calculation for a low statistic charge state. A two-dimensional Monte Carlo
calculation of charge state distributions is shown on the left. The red rectangle highlights a low
𝑞 = 5. The red X indicates the absence of any events
statistics charge state exiting the target at 𝑍
𝑞 = 5 after exiting the scintillator. The plot on the right compares
where the ion remains at 𝑍
the results of the Monte Carlo calculation (MC in grey) and an ETACHA calculation (in orange) of
the charge state distribution of 196Os71
+ exiting the scintillator. The MC data shown in grey is the
y-projection of the data in the red rectangle.

−

−

values from 0 to 17 are physically possible because the primary beam was in charge state 𝑍

𝑞 = 17+,

−

the physically probable range is much smaller due to the rapid ionization of high energy particles

passing through material. Therefore, the charge-related transmission factors were sampled for three

different elements within a limited range of 𝑁𝑒𝑅 = 0 to 𝑁𝑒𝑅 = 7. These factors changed slowly

at first and then a large jump was noticed from 𝑁e𝑅 = 4 to 𝑁e𝑅 = 5, and then remained constant

afterward, as depicted in Figure 3.13. This led to a focused analysis of only 𝑁e𝑅 values less than

five.

It was then necessary to quantify the probabilistic likelihood of each 𝑁e𝑅 shown in Figure 3.13,

as described in step 10 of Figure 3.7. During quantification, the following three factors were

considered: (i) agreement of cross section measurements between ions of the same nuclei (𝐸), (ii)

physically possible cross section measurements (𝑁), and (iii) the consistency of production cross

sections for a given isotopic chain as a function of mass (𝐶).

39

Figure 3.13: The cross sections measurement of rhenium isotopes (𝑍 = 75) were calculated for
𝑁e𝑅 = 0 to 𝑁e𝑅 = 7, six of which are shown here (Be target data). Four charge states are present,
𝑞 = 5, 4, 3, and 2, and are shown in purple, cyan, red, and green, respectively. EPAX3 is
𝑍
plotted as a reference (solid black line). In the instance of 𝑁e𝑅 = 3, the cross sections are consistent
between ions of the same isotope and the overall magnitude is physically reasonable.

−

The first consideration was quantified by the average log error of each measurement and will

be denoted as 𝐸. It can be seen by comparison of Figure 3.13 and 3.14 that when the underlying

individual cross section measurements of different charge states do not overlap, the resulting error

(𝐸) is large (for example 𝑁e𝑅 = 5). The second consideration, denoted as 𝑁, was quantified by

a normalization factor which would shift the cross section lines to a physically reasonable range.

𝑁 was simply a multiplicative factor that shifted the data up or down on the cross section plot. A

value of 𝑁 = 1 corresponded to no shift and indicated the data was within a physically acceptable

range. The third consideration, denoted as 𝐶, was quantified by the average log difference of the

experimental data and the cross section model COFRA [32]. 𝐶 was interpreted as a simple residual

in log space, where a value of 𝐶 = 1 would indicate the experimental data is, on average, an order

40

&URVV6HFWLRQPENeR =T =T =T =T NeR NeR NeR 0DVV1XPEHU$NeR NeR Figure 3.14: The cross sections of rhenium isotopes (𝑍 = 75) for three separate possibilities of
𝑁e𝑅 (0, 3, and 5), as presented in Haak et al. [25]. Each possibility shown here was calculated by
an AEWA of charge states from its corresponding plot shown in Figure 3.13. The COFRA model
has also been added in for reference (dashed orange line).

of magnitude away from the model for a given data point. This consideration ensures that the

functional form of the cross section data is roughly a decaying exponential.

With a collection of optimization factors defined, a final optimization was performed. The

numerical results of the normalization factor, 𝑁, were adjusted so that a value of 𝑁 = 1 corresponded

to the global minimum in that parameter space. Then the numerical results of each consideration was

summed together with equal weight. This produced a quantifiable numerical value that represented

the physical likelihood of each instance of 𝑁e𝑅 . The functional form of this value was such that

a smaller value represented a more likely scenario. A three-dimensional figure of this discrete

function is presented in Figure 4.8 of the following chapter.

Each point in the discrete function was then exponentially inverted using Equation 3.12 and

smoothed out following the constraint in Equation 3.13. This ensured that the most likely 𝑁e𝑅

value occupied roughly 68% of the total probability for a given 𝑍. These discrete probabilities

were used as the weights for the AEWA that condensed all possibilities of 𝑁e𝑅 into a single cross

section measurement. One final AEWA was performed with the thick and thin target data sets to

produce the final result of the cross section measurements.

41

0DVV1XPEHU&URVV6HFWLRQPENeR NeR NeR &2)5$(3$;𝑓𝑁𝑒𝑅

𝑥

(

)

= 𝑥1
−

𝑃𝑁 𝑒𝑅

𝑁𝑒𝑅=5∑︁

𝑖=1

1

/

!= 68%

𝑓𝑖

𝑥

(

)

(3.12)

(3.13)

In order to consider the bias of using COFRA as a reference, this final optimization process was

performed using both COFRA and EPAX3 as the reference for the 𝑁 and 𝐶 optimization parameters.

The cross section data from the thin and thick target data sets are shown in Figure 3.15. In the case

of using COFRA as the reference in optimization, the cross section data from both thin and thick

target data sets agreed well with one another. However, when using EPAX3 as the reference for

optimization, there was noteable disagreement for higher 𝑍 elements. The results of both the cross

section calculation and evidence of a new observation in this method of analysis will be presented

in Section 4.3, and the motivation for this novel method will be discussed in Section 5.3.

The Ni target runs did not use this charge state analysis because the Ni target was relatively

thick. Instead the charge state fractions were modified by a normalization constant determined in

Figure 3.16. The yield patterns of each charge state predicted in LISE++ were normalized to match

experimental data. The normalization constant was calculated by minimizing a weighted average

of differences in log space between LISE++ predictions and experimentally recorded values. Each

weight was proportional to the log of the transmission. The normalization constant was then applied

to each respective charge state fraction in the Ni target analysis.

42

Figure 3.15: A comparison between the final cross section measurements produced from a COFRA
based optimization (lower row) and EPAX3 based optimization (upper row). The result of both
thin and thick target data sets are shown in red and blue respectively. As a reference, the cross
sections predicted from EPAX3 and COFRA are shown by the the dashed black line and dashed green
line, respectively. When using EPAX3 as a basis for optimization, the thin and thick target results
disagree. The COFRA based optimization shows overlap within error for most data points.

43

Figure 3.16: Yield curves for ions detected in data set D4a (see Table 2.1) are compared to
LISE++ predictions. The LISE++ curves are shifted (blue) to match the yield curves observed in
experiment. A total of six elements are shown, hafnium through iridium.

44

CHAPTER 4: RESULTS
In both NSCL and FRIB experiments, new isotopes were identified and hence discovered. Ad-

ditionally, the cross sections of rare isotopes produced in the NSCL experiment were extracted.

Finally, a novel Monte Carlo based approach to charge state fraction calculations led to evidence

of a new observation regarding the charge state of a projectile fragment immediately after reaction.

These three results will be presented in the aforementioned order. The experimental results for the

NSCL and FRIB experiments are presented here in a form closely following their descriptions in the

2023 Physical Review C publication [25] and the 2024 Physical Review Letters publication [58],

respectively.

4.1 Particle Identification and New Isotope Discovery

Particle identification (PID) was performed using the magnetic rigidity (𝐵𝜌), time of flight (ToF),

and total kinetic energy (TKE) method as described in Section 3.1. ToF was used to calculate the

velocity and then extract the mass to charge ratio from 𝐵𝑝. The proton number (𝑍) was determined

from energy loss (Δ𝐸) in silicon detectors, and charge (𝑞) was determined from the velocity and

Figure 4.1: Particle identification spectra obtained from D4b settings (see Table 2.1), as presented
𝑞 spectra (center)
in Haak et al. [25]. The separation of charge states is demonstrated in the 𝑍
where helium-like and lithium-like charge states were observed. The charge state selection gate
at 𝑍
3𝑞 (left) and
3𝑞 (right) spectra demonstrate mass, ion charge, and elemental separation quality. A
𝑞 vs. 𝐴
𝛾-ray spectrum observed in coincidence with 190W72
+ ions labeled here was used to confirm the
identification (Figure 3.1).

𝑞 = 2 (red rectangle) is applied to both left and right plots. The 𝑍 vs. 𝐴

−

−

−

−

45

TKE. The visualization of PID spectra with multiple charge states was performed with a gate on a

single charge state (𝑍

−

𝑞), as shown in Figure 4.2. The quantity 𝐴

3𝑞 was selected to represent

−

the mass of each particle group due to a cancellation of underlying systematic error in ToF [79].

Multiple charge states were successfully separated in particle identification (PID) spectra of

both fragmentation experiments. The quality of mass, charge, and elemental separation can be

seen in Figures 4.1 and 4.2. The resolution of the mass to charge ratio was 𝜎

𝐴

𝑞

)

/

(

= 0.005

and 𝜎

𝐴

𝑞

)

/

(

= 0.001 for the NSCL and FRIB experiments, respectively. This improvement in

resolution was possible due to the use of multiple PPACs to reconstruct the 𝐵𝜌 of charged particles,

as opposed to using a single SSSD.

Figure 4.2: Two dimensional PID spectra of the fragments detected in the FRIB experiment, as
presented in Tarasov et al. [58]. Spectrum (a) shows charge (𝑞) vs charge state (𝑍
𝑞), and spectrum
3𝑞). The separation of charge states is visible in (a) and
(b) shows proton number (𝑍) vs mass (𝐴
𝑞 = 2). This gate is applied to the spectrum shown
a gate is drawn on the He-like charge state (𝑍
in (b). The red line in the right spectrum indicates the limit of previously observed nuclides. 188Ta
is designated with a pink arrow for reference.

−

−

−

During the course of the NSCL experiment, three new isotopes, namely 189Lu and 191,192Hf,

46

=TTD$3T=1887DZq=2Ewere discovered. The measured cross sections of these nuclides were found to be 0.037(24), 0.13(5),

and 0.061(44) nb, respectively. The evidence for these new isotopes is shown in Figure 4.3. These

one-dimensional mass spectra were generated by applying a series of PID gates as was outlined in

Section 3.2. In this case, a 𝑍 and 𝑍

−

𝑞 gate were used. Counts to the right of the blue dashed line

indicate previously undiscovered nuclides. These discoveries push the limit of Hf isotopes up to

the point where the production of heavier isotopes would involve the pick-up of neutrons from the

target. Although the experimental settings allowed for the potential observation of new isotopes

down to 181Er, they were not detected.

(a) Hafnium isotopes.

(b) Lutetium isotopes.

Figure 4.3: Mass spectra of hafnium and lutetium isotopes produced in the D7 settings of this
experiment (see Table 2.1). This figure is presented as shown in Haak et al. [25]. Standard
deviations produced with Gaussian functions at constant width (dashed red line) are given for each
element. The dashed vertical blue line shows the limit of previously discovered isotopes for each
element. The counts at 𝐴 = 189 for 𝑍 = 71 and 𝐴 = 191,192 for 𝑍 = 72 are evidence for the
discovery of new isotopes.

The FRIB 198Pt fragmentation experiment also produced new isotopes in this region. The five

new isotopes were 182Tm (29 events), 183Tm (7), 186Yb (27), 187Yb (3), and 190Lu (5). Evidence

of these nuclides are presented in Figure 4.4. 52 counts of 189Lu are also present, which is slightly

over an order of magnitude higher than the NSCL results. One count of both 191Lu and 184Tm were

observed. Assuming that the momentum distributions of each isotope are well within the acceptance

47

of the separator and extrapolating the exponentially decreasing peaks along each isotopic chain,

three counts are expected for 191Lu and two counts are expected for 184Tm. It is plausible these are

the first observed events of 191Lu and 184Tm, however using Poisson statistics, the uncertainty is

equal to the number of counts and cannot be claimed.

Figure 4.4: One dimensional mass spectra of fragments detected in the FRIB experiment, as
presented in Tarasov et al. [58]. The black line is a histogram of the experimental data, the dashed
red line is the series of Gaussian peaks fitted to the experimental data, and the blue dashed line is
the previous boundary of discovery.

All together, eight new isotopes were discovered between these two experiments. Figure 4.5

summarizes these discoveries. Additionally, pick-up reactions of one to two neutrons were observed

in both experiments. pick-up reactions closer to the primary beam were observed in the NSCL

experiment, whereas pick-up reactions further out were observed in the FRIB experiment. This

difference is most likely due to the fact that the FRIB experiment was tuned to more exotic 𝐵𝜌

settings than the NSCL experiment.

48

172174176178180182184100101102103174176178180182184186178180182184186188190Yield Tm (69)s(A) = 0.274  Yb (70)s(A) = 0.274 Yield Mass numberLu (71)s(A) = 0.277Figure 4.5: Chart of nuclides in the neutron-rich region “south" of 198Pt, modified from Tarasov
et al. [58]. New isotopes discovered at NSCL are shown in green, and new isotopes discovered
at FRIB are shown in yellow. The small blue, red, and purple marks indicate pick-up reactions
observed in the FRIB experiment, the NSCL experiment, and both, respectively.

4.2 Cross Sections

Using PDFs derived from discrete functionals, such as the one shown in Figure 4.8, the production

cross sections were obtained for a total of 60 nuclides in the NSCL experiment. A selection of nine

isotones are shown in Figure 4.6. Numerical details are available in Table A.1 of the appendix.

Experimental cross sections follow trends predicted by EPAX3 and COFRA models. However, there

is a slight deviation away from the models for lower 𝑍, where the measured cross section is lower

than predicted. This effect possibly appears in an odd-even pattern, where the cross sections of

isotones with an even number of neutrons are often much lower than their odd counterparts.

49

No fragments with atomic number 𝑍 < 70 were produced in significant quantities at the

rigidity settings employed in the NSCL experiment.

Initially, the contribution of the “break-

up" channel in terms of the abrasion-ablation model can explain this phenomenon, where the

temperature of the excited pre-fragment exceeds the limiting temperature [80, 81]. However, a

more detailed explanation involving the mean excitation energy of the prefragment can be provided

with intranuclear cascade codes such as BeAGLE [82]. The average excitation energy for fragments

of a 198Pt projectile is several MeV per abraded nucleon higher than fragments of a 208Pb or

Figure 4.6: Cross section measurements of isotones (112
120) as a function of atomic
number, as presented in Haak et al. [25]. These isotones were produced in the fragmentation
reaction of 198Pt (85 MeV/u) with 9Be and are compared to EPAX3 and COFRA . New isotopes are
denoted with red circles.

≤

≤

𝑁

50

238U projectile. This finding was acquired through private communications with Dr. Oleg Tarasov

(2024).

The measurement of 198Pt (85 MeV/u) + Ni production cross sections was also performed with

data set D4 (see Table 2.1). The estimated yield due to the Be stripper was calculated using the

cross sections obtained from the Be only target runs. The Ni target was well above equilibrium

thickness, resulting in the same outcome regardless of 𝑁e𝑅 . Therefore, instead of the Monte Carlo

method described in Section 3.4, the transmission values provided by LISE++ were normalized to

roughly match the experimental yield patterns. The results are shown in Figure 4.7. Assuming

the cross section should scale geometrically with increasing size of the target nucleus, the Ni cross

sections should be roughly 24% larger than the Be cross sections. However, for data with physical

results, the Ni target cross sections were on average 20 times larger than the Be target cross sections.

The cross sections of these 50 fragmentation products are listed in Table A.2 of the appendix.

51

Figure 4.7: Experimentally measured cross sections of 198Pt + Ni plotted with model estimates for
reference. The subtraction of events due to the Be stripper resulted in negative values for the mean
and lower error bar for many measurements. These cases were set to values off the chart.

52

= = &URVV6HFWLRQPE= = = = 0DVV1XPEHU$= (3$;&2)5$$%/$([SHULPHQW4.3 Evidence of Residual Electrons

Following the novel charge state analysis outlined in Section 3.4, two separate probability distri-

bution functions (PDF) of 𝑁e𝑅 were created from experimental data. The results are presented

in Figure 4.8. 𝑁e𝑅 , or the number of electrons on the projectile residual immediately after frag-

mentation, was explored for the range of zero to five electrons. The PDFs in Figure 4.8 represent

the likelihood that a given 𝑁e𝑅 is valid for a given number of protons removed (Δ𝑍). Each Δ𝑍

represents an entire isotopic chain, from iridium to lutetium. The PDF for the thinner 23 mg/cm2

beryllium target exhibits a relationship between Δ𝑍 and 𝑁e𝑅 . The PDF for the thicker 47 mg/cm2

target contains a less discernible trend.

(a) 23 mg/cm2 target thickness.

(b) 47 mg/cm2 target thickness.

Figure 4.8: A summary of the most probable 𝑁e𝑅 values are presented for several values of abraded
proton number (Δ𝑍), derived from the analysis of experimental data, modified from Haak et al. [25].
Two different target thicknesses are shown, the thinner 23 mg/cm2 target and the thicker 47 mg/cm2
target. The vertical color axis represents a combination of three optimization considerations:
agreement of cross section measurements between ions of the same nuclei, physically possible
cross sections measurements, and the consistency of the production cross section for a specific
element as a function of nucleon number.

The presence of this trend in one data set and the absence in another can be explained by

an equilibrium thickness argument. After a certain depth in a material, the electron pickup and

stripping effect becomes balanced in an equilibrium, and this depth can be calculated from properties

53

of the material and the beam [32, 25]. The approximate equilibrium thickness of beryllium for

ions between 71

𝑍

≤

≤

77 at roughly 85 MeV/u is somewhere between 60 and 235 mg/cm2

depending on the charge state model used [25]. This calculation demonstrates that the thinner

target is considerably below equilibrium, but the thicker target is approaching equilibrium.

A relationship between the number of protons abraded in fragmentation (Δ𝑍) and the residual

number of electrons on the fragmentation product immediately after reaction (𝑁e𝑅 ) was observed

for the first time. As Δ𝑍 increased 𝑁e𝑅 decreased. This could be related to the fact that as the

difference between initial and final atomic ionization energies increases, fewer electrons will remain

bound to the fragmenting nucleus. An additional factor could also be electron shake-off from the

sudden change of velocity during the abrasion step, where more velocity is lost with more abraded

nucleons. While such effects are challenging to detect due to continuous ionization and electron

pickup of ions passing through a medium, this observation was possible due to the following three

factors: (i) the relative excess of electrons on the primary beam (198Pt61

+ has 17 electrons), (ii)

the use of a thin production target well under equilibrium thickness, and (iii) the limited use of

materials in the beam path.

54

CHAPTER 5: DISCUSSION
The primary goal of this work was to study the production of neutron-rich rare isotopes near

𝑁 = 126 via medium energy fragmentation reactions. This previously unexplored fragmentation

of 50 - 200 MeV/u 198Pt led to the discovery of eight new isotopes, and provided insight into the

reaction mechanism that produced them. The implications of these isotopes and their production

cross sections for nuclear structure and reaction studies will be discussed in this chapter. The

cross section data were used to test the validity of several fragmentation models in the neutron-rich

region near 𝑁 = 126. Finally, the significant issue of charge states associated with high 𝑍 isotopes

at intermediate energies will be discussed. While this issue impacts PID to a significant degree,

its impact on cross section calculations arguably adds a much greater challenge to understanding

the production of rare isotopes in the 𝑁 = 126 region. Therefore the novel charge state analysis

developed in this work will be discussed in detail in this chapter.

5.1 Uses for New Isotopes

As presented in Section 4.1, eight new isotopes were discovered in this work. In principle, these

isotopes could now be prepared and delivered to nuclear experiments. On the basis of beam intensity

and time extrapolation, the new isotopes could be delivered anywhere between 373 particles of

187Yb to 23,271 particles of 191Hf in the span of a week-long experiment. Operation of ARIS in

the standard 𝑘 = 3 optics setting [66] would likely yield a gain of 20 times these numbers. It is also

important to note that with successive accelerator upgrades, the increase of primary beam intensity

is likely to continue to push the boundary of discovery in this region. This experiment was run at

1.5 kW, and eventually 400 kW should be possible. With the FRIB400 upgrade [26], additional

gains of 10x are likely. Delivering new isotopes to scientific users of FRIB, or producing these

isotopes in other facilities, can make an impact in a wide variety of nuclear physics experiments,

such as isomer studies, shape evolution, and reaction mechanism studies. A selection of useful

isotopes for nuclear reactions and structure studies are visualized in Figure 5.1.

The NSCL 198Pt fragmentation experiment was a collaboration with the University of Mas-

sachusetts Lowell to explore nuclear structure in the neutron-rich Hf region. These experimental

55

settings produced not only new isotopes but significant rates of other exotic isotopes, such as 186Hf.

The main goal of the nuclear structure study was to explore K isomers in neutron-rich Hf isotopes,

and a manuscript is currently in preparation [P. Chowdhury, Private Communciations]. The iso-

meric decays of these heavy nuclides provide useful insight to the collective motion of nuclear

matter. Neutron-rich nuclides near 𝑁 = 126 provide a parallel to the super-heavy element region,

where deformations are the key to observing longer lived isomers than the ground state [83].

The low-lying excited states of neutron-rich tungsten isotopes are also of interest to nuclear

Figure 5.1: The chart of nuclides near 𝑁 = 126, generated with LISE++ . Isotopes that can extend
the reach of previous nuclear structure studies through the 𝐸4
ratio are denoted by a green
square. Isotopes that can aid in the development of existing nuclear reaction models through the
measurement of momentum distributions are denoted with a white square. All nuclei which have
not had their ground state beta-decay half-life directly measured are denoted with the gold square.
The color of each isotope tile represents a decay mode, with grey indicating stable isotopes.

/𝐸2
+

+

56

structure, specifically nuclear shape evolution studies [84, 43]. The ratio of the first 4+ excited

state and 2+ excited state for even-even nuclei, such as certain isotopes of tungsten, can provide

information about the shape of the ground state of the nucleus [84]. Previous studies have explored

this ratio up to 𝑁 = 116 for W isotopes and 𝑁 = 112 for Hf isotopes [43], but these can now be

expanded all the way out to 𝑁 = 120 for both elements (see Fig. 5.1). Even-even Yb isotopes are

also relatively unexplored and may also be considered for nuclear shape evolution studies.

Reaction mechanism studies can also benefit from these new isotopes by extending our exper-

imental knowledge of momentum distributions populated in fragmentation reactions. One such

example of using momentum distributions to formulate a better understanding of fragmentation is

the design of LISEAA [85]. Experimental measurements of momentum distributions are sparse for

projectile fragments in the neutron-rich region near 𝑁 = 126. The momentum distributions of ions

produced in the fragmentation of 950 MeV/u 197Au were measured, however this data only reached

the five proton removal channel. The discovery of 192Hf from the fragmentation of 198Pt extends this

reach to 6 proton removal (Δ𝑍 = 6). Additionally, elements below Δ𝑍 = 7 were not considered in

the cross sections measurements, whereas the FRIB experiment was capable of producing Δ𝑍 = 8

and 9. Another significant contribution to the understanding of heavy-ion collisions at intermediate

energy is the pick-up of nucleons from the target. A total of eight nuclides created from pick-up

reactions were observed between the two fragmentation experiments in this work. All 21 nuclides

mentioned here are highlighted in Figure 5.1. The COFRA reaction model, along with others, is

considered in the next section for the interpretation of cross section results.

5.2

Interpretation of Cross Section Results

The cross section results from Section 4.2 were compared to four separate models: EPAX3 [15],

COFRA [32], ABRABLA 07 [46], LISEAA [85]. The strengths and weaknesses of each model will

be discussed, along with the available user options. Finally, a comparison of the 198Pt + Ni cross

sections to the 198Pt + Be cross sections will be briefly discussed.

EPAX3 is a parametrization of experimental production cross sections measured from various

fragmentation reactions [15]. The EPAX formula is a product of two main components: the mass

57

yield and the charge dispersion. The mass yield is a sum of all isobars of a given fragment mass

𝐴, and the charge dispersion is a Gaussian-like function that describes the distribution of elements

within a given isobaric chain. There is no underlying physics in the EPAX formula, and it simply

aims to reproduce the functional shape of experimental data. Despite this disadvantage, EPAX3 still

provides reasonable estimates for a wide variety of cases. However, EPAX3 was unable to produce

consistent agreement with the experimentally measured cross sections in this work. Most notably,

EPAX3 underestimates cross sections for the high-𝑍 fragments in this work, and overestimates

cross sections for low-𝑍 fragments (see Fig. 5.2).

COFRA (cold-fragmentation) is an analytical abrasion-ablation code which only considers neu-

tron evaporation in the ablation step. The publicly available code [86] only allows four parameters

to be varied: mass number and atomic number for both the projectile and the target. All other

physical parameters, including beam energy, are contained within the source code and cannot

be modified directly. This prohibits testing the impact and validity of given assumptions in the

model. However, COFRA was designed to provide accurate estimates for cross sections of cold-

fragmentation, a process where relatively small excitation energies are populated in the projectile

during peripheral collisions. This is the case when comparing COFRA to experimental data in this

work. COFRA estimates cross sections of higher mass elements closer to the projectile reasonably

well, only significantly deviating beyond the removal of four protons (see Fig 5.2).

58

Figure 5.2: Experimental cross section measurements of 85 MeV/u 198Pt + 9Be are compared to five
different models: EPAX3 , COFRA , ABLA , LISEAA+PGD , and LISEAA+ME . The closest agreement
occurs with LISEAA+PGD and ABLA models. A quantitative measure, calculated from an error-
weighted average of residuals in log space is given in Table 5.1.

ABRABLA07 (ABLA ) is a Monte Carlo abrasion-ablation code which considers a wide range of

decay channels including fission and emission of intermediate mass fragments (IMF). ABLA has

a couple more adjustable parameters than COFRA , allowing the user to set the projectile energy

59

= = &URVV6HFWLRQPE= = = = 0DVV1XPEHU$= = (3$;&2)5$$%/$/,6($$3*'/,6($$0(([SHULPHQWand toggle thermal expansion of the projectile residual on and off [46]. The impact of thermal

expansion on cross section estimates for 85 MeV/u 198Pt + Be was tested, but no significant

difference was noted. When compared to experimental results in this work, ABLA estimated cross

sections reasonably well for both high-𝑍 and low-𝑍 isotopes (see Fig 5.2). This is most notably true

for the heaviest neutron-rich isotopes of lutetium and hafnium, which were measured to be over

an order of magnitude lower than both COFRA and EPAX3 . However, ABLA struggled providing

an isotopic slope that could match experimental data for every element. For intermediate elements

(73

𝑍

≤

≤

75) ABLA estimated a cross section slope steeper than experimental values.

It is

important to note that this feature in the experimental data could be influenced by charge states as

can be seen in the cross sections of individual ions in Figure 5.6.

The statistical nature of Monte Carlo codes makes estimating small cross sections challenging.

In order to extend the reach of ABLA , the source code was modified to consider a restricted range

of values for impact parameter and excitation energy of the prefragment. These changes led to a

decrease in runtime by roughly two orders of magnitude. A qualitative depiction of this impact is

shown in Figure 5.3, demonstrating the difference between default ABLA and modified ABLA . The

most significant impact to runtime was the restriction of the impact parameter. This is one of the first

Figure 5.3: Experimental cross section measurements of 85 MeV/u 198Pt + 9Be are shown in blue
for three representative isotopic chains: 𝑍 = 71 lutetium, 𝑍 = 72 hafnium, and 𝑍 = 73 tantalum.
EPAX3 , ABRABLA07 , and modified ABRABLA predictions for this reaction are indicated by the solid
black line, dotted-dashed red line, and dotted cyan line, respectively.

60

&URVV6HFWLRQPE= 0DVV1XPEHU$= = (3$;$%5$%/$$%5$%/$
([SHULPHQWcalculations performed, and runtime can be saved by not considering small impact parameters that

lead to large excitation energies or breakup of the projectile. Other minor changes that contributed

to these improvements included disabling evaporation channels known to play little to no role in

the creation of fragments of interest. Both IMF and fission channels were disabled during the use

of ABLA in this work.

Individual events can be inspected in Monte Carlo codes, allowing for the step-by-step descrip-

tion of low statistics processes. ABLA allows the user to generate an event file that contains detailed

information about every product generated during runtime. This includes impact parameter, exci-

tation energy of the prefragment, velocity distributions of the prefragment, and both the initial and

final values of mass and charge of the projectile fragment. This functionality allowed for the precise

definition of impact parameter and excitation energy limits that were used to reduce runtime. A

representative example of this functionality is shown in Figure 5.4. The total events generated are

Figure 5.4: A histogram of pre-fragment excitation energies for events generated in the ABLA code.
The impact of several gates are shown in the excitation energy spectrum. An impact parameter (𝐵)
gate is shown in orange. Within the 𝐵 gate, another excitation energy gate is shown in purple. The
excitation energy of specific isotope regions are shown in red and green, as indicated in the key.

61

shown in blue and every subsequent color is a subset of the total. The first cut applied was to impact

parameter, reducing the data to only peripheral collisions. The second cut was simply drawn on

low excitation energy events of the impact parameter subset. To demonstrate the location of exotic

fragments within this excitation energy spectrum, two specific regions were selected, shown in

green and red. These are the most neutron-rich fragments just below the primary beam. Their

excitation energies are small.

LISEAA is an analytical abrasion-ablation code with multiple adjustable parameters for both the

abrasion and the ablation step. In the abrasion step, several excitation energy models are provided

as options in the LISE++ code. The two models selected to be presented in this work are the

Parametrized Gaussian Distribution (PGD) [87] and the Mean Exponential (ME) model [88]. The

PGD model assumes the excitation energy follows the functional form of a Gaussian distribution.

Both the mean excitation energy and the width of the Gaussian distribution is calculated from a

second order polynomial that is a function of the number of abraded nucleons. The ME model

assumes the functional form of the excitation energy is exponential with a mean value 𝑇 that is

used to normalize the function. In the ablation step, the user can choose to enable or disable any

Table 5.1: The error weighted average of residuals in log-space for each model compared to
experiment was tabulated. A value of 1.00 indicates the model deviated on average one order of
magnitude from experimental data. Values are given for each element, as well as a sum for each
model. The minimum for each isotopic chain is bolded. For the complete list of parameter values
used in the LISEAA+PGD model, see Table A.4 of the appendix.

Z

70

71

72

73

74

75

76

77

Sum

EPAX3

COFRA

ABLA

LISEAA+PGD

LISEAA+ME

0.566

0.421

0.368

0.297

0.165

0.197

0.178

0.385

2.577

0.754

0.887

0.898

0.906

0.562

0.641

0.595

0.694

5.937

1.071

0.940

0.677

0.507

0.379

0.544

0.484

0.829

5.431

1.111

1.043

0.839

0.631

0.388

0.331

0.145

0.212

4.700

0.509

0.534

0.430

0.897

0.532

0.390

0.170

0.179

3.641

62

number of decay modes, including 1n, 2n, 1p, 2p, 𝛼, and several others. This work only considered

the 1n, 1p, 𝛼, fission, and breakup modes. Both LISEAA+PGD and LISEAA+ME were optimized

to best fit the experimental data. LISEAA+PGD was able to provide reasonable estimates for most

nuclei observed in this work (see Fig. 5.2). Specifically, the agreement between LISAA+PGD and

experimental data for light isotopes of lighter elements was unrivaled among all models tested. On

the other hand, LISEAA+ME had the polar opposite result consistently deviating from experimental

cross sections of lighter isotopes for every element by several orders of magnitude.

Experimentally measured cross sections for 85 MeV/u 198Pt + Be were most accurately repro-

duced by LISEAA+PGD and ABLA . A quantitative measure of each model’s accuracy is presented in

Table 5.1. It is important to keep in mind the differences between each model to understand the im-

plications for future experiments. LISEAA+PGD was numerically optimized to fit the experimental

data, and is therefore a tightly trained model on a specific data set. The results of this optimiza-

tion should be used for future experiments under similar settings. The complete list of optimized

parameter values for this data are listed in Table A.4 of the appendix. In order for LISEAA+PGD

to play a role in planning experimental rates of secondary RI beams, previous experimental results

are needed to lay the groundwork. As for ABLA , estimates were generated without prior knowledge

of the experimental data. Therefore, while not as accurate as LISEAA , ABLA can be referenced for

a wider range of scenarios, even in the absence of pre-existing experimental data.

The production cross sections of 85 MeV/u 198Pt + Ni was extracted from a Ni target + Be

stripper setup using the experimental Be cross sections presented in this work. The experimental

198Pt + Be cross sections were used to estimate the number of fragments produced in the stripper,

and the observed counts were adjusted by this estimate. This introduced significant error into the

calculation in two ways. Firstly, the experimental measurements of production cross sections for

198Pt + Be contained their own significant errors from the previous analysis. Second, the two step

process of first estimating the counts due to the stripper and then calculating the 198Pt + Ni cross

sections from the remaining counts, doubled the contribution of the transmission error in the Ni

target settings. The consequence of these significant errors are demonstrated in Figure 5.5. While

63

the upper limit of most fragments was successfully calculated, the lower limit was non-physical

when the estimated counts due to the Be stripper was greater than the experimentally observed

counts.

Figure 5.5: A comparison of cross section measurements for isotopes produced from 198Pt + 9Be
fragmentation (shown in blue) and 198Pt + 59Ni fragmentation (shown in red). Both EPAX3 and
COFRA are plotted in solid lines and dash-dotted lines, respectively for reference. The color for the
references match the data sets.

It is difficult to draw a meaningful conclusion with the large uncertainties presented in the

data. However, it can be noted that Ni cross sections are systematically higher. This indicates that,

within error, the nickel target cross sections are larger than the beryllium target cross sections. On

average, the Ni cross sections were approximately 20 times larger than the Be cross sections for

data with physical results. This is considerably larger than the increase in cross section that would

be expected due to the difference in size between the Be and the Ni nucleus. This result suggests

that, for projectile fragmentation, heavy neutron-rich targets could be preferable over beryllium and

carbon targets if the multiple charge states could be handled effectively.

64

5.3 Motivations and Limits of the Novel Charge Analysis

As presented in Section 4.3, the charge state of the projectile residual immediately after reaction

(𝑁e𝑅 ) can significantly impact charge state distributions of fragments produced in thin targets.

The effects of 𝑁e𝑅 are great enough that a rough value can be extracted from experimental data. A

novel charge state analysis, involving the enumeration of all possible 𝑁e𝑅 values via Monte Carlo

simulation, was designed and applied. The motivation, strengths, and weaknesses of this method

will be discussed in this section. Finally, alternative methods will be briefly discussed.

There was a charge-related inconsistency in cross section measurements when using the default

charge state model in LISE++ (see Figure 5.6). The production cross section of a given nuclide

is independent of its charge, however there was a considerable discrepancy between two ions of

the same nuclide in the experimental data. The measurements did not overlap, even within error.

In order to correct this, the fractions for each charge state were manually adjusted until the cross

section measurements overlapped. For example, the 𝑍

𝑞 = 3 charge state for 𝑍 = 76 in Figure 5.6

−

was shifted down until both the 195Os73

+ and 196Os73

+ measurements overlapped with the 195Os74
+

and 196Os74

+ measurements of the 𝑍

𝑞 = 2 charge state. Next, the 𝑍

𝑞 = 4 charge state was

−

−

shifted down to overlap with the already shifted 𝑍

𝑞 = 3 charge state. However, this procedure

−

Figure 5.6: Preliminary cross section calculations using the default settings in LISE++ . Default
settings include 𝑁e𝑅 = 0, the GLOBAL charge state model, and the distribution method of calculating
charge states (as opposed to the Monte Carlo method). The data set presented here is D3b from
Table 2.1.

65

&URVV6HFWLRQPE= 0DVV1XPEHU$= = (3$;=T =T =T did not apply a shift to the final charge state, 𝑍

𝑞 = 2.

In other words, there was no global

−

normalization. Despite the fact that the charge state fraction of 𝑍

𝑞 = 2 contained uncertainty,

−

there was no statistically defined range for the uncertainty. Therefore, the ambiguity of this final

normalization step led to reconsidering the methodology of the charge state analysis.

In order to solve the charge-related inconsistency, the underlying physical processes of the

charge state model were systematically explored and questioned. Initially, the 85 MeV/u 198Pt61
+

beam enters the production target with 17 electrons and experiences both electron pickup and

ionization, simultaneously. At the given beam energy and initial charge state, the ionization cross

sections dominate, rapidly stripping the projectile of its electrons (see Figure 5.7). At a certain

depth, the electron pickup and ionization effects begin to balance each other out, and the variance

of the mean charge state, < 𝑞 >, approaches a minimum. This behavior is illustrated in Figure 5.7,

where < 𝑞 > can be seen rapidly increasing upon entering the target, and eventually leveling off at

around < 𝑞 >= 75.5

. The thickness at which this balance of electron pickup and ionization occurs

+

is defined as the equilibrium thickness. Increasing the thickness past this point leads to only minor

changes in the charge state distribution, provided the beam does not deposit a significant portion of

its kinetic energy in the target. According to Scheidenberger [77], the equilibrium thickness can be

estimated via the following expression:

𝐾 +
𝐾 is the ionization cross section for an electron on the K-shell, and 𝜎

(

where 𝜎1

𝑥𝑒𝑞

≃

𝜎1

4.6
𝜎

0, 1

2
)/

(5.1)

0, 1

)

(

is the one-

electron attachment cross section into the bare projectile from all filled target shells. Ionization cross

sections can be approximated by first order perturbation theory methods such as the plane-wave born

approximation (PWBA). The electron attachment cross section is a combination of two processes,

radiative electron capture (REC) and non-radiative electron capture (NRC). REC dominates for

small Z of the target nucleus. NRC becomes significant at larger Z of the target nucleus, granted the

beam energy is sufficiently low (less than 300 MeV/u) [77]. Using Equation 5.1, the equilibrium

thickness for a 85 MeV/u 198Pt beam passing through beryllium is 𝑥𝑒𝑞 = 121.60 mg/cm2. The

66

Figure 5.7: ETACHA4v3 was used to calculate the mean charge state (first row), charge state
distributions (second row), and charge state evolution (bottom three) of 198Pt61
+ passing through
9Be. A total of five increasingly thick samples of 9Be are shown (A,B,C,D,E = 0.5,2.5,10,23,47
mg/cm2). In the first row, the mean charge state is indicated by the pink solid line, the standard
deviation is indicated by the dashed blue line. Samples A, C, and E are chosen for the charge state
evolution plots.

67

same beam passing through nickel results in an equilibrium thickness of 𝑥𝑒𝑞 = 52.09 mg/cm2.

For a higher energy 186 MeV/u 198Pt beam passing through carbon, the equilibrium thickness is

𝑥𝑒𝑞 = 195.40 mg/cm2.

The fragmentation of the primary beam may occur at any depth in the production target. The

probability of the fragmentation reaction occurring in a given charge state of the primary beam is

proportional to the integral of the charge state evolution curves in Figure 5.7, and several examples

are provided in Figure 5.8. These curves indicate that a considerable number of primary beam

electrons are present during most reactions in the target.

The projectile fragmentation reaction mechanism can be described by the two step Abrasion-

Ablation model. In the abrasion step, the smaller target nucleus punches a hole through the larger

projectile nucleus, removing several nucleons in a near instantaneous time step. The removal of

nucleons imparts an excitation energy to the residual nucleus. In the ablation step the projectile

residual will evaporate nucleons and emit gamma radiation until it reaches a particle bound state.

The ablation step is relatively short lived, and the prefragment will evaporate to the final fragment

Figure 5.8: ETACHA4v3 was used to calculate the probability of the fragmentation reaction
occurring in every possible primary beam charge state while in the production target. Values are
calculated for the three targets used in the NSCL experiment: 47 mg/cm2 Be, 23 mg/cm2 Be, and
17.8 mg/cm2 Ni.

68

before the projectile residual exits the target. This model does not consider or predict the behavior

of the electrons bound to the projectile.

The default settings in LISE++ produce projectile fragments that are fully stripped of all primary

beam electrons immediately after reaction (𝑁e𝑅 = 0). This standard assumption was questioned,

and an investigation into the probability of electron shake-off in a nuclear reaction was explored.

A recent publication [89] generalizes the electron shake-off probability for any number of proton

removal by calculating the overlap of electron orbital wave functions for the initial nucleus bound

state and the final nucleus continuum state. This calculation was parameterized by the ratio

𝑍, where 𝑍 and 𝑍′ are the proton numbers for the initial and final nucleus, respectively.

𝛾 = 𝑍′/
In the NSCL experiment, 𝛾 ranged between 1 and 0.91. This corresponds to a probability of

less than 1% to lose electrons in the 1s, 2s, and 3s electron shells. The wave function overlap

methodology also predicted that for a fixed principal quantum number, the electron shake-off

probability decreases with increasing angular momentum quantum numbers. These predictions

indicate that the electrons from the primary beam will play a significant role in the charge state

distributions of fragments exiting a thin target.

The impact of primary beam electrons on the charge state distributions of fragments exiting the

target was probed by exploring a newly defined parameter: the number of electrons bound to the

projectile residual immediately after interaction, or 𝑁e𝑅 . The implementation of this methodology

was described in Section 3.4, the dependence of 𝑁e𝑅 on Δ𝑍 was presented in Section 4.3, and an

argument for the value of this method will be made here in two main points: (i) the enumeration

of all physical possibilities via Monte Carlo simulations contains less assumptions than analytical

codes, and (ii) 𝑁e𝑅 provides an insight into the reaction mechanism.

The calculation of modified charge state fractions by way of Monte Carlo simulation removes the

standard assumption that a projectile fragment is formed fully stripped after a reaction. Additionally,

due to the probabilistic nature of enumerating all possible scenarios, there is a justified normalization

of charge state fractions. This is an improvement compared to the standard analysis briefly discussed

at the beginning of this section. After aligning all charge states in Figure 5.6, there was no accurate

69

method for a final normalization step nor a quantification of error. This is the fundamental ambiguity

of standard charge state analysis that was addressed with the Monte Carlo method.

Figure 5.9: A PID spectra from data set D3b (see Table 2.1) with no calibration and no cleaning.
Proton number, 𝑍, is on the y-axis and charge state is 𝑍
𝑞 on the x-axis. A trend between 𝑍 and
𝑞 is indicated with the red and black lines. Lower lying Z has lower lying charge states. Charge
𝑍
−
𝑞 = 4
state 𝑍
−
charge state. Two ions predicted to be well within the acceptance of the separator, 198Ir75
+ and
181Ta69
+, are not present in the PID spectra. The missing ion group positions are indicated by a
black X. Figure 5.10 shows the predicted particle distribution of each ion on the detector.

𝑞 = 5 only extends down to 𝑍 = 77, and iridium isotopes only extend to the 𝑍

−

−

The physical relationship between 𝑁e𝑅 and Δ𝑍 presented in Section 4.3 potentially provides a

new experimental observable for the fragmentation reaction. This relationship was strong enough

that it was observed in the PID patterns of experimental data before calibration and before cleaning

(see Figure 5.9). The PID spectra exhibited a clear relationship between 𝑁e𝑅 and Δ𝑍, even to the

naked eye. This pattern was further confirmed by inspecting spatial distributions of 181Ta ions with

the LISE++ program. The 𝑍

−

𝑞 = 5 charge state was clearly within the acceptance of the fragment

separator at both momentum selection slits (see Figure 5.10). However, no instances of this charge

70

Figure 5.10: LISE++ was use to calculate particle distributions of Ta and Ir ions at the detector
position (see Fig. 2.1) for the D3b settings (see Table 2.1). Two 181Ta ions, are shown on the left,
𝑞 = 3. The green
𝑍
vertical line represent the extent of the slit width. He-like 198Ir and B-like 181Ta are well within the
acceptance of the separator, but are absent in the PID of Figure 5.9.

𝑞 = 4. Two 198Ir ions are shown on the right, 𝑍

𝑞 = 5 and 𝑍

𝑞 = 2 and 𝑍

−

−

−

−

state were observed in experiment. This indicates the pattern in Figure 5.9 is not an illusion created

from the ion optics settings of the fragment separator. It is interesting to note that such a pattern

may be even more noticeable in proton rich nuclei. The cross section of proton removal would

be considerably higher than for neutron-rich nuclei, and the 𝑁e𝑅 vs Δ𝑍 trend may even be more

visible.

The Monte Carlo enumeration of 𝑁e𝑅 also has its limitations, as the method relies on very

little change to the charge of an ion after it is created. Therefore, if the production target is thick,

or if there is a significant amount of material in the beam path after the target, the charge state

information related to the reaction will be erased upon repeated ionization and electron pickup.

This effect was highlighted in Figure 4.8, where the 𝑁e𝑅 vs Δ𝑍 trend was washed out for the 47

mg/cm2 target.

While not a critique on the method itself, it is important to remember that an underlying charge

state model was used to calculate the Monte Carlo charge state distributions. Specifically, GLOBAL

in Non-Equilibrium mode was used, which was shown to perform less accurately than ETACHA4v3

in the charge state study of the primary beam (see Fig. 5.11). However, scripting ETACHA for

71

Figure 5.11: Charge state distribution of the primary beam, 198Pt61
+, exiting the Ni target + Be
stripper setup. Experimental data is shown with red diamonds, ETACHA4.v3 [78] is shown in
black triangles, GLOBAL [77] is shown in green, and Winger [90] is shown in purple.

extended calculation was avoided due to the time cost of development. A possible upgrade for this

method could be utilizing the closest matching charge state model for the underlying calculations

rather than using what is fast.

Despite improvements to the accuracy of charge state fraction predictions, the error of the

charge state model was uncertain. The probability weighted average of all possible outcomes of

𝑁e𝑅 helped reduce reliance on the charge state model. Each weight was defined by the optimization

of physical parameters, which were defined by the experimental data. This resulted in a correct

estimate of the most likely mean value for the charge state fraction and supplied an error estimate

based on the available data. However, each Monte Carlo calculation still utilized the GLOBAL charge

state model to define its underlying probability distributions. These model based predictions, which

do not contain clearly defined uncertainties, were reduced in the novel charge state analysis but

were not completely eliminated. Examples of this behavior can be seen in Figure 5.2 for rhenium,

𝑍 = 75, where a charge-related inconsistency can still be observed in the final data.

Further improvements to this charge state analysis method should be considered, and one

such improvement is discussed here. Rather than defining each possible scenario by 𝑁e𝑅, a new

parameter equal to the number of electrons removed during reaction, Δ𝑁𝑒, would be a more suitable

72

parameter for Monte Carlo calculations. As seen in Figure 5.8, the fragmentation reaction may

occur in several different charge states of the primary beam. The most probable charge state for

the thin Be target was 𝑍

−

𝑞 = 3. If 𝑁e𝑅 is set to a value of five, it is implied that the projectile

fragment is picking up two electrons during fragmentation. The pickup of two electrons from

beryllium is technically possible. However, when this situation is extrapolated to 𝑍

𝑞 = 0 and

−

𝑁e𝑅 = 5, a five-electron pick-up is implied, which is greater than the number of electrons bound

to a Be atom. Exploring the newly proposed Δ𝑁𝑒 parameter would eliminate such issues as long

as a simple conditional was included to prevent Δ𝑁𝑒 > 𝑍

𝑞, another non-physical scenario. To

−

go a step further, the probabilities of electron shake-off due to the sudden removal of protons could

be calculated and then included in the Monte Carlo code to further increase the accuracy of such

calculations.

73

CHAPTER 6: CONCLUSION
Fragmentation of a 198Pt beam was explored at 85 MeV/u and 186 MeV/u, and both instances resulted

in the discovery of new isotopes. This is the first progress toward reaching the neutron dripline

in this region in over a decade. The cross sections of fragmentation products for both beryllium

and nickel targets were measured, and noticeably larger cross sections were observed for the nickel

target. The experimental data was most accurately reproduced by the ABRABLA07 and LISEAA

models. A novel charge state analysis was developed and applied to the charge state distributions

of materials below equilibrium thickness. Probability distributions for the newly considered 𝑁e𝑅

parameter were generated from Monte Carlo calculations, and a relationship between the number

of protons removed and 𝑁e𝑅 was observed. Greater proton removal corresponded to less electrons

remaining on the projectile residual, and this relationship has the potential to provide additional

insight into the fragmentation reaction upon further study.

Future studies of heavy isotope production will be necessary. This can be accomplished by

focusing on increasing primary beam intensity, studying the details of all reaction mechanisms at

play, and accurately modeling the charge state and trajectory of ions as they pass through materials

in a fragment separator. An improved, or entirely new, model for the fragmentation reaction is one

of the most urgent issues needed to keep up with the increasing reach of next generation facilities

and their ability to produce exotic nuclei at exceedingly small cross sections. Each one of these

points will be briefly discussed in this chapter, and the final section will offer a few perspectives

regarding the future of rare isotope production.

6.1 Summary
Two medium energy fragmentation experiments of 198Pt were performed at two distinct energies, 85

MeV/u and 186 MeV/u. The fragmentation of 85 MeV/u 198Pt on Be and Ni targets was executed at

the NSCL with the coupled cyclotron accelerators and the A1900 fragment separator [59]. The PID

was performed using the Δ𝐸-TKE-ToF-𝐵𝜌 method, where the majority of detectors were located

at the end of the S800 analysis beam line [60]. The fragmentation of 186 MeV/u 198Pt on a carbon

target was executed at FRIB using a linear accelerator and ARIS [26, 67]. The fragment separator

74

was utilized as the analysis line, and all PID detectors were contained in the C-Bend.

The products from both experiments were identified using the same Δ𝐸-TKE-ToF-𝐵𝜌 method,

and cross sections were measured for the NSCL data. The cross section for each ion detected in the

NSCL experiment was calculated using the yield of the ion, the total number of beam particles, the

particle density of the target, and the transmission fraction of ions that made it from the target to the

PID detectors. The asymmetric errors of transmission values were preserved in most conservative

manner: by direct calculation of upper and lower limits of the cross section. Multiple cross

section measurements of the same isotope across multiple charge states and experimental runs

were averaged together by the analytic AEWA method describe in Section 3.3. The fractions of

charge state distributions were modified for the Be target data using a novel Monte Carlo calculation

method. The cross sections for Ni target data were calculated without any modifications to the

charge state fractions. Calculations for both the Be and Ni target data used the charge state model

GLOBAL .

Successful event-by-event particle identification and the discovery of new isotopes was carried

out in both experiments. The separation of charge states was achieved in both experiments with an

increase in 𝐴

/

𝑞 resolution by a factor of five from the NSCL experiment to the FRIB experiment.

191,192Hf and 189Lu were discovered in the NSCL experiment, and 190Lu, 186,187Yb, and 182,183Tm

were discovered in the FRIB experiment. Pick-up reactions were observed in both experiments.

The cross sections for 72 nuclides produced in the 198Pt + Be reaction and 50 nuclides produced

in the 198Pt + Ni reaction were measured in the NSCL experiment. In addition, the first known

evidence of electrons on the projectile residual immediately after reaction (𝑁e𝑅 ) was observed.

The PDFs generated during the novel Monte Carlo charge state analysis exhibited evidence of a

trend between the number of protons removed (Δ𝑍) and 𝑁e𝑅. For the first time, it was observed

that as Δ𝑍 increased, 𝑁e𝑅 decreased. This trend was more evident for the thinner of the two

beryllium targets. The Ni target cross sections were, on average, an order of magnitude larger than

the Be cross sections. However, these results have large uncertainty due to multiple contributions

of transmission errors (see Section 5.2).

75

The new territory claimed by these experiments can be used for future studies on nuclear

structure and reactions. Several nuclear structure studies exploring the shape evolution of even-

even nuclei can be expanded with the isotopes produced by 198Pt fragmentation [84, 43]. The

experimental basis for fragmentation reaction models can also be expanded upon with momentum

distribution measurements of these rare isotopes.

A comparison of EPAX3 , COFRA , ABRABLA07 , and LISEAA was performed within the region

explored in this study [15, 32, 46, 85]. COFRA performs well for the removal of relatively few

protons, whereas EPAX3 underestimates for high-Z elements and overestimates for low-Z elements.

ABRABLA07 reproduced experimental data relatively well across the entire range of the experiment,

highlighting the importance of the de-excitation step in the abrasion-ablation model. However, there

was a noticeable difference in the cross section slope for a given element as a function of isotopic

mass. The LISEAA model, when used with a parametrized Gaussian distribution for the excitation

energy, was optimized to best fit the experimental data. This was quantitatively demonstrated with

an error-weighted log-residual calculation.

The novel Monte Carlo method for charge state analysis was motivated by the need to reduce

uncertainties on the charge state model. The consideration of 𝑁e𝑅 as an experimentally relevant

parameter is justified based on the low probability of shaking off electrons during a sudden removal

of protons. An enumeration of all the possible values for 𝑁e𝑅 led to the least possible reliance

on the charge state model. Additionally, the PDFs associated with 𝑁e𝑅 provide an insight into

the intensity of the reaction mechanism, exhibiting a relationship between Δ𝑍 and 𝑁e𝑅 . This

relationship is strong enough to be visible in PID spectra. On the other hand, the novel method of

charge state analysis presented in this work crucially depends on the 𝑁e𝑅 parameter. Information

of 𝑁e𝑅 is only experimentally detectable with thin production targets and few materials in the beam

path.

6.2 Outlook

The results presented in this work should be expanded upon by pursuing three separate directions

of exploration: (i) increased beam intensity, (ii) reaction mechanism focused experiments, and (iii)

76

charge states evolution of ions in materials. Increased beam intensity experiments should focus on

pushing the boundary of discovery further while collecting fundamental information about these

new isotopes, such as beta-decay half-lives. Reaction mechanism focused studies should reconsider

the role of excitation energy in leading models and make efforts to include more physical observables

in the models. The charge state evolution of ions passing through multiple materials in a fragment

separator should be more precisely described by optimizing existing models to large scale data sets

of secondary beam yields with multiple charge states.

Increased beam intensity will help establish a foothold of understanding in the neutron-rich

region near 𝑁 = 126. This understanding begins with the identification of new isotopes. Limiting

our consideration to the neutron-rich region between 104

𝑁

≤

≤

131, the production of over

109 new isotopes are predicted to be possible at 400 kW of beam power and optimal optics using

the 𝑘 = 3 setting of ARIS [26]. All 109 of these isotopes are shown in Figure 6.1, alongside the

new isotopes presented in this work. The cross sections of each new isotope, including the five

discovered in the FRIB experiment of this work, should be measured. Other fundamental properties

of nuclei, such as mass, half-life, and charge radius, should also be measured. FRIB is equipped

with the LEBIT [91], FDSi [92], and BECOLA [93] projects to perform such tasks.

Reaction mechanism studies are also essential for pushing further into the unknown. Several

directions include: considering new mechanisms that come into play at low cross sections, revising

fragmentation models to be accurately tested in an experiment, and exploring new observables

related to the details of the nuclear reaction. The increasingly high primary beam rates available

at next-generation facilities can probe reactions with much smaller cross sections than fragmenta-

tion [26]. For example, the pick-up of several nucleons is significantly lower than the fragmentation

of several nucleons, however pick-up reactions were still observed in this work and could be used to

deliver RI beams to the "right" of neutron-rich primary beams. Another contribution to production

that is not normally significant, unless to act as a contaminant, is secondary reactions [94]. How-

ever, now that beams can be provided at high energies and high intensities, the production target

can be made very thick, increasing the cross section of fragmentation for the primary beam and

77

Figure 6.1: The neutron-rich region between 104
131 as presented in Section 1.3, now
highlighting the discovery capabilities of FRIB at 400 kW. The new isotopes discovered in this
work are shown in green, and new isotope discoveries possible at the 400 kW setting at FRIB are
shown in yellow. These estimates were made assuming a rate of roughly 1e-5 pps was necessary
to detect a new isotope. Isotopes still out of reach are shown in dark grey and the dripline can be
seen on the bottom right in white, indicating unbound nuclei.

≤

≤

𝑁

the fragments themselves. A key future advancement will be FRIB400, that may provide ten times

more reach [26].

Fragmentation models rely heavily on excitation energy, a quantity that cannot be experimen-

tally measured [32, 46, 85]. This is a major weakness of the theoretical framework surrounding

fragmentation and should be reconsidered to create a stronger link between experiment and theory.

78

This can be done in either one of two ways: (i) develop experimental techniques to measure the

excitation energy of projectile fragments immediately after reaction, or (ii) restructure theoretical

models to include more physical observables that directly relate to the excitation energy. The latter

of these two methods could be developed by considering the relationship between the 𝑁e𝑅 param-

eter and excitation energy. This would add an extra physical observable, alongside momentum

distributions, that could potentially lead to a more accurate description of the nuclear reaction.

The charge state evolution of ions passing through multiple materials in a fragment separator

is a valuable direction of research for furthering our understanding of heavy-ion fragmentation at

intermediate energies. At intermediate energies, heavy-ion fragments will come in several charge

states for a given isotope [25].

In order to efficiently use the wealth of information produced

in these experiments, it is crucial to understand the behavior of charge state fractions above just

He-like, H-like, and fully-stripped ions. Accurate measurements of fractions above 𝑍

𝑞 = 2

−

can be performed if the momentum acceptance of the fragment separator is increased to the point

where multiple charge states are transmitted for each isotope. The experiments presented in this

work had, at most, two ions for a given isotope. Often times, one of those ions was on the edge

of the acceptance of the separator leading to a very uncertain transmission. The data set was too

limited to paint a complete picture of the complexity of all charge states involved, and a larger data

set should be collected.

Ultra-thin target experiments are well suited for studying charge state distributions of heavy-ions

at intermediate energies. With less material, the charge state distributions do not reach equilibrium

and a greater number of charge states are experimentally observable [25]. This can be paired

with a large acceptance fragment separator to create very large data sets, rich with charge state

information. While such an outcome may have traditionally been undesirable due to the difficulty

of separating charge states, the progress in high resolution spectrometers and particle identification

allows for unequivocal charge state separation, which should be used advantageously.

Thin materials will also preserve charge state information related to the 𝑁e𝑅 parameter. The

results of this work included the first known evidence of a relationship between 𝑁e𝑅 and Δ𝑍 of

79

heavy-ion projectile fragments. This relationship should be further studied in a more comprehensive

experiment using a very thin target and few materials in the beam line. Such an experimental

design would create the least possible disturbance to the 𝑁e𝑅 parameter, and would provide a

crucial confirmation of the relationship between 𝑁e𝑅 and Δ𝑍. Performing this experiment with

proton-rich nuclei should also be considered because the proton removal cross section will be much

higher, providing a larger range of Δ𝑍 to explore.

6.3 Perspectives

While there remains a considerable number of new isotopes to be discovered with projectile frag-

mentation, the reach of this nuclear reaction is fundamentally limited by exponentially decreasing

cross sections away from stability [25, 47]. Projectile fragmentation will most likely continue to

see widespread use, well into the future, as the convenience of in-flight separation is truly unrivaled

by any other means of RI production [50]. However, projectile fragmentation cannot be the answer

for exhaustively exploring the neutron dripline all the way up to the heaviest elements.

There is ample opportunity for fragmentation to be used as a tool for producing RI beams, and

it will most likely dominate nuclear physics in the next couple decades. A wide variety of rare

isotopes can be delivered in steady beams at a desired purity and rate, without needing chemical

extraction from the production target [17]. With increasing upgrades to the intensity of primary

beams [26], the rates of secondary fragments will increase and more new isotopes will most likely be

discovered. As the capabilities of new RI beam facilities are fully realized, accelerator technology

and fragment separation will likely see growth as well. Furthermore, even after new isotopes are

exhausted there still remains a wide variety of nuclear properties to be measured and studied for

each and every nuclide.

On the other hand, exponentially decreasing fragmentation cross sections necessitate a new

reaction mechanism for the long term development of rare isotope production toward the neutron

drip-line of heavy isotopes [47]. In this work, the cross section for pure proton removal decreased

by roughly two orders of magnitude with each proton removed. Improvements made to primary

beam intensities will quickly be used up, and the boundary of discovery will still remain far from

80

the dripline. This is shown in Figure 6.1 where the dripline for elements around 𝑍 = 60 is still

more than 20 neutrons away. Therefore, in order to reach the neutron dripline up to 𝑁 = 126 and

beyond, other strategies beyond single step fragmentation will be required. For example, the pick-up

reactions observed in this work present a potential candidate. While the cross sections of pick-up

products are small compared to neighboring fragmentation products, they could offer a viable

alternative to the production of increasingly exotic neutron-rich fragments where fragmentation

cross sections diminish exponentially with pure proton removal. In these cases, heavy neutron-rich

targets, such as nickel, would offer the excess neutrons to facilitate this strategy.

Ultimately, whether new strategies involve the use of multi-nucleon transfer, secondary reactions

in thick targets, or an altogether new reaction that dominates at small cross sections, is yet to be

discovered. This work represents a step into the terra incognita. Like the explorations of old, our

ship has sailed, and we are on the way. There is a long voyage ahead with multiple discoveries

likely.

81

REFERENCES

[1] R Casten and Nazarewic W. RIA physics white paper, 2000. Accessed: July 9, 2024.

[2] John D Cockcroft and Ernest Thomas Sinton Walton. Disintegration of lithium by swift

protons. Nature, 129(3261):649–649, 1932.

[3] John J. Cowan, Christopher Sneden, James E. Lawler, Ani Aprahamian, Michael Wiescher,
Karlheinz Langanke, Gabriel Martínez-Pinedo, and Friedrich-Karl Thielemann. Origin of
the heaviest elements: The rapid neutron-capture process. Rev. Mod. Phys., 93:015002, Feb
2021.

[4] H. Alvarez-Pol, J. Benlliure, E. Casarejos, et al. Production of new neutron-rich isotopes
of heavy elements in fragmentation reactions of 238U projectiles at 1𝑎 gev. Phys. Rev. C,
82:041602, Oct 2010.

[5] J. Kurcewicz, F. Farinon, H. Geissel, et al. Discovery and cross-section measurement of
neutron-rich isotopes in the element range from neodymium to platinum with the frs. Physics
Letters B, 717(4):371–375, 2012.

[6] O. B. Tarasov, D. Bazin, M. Hausmann, M. P. Kuchera, P. N. Ostroumov, M. Portillo, B. M.
Sherrill, K. V. Tarasova, and T. Zhang. Lise cute++, the latest generation of the lise ++
package, to simulate rare isotope production with fragment-separators. Nuclear Instruments
and Methods in Physics Research B, 541:4–7, 2023.

[7] M Kortelainen, J McDonnell, Witold Nazarewicz, P-G Reinhard, J Sarich, N Schunck,
MV Stoitsov, and SM Wild. Nuclear energy density optimization: Large deformations.
Physical Review C, 85(2):024304, 2012.

[8] National Nuclear Data Center. Information extracted from the nudat database. https://www.

nndc.bnl.gov/nudat/. Accessed: 2024-06-13.

[9] M. Thoennessen. The Discovery of Nuclides, page 5. Springer Cham, 2016.

[10] F.G. Kondev, M. Wang, W.J. Huang, S. Naimi, and G. Audi. The nubase2020 evaluation of

nuclear physics properties *. Chinese Physics C, 45(3):030001, mar 2021.

[11] Meng Wang, Wen Jie Huang, Filip G Kondev, Georges Audi, and Sarah Naimi. The ame 2020
atomic mass evaluation (ii). tables, graphs and references. Chinese Physics C, 45(3):030003,
2021.

[12] D. S. Ahn, N. Fukuda, et al. Location of the neutron dripline at fluorine and neon. Phys. Rev.

Lett., 123:212501, Nov 2019.

[13] Hans Geissel, P Armbruster, KH Behr, A Brünle, K Burkard, M Chen, H Folger, B Franczak,
H Keller, O Klepper, et al. The gsi projectile fragment separator (frs): a versatile magnetic
system for relativistic heavy ions. Nuclear Instruments and Methods in Physics Research
Section B: Beam Interactions with Materials and Atoms, 70(1-4):286–297, 1992.

82

[14] B.M. Sherrill, D.J. Morrissey, J.A. Nolen, and J.A. Winger. The a1200 projectile fragment
separator. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions
with Materials and Atoms, 56-57:1106–1110, 1991.

[15] K. Summerer. Improved empirical parametrization of fragmentation cross sections. Phys.

Rev. C, 86:014601, Jul 2012.

[16] O. B. Tarasov and D. Bazin. Lise++: Exotic beam production with fragment separators and
their design. Nuclear Instruments and Methods in Physics Research B, 376:185–187, 2016.

[17] DF Geesaman, CK Gelbke, RVF Janssens, and BM Sherrill. Physics of a rare isotope

accelerator. Annu. Rev. Nucl. Part. Sci., 56(1):53–92, 2006.

[18] T. Yamaguchi, H. Koura, Yu.A. Litvinov, and M. Wang. Masses of exotic nuclei. Progress in

Particle and Nuclear Physics, 120:103882, 2021.

[19] I. Angeli and K.P. Marinova. Table of experimental nuclear ground state charge radii: An

update. Atomic Data and Nuclear Data Tables, 99(1):69–95, 2013.

[20] I. Hadjas, P. Ascough, M.H. Garnett, et al. Radiocarbon dating. Nature Reviews Methods

Primers, 1(1):62, 2021.

[21] D. Bardayan. Recent experimental progress in nuclear astrophysics. Physics Procedia,

66:457–464, 12 2015.

[22] Bradley S Meyer. The r-, s-, and p-processes in nucleosynthesis. Annual Review Astronomy

and Astrophysics, 32(NAS 1.26: 204924), 1994.

[23] O. B. Tarasov, O. Delaune, F. Farget, D. J. Morrissey, et al. Fission fragment yields from
heavy-ion-induced reactions measured with a fragment separator. The European Physical
Journal A, 54(4):66, Apr 2018.

[24] H. M. Devaraja, S. Heinz, D. Ackermann, T. Göbel, F. P. Heßberger, S. Hofmann, J. Maurer,
G. Münzenberg, A. G. Popeko, and A. V. Yeremin. New studies and a short review of heavy
neutron-rich transfer products. The European Physical Journal A, 56(9):224, 2020.

[25] K. Haak, O. B. Tarasov, P. Chowdhury, A. M. Rogers, K. Sharma, et al. Production and
discovery of neutron-rich isotopes by fragmentation of 198Pt. Phys. Rev. C, 108:034608, Sep
2023.

[26] J. Wei et al. Accelerator commissioning and rare isotope identification at the facility for rare

isotope beams. Modern Physics Letters A, 37(09):2230006, 2022.

[27] P.-A. Söderström, J. Nyberg, P. H. Regan, et al. Spectroscopy of neutron-rich 168,170Dy: Yrast
band evolution close to the 𝑁 𝑝 𝑁𝑛 valence maximum. Phys. Rev. C, 81:034310, Mar 2010.

[28] K. Rykaczewski, K.-L. Gippert, N. Kaffrell, et al. Investigation of neutron-rich rare-earth
nuclei including the new isotopes 177tm and 184lu. Nuclear Physics A, 499(3):529–545,
1989.

83

[29] T. Kubo, M. Ishihara, N. Inabe, et al. The riken radioactive beam facility. Nuclear Instruments
and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms,
70(1):309–319, 1992.

[30] R. Anne, D. Bazin, A.C. Mueller, J.C. Jacmart, and M. Langevin. The achromatic spectrometer
lise at ganil. Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment, 257(2):215–232, 1987.

[31] M. Pfützner, P. Armbruster, T. Baumann, et al. New isotopes and isomers produced by the

fragmentation of 238u at 1000 mev/nucleon. Physics Letters B, 444(1):32–37, 1998.

[32] J. Benlliure, K. H. Schmidt, D. Cortina-Gil, T. Enqvist, F. Farget, A. Heinz, A. R. Junghans,
J. Pereira, and J. Taieb. Production of neutron-rich isotopes by cold fragmentation in the
reaction 197Au + Be at 950 A MeV. Nucl. Phys. A, 660:87–100, 1999. [Erratum: Nucl.Phys.A
674, 578–578 (2000)].

[33] K. Sümmerer, W. Brüchle, D. J. Morrissey, M. Schädel, B. Szweryn, and Yang Weifan. Target
fragmentation of au and th by 2.6 gev protons. Phys. Rev. C, 42:2546–2561, Dec 1990.

[34] F Marti, P Miller, D Poe, M Steiner, J Stetson, and XY Wu. Commissioning of the coupled
cyclotron system at nscl. In AIP Conference Proceedings, volume 600, pages 64–68. American
Institute of Physics, 2001.

[35] H. Okuno, T. Dantsuka, M. Fujimaki, et al. Present status of and recent developments at riken

ri beam factory. Journal of Physics: Conference Series, 1401(1):012005, jan 2020.

[36] T. Ohnishi, T. Kubo, K. Kusaka, et al.

Identification of new isotopes 125pd and 126pd
produced by in-flight fission of 345 mev/nucleon 238u: First results from the riken ri beam
factory. Journal of the Physical Society of Japan, 77(8):083201, 2008.

[37] O. B. Tarasov, D. S. Ahn, et al. Discovery of 60Ca and implications for the stability of 70Ca.

Phys. Rev. Lett., 121:022501, Jul 2018.

[38] O. B. Tarasov, M. Portillo, et al. Production of very neutron-rich nuclei with a 76Ge beam.

Phys. Rev. C, 80:034609, Sep 2009.

[39] O. B. Tarasov, M. Portillo, D. J. Morrissey, et al. Production cross sections from 82se
fragmentation as indications of shell effects in neutron-rich isotopes close to the drip-line.
Phys. Rev. C, 87:054612, May 2013.

[40] H Suzuki, T Kubo, N Fukuda, N Inabe, D Kameda, H Takeda, K Yoshida, K Kusaka,
Y Yanagisawa, M Ohtake, et al. Discovery of new isotopes mo 81, 82 and ru 85, 86 and a
determination of the particle instability of 103 sb. Physical Review C, 96(3):034604, 2017.

[41] P. N. Ostroumov, O. B. Tarasov, et al. Acceleration of uranium beam to record power of
10.4 kw and observation of new isotopes at facility for rare isotope beams. Phys. Rev. Accel.
Beams, 27:060101, Jun 2024.

84

[42] T. Kurtukian-Nieto, J. Benlliure, K.-H. Schmidt, L. Audouin, F. Becker, B. Blank, E. Casare-
jos, F. Farget, M. Fernández-Ordóñez, J. Giovinazzo, D. Henzlova, B. Jurado, J. Pereira,
and O. Yordanov. Production cross sections of heavy neutron-rich nuclei approaching the
nucleosynthesis r-process path around 𝑎 = 195. Phys. Rev. C, 89:024616, Feb 2014.

[43] N. Alkhomashi, P. H. Regan, Zs. Podolyák, S. Pietri, A. B. Garnsworthy, S. J. Steer, et al.
𝛽−-delayed spectroscopy of neutron-rich tantalum nuclei: Shape evolution in neutron-rich
tungsten isotopes. Phys. Rev. C, 80:064308, Dec 2009.

[44] S. J. Steer, Zs. Podolyák, S. Pietri, M. Górska, H. Grawe, K. H. Maier, P. H. Regan, D. Rudolph,
A. B. Garnsworthy, R. Hoischen, J. Gerl, H. J. Wollersheim, et al. Isomeric states observed
in heavy neutron-rich nuclei populated in the fragmentation of a 208pb beam. Phys. Rev. C,
84:044313, Oct 2011.

[45] A. I. Morales, J. Benlliure, J. Agramunt, et al. Synthesis of 𝑛 = 127 isotones through (𝑝,𝑛)
charge-exchange reactions induced by relativistic 208pb projectiles. Phys. Rev. C, 84:011601,
Jul 2011.

[46] Aleksandra Kelic, M. Valentina Ricciardi, and Karl-Heinz Schmidt. ABLA07 - towards a
complete description of the decay channels of a nuclear system from spontaneous fission to
multifragmentation. In Joint ICTP-IAEA Advanced Workshop on Model Codes for Spallation
Reactions. IAEA INDC, June 2009. arXiv:0906.4193 [nucl-th].

[47] T. Kurtukian-Nieto, J. Benlliure, Schmidt, et al. Production cross sections of heavy neutron-
rich nuclei approaching the nucleosynthesis r-process path around 𝑎 = 195. Phys. Rev. C,
89:024616, Feb 2014.

[48] Valery Zagrebaev and Walter Greiner. Production of new heavy isotopes in low-energy

multinucleon transfer reactions. Physical review letters, 101(12):122701, 2008.

[49] EM Kozulin, Emanuele Vardaci, GN Knyazheva, AA Bogachev, SN Dmitriev, IM Itkis,
MG Itkis, AG Knyazev, TA Loktev, KV Novikov, et al. Mass distributions of the system 136
xe+ 208 pb at laboratory energies around the coulomb barrier: a candidate reaction for the
production of neutron-rich nuclei at n= 126. Physical Review C, 86(4):044611, 2012.

[50] O. Beliuskina, S. Heinz, V. Zagrebaev, V. Comas, C. Heinz, S. Hofmann, R. Knöbel, M. Stahl,
D. Ackermann, F. P. Heßberger, B. Kindler, B. Lommel, J. Maurer, and R. Mann. On the
synthesis of neutron-rich isotopes along the n = 126 shell in multinucleon transfer reactions.
The European Physical Journal A, 50(10):161, Oct 2014.

[51] JS Barrett, W Loveland, R Yanez, Shaofei Zhu, AD Ayangeakaa, MP Carpenter, JP Greene,
RVF Janssens, T Lauritsen, EA McCutchan, et al. Xe 136+ pb 208 reaction: A test of models
of multinucleon transfer reactions. Physical Review C, 91(6):064615, 2015.

[52] Y. X. Watanabe, Y. H. Kim, S. C. Jeong, and other. Pathway for the production of neutron-rich

isotopes around the 𝑛 = 126 shell closure. Phys. Rev. Lett., 115:172503, Oct 2015.

85

[53] G. Savard, M. Brodeur, J.A. Clark, R.A. Knaack, and A.A. Valverde. The n=126 factory: A
new facility to produce very heavy neutron-rich isotopes. Nuclear Instruments and Methods
in Physics Research Section B: Beam Interactions with Materials and Atoms, 463:258–261,
2020.

[54] Julia Even, Xiangcheng Chen, Arif Soylu, et al. The next project: Towards production and

investigation of neutron-rich heavy nuclides. Atoms, 10(2), 2022.

[55] T. Niwase, Y. X. Watanabe, Y. Hirayama, et al. Discovery of new isotope 241U and sys-
tematic high-precision atomic mass measurements of neutron-rich pa-pu nuclei produced via
multinucleon transfer reactions. Phys. Rev. Lett., 130:132502, Mar 2023.

[56] V. V. Desai, A. Pica, W. Loveland, J. S. Barrett, E. A. McCutchan, S. Zhu, A. D. Ayangeakaa,
M. P. Carpenter, J. P. Greene, T. Lauritsen, R. V. F. Janssens, B. M. S. Amro, and W. B.
Walters. Multinucleon transfer in the interaction of 977 mev and 1143 mev 204Hg with 208Pb.
Phys. Rev. C, 101:034612, Mar 2020.

[57] VI Zagrebaev. Synthesis of superheavy nuclei: Nucleon collectivization as a mechanism for

compound nucleus formation. Physical Review C, 64(3):034606, 2001.

[58] O. B. Tarasov, A. Gade, et al. Observation of new isotopes in the fragmentation of 198Pt at

frib. Phys. Rev. Lett., 132:072501, Feb 2024.

[59] D.J. Morrissey, B.M. Sherrill, M. Steiner, A. Stolz, and I. Wiedenhoever. Commissioning the
a1900 projectile fragment separator. Nuclear Instruments and Methods in Physics Research
B, 204:90–96, 2003.

[60] D. Bazin, J.A. Caggiano, B.M. Sherrill, J. Yurkon, and A. Zeller. The s800 spectrograph.

Nuclear Instruments and Methods in Physics Research B, 204:629–633, 2003.

[61] S. Paschalis, I.Y. Lee, A.O. Macchiavelli, et al. The performance of the gamma-ray energy
tracking in-beam nuclear array gretina. Nuclear Instruments and Methods in Physics Research
A, 709:44–55, 2013.

[62] Micron Semiconductor Limited. Msx25-140um 2m/2m em grade ceramic package, August

2016.

[63] N. Fukuda, T. Kubo, D. Kameda, et al. Identification of new neutron-rich isotopes in the
rare-earth region produced by 345 mev/nucleon 238u. Journal of the Physical Society of
Japan, 87(1):014202, 2018.

[64] H. Suzuki, K. Yoshida, N. Fukuda, et al. Experimental studies of the two-step scheme with
an intense radioactive 132Sn beam for next-generation production of very neutron-rich nuclei.
Phys. Rev. C, 102:064615, Dec 2020.

[65] Thomas Glasmacher, Bradley Sherrill, Witek Nazarewicz, Alexandra Gade, Paul Mantica, Jie
Wei, Georg Bollen, and Brad Bull. Facility for rare isotope beams update for nuclear physics
news. Nuclear Physics News, 27(2):28–33, 2017.

86

[66] M. Hausmann et al. Design of the advanced rare isotope separator aris at frib. Nuclear

Instruments and Methods in Physics Research Section B, 317:349–353, 2013.

[67] M. Portillo, B.M. Sherrill, et al. Commissioning of the advanced rare isotope separator aris
at frib. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions
with Materials and Atoms, 540:151–157, 2023.

[68] P. N. Ostroumov, K. Fukushima, T. Maruta, A. S. Plastun, J. Wei, T. Zhang, and Q. Zhao.
First simultaneous acceleration of multiple charge states of heavy ion beams in a large-scale
superconducting linear accelerator. Phys. Rev. Lett., 126:114801, Mar 2021.

[69] Micron Semiconductor Limited. Msx25 (ss) 300, 500, 1000 2m/2m, September 2022.

[70] M. Caamaño, P. M. Walker, P. H. Regan, et al. Isomers in neutron-rich a

190 nuclides from
208pb fragmentation. The European Physical Journal A - Hadrons and Nuclei, 23:201–215,
2005.

≈

[71] P. Sigmund. Dielectric Stopping Theory, pages 141–180. Springer Berlin Heidelberg, Berlin,

Heidelberg, 2006.

[72] Zs. Podolyák, P.H. Regan, M. Pfützner, et al. Isomer spectroscopy of neutron rich 190w116.

Physics Letters B, 491(3):225–231, 2000.

[73] O. B. Tarasov and D. Bazin. Lise++: Radioactive beam production with in-flight separators.
Nuclear Instruments and Methods in Physics Research B, 266:4657–4664, 2008. https:
//lise.nscl.msu.edu.

[74] Jens Lindhard and Allan H. So/rensen. Relativistic theory of stopping for heavy ions. Phys.

Rev. A, 53:2443–2456, Apr 1996.

[75] O. Tarasov. Analysis of momentum distributions of projectile fragmentation products. Nucl.

Phys. A, 734:536, 2004.

[76] F. Hubert, R. Bimbot, and H. Gauvin. Range and stopping-power tables for 2.5–500

MeV/nucleon heavy ions in solids. Atom. Data Nucl. Data Tabl., 46:1–213, 1990.

[77] C Scheidenberger, Th Stöhlker, W.E Meyerhof, H Geissel, P.H Mokler, and B Blank. Charge
states of relativistic heavy ions in matter. Nuclear Instruments and Methods in Physics
Research B, 142(4):441–462, 1998.

[78] E. Lamour, P. D. Fainstein, M. Galassi, C. Prigent, C. A. Ramirez, R. D. Rivarola, J.-P.
Rozet, M. Trassinelli, and D. Vernhet. Extension of charge-state-distribution calculations for
ion-solid collisions towards low velocities and many-electron ions. Phys. Rev. A, 92:042703,
Oct 2015.

[79] H. Suzuki, T. Kubo, N. Fukuda, et al. Discovery of new isotopes 81,82Mo and 85,86Ru and a
determination of the particle instability of 103Sb. Phys. Rev. C, 96:034604, Sep 2017.

[80] J. Besprosvany and S. Levit. Limiting temperature and limits of statistical particle emission

in hot nuclei. Physics Letters B, 217(1):1–4, 1989.

87

[81] Zhuxia Li and Min Liu. Mass and isotope dependence of limiting temperatures for hot nuclei.

Phys. Rev. C, 69:034615, Mar 2004.

[82] Mark D Baker, Wan Chang, Markus Diefenthaler, Florian Hauenstein, Or Hen, Douglas
Higinbotham, Alex Jentsch, Jeong-Hung Lee, Wenliang Li, Pawel Nadel-Turonski, et al.
Generic r&d proposal: Beagle, a tool to refine ir and detector requirements for the eic.
Technical report, Jefferson Lab, 2022. Accessed: 2023-07-10.

[83] S. K. Tandel, T. L. Khoo, D. Seweryniak, G. Mukherjee, et al. 𝑘 isomers in 254No: Prob-
ing single-particle energies and pairing strengths in the heaviest nuclei. Phys. Rev. Lett.,
97:082502, Aug 2006.

[84] P. D. Stevenson, M. P. Brine, Zs. Podolyak, P. H. Regan, P. M. Walker, and J. Rikovska Stone.
Shape evolution in the neutron-rich tungsten region. Phys. Rev. C, 72:047303, Oct 2005.

[85] O. B. Tarasov. References therein; LISE++ abrasion-ablation web page. https://lise.nscl.msu.

edu/AA, Michigan State University.

[86] J. Benlliure and K. H. Schmidt. References therein; COFRA web page. http://www.usc.es/

genp/cofra, Universidade de Santiago de Compostela.

[87] K-H Schmidt, MV Ricciardi, AS Botvina, and T Enqvist. Production of neutron-rich heavy
residues and the freeze-out temperature in the fragmentation of relativistic 238u projectiles
determined by the isospin thermometer. Nuclear Physics A, 710(1-2):157–179, 2002.

[88] L Audirac, A Obertelli, P Doornenbal, Davide Mancusi, Satoshi Takeuchi, Nori Aoi, Hidetada
Baba, Simon Boissinot, Alain Boudard, A Corsi, et al. Evaporation-cost dependence in heavy-
ion fragmentation. Physical Review C—Nuclear Physics, 88(4):041602, 2013.

[89] T. Mukoyama. Electron shake probability for arbitrary shell. X-Ray Spectrom, 52, 2023.

[90] J.A. Winger, B.M. Sherrill, and D.J. Morrissey.

Intensity: a computer program for the
estimation of secondary beam intensities from a projectile fragment separator. Nuclear
Instruments and Methods in Physics Research Section B: Beam Interactions with Materials
and Atoms, 70(1):380–392, 1992.

[91] S. Schwarz, G. Bollen, R. Ringle, J. Savory, and P. Schury. The lebit ion cooler and buncher.
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment, 816:131–141, 2016.

[92] I. Cox, Z. Y. Xu, R. Grzywacz, W.-J. Ong, et al. Proton shell gaps in 𝑛 = 28 nuclei from the first
complete spectroscopy study with frib decay station initiator. Phys. Rev. Lett., 132:152503,
Apr 2024.

[93] K. Minamisono, P.F. Mantica, A. Klose, S. Vinnikova, A. Schneider, B. Johnson, and B.R.
Barquest. Commissioning of the collinear laser spectroscopy system in the becola facility
at nscl. Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment, 709:85–94, 2013.

88

[94] David J Morrissey and Brad M Sherrill. In-flight separation of projectile fragments. The

Euroschool Lectures on Physics with Exotic Beams, Vol. I, pages 113–135, 2004.

89

Z

70

70

70

71

71

71

71

71

71

71

71

71

71

72

72

72

72

72

72

72

72

72

73

APPENDIX

Table A.1: 198Pt + 9Be Cross Sections and Errors.

A Cross Section (mb) Plus Error Bar Minus Error Bar

180

181

182

180

181

182

183

184

185

186

187

188

189

184

185

186

187

188

189

190

191

192

185

1.80E-03

3.77E-05

3.63E-06

8.58E-04

1.31E-03

1.28E-05

1.41E-05

9.87E-07

9.48E-07

2.14E+00

1.17E+00

1.43E+00

3.02E-02

1.20E-03

2.20E-04

1.38E-04

1.11E-05

1.80E-05

5.54E-07

6.01E-08

4.02E-08

3.14E-02

2.26E-03

4.31E-04

1.96E-04

3.45E-05

1.36E-05

8.40E-07

1.47E-07

6.92E-08

4.27E-01

1.27E-02

1.90E-02

3.65E-04

6.97E-04

8.50E-05

2.47E-04

3.68E-05

3.55E-05

3.17E-06

5.91E-06

5.92E-06

6.79E-06

1.36E-07

1.50E-07

1.60E-08

2.13E-08

2.30E-08

2.82E-08

1.27E-02

1.93E-02

1.10E-03

2.18E-03

2.96E-04

9.70E-04

5.58E-05

5.57E-05

9.94E-06

1.30E-05

3.93E-06

4.94E-06

1.94E-07

1.83E-07

4.27E-08

6.90E-08

3.73E-08

6.18E-08

1.64E-01

2.90E-01

90

Z

73

73

73

73

73

73

73

73

74

74

74

74

74

74

74

74

75

75

75

75

75

75

75

75

76

Table A.1 (cont’d)

A Cross Section (mb) Plus Error Bar Minus Error Bar

186

187

188

189

190

191

192

193

186

188

189

190

191

192

193

194

188

189

190

191

192

193

194

195

190

7.95E-02

3.26E-02

3.67E-03

1.21E-03

3.53E-04

1.01E-04

1.13E-05

9.85E-07

3.52E-02

7.55E-02

1.69E-02

3.62E-02

2.35E-03

6.71E-03

7.74E-04

2.21E-03

8.24E-05

7.82E-05

2.41E-05

2.54E-05

2.87E-06

3.89E-06

2.33E-07

1.59E-07

2.56E+00

2.07E+00

5.72E+00

3.67E-01

1.76E-01

7.18E-02

6.33E-03

3.40E-03

4.60E-04

1.29E-04

1.34E-01

1.98E-01

7.85E-02

1.60E-01

1.91E-02

2.88E-02

2.27E-03

3.91E-03

1.88E-03

4.33E-03

8.83E-05

1.80E-04

2.95E-05

5.33E-05

7.43E+00

4.91E+00

7.14E+00

5.01E+00

3.10E+00

5.05E+00

3.98E+00

1.15E+00

1.51E+00

5.62E-01

2.69E-01

1.07E-01

1.51E-02

9.68E-03

2.23E-01

4.08E-01

1.29E-01

2.60E-01

1.39E-02

2.37E-02

5.69E-03

9.42E-03

1.97E-03

2.60E-03

1.77E+01

4.73E+00

1.12E+01

91

Table A.1 (cont’d)

A Cross Section (mb) Plus Error Bar Minus Error Bar

191

192

193

194

195

196

197

192

193

194

195

196

4.98E+00

9.34E-01

1.89E+00

5.54E+00

1.29E+00

3.10E+00

3.34E+00

1.37E+00

2.85E+00

1.82E+00

1.07E+00

4.00E-01

4.07E-02

6.04E-01

1.08E+00

2.36E-01

3.97E-01

7.24E-02

1.59E-01

1.46E-02

2.44E-02

5.17E+01

4.36E+01

2.78E+02

4.20E+01

2.05E+01

3.03E+01

2.94E+01

1.28E+01

1.80E+01

6.45E+01

2.28E+01

2.78E+01

1.23E+01

6.70E+00

1.54E+01

Z

76

76

76

76

76

76

76

77

77

77

77

77

92

Z

Z

71

71

71

71

71

71

72

72

72

72

72

72

73

73

73

73

73

73

73

74

74

74

74

Table A.2: 198Pt + Ni Cross Sections and Errors.

A Cross Section (mb) Plus Error Bar Minus Error Bar

A

181

182

183

184

185

186

182

183

184

185

186

187

185

186

187

188

189

190

191

185

186

188

189

CS

7.25E-02

2.26E-02

1.51E-02

4.36E-03

1.32E-03

8.80E-04

N/A

N/A

N/A

3.24E-02

1.38E-02

3.36E-03

N/A

4.77E-02

3.21E-02

5.90E-02

1.47E-02

1.15E-03

8.63E-04

N/A

CS-

CS+

7.25E-02

2.85E-01

9.70E-03

1.93E-01

5.50E-03

8.81E-02

1.43E-03

1.84E-02

3.88E-04

3.85E-03

4.38E-04

3.84E-03

N/A

N/A

N/A

1.54E-01

2.49E-01

7.51E-02

9.38E-03

3.48E-02

1.03E-02

2.60E-02

2.58E-03

9.87E-03

N/A

2.06E-01

4.77E-02

2.53E-01

3.21E-02

9.68E-02

2.41E-02

5.11E-02

1.45E-02

6.90E-03

1.07E-03

1.17E-02

3.37E-04

3.76E-03

N/A

2.35E+00

1.85E+00

1.85E+00

9.30E+00

6.15E-01

6.15E-01

4.80E-01

N/A

N/A

1.87E-01

93

Z

74

74

74

74

74

75

75

75

75

75

75

75

75

75

76

76

76

76

76

76

76

76

77

77

77

Table A.2 (cont’d)

A Cross Section (mb) Plus Error Bar Minus Error Bar

190

191

192

193

194

187

188

189

191

192

193

194

195

196

190

191

192

193

194

195

196

197

193

194

195

N/A

6.29E-02

4.22E-03

3.61E-03

2.17E-03

N/A

N/A

N/A

N/A

1.01E-01

3.68E-02

2.83E-02

4.22E-03

2.23E-02

1.26E-03

6.78E-03

8.19E-04

8.95E-03

N/A

N/A

N/A

1.75E+01

1.57E+01

1.46E+01

2.28E+00

2.00E+00

1.69E+00

1.95E-01

4.36E-01

7.49E-02

1.87E-01

3.29E-02

N/A

1.95E-01

6.78E-01

1.79E-01

2.07E-01

7.34E-02

3.42E-02

7.52E-02

1.06E-01

7.86E-03

1.29E-02

N/A

6.87E+01

1.61E+01

1.14E+01

1.08E+01

5.50E+00

5.50E+00

3.70E+01

1.65E+00

1.65E+00

1.10E+01

2.01E-01

2.01E-01

3.42E+00

N/A

N/A

N/A

N/A

3.31E+00

1.30E-01

2.68E-01

1.42E-01

1.42E-01

N/A

N/A

5.01E+02

4.76E-01

4.76E-01

6.53E+01

3.31E+01

3.31E+01

1.88E+02

94

Table A.2 (cont’d)

Z

77

77

A Cross Section (mb) Plus Error Bar Minus Error Bar

196

198

5.18E+01

5.18E+01

6.23E+03

N/A

N/A

2.93E+01

95

Table A.3: Charge state distributions of ions after the FP scintillator (see Fig. 2.1 of Section 2.1)
for the 23 mg/cm2 Be target settings. Calculations were performed for elements from hafnium
(𝑍 = 72) to iridium (𝑍 = 77) for several values of 𝑁e𝑅 . The fractions listed in this table are the
product of the target and the scintillator fractions for a given charge state.

𝑍 𝑁𝑒𝑅

77

76

75

5

4

3

2

1

0

5

4

3

2

1

0

7

6

5

4

3

2

1

0

𝑍

𝑞

−

0

1

2

3

4

5

1.92e-05

5.38e-03

3.41e-01

3.34e-02

2.49e-03

2.90e-04

1.56e-05

6.36e-03

3.88e-01

3.61e-02

2.27e-03

1.65e-05

2.88e-05

8.59e-03

4.68e-01

3.74e-02

3.04e-04

2.50e-06

5.14e-05

1.38e-02

6.34e-01

1.05e-02

4.63e-05

5.27e-07

5.76e-04

1.03e-01

3.13e-01

4.33e-03

1.79e-05

2.24e-07

1.09e-02

7.82e-02

1.80e-01

2.22e-03

7.82e-06

7.62e-08

0.00e+00

6.57e-03

3.54e-01

3.04e-02

2.05e-03

2.18e-04

2.45e-05

8.14e-03

3.98e-01

3.15e-02

1.95e-03

1.18e-05

4.27e-05

1.04e-02

4.73e-01

3.34e-02

2.46e-04

2.51e-06

6.85e-05

1.63e-02

6.31e-01

8.71e-03

5.34e-05

4.57e-07

6.67e-04

1.14e-01

3.04e-01

3.52e-03

1.93e-05

0.00e+00

1.29e-02

8.51e-02

1.71e-01

1.72e-03

1.17e-05

0.00e+00

1.26e-05

6.28e-03

3.07e-01

2.46e-02

1.70e-03

1.83e-05

7.09e-03

3.31e-01

2.53e-02

1.59e-03

4.19e-05

7.99e-03

3.63e-01

2.62e-02

1.80e-03

4.87e-05

9.93e-03

4.07e-01

2.77e-02

1.61e-03

5.03e-05

1.26e-02

4.79e-01

2.86e-02

1.81e-04

8.58e-05

1.93e-02

6.25e-01

7.44e-03

3.06e-05

9.26e-04

1.26e-01

2.95e-01

2.82e-03

1.54e-05

1.56e-02

9.18e-02

1.61e-01

1.50e-03

1.00e-05

-

-

-

-

-

-

-

-

96

𝑍 𝑁𝑒𝑅

Table A.3 (cont’d)

𝑍

𝑞

−

0

1

2

3

4

5

7

6

5

4

3

2

1

0

7

6

5

4

3

2

1

0

5

4

3

2

1

0

3.01e-05

8.24e-03

3.49e-01

2.31e-02

1.48e-03

4.58e-05

8.83e-03

3.43e-01

2.26e-02

1.38e-03

6.12e-05

9.94e-03

3.70e-01

2.32e-02

1.38e-03

2.61e-05

1.21e-02

4.12e-01

2.44e-02

1.26e-03

8.98e-05

1.57e-02

4.81e-01

2.43e-02

1.57e-04

1.59e-04

2.26e-02

6.17e-01

6.15e-03

2.69e-05

1.19e-03

1.39e-01

2.83e-01

2.50e-03

6.53e-06

1.84e-02

9.93e-02

1.52e-01

1.20e-03

8.80e-06

4.02e-05

9.58e-03

3.25e-01

1.93e-02

1.15e-03

6.08e-05

1.06e-02

3.48e-01

1.92e-02

1.14e-03

9.12e-05

1.27e-02

3.75e-01

2.00e-02

1.07e-03

5.93e-05

1.46e-02

4.16e-01

2.09e-02

1.11e-03

1.20e-04

1.85e-02

4.79e-01

2.16e-02

7.70e-05

2.16e-04

2.67e-02

6.08e-01

4.96e-03

2.07e-05

1.52e-03

1.52e-01

2.70e-01

2.01e-03

4.25e-06

2.15e-02

1.07e-01

1.42e-01

9.32e-04

1.90e-06

9.80e-05

1.50e-02

3.79e-01

1.76e-02

9.16e-04

7.98e-05

1.77e-02

4.15e-01

1.88e-02

8.71e-04

2.29e-04

2.20e-02

4.74e-01

1.88e-02

6.08e-05

2.94e-04

3.45e-02

5.53e-01

4.65e-03

1.81e-05

2.23e-03

1.65e-01

2.57e-01

1.38e-03

0.00e+00

2.60e-02

1.13e-01

1.32e-01

6.46e-04

0.00e+00

74

73

72

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

97

Table A.4: Parameter values used to obtain best fit between LISEAA and experimental cross
sections of 198Pt + Be. The LISE++ documentation should be referenced for detailed definitions of
parameters [6, 85].

Parameters

LISEAA+PGD

Common Parameters

AA Cross Sections Amplitude
dR Correction

Limiting Temperature

𝐴 = 50
𝐴 = 150
𝐴 = 250

Gaussian

𝐸 ∗ 0th Order
𝐸 ∗ 1st Order
𝐸 ∗ 2nd Order
𝐸 ∗)
𝜎
𝜎
𝐸 ∗)
𝐸 ∗)
𝜎

0th
1st
2nd

(
(
(

0.5172
5.7

7.9036
4.465
2.9413

0
22.3787
1.5825
0
19.2973
-1.779

98