MONTE-CARLO SIMULATIONS OF THE (d,2He) REACTION IN

INVERSE KINEMATICS

By

Alexander B. Carls

A THESIS

Submitted to

Michigan State University

in partial fulﬁllment of the requirements

for the degree of

Physics - Master of Science

2019

ABSTRACT

MONTE-CARLO SIMULATIONS OF THE (d,2He) REACTION IN

INVERSE KINEMATICS

By

Alexander B. Carls

Charge-exchange reactions oﬀer an indirect method for the testing of theoretical models

for Gamow-Teller strengths that are used to calculate electron-capture rates on medium-

heavy nuclei, which play important roles in astrophysical phenomena. Many of the relevant

nuclei are unstable. However, a good general probe for performing charge-exchange reac-

tions in inverse kinematics in the (n,p) reaction has not yet been established. The (d,2He)

reaction in inverse kinematics is being developed as a potential candidate for this probe.

This method uses the Active-Target Time Projection Chamber (AT-TPC) to detect the two

protons from the unbound 2He system, and the S800 spectrograph to detect the heavy re-

coil. The feasibility of this method is demonstrated through Monte-Carlo simulations. The

ATTPCROOTv2 code is the framework which allows for simulation of reactions within the

AT-TPC as well as digitization of the results in the pad planes for realistic simulated data.

The analysis performed on this data using the ATTPCROOTv2 code shows the techniques

that can be done in experiment to track the scattered protons through the detector using

Random Sampling Consensus (RANSAC) algorithms.

ACKNOWLEDGMENTS

The ﬁrst person I have to thank is my advisor, Remco Zegers. Your patience for ﬁelding

my questions, whether naive or complex, and for focusing my eﬀorts when I needed guid-

ance made my experience doing research much less stressful. Your unwavering support as I

struggled through classes is the reason I made it to the end. Thank you.

To my committee: Sean Liddick and Wolfgang Mittig. Thank you for your insight-

ful commentary on my thesis and for asking the right questions to push the limits of my

understanding.

To the faculty and post-docs of NSCL who helped along the way: Juan Zamora. Thank

you for beginning my venture into these simulations and for drilling an understanding of the

kinematics of the (d, 2He) reaction into my mind. Yassid Ayyad. Thank you for the constant

back-and-forth as I set out to understand the code down to the smallest detail and for the

endless troubleshooting support. Daniel Bazin, Shumpei Noji, and Jorge Pereira. Thank

you for being an ever present support and for the help you have given me along the way.

To my groupmates: Jaclyn Schmitt, Miles DeNudt, Rachel Titus, Felix Ndayisabye, and

Cavan Maher. Thank you for reminding me I am not alone in the struggle of graduate life

and for making work feel less like work sometimes.

To my friends from home: Kevin, Will, Alex, and Aaron. Thank you for making hundreds

of miles not seem so far away.

To my friends in Michigan: The men and women of MSU Ultimate. Thank you for being

my second family for the past few years and for forcing me to stay in shape when I would

otherwise be sitting on my couch. Jared, Ryan, and Cody. Thank you for all the movie

nights and for getting me to come out of my apartment every so often.

iii

Finally, to my family: Mom. Thank you for updating the world every time I come home

and for calling every week to make sure I am still alive. Dad. Thank you for keeping me

up-to-date with all the best movies and shows and for walking me through some of the

challenges of adulthood (taxes, insurance, etc.) that I promise I will learn to do myself one

day. Jamie. Thanks for letting me hack into all of your streaming services to binge watch

shows all this time. One day I will repay you. All of you have been a constant source for

support and love without which I would not have succeeded.

iv

TABLE OF CONTENTS

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

vi

Chapter 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Electron-Capture Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(d,2He) Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3

Chapter 2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Active Target-Time Projection Chamber . . . . . . . . . . . . . . . . . . . .

Chapter 3

Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Data Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Parameters
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Clusterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Pulse Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Pulse Shape Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 RANSAC Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 RANSAC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 RANSAC Implementation . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Reconstruction of 2He

1
1
3
6

9
9
12

16
16
21
21
25
27
30
35
35
36

39
39
41
41
43
44

Chapter 5 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . .

47

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix A ATTPCROOTv2 Manual
. . . . . . . . . . . . . . . . . . . . . . . .
Appendix B Index of File Directories . . . . . . . . . . . . . . . . . . . . . . . . .

48
49
81

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

v

LIST OF FIGURES

Figure 1.1: The inert iron core increases in mass as the silicon burning phase pro-
gresses (a) until it reaches the Chandrasekhar mass limit and the gravi-
tational force overcomes thermonuclear energy and degeneracy pressures.
(b) The core begins to contract and electron-capture occurs (c) until core
density reaches ρ ≈ 10−14 g cm−3 and contraction quickly stops, (d) after
which the outer layers bounce oﬀ the core creating an outward propagat-
ing shock wave. (e) The shock wave slows as it passes through the outer
layers (f) but is reinvigorated by a burst of neutrinos. Figure credit [11].

Figure 1.2:

(a) Electron-capture on a nucleus, decreasing atomic number by one while
maintaining atomic mass and releasing an electron neutrino. (b) Example
of a charge exchange reaction, t(A
Z−1X)3He, in which a neutron from
a triton is exchanged for a proton from the target nucleus, resulting in the
release of a 3He and a product nucleus with atomic number decreased by
one but atomic mass unchanged . . . . . . . . . . . . . . . . . . . . . . .

Z X, A

Figure 1.3: The excitation energies of the daughter nucleus are limited to states within
the Q-value window, Qg.s, for electron-capture and β decay reactions be-
tween the ground states of the nuclei. In charge-exchange reactions, the
excitation energy of the daughter nucleus is not limited by the Q-value. .

Figure 1.4: The (d, 2He) reaction in inverse kinematics, where the unstable heavy
nucleus is projected onto a deuterium target nucleus. The 2He recoil
immediately decays into two protons with relative energy, pp.
. . . . . .

Figure 2.1: The AT-TPC is placed in front of the S800 spectrograph to utilize its
ability to do particle identiﬁcation, as well as to provide a trigger for
events in the AT-TPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.2: Double diﬀerential cross-section as a function of the center-of-mass angle
(θcm) and the relative energy of the two protons (pp) for the transition
to the 3.95 MeV 1+ 14N state via the 14O(d, 2He) reaction. Calculations
based oﬀ of the Adiabatic Coupled-Channels Born Approximation (AC-
CBA) code.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.3: Kinetic energy versus the angle in the laboratory for the 2He particle for
the 14O(d, 2He) reaction in inverse kinematics at 115 MeV/u. The dotted
colored lines indicate the excitation energy of 14N, in steps of 5 MeV. The
brown lines indicate center-of-mass scattering angles (2◦ and 5◦).
. . . .

3

5

5

8

10

11

11

vi

Figure 2.4:

Illustration of the AT-TPC. A beam of 14O particles enters the right side
of the diagrammed detector. The active volume is ﬁlled with deuterium
gas at 0.7 atm pressure, which reacts with the beam and produces two
protons. The ejectile leaves the left side of the diagrammed detector and
. . . . . . . . . . . . . . . . . . .
continues on to the S800 spectrograph.

Figure 2.5: Visualization of the simulation of one (d, 2He) event. Since the ejectile
retains most of its momentum, it is carried through an aperture in the
back of the detector into the S800 spectrograph. The two protons create
tracks of ionized electrons in the gas as illustrated.
. . . . . . . . . . . .

Figure 3.1: Flow of ATTPCROOTv2 data types at each step in the process from
generation of data to user analysis. Example generators are those used
in simulations of (d, 2He) reactions. Each FairRoot analysis task requires
a speciﬁc input data type and produces a diﬀerent output data type as
shown in the ﬁgure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.2: Workﬂow of FairRoot simulation, including the outline of a simulation
. . . . . . . . . . . . . . . . . . .

macro. Illustrations adapted from [52].

Figure 3.3: Workﬂow of FairRoot analysis, including the outline of an analysis macro.
. . . . . . . . . . . . . . . . . . . . . . .

Illustrations adapted from [52].

Figure 3.4: Examples of media deﬁnitions for air (1 atm), aluminum metal, deuterium
gas (0.7 atm), and HeCO2 gas. Note that since the ncomp parameter
(ﬁrst row, ﬁrst number) for each mixture is positive, the wm parameters
(ﬁrst row, last ncomp numbers) are listed by weight proportion.
. . . . .

Figure 3.5: A very basic geometry of the AT-TPC with a drift volume of deuterium
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

gas.

Figure 3.6: Parameter ﬁle (ATTPCROOTv2/parameters/ATTPC.d2He.par) for use
. . . . . . . . . . . . . . . . . .

in FairRoot analysis of simulation data.

Figure 3.7: Example macro code showing input required in deﬁnition of ATTPC-
ROOTv2 generators, ATTPCIonGenerator and ATTPC d2He, for simu-
lation of a (d, 2He) reaction.
. . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.8: A total of 20305 AtTpcPoints were created in a 100 event simulation of the
14O(d, 2He) 14N reaction. Each point holds the position, momentum, and
energy of a particle at one moment in its trajectory. These positions are
plotted in the histograms shown. (a) Radius versus Z-component of tracks
made by protons in the AT-TPC. (b) Y-component versus X-component.

14

15

18

19

20

24

25

26

29

32

vii

Figure 3.9: Results of invariant mass calculation for a 10000 event simulation calcu-
lated from AtTpcPoint parameters. (a) Angular distribution of the 2He
particle center-of-mass. (b) Kinetic energy versus angle in the laboratory
for the 2He particle.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.10: Results of invariant mass calculation for a 10000 event simulation cal-
culated graphical ﬁt of each proton to reconstruct the 2He particle. (a)
Angular distribution of the 2He particle center-of-mass. (b) Kinetic energy
versus angle in the laboratory for the 2He particle.
. . . . . . . . . . . .

Figure 3.11: Illustration of the ionization of the deuterium gas as the two protons from
a (d, 2He) reaction travel through the AT-TPC volume. Ionized electrons
drift toward the pad plane in the presence of the electric ﬁeld and undergo
a Gaussian diﬀusion through the deuterium gas, adding width to the tracks
detected in the pads. Figure adapted from [42].
. . . . . . . . . . . . . .

Figure 3.12: Visualization of the digitized data displayed as a map of the AT-TPC
pad plane. Each pad in the interactive map can be selected to view the
pulse produced by the ATPulseTask task. One the right side of the ﬁgure,
four pads are selected showing the change in the timing of the pulse for
each subsequent point in the proton’s trajectory. The plot on the bottom
shows the pulse created in a pad where electrons arrived to the same pad
at diﬀerent times, resulting in multiple response functions superimposed.

33

34

36

38

Figure 4.1: The 20305 AtTpcPoints created in a 100 event simulation of the 14O(d, 2He) 14N

reaction resulted in 3911 ATHits after digitization and pulse shape anal-
ysis. It is important that the spatial components of the tracks remain the
same before and after this process. The radius versus Z-component for
the tracks are plotted for data (a) just after simulation as in Figure 3.8a
. . . . . . . . . . . .
(b) and after digitization and pulse shape analysis.

40

Figure 4.2: The 20305 AtTpcPoints created in a 100 event simulation of the 14O(d, 2He) 14N

reaction resulted in 3911 ATHits after digitization and pulse shape anal-
ysis. It is important that the spatial components of the tracks remain the
same before and after this process. The Y-component versus X-component
for the tracks are plotted for data (a) just after simulation as in Figure
3.8b (b) and after digitization and pulse shape analysis. . . . . . . . . . .

Figure 4.3: Data calculated by the SRIM program [55] for the stopping range of the
hydrogen ion in deuterium gas at 0.7 atm pressure. Data is modeled by a
cubic smoothing spline function. . . . . . . . . . . . . . . . . . . . . . . .

Figure A.1: View of root ﬁle loaded into TBrowser, showing “cbmsim” tree and some
. . .

examples of the data arrays that may be contained within the tree.

41

45

70

viii

Chapter 1

Introduction

1.1 Astrophysics

Astrophysics and nuclear physics are studies of nature separated by many orders of magni-

tude, yet in massive stars the concepts in each ﬁeld are closely intertwined. Due to the intense

gravitational pressure, fusion occurs in the core binding nuclei together in an exothermic re-

action to form more massive elements. The thermonuclear energy produced in this process

along with the degeneracy pressure due to high electron density in the core counteract the

inward gravitational force [1]. This process begins with hydrogen burning, forming helium.

Once the core exhausts its hydrogen as a fuel for fusion, the outward force due to internal

pressures begins to decrease and the core contracts. Depending on the mass of the star M ,

the core will contract either until the electron degeneracy pressure balances the gravitational

force or the core reaches the temperature required for helium fusion (M > 0.4 M(cid:12)) [2].

Over the life-time of a massive star, this cycle of fuel burning, core contraction, and

fusion ignition continues beyond helium creating a structure of ash shells. The average

binding energy per nucleon increases to a peak near 56Fe after which the decreasing binding

energy corresponds to energy consumption for further fusion. Once the star reaches the

silicon burning phase, an iron core develops which will not act as fuel for the outward

force counteracting gravity. The core will continue to grow until its mass surpasses the

1

Chandrasekhar limit (M ≈ 1.4 M(cid:12)) [3] at which point the thermonuclear energy combined

with the increasing degeneracy pressure is no longer suﬃcient to support the core against

gravitational collapse. In the mass range 8 M(cid:12) < M < 40 M(cid:12) [4], this leads to the death of

the star as a core-collapse supernova.

As core-collapse progresses, the pressure in the core increases to the point where further

compression would cause electrons to occupy the same energy states, violating the Pauli

exclusion principle. In order to reduce lepton number and decrease degeneracy, heavy nuclei
undergo electron-capture reactions, p + e− → n + νe, where a proton inside the nucleus and

an electron fuse to produce a neutron and an electron neutrino. The decrease in electron

degeneracy pressure along with the energy carried away by neutrinos accelerates the collapse
[2]. Once the core reaches nuclear density, ρ ≈ 1014 g cm−3, the matter can no longer be

compressed and the outer layers bounce oﬀ the core. Initially, the resulting shock wave slows

as it loses energy to the dissociation of nuclei in the surrounding shells, but it is thought that

the wave is reinvigorated by the burst of neutrinos [5]. The shock wave propagates outward

causing the outer layers to be ejected in an explosion.

Sensitivity studies have shown that electron-captures on neutron-rich nuclei in the N = 50

region contribute strongly to the change in electron fraction in the core of the star [6], which

places importance on studying neutron-rich unstable nuclei for understanding core-collapse.

This sequence of events, illustrated in Figure 1.1, ends with the astrophysical phenomenon

known as a core-collapse supernova, which is believed to contribute to nucleosynthesis [7].

These events are also predicted to be sources for gravitational waves and neutrinos [8, 9,

10]. The role that core-collapse supernova play in stellar evolution make the astrophysical

processes involved essential to understanding the evolution of the universe.

2

Figure 1.1: The inert iron core increases in mass as the silicon burning phase progresses (a)
until it reaches the Chandrasekhar mass limit and the gravitational force overcomes ther-
monuclear energy and degeneracy pressures. (b) The core begins to contract and electron-
capture occurs (c) until core density reaches ρ ≈ 10−14 g cm−3 and contraction quickly stops,
(d) after which the outer layers bounce oﬀ the core creating an outward propagating shock
wave. (e) The shock wave slows as it passes through the outer layers (f) but is reinvigorated
by a burst of neutrinos. Figure credit [11].

1.2 Electron-Capture Rates

Electron-capture in these massive stars is one of the driving reactions behind the evolution

of the inert iron core from growth to collapse. The rates at which these reactions occur are

essential inputs in astrophysical simulations and, thus, need to be understood with good

precision for a large range of energies and many nuclei.

Electron-capture reactions as illustrated in Figure 1.2a are mediated by the weak force

with rates dominated by Gamow-Teller (GT) transition strengths and distributions [12, 13,

3

14, 15], from the initial to the ﬁnal states. These transitions involve a transfer of spin

(∆S = 1), with no change in angular momentum (∆L = 0). The total electron-capture rate

for a nucleus is the sum of the of the individual electron-capture rates for each transition

between parent nucleus state i and daughter nucleus state j, formulated as [12, 16]

(cid:88)

λEC = ln(2)

fij(T, ρ, UF )B(GT )ij.

(1.1)

ij

The Gamow-Teller strength for each (cid:104)i|j(cid:105) transition, B(GT )ij, is weighted by a phase-

space factor, fij(T, ρ, UF ), which is calculable and dependent on the stellar temperature,

T , density, ρ, and the electron chemical potential, UF . The Gamow-Teller strengths can be

studied experimentally but the direct measurement through electron-capture and β+ decay

studies is limited by the decay Q-value.

The Q-value of a reaction is the total energy absorbed or released by the reactants in

creation of the products. For electron-capture and β decay, this Q-value sets a limitation on

the allowed energies of the daughter nucleus as seen in Figure 1.3. Due to this limitation,

from these measurements only Gamow-Teller transition strengths for a few levels can be

extracted, providing an incomplete estimate of the electron-capture rate.

Charge-exchange reactions as illustrated in Figure 1.2b do not restrict the excitation of

the daughter nucleus to a Q-value window.

In these reactions, the target nucleus either

exchanges a neutron for a proton from the beam particle, denoted a reaction in the (n, p)

direction, or vice versa, denoted (p, n). While charge-exchange is mediated by the strong

force, there exists a proportionality between the Gamow-Teller transition strength and the

charge-exchange reaction cross section that allow charge-exchange reactions to be useful tools

4

(a) Electron-Capture

(b) Charge-Exchange Reaction

Figure 1.2: (a) Electron-capture on a nucleus, decreasing atomic number by one while main-
taining atomic mass and releasing an electron neutrino. (b) Example of a charge exchange
reaction, t(A
Z−1X)3He, in which a neutron from a triton is exchanged for a proton from
the target nucleus, resulting in the release of a 3He and a product nucleus with atomic
number decreased by one but atomic mass unchanged

Z X, A

Figure 1.3: The excitation energies of the daughter nucleus are limited to states within the
Q-value window, Qg.s, for electron-capture and β decay reactions between the ground states
of the nuclei. In charge-exchange reactions, the excitation energy of the daughter nucleus is
not limited by the Q-value.

5

for extracting Gamow-Teller strength and calculating electron-capture rates [17, 18, 19, 20].
This relationship is taken as momentum transfer is reduced to zero (q → 0) for Gamow-Teller

transitions at intermediate energies, given by

(cid:18) dσ

(cid:19)

dΩ

q=0

= ˆσB(GT ),

(1.2)

where the unit cross section, ˆσ, can be determined by calibrating cross sections against data

from β decay experiments or, if β decay data is unavailable, it can be calculated using a

mass-dependent relationship formulated by Zegers et al [20].

Since the charge-exchange reactions can populate states of the daughter nucleus up to

high excitation, the electron-capture rates can be calculated using more individual Gamow-

Teller transition rates, providing more accurate results. However, such measurements can

only be performed for a limited set of nuclei. In addition, in the hot stellar environment,

transition from excited states can occur, which cannot be measured in the laboratory. There-

fore, one has to rely on theory to estimate Gamow-Teller strengths. These theories must be

benchmarked and guided by the data obtained from charge-exchange experiments.

1.3

(d,2He) Reaction

Charge-exchange can be performed by a variety of reaction probes, each with its own sen-

sitivities, to study the characteristics of nuclei. In forward kinematics, where a low-mass

ion beam strikes the nucleus of a heavy-mass target, many charge-exchange experiments

have been performed using probes like (p, n) [21] and (3He, t) [22] for reactions in the (p, n)

direction and (n, p) [23], (d, 2He) [24, 25, 26, 27], and (t, 3He) [22, 28] for reactions in the

6

(n, p) direction. Reactions in forward kinematics, however, are limited to targets made from

stable isotopes, which is problematic since most of the nuclei relevant to this astrophysical

study are unstable.

Experiments in inverse kinematics utilize a heavy-mass ion beam striking a low-mass

nuclide target. Since the beam can travel at high velocities, the reaction can occur before

unstable isotopes decay, allowing for charge-exchange reactions on nuclei in regions away

from the valley of stability. Development of eﬀective probes in inverse kinematics direction

is then essential to studying nuclei, such as those in the high-sensitivity region around N = 50

described by Sullivan et al. The (p, n) reaction in inverse kinematics has been successfully

developed and used to study unstable nuclei, including 56Ni [29], 55Co [30], 16C [31], and

132Sn [32]. In the (n, p) direction, the (7Li, 7Be) reaction has been employed for experiments

in inverse kinematics [33, 34], but this probe is restricted to experiments involving low-mass

nuclei (A < 40) and to excitation energies below the particle-decay threshold. Therefore, a

better probe for (n, p)-type charge-exchange reactions is very desirable.

The (d, 2He) reaction, illustrated in Figure 1.4, is a probe that has been proposed by the

Charge-Exchange Group at the National Superconducting Cyclotron Laboratory (NSCL)

for (n, p)-type experiments in inverse kinematics. The (d, 2He) reaction has been studied in

many experiments in forward kinematics [24, 25, 26, 27], but such an experiment has not

been performed in inverse kinematics. In this reaction, the 2He recoil presents a challenge

since it is unstable and immediately decays into two protons. In order to extract information

on the ejected beam, the momentum vector of the 2He must be reconstructed from the tracks

of the two protons. The goal of this thesis and the experiment it describes is to establish the

(d, 2He) reaction in inverse kinematics as a probe for charge-exchange reactions and provide

the analytical techniques required to track the protons.

7

Figure 1.4: The (d, 2He) reaction in inverse kinematics, where the unstable heavy nucleus
is projected onto a deuterium target nucleus. The 2He recoil immediately decays into two
protons with relative energy, pp.

8

Chapter 2

Experimental Setup

2.1 Overview

The Charge-Exchange Group at the NSCL has proposed an experiment using the 14O(d, 2He)

reaction in inverse kinematics as proof-of-principle for (d, 2He) as a probe for measuring

Gamow-Teller transition strengths of unstable nuclei. To measure the momentum vectors of

both protons with good accuracy, the Active-Target Time Projection Chamber (AT-TPC)

ﬁlled with deuterium gas will be used for tracking of charged particles within the detector.

The AT-TPC will be used in conjunction with the S800 spectrograph [35], which serves to

measure the heavy ejectile (14N) or one of its decay products and to provide an event trigger

for the AT-TPC. The experimental set up is illustrated in Figure 2.1.

In order to determine the excitation energy and center-of-mass scattering angle of the

14N ejectile, a missing-mass calculation is performed with the 2He particle whose momentum

is reconstructed in an invariant-mass analysis from the two protons. The relative energy of

the two protons is given by [36]

pp =

E1 + E2 − 2(E1E2)1/2cos θ12

(cid:21)

,

(cid:20)

1
2

(2.1)

where E1 and E1 are the laboratory energies of the two protons and θ12 is the angle between

the directions that each proton travels. In order to ensure that the spin-singlet 1S0 pp state is

9

Figure 2.1: The AT-TPC is placed in front of the S800 spectrograph to utilize its ability to
do particle identiﬁcation, as well as to provide a trigger for events in the AT-TPC.

created and the reaction is exclusively of spin-transfer type, the data must be gated on events

for which pp < 1 MeV, which corresponds to low-energy protons. The diﬀerential cross-

sections for excitations of 14N are calculated with the code “Adiabatic Coupled-Channels

Born Approximation” (ACCBA) [37] and an example for the 14O(d, 2He) reaction can be

seen in Figure 2.2.

The Gamow-Teller transition strengths from a nucleus follows a general sum rule: Sβ− −
Sβ+ = 3(N − Z), where Sβ± corresponds to the summed Gamow-Teller strength in the β±
direction. However, measurements only account for about 50 − 60% of this strength [38].

Diﬀerent mechanisms thought to contribute to this quenching of the Gamow-Teller strength

[39, 40, 41]. To better understand the diﬀerent contributions to the quenching, accurate

measurements of the Gamow-Teller strength distributions are important. Charge-exchange

reactions on light systems are a good way to obtain these distributions. In the case of 14O,
Gamow-Teller transitions in the β− (or (p, n)) direction are Pauli blocked because the

10

Figure 2.2: Double diﬀerential cross-section as a function of the center-of-mass angle (θcm)
and the relative energy of the two protons (pp) for the transition to the 3.95 MeV 1+ 14N
state via the 14O(d, 2He) reaction. Calculations based oﬀ of the Adiabatic Coupled-Channels
Born Approximation (ACCBA) code.

Figure 2.3: Kinetic energy versus the angle in the laboratory for the 2He particle for the
14O(d, 2He) reaction in inverse kinematics at 115 MeV/u. The dotted colored lines indicate
the excitation energy of 14N, in steps of 5 MeV. The brown lines indicate center-of-mass
scattering angles (2◦ and 5◦).

11

protons ﬁll the p-shell. Therefore, Sβ− = 0, and the sum rule can be assessed by a mea-
surements of the β+ Gamow-Teller transition only. Hence, in a single measurement, the

Gamow-Teller sum rule can be evaluated. The strong transitions to the 3.95-MeV 1+ and

2.31-MeV 0+ states in 14N make the 14O(d, 2He) reaction a good candidate for testing the

basic properties of this new probe.

2.2 Active Target-Time Projection Chamber

Reconstruction of the 2He recoil requires measuring each proton with good accuracy. Solid

targets (e.g. CD2) suﬀer the trade-oﬀ between resolution and luminosity. This option is not

possible due to the poor luminosity that would result from a target thin enough to let the

reaction products escape in combination with the relatively low beam intensities associated

with the use of rare-isotope beams. A time projection chamber (TPC) contains a large

volume of gas which is ionized as charged particles pass through. The chamber utilizes

electric ﬁelds to guide the ejected electrons to a wire mesh or pad plane detection system.

A three-dimensional reconstruction of the trajectory of the charged particles can be made

using the signal readout from the incident electrons, where the X- and Y-coordinates are

determined from the pad position and the Z-coordinate is determined from the timing of the

signal and the drift velocity of electrons in the gas.

The Active Target-Time Projection Chamber (AT-TPC) [42] utilizes this TPC technology

with the added functionality of the gas tracking medium working simultaneously as the

reaction target. The concepts behind this detector eliminate the need to compromise between

resolution and luminosity since the energy of the reaction products can be measured as they

emerge from the detector, regardless of the thickness of the target medium.

12

The detector, illustrated in Figure 2.4, consists of a cylindrical active volume, 1 m in

length and 29.2 cm in radius, which contains the deuterium gas target and tracking medium.
A uniform electric ﬁeld (∼ 104 V) is generated inside the active volume in the direction of the

beam axis by creating a potential diﬀerence between the cathode near the beam entrance and

an anode near the end of the detector. To ensure uniformity of the electric ﬁeld, a ﬁeld cage

consisting of 50 concentric ring-shaped electrodes establishes evenly spaced equipotentials

between each ring. As the charged protons travel through the detector, ionized electrons in

the electric ﬁeld drift down the length of the active volume to the sensor plane composed

of 10240 Micromegas pads, which provide the signal read by the digital electronics on the

back face of the detector. As seen in Figure 2.5, an aperture, 40 mm in diameter, was

constructed in the sensor plane of the AT-TPC to allow the ejectile to continue into the

S800 spectrograph. During the (d, 2He) experiment, the particle detection in the S800 will

serve as a trigger for reading out the event in the AT-TPC.

13

Figure 2.4: Illustration of the AT-TPC. A beam of 14O particles enters the right side of the
diagrammed detector. The active volume is ﬁlled with deuterium gas at 0.7 atm pressure,
which reacts with the beam and produces two protons. The ejectile leaves the left side of
the diagrammed detector and continues on to the S800 spectrograph.

14

Figure 2.5: Visualization of the simulation of one (d, 2He) event. Since the ejectile retains
most of its momentum, it is carried through an aperture in the back of the detector into
the S800 spectrograph. The two protons create tracks of ionized electrons in the gas as
illustrated.

15

Chapter 3

Simulation

3.1 Framework

The ATTPCROOTv2 code this thesis describes is the framework for simulation and analysis

of data from the AT-TPC as well as the Prototype AT-TPC [43]. The framework allows

the end user to unpack and analyze the data, as well as perform realistic simulations based

on a Virtual Monte Carlo (VMC) package. ATTPCROOTv2 allows the user to create a

customized geometry to simulate the detector environment and to simulate the reaction on

an event-by-event basis. Each generated event can be tailored to the reaction mechanism,

whether it be, for example, ﬁssion or the (d, 2He) reaction. After unpacking raw data or

creating simulated data, the read out from the ATTPC pad planes can be processed by

pulse shape analysis. The collection of points from each event can be analyzed using pattern

recognition algorithms and the trajectories of particles in the detector can then be tracked.

The framework is built upon ROOT [44] and requires external libraries (FairSoft [45] and

FairRoot [46]) to be compiled and executed, which are developed by other groups. Additional

libraries for analysis are needed, like PCL [47], FLANN [48], and Eigen [49] and libraries

like the HDF5 library [50] are needed for data formatting. The Monte Carlo simulations

are handled by the Geant4 toolkit [51]. Details on installation of the code can be found in

Appendix A.

16

FairRoot analyses and simulations are deﬁned using ROOT macros and executed by

ROOT. The processes involved in each macro are managed by a FairRoot class Run Manager.

The FairRunSim class is used for simulation runs and the FairAnaSim class is used for

analysis runs. The simulation or analysis is constructed by deﬁning and adding components

to the run manager. The parameters required by and created in simulation and used as inputs

to analysis are managed by the FairRuntimeDb class (Parameter Manager). The input and

output of data is organized by the FairRootManager class (IO Manager) which can provide

access to or create branches in the input and output ﬁles. Figure 3.1 illustrates the ﬂow of

data types as input and output for the diﬀerent processes involved in ATTPCROOTv2.

For simulations, the FairRoot classes FairRunSim, FairPrimaryGenerator, and FairM-

CApplication are used as they are with the user only calling functions on the classes. Fair-

RunSim deﬁnes the experimental set up, including the Monte Carlo engine, detector geome-

tries and event generators, through its member functions. FairPrimaryGenerator deﬁnes the

primary beam conditions as well as any additional event generators that may be involved

in the reaction. FairMCApplication is only used internally and serves as the interface be-

tween FairRoot and Geant4. The FairRoot classes that must be implemented by the user

are FairModule, FairDetector, FairGenerator, and FairGenericStack. The FairModule are

components of the geometry that particles do not interact with, such as the “Cave” in which

all other components are anchored. The FairDetector are components of the geometry that

constitute an active volume with which particles can interact. The FairGenerator creates

particles for an speciﬁed event, like the instance of a beam particle or a two-body reaction,

and puts the particle on the FairGenericStack. The FairGenericStack contains particles or

tracks generated in an event. The processes involved after execution of a FairRoot simulation

macro is illustrated in Figure 3.2.

17

Figure 3.1: Flow of ATTPCROOTv2 data types at each step in the process from generation of
data to user analysis. Example generators are those used in simulations of (d, 2He) reactions.
Each FairRoot analysis task requires a speciﬁc input data type and produces a diﬀerent
output data type as shown in the ﬁgure.

For analysis, the FairRoot class FairRunAna is used as it is with the user only calling

its member functions. This class deﬁnes the analysis tasks and the order in which they are

executed. The FairRoot class that must be implemented by the user is the FairTask class.

This class connects with a speciﬁed type of data in the input ﬁle, performs analysis on that

data, and registers the results in a branch of the output ﬁle. Subsequent tasks can connect to

data in the output ﬁle registered by previous tasks. The processes involved after execution

of a FairRoot analysis macro is illustrated in Figure 3.3.

The code shown in Figures 3.2 and 3.3 can be used as outlines that should be included

in every FairRoot simulation and analysis macro for the (d, 2He) reaction. The input for

the arguments of the FairGenerators will be explained in more detail in Section 3.2.3. Each

FairTask has parameters that need to be speciﬁed in the macro, which will be explained in

more detail in Section 3.3.

18

Figure 3.2: Workﬂow of FairRoot simulation, including the outline of a simulation macro.
Illustrations adapted from [52].

19

Figure 3.3: Workﬂow of FairRoot analysis, including the outline of an analysis macro. Illus-
trations adapted from [52].

20

3.2 Data Generation

There are four components involved in creating accurate simulation data for reactions within

the AT-TPC: the geometry, the parameter ﬁle, the event generators, and the ROOT sim-

ulation macro. For new reactions, each will need to be adjusted. The following examples

are used to simulate the 14O(d, 2He) 14N reaction in inverse kinematics, using a 115 MeV/u

beam and a deuterium gas target at 0.7 atm.

3.2.1 Geometry

Some of the inputs to the FairRunSim needed for propagation of the particles through space

by Monte Carlo engine are the geometry position of detectors and the media involved in

the reaction environment. In the ATTPCROOTv2/geometry directory, there are macros for

creating these geometries that utilize TGeoManager object and accompanying classes from

the ROOT geometry package.

To construct the detector, the geometry ﬁle contains a list of volumes characterized by

a number of parameters. The geometry will consist of a top volume which contains all of

the other modules that make up speciﬁc detector components. To describe a module, the

following requirements need to be met:

• Construct all necessary materials
• Deﬁne shapes/solids required to describe the geometry
• Construct and place volumes of the detector geometry
• Deﬁne sensitive detectors and identify detector volumes with which to associate

them

• Deﬁne visualization attributes for the detector elements

21

The media.geo ﬁle acts a dictionary for materials that are commonly used in simulations

since there are no predeﬁned materials in FairRoot. Each medium is deﬁned by several

numerical parameters as seen below and described on the FairRoot HowTo page [46]. The

following parameters are required:

• int ncomp - number of components in the material (ncomp= 1 for a basic
material and < 1 or > 1 for a mixture. If ncomp > 0 the array wm contains the
proportion by weight of each material in the mixture. If ncomp < 0 the array
wm contains the proportion by number of atoms of each kind.)

• ﬂoat aw[ncomp] - atomic weights A for the components
• ﬂoat an[ncomp] - atomic numbers Z for the components
• ﬂoat dens - density DENS in g/cm−3
• ﬂoat wm[ncomp] - weights WMAT of each component in a mixture (only for

a mixture)

• int sensﬂag - sensitivity ﬂag ISVOL
• int ﬂdﬂag - ﬁeldﬂag IFIELD
• ﬂoat ﬂd - maximum ﬁeld value FIELDM in kilogauss
• ﬂoat epsil - boundary crossing precision EPSIL
• int npckov - number of values used to deﬁne the optical properties of the
medium. This variable is 0 for all media except some special media used for the
Rich where the tracking of the Cherenkov photons is necessary. These media
have additional parameters

– ﬂoat ppckov[npckov] - photon momentum in eV

– ﬂoat absco[npckov] - absorption length in case of dielectric and of ab-

sorption probabilities in case of a metal

– ﬂoat eﬃc[npckov] - detection eﬃciency

– ﬂoat rindex[npckov] - refraction index for a dielectric, rindex[0]=0 for a

metal

Remark: In the present program version a mixture may contain a maximum
of 5 components.
If this is not suﬃcient one has to change MAXCOMP in
hgeomedium.h.

22

The following parameters are normally not read. The default values are -1 and the real

values are automatically calculated by Geant. If the user wants to set these values manually,

they must type the keyword AUTONULL in the media ﬁle. After this keyword all media

must contain these additional 4 parameters before the Cherenkov (int npckov).

• ﬂoat madﬂd - maximum angular deviation TMAXFD due to ﬁeld
• ﬂoat maxstep - maximum step permitted STEMAX
• ﬂoat maxde - maximum fractional energy loss DEEMAX
• ﬂoat minstep - minimum value for step STMIN

The ATTPCROOTv2/geometry/ directory is the location of the geometry macros as

well as the geometry ﬁles that they create. These macros are basically comprised of three

functions. The main function, which ought to have the same name as the ﬁle name, builds

the geometry using the TGeo ROOT geometry package and writing it to a ﬁle. The cre-

ate materials from media ﬁle() function loads the parameters deﬁning the materials in an

external dictionary of materials called media.geo. The create detector() function is what de-

ﬁnes the volumes of the detector, their dimensions, and the material of which each component

is made.

A working macro to create a basic version of the AT-TPC geometry for use with a

(d,2He) reaction is ATTPCROOTv2/geometry/ATTPC d2He.C, which can be run using

the command root -l ATTPC d2He.C . In general, the main function will not need to be

edited. If new materials need to be used (e.g. same gas at new pressure), they must ﬁrst be

deﬁned in the ATTPCROOTv2/geometry/media.geo ﬁle if they are not already. Examples

of media deﬁnitions following the parameters outlined above are shown in Figure 3.4.

If

new volumes need to be added, simply create a new TGeoVolume in the create detector()

23

function in a similar manner to those already deﬁned. Then changes needed in the macro

include:

1. Add its predeﬁned name as a constant TString for later use (after included

packages at beginning of macro)

2. Load

the

new material

as FairGeoMedium objects

in

the

cre-

ate materials from media ﬁle() function

3. Create TGeoMedium objects of the material for use in the TGeoVolume deﬁni-

tions

Two ROOT ﬁles are created, like ATTPC d2He.root and ATTPC d2He geomanager.root

as in the example macro above. The ﬁrst ﬁle is the geometry ﬁle that contains the TGeoVol-

ume which consists of the top volume (vacuum) and nodes corresponding to the components

of the detector and target added in the macro. A visualization of this geometry is shown

in Figure 3.5. The second ﬁle created is the TGeoManager ﬁle which contains a list of the

media, volumes, and their positions deﬁned in the macro.

Figure 3.4: Examples of media deﬁnitions for air (1 atm), aluminum metal, deuterium gas
(0.7 atm), and HeCO2 gas. Note that since the ncomp parameter (ﬁrst row, ﬁrst number)
for each mixture is positive, the wm parameters (ﬁrst row, last ncomp numbers) are listed
by weight proportion.

24

Figure 3.5: A very basic geometry of the AT-TPC with a drift volume of deuterium gas.

3.2.2 Parameters

FairRoot analysis of simulation results requires numerical parameters to process the data.

Some information required by the analysis tasks can include geometry positions of detectors

or digitization parameters related to the experimental set up or detector response speciﬁca-

tions. The FairRuntimeDB class is a repository for these parameters used in FairRoot for

simulation and analysis. This class contains a list of parameter containers as well as a list

of runs performed and the diﬀerent versions of the parameters used in each run. Inputs to

this class can either be ROOT ﬁles or ASCII ﬁles.

25

Figure 3.6: Parameter ﬁle (ATTPCROOTv2/parameters/ATTPC.d2He.par) for use in Fair-
Root analysis of simulation data.

FairRoot simulations automatically create a parameter container that contains informa-

tion on the geometry used and the runtime database outputs the information to a ROOT

ﬁle which can be used later as input in analysis. Additional parameters are needed for

analysis that the user has to specify which are deﬁned in ASCII ﬁles in the ATTPC-

ROOTv2/parameters/ directory. The example shown in Figure 3.6 is used in the simulation

and analysis that follows.

These ﬁles contain a number of parameters related to the AT-TPC design (outlined with

red in the ﬁgure), like speciﬁcations on the Micromegas pad plane and the location of the an-

ode and cathode wires, which are independent of the experiment and should not be changed.

26

Additional parameters pertain to the conﬁguration of the AT-TPC in the experimental set

up (outlined with blue in the ﬁgure), which could change between experiments. Of the re-

maining parameters, NumTbs and SamplingRate are parameters used for digitization and

should not be changed. The rest of the parameters are dependent on the properties of the

gas used in the AT-TPC. Eionize and Density will change depending on the isotope used as

the target and the density will depend on the pressure deﬁned by GasPressure. The DriftVe-

locity parameter refers to the drift velocity of electrons through the gas and is dependent on

the magnitude of the electric ﬁeld in the AT-TPC deﬁned by the EField parameter and the

pressure of the gas [53].

3.2.3 Generators

Another input to the FairRunSim is provided using particle generators classes with inherited

members from the FairGenerator class. These generators create single particles or multi-

ple particles involved in a reaction, calculating the kinematics involved, given the initial

conditions of the particles. Each contains the ReadEvent() function that adds tracks to

the stack in the PrimaryGenerator. Predeﬁned generators can be found in the ATTPC-

ROOTv2/ATGenerators/ directory.

The FairPrimaryGenerator class handles the MC input of the event generation, allowing

the user to set various aspects of the beam, target, and number of events. This object

is only instantiated once but several generators can be registered to it depending on the

reaction being simulated. The primary generator contains a FairGenericStack which holds

information on every particle generated in a list of “tracks”, which describes the particle

type, momentum, and position.

Reactions in the AT-TPC must be simulated using two events. In simulations involving

27

solid targets, the beam prior to the reaction does not need to be considered. However in the

case of a gas target like in the AT-TPC, the gas has an eﬀect on the energy and trajectory

of the beam in the moments leading up to the reaction. This means that an event must be

generated for both the beam and the reaction itself so that the physics engine can propagate

the particles before and after the reaction. An example of the declaration of generators for

the simulation of the 14O(d, 2He) 14N reaction in inverse kinematics is shown in Figure 3.7.

Each simulation macro in the AT-TPC will ﬁrst register an ATTPCIonGenerator object

to the primary generator. It is important to note the units of the arguments used in the

constructor of this class. The momenta must be deﬁned in units of GeV per nucleon and the

beam energy, beam mass, and nominal energy must be deﬁned in units of GeV. The nominal

energy is the amount of energy that the beam would lose to the gas if it passed through the

entire active volume of the AT-TPC without reacting. The generator randomly chooses an

energy between zero and the nominal energy. This determines the reaction vertex location

in the detector as it would correspond to the amount of energy lost up to that location.

For the (d, 2He) reaction, the ATTPC d2He object is registered as the second event

generator. When this class generates an event, it calculates the relativistic kinematics of the

two-body reaction as well as the kinematics for the two protons produced. The argument

for its constructor takes an array with an entry corresponding to each particle considered

in the reaction: (1) beam (14O), (2) target (d), (3) ejectile (14N), (4) recoil (2He), and

(5,6) each proton. The arguments of this class require diﬀerent units, namely momenta and

excitation energy must be deﬁned in units of MeV and the mass must be deﬁned in atomic

mass units. An additional input to this generator is the data from the ACCBA calculations

of the double diﬀerential cross-sections for this reaction. The macro shown in Figure 3.7

reformats the resulting data ﬁle from these calculation for use in the generator.

28

Figure 3.7: Example macro code showing input required in deﬁnition of ATTPCROOTv2
generators, ATTPCIonGenerator and ATTPC d2He, for simulation of a (d, 2He) reaction.

29

3.2.4 Monte Carlo Simulation

The Geant4 platform is the software toolkit that handles the simulation of particles through

matter using Monte Carlo methods. Some of the relevant capabilities of this software include

[51]:

• Geometry Management - handles the physical layout of the detector including
the various media involved and considers the eﬀects these materials have on the
path of particles.

• Tracking - propagates particles through matter and considers possible interac-

tions and decay processes.

• Detector response - records when a particle passes through the detector volume

and approximates how a real detector would respond.

• Run management - records the details of each run (a set of events), as well as

setting up the experiment in diﬀerent conﬁgurations between runs.

While the generators deﬁne the initial conditions of the beam and the reaction, Geant4

determines what happens to the particles in between the two events and afterwards, taking

into consideration the energy loss that occurs during transport and the interactions that may

occur with each material in the geometry. In order to carry the information of the vertex

location and energy loss between the event generators, an object called ATVertexPropagator

is created at the beginning of the simulation and its member variables (e.g. momenta, energy

loss, and position) are set. Each generator can then read this information to initialize the

properties of the particles it generates.

Predeﬁned ROOT macros for FairRoot simulations are found in the ATTPCROOTv2/-

macro/Simulation/ directory. For simulation of the 14O(d, 2He) 14N reaction in inverse kine-

matics at 115 MeV/u beam energy and 0.7 atm deuterium gas pressure, data is produced

using the d 2He sim 14O.C macro in the ATTPCROOTv2/macro/Simulation/d2He/ direc-

30

tory. This ﬁle reads data from the ACCBA calculations stored in all2 14O.dat in the same

directory. Additionally, it requires the geometry ﬁle ATTPC d2He 07atm.root to be present

in the ATTPCROOTv2/geometry/ directory which can be created using the ATTPC d2He.C

macro in the geometry folder.

The output of ATTPCROOTv2 simulations is a ROOT ﬁle which contains a branch

of AtTpcPoint objects and a ROOT ﬁle which holds the parameter containers that are

used later in FairRoot analysis macros. Each AtTpcPoint corresponds to a particle and is

designated by an event ID, track ID, and the volume it occupies as well as the particle’s

position, momentum, and initial energy and angle. Since the simulation run is deﬁned by an

ion generator and a (d, 2He) reaction generator, each even event ID corresponds to a beam

event and each odd event ID corresponds to a reaction event. Track ID numbers and their

corresponding particles are: (0) 14O, (1) 14N, and (2/3) protons.

The kinematic parameters can be studied using the macro d2He ana 14O 07atm.C in

the ATTPCROOTv2/macro/Simulation/d2He/Analysis d2He/ directory. This analysis ﬁle

creates three sets of histograms stored in branches of a ROOT ﬁle called “Parameters”,

“He2 reconstr”, and “He2 reconstr resol”. The histograms in the “Parameters” directory

display information taken directly from each AtTpcPoint in the simulation run being ana-

lyzed with such plots as “Z vs R” and “X vs Y” as seen in Figure 3.8. The histograms in

the “He2 reconstr” directory provide information on the reconstruction of each 2He particle

with calculations based oﬀ of the information taken directly from the AtTpcPoints in each

event. Histograms such as the θcm distribution and “KElab vs θlab” are display in Figure 3.9.

The histograms in the “He2 reconstr resol” directory contain many of the same histograms

as in “He2 reconstr” except the information on the reconstruction of each 2He particle is

calculated based oﬀ of a graphical ﬁt of each proton track, which is then used to determine

31

the proton energy and angles needed for reconstruction. The results of this are displayed in

Figure 3.10 and can be compared to those from “He2 reconstr”.

(a)

(b)

Figure 3.8: A total of 20305 AtTpcPoints were created in a 100 event simulation of the
14O(d, 2He) 14N reaction. Each point holds the position, momentum, and energy of a particle
at one moment in its trajectory. These positions are plotted in the histograms shown. (a)
Radius versus Z-component of tracks made by protons in the AT-TPC. (b) Y-component
versus X-component.

32

(a)

(b)

Figure 3.9: Results of invariant mass calculation for a 10000 event simulation calculated
from AtTpcPoint parameters. (a) Angular distribution of the 2He particle center-of-mass.
(b) Kinetic energy versus angle in the laboratory for the 2He particle.

33

(a)

(b)

Figure 3.10: Results of invariant mass calculation for a 10000 event simulation calculated
graphical ﬁt of each proton to reconstruct the 2He particle. (a) Angular distribution of the
2He particle center-of-mass. (b) Kinetic energy versus angle in the laboratory for the 2He
particle.

34

3.3 Digitization

The data that comes from prior simulation is not very useful for analysis because it is not

formatted similarly to the data that will be taken during the experiment. The experimental

data is blind to the type of particle producing each track detected in the pad plane and

provides no information on the momentum, energy, or trajectory angle for each point. This

information must be extracted from a collection of pulses created in the pad plane by using

the location of the each pad and the timing of the pulse to construct the tracks in three

dimensions.

The digitization of the simulated data is performed using the rundigi sim.C macro found

in the ATTPCROOTv2/macro/Simulation/d2He/Analysis d2He/ directory. This FairRoot

analysis requires two ﬁles as input to the runtime database, which are the parameter ﬁle

created by the simulation macro and the parameters described in Section 3.2.2.

3.3.1 Clusterization

The ATClusterizeTask class found in the ATTPCROOTv2/digi/ directory is a FairTask

that accepts a branch of AtTpcPoint objects as input. The name of this task is simply

refers to the process of creating groups of electrons between each point along the proton

trajectories. This task loops through every point in each event and calculates the number

of electrons (with some Gaussian ﬂuctuation dependent on the Fano factor) ionized by a

particle passing through the detector’s gas using the energy loss since the previous point.

The distance between the current point and the previous point is divided into equal spaces

such that one of the ionized electrons can be placed at a point in each one. Each electron’s

position is calculated with some Gaussian ﬂuctuation using the longitudinal and transverse

35

Figure 3.11: Illustration of the ionization of the deuterium gas as the two protons from a
(d, 2He) reaction travel through the AT-TPC volume.
Ionized electrons drift toward the
pad plane in the presence of the electric ﬁeld and undergo a Gaussian diﬀusion through the
deuterium gas, adding width to the tracks detected in the pads. Figure adapted from [42].

coeﬃcients of diﬀusion found in the parameter ﬁle to account for dispersion. The drift time

is determined by dividing the Z-component of each electron’s position by the drift velocity

found in the parameter ﬁle. The task produces a branch of ATSimulatedPoints each of which

contain the X- and Y-components of an electron as well as the drift time. An illustration of

the process that is simulated by this task can be seen in Figure 3.11.

3.3.2 Pulse Creation

The ATPulseTask class found in the ATTPCROOTv2/digi/ directory is a FairTask that

accepts a branch of ATSimulatedPoint objects as input. The task produces a branch of

ATRawEvent objects each of which contain the collection of ATPad objects. An AtTpcMap

object is created which can be used to map the X- and Y-components of each ATSimulat-

36

edPoint to one of 10240 pads in the pad plane. This task loops over each event, creating

an ATPad for every new X- and Y-coordinate and adding hits to existing ATPads when

multiple electrons are mapped to the same pad. Each hit is registered with a time stamp

corresponding to the electron’s drift time. Once all ATSimulatedPoints in the event have

been registered to a pad, the task loops over the pads and creates signals according to a pad

response function. Multiple hits result in a superimposition of pulses. The binning param-

eters and gain in ATTPC.d2He.par are needed for this task. A visualization of the pulses

is shown in Figure 3.12 created using the runeve.C macro in the analysis directory, which

produces an interactive pad plane that displays the hits and their pulses for each event.

37

Figure 3.12: Visualization of the digitized data displayed as a map of the AT-TPC pad
plane. Each pad in the interactive map can be selected to view the pulse produced by the
ATPulseTask task. One the right side of the ﬁgure, four pads are selected showing the change
in the timing of the pulse for each subsequent point in the proton’s trajectory. The plot on
the bottom shows the pulse created in a pad where electrons arrived to the same pad at
diﬀerent times, resulting in multiple response functions superimposed.

38

Chapter 4

Analysis

The data up to this point came from simulation of charge-exchange reactions. The analysis

in the following discussions pertains to both data created in simulation and data recorded

in experiment. After the simulated data undergoes digitization, it is formatted similarly to

experimental data and is an accurate representation of what will be observed. Therefore,

the techniques proposed in this chapter and executed on simulation data serve as proof of

their viability for analyzing experimental data.

4.1 Pulse Shape Analysis

The ATPSATask class found in the ATTPCROOTv2/reco/ directory is a FairTask that

accepts a branch of ATRawEvent objects as input. The task produces a branch of ATEvent

objects each of which contain the collection of ATHit objects. Each ATHit object contains

the X-, Y-, and Z-coordinates of a particle. An ATHit is created for each ATPad in the

ATRawEvent where the X- and Y-coordinates correspond to the position of the pad in the

plane. The Z-coordinate is determined by analyzing the pulse in the ATPad in one of two

ways: (1) ﬁnding the maximum value of the pulse or (2) ﬁtting the pulse and and ﬁnding

peaks. This provides the time of the hit which can be used with the drift velocity to ﬁnd

the Z-coordinate. An comparison of the data before and after digitization and pulse shape

analysis can be seen in Figures 4.1 and 4.2.

39

(a)

(b)

Figure 4.1: The 20305 AtTpcPoints created in a 100 event simulation of the 14O(d, 2He) 14N
reaction resulted in 3911 ATHits after digitization and pulse shape analysis. It is important
that the spatial components of the tracks remain the same before and after this process. The
radius versus Z-component for the tracks are plotted for data (a) just after simulation as in
Figure 3.8a (b) and after digitization and pulse shape analysis.

40

(a)

(b)

Figure 4.2: The 20305 AtTpcPoints created in a 100 event simulation of the 14O(d, 2He) 14N
reaction resulted in 3911 ATHits after digitization and pulse shape analysis. It is important
that the spatial components of the tracks remain the same before and after this process. The
Y-component versus X-component for the tracks are plotted for data (a) just after simulation
as in Figure 3.8b (b) and after digitization and pulse shape analysis.

4.2 RANSAC Tracking

Unlike in simulation, particle tracks observed in experiment are often obscured by noise

from external sources and other reaction mechanisms. Furthermore, there is no method for

directly diﬀerentiating the tracks made by each proton in the detector. Classical ﬁtting

techniques, such as least squares, include the entire data set in pursuit of optimizing a ﬁt to

the model, meaning noise and multiple tracks can skew a single linear ﬁt.

4.2.1 RANSAC Algorithm

The Random Sampling Consensus (RANSAC) algorithm is a technique for determining the

subset of a data set that includes outliers which best ﬁts a given model and providing

41

parameters for that ﬁt. When applied iteratively to a data set, removing the subset of data

best ﬁtting the model after each iteration, multiple features in the data can be extracted

each with its own parameters for the given model.

Suppose the problem involves a data set P where the features of the data are deﬁned

by a model M that requires a minimum of n points to ensure a unique ﬁt. The general

implementation of the algorithm is outlined as follows [54]:

(i) Select a random subset of n points from P .

(ii) Fit the subset to a model Mtest.

(iii) Test all points in P against Mtest according to some loss function. Points within

a certain threshold are considered inliers and form a subset Sinliers.

(iv) Repeat steps (i) through (iii) until Sinliers contains a suﬃcient number of points

and the best model, Mbest, for a single feature has been found.

(v) Return Sinliers as an extracted feature with parameters given by Mbest.

(vi) Remove Sinliers from P and repeat steps (i) through (v) to obtain additional

features in P .

The eﬃciency of this process relies on two assumptions on the data set: the noise in the

data will not consistently agree with a given model, meaning there are few outliers compared

to the data in the features, and the features are prominent enough to agree on a good model,

meaning there are few missing data.

The RANSAC algorithm leaves three parameters to be speciﬁed: (1) the threshold for

agreement with the model, (2) the number of iterations to ﬁnd one feature, and (3) a standard

for what constitutes a good model (i.e., how many inliers is suﬃcient?).

The tracks left by protons in the AT-TPC can be modeled by a straight line in three

dimensions. The minimum number of points for the initial subset of inliers found in step

(i) is then n = 2. For a linear model, an simple loss function is the distance from the data

42

point to the line, which leaves the ﬁrst parameter to be a minimum distance threshold. An

appropriate threshold to capture much of the data in a track should be on the order of the

standard deviation of the diﬀusion of the electron Gaussian cloud.

Since the tracks are presumed to contain the most data points, the third parameter does

not need to be considered if the number of iterations in the second parameter is large enough.

In this case, returning the model which ﬁt the most inliers after all iterations must yield the

most populous track. In order to guarantee this case, the number of iterations would have

to be large enough to consider every two-element permutation of the data set but this is

still an arbitrary number since the total number of data points is still unknown. In practice

for simulations, good events have around 50 pad plane hits. Thus, (cid:0)50

(cid:1) ≈ 103 should be

2

suﬃcient to yield a track. An additional parameter for the least squares error can be added

when a track is ﬁt by many models corresponding to diﬀerent pairs of the track’s inliers.

4.2.2 RANSAC Implementation

The method for implementing the RANSAC algorithm used in the ATTPCROOTv2 frame-

work utilizes the Point Cloud Library (PCL) [47]. This library is useful for creating objects

of three-dimensional data points called point clouds which can be modeled. The library has

options for modelling using a RANSAC algorithm that returns the parameters for a line in

three-dimensions.

The ATRansacTask class found in the ATTPCROOTv2/reco/ directory is a FairTask

that accepts a branch of ATEvent objects as input. For each ATEvent, the task converts the

positions contained by the ATHit objects into individual points in a point cloud. The PCL

RANSAC algorithm is applied to the point cloud and a set of parameters and the inliers

they correspond to are extracted. These parameters and points are registered to an ATTrack

43

object. The inliers are removed from the point cloud and additional tracks are extracted

as the algorithm reiterates until the number of points has reduced to 10% of the original

point cloud. The task results in an ATRansac object which contains the stack of ATTrack

objects. This task, like the pulse shape analysis task, can be added to the FairAnaRun in

rundigi sim.C to analyze simulation data from clusterization to RANSAC analysis in one

run.

4.3 Reconstruction of 2He

The code d2He ana ransac.C in the ATTPCROOTv2/macro/Simulation/d2He/Analysis d-

2He/ directory performs the invariant-mass analysis to calculate the He momentum vector.

For each event where the RANSAC algorithm found more that one track, this macro uses

the parameters to construct the momentum vector for each proton. The parameters found

by RANSAC are the four coeﬃcients to the parametric form of a three-dimensional line. A

point along this line will have coordinates of the form



p[0] + p[1] ∗ t
p[2] + p[3] ∗ t

t



where p is the parameter vector given by RANSAC. To ﬁnd a vector in the direction of the

line, subtract the vectors for two coordinates along the line. Take the points for t = 0 and

t = 1 to get a general form for the vector in the direction of the track:

44

Figure 4.3: Data calculated by the SRIM program [55] for the stopping range of the hydrogen
ion in deuterium gas at 0.7 atm pressure. Data is modeled by a cubic smoothing spline
function.



p[0] + p[1]

p[2] + p[3]

1

 −



p[0]

p[2]

0

 =





p[1]

p[3]

1

(4.1)

which can be used to determine the angles of each proton, φ and θ, as well as the vertex

of the reaction. The φ-angle is the azimuthal angle about the beam axis (Z-axis) and the

θ-angle is the angle with respect to the forward direction of the beam axis.

The energy loss of each proton, Eloss, depends on the range that it travels in the detector.

The Stopping and Range of Ions in Matter program [55] calculates the stopping range for a

set of energies. Fitting this data provides a method for determining the energy loss given the

stopping range. The data calculated for a hydrogen ion in deuterium gas at 0.7 atm pressure

is shown in Figure 4.3 and is ﬁt using a cubic smoothing spline. The parameters of this

ﬁt are stored in the ﬁles, energyRangeCoefs.txt and energyRangeKnots.txt, in the analysis

45

directory. The momentum of each proton, (cid:126)p, can then be calculated using the relativistic

momentum

(cid:113)

loss − (mprotonc2)2 ∗
E2

(cid:126)pproton =





sin θ cos φ

sin θ sin φ

cos θ

(4.2)

where mprotonc2 is the rest mass of the proton. The reconstructed 2He momentum vector is

given by

(cid:126)p = (cid:126)pproton,1 + (cid:126)pproton,2.

(4.3)

The ATd2HeAnalysis class found in the ATTPCROOTv2/reco/ATAnalysis/ directory

has a function that performs the relativistic kinematics calculations needed to ﬁnd the exci-

tation energies of 14N and the center-of-mass scattering angles.

46

Chapter 5

Conclusions and Outlook

Electron-capture rates for unstable nuclei play an important role in the evolution of core-

collapse supernovae. The well-established proportionality between the Gamow-Teller tran-

sition strengths, on which the electron-capture rates strongly depend, and the cross-section

of charge-exchange reactions makes such reactions powerful tools for estimating electron-

capture rates. Establishing (d, 2He) reaction in inverse kinematics as a viable probe for

studying unstable nuclei will enable studies of nuclei in the region around N = 50 described

by Sullivan et al for which the change in electron number is highly sensitive in core-collapse

simulations.

The experiment described in Chapter 2 is expected to run at the NSCL in 2020. The

results of this experiment will serve as the ﬁrst test of the (d, 2He) reaction in inverse kine-

matics as a new probe in the (n, p) direction for unstable nuclei. The ATTPCROOTv2

framework provides a useful tool for the simulation and analysis of reactions involving the

AT-TPC detector. The RANSAC algorithm together with the concepts behind the AT-TPC

will enable the accurate measurement of proton tracks in experiment. The code described in

this thesis needs further optimization to ensure the simulation and future analysis yields the

most realistic results and the tracking algorithm properly estimates the range and energy of

each proton. A manual for installation and use of the code as a simulation and analysis tool

for a broader range of experiments in the AT-TPC was developed as part of this work.

47

APPENDICES

48

Appendix A

ATTPCROOTv2 Manual

This manual is a guide to installation of and implementation of the ATTPCROOTv2 code,

which is the framework based on FairRoot for data analysis and simulations of reactions in the

Active-Target Time-Projection Chamber (AT-TPC). While this thesis describes use of this

code speciﬁcally for the 14O(d, 2He) 14N reaction in inverse kinematics, use of the framework

code can be extended to any experiment that may involve the use of the AT-TPC. This

manual will describe the general building blocks for simulations using this broader range of

reaction mechanisms.

A.1

Installation

The framework is built upon ROOT [44] and requires external libraries (FairSoft [45] and

FairRoot [46]) to be compiled and executed, which are developed by other groups. Additional

libraries for analysis are needed, like PCL [47], FLANN [48], and Eigen [49] and libraries

like the HDF5 library [50] are needed for data formatting. The Monte Carlo simulations are

handled by the Geant4 toolkit [51].

For NSCL users, log into ﬁshtank. The dependent packages are already installed on the

server. The modules will simply need to be loaded at each login. Change directories to the

one where the analysis and simulations will be performed and data will be stored. Input the

following commands:

49

module load gnu/gcc/6.5

module load fairroot/18.00

git clone -b develop https://github.com/ATTPC/ATTPCROOTv2.git

cd ATTPCROOTv2

mkdir build

cd build

cmake ../

make -j8

This should install the ATTPCROOTv2 libraries and headers. The conﬁg.sh ﬁle that is

now in the build/ directory loads the environment variables but, in this process, destroys

some of the FairRoot settings. After sourcing the conﬁguration ﬁle, the FairRoot and com-

piler modules need to be loaded again.

source /path/to/ATTPCROOTv2/build/config.sh

module load gnu/gcc/6.5

module load fairroot/18.00

At each login, these three commands need to be run for the environment variables to be

set and the needed modules to be available. They can be added to the user’s bash script ﬁle

for convenience. After this process, the macros for simulation and analysis described in the

following two chapters are ready to be compiled and executed.

For non-NSCL users, installation on a personal computer will require the following de-

pendent packages before installing ATTPCROOTv2:

1. FairSoft

50

2. FairRoot

3. FLANN, Eigen, PCL, and HDF5 libraries

Once these packages are installed, the ATTPCROOTv2 code can be cloned from https://git-

hub.com/ATTPC/ATTPCROOTv2. As of September 2018, the ATTPCROOTv2 code has

been compiled with the following versions:

• FairSoft may18 [45],

• FairRoot 17.10 [46],

• boost 1.67.0,

• CMake 3.12.0,

• ﬂann 1.9.1 [48],

• eigen 3.3.6 [49],

• pcl 1.8.0 [47],

• hdf5 1.10.2 [50]

Operating systems tested:

• Mac OS X 10.13 (High Sierra) & clang 10.0

• Ubuntu 16.04.2 &

• Debian GNU/Linux 8.11 & gcc 6.4.1

51

If the code needs to be installed on a server where the environment might change often,

consider using CMake provided in FairSoft to make sure everything is compiled with the

same versions.

FairSoft:

FairSoft is a software package that includes the external software to compile and run

FairRoot. The package can be installed through git either in any Linux distribution (suc-

cessfully tested in Fedora/Red Hat, Scientiﬁc Linux, Ubuntu/Debian and MacOs Yosemite

and Mavericks.

In order to avoid permission problems, it is better to install it in any

folder below the home directory. Here is the link to the GitHub account for FairSoft:

https://github.com/FairRootGroup/FairSoft and a link the oﬃcial web-page and forums:

https://fairroot.gsi.de.

There are several libraries needed to install FairSoft (detailed explanation in DEPEN-

DENCIES text ﬁle on FairSoft repository). First, one should have installed CMake. Then

other packages are needed that depend on the OS and are detailed below.

For installation of FairSoft on a Mac OS, see the following for the speciﬁc dependencies

each version requires and some methods for install:

• Mac OS X 10.8 and earlier

Xcode developer package (for make, g++, gcc, ld, libX11, etc.) X11User (for the X11

server) gfortran

• Mac OS X 10.9 (Mavericks) and 10.10 (Yosemite)

Xcode from AppStore (after installing, run sudo xcode-select --install from a

Terminal) XQuartz version 2.7.5 and later gfortran version 4.9 only. Note: It will be

mandatory to install dpkg library through macports or brew (Install macports and

52

then sudo port install dpkg ). The procedure using brew is explained in the next

section.

• Mac OS X 10.11 (El Capitan) and newer

In El Capitan other packages are needed. The easiest way is to install them with brew:

ruby -e "\$(curl -fsSL https://raw.githubusercontent.com/

Homebrew/install/master/install)"

Then:

brew install gcc cmake autoconf automake libtool openssl pkg-config

ln -s /usr/local/opt/openssl/include/openssl /usr/include

El Capitan OS includes a System Integrity protection that prevents users to write

in the /usr folder. If there are problems installing the packages because of this fea-

ture, disable it rebooting the computer pressing CMD+R and open a terminal to type

csrutil disable . Then, reboot computer.

For installation of FairSoft on Linux, refer to this link depending on the user’s OS

https://gith- ub.com/FairRootGroup/FairSoft/blob/master/DEPENDENCIES. After inst-

alling these packages, one has to create a folder in the home directory and pull FairSoft from

GitHub. It is recommended to check on their website which OS systems the new release

has been tested with. It is hard to install FairSoft with an untested OS, so be sure to take

the correct release for the OS being used (optional: check for new patches and tags with git

tag). This can be done using the following commands:

53

cd ~

mkdir fair_install (for example)

cd fair_install

git clone https://github.com/FairRootGroup/FairSoft fairsoft.source

cd fairsoft.source

./configure.sh

Then, answer the questions depending on the OS:

1. Which compiler you want to use to compile the external packages?

(i) GCC (Linux, and older versions of Mac OSX) ←

(ii) Intel Compiler (Linux)

(iii) CC (Solaris)

(iv) Portland Compiler

(v) Clang (Mac OSX) ←

(vi) Quit

2. Do you want to compile the external packages with or without debug information or

with optimization?

(i) No Debug Info

(ii) Debug Info ←

(iii) Optimize

(iv) Quit

54

3. Would you like to install FairMQ only? Choosing ’Yes’ will skip building ROOT,

GEANT, etc. The default option is ’No’.

(i) Yes

(ii) No ←

(iii) FairMQ dependencies only

(iv) Quit

4. Would you like to install Simulation engines and event generators?

(i) Yes ←

(ii) No

(iii) Quit

5. Would you like to install the additionally available data ﬁles for the Geant4 package?

To do so, you either need an internet connection (Internet) or you have to provide the

ﬁles in the transport subdirectory (Directory).

(i) Don’t install

(ii) Internet ←

(iii) Directory

(iv) Quit

55

6. Would you like to compile Geant4 in multithreaded mode? For that to work all detec-

tors have to implement CloneModule.

(i) Yes ←

(ii) No

(iii) Quit

7. Would you like to install the python bindings for ROOT and Geant4 (only if simulation

engines are installed)?

(i) Yes ←

(ii) No

(iii) Quit

Please deﬁne a directory for the installation of the external packages. An installation

in the source directory is not possible any longer. Please enter the full path of the

installation directory

path: ∼/fair install/FairSoft Inst (put the destination here)

8. Is /home/user/fair install/FairSoft Inst the correct path?

(i) No

(ii) Yes ←

(iii) Quit

56

Then, the installation starts downloading and installing every package. Once this is done

one has to export the SIMPATH variable, and the ROOTSYS variable (if there is another

ROOT or GEANT4 version, all this can be put in a function in the user bash script to avoid

for conﬂicts). This can be done using the following code:

export SIMPATH=~/fair_install/FairSoft_Inst

export ROOTSYS=~/fair_install/FairSoft_Inst

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$ROOTSYS/lib

export PATH=$PATH:$ROOTSYS/bin

FairRoot:

FairRoot contains the base classes used by ATTPCROOTv2. The package is developed

at GSI and allows the user to create simple detector geometries and analysis and simulation

ﬂows. First, one needs to clone the latest FairRoot repository:

cd ~/fair_install (Where FairSoft is installed)

git clone https://github.com/FairRootGroup/FairRoot.git

cd FairRoot

git tag

# (optional) check older versions with git reset --hard tagname

mkdir build

cd build

cmake -DCMAKE_INSTALL_PREFIX=~/fair_install/FairRoot_Inst

-DCMAKE_CXX_COMPILER=(FairSoft compiler)

-DCMAKE_C_COMPILER=(FairSoft compiler) ../

make -j(number of cores)

make install

57

This should install the libraries and binaries in the folder speciﬁed in the cmake command.

After the installation is done, the path variable for FairRoot must be exported:

export FAIRROOTPATH=~/fair_install/FairRoot_Inst

Additional Libraries:

ATTPCROOTv2 introduces support for the Point Cloud Library [47]. Several additional

packages will be needed in order to compile and run this new version. The ATTPCROOTv2

folder contains a script folder which can be used to download and build each package from

the source.

• Pre-requisites for installation: boost, cmake, (ccmake for pcl recommended).

• The minimal install consists of FLANN, Eigen, PCL, and HDF5 libraries.

• The full installation (with visualization) requires also Qt4/5 and VTK (these are ex-

plained at the bottom of this page and are NOT necessary for most users).

It is recommended to follow the minimal install. Follow the instructions below for ﬂann

(don’t forget to delete static libraries as explained in PCL section) and eigen.

For PLC, it is recommended to install ccmake (cmake curses interface) to disable the op-

tional libraries. To install ccmake use sudo apt-get install cmake-curses-gui . Once

FLANN and Eigen are installed following the instructions below, just proceed manually (as

explained below) for PCL but instead of typing the cmake command from the build folder,

just type ccmake ../ (from build). A menu will appear (with several pages that can be

navigated with scroll down) wherethe cmake options can be enabled or disabled.

To build PCL without QT and VTK just disable (OFF): BUILD surface (page 2),

WITH QT and WITH VTK (page 5). Alternatively, just use the command line proce-

58

dure with -D (for example -DWITH QT=OFF) for all of them as explained below, if ccmake

does not need to be installed.

Minimal Install:

FLANN - The Fast Library for Approximate Nearest Neighbors (FLANN) is a library for

performing fast approximate nearest neighbor searches in high dimensional spaces. Download

the tar from http://www.cs.ubc.ca/research/ﬂann/. Unpack and compile with:

cd ~/path_to_flann/flann-X.X.X

mkdir build

cd build

cmake ../

make install

Eigen3 - Eigen is a C++ template library for linear algebra: matrices, vectors, numerical

solvers, and related algorithms. Download at http://eigen.tuxfamily.org/index.php?title=M-

ain Page. Same procedure as Flann (except make is not needed as Eigen3 is a header library,

sudo make install is needed though). IMPORTANT: PCL MUST be linked with the dynamic

version of FLANN (libﬂann cpp.so). The easiest way is to delete the static libraries if they

are not needed (libﬂann cpp s.a). This is similar to the OpenCV implementation of FLANN.

In addition, boost libraries are needed to compile PCL. With a previous installation of

ATTCROOT, just run the conﬁg.sh script on the build folder. For a fresh installation, one

can run the same script on the FairRoot installation folder or install boost manually (with

yum, apt-get, dnf, brew...). For the latter, just try to choose the latest version and be

cautious which boost library will the ATTPCROOTv2 cmake will ﬁnd (it is always better

to use the same version to compile PCL and ATTCROOTv2).

59

PCL - The Point Cloud Library (PCL) is a standalone, large scale, open project for

2D/3D image and point cloud processing. Download source code from https://github.com/P-

ointCloudLibrary/pcl/releases. Note: Support for visualization must be enabled here though

not mandatory. Unpack and compile with:

tar xvfj pcl-pcl-1.X.X.tar.gz

cd pcl-pcl-1.X.X

mkdir build

cd build

cmake -DCMAKE_BUILD_TYPE=Release ../ (or ccmake ../)

make -j(number of cores)

sudo make -j(number of cores) install

HDF5 Library - The Hierarchical Data Format (HDF) is a set of ﬁle formats designed to

store and organize large amounts of data. Download the source code from https://www.hdf-

group.org/downloads/hdf5/source-code/. Unpack and compile with:

cd ~/path_to_hdf5/hdf5-X.X.X

mkdir build

cd build

cmake ../

make -j(number of cores)

make install

60

Optional:

For the full install, just follow the instructions below to install VTK (http://www.vtk.org-

/Wiki/VTK/Conﬁgure and Build) with QT (version 4.8.6 tested):

cd ~

mkdir qt-X.X.X-build

cd qt-X.X.X-build

wget http://download.qt-project.org/official_releases/qt/X.X/

X.X.X/qt-everywhere-opensource-src-X.X.X.tar.gz

tar xzf qt-everywhere-opensource-src-X.X.X.tar.gz

cd qt-everywhere-opensource-src-X.X.X

./configure # go through the dialogue

make -j(number of cores)

sudo make install

cd ~/

git clone git://vtk.org/VTK.git

cd VTK

mkdir build

cmake -DQT_QMAKE_EXECUTABLE:PATH=/path/to/qt-X.X.X-build/qt-

everywhere-opensource-src-X.X.X/bin/qmake \

-DVTK_Group_Qt:BOOL=ON \

-DBUILD_SHARED_LIBRARIES:BOOL=ON \

/path/to/VTK

make -j(number of cores)

sudo make install

61

ATTPCROOTv2:

The installation of the ATTPCROOTv2 framework is rather straightforward. Currently,

ATTPCROOTv2 only supports ROOT6, which should be taken care of in the installation

of FairSoft:

cd ~/fair_install

git clone -b develop https://github.com/ATTPC/ATTPCROOTv2.git

cd ATTPCROOTv2

mkdir build

cd build

cmake ../

make -j(number of cores)

This should install the libraries and the headers. Then, load the environmental variables

for ATTPCROOTv2:

source config.sh (In the build folder)

At each login, this command needs to be run for the environment variables to be set.

It can be added to the user bash script ﬁle for convenience. After this process, the macros

for simulation and analysis described in the following two chapters are ready to be compiled

and executed.

62

A.2 ATTPCROOTv2 Simulation

A.2.1 FairRoot Simulation

ATTPCROOTv2 utilizes FairRoot for simulation of events within user deﬁned environ-

ments. The runs are completely deﬁned in ROOT macros and can be executed using the

following code:

root -l macroName.C

where macroName ought to be the same name as the main function within the macro for

convenience of execution. A basic FairRoot macro can be constructed using the C++ code

outlined below.

1. Create Simulation Run

The experimental set up is deﬁned by calling the member functions of the FairRunSim()

class. Here the user sets up the Monte Carlo engine (e.g. “TGeant4”) and the ﬁnal

output ﬁle for the data (e.g. “./data/attpcsim reactionName.root”).

FairRunSim* run = new FairRunSim();

run->SetName(mcEngine);

run->SetOutputFile(outFile);

2. Create Run-time Database

The run-time database works as a parameter manager which handles initialization

and saving to an output ﬁle (e.g. “./data/attpcpar reactionName.root”) and which

contains a complete list of runs.

63

FairRuntimeDb* rtdb = run->GetRuntimeDb();

Bool_t kParameterMerged = kTRUE;

FairParRootFileIo* parOut = new FairParRootFileIo(kParameterMerged);

parOut->open(parFile.Data());

rtdb->setOutput(parOut);

rtdb->saveOutput();

rtdb->print();

3. Create Media

Load the deﬁnitions for the materials involved in the simulation environment.

run->SetMaterials("media.geo");

4. Create Geometry

In order to create the simulation environment, a “world” volume to contain all other

object must ﬁrst be created with the AtCave() FairModule. Then the user can add

detectors created using the geometry ﬁles described in Section A.2.2.

FairModule* cave= new AtCave("CAVE");

cave->SetGeometryFileName("cave.geo");

run->AddModule(cave);

FairDetector* ATTPC = new AtTpc("ATTPC", kTRUE);

ATTPC->SetGeometryFileName("ATTPC_versionName.root");

run->AddModule(ATTPC);

64

5. Create PrimaryGenerator

After creating the PrimaryGenerator, generators for each event must be added to it.

The beam event must be added ﬁrst. It is generated by the ATTPCIonGenerator().

The reaction event is added second. This generator will be speciﬁc to the reaction

involved, like a two-body reaction in the example below. The initial particle param-

eters, like charge, momentum, and energy, used as inputs for the generators must be

deﬁned before creating the new generator. Information on the vertex location and the

momentum and energy of the beam particle at this location is carried between the

generators by a global variable called the ATVertexPropagator.

FairPrimaryGenerator* primGen = new FairPrimaryGenerator();

ATVertexPropagator* vertex_prop = new ATVertexPropagator ();

ATTPCIonGenerator* ionGen = new

ATTPCIonGenerator("Ion",z,a,q,m,px,py,pz,BExcEner,Bmass, NomEnergy);

ionGen->SetSpotRadius(0,-100,0);

primGen->AddGenerator(ionGen);

// Add beam event

ATTPC2Body* TwoBody = new

ATTPC2Body("TwoBody",Zp,Ap,Qp,mult,Pxp,Pyp,Pzp,Mass,ExE,

ResEner,ThetaMinCMS,ThetaMaxCMS);

primGen->AddGenerator(TwoBody);

// Add reaction event

run->SetGenerator(primGen);

65

6. Initialize and Start Simulation Run

After the following code, the simulation will begin and run for nEvents

2

runs (since

each run generates two events). The events will be stored in the ROOT ﬁle designated

earlier by the outFile.

run->Init();

run->Run(nEvents);

A.2.2 Geometry

Some of the inputs to the FairRunSim needed for propagation of the particles through

space by Monte Carlo engine are the geometry position of detectors and the media involved

in the reaction environment. In the ATTPCROOTv2/geometry/ directory, there are macros

for creating these geometries that utilize TGeoManager object and accompanying classes

from the ROOT geometry package.

To construct the detector, the geometry ﬁle contains a list of volumes characterized by

a number of parameters. The geometry will consist of a top volume which contains all of

the other modules that make up speciﬁc detector components. To describe a module, the

following requirements need to be met:
• Construct all necessary materials
• Deﬁne shapes/solids required to describe the geometry
• Construct and place volumes of the detector geometry
• Deﬁne sensitive detectors and identify detector volumes with which to associate them
• Associate magnetic ﬁeld to detector regions (if needed)
• Deﬁne visualization attributes for the detector elements

66

The media.geo ﬁle acts a dictionary for materials that are commonly used in simulations

since there are no predeﬁned materials in FairRoot. Each medium is deﬁned by several

numerical parameters as seen below and described on the FairRoot HowTo page [46]. The

following parameters are required:

• int ncomp - number of components in the material (ncomp= 1 for a basic material
and < 1 or > 1 for a mixture. If ncomp > 0 the array wm contains the proportion
by weight of each material in the mixture. If ncomp < 0 the array wm contains the
proportion by number of atoms of each kind.)

• ﬂoat aw[ncomp] - atomic weights A for the components
• ﬂoat an[ncomp] - atomic numbers Z for the components
• ﬂoat dens - density DENS in g/cm−3
• ﬂoat wm[ncomp] - weights WMAT of each component in a mixture (only for a

mixture)

• int sensﬂag - sensitivity ﬂag ISVOL
• int ﬂdﬂag - ﬁeldﬂag IFIELD
• ﬂoat ﬂd - maximum ﬁeld value FIELDM in kilogauss
• ﬂoat epsil - boundary crossing precision EPSIL
• int npckov - number of values used to deﬁne the optical properties of the medium.
This variable is 0 for all media except some special media used for the Rich where
the tracking of the Cherenkov photons is necessary. These media have additional
parameters

– ﬂoat ppckov[npckov] - photon momentum in eV

– ﬂoat absco[npckov] - absorption length in case of dielectric and of absorption

probabilities in case of a metal

– ﬂoat eﬃc[npckov] - detection eﬃciency

– ﬂoat rindex[npckov] - refraction index for a dielectric, rindex[0]=0 for a metal

Remark:
In the present program version a mixture may contain a maximum of 5
components. If this is not suﬃcient one has to change MAXCOMP in hgeomedium.h.

The following parameters are normally not read. The default values are -1 and the real

values are automatically calculated by Geant. If the user wants to set these values manually,

67

they must type the keyword AUTONULL in the media ﬁle. After this keyword all media

must contain these additional 4 parameters before the Cherenkov (int npckov).

• ﬂoat madﬂd - maximum angular deviation TMAXFD due to ﬁeld
• ﬂoat maxstep - maximum step permitted STEMAX
• ﬂoat maxde - maximum fractional energy loss DEEMAX
• ﬂoat minstep - minimum value for step STMIN

Many materials have already been deﬁned but new deﬁnitions can be added to the ﬁle

as needed, examples of which are shown in Figure 3.4.

A.2.3 Generators

Another input to the FairRunSim is provided using particle generators classes with in-

herited members from the FairGenerator class. These generators create single particles or

multiple particles involved in a reaction, calculating the kinematics involved, given the initial

conditions of the particles. Each contains the ReadEvent() function that adds tracks to the

the stack in the PrimaryGenerator.

The FairPrimaryGenerator class handles the MC input of the event generation, allowing

the user to set various aspects of the beam, target, and number of events. This object is only

instantiated once but several generators can be registered to it depending on the reaction

being simulated.

Reactions in the AT-TPC must be simulated using two events. In simulations involving

solid targets, the beam prior to the reaction does not need to be considered. However in the

case of a gas target like in the AT-TPC, the gas has an eﬀect on the energy and trajectory

of the beam in the moments leading up to the reaction. This means that an event must be

generated for both the beam and the reaction itself so that the physics engine can propagate

68

the particles before and after the reaction.

A.2.4 FairRoot Analysis

Data analysis in FairRoot is managed using the FairRunAna class. The input to this

class is a root ﬁle with the “cbmsim” tree containing the data arrays to be analyzed. The

output from simulation will be such a root ﬁle. Files containing real data from experiment

will need to be unpacked prior to analysis to create this input. The output of data analysis

using this class will be a new root ﬁle containing the “cbmsim” tree with arrays of analyzed

data.

The data analysis is processed using a list of user-deﬁned tasks derived from the FairTask

class. Each task processes a speciﬁc type of data that could be a branch in the input ﬁle or

output from another task. Every task produces a data array that becomes a branch in the

“cbmsim” tree of the ﬁnal output ﬁle. To check the available data arrays, load the root ﬁle

into Root by entering root -l myRootFile.root into the terminal and open a TBrowser

using new TBrowser in the Root terminal, as seen in Figure A.1.

Many of the tasks will need to access parameter ﬁles in order to process the data. The

parameter ﬁles are managed by the FairRuntimeDb class. Depending on the format of the

parameter ﬁle, they can be opened in the FairParRootFileIo or FairParAsciiFileIo classes

and added to the run-time database.

Below is the framework for an analysis macro showing the methods for setting input,

output, and parameter ﬁles. Additional tasks can be added to the FairRunAna object in

the order in which the data arrays need to be processed. Some tasks may have additional

methods to deﬁne parameters of the analysis. Descriptions of the tasks already in the

ATTPCROOTv2 framework are in the following sections.

69

Figure A.1: View of root ﬁle loaded into TBrowser, showing “cbmsim” tree and some exam-
ples of the data arrays that may be contained within the tree.

70

// ----- Files

-------------------------------------------------

TString inputFile = "myInputFile.root",

TString outputFile = "myOutputFile.root",

TString parFile1 = "myParFile1.root",

TString parFile2 = "myParFile2.par"

// ----- Timer

-------------------------------------------------

TStopwatch timer;

timer.Start();

// ----- Run Manager ---------------------------------------------

FairRunAna* fRun = new FairRunAna();

fRun -> SetInputFile(inputFile);

fRun -> SetOutputFile(outputFile);

// ----- Parameters ----------------------------------------------

FairRuntimeDb* rtdb = fRun->GetRuntimeDb();

FairParRootFileIo* parIo1 = new FairParRootFileIo();

parIo1 -> open(parFile1.Data(), "in");

rtdb -> setFirstInput(parIo1);

71

FairParAsciiFileIo* parIo2 = new FairParAsciiFileIo();

parIo2 -> open(parFile2.Data(), "in");

rtdb -> setSecondInput(parIo2);

// ----- Tasks

------------------------------------------------

ATMyFirstTask* myFirstTask = new ATMyFirstTask();

myFirstTask -> SetPersistence(kTRUE);

ATMySecondTask* mySecondTask = new ATMySecondTask();

mySecondTask -> SetPersistence(kTRUE);

fRun -> AddTask(myFirstTask);

fRun -> AddTask(mySecondTask);

// ----- Init & Run ----------------------------------------------

fRun -> Init();

fRun -> Run();

std::cout << std::endl << std::endl;

std::cout << "Macro finished succesfully." << std::endl << std::endl;

// ----- Finish

------------------------------------------------

72

timer.Stop();

Double_t rtime = timer.RealTime();

Double_t ctime = timer.CpuTime();

cout << endl;

cout << "Real time " << rtime << " s, CPU time " << ctime << " s" << endl;

cout << endl;

A.2.5 Digitization

The resulting root ﬁle from simulation has an array of AtTpcPoint objects. These ob-

jects contain the information describing a particle in an event, including the position and

momentum in three dimensions, the volume occupied, the energy and angle, and the mass

and charge. In a real experiment, this information is not explicitly available and must be ex-

tracted by analysis. In order to reformat the data from the FairRoot simulation to the same

data type as from experiment, FairRoot Analysis must be performed. This is the last step

in ATTPCROOTv2 simulation and all the ATTPCROOTv2 analysis described in Section

A.3 can be applied to these results in the same manner as experimental data.

In order to get experiment-like results from the simulation data, the data must undergo

digitization through a few analysis tasks. After running the simulation, two ﬁles were cre-

ated: the simulation ﬁle (“attpcsim *.root”) and the parameter ﬁle (“attpcpar *.root”). The

simulation ﬁle will be the input ﬁle for the FairRunAna object and the parameter ﬁle will

be the ﬁrst input for the run-time database.

Clusterization: The ATClusterizeTask class found in the ATTPCROOTv2/digi/ di-

rectory is a FairTask that accepts a branch of AtTpcPoint objects as input. This task

73

loops through every point in each event and calculates the number of electrons (with some

Gaussian ﬂuctuation dependent on the Fano factor) ionized by a particle passing through

the detector’s gas using the energy loss since the previous point. The distance between the

current point and the previous point is divided into equal spaces such that one of the ion-

ized electrons can be placed at a point in each one. Each electron’s position is calculated

with some Gaussian ﬂuctuation using the longitudinal and transverse coeﬃcients of diﬀusion

found in the parameter ﬁle to account for dispersion. The drift time is determined by divid-

ing the Z-component of each electron’s position by the drift velocity found in the parameter

ﬁle. The task produces a branch of ATSimulatedPoints each of which contain the X- and

Y-components of an electron as well as the drift time.

This task requires adding the AT.digi.par parameter ﬁle in the ATTPCROOTv2/param-

eters/ directory as the second input to the run-time database. The parameter ﬁle provides

the ionization energy, the drift velocity, and the coeﬃcients of diﬀusion. Instantiation of this

task in a FairRoot analysis macro should be done using the following code:

ATClusterizeTask* clusterizer = new ATClusterizeTask();

clusterizer -> SetPersistence(kFALSE);

fRun -> AddTask(clusterizer);

Pulse Creation: The ATPulseTask class found in the ATTPCROOTv2/digi/ directory

is a FairTask that accepts a branch of ATSimulatedPoint objects as input. The task produces

a branch of ATRawEvent objects each of which contain the collection of ATPad objects. An

AtTpcMap object is created which can be used to map the X- and Y-components of each

ATSimulatedPoint to one of 10240 pads in the pad plane. This task loops over each event,

creating an ATPad for every new X- and Y-coordinate and adding hits to existing ATPads

74

when multiple electrons are mapped to the same pad. Each hit is registered with a time

stamp corresponding to the electron’s drift time. Once all ATSimulatedPoints in the event

have been registered to a pad, the task loops over the pads and creates signals according to

a pad response function. Multiple hits result in a superimposition of pulses. The binning

parameters and gain in ATTPC.d2He.par are needed for this task.

This task requires adding the AT.digi.par parameter ﬁle in the ATTPCROOTv2/param-

eters/ directory as the second input to the run-time database. The parameter ﬁle provides

the gain in the pads of the detector. Instantiation of this task in a FairRoot analysis macro

should be done using the following code:

ATPulseTask* pulse = new ATPulseTask();

pulse -> SetPersistence(kTRUE);

fRun -> AddTask(pulse);

A.3 ATTPCROOTv2 Analysis

The data up to this point came from FairRoot simulation of reactions in the AT-TPC

and digitization through FairRoot Analysis. The ATTPCROOTv2 analysis described in the

following discussions can be applied to both data created in simulation and data recorded in

experiment. After digitizing simulated data and unpacking experimental data, each should

have the same data type: a collection of pulses in the AT-TPC pad plane.

A.3.1 Pulse Shape Analysis

The ATPSATask class found in the ATTPCROOTv2/reco/ directory is a FairTask that

accepts a branch of ATRawEvent objects as input. The task produces a branch of ATEvent

75

objects each of which contain the collection of ATHit objects. Each ATHit object contains

the X-, Y-, and Z-coordinates of a particle. An ATHit is created for each ATPad in the

ATRawEvent where the X- and Y-coordinates correspond to the position of the pad in the

plane. The Z-coordinate is determined by analyzing the pulse in the ATPad in one of two

ways: (1) ﬁnding the maximum value of the pulse or (2) ﬁtting the pulse and and ﬁnding

peaks. This provides the time of the hit which can be used with the drift velocity to ﬁnd

the Z-coordinate.

This task requires adding the AT.digi.par parameter ﬁle in the ATTPCROOTv2/parame-

ters/ directory as the second input to the run-time database. The parameter ﬁle provides

the gain in the pads of the detector. Instantiating this task in a FairRoot analysis macro

requires setting a few of its parameters as seen in the following code:

ATPSATask* psaTask = new ATPSATask();

psaTask -> SetPersistence(kTRUE);

psaTask -> SetThreshold(10);

psaTask -> SetPSAMode(1); //NB: 1 is ATTPC - 2 is pATTPC - 4 is FULL

// Use either peak finder or maximum finder but not both at the same time

psaTask -> SetMaxFinder(); // psaTask -> SetPeakFinder();

psaTask -> SetBaseCorrection(kFALSE); //Directly apply the base line

correction to the pulse amplitude to correct for the mesh induction. If

false the correction is just saved

psaTask -> SetTimeCorrection(kFALSE); //Interpolation around the maximum of

the signal peak

fRun -> AddTask(psaTask);

76

A.3.2 RANSAC Tracking

In order to ﬁt the tracks made by particles passing through the detector, a method for

modeling in the presence of outliers (background, multiple tracks, etc.) is needed. The Ran-

dom Sampling Consensus (RANSAC) algorithm satisﬁes this need, as it can extract features

of a data set that ﬁt a speciﬁed model. This model depends on the particle trajectories

expected, e.g. linear (no magnetic ﬁeld) or circular (with magnetic ﬁeld).

The ATRansacTask class found in the ATTPCROOTv2/reco/ directory is a FairTask that

accepts a branch of ATEvent objects as input. The task produces a branch of ATRansac

objects each of which contain an array of ATTracks found by the algorithm and the vertex

between each track (point closest to each pair). Each ATTrack object contains an array of

ATHits, the parameters for their ﬁt, and can calculate the angles of the track.

This task does not require a parameter ﬁle as input. Instantiating this task in a FairRoot

analysis macro requires setting a few of its parameters as seen in the following code:

ATRansacTask* RansacTask = new ATRansacTask();

RansacTask->SetPersistence(kTRUE);

RansacTask->SetDistanceThreshold(10);

RansacTask->SetFullMode();

fRun -> AddTask(RansacTask);

A.3.3 User Analysis

In order to perform further analysis using the results of the tasks, a macro can be created

which opens a branch of the ﬁnal output ﬁle from FairRoot analysis. This ﬁle contains a tree

77

as seen in Figure A.1 with branches corresponding to the results from each task. Loading

this ﬁle in a ROOT macro and opening the desired branch will allow the user to perform

their own analysis using the parameters stored in whichever ATTPCROOTv2 object that

branch contains.

Below is an sample of the code that can be used to analyze the results from FairRoot

simulation which is done before digitization (ﬁgures in Section 3.2.4 of thesis):

AtTpcPoint *point = new AtTpcPoint ();

TClonesArray *pointArray = 0;

TFile *file = new TFile (mcFileName.Data (), "READ");

TTree *tree = (TTree *) file->Get ("cbmsim");

tree = (TTree *) file->Get ("cbmsim");

tree->SetBranchAddress ("AtTpcPoint", &pointArray);

Int_t nEvents = tree->GetEntriesFast ();

for (Int_t iEvent = 0; iEvent < nEvents; iEvent++) {

tree->GetEvent (iEvent);

Int_t Npoints = pointArray->GetEntries ();

for (Int_t i = 0; i < Npoints; i++) {

point = (AtTpcPoint *) pointArray->At (i);

...

}

}

This code opens the “AtTpcPoint” branch of the “cbmsim” tree, which provides the param-

eters detailing the trajectory of every particle in the reaction stored in AtTpcPoint objects.

This data can be used to create the “real” results of analysis that the results of analysis from

78

digitized data can be compared against.

To open the data produced using FairRoot analysis (i.e. digitization, pulse shape analysis,

and RANSAC tracking), the following code can be used:

FairRunAna* fRun = new FairRunAna(); // Force dummy run

TFile* file = new TFile(anaFileName.Data(),"READ");

TTree* tree = (TTree*) file -> Get("cbmsim");

TTreeReader Reader1("cbmsim", file);

TTreeReaderValue<TClonesArray> eventArray(Reader1, "ATEventH");

Int_t nEvents = tree -> GetEntries();

for(Int_t iEvent=0;iEvent<nEvents;iEvent++){

Reader1.Next();

ATEvent* event = (ATEvent*) eventArray->At(0);

if(event!=NULL){

Int_t nHits = event->GetNumHits();

for(Int_t iHit=0; iHit<nHits; iHit++){

ATHit* hit = event->GetHit(iHit);

...

}

}

}

79

This code opens the “ATEventH” branch of the “cbmsim” tree, which provides the results

from pulse shape analysis stored in ATEvent objects, each of which contain ATHit objects.

This is a general method for opening branches of the analysis output ﬁles. Users can then

access the member functions of the ATTPCROOTv2 objects to extract the parameters. For

example, the X-, Y-, Z-components deﬁned by a hit in the pad plane is given by a TVector3

object returned from the GetPosition() function of the ATHit object class.

These ATTPCROOTv2 classes are deﬁned in ﬁles that can be found using the index of

ﬁle directories in Appendix B.

80

Appendix B

Index of File Directories

Macros

ATTPC d2He.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . geometry/

d 2He sim 14O.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . macro/Simulation/d2He/

d2He ana 14O 07atm.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . macro/Simulation/d2He/Analysis d2He/

rundigi sim.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . macro/Simulation/d2He/Analysis d2He/

d2He ana ransac.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . macro/Simulation/d2He/Analysis d2He/

Inputs

all2 14O.dat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . macro/Simulation/d2He/

ATTPC.d2he.par . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . parameters/

Lookup20150611.xml

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . scripts/

energyRangeCoefs.txt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .macro/Simulation/d2He/Analysis d2He/

energyRangeKnots.txt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . macro/Simulation/d2He/Analysis d2He/

FairGenerators

ATTPCIonGenerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ATGenerators/

ATTPC2Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ATGenerators/

ATTPC d2He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ATGenerators/

ATVertexPropagator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ATGenerators/

81

FairTasks

ATClusterizeTask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . digi/

ATPulseTask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . digi/

ATPSATask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reco/

ATRansacTask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reco/

ATTPCROOTv2 Data Types

AtTpcPoint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tpc/

ATSimulatedPoint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . digi/

ATRawEvent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reco/ATDecoder/

ATEvent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reco/ATDecoder/

ATRansac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reco/ATRansac/

ATPad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reco/ATDecoder/

AtTpcMap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AtMap/

ATHit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reco/ATDecoder/

ATTrack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .reco/ATDecoder/

ATd2HeAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reco/ATAnalysis/

82

BIBLIOGRAPHY

83

BIBLIOGRAPHY

[1] H. A. Bethe. Supernova mechanisms. Rev. Mod. Phys., 62:801, 1990.

[2] C. Iliadis. Nuclear Physics of Stars. Wiley-VCH, Weinheim, Germany, 2015.

[3] S. Chandrasekhar. The Maximum Mass of Ideal White Dwarfs. Astrophys. J., 74:81,

1931.

[4] A. Heger, C. L. Fryer, S. E. Woosley, N. Langer, and D. H. Hartmann. How Massive

Single Stars End Their Life. Astrophys. J., 591(1):288, 2003.

[5] Chris L Fryer and Kimberly C. B. New. Gravitational Waves from Gravitational Col-

lapse. Living Rev. Relativity, 6(2), 2003.

[6] C. Sullivan, E. O’Connor, R. G. T. Zegers, T. Grubb, and S. M. Austin. The Sensitivity
of Core-collapse Supernovae to Nuclear Electron Capture. Astrophys. J., 816(1):44,
2016.

[7] S. E. Woosley and T. A. Weaver. The Evolution and Explosion of Massive Stars. II.
Explosive Hydrodynamics and Nucleosynthesis. Astrophys. J., Supplement, 101:181,
1995.

[8] C. D. Ott, E. P. O’Connor, S. Gossan, E. Abdikamalov, U. C. T. Gamma, and S. Drasco.
Core-Collapse Supernovae, Neutrinos, and Gravitational Waves. Nucl. Phys B Proceed-
ings Supplements, 235:381, 2013.

[9] H. Dimmelmeier, C. D. Ott, A. Marek, and H.-T. Janka. Gravitational wave burst

signal from core collapse of rotating stars. Phys. Rev. D, 78:064056, 2008.

[10] S. Richers, C. D. Ott, E. Abdikamalov, E. O’Connor, and C. Sullivan. Equation of state
eﬀects on gravitational waves from rotating core collapse. Phys. Rev. D, 95:063019, 2017.

[11] R. J. Hall. “What is a Supernova?”, 2006. Fact sheet created by undergraduates in the

Department of Physics, University of Warwick.

[12] G. M. Fuller, W. A. Fowler, and M. J. Newman. Astrophys. J., 42:447, 1980.

[13] G. M. Fuller, W. A. Fowler, and M. J. Newman. Astrophys. J., 252:715, 1982.

[14] G. M. Fuller, W. A. Fowler, and M. J. Newman. Astrophys. J., 48:279, 1982.

84

[15] G. M. Fuller, W. A. Fowler, and M. J. Newman. Astrophys. J., 293:1, 1985.

[16] Georgios Perdikakis, R. Zegers, Sam Austin, D. Bazin, C. Caesar, Jenna Deaven,
A Gade, D. Galaviz, Gwen Grinyer, Carlos Guess, C. Herlitzius, George Hitt,
M. Howard, R. Meharchand, S Noji, Hideyuki Sakai, Yoshihiro Shimbara, E. Smith,
and C. Tur. Gamow-Teller Unit Cross Sections for (t, 3He) and (3He, t) Reactions.
Phys. Rev. C, 83, 2011.

[17] T. N. Taddeucci, C. A. Goulding, T. A. Carey, R. C. Byrd, C. D. Goodman, C. Gaarde,
J. Larsen, D. Horen, J. Rapaport, and E. Sugarbaker. The (p, n) reaction as a probe of
beta decay strength. Nucl. Phys. A, 469(1):125, 1987.

[18] F. Osterfeld. Nuclear spin and isospin excitations. Rev. Mod. Phys., 64:491, 1992.

[19] R. G. T. Zegers, H. Akimune, Sam M. Austin, D. Bazin, A. M.van den Berg, G. P. A.
Berg, B. A. Brown, J. Brown, A. L. Cole, I. Daito, Y. Fujita, M. Fujiwara, S. Gal`es,
M. N. Harakeh, H. Hashimoto, R. Hayami, G. W. Hitt, M. E. Howard, M. Itoh,
J. J¨anecke, T. Kawabata, K. Kawase, M. Kinoshita, T. Nakamura, K. Nakanishi,
S. Nakayama, S. Okumura, W. A. Richter, D. A. Roberts, B. M. Sherrill, Y. Shim-
bara, M. Steiner, M. Uchida, H. Ueno, T. Yamagata, and M. Yosoi. The (t,3He) and
(3He, t) reactions as probes of Gamow-Teller strength. Phys. Rev. C, 74:024309, 2006.

[20] R. G. T. Zegers, T. Adachi, H. Akimune, Sam M. Austin, A. M. van den Berg, B. A.
Brown, Y. Fujita, M. Fujiwara, S. Gal`es, C. J. Guess, M. N. Harakeh, H. Hashimoto,
K. Hatanaka, R. Hayami, G. W. Hitt, M. E. Howard, M. Itoh, T. Kawabata, K. Kawase,
M. Kinoshita, M. Matsubara, K. Nakanishi, S. Nakayama, S. Okumura, T. Ohta,
Y. Sakemi, Y. Shimbara, Y. Shimizu, C. Scholl, C. Simenel, Y. Tameshige, A. Tamii,
M. Uchida, T. Yamagata, and M. Yosoi. Extraction of Weak Transition Strengths via
the (3He, t) Reaction at 420 MeV. Phys. Rev. Lett., 99:202501, 2007.

[21] R. Madey, B. S. Flanders, B. D. Anderson, A. R. Baldwin, C. Lebo, J. W. Watson,
Sam M. Austin, A. Galonsky, B. H. Wildenthal, and C. C. Foster. Gamow-Teller
strength in the 26Mg(p, n) 26Al reaction at 135 MeV and its fractionation into T = 0,
1, and 2 isospin channels. Phys. Rev. C, 35:2011, 1987.

[22] M. E. Howard, R. G. T. Zegers, Sam M. Austin, D. Bazin, B. A. Brown, A. L. Cole,
B. Davids, M. Famiano, Y. Fujita, A. Gade, D. Galaviz, G. W. Hitt, M. Matos, S. D.
Reitzner, C. Samanta, L. J. Schradin, Y. Shimbara, E. E. Smith, and C. Simenel.
Gamow-Teller strengths in 24Na using the 24Mg(t, 3He) reaction at 115A MeV. Phys.
Rev. C, 78:047302, 2008.

[23] S. El-Kateb, K. P. Jackson, W. P. Alford, R. Abegg, R. E. Azuma, B. A. Brown,
A. Celler, D. Frekers, O. H¨ausser, R. Helmer, R. S. Henderson, K. H. Hicks, R. Jeppe-
sen, J. D. King, G. G. Shute, B. M. Spicer, A. Trudel, K. Raywood, M. Vetterli, and

85

S. Yen. Spin-isospin strength distributions for fp shell nuclei: Results for the 55Mn(n, p),
56Fe(n, p), and 58Ni(n, p) reactions at 198 MeV. Phys. Rev. C, 49:3128, 1994.

[24] H. Ohnuma, K. Hatanaka, S. I. Hayakawa, M. Hosaka, T. Ichihara, S. Ishida, S. Kato,
T. Niizeki, M. Ohura, H. Okamura, H. Orihara, H. Sakai, H. Shimizu, Y. Tajima,
H. Toyokawa, H. Y. Yoshida, and M. Yosoi. (d,2He) reactions at Ed=260 MeV as a
possible probe to nuclear spin-isospin excitation. Phys. Rev. C, 47:648, 1993.

[25] H. M. Xu, G. K. Ajupova, A. C. Betker, C. A. Gagliardi, B. Kokenge, Y. W. Lui, and

A. F. Zaruba. (d,2He) reactions at Ed=125.2 MeV. Phys. Rev. C, 52:R1161, 1995.

[26] C. B¨aumer, A. M. van den Berg, B. Davids, D. Frekers, D. De Frenne, E.-W. Grewe,
P. Haefner, M. N. Harakeh, F. Hofmann, M. Hunyadi, E. Jacobs, B. C. Junk, A. Ko-
rﬀ, K. Langanke, G. Mart´ınez-Pinedo, A. Negret, P. von Neumann-Cosel, L. Popescu,
S. Rakers, A. Richter, and H. J. W¨ortche. High-resolution study of the Gamow-
Teller strength distribution in 51Ti measured through 51V(d,2He)51Ti. Phys. Rev. C,
68:031303, 2003.

[27] D. Frekers and M. Alanssari. Charge-exchange reactions and the quest for resolution.

The European Physical Journal A, 54(10):177, 2018.

[28] M. Scott, Y. Shimbara, Sam M. Austin, D. Bazin, B. A. Brown, J. M. Deaven, Y. Fu-
jita, C. J. Guess, S. Gupta, G. W. Hitt, D. Koeppe, R. Meharchand, M. Nagashima,
G. Perdikakis, A. Prinke, M. Sasano, C. Sullivan, L. Valdez, and R. G. T. Zegers.
Gamow-Teller transition strengths from 56Fe extracted from the 56Fe(t,3 He) reaction.
Phys. Rev. C, 90:025801, 2014.

[29] M. Sasano, G. Perdikakis, R. G. T. Zegers, Sam M. Austin, D. Bazin, B. A. Brown,
C. Caesar, A. L. Cole, J. M. Deaven, N. Ferrante, C. J. Guess, G. W. Hitt, R. Meharc-
hand, F. Montes, J. Palardy, A. Prinke, L. A. Riley, H. Sakai, M. Scott, A. Stolz,
L. Valdez, and K. Yako. Gamow-Teller Transition Strengths from 56Ni. Phys. Rev.
Lett., 107:202501, 2011.

[30] M. Sasano, G. Perdikakis, R. G. T. Zegers, Sam M. Austin, D. Bazin, B. A. Brown,
C. Caesar, A. L. Cole, J. M. Deaven, N. Ferrante, C. J. Guess, G. W. Hitt, M. Honma,
R. Meharchand, F. Montes, J. Palardy, A. Prinke, L. A. Riley, H. Sakai, M. Scott,
A. Stolz, T. Suzuki, L. Valdez, and K. Yako. Extraction of Gamow-Teller strength
distributions from 56Ni and 55Co via the (p, n) reaction in inverse kinematics. Phys.
Rev. C, 86:034324, 2012.

[31] Samuel Lipschutz and NSCL E10003 Collaboration. (p, n) Charge-Exchange Reactions
in Inverse Kinematics. In APS Division of Nuclear Physics Meeting Abstracts, volume
2014, page FF.002, 2014.

86

[32] J. Yasuda, M. Sasano, R. G. T. Zegers, H. Baba, D. Bazin, W. Chao, M. Dozono,
N. Fukuda, N. Inabe, T. Isobe, G. Jhang, D. Kameda, M. Kaneko, K. Kisamori,
M. Kobayashi, N. Kobayashi, T. Kobayashi, S. Koyama, Y. Kondo, A. J. Kraszna-
horkay, T. Kubo, Y. Kubota, M. Kurata-Nishimura, C. S. Lee, J. W. Lee, Y. Matsuda,
E. Milman, S. Michimasa, T. Motobayashi, D. Muecher, T. Murakami, T. Nakamura,
N. Nakatsuka, S. Ota, H. Otsu, V. Panin, W. Powell, S. Reichert, S. Sakaguchi, H. Sakai,
M. Sako, H. Sato, Y. Shimizu, M. Shikata, S. Shimoura, L. Stuhl, T. Sumikama,
H. Suzuki, S. Tangwancharoen, M. Takaki, H. Takeda, T. Tako, Y. Togano, H. Tokieda,
J. Tsubota, T. Uesaka, T. Wakasa, K. Yako, K. Yoneda, and J. Zenihiro. Extraction of
the Landau-Migdal Parameter from the Gamow-Teller Giant Resonance in 132Sn. Phys.
Rev. Lett., 121:132501, 2018.

[33] R. G. T. Zegers, R. Meharchand, Y. Shimbara, Sam M. Austin, D. Bazin, B. A. Brown,
C. Aa. Diget, A. Gade, C. J. Guess, M. Hausmann, G. W. Hitt, M. E. Howard, M. King,
D. Miller, S. Noji, A. Signoracci, K. Starosta, C. Tur, C. Vaman, P. Voss, D. Weisshaar,
and J. Yurkon. 34P(7Li,7 Be + γ) Reaction at 100A MeV in Inverse Kinematics. Phys.
Rev. Lett., 104:212504, 2010.

[34] R. Meharchand, R. G. T. Zegers, B. A. Brown, Sam M. Austin, T. Baugher, D. Bazin,
J. Deaven, A. Gade, G. F. Grinyer, C. J. Guess, M. E. Howard, H. Iwasaki, S. McDaniel,
K. Meierbachtol, G. Perdikakis, J. Pereira, A. M. Prinke, A. Ratkiewicz, A. Signoracci,
S. Stroberg, L. Valdez, P. Voss, K. A. Walsh, D. Weisshaar, and R. Winkler. Probing
Conﬁguration Mixing in 12Be with Gamow-Teller Transition Strengths. Phys. Rev.
Lett., 108:122501, 2012.

[35] D. Bazin, J.A. Caggiano, B.M. Sherrill, J. Yurkon, and A. Zeller. The S800 Spectro-
graph. Nuclear Instruments and Methods in Physics Research Section B: Beam Inter-
actions with Materials and Atoms, 204:629, 2003. 14th International Conference on
Electromagnetic Isotope Separators and Techniques Related to their Applications.

[36] D. P. Stahel, R. Jahn, G. J. Wozniak, and Joseph Cerny. Charge-exchange reaction

(d,2He). Phys. Rev. C, 20:1680, 1979.

[37] H. Okamura. Three-body treatment of the (d,2He) reaction on the basis of the adiabatic

approximation. Phys. Rev. C, 60:064602, 1999.

[38] Carl Gaarde. Spin-isospin excitations. Nucl. Phys A, 507(1):79, 1990.

[39] M. Ericson, A. Figureau, and C. Thvenet. Pionic ﬁeld and renormalization of the axial

coupling constant in nuclei. Physics Letters B, 45(1):19, 1973.

[40] H. Hyuga, A. Arima, and K. Shimizu. Exchange magnetic moments. Nucl. Phys A,

336(3):363, 1980.

87

[41] A. Arima. History of giant resonances and quenching. Nucl. Phys A, 649(1):260, 1999.

Giant Resonances.

[42] J. Bradt, D. Bazin, F. Abu-Nimeh, T. Ahn, Y. Ayyad, S. Beceiro Novo, L. Carpenter,
M. Cortesi, M.P. Kuchera, W.G. Lynch, W. Mittig, S. Rost, N. Watwood, and J. Yurkon.
Commissioning of the Active-Target Time Projection Chamber. Nuclear Instruments
and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment, 875:65, 2017.

[43] D. Suzuki, M. Ford, D. Bazin, W. Mittig, W.G. Lynch, T. Ahn, S. Aune, E. Galyaev,
A. Fritsch, J. Gilbert, F. Montes, A. Shore, J. Yurkon, J.J. Kolata, J. Browne,
A. Howard, A.L. Roberts, and X.D. Tang. Prototype AT-TPC: Toward a new genera-
tion active target time projection chamber for radioactive beam experiments. Nuclear
Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment, 691:39, 2012.

[44] ROOT Version 6.12/06, 2018. http://root.cern.ch/.

[45] FairSoft may18 Release, 2018. https://fairroot.gsi.de/.

[46] FairRoot Version 18.00, 2018. https://fairroot.gsi.de/.

[47] PCL 1.8.1, 2018. http://www.pointclouds.org/.

[48] FLANN 1.9.1, 2018. https://www.cs.ubc.ca/research/ﬂann/.

[49] Eigen 3.3.6, 2018. eigen.tuxfamily.org/.

[50] HDF5 1.10.2, 2018. https://www.hdfgroup.org/solutions/hdf5/.

[51] Geant4 10.4.1, 2018. https://geant4.web.cern.ch/.

[52] Florian Uhlig. Fairroot tutorial, 2015. R3BRoot Development Workshop.

[53] J. L. Pack and A. V. Phelps. Drift Velocities of Slow Electrons in Helium, Neon, Argon,

Hydrogen, and Nitrogen. Phys. Rev., 121:798, 1961.

[54] Martin A. Fischler and Robert C. Bolles. Random Sample Consensus: A Paradigm
for Model Fitting with Applications to Image Analysis and Automated Cartography.
Commun. ACM, 24(6):381, 1981.

[55] The Stopping and Range of Ions in Matter (SRIM), 2008. http://www.srim.org/.

88