Study of a Neutron Reflector for the HALO-1Kt Supernovae Neutrino Detector

Study of a Neutron Reflector for the HALO-1kT Supernovae Neutrino Detector

A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulﬁllment of the Requirements for the Degree of Master of Science in Physics University of Regina

Divyaben Ashvinkumar Patel

Regina, Saskatchewan

May 2020

UNIVERSITY OF REGINA

FACULTY OF GRADUATE STUDIES AND RESEARCH

SUPERVISORY AND EXAMINING COMMITTEE

Divyaben Ashvinkumar Patel, candidate for the degree of Master of Science in Physics, has presented a thesis titled, Study of Neutron Reflector for the HALO-1kT Supernovae Neutrino Detector, in an oral examination held on May 13, 2020. The following committee members have found the thesis acceptable in form and content, and that the candidate demonstrated satisfactory knowledge of the subject material.

External Examiner: *Dr. Josef Buttigieg, Department of Biology

Co-Supervisor: *Dr. Mauricio Barbi, Department of Physics

Co-Supervisor: *Dr. Nikolay Kolev, Department of Physics

Committee Member: *Dr. Gwen Grinyer, Department of Physics

Chair of Defense: *Dr. Harold Weger, Department of Biology

*via Zoom Conferencing Abstract

The Helium and Lead Observatory 1 Kilotonne (HALO-1kT) is a lead-based detector to study electron neutrinos emitted from core-collapse supernovae. It is proposed to follow the same purpose as the HALO detector located at SNOLAB but with higher detection efficiency. The sensitivity to electron neutrinos makes HALO-1kT (and also the current HALO detector) unique in the sense that all other detectors with capability to detect supernova neutrinos are sensitive to anti-electron neutrinos through charged- current inverse beta-decay such as the Super-Kamiokande, LVD, IceCube and KamLAND. HALO-1kT’s sensitivity to supernova neutrinos is larger than that for HALO due to its proposed 12-fold target-mass increase relative to HALO and a more efficient neutron detection. The detector will consist of 1 kT of lead. Neutrinos from a supernova will interact with the lead via inverse beta-decay process producing bismuth or lead in highly-excited states (the excitation states depend on the incoming neutrino flavour). The daughter nuclei emit neutrons during de-excitation, which are then detected by 3He proportional counters. The layer of the detector immediately following the lead volume consists of a graphite reflector to recover neutrons that would otherwise escape the detector fiducial volume. The main goal of this thesis is to develop simulation studies for the design of a graphite layer which will serve as a neutron moderator and reflector, redirecting escaping neutrons back into the detector lead volume. The reflector layer will increase the detection efficiency by up to 50% relative to the 28% efficiency achieved in HALO. Geant4 simulations have been used to assess the optimal thickness and grade of the graphite to be used. It was found that a graphite material of 15 cm thickness is the favourable choice for a neutron reflector. As for the graphite grade, it should, ideally, be nuclear-reactor quality. However, costs involved in the acquisition of such high grade material should be considered. It was found that a < 1.0 ppm concentration level of boron in the graphite layer is

i an acceptable compromise between cost and eﬀectiveness.

ii Acknowledgements

I want to thank my supervisor, Mauricio Barbi, for his support, motivation, enthusiasm, and patience. His guidance helped me throughout my research work and this thesis writing. I would also like to thank my co-supervisor, Nikolay Kolev, for helping me during the simulation work by guiding me in the right direction whenever he thought I need it and also for proof-reading my thesis. Besides my advisors, I want to thank the HALO-1kT collaborators for their support, especially Dr. Clarence Virtue, Dr. Stanley Yen and Dr. Paul Voytas for all the help and insightful comments required to ﬁnalize this work. Additionally, I would like to thank my fellow lab mates, Luan Koerich and Bruno Ferrazzi, for all the fruitful discussions. I acknowledge the Department of Physics at the University of Regina for all the support, and the Faculty of Graduate Studies and Research for the partial funding through many teaching assistantships, and a Graduate Research Award. I am also greatly thankful to my parents for their love, care and support in all my decisions from distance. I express my thanks to my brother, Yash Patel, for tolerating all my madness and supporting me in hard times. Lastly, I need to thank all my friends for fun and chatting, and special thanks goes to Jay Parikh for the keen interest shown to complete this thesis successfully.

iii Post Defense Achnowledgments

I would like to acknowledge to my external examiner, Dr. Josef Buttigieg from the department of biology at the University of Regina, for his excellent questions during the defense and suggestions for thesis. I would also like to thank Dr. Gwen Grinyer, the member of examining committee for her valuable comments in thesis.

iv Dedication

This thesis is dedicated to my mother and father who have supported me throughout my education. Thanks for making me see this adventure through to the end. Special dedication to my late grandfather whom I lost in the half way journey. Thanks for always believing in me, miss you.

v Contents

Abstract ii

Acknowledgements iii

Post Defense Achnowledgments iv

Dedication v

Table of Contents vi

List of Abbreviations x

List of Figures xi

List of Tables xiv

1 Introduction to Neutrino Physics 1 1.1 Theoretical Evidence of Neutrinos ...... 1 1.1.1 Discovery of Neutrinos ...... 3 1.2 The Standard Model of Particle Physics ...... 4 1.2.1 Fermions ...... 5 1.2.2 Bosons ...... 6 1.2.3 Higgs Boson ...... 7 1.3 Properties of Neutrinos ...... 7 1.3.1 Neutrino Interactions with Matter ...... 8

vi CONTENTS

1.3.2 Neutrino Oscillations ...... 10

2 Study of Neutrino Production in Supernova Explosions 17 2.1 The End of Stellar Evolution ...... 17 2.1.1 Supernovae Types ...... 19 2.2 Neutrino Production in Supernovae ...... 20 2.3 SN 1987a Supernova and the Supernova Early Warning System (SNEWS) ...... 24 2.3.1 The Three P’s ...... 26 2.4 Supernovae Neutrino Detectors ...... 29

3 The HALO-1kT Experiment 31 3.1 Physics of HALO-1kT ...... 33 3.1.1 Flavor Sensitivity of HALO-1kT ...... 33 3.1.2 The Working Mechanism of the HALO-1KT Detector . . . . 35 3.1.3 3He Proportional Counters ...... 37 3.2 Background and Noise for HALO-1kT ...... 41

4 Monte Carlo Simulations for Optimization of the HALO-1kT Neutron Reflector Design 43 4.1 The Detector Design Concept ...... 43 4.2 Physical Aspect on Graphite as Reflector ...... 45 4.3 Efficiency of the Detector Under Different Cases of Reflecting Material 47 4.3.1 Case 1: No Reflector & Shielding Material ...... 48 4.3.2 Case 2: Water Reflector ...... 51 4.3.3 Case 3: Graphite Reflector ...... 53 4.3.4 Case 4: Graphite Reflector and Water Shielding ...... 56 4.4 Grades of Graphite ...... 58 4.4.1 Study of Graphite for Different Degrees of Boron Content . . 60 4.4.2 Graphite Grades in the Market ...... 62

vii CONTENTS

5 Conclusions 65 5.1 Summary of the Selection of the Reflector Material ...... 66 5.2 Summary of the Cost-Benefit of Adding Graphite as Reflector Material ...... 67

viii List of Abbreviations

ATLAS - A Toroidal LHC ApparatuS BNL - Brookhaven National Laboratory CC - Charged Current CMS - Compact Muon Solenoid CNO - Carbon-Nitrogen-Oxygen CP - Charged Parity DIS - Deep Inelastic Scattering DONUT - Direct observation of the nu tau ES - Elastic Scattering GNO - Gallium Neutrino Observatory HALO - Hellium And Lead Observatory HALO-1kT - Hellium And Lead Observatory 1 Kiloton kpc - Kiloparsec LHC - Large Hadron Collider LNGS - Laboratori Nazionali del Gran Sasso LVD - Large Volume Detector MINOS - Main Injector Neutrino Oscillation Search NC - Neutral Current 1n - One neutron OPERA - Oscillation Project with Emulsion-tRacking Apparatus PMNS - Pontecorvo–Maki–Nakagawa–Sakata IBD - Inverse Beta Decay

ix CONTENTS

SAGE - Soviet American Gallium Experiment SM - Standard Model SN - Supernova SNEWS - Supernova Early Warning System SNO - Sudbury Neutrino Observatory SSM - Standard Solar Model 2n - Two neutrons

x List of Figures

1.1 The beta decay spectrum of 64Cu...... 2 1.2 Standard Model of particle physics ...... 5 1.3 Feynman diagrams for µ decay and inverse β+ decays ...... 9 1.4 NC interaction of neutrino with matter ...... 9 1.5 Feynman diagrams for CC Quasi-Elastic Scattering and Deep Inelastic Scattering ...... 10 1.6 The pp chain and the CNO cycle in the sun and other stars . . . . 11 1.7 Solar neutrino ﬂux with corresponding energy calculated as per the SSM ...... 12 1.8 Two possible neutrino mass ordering ...... 15

2.1 Interior of a star with mass greater than 8M ...... 18 2.2 Classification of different type of SN ...... 20 2.3 Different neutrino flavours along with their average kinetic energy emitted during SN explosion ...... 23 2.4 Anti-neutrino events detected from SN 1987a explosion...... 25 2.5 Flow chat of the neutrino burst signal implemented in The SNEWS 26 2.6 Feynman diagram for neutrino-electron ES process ...... 28 2.7 The average time interval between false alerts for different fold coincidences and active experiments, in a 10 seconds window frame 29

3.1 HALO detector at SNOLAB ...... 32

xi LIST OF FIGURES

3.2 Interaction cross sections for different target nuclei with respect to neutrino energies ...... 33 3.3 Neutrino flavor sensitivity for different target material ...... 35 3.4 Conceptual design for HALO-1kT at LNGS ...... 36 3.5 Working mechanism for HALO and HALO-1kT ...... 37 3.6 Neutron energy spectrum for CC reactions inside 208Pb ...... 38 3.7 Neutron energy spectrum for NC reactions inside 208Pb ...... 38 3.8 3He proportional counter diagram ...... 39 3.9 Energy Spectrum of 3He neutron proportional counters ...... 40

4.1 HALO-1kT Detector Monte Carlo simulation ...... 44 4.2 Case 1: No reflector and shielding material surrounding the lead volume ...... 49 4.3 The detection efficiency plot for case 1 ...... 50 4.4 Plot for the percentage of neutrons getting captured in lead volume for case 1 ...... 50 4.5 Plot for the percentage of neutrons escaping the lead volume for case 1 ...... 51 4.6 Case 2: 20 cm thick water layer outside the lead volume as reflector 52 4.7 Plot for the percentage of neutrons getting captured in the water layer for case 2 ...... 53 4.8 case 3: 15 cm graphite layer outside lead block as reflector . . . . . 54 4.9 Plot for the percentage of neutrons getting captured in the graphite layer for case 3 ...... 55 4.10 Case 4: 15 cm graphite layer as neutron reflector and 20 cm water layer as shielding material installed outside the lead volume . . . . 58 4.11 Plot for the percentage of neutrons getting captured in the water layer for case 4 ...... 59

xii LIST OF FIGURES

4.12 Plot for the percentage of neutrons getting captured in the graphite layer for case 4 ...... 59 4.13 Plot summarizing the detection efficiency of HALO-1kT for all the cases analysed in this chapter ...... 60 4.14 Plot of HALO-1kT detection efficiency for different grades of graphite and G4 GRAPHITE ...... 62 4.15 Plot of HALO-1kT detection efficiency for different Company Graphite and G4 GRAPHITE ...... 64

xiii List of Tables

1.1 Elementary particles characteristics ...... 8

2.1 Neutrino emission in diﬀerent stages of SN explosion ...... 21 2.2 Summary of neutrino detectors associated to SNEWS ...... 27

4.1 Percentage of neutrons captured in each of the detector volumes for case 1 ...... 48 4.2 Percentage of neutrons captured in each of the detector volumes for case 2 ...... 53 4.3 Percentage of neutrons captured in each of the detector volumes for case 3 (15 cm graphite layer) ...... 55 4.4 Percentage of neutrons captured in each of the detector volumes for case 3 (10 cm graphite layer) ...... 56 4.5 Percentage of neutrons captured in each of the detector volumes for case 3 (20 cm graphite layer) ...... 56 4.6 Percentage of neutrons captured in each of the detector volumes for case 4 ...... 57 4.7 Percentage of neutrons captured in each of the detector volumes for different grades of graphite material (1.0 ppm, 2.0 ppm and 5.0 ppm) 61 4.8 Boron content as provided by different graphite suppliers ...... 63 4.9 Percentage of neutrons captured in each of the detector volumes for different graphite grades as provided by commercial graphite suppliers 63

xiv Chapter 1

Introduction to Neutrino Physics

Neutrinos are the least known fundamental particle in the standard model with many unsolved questions in neutrino physics. The aim of this thesis is to design a neutron reﬂector for HALO-1kT detector which is a lead based detector to study

νe coming from supernova explosion. Chapter 1 provides the basics of neutrino physics starting with the discovery of neutrinos and Standard Model. Later in this chapter, the neutrino properties like neutrino interaction with matter, mass ordering, neutrino oscillation, and solar neutrino problem are described leading to supernovae neutrino discussion in Chapter 2.

1.1 Theoretical Evidence of Neutrinos

The history of neutrinos began with the investigation of β-decay. A simple β-decay is a process where a proton converts into a neutron or a neutron into a proton. As shown in Equation 1.1.

n −→ p + e− negative beta decay (β−)

p −→ n + e+ positive beta decay (β+) (1.1)

p + e− −→ n orbital electron capture

In a two-body decay, conservation of energy requires that an outgoing electron

1 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

(or positron) must have a well-defined monochromatic energy like in α-decay [1]. However, different experiments in the 1920’s provided results showing a continuous energy spectrum for the electron (or positron) as shown in Figure 1.1, which was clearly in violation of the total energy conservation law. It was then thought, that the above equations were incomplete. To account for this missing energy problem, Wolfgang Pauli proposed the existence of a neutral particle [2, 3], making beta-decay into a three-body process and restoring the conservation of total energy of the system. This neutral particle was later called the neutrino by Enrico Fermi while presenting a theoretical model for β-decay [2, 3]. The Q value in Figure 1.1 is defined as the total kinetic energy realised in a beta decay, in this case it is the sum of the energies of the emitted beta particle, neutrino, and recoiling nucleus.

Figure 1.1: The beta decay spectrum of 64Cu [4].

In beta-decay, due to conservation of electric charge, neutrinos are required to be electrically neutral. Also, to ensure conservation of total angular momentum, neutrinos are spin 1/2 particles (like electrons). To explain the lack of their detection, they were assumed to be massless (we now know that neutrinos have a small mass) and weakly interacting particles [2, 5]. Equation 1.1 was then modiﬁed to, − − n −→ p + e + ν e negative beta decay(β )

+ + p −→ n + e + νe positive beta decay(β ) (1.2)

− p + e −→ n + νe orbital electron capture

2 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

1.1.1 Discovery of Neutrinos

“Everything comes to him who knows how to wait” -Wolfgang Ernst Pauli By 1950, there were several theoretical pieces of evidence for the existence of neutrinos [6]. However, neutrinos were just hypothetical particles introduced to ensure the preservation of the known conservation laws. In reality, the reason for their lack of detection was that, neutrinos interact very weakly with matter. For example a 1.0 MeV neutrino can travel through thousand light-years of lead. It was not before the mid 1950’s that F. Reines and C. Cowan [7] succeeded in discovering neutrinos (in fact, anti-neutrinos) by observing inverse beta-decay reactions using a large tank of water and liquid scintillator as detector which produces a ﬂash of light when struck by a charged particle or high-energy photon. The experiment was conducted near a nuclear reactor in South Carolina with a predicted anti-neutrino ﬂux of 1013 particles per square centimeter per second. Reines and Cowan observed 3.0 ± 0.2 events per hour [8]. The following Equation (1.3) was observed:

+ ν e + p −→ n + e (1.3)

After the conﬁrmation of the existence of neutrinos, Tsung-Dao Lee, Chen-Ning Yang, and other scientists suggested that neutrinos violate parity, (parity transformation in quantum mechanics is the rotation of spatial coordinate simultaneously in N-dimension) because only left-handed neutrinos and right-handed anti-neutrinos are observed in neutrino interaction. The left-handed particles have spin and momentum anti-aligned to each other, while for the right-handed particles the spin and momentum are parallel to each other. The proof came from an experiment performed at Brookhaven National Laboratory (BNL) by Maurice Goldhaber and his colleagues [9]. They studied electron capture of 152Eu and measured the spin of recoiling 152Sm along with emission of neutrino,

3 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS concluding that neutrinos are always left-handed [8]. In 1962, Lederman, Schwartz, and Steinberger [10] discovered that there are in fact two diﬀerent kinds of neutrinos: muon neutrinos and electron neutrinos.

− − They used anti-neutrinos generated in pion decay (π −→ µ + ν µ) and tried to observe the following reactions [8]:

+ ν µ + p −→ µ + n (1.4)

+ ν µ + p −→ e + n (1.5)

A total of 29 muon-like events (Equation 1.4) were observed, while no electron-like events (Equation 1.5) were detected, suggesting that νe 6= νµ. In 1975, after the discovery of the tau lepton by M. L. Perl, it was suggested that a third type of neutrino should exist [11]. However, it took 26 years to conﬁrm the existence of a third species of neutrinos. In 2001, the DONUT experiment discovered the tau neutrino at Fermilab [11]. Meanwhile, experiments performed at the Linear Electron-Positron (LEP) collider at the CERN laboratory in Switzerland indicate that only three species of neutrinos [12] seem to exist.

1.2 The Standard Model of Particle Physics

The Standard Model (SM) is a collaborative eﬀort of physicists aiming to explain the interactions between the fundamental subatomic particles. Its conception began in 1961 when Glashow proposed a theory unifying two fundamental forces: electromagnetism and weak force [14]. At high energies, at the order of 246 GeV, these two forces merge into a single one: the electroweak force. Abdus Salam and Steven Weinberg [15] in 1967 added the Higgs mechanism, which gives mass to elementary particles, into Glashow’s uniﬁcation theory [16, 17]. Further addition of the strong interaction lead to the SM as we know it today [18]. The strong

4 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

Figure 1.2: Standard Model including Quarks, Leptons and Mediators [13]. force is a short-range force holding quarks together forming hadrons, such as protons and neutrons [2]. The theory that describes the strong interactions is known as Quantum Chromodynamics (QCD) [19]. The Standard Model contains 61 fundamental particles in total with 12 leptons, 36 quarks (each quark comes in three ﬂavor) and 13 mediators [2]. Table 1.1 refers to the properties of all elementary particle along with the place they were discovered.

1.2.1 Fermions

Fermions are spin-1/2 particles including all quarks and leptons, as well as all baryons, and other composite nuclei and atoms made from them. The leptons and quarks in the SM each have two families: one with six particles and another with six anti-particles. The families are further subdivided into generations, each formed by a pair of particles of similar characteristics. The lightest and most stable pairs make the ﬁrst generation and the heavier and less stable pairs belong to the second and third generations (Figure 1.2). Leptons are classiﬁed according to their charge and lepton numbers. The electron, muon, and tau are charged and

5 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

have sizeable masses, whereas their corresponding neutrinos are electrically neutral and have small masses. Charged leptons can interact via the electromagnetic and weak force, while neutrinos can interact only through the weak interaction. Six quarks are also paired into three generations with increasing mass. Quarks have fractional charges like Q = 2/3 corresponds to up(u), charm(c) and top(t) quark, while Q = -1/3 is for down(d), strange(s) and bottom(b) quark. Free quarks are not observed in nature, but they bind together forming two categories of hadrons: mesons, bound states of a quark q and an anti-quarkq ¯, and baryons, bound states of three quarks. Like leptons, quarks can also interact via electromagnetic and week force along with strong interaction which is responsible for the conﬁnement of hadrons. Each quark comes in three diﬀerent colors (anti-colors): red (r), blue (b) and green (g) which gives a total of 36 quarks. Hadrons are such that they are colourless; the sum of the constituent quark colours is colourless: r + b + g = 0 and i + ¯i = 0 (i = r, b, g).

1.2.2 Bosons

Bosons are particles that obey Bose-Einstein statistics and have integer spin value. The SM contains elementary bosons, known as force-carriers because they work as the mediator of the fundamental forces. The strong force is mediated by gluons, the electromagnetic force is carried by photons, and the W ± and Z (neutral) bosons are responsible for the weak force. The strong, electromagnetic and weak forces carriers have all been observed [6, 17]. However, the most familiar force in our everyday life, gravity, is not part of the Standard Model because it is much weaker than the other fundamental forces (relative strengths of four forces are given as: strong force = 1, electromagnetic force = 10−3, weak force =10−13, gravitational force = 10−41), which makes it diﬃcult to include their carriers, gravitons, in the model. It is also harder to merge this force with the other ones into a Grand Uniﬁed Theory. However, given its remarkable weakness relative to

6 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS the other forces, gravity can be neglected in the SM [2, 8].

1.2.3 Higgs Boson

The Higgs mechanism is an essential element of the SM, explaining the origin of mass and playing a key role in the physics of electroweak symmetry breaking [14, 16]. A Higgs particle, also known as Higgs boson is a carrier particle for the Higgs field. The ATLAS and CMS experiments at CERN Large Hadron Collider (LHC) in 2012 found a suitable Higgs boson candidate, predicted by the Higgs mechanism, with a mass of 125 GeV [20]. The scalar property of Higgs field, makes it different from other fundamental fields (i.e electromagnetic field), which implies that the Higgs particle is a boson with spin zero, no electric charge and no color charge. The unusual feature of the Higgs field, is that it would take less energy for the field to have a non-zero value than a zero value, so it is non-zero (in a vacuum as well) everywhere. The elementary particles, therefore, acquire their masses through interactions with a nonzero Higgs field only when the universe cooled down and became less energetic in the aftermath of the big bang. The variety of masses characterizing the elementary subatomic particles arises because different particles have different strengths of interaction with the Higgs field. It is also possible that there is more than one type of Higgs boson [8]. Table 1.1 refers to properties of SM particles along with the place they where discovered with there lifespans.

1.3 Properties of Neutrinos

Among all the particles, neutrinos are the most notorious for being diﬃcult to be detected as they are neutral, do not interact electromagnetically and only feel the weak and gravitational forces. Neutrinos are the least massive particles among all fermions in the SM. e.g. νe has a mass that is at least 250,000 times lighter than that of an electron. Neutrinos are detected indirectly in observations such as

7 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

Name Discovered location Mass Charge Color Spin Lifetime electron e Cavendish Laboratory (1897) 0.511 MeV -1 no 1/2 stable muon µ Caltech & Harvard (1937) 105.66 MeV -1 no 1/2 2.2 × 10−6sec tau τ SLAC (1976) 1776.82 MeV -1 no 1/2 2.9 × 10−13sec

electron neutrino νe South Carolina nuclear plant(1956) < 2 eV 0 no 1/2 stable muon neutrino νµ Brookhaven (1962) < 0.19 MeV 0 no 1/2 stable tau neutrino ντ Fermilab (2000) < 18.2 MeV 0 no 1/2 stable up quark u SLAC (1968) 2.3 MeV 2/3 yes 1/2 stable down quark d SLAC (1968) 4.8 MeV -1/3 yes 1/2 stable charm quark c Brookhaven & SLAC (1974) 1.275 GeV 2/3 yes 1/2 1.1 × 10−12sec strange quark s Manchester University (1947) 95 MeV -1/3 yes 1/2 1.24 × 10−8sec top quark t Fermilab (1995) 173.21 GeV 2/3 yes 1/2 4.2 × 10−25sec bottom quark b Fermilab (1977) 4.18 GeV -1/3 yes 1/2 1.3 × 10−12sec photon γ Washington University (1903) 0 0 no 1 stable gluon g DESY (1979) 0 0 yes 1 stable W boson CERN (1983) 80.385 GeV ±1 no 1 3 × 10−25sec Z boson CERN (1983) 91.1876 GeV 0 no 1 3 × 10−25sec Higgs boson H CERN (2012) 125.7 GeV 0 no 0 1.56 × 10−22sec Table 1.1: Elementary particles characteristics. Parameters extracted from [6]. through the products of a neutrino interaction with matter or from the decay of a particle. Their presence can be inferred by conservation laws such as total energy, momentum, angular and lepton number conservation.

1.3.1 Neutrino Interactions with Matter

As neutrinos do not feel strong or electromagnetic forces, they interact with matter by W ± or Z boson exchange. In charge current (CC) processes, the bosons W ± are mediators and the neutrinos convert into their corresponding charged leptons as shown in Figure 1.3. Examples are inverse beta decay and µ decay. The pictorial representation of the above equations are given by Feynman diagram which describes the behaviour and interaction of subatomic particles.

− − νe + n −→ p + e inverse β decay

− − e + νµ −→ µ + ν e inverse µ decay

In neutral current (NC) processes, neutrinos are coupled with Z bosons. In this case, they preserve their identities but change their 4-momenta (refer to Figure 1.4). Examples are neutrino-electron scattering and neutrino scattering from nucleons [2, 22].

8 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

Figure 1.3: The ﬁrst and second images correspond to Feynman diagram of µ decay and inverse β+ decay, respectively [21].

Figure 1.4: Neutral Current (NC) interaction of neutrino with matter [21].

High energy neutrino interactions are more diverse and complicated to understand because, beyond a certain energy scale, the nucleus is no longer a point-like structure but can be described in terms of individual, quasi-free nucleons. Given enough energy, the neutrino can actually begin to resolve the internal structure of the target. The Elastic and Quasi-Elastic Scattering: The charged current (CC) interactions for the energy range of Eν 0.1 -20 GeV) are referred to as Quasi-Elastic scattering (QE), whereas neutral current scatterings are referred to as elastic scattering [23]. Intermediate energy neutrinos [23], can scatter oﬀ elastically from entire nucleon resulting in a variety of ﬁnal states depending on NC or CC type of interaction with the target. The examples of QE Scattering are given by Equation 1.6, while Equation 1.7 refers to Elastic Scattering.

− + νµ + n −→ µ + p, ν µ + p −→ µ + n (1.6)

9 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

ν + n −→ ν + n, ν + n −→ ν + n (1.7) ν + p −→ ν + p, ν + p −→ ν + p

The Deep Inelastic Scattering (DIS): DIS is a process whereby high energy

neutrinos with a range of Eν ∼20 - 500 GeV are used to probe inside the nucleons to study individual quarks and validate the standard model. The neutrinos interact with quarks via an exchange of W ± or Z bosons, resulting in leptons or hadronic systems in the final state [23]. N and X in below equations are initial and final state quarks of different flavor. Equations 1.8 and 1.9 refers to CC and NC DIS processes respectively, while Figure 1.5 shows Feynman diagram for QE Scattering and DIS processes.

− + νµ + N −→ µ + X, ν + N −→ µ + X (1.8)

νµ + N −→ νµ + X, ν µ + N −→ ν µ + X (1.9)

Figure 1.5: Left side, Feynman diagram for CC Quasi-Elastic Scattering. Right

side, Feynman diagram for Deep Inelastic Scattering of νµ and quarks [21].

1.3.2 Neutrino Oscillations

In the SM, neutrinos were initially assumed to be massless fermions. However, a problem known as the “Solar Neutrino problem” quickly lead scientists to question the massless property of neutrinos. In brief - the number of sun powered electron neutrinos arriving to Earth was measured to be about 1/3 of the predicted value

10 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

[24, 25]. The anticipated electron neutrino ﬂux at the earth’s surface, as calculated by John Bahcall and collaborators within the Standard Solar Model (SSM) is ∼ 6 × 1010cm−2s−1 [25]. This ﬂux is delivered primarily by the nuclear fusion initiated by proton–proton (pp) combinations (Figures 1.6, 1.7). The involvement of the Carbon-Nitrogen-Oxygen (CNO) chain is less in the sun, but the main source of energy in heavier stars . The prevailing pp (proton-proton) reactions

( 90% of the entire ﬂux), produce low energy (< 0.42 MeV) νe as shown in Figure

1.7. The “pep” (proton-electron-proton) reactions produce νe with energy of 1.44 MeV, whereas the 7Be line in Figure 1.7 with blue at 0.86 MeV is the second most

8 important νe source (7–8%). Neutrinos from B reactions are created within the “ppIII” chain, with energy ranges up to 15 MeV. Despite their low ﬂux ( 0.1%), most of the existing neutrino detectors are sensitive to these neutrinos. [26].

Figure 1.6: The pp chain and the Carbon-Nitrogen-Oxygen (CNO) cycle in the sun and other stars [27].

In 1968, the ﬁrst measurement of the solar neutrinos ﬂux was performed by Ray

Davis etal. utilizing a large tank ﬁlled with 100,000 gallons of C2Cl4 [24] located at the Homestake mine in South Dakota. They used the following neutrino-induced

11 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

Figure 1.7: Solar neutrino flux with corresponding energy calculated as per the Standard Solar Model [27]. Each reaction is represented by a different colour in the figure. reaction [2]:

37 37 − νe + Cl −→ Ar + e (1.10)

The measured electron neutrino rate was about one-third of the anticipated ﬂux [24]. At that time, most physicists believed that the experiment was incorrect. However, later on when other distinct experiments, such as Super-Kamiokande using a water Cherenkov detector [28], SAGE [29] and GALLEX/GNO [30,

71 71 − 31] using gallium (νe + Ga −→ Ge + e ), confirmed the deficit, this was then considered a serious problem to the SM. A possible explanation by Bruno Pontecorvo back in 1957 [8, 26], could potentially explain this problem, when he suggested that neutrinos can oscillate between different neutrino flavors. Experimental confirmation of neutrino oscillation was provided by the Sudbury Neutrino Observatory (SNO) experiment in 2004 [32]. Neutrino oscillation is a quantum mechanical phenomenon where a wave-like neutrino changes its flavor due to a non-zero mass leading to what is known as neutrino mixing. For example,

12 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

an electron neutrino with energy E can oscillate into another neutrino ﬂavor, for example, muon neutrino, after travelling a distance L. Assuming three neutrino species as included in the SM, the oscillation can be described considering that the mass eigenstates (ν1, ν2, ν3) and the ﬂavors

eigenstates (νe, νµ, ντ ) for neutrinos are distinct, i.e an electron neutrino is a mixture of three mass eigenstates, and so are the other two neutrino ﬂavors, each with their own mixing rates [33]. The ﬂavor eigenstates |ναi (α = [e, µ, τ])

and mass eigenstates |νii (i = [1, 2, 3]) are related to each other through the

Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix Uαi [33]:

N N X ∗ X |ναi = Uαi |νii |νii = Uαi |ναi (1.11) i=1 α=1 where N is the total number of neutrino ﬂavors or mass states (N = 3 in the SM). The above expression for the neutrino mass mixing can be written as [2, 34]:

      νe Ue1 Ue2 Ue3 ν1             ν  = U U U  ν  (1.12)  µ  µ1 µ2 µ3  2       ντ Uτ1 Uτ2 Uτ3 ν3

The mixing matrix U can be further factorized into three other matrices:

      −iδ 1 0 0 cosθ13 0 sinθ13e cosθ12 sinθ12 0             U = 0 cosθ sinθ   0 1 0  −sinθ cosθ 0  23 23    12 12     −iδ    0 −sinθ23 cosθ23 −sinθ13e 0 cosθ13 0 0 1 (1.13)

The parameters θ12, θ13, and θ23 are known as mixing angles, while the parameter δ is known as a Charge Parity (CP) phase factor. The non-zero value

of δCP is of signiﬁcant importance as it can help understanding the asymmetry between matter and anti-matter in the universe [35]. Neutrino oscillations in vacuum can be calculated using the PMNS matrix [34]:

13 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

3 X ∗ |ν(t = 0)i = |ναi = Uαi |νii (1.14) i=1

The eigensates have time dependency of e−iEit, where energy for ith state is

p 2 2 given as Ei = p + mi . At a time t, the ﬂavor state changes as the energy eigenstate evolves:

3 X ∗ −iEit |να(t)i = Uαie |νii (1.15) i=1

p 2 2 2 Using natural units (~ = c = 1), t ≈ L and Ei = p + mi ≈ p + mi /2E,E ≈ p equation 1.15 can be modiﬁed as:

2 mi X X ∗ −i L |να(L)i = UαiUβie 2E νβ (1.16) i β

Starting with a neutrino να, the probability of observing a neutrino νβ after a travelling distance L and at a time t can be obtained using equation 1.16:

2 mi X ∗ −i L 2 P (να −→ νβ) = νβ να(L) = | UαiUβie 2E | (1.17) i

2 X ∆mij P (ν −→ ν ) = δ − 4 Re(U ∗ U U U ∗ )sin2( L) α β αβ αi βi αj βj 4E i>j 2 (1.18) X ∆mij +2 Im(U ∗ U U U ∗ )sin( L) αi βi αj βj 2E i>j

2 2 2 where ∆mij = mi − mj is the mass square diﬀerence of two eigenstates i and j. KamLAND [36] with other solar neutrino experiments [6] have measured

2 2 2 2 ∆msol = ∆m21 (Equation 1.19), while the atmospheric parameter ∆matm = ∆m32 (Equation 1.20) was given by Super-Kamiokande together with the K2K [37] and MINOS [38] long baseline neutrino experiments [39]. The detailed derivation of neutrino oscillation probability can be found in Reference [40]

14 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

eV 2 ∆m2 = ∆m2 = 7.56 ± 0.20 × 10−5 (1.19) sol 21 c4

eV 2 ∆m2 = ∆m2 = 2.43 ± 0.13 × 10−3 (1.20) atm 32 c4

The value of masses are given as per normal mass hierarchy (if m2 is lighter

than m3 it is known as normal mass ordering but if it is heavier then it is considered as inverted hierarchy) but it is yet unknown whether these mass states follow the

“normal hierarchy” (m1 < m2 < m3) or the “inverted hierarchy” (m3 < m1 < m2) (Figure 1.8).

Figure 1.8: Two possible neutrino mass ordering [41].

The value of the three mixing angles and the phase factor, considering normal mass hierarchy, are (as of July 2019) [39, 35]:

◦+0.78 ◦+1.10 θ12 = 33.82−0.76 ; θ23 = 48.30−1.90

◦+0.13 +0.70 θ13 = 08.61−0.13 ; δCP = −1.89−0.58

15 CHAPTER 1. INTRODUCTION TO NEUTRINO PHYSICS

In nature, neutrinos are created inside the core of astronomical bodies, such as the sun and supernovae blasts due to nuclear fusion. The sun-generated neutrino flux at the surface of the earth calculated using the Standard Solar Model is 6 × 1010cm−2s−1 [22]. As a result, they can be used as a tool to probe inside the core of stars, unlike light that only gives information about stellar surfaces [26]. In spite of their huge flux, enormous detectors are required to observe a significant signal, as neutrinos are weakly interacting particles. Typically, kilotons or more of target material are required to observe a few hundred interactions[22]. Understanding the phenomenon of neutrino oscillation is crucial in experiments that use neutrinos as means to extract information about the mechanisms involved in stellar evolution, and in particular, in stellar core collapsing leading to supernova explosions. The next chapters will be dedicated to expanding on the mechanisms leading to supernova explosions, and in particular, to a detailed description and study of a neutrino detection experiment dedicated to study such mechanisms.

16 Chapter 2

Study of Neutrino Production in Supernova Explosions

Supernovae are the events that mark the end of the active period of some massive stars. The number of neutrinos emitted by the core-collapse supernova are around 1058 in a period of ∼10 seconds [42]. Such a signal contains a wealth of information about the details of the explosion, which allows us to test our current understanding of the supernova phenomenon. It can also provide information about the properties of the neutrinos themselves, such as their mass ordering, which are notoriously diﬃcult to determine [43].

2.1 The End of Stellar Evolution

Stars have an onion-like structure with an outermost layer made of hydrogen and inner shells made of heavy stable elements like helium, carbon, neon, oxygen and silicon as shown in Figure 2.1. A star’s life consists of balancing the opposing forces of gravity with internal pressure, while simultaneously compensating the energy lost in the form of emitted light from the surface, by gaining it through thermonuclear fusion. The amount of nuclear fuel available to the star is ﬁnite and when the star runs out of hydrogen fuel, nuclear fusion in the core stops

17 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS temporarily because all hydrogen has fused to helium, and helium burning requires much higher core temperatures. At this point, the outward pressure generated by nuclear fusion that balances the star loses against gravity and the star starts to collapse. The immense gravity increases pressure and temperature inside the stellar core (core for a star going under supernova explosion depends on the type of supernova as discussed in Section 2.1.1). The temperature reaches the point where nuclear fusion of light elements takes place. The star passes through several similar stages of nuclear burning, each one resulting in gravitational collapse. As the fusion of light elements reduces the amount of energy released, the burning of this element increases to liberate enough energy to sustain the internal core pressure. Neutrino production increases in the core during the late burning stages of stellar evolution, and as neutrinos take most of the energy from the core, this leads to an increased burning rate. This process occurs up to some heavy element like Fe until the star is no longer capable of generating the required temperature to start the nuclear fusion of heavy elements in the core, ultimately collapsing due to its own gravity [43, 44].

Figure 2.1: Interior of a star with mass greater than 8 solar masses. It resembles onion-like layers, with shells of progressively heavier elements burning at smaller and smaller radii and at higher and higher temperatures [45].

18 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

2.1.1 Supernovae Types

Different types of supernovae have been discovered depending on the kind of star that undergoes explosion and its remnants. In general, there are two types of supernovae: type I and type II (Figure 2.2). Astronomer Rudolph Minkowski in 1941 found out that if hydrogen is present in the emission spectrum it is a type II supernova. Otherwise it is type I [46]. Type I supernovae are further divided into three categories: type Ia, with Si in the emission spectrum; type Ib, with He showing in the emission spectrum; and type Ic displaying neither Si nor He in the spectrum [46]. Type Ia supernovae occurs with a white dwarf in a binary system orbit with its companion star of any type, e.g red giant. A white dwarf is a star that does not have sufficient mass to activate fusion reaction above helium. Once its helium content is used, the star starts to cool down. The sun, for example will become a white dwarf. In a white dwarf-companion binary system, the white dwarfs orbit around the common mass axis of the companion star and absorbs matter until its mass increases to 1.4 times the solar mass (Chandrasekhar limit - an upper limit on the mass value for white dwarf to be stable [47]). At this point, the star cannot withstand its own weight with electron degeneracy pressure, resulting in uncontrolled burning of carbon, leading the white dwarf to explode. The explosion is so tragic that no remnants are left at the end. Type Ia supernovae are known as “standard candles” because of the systematic 1.4 solar mass ratio. They are used to measure distances in the universe by measuring peak brightness of their light curve (the graph representing light intensity distribution of celestial object) [48]. Types Ib and Ic supernovae arise from massive stars whose hydrogen layers have been taken off. The main difference between them is that while type Ib loses the hydrogen envelope but retains the helium envelope, type Ic supernovae loses both the hydrogen and helium envelopes before the core-collapse explosion [46].

19 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

Type Ib and type Ic supernovae are essentially the same as type II supernovae. In all these types, the iron core of a massive star collapses; the differences in the spectra of type Ib, type Ic, and type II supernovae are due to superficial differences in the exploding stars. Type II supernovae occurs in stars with masses M > 8M (M = 1.989 × 1030 Kg), and it follows the process explained in Section 2.1. Gravity wins and the star undergoes “core-collapse” resulting in a neutron star or black-hole. If the mass of a star is > 25M , it is more likely to form a black-hole [48, 49].

Figure 2.2: Supernova Classiﬁcation as proposed by Astronomer Rudolph Minkowski [46].

2.2 Neutrino Production in Supernovae

The formation and ejection of neutrinos in core-collapse supernovae is an essential part of an explosion, as they carry 99% of the emitted energy, escaping almost unimpeded from the supernova core [48]. Table 2.1 shows the emission of neutrinos at diﬀerent burning stages of a star along with the products, density and temperature values for each stage. Around 1058 neutrinos are produced in core collapse supernovae within 10 s time scale (Figure 2.3). They can be used as “astrophysical messengers” because they reach the earth surface several hours

20 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

before visible light and also helps us in understanding more about the explosion. As discussed in Section 2.1, when the iron core reaches the Chandrasekhar limit

(1.4M ) it gets unstable, with the temperature in the core rising to around 5 billion kelvins. At that temperature photons generated inside the core are energetic enough to break apart iron nuclei into free protons and neutrons as shown in Equation 2.1. This is an endothermic process which lowers the adiabatic index of gravitational instability (γ) from the relativistic ideal gas value of 4/3 [50].

Element Time Scale Products Temperature Density Neutrino Losses Burning (109K) (gm/cm3) (solar unit) Hydrogen 11 My He 0.035 5.8 1800 Helium 2.0 My C, O 0.18 1390 1900 Carbon 2000 y Ne, Mg 0.81 2.8 × 105 3.7 × 105 Neon 0.7 y O, Mg 1.6 1.2 × 106 1.4 × 108 Oxygen 2.6 y Si, S 1.9 8.8 × 106 9.1 × 108 Ar, Ca Silicon 18 d Fe, Ni.. 3.3 4.8 × 107 1.3 × 1011 9 15 Fe core v 1s Neutron > 7.1 > 7.3 × 10 > 3.6 × 10 Star Table 2.1: Stages of burning elements and neutrino emission before a supernova explosion for stars with M > 15M [42].

The two processes that make the iron core unstable are:

Photo disintegration γ +56 F e −→ 134He + 4n −→ 26p + 30n (2.1)

− electron capture e + p −→ n + νe (2.2)

The formula for adiabatic index is given as [50]:

∂ ln P 4 γ = < (2.3) ∂ ln ρ S 3 P = pressure, ρ = density, S = entropy. As the core begins to collapse, the temperature and density increase and core electrons become energetic enough to react with free protons through electron capture process as shown in equation 2.2. Electron capture accelerates the

21 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS catastrophic in fall due to reduction in lepton number and produces a huge ﬂux of electron neutrinos. This process is known as neutralization or νe burst [51]. It lasts for a few milliseconds and neutrinos can easily escape until the core reaches a density of around 1012g/cm3. The average kinetic energy of neutrinos increases as the temperature and density of the core increases, the infalling materials become opaque to neutrinos, trapping them in the core. The captured νe undergoes

− charged-current (CC) inverse beta-decay with nearby nuclei (νe + n −→ e + p), producing electrons, the reverse process of Equation 2.2. This accounts for the balance of electrons which created deficit during the neutralization process, lowering the core potential energy. This continues until it reaches a nuclear matter density of around 3 × 1014g/cm3. At this density, the infalling core is divided into two parts: inner core and outer core. The inner core contracts with v(velocity) ∝ r(radius), so nuclei are closely packed and the adiabatic index (γ) increases suddenly due to the repulsive nuclear force. Protons and electrons combine to form neutrons, restoring the core stability. While the outer core infalls supersonically like free-fall (v ∝ r−1/2) forming a compact object known as a proto-neutron star (the degenerate core of a massive star, prior to its emergence after a supernova as a neutron star). The sudden “core bounce” produces shock waves that propagate outward of the newly formed star and matter from the outer core keeps falling in, heating the outer layer of the neutron star and generating energetic neutrinos of different flavours [50, 51]. This is known as the accretion phase of the supernovae. Neutrinos and anti-neutrinos of all flavours are thermally produced along with the electron neutrinos resultant from CC electron capture by infalling material. The neutrino emission region with a thickness of a few tens of kilometers above the proto-neutron star preferentially emits electron neutrinos and anti-electron neutrinos with energy range of few MeV, as shown in Figure 2.3. Other flavours are emitted from the somewhat deeper and hotter regions as the outer regions do not provide the necessary energy for the production of muon and tau neutrinos. During the

22 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

accretion phase, the production of νe and ν e are similar, but are expected to be about twice as large compared to the production of νx (x = µ, τ) as shown in Figure 2.3 [52]. After mass accretion, the proto-neutron star starts cooling, a process known as neutrino cooling phase. This is responsible for 90% of the neutrino emission in core-collapse supernovae. Neutrinos of all ﬂavours are equally produced (Figure 2.6) through electron capture (Equation 2.2) and a neutral current scattering process such as [53]:

Nucleon-nucleon bremsstrahlung N + N ←→ N + N + ν + ν (2.4)

Electron-positron pair process e− + e+ ←→ ν + ν (2.5)

Plasmon pair-neutrino process γ + e− ←→ e− + ν + ν (2.6)

Figure 2.3: Different neutrino flavours emitted in different stages of a supernova

explosion along with their average kinetic energy. The νe burst from electron capture of protons is the dominant process. The accretion phase yields relatively

similar ﬂuxes of νe & ν e, while all ﬂavours are similarly favored during the proto-neutron star cooling phase [54] .

23 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

2.3 SN 1987a Supernova and the Supernova

Early Warning System (SNEWS)

Supernova SN 1987a occurred in the vicinity of our Milky Way galaxy at 50 kpc away in the Large Magellanic Cloud. It was the only supernova from which neutrinos were observed by several underground detectors sensitive to electron anti-neutrinos. A total of 26 events were observed within a 10-second interval (Figure 2.4): 12 by the Kamiokande II [55] detector in Japan; 8 by

Irvine-Michigan-Brookhaven detector(IMB) [56] in USA; and remaining ν e by the Baksan detector [57] in Russia. The small number of events in these observations did not allow for a detailed quantitative modeling of SN1987A, but it confirmed that the baseline model of core-collapse supernova is true: A neutron star forms and cools by neutrino emission [53]. The possibility of using neutrinos as a supernova early warning signal was fully realized with of SN 1987A. The Supernova Early Warning System (SNEWS) was then developed to provide the astronomical community with an early warning of a supernova’s occurrence, as well as to improve global sensitivity to supernova neutrino bursts through an inter-experiment collaboration [58]. There are currently seven neutrino detectors associated with SNEWS: Borexino neutrino observatory, Daya Bay Reactor Neutrino Experiment, Kamioka Liquid Scintillator Antineutrino Detector (KamLAND), Helium And Lead Observatory (HALO), IceCube Neutrino Observatory, Large Volume Detector (LVD), and Super-Kamiokande (SK) [58] as shown in Table 2.2. These experiments share a connection to the central coincidence server at The Brookhaven National Laboratory (BNL), with an additional center at the Istituto Nazionale di Fisica Nucleare, Italy, serving as backup in case BNL goes offline [58]. Each experiment implements a neutrino burst monitoring system and sends alert to the central coincidence server if a neutrino burst is detected. If the server finds a coincidence between two different experiments within a 10 seconds window, it sends a warning

24 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

Figure 2.4: Anti-neutrino events from the SN 1987a explosion detected by the underground Kamiokande II blue), IMB (green) and Baksan (red) experiments. signal to the SNEWS members mailing list (Figure 2.5). The alerts generated by server are classified as “gold” or “silver”: the gold alert goes directly to the astronomical community, whereas the silver alert goes to the experiments for further verification of the burst. After the coincidence between the signals are achieved, a further requirement for a gold alert is that the experiments involved must be working under normal conditions and that no false alarms at higher rates than usual should have been sent. Also, two experiments at different locations are preferred for gold alert coincidences. If these criteria are not fulfilled, the alert goes under the silver category, with the possibility of being upgraded to gold upon verification and confirmation from the experiments. An alert sent to the community will contain information about the time of the event and approximate location in the sky. However, the direction of the signal may not be available in all the cases as many experiments are unable to provide this information [58, 59]. It has been proposed that the next generation of high-statistics neutrino observatories (eg. Hyper-Kamiokande) may be able to use

25 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS triangulation to determine a rough location in the sky [60]. Figure 2.5 refers to algorithm followed at BNL for sending SNEWS alert to astronomical community and general public.

Figure 2.5: Flow chart of the neutrino burst signal coincidence logic as implemented in the SNEWS central server at the Brookhaven National Laboratory [58].

2.3.1 The Three P’s

The three P’s: “Prompt”, “Pointing” and “Positive” are an integrated part of SNEWS for the astronomical community to rely on the data and alert produced

26 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS by neutrinos detectors [58, 59]. P rompt:- In core-collapse supernovae, neutrinos are emitted over a total timescale of tens of seconds, with about half emitted during the first 1 - 2 seconds(figure 2.3), followed by an electromagnetic signal (visible light) after several hours because of getting trapped before reaching the surface. If the coincidence between two detectors generates a gold alert, SNEWS should be capable to quickly spread the news to astronomers to ensure that maximum information can be collected as supernova explosions are very rare and bring a wealth of scientific information such as on stellar evolution, possible gravitational waves, neutrino properties, etc. To achieve this, the system is automated at both the detector and central server end. Each experiment is responsible for developing its own trigger algorithms to alert SNEWS when a supernova candidate is detected.

Detector Type Mass Events Location (Ktonne) @10 kpc Borexino Scintillator 0.3 100 Italy Daya Bay Scintillator 0.33 100 china KamLAND Scintillator 1 300 Japan HALO Lead 0.079 20 Canada IceCube Long string 600 106 South Pole LVD Scintillator 1 300 Italy SK Water 32 8000 Japan

Table 2.2: Summary of neutrino detectors associated to SNEWS [61]

P ointing:- Providing information regarding where the supernova is going to occur is very useful and neutrinos can help, but finding the direction of incoming neutrinos is notoriously difficult. The neutral current neutrino-electron elastic scattering process (Figure 2.6) is the best source for pointing because by knowing the momentum, the outgoing particles can be worked back to find the direction of the incoming neutrino, providing the location of the supernova. Except for the Super-Kamiokande, no other existing detector have directional capability. Triangulation between detectors across the globe is possible using timing signal, but it is practically difficult as millisecond precision is required. Even if no pointing

27 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

Figure 2.6: Feynman diagram for neutrino-electron elastic scattering process [62].

information is available, it is still useful information for astronomers to know that a core-collapse supernova is in the process of occurring [60]. P ositive:- To ensure that the astronomical community does not receive an accidental warning, the false alerts from each experiment should be low so that alerts generated by SNEWS are considered valid. Considering two or more diﬀerent detectors for coincidence, the false alert rate of SNEWS is chosen to be one per century, which requires the false rate from an individual experiment to be less than one per week and at least two detectors sending an alert signal within ten seconds of each other. Figure 2.7 shows the average interval between false alerts for n-fold coincidence of N experiments, for 10 sec time coincidence window and individual experiments having false alarm rate of one per week. As per the plot, to have false alarm rate of one per century with 2-fold coincidence (two detector coincidences in 10 sec time window), only three active detectors are required, so if more experiments are participating, the coincidence between detectors must be at least 3-fold (three detector coincidences in 10 sec time window) if each detector is to maintain an once-per-week false alarm rate. Neutrinos coming from supernova explosion can be detected using various techniques and Section 2.4 refers to criteria associated with building SN neutrino detectors.

28 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

Figure 2.7: The average time interval between false alerts for diﬀerent fold coincidences and active experiments, in a 10 seconds window frame [58].

2.4 Supernovae Neutrino Detectors

The following are the requirements imposed on SN neutrino detectors:

1. Reliability and simple method of detection.

+7.3 As supernova occurs at a rate of 3.2−2.6 per century [63], detectors will have to operate for decades with accuracy and low maintenance.

2. Appropriate cross-sections for neutrino interactions.

Larger cross-sections in supernovae neutrino energy range (Average neutrino

energies are expected to be about 13-14 MeVfor νe, 14-16 MeV for ν e, and 20-21 MeV for all other ﬂavours.) help in increasing the event rate observed by a detector within the maximum observable distance in our galaxy.

3. Good energy/time resolution.

Time resolution is extremely important for the three P’s and to ensure that a reliable early warning alarm is issued, while energy resolution helps in

29 CHAPTER 2. STUDY OF NEUTRINO PRODUCTION IN SUPERNOVA EXPLOSIONS

an accurate measurement of the neutrino energy, providing thus means to better understand supernovae explosions.

4. Accuracy in measuring all types of neutrinos.

For investigation of the neutrino mass ordering and neutrino oscillation parameters, having the capability to identify the diﬀerent ﬂavours of neutrinos is essential.

5. Large scale detectors with multi-ﬂavour neutrino sensitivity.

Neutrinos interact only via weak force. Extracting most of the information from the next galactic supernovae requires large scale detectors with significant target material along with different flavour sensitive covering the entire spectrum of supernova neutrinos.

Most supernova neutrino detectors presented in Table 2.2 were designed primarily for other purposes such as proton decay searches, solar and atmospheric neutrino physics, accelerator neutrino oscillation studies, and searches for high energy cosmic neutrinos and their astrophysical sources. These are high maintenance and operational cost experiments. The subject of this thesis, the Helium And Lead Observatory 1 Kilotonne (HALO-1kT) detector will be a dedicated supernovae neutrino detector to be installed at Gran Sasso, Italy. Its design will provide low maintenance and a robust detector capable of operating for centuries. The design and physics of HALO-1kT are discussed in chapter 3.

30 Chapter 3

The HALO-1kT Experiment

The supernova phenomenon is rich in physics and complex. It can be approached from several viewpoints: presupernova (Describing the period, and the events, prior to a star undergoing a supernova explosion), material science of blast, nucleosynthesis, neutrino oscillation. As galactic supernovae are rare occasions, neutrinos can help us in understanding the supernovae blast much in-depth with detectors having sensitivity to distinctive neutrino ﬂavors. All experiments associated with SNEWS (Table 2.2), with the only exception of HALO, are

dedicated for the measurement of ν e ﬂux since liquid scintillator or water is used

as the target material. The νe flavor sensitivity of HALO-1kT and HALO is due to the use of lead (208Pb) as a target material. This complementary data makes the supernovae neutrino signal wealthier and valuable to extract information on the physics of core-collapse supernovae explosions. Figure 3.1 shows the front view of the HALO detector. This detector has been taking data since 2012 and it has been a member of SNEWS since fall 2015. HALO is composed of 79 tonnes of lead, with a detection efficiency of 28%. Its size and detection efficiency, coupled with current knowledge of physics involved in supernovae explosion lead to an estimation of only 20 neutrino interaction events from a core-collapse supernova occurring at 10 kpc. The proposed HALO-1kT detector is to be constructed at Laboratori Nazionali

31 CHAPTER 3. THE HALO-1KT EXPERIMENT

Figure 3.1: HALO detector at SNOLAB. The lead blocks are painted green. Inside each circle there are moderators and four pairs of 3He proportional counters, totalling 128 neutron counters and 79 tonnes of lead, with a detection eﬃciency of 28%. The white boxes represent 30 cm of water layer covering entire detector to reduce background.

del Gran Sasso (LNGS), Gran Sasso, Italy. It will also be a lead-based detector

to study νe flux emitted from supernovae events. The expected increase in the number of νe detected per supernova explosion is by a minimum factor of 10, with calculations estimating between 200-300 neutrinos/supernova at 10 kpc [64]. This will be achieved by scaling the amount of the target material up and by improving the detector design and thus increasing the detection efficiency when compared to HALO. HALO-1kT will consist of 1 kilotonne of target lead. This represents a 12-fold increase in target mass when compared to HALO, with an expected 2-fold increase in detection efficiency (As per simulations performed in chapter 4 of this thesis the efficiency of HALO-1kT is 50%). See equations 3.3, 3.4, 3.5 and 3.6 for the process used in HALO-1kT for neutrino interaction detection. Lead is especially promising for neutron detection because of its stability and ease to handle in large quantities [61].

32 CHAPTER 3. THE HALO-1KT EXPERIMENT

3.1 Physics of HALO-1kT

3.1.1 Flavor Sensitivity of HALO-1kT

The use of high Z material, like Pb, can give the best possible detection efficiency for wide range of supernova neutrino energies due to large neutrino scattering cross section per nucleon compared to other elements shown in Figure 3.2 . This is because the weak interaction cross section for few MeV energy neutrinos increases with Z due to correlated nucleon effects and the nuclear Coulomb factor. Figure 3.2 shows the cross sections for different target material with the possible relevant interactions for a given neutrino energy range [61]. For reference the Inverse Beta Decay and Neutral Current cross sections are also shown.

Figure 3.2: Interaction cross sections for diﬀerent target nuclei along with the cross section for inverse beta-decay with respect to neutrino energies[64].

The possible reactions in lead-based detector are:

− νe + n −→ e + p allowed due to excess number of neutrons (3.1)

33 CHAPTER 3. THE HALO-1KT EXPERIMENT

+ ν e + p −→ e + n suppressed, blocked by Pauli exclusion principle. (3.2)

208Pb is a doubly magic nucleus with 126 neutrons and 82 protons. As there are more neutrons (126) than protons, the lower states in Pb are filled and a proton is less likely to make the transition into a neutron by beta-decay due to the Pauli exclusion principle, so ν e flux is suppressed by Pauli blocking. The electron neutrino interacts with lead via Charged Current (CC) reaction, where the W ± bosons are the mediators. Neutral current (NC) interactions are responsible for the communication of other flavors of the neutrino with lead nuclei. In CC interactions, electron neutrinos interact with lead producing excited 208Bi which de-excite by emitting one neutron (1n) or two neutron (2n) depending on the neutron separation energy (separation energy required to remove neutron from an atomic nucleus)and the 208Bi excited-state energy. In NC interactions, any flavor of neutrino strikes the lead nuclei and excites it, resulting in the emission of one or two neutrons during de-excitation. The electron neutrino sensitivity makes HALO-1kT (and also the current HALO detector) unique in the sense that all other detectors with capability to detect supernova neutrinos are sensitive to anti-electron neutrinos through charged-current inverse beta decay such as the Super-Kamiokande, Large-Volume Detector (LVD), IceCube and KamLAND (As shown in Figure 3.3). The 1n and 2n neutron emission equations via CC and NC interactions of different neutrino flavors with A lead target are given as:

208 208 ∗ − Charged Current: νe + P b −→ Bi + e (3.3) 208Bi∗ −→207 Bi + n − 10.3 MeV

34 CHAPTER 3. THE HALO-1KT EXPERIMENT

Figure 3.3: Detectors using target material with Z >> N, such as water Cherenkov and liquid scintillator detectors, have dominant sensitivity to charged

current ν e interaction. Iron with N = Z and liquid Argon have sensitivity to neutral current processes of all neutrino ﬂavors, while Lead with N >> Z can be sensitive to charged current νe interactions.

208 208 ∗ − Charged Current: νe + P b −→ Bi + e (3.4) 208Bi∗ −→206 Bi + 2n − 18.4 MeV

208 208 ∗ Neutral Current: νx + P b −→ P b (3.5) 208P b∗ −→207 P b + 1n − 7.4 MeV

208 208 ∗ Neutral Current: νx + P b −→ P b (3.6) 208P b∗ −→206 P b + 2n − 14.1 MeV

3.1.2 The Working Mechanism of the HALO-1KT

Detector

Figure 3.4 shows the design of HALO-1kT detector. HALO-1kT will use 1 kilotonne of lead blocks, available from the decommissioning of the Oscillation Project with Emulsion-tRacking Apparatus (OPERA) at the Gran Sasso Lab

35 CHAPTER 3. THE HALO-1KT EXPERIMENT

Figure 3.4: Conceptual design for HALO-1kT at LNGS. All components of the detector with dimensions are illustrated in the ﬁgure.

[65]. Throughout the lead blocks, there are 3He proportional counters covered by polystyrene moderators of cylindrical shape arranged in a 28 ×28 array. The entire detector is covered with 15 cm layer of graphite reflector, which improves the detection efficiency by reflecting neutrons that would otherwise escape the detector back into the fiducial volume. Outside the graphite reflector there is a 20 cm of water layer which works as shielding from externally produced neutrons that act as background. This layer also recovers some neutrons that eventually escape the graphite reflector, further improving the detection efficiency. The working mechanism of HALO and HALO-1kT can be visualized in Figure 3.5. The neutrons produced by CC and NC interactions of neutrinos with lead are first thermalized by colliding with Pb and then with the 8.0 mm thick polystyrene moderator before being captured by the 3He gas in the proportional counters. Only the neutrons appearing in the reactions 3.3, 3.4, 3.5 and 3.6 are detected by the 3He counters. As the neutrons are thermalized, the information on the neutrino energy and momentum are lost but timing information is retained, which

36 CHAPTER 3. THE HALO-1KT EXPERIMENT combined with a short neutron capture timing (<200 µs) allows to identify 2n events [66].

Figure 3.5: Working mechanism for HALO and HALO-1kT The neutrinos undergo CC or NC interaction with Pb nuclei and produce Pb or Bi in excited state which de-excites by emission of neutrons. These neutrons are ﬁrst thermalized by collision with Pb, then with moderator, prior being getting captured by 3He proportional counter.

The neutrons produced by NC and CC interactions in lead have energies in the range from 0.1 MeV to 5.0 MeV with a peak at 1.0 MeV as shown in Figures 3.6 and 3.7 [67]. A 1.0 MeV of neutron, lead has low neutron capture cross-section and relatively high inelastic scattering cross-section, so neutrons slow down by inelastic collisions, being further brought to thermal energy by the moderator, allowing them to reach the 3He counters at detection energy range (0.025 eV) [68].

3.1.3 3He Proportional Counters

3He neutron counters are sensitive to thermal neutrons as the cross section of 3He is 5330 barns for thermal neutrons [69] compared to any other elements shown in Reference [68]. The thermal energy is reached in HALO and HALO-1kT by

37 CHAPTER 3. THE HALO-1KT EXPERIMENT

Figure 3.6: Neutron energy spectrum for charged current reactions inside 208Pb as shown in Equations 3.3 and 3.4 [67].

Figure 3.7: Neutron energy spectrum for neutral current reactions inside 208Pb as shown in Equations 3.5 and 3.6 [67].

38 CHAPTER 3. THE HALO-1KT EXPERIMENT

employing a 8.0 mm thick polystyrene moderator that slows down (de-excites)

neutrons produced in CC and NC interactions between νe and νx (x = µ or τ) and lead. These neutrons are captured in the proportional counters shortly after entering the 3He tubes following the reaction[69]:

3He + n −→ p + 3H + 764 keV (3.7)

Figure 3.8: 3He proportional counter diagram [70] For HALO-1kT the cylinder is made of 0.508 mm thick stainless steel, thermal neutron ionizes the gas producing ion pairs that are accelerated in opposite direction due to high potential diﬀerence between copper anode and cathode. The output signal is proportional to original ion pair production (764 keV).

In Equation 3.7 the proton moves with a kinetic energy of 573 keV, while 191 keV is taken by the triton (3H) which moves in the opposite direction of the proton ionizing gas molecules in the proportional counter, providing an output signal proportional to 764 keV, Figure 3.8 explains the working mechanism of the 3He proportional counters. Charged particles produced in Equation 3.7 ionizes the nearby gas while moving, resulting in the production of ion pairs that accelerate in the opposite direction due to the potential diﬀerence between the anode and cathode. Secondary ionization is produced in the surrounding gas by the accelerating electrons due to a strong electric ﬁeld near the anode. This results in an avalanche-like multiplication process, with the charges collected as

39 CHAPTER 3. THE HALO-1KT EXPERIMENT measurable electric pulses with an output proportional to the original number of ion pairs [69, 71].

Figure 3.9: Energy Spectrum of 3He neutron proportional counters. The full energy (combined energy of proton and triton) peak is at 764 keV shown with label c, with two discrete peaks to the left: one at 573 keV (label b) due to energy loss in collision of 3H with walls of the counter; another at 191 keV (label c) due to proton collision with the walls of the counters [72].

Figure 3.9 shows neutron capture energy spectrum along with explanation of all the peaks inside the proportional counter. If both proton and triton deposit their energies (573 keV and 191 keV respectively.) in the proportional counter by ionizing the gas, the output energy peak will be at 764 keV. If one of the charged particle collides with a wall then some of its energy will be lost, and total energy will be less than 764 keV. This is known as Wall eﬀect. The 573 keV peak arise due to energy deposition by only proton as triton strikes the wall and its energy is lost, while 191 keV energy peak is due to energy lost by the proton. The 3He counters that will be used for HALO-1kT will be ﬁlled with a mixture

3 of 85% He and 15% CF4 at a total pressure of 2.5 atm. The CF4 accomplishes three purposes:

1. It increases the stopping power of the gas, keeping proton and triton tracks short.

2. It works as a quenching gas, preventing emitted photons from causing further avalanches in the counter.

40 CHAPTER 3. THE HALO-1KT EXPERIMENT

3. It speeds up the drift time for better pulse shape discrimination for 1n and 2n events.

3.2 Background and Noise for HALO-1kT

The neutrons detected inside the HALO-1kT detector are due to interaction of supernovae neutrinos by CC or NC reactions with lead. The neutrons are recognized as events in the proportional counter with energies in the range of 191 to 764 keV. The output signal created by neutrons through other physics process inside the detector are considered as unwanted noise or background which can provide false signals. The tolerable summed background “neutron” rate set by SNEWS trigger condition and for HALO-1kT’s detector design is < 6.7 Hz, while the targeted neutron background rate for HALO-1kT is < 1 Hz. The overburden rock at LNGS, Italy where HALO-1kT is to be placed is ∼ 1400 m, which provides low cosmic ray muon flux (1.1 muons per square meter per hour) [73]. But still these muons can generate background signal by interacting with the surrounding rock and producing neutrons. The problem can be solved by covering the detector with water, as hydrogen is good shielding material which slows down neutrons and prevents from generating false output signal. Gamma rays are another source of noise produced due to neutron capture inside other volumes of the detector like Pb or moderator along with spontaneous fission of uranium and thorium. Uranium and thorium decay via α or β emission, but the decay of daughter nuclei can produce gammas which can interact with electrons inside the proportional counters through compton scattering and induce ionization within the 3He detectors. They are easy to distinguish from the actual output signal of neutrino interaction due to energy less than few 100 keV, so they lie at the tail in figure 3.9. But this can overlap with the neutron peak in the 191 keV region, so for safety and better signal it is preferred that less neutrons produced by neutrino interactions are captured in that region. To prevent this we

41 CHAPTER 3. THE HALO-1KT EXPERIMENT

require the stopping power in 3He gas shorter than the diameter of the counter

3 to avoid the wall effect. For this reason He/CF4 mixture is used inside the proportional counters. Stainless steel is going to be used for the 3He cylindrical counters and if by chance neutron get captured inside this volume before reaching the 3He gas the common byproduct will be an alpha particle that can create noise in the signal. Fortunately, alpha particles have charge and are very heavy, so they have a very short range. This prevents them in many cases from arriving at the detector wall with sufficient energy to initiate radioactive decay. Chapter 4 deals with Monte Carlo simulations for the HALO-1kT detector, including explanations of each detector component along with my studies addressing the different reflector materials considered in my research project. I will discuss the impact of each material, their thickness and grade of graphite purity on the detector performance.

42 Chapter 4

Monte Carlo Simulations for Optimization of the HALO-1kT Neutron Reﬂector Design

The HALO-1kT detector simulation is performed using the Geant4 software package [74]. The files generated using root will be referred to as “root files”. The main aim of my study is to design a neutron reflector in order to increase the efficiency of the detector. This is achieved using a layer of graphite as described in this chapter. Section 4.1 covers the geometry and physics of the HALO-1kT detector as implemented in Geant4. Section 4.2 discusses the physics behind using graphite as a reflector. The implication of the introduction of a graphite layer as neutron reflector to study the detector efficiency is elaborated on Section 4.3.3. The chapter concludes with a discussion on the impact of using different graphite grades.

4.1 The Detector Design Concept

The Detector target volume consists of 1000 tonnes of lead (Pb) with a dimension of 4 × 4 × 5.5 m. It serves as a passive material for neutrino interactions. 784

43 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN cylindrical 3He proportional counters are arranged in a 28 × 28 array. Each one 5.5 m long, 50.8 mm diameter counter runs along the Z-direction (See Figure

3 4.1), filled with a mixture of 85% He and 15% CF4 gas to a total pressure of 2.5 atm. (refer to Section 3.1.3 for a more detailed description of the 3He working mechanism). These neutron counters are surrounded by an 8.0 mm thick polystyrene moderator which slows down generated neutrons to thermal energy. A 15 cm thick graphite reflector layer surrounds the detector target region, followed by a 20 cm thick water layer for shielding against external neutron background. The graphite plus water layer combination reflects escaping neutrons back into the detector, increasing its detection efficiency. This setup can be seen in Figure 4.1.

Figure 4.1: HALO-1kT Detector Monte Carlo simulation. The ﬁgure shows X and Y coordinates of the detector with the origin at center, the 3He proportional counter are along the Z direction represented by small white dots inside the target material arranged in a 28×28 array. The Graphite thickness of 15 cm is found after optimizing the detector for high eﬃciency. The entire detector is covered with a 20 cm thick water layer to reduce the background rate. Neutrons of 0.1 MeV, 1.0 MeV, 5.0 MeV are randomly generated inside the lead volume.

44 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

The predefined FTFP BERT HP1 physics list in Geant4 is used for the simulations. This list provides a neutron interaction model used for neutrons below 20 MeV. It contains all standard electromagnetic (EM) processes along with improved neutron cross section calculations for elastic, inelastic, capture and fission processes. The list is also responsible for the transportation and interaction of neutrons in all the materials inside the detector. Mono-energetic neutrons of 0.1 MeV, 1.0 MeV and 5.0 MeV are randomly generated in the lead volume in x, y and z direction. The information regarding each step for all volume through which neutrons passes is recorded. The number of neutrons absorbed in different components along with information on the energy depositions are stored in root files. For HALO-1kT efficiency calculations, thermal neutron absorption in 3He is considered, with the energy peak of proton and triton produced in the reaction 3.7 also stored in root files. Different cases, assuming different detector configurations, are considered in section 4.3, in order to establish an optimal design for the neutron reflector and shielding material of HALO-1kT.

4.2 Physical Aspect on Graphite as Reﬂector

A very descriptive feature of the transmission of neutrons through bulk matter is the mean-free-path length (λ), which is the mean distance a neutron travels between interactions. The mean-free-path of neutron for a given material depends on the macroscopic cross section (λ = 1/Σt). The macroscopic cross-section (Σ) represents the eﬀective target area of all of the nuclei contained in the volume of the material. The units are given in cm−2. The microscopic cross section (σ) represents the eﬀective target area of a single target nucleus for an incident particle. The units are given in barns (b) or cm2. The mean-free-path has numerous applications

1FTFP BERT HP physics list extensive in Geant4: FTF −→Fritiof string model (>∼5 GeV ) P −→ G4Precompund model used for de−excitation BERT −→ Bertini-style cascade (<∼ 10 GeV ) HP −→ High Precision neutron model ( < 20 MeV)

45 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

in the detector target material, reﬂector, and shielding material such as:.

1. Reﬂector: If the number of collisions required to thermalize a neutron is known, the necessary reﬂector thickness can be assessed.

2. Shielding: The shielding material would have to be such that the mean-free-path of the neutron in it should be small, with the shielding thick enough to absorb most of the neutron background.

The mean-free-path of a 1.0 MeV neutron in lead is 6.8 cm for elastic or

−2 inelastic scatterings (σt = 4.39 b, Σt = 0.147 cm ) and 100 m for absorption

−2 2 (σt = 0.0033 b, Σt = 0.0001 cm ) . Elastic scattering is a process were the kinetic energy of neutron and nucleus is unchanged after interaction only fraction of neutron energy is transferred to nucleus through which it recoils. The total kinetic energy of neutron and nucleus in inelastic scattering is less then the kinetic energy of the incoming neutron since the part of it is used to place the nucleus in excited state. Because of their small absorption cross-section compared to scattering cross-section, neutrons are most likely to undergo elastic or inelastic scattering. As the scattering cross-section is large, if the neutrons are produced

near the wall of the detector lead volume by CC (NC) reactions between νe (νx) and 208P b, then one can imagine they are probably going to escape rather than being thermalized and captured by the neutron counters. This problem can be partially mitigated by surrounding the lead volume with a material that can reflect neutrons back into the detector fiducial volume. Usually, neutrons will undergo multiple scatterings within the reflector volume, experiencing random walk, with some having a chance to relocate back into the lead volume. In the HALO detector, a water volume is used as shielding material surrounding the detector. This volume also serves the purpose of neutron reflector. The total

2 σt = Total microscopic cross section (σs + σa). σs = Total scattering cross section (elastic + inelastic) σa = Absorption or capture cross section Σt = Total macroscopic cross section. (Σ = microscopic cross-section (σ) × atomic number density (N))

46 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

cross section of hydrogen present inside water for neutrons to thermalize is σt = 30.62 b, making it a better moderator compared to any other material with low scattering cross section like deuterium ( σt = 4.25 b) or graphite ( σt = 4.95 b). However hydrogen also provides a large absorption cross-section σa = 0.33 b when compared to Pb (σa = 0.18 b for thermal neutrons) or any other material, hence the chances of detecting neutrons in the proportional counter decreases as they get absorbed inside the reflector material, resulting in low detection efficiency. Use of Polyethylene-based material is also not recommended as it has high moderating power so neutrons are thermalized far from the 3He counters, an undesirable feature as this increases the likelihood that the neutrons would be absorbed inside Pb. Graphite, on the other hand, is a better reflecting material, with low moderating and neutron absorption cross-section (σa=0.003 b for thermal neutrons).

4.3 Eﬃciency of the Detector Under Diﬀerent

Cases of Reﬂecting Material

The efficiency of the detector is calculated by counting the number of neutrons absorbed in the 3He counters relative to the total number of neutrons generated for a particular neutron energy. Figures 3.6 and 3.7 shows neutrons produced in neutrino-lead interaction peaking at 1.0 MeV, with an energy tail extending up to 5.0 MeV. Based on these distributions, I selected three values of energies for the simulation used to evaluate the detection efficiency : 0.1 MeV, 1.0 MeV and 5.0 MeV. The uncertainties evaluated for all cases considered in this thesis are at the order of ±0.2% calculated using statistical error. Given the small order of magnitude of these errors, I have opted to omit them when quoting the values for the calculated detection efficiencies listed in the tables or quoted in the text of

47 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

the subsequent sections and chapters.

4.3.1 Case 1: No Reﬂector & Shielding Material

In this section, the detection efficiency is studied in the absence of reflector and shielding material. Figure 4.2 shows the schematic of the detector in this configuration, with the magenta lines making the external walls of the lead volume, the blue dots representing the 3He counters. The volume between the magenta and white lines (outside the lead volume) is filled with air. This will serve as the basis for the comparative analysis between the effectiveness of different materials considered in the following sections. 10,000 neutrons of 0.1 MeV, 1.0 MeV and 5.0 MeV are randomly generated inside a 4.0 × 4.0× 5.5 m volume of lead. Table 4.1 gives the percentage of neutrons absorbed in each of the detector volumes for the three different energies listed above along with each respective detector efficiency (neutrons absorbed in the 3He gas).

Energy Lead Gas Graphite/ Moderator Steel Escape (MeV) (Eﬃciency) Water 0.1 23.79% 48.36% Not Present 5.06% 3.46% 19.30% 1.0 21.11% 45.75% Not Present 5.01% 3.33% 23.89% 5.0 20.84% 43.78% Not Present 4.51% 2.90% 27.06%

Table 4.1: Case 1 (no neutron reﬂector) - Percentage of neutrons captured in each of the detector volumes for case 1. The eﬃciency of the detector for 0.1 MeV, 1.0 MeV and 5.0 MeV is 48.36%, 45.75% and 43.78%, respectively.

Table 4.1 also shows that for 1.0 MeV neutrons, only 45.75% were thermalized and reached the 3He counters to produce protons and tritons of 573 keV and 191 keV, respectively (Figure 4.3). The eﬃciency of HALO-1kT is better than in HALO (28%) due to the increase in target mass and the number of 3He proportional counters. Table 4.1 also shows that the percentage of neutrons captured in the lead volume is 21.11%. These neutrons have peak energy at the thermal energy for neutrons (0.025 eV) after multiple scattering processes as depicted in Figure 4.4. The number of 1.0 MeV generated neutrons escaping the

48 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Figure 4.2: Case 1: No reflector and shielding material surrounding the lead volume. The magenta colour represents the lead volume of 4.0 × 4.0 × 5.5 m, while the blue dots represents 3He proportional counters. sitting outside the lead volume is a world box filled with air limited by a white full line. (Air fills the detector volume enclosed between the outside white full lines and the outer walls (magenta) of the lead volume). 100 neutrons of 1.0 MeV energy (yellow tracks) are randomly generated inside the target material (lead) for illustration purposes. As shown in the figure, 21 out of the 100 generated neutrons escape from the lead material, with a consequent reduction of the detection efficiency. target region is 23.89%, as shown in Table 4.1. The escaping neutrons have energy between 0.1 MeV and 1.0 MeV, as can be seen in figure 4.5, suggesting that they are produced at the boundary of the lead volume. In this case, their large mean free path allowed them to escape the detection volume without thermalizing. The percentage of escaping neutrons is rather large and certainly impact the detection efficiency. Part of this efficiency can be recovered if a reflector is introduced in order to redirect these neutrons back into the detector fiducial region, making it possible for them to thermalize and be detected.

49 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Figure 4.3: The detection efficiency is computed by counting the number of tritons (energy peak at 191 keV) and protons (energy peak at 573 keV). The efficiency of the detector is 45.75% for 1.0 MeV incident neutrons in the absence of reflector

and shielding material. The X-axis represents the energy in log10 per MeV., i.e log10(0.573) = −0.24.

Figure 4.4: Energy range of the neutrons getting captured inside lead volume for 1.0 MeV randomly generated neutrons. From 10,000 neutrons generated inside lead volume, 2111 got captured with highest number of counts for thermal energy.

50 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Figure 4.5: Energy range of the neutrons escaping the detector volume for 1.0 MeV generated neutrons. From 10,000 neutrons randomly generated inside lead volume, 2389 escape the lead block with most of them having energy range of 0.1 - 1.0 MeV.

4.3.2 Case 2: Water Reﬂector

The efficiency of HALO-1kT in this case is studied by surrounding the lead block with 20 cm thick water layer (blue box shown in Figure 4.6) which works as reflector and shielding material. The same procedure described in case 1 is followed: 10,000 neutrons of three different energies (0.1 MeV, 1.0 MeV and 5.0 MeV) are generated inside the lead volume, and neutrons captured in each of the detector volumes are measured to study variations in the detection efficiency due to the presence of the water layer. As per Table 4.2, the detection efficiency of HALO-1kT in the presence of water material as reflector increased by ∼2.5% compared to case 1. The escaping percentage of neutrons is also lower compared to the previous case. However, the counts for neutrons captured in water is high. For example, 15.93% of the 1 MeV generated neutrons are captured in water. Figure 4.7 gives the energy of 1.0 MeV neutrons captured in water. Most of the captured neutrons have thermal energy due to the presence of hydrogen in water which incorporates a high

51 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Figure 4.6: Case 2: 20 cm thick water layer outside the lead volume as reﬂector shown with blue box.

neutron absorption cross-section (σa = 0.33 b) along with large elastic scattering cross-section. For a neutron of kinetic energy E undergoing elastic collision with a nucleus of atomic weight A, the average energy loss is 2EA/(A + 1)2 [68]. By using hydrogen, where A = 1, a single collision results in a energy loss of E/2 Hence, if we start with 1.0 MeV neutrons in water, ∼ 26 collisions are required to reach thermal energy (0.025 eV). These neutrons might be absorbed in the 20 cm thick water layer before reaching a 3He counter to be detected, resulting in not very signiﬁcant increase in the detection eﬃciency.

52 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Energy Lead Gas Water Graphite Moderator Steel Escape (MeV) (Eﬃciency) 0.1 26.98% 51.90% 11.61% - 5.33% 3.86% 0.31% 1.0 26.31% 48.20% 15.93% - 5.46% 3.51% 0.52% 5.0 25.99% 46.94% 16.82% - 5.25% 3.34% 1.48%

Table 4.2: Case 2 (water layer)- Percentage of neutrons captured in each of the detector volumes for case 2. The eﬃciency of the detector for 0.1 MeV, 1.0 MeV and 5.0 MeV is 51.90% 48.20% and 46.94%, respectively.

Figure 4.7: Energy range of the neutrons captured in the water volume for 1.0 MeV generated neutrons. From 10,000 neutrons generated inside lead volume, 1593 were captured with the highest number of counts for neutron at thermal energy.

4.3.3 Case 3: Graphite Reﬂector

Graphite is a better alternative than water because it has low neutron absorption and high scattering cross sections. The average energy loss by single elastic collision of a neutron with carbon (A = 12), using the formula 2EA/(A + 1)2, is 0.14E (E is the initial energy of neutron). This neutron will undergo a random walk in the graphite layer, reducing its energy by 0.14E each time it is subjected to an elastic scattering. These multi-scattering processes can eventually lower the neutron energy to 0.025 eV (Thermal energy), Allowing it to be captured in a 3He counter. Graphite works, as a neutron energy moderator besides serving as a

53 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN reflector material by redirecting some neutrons back into the detector fiducial volume. The detection efficiency, in this case, is studied by surrounding the lead volume with 15 cm of graphite (yellow box shown in Figure 4.8). To keep consistency, again 10,000 neutrons of three different energies (0.1 MeV, 1.0 MeV and 5.0 MeV) are generated inside the lead volume and neutrons captured in each of the detector volumes are noted. The material used for reflector volume is G4 GRAPHITE3 with a density of 2.1 g/cm3.

Figure 4.8: case 3: 15 cm graphite layer outside lead block as reﬂector shown with yellow box.

As shown in Table 4.3, in the presence of 15 cm graphite, the eﬃciency of the detector is 52.13% for 1.0 MeV randomly generated neutrons. This represents an increase of ∼7% in the detection eﬃciency when compared to case 1. The number of neutrons captured in graphite is also considerably smaller (0.27% for 1.0 MeV)

3More information about the material is available in the Geant4 Material Database.

54 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Energy Lead Gas Water Graphite Moderator Steel Escape (MeV) (Eﬃciency) 0.1 27.01% 54.80% - 0.41% 5.73% 3.94% 8.15% 1.0 26.63% 52.13% - 0.27% 5.44% 3.85% 11.61% 5.0 26.11% 51.06% - 0.26% 5.31% 3.93% 13.25%

Table 4.3: Case 3 (15 cm graphite layer) - Percentage of neutrons captured in each of the detector volumes for a 15 cm thick graphite layer. The eﬃciency of the detector for 0.1 MeV, 1.0 MeV and 5.0 MeV is 54.80%, 52.13%, 51.06%, respectively. compared to the capture rate of water in case 2.

Figure 4.9: Energy range of the neutrons captured in the graphite material for 1.0 MeV generated neutrons. From 10,000 neutrons generated inside lead volume, only 27 were captured with the highest number of counts for neutron at thermal energy.

Two other thicknesses of the graphite layer, 10 cm and 20 cm, were considered to evaluate the gain in detection efficiency compared to the 15 cm layer. The same procedure applied in the previous cases are repeated here. Comparing Tables 4.3 (15 cm graphite layer) and 4.4 (10 cm graphite layer) we observe and increase of 2% for 1.0 MeV generated neutrons from 10 cm to 15 cm thickness. On the other hand, when comparing Tables 4.3 and 4.5, we observe that while the 20 cm thick reflector yields an efficiency of 52.48%, the 15 cm thick

55 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN detector provides an efficiency of 52.13%, a difference of only 0.67%. This data shows that we do not gain much in efficiency by increasing the reflector thickness by 5 cm. In fact, this will only reflect in detector costs without much benefit toward the detection efficiency. It is, therefore, preferable to consider a 15 cm thickness as the baseline for a graphite layer in HALO-1kT.

Energy Lead Gas Water Graphite Moderator Steel Escape (MeV) (Eﬃciency) 0.1 26.43% 53.32% - 0.07% 5.58% 3.92% 10.66% 1.0 25.28% 50.29% - 0.10% 5.26% 3.71% 15.32% 5.0 24.26% 49.60% - 0.16% 5.11% 3.54% 17.33%

Table 4.4: Case 3 (10 cm graphite layer)- Percentage of neutrons captured in each of the detector volumes for 10 cm thick graphite layer. The eﬃciency of the detector for 0.1 MeV, 1.0 MeV and 5.0 MeV is 53.32%, 50.29% and 49.60%, respectively.

Energy Lead Gas Water Graphite Moderator Steel Escape (MeV) (Eﬃciency) 0.1 27.42% 55.08% - 0.61% 5.97% 3.92% 6.49% 1.0 27.67% 52.48% - 0.58% 5.72% 4.04% 9.22% 5.0 26.49% 51.73% - 0.70% 5.73% 4.07% 11.66%

Table 4.5: Case 3 (20 cm graphite layer) - Percentage of neutrons captured in each of the detector volumes for 20 cm thick graphite layer. The eﬃciency of the detector for 0.1 MeV, 1.0 MeV and 5.0 MeV is 55.08%, 52.48% AND 51.73%, respectively.

4.3.4 Case 4: Graphite Reﬂector and Water Shielding

The efficiency of HALO-1kT significantly increased when using 15 cm of graphite layer outside the lead volume as reflecting material when compared to using no reflecting material. In Table 4.3, even though the detection efficiency is higher, the escaping percentage of the neutrons is more when compared to case 2 where water is used instead of graphite: for 1.0 MeV generated neutrons in case 3, 11.61% neutrons escaped, while 0.52% neutrons escaped the detector in case 2. The reason behind this fact is that water has a higher neutron absorption cross section(σa = 0.33b) when compared to graphite (σa = 0.003b). Thus, neutrons

56 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN are thermalized faster in the water layer. This works as a drawback when using water as reflector material because neutrons reaching this medium tend to be absorbed instead of reflected back into the detector fiducial region. Due to this, graphite is a better alternative as a neutron reflector. However, water can still be effectively used in HALO-1kT as shielding material outside the graphite layer due to its high neutron absorption power, reducing neutron background from outside sources such as the Gran Sasso mountains surrounding LNGS, while, at the same time, redirecting some of the neutrons back into the detector volume. The HALO-1kT detector configuration using a 15 cm graphite layer as reflector material and a 20 cm water layer as shielding material is depicted in Figure 4.10. This thickness of the water layer was used for study purposes and might be varied in the final design of HALO-1kT depending upon the requirements for an acceptable background rate, on the capability of the lead to withstand the weight of this layer, and on the cost involved.

Energy Lead Gas Water Graphite Moderator Steel Escape (MeV) (Eﬃciency) 0.1 27.72% 55.30% 6.76% 0.51% 5.63% 3.87% 0.10% 1.0 27.89% 53.70% 9.23% 0.72% 4.80% 3.50% 0.15% 5.0 27.68% 52.05% 10.29% 0.80% 4.96% 3.85% 0.37%

Table 4.6: Case 4 (15 cm graphite reﬂector and 20 cm water shielding layers) - Percentage of neutrons captured in each of the detector volumes for 15 cm thick graphite layer and 20 cm thick water layer. The eﬃciency of the detector for 0.1 MeV, 1.0 MeV and 5.0 MeV is 55.30%, 53.70% AND 52.05%, respectively.

As per Table 4.6, the efficiency of the detector is highest among all the cases studied so far with 53.70% for 1.0 MeV generated neutrons. Figures 4.11 and 4.12 represents the energies of the neutrons captured in the water and graphite layers, respectively. Figure 4.13 summarizes the efficiency of HALO-1kT for all cases considered in this chapter so far. It is clear that the combination of 15 cm graphite and 20 cm water provides the highest efficiency among all the detector configurations tried.

57 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Figure 4.10: Case 4: 15 cm graphite layer (yellow box) as neutron reﬂector and 20 cm water layer (blue box) as shielding material installed outside the lead volume.

4.4 Grades of Graphite

The graphite material considered in the above studies is G4 graphite. This type of graphite was used given that it is already built into the Geant4 simulation package. It has no impurities and a density of 2.1 g/cm3. But in reality, graphite is a specific crystalline form of carbon which exists in nature in limited quantities. The quality of manufactured graphite depends on the raw material from which it is extracted. The main concern while using graphite as a reflector is the presence of neutron-absorbing impurities, especially boron, which has a large neutron capture cross section (σa = 3843 b for thermal neutrons). Nuclear-grade (used in nuclear reactor) graphite can be defined as graphitized carbon that is as free of elements that can absorb neutrons as possible. Boron concentration in this type of graphite can be less than 0.4 ppm (parts per million). The use of high-quality graphite

58 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Figure 4.11: Energy range of the neutrons captured in the water volume for 1.0 MeV generated neutrons in case 4. From 10,000 neutrons generated inside lead volume, 923 were captured with the highest number of counts for neutron at thermal energy.

Figure 4.12: Energy range of the neutron captured in the graphite volume for 1.0 MeV generated neutrons in case 4. From 10,000 neutrons generated inside lead volume, 72 were captured with the highest number of counts for neutron at thermal energy after multiple scattering inside graphite and water layers.

59 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

57.5 No Reflection & Shielding Water 20 cm Graphite 10 cm 55 Graphite 15 cm Graphite 20 cm Graphite 15 cm & Water 20 cm

52.5 ) % (

y c n e i 50 c i f f E

47.5

0 1 2 3 4 5 Energy (MeV)

Figure 4.13: Summary of the HALO-1kT detection eﬃciencies for all cases analysed in this chapter for neutrons generated with 0.1 MeV, 1.0 MeV and 5.0 MeV energies. in such a large quantity as required in the HALO-1kT detector (120 m2 of 15 cm thickness) is very costly. Thus, alternate types (lower quality than the nuclear-type) of graphite are considered in the following sections.

4.4.1 Study of Graphite for Diﬀerent Degrees of Boron

Content

The efficiency of the detector will be affected as the boron content in graphite increases due to the boron tendency to absorb neutrons. In this section simulations were performed for different boron content (impurity) in the graphite material in order to investigate its impact on the efficiency of the detector. The 15 cm of graphite layer and 20 cm of water layer configuration (Case-4, Section 4.3.4, Figure 4.10) was employed for three different concentration (in ppm)

60 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN of boron present in the graphite material: 1.0 ppm; 2.0 ppm; and 5.0 ppm. These boron impurities contents were selected based on the available graphite grades found in the market (see Section 4.4.2). Table 4.7 shows the neutrons captured in each of the detector volumes for 1.0 ppm, 2.0 ppm, and 5.0 ppm boron content, respectively, along with the neutrons captured inside the different volumes in the case where pure graphite is used for comparison purposes. The simulation was performed for 10,000 neutrons of three distinct energies (0.1 MeV, 1.0 MeV and 5.0 MeV), randomly generated inside the lead volume. Energy Lead Gas Water Graphite Moderator Steel Escape (MeV) (Efficiency) 0.1 27.72% 55.30% 6.76% 0.51% 5.63% 3.87% 0.10% G4 GRAPHITE 1.0 27.89% 53.70% 9.23% 0.72% 4.80% 3.50% 0.15% 5.0 27.68% 52.05% 10.29% 0.80% 4.96% 3.85% 0.37% 0.1 26.44% 54.45% 4.81% 5.26% 5.09% 3.69% 0.10% 1.0 ppm Boron 1.0 26.78% 51.48% 7.43% 5.82% 4.06% 3.77% 0.11% 5.0 26.25% 50.31% 8.46% 5.88% 4.83% 3.59% 0.62% 0.1 25.51% 53.20% 4.25% 7.03% 5.90% 3.65% 0.09% 2.0 ppm Boron 1.0 24.99% 50.62% 6.78% 8.58% 5.28% 3.55% 0.18% 5.0 25.05% 49.29% 7.61% 8.13% 5.48% 3.73% 0.64% 0.1 23.96% 51.50% 5.57% 10.63% 4.40% 3.81% 0.13% 5.0 ppm Boron 1.0 25.21% 49.95% 5.80% 10.52% 4.79% 3.50% 0.22% 5.0 24.92% 48.88% 6.36% 10.14% 5.53% 3.68% 0.44% Table 4.7: Percentage of neutrons captured in each of the detector volumes for different grades of graphite material (1.0 ppm, 2.0 ppm and 5.0 ppm).

A clear trend that can be observed in Table 4.7 and Figure 4.14 is that while neutron capture in graphite increases with the rise in boron content, the detection efficiency drops down. For example, for 1.0 MeV generated neutron in the case of 1.0 ppm boron content, 5.82% of the neutrons were captured in the graphite layer, while for pure graphite (G4 GRAPHITE) this number is only 0.72%. In the case of 5.0 ppm boron content the efficiency drops to 49.95% for 1.0 MeV generated neutrons because the number of neutrons captured in graphite rises to 10.52%. This is equivalent to only using 20 cm of water layer as reflector material (see Section 4.3.2) instead of graphite as the efficiency in this case is 48.20% for 1.0 MeV generated neutrons (see Table 4.2). It is clear that such level of impurity significantly impacts on the detection efficiency and should be disfavoured.

61 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

Figure 4.14 shows the efficiency of HALO-1kT detector for different boron contents along with the detection efficiency. Pure graphite (G4 GRAPHITE) is also considered for comparison purposes.

G4_GRAPHITE 1 ppm Boron 2 ppm Boron 5 ppm Boron 54 ) % (

y c

n 52 e i c i f f E

48 0 1 2 3 4 5 6 Energy (MeV)

Figure 4.14: Eﬃciency of HALO-1kT for 0.1 MeV, 1.0 MeV and 5.0 MeV generated neutrons in the following cases: pure graphite (G4 GRAPHITE) (red); 1.0 ppm (blue); 2.0 ppm (green); and 5.0 ppm (magenta) boron content. The HALO-1kT detector conﬁguration using 15 cm of graphite layer and 20 cm of water layer is considered.

4.4.2 Graphite Grades in the Market

Table 4.8 refers to the graphite properties as provided by some companies that I have contacted. One company (Graphitestore, INC.) could not provide the boron content present in the graphite material 4. The total volume of graphite required for HALO-1kT is 18 m3 (the lead volume is 4 × 4 × 5.5 m3 with a surface area of

4For conﬁdentiality purposes the prices of graphite provided by the company are not quoted in the thesis.

62 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

4(4 × 5.5) + 2(4 × 4) = 120 m2, so the graphite volume is 120 m2 × 0.15 m = 18m3 ).

Company Country Boron content Purity Density Graphitestore.com US - 99.9% 1.75 g/cm3 XRD Graphite Manufacturing Co., Ltd. China 0.17 ppm 99.9% 1.76 g/cm3 Olmec Advanced Material England 0.53 ppm (MCCA) 99.9% 1.74 g/cm3 SGL Group Germany 0.9 ppm 99.98% (ash 200 ppm, high purity) 1.83 g/cm3 SGL Group Germany 0.9 ppm 99.92 % (standard purity) 1.75 g/cm3 Table 4.8: Boron content as provided by diﬀerent graphite suppliers.

Energy Lead Gas Water Graphite Moderator Steel Escape (MeV) (Eﬃciency) 0.1 27.72% 55.30% 6.76% 0.51% 5.63% 3.87% 0.10% G4 GRAPHITE 1.0 27.89% 53.70% 9.23% 0.72% 4.80% 3.50% 0.15% 5.0 27.68% 52.05% 10.29% 0.80% 4.96% 3.85% 0.37% 0.1 25.80% 54.95% 5.92% 3.72% 5.96% 3.90% 0.09% XRD Graphite (0.17 ppm) 0.1 26.43% 52.93% 9.71% 1.55% 5.57% 3.43% 0.20% 5.0 26.25% 51.47% 10.28% 1.43% 5.69% 3.87% 0.49% 0.1 26.33% 54.73% 5.49% 3.62% 5.92% 3.53% 0.10% Olmec (0.53 ppm) 1.0 25.44% 52.15% 8.42% 4.22% 5.48% 3.72% 0.18% 5.0 25.19% 51.07% 9.81% 3.52% 5.65% 3.82% 0.46% 0.1 25.96% 54.45% 4.57% 4.60% 5.59% 3.89% 0.08% SGL (0.9 ppm) 1.0 26.09% 51.55% 7.62% 5.37% 5.38% 3.80% 0.19% 5.0 25.01% 50.80% 9.37% 5.49% 4.85% 3.65% 0.58% Table 4.9: Percentage of neutrons captured in each of the detector volumes for diﬀerent graphite grades as provided by commercial graphite suppliers.

Dedicated Geant4 simulations were carried out for the boron content in the graphite material as provided by the different companies along with the change in density value for each case. Table 4.9 shows the number of neutrons absorbed in each case listed in table 4.8 (0.17 ppm, 0.53 ppm and 0.9 ppm). Also added to the table is pure Graphite (G4 GRAPHITE) for comparison purposes. The results reveal the trend already observed in the previous case 4.4.1, with an increase of boron content in the graphite the detection efficiency decreases. Figure 4.15 summaries the efficiency of HALO-1kT for the different grades as provided by the different companies listed in Table 4.9. It is interesting to observe that there are many options available with < 1.0 ppm boron content along with reasonable prices from XRD Graphite and Olmec companies. The detection efficiencies in these cases are ∼ 52% for 1.0 MeV generated neutrons. Olmec Advanced Material supplies a high-quality graphite grade called MCCA with a claimed purity of 99.9%. Its density is 1.74 g/cm3 with a cost per m3

63 CHAPTER 4. MONTE CARLO SIMULATIONS FOR OPTIMIZATION OF THE HALO-1KT NEUTRON REFLECTOR DESIGN

G4_GRAPHITE XRD Graphite (0.17 ppm) 55 Olmec (0.53 ppm) SGL (0.9 ppm)

54 ) % (

y c

n 53 e i c i f f E

50 0 1 2 3 4 5 Energy (MeV)

Figure 4.15: Summary of the detection efficiencies for different grades of graphite As listed in Table 4.9: Pure graphite (G4 GRAPHITE) (red); XRD graphite (0.17 ppm) (blue); Olmec graphite (0.53 ppm) (green); and SGL graphite (0.9 ppm) (magenta). ranging between $15,067 to $18,667 USD for a total cost of $271,200 - $336,000 USD (considering 18 m3 of graphite in HALO-1kT). Their lower-quality grade is called MCCN. It is quoted as containing < 0.9% ash (about 9 times more impurities than MCCA graphite). However, the price for MCCN graphite was only about 12% less than that of MCCA graphite. We can conclude that, based on the studies performed here, and considering the cost-effectiveness of adding a 15 cm graphite layer in HALO-1kT, the MCCA graphite grade supplied by the Olmec company is the better option.

64 Chapter 5

Conclusions

Neutrino astronomy is a new and fast-developing field because core-collapse supernovae are not very well understood and the study of neutrinos produced within their collapsing core can reveal more about physics in the universe. There are several detector upgrades and new experimental projects in the works for the study of neutrinos coming from supernovae, and HALO-1kT is one of them. HALO-1kT and HALO are unique as they provide νe sensitivity and are low-maintenance, low-cost, long-lasting detectors that can wait for decades to detect supernovae signals. The main objective of this thesis was to evaluate the effectiveness of adding a neutron reflector material to HALO-1kT with the intention of optimizing its detection efficiency and, thus, its chances to detect a supernovae event. It also included finding a suitable neutron reflector material, define its geometry and evaluate the impact of the costs introduced with its implementation in HALO-1kT. Also, I evaluated the use of a water shield to suppress external neutron background as a complement to help recover neutrons that would otherwise escape the HALO-1kT fiducial volume. Due to the high absorption cross section of hydrogen present inside the water it works best as shielding material. It was found that graphite is an effective material to redirect escaping neutrons back into the detector lead volume. It also helps decreasing the neutrons

65 CHAPTER 5. CONCLUSIONS energy towards the thermal energy range necessary to be absorbed by the 3He proportional counters. Ultimately, I studied the effect of impurities (boron) contents in the graphite material on the HALO-1kT detection efficiency. Further work was to explore actual grades of graphite available in the market and find the optimal one that meets a balance between cost and benefit to the experiment. The Geant4 simulation software package was used to develop the studies presented in Chapter 4. This package contains the necessary tools to define the geometry of the detector. It also includes the cross sections for the interactions between several different particles and different detector materials. Among these materials, a pure graphite (called G4 GRAPHITE), as implemented in Geant4, was initially used in my studies (Sections 4.3.1 - 4.3.4). Impurities (boron) in the graphite material were included in the simulations in Section 4.4.

5.1 Summary of the Selection of the Reﬂector

Material

First, to compare different reflecting materials, analysis of the HALO-1kT detector efficiency without any reflecting material outside the lead volume was performed (Section 4.3.1). It was found that HALO-1kT was able to achieve better efficiency than HALO due to its larger fiducial volume and number of 3He proportional counters. Then, in order to evaluate the effectiveness of adding some neutron reflector material to recover otherwise escaping neutrons back into the lead volume, different materials and detector configurations were considered as shown in section 4.3. It was found that a 15 cm layer of graphite immediately sitting outside the lead volume was the best choice in terms of the efficiency and cost. For background shielding, water was used due to its high neutron absorption cross-section (σ = 0.30 b), accomplishing two main purpose : 1) Prevent neutrons from outside sources, such as the walls from the mountain surrounding the

66 CHAPTER 5. CONCLUSIONS

Gran Sasso laboratory, to enter the detector target volume and thus limit the background rate to acceptable levels (the targeted neutron background rate for HALO-1kT is < 1 Hz.) 2) As a complement to the graphite layer, it can help redirecting some of the escaping neutrons back into the lead volume. The combination of a 15 cm graphite layer as reﬂector sitting immediately outside the lead volume and a 20 cm water layer covering the whole detector as shielding material provided a complete picture of HALO-1kT (Figure 4.1) with an eﬃciency of 53.70% for 1.0 MeV neutrons randomly generated inside the target material (Table 4.6).

5.2 Summary of the Cost-Beneﬁt of Adding

Graphite as Reﬂector Material

The main problem in using graphite as reﬂector material is its boron content. Boron can eﬀectively absorb neutrons due its large neutron absorption cross section

(σa=0.005 b for thermal neutrons), and thus reduce the detector efficiency. To understand the response of the neutron detection efficiency to boron impurities, simulations were performed for three different levels of concentration of boron in the graphite material: 1.0 ppm, 2.0 ppm and 5.0 ppm (Section 4.4.1). As a result, 5.0 ppm boron impurity was not favourable because the efficiency for 1.0 MeV generated neutron, in this case, is 49.95% (Table 4.7). This was found to be equivalent of using only a 20 cm of water layer as reflector (in addition to shielding material), where the achieved neutron detection efficiency for 1.0 MeV neutron is 48.20% (Table 4.2), a cheaper alternative. Ultimately, for a more realistic selection of an acceptable graphite grade for HALO-1kT, I contacted some graphite supply companies to obtain information regarding the availability of different graphite grades (based on boron impurity) along with costs for the acquisition of these graphite materials. I then developed

67 CHAPTER 5. CONCLUSIONS

Geant4 simulations accounting for the different boron contents as informed by the vendors (Tables 4.8 and 4.9). The graphite material available from the Olmec company sees to show an optimal balance between cost and effectiveness, with a 0.53 ppm boron content translating into a 52.15% neutron detection efficiency and a total cost of $271,200 to $336,000 USD for total graphite volume of 18 m3 in the HALO-1kT configuration using a 15 cm layer of graphite and 20 cm layer of water.

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