Precise Measurement of the Photon Directional Asymmetry

in the ~np→ dγ Reaction

by

David Blyth

A Dissertation Presented in Partial Fulfillmentof the Requirement for the Degree

Doctor of Philosophy

Approved Apr 2017 by theGraduate Supervisory Committee:

Ricardo Alarcon, ChairKevin SchmidtJoseph ComfortBarry Ritchie

ARIZONA STATE UNIVERSITY

May 2017

ABSTRACT

This work presents analysis and results for the NPDGamma experiment, measuring

the spin-correlated photon directional asymmetry in the ~np → dγ radiative capture

of polarized, cold neutrons on a parahydrogen target. The parity-violating (PV) com-

ponent of this asymmetry Aγ,PV is unambiguously related to the ∆I = 1 component

of the hadronic weak interaction due to pion exchange. Measurements in the second

phase of NPDGamma were taken at the Oak Ridge National Laboratory (ORNL)

Spallation Neutron Source (SNS) from late 2012 to early 2014, and then again in the

first half of 2016 for an unprecedented level of statistics in order to obtain a mea-

surement that is precise with respect to theoretical predictions of Aγ,PV = O(10−8).

Theoretical and experimental background, description of the experimental apparatus,

analysis methods, and results for the high-statistics measurements are given.

i

DEDICATION

I dedicate this thesis to my parents, Barry and Joni, for their never-ending support.

Mahalo.

ii

ACKNOWLEDGMENTS

I would like to thank my research advisor, Ricardo Alarcon for constantly working

to provide excellent research opportunities for myself and others. Furthermore, his

guidance and perspective has been invaluable throughout my time at Arizona State

University. I would also like to thank the rest of my graduate committee, Joseph Com-

fort, Barry Ritchie, and Kevin Schmidt for their thorough and constructive feedback

during my prospectus and leading up to my defense.

I must give a broad, sweeping thank you to all who contributed to the NPDGamma

experiment for their incredible work on this experiment. The level of expertise and

passion exhibited by the senior physicists is inspiring, and I’m glad that I could come

along for the ride. I would especially like to thank Nadia Fomin, Jason Fry, Vince

Cianciolo, David Bowman, Seppo Penttila, Chad Gillis, and Latiful Kabir for the

positive impact that they made on my work.

Back here in the desert, I couldn’t have remained sane over the years without the

support of many friends and family members. I would especially like to thank my

sister Roberta for looking out for me and being someone I can look up to. Brittany,

Jason, Bob, Chris, and others, thank you for putting up with me and keeping my

spirits up. Also, many thanks to my labmates who have proven to be not only great

sounding boards, but also great friends over recent years: Lauren, Jason, Glenn, and

Eugene.

iii

TABLE OF CONTENTS

Page

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

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

CHAPTER

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 PARITY VIOLATION AS A PROBE OF FUNDAMENTAL PHYSICS . 3

2.1 NN Weak Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Experimental Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 The NPDGamma Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 THE NPDGAMMA EXPERIMENTAL APPARATUS . . . . . . . . . . . . . . . . . 17

3.1 ORNL Spallation Neutron Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1.1 Fundamental Neutron Physics Beamline . . . . . . . . . . . . . . . . . . . 20

3.2 Beam Choppers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Beam Monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.4 Supermirror Polarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.5 Magnetic Holding Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.6 Spin Rotator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.7 Gamma Detector Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.8 Data Acquisition Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.8.1 Hydrogen Target DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.8.2 n3He Delta-Sigma DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.9 lH2 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 ASYMMETRY MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 General Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Overview of Hydrogen Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

iv

CHAPTER Page

4.3 Background Subtraction Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.4 Overview of Background Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.5 Gamma Detector Phosphorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.6 30 Hz Beam Power Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.7 Dropped Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.8 Hydrogen DAQ Transient Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.9 Chopper Phasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5 MONTE-CARLO SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.1 Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6 DATA REDUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.1 Detector Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.2 Asymmetry Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.3 Beam Power Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.4 Pedestal Drift Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.5 Geometric Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.6 Grand χ2 Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7 DATA SELECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.1 Manual Batch Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

7.2 Normalization Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

7.3 Data Integrity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

7.4 Spin Rotator Sequencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.5 Beam Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.6 Analysis of Reduced Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

v

CHAPTER Page

8 SYSTEMATIC UNCERTAINTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

8.1 Geometric Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

8.2 Beam Power Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

9 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

9.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

9.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

APPENDIX

A GARDNER TRANSFORM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

B DERIVATION OF THE GRAND χ2 SOLUTION . . . . . . . . . . . . . . . . . . . . . . 123

C DIAGONALIZATION OF THE GRAND χ2 FIT . . . . . . . . . . . . . . . . . . . . . . 125

vi

LIST OF TABLES

Table Page

2.1 DDH Couplings and Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1 2016 Background Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.1 Beam Power Modulation Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.1 Hydrogen Batch Cut Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.2 Background Batch Cut Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

8.1 Systematic Uncertainties From False Asymmetries . . . . . . . . . . . . . . . . . . . . 110

8.2 Multiplicative Factors and Systematic Uncertainties . . . . . . . . . . . . . . . . . . 110

vii

LIST OF FIGURES

Figure Page

2.1 DDH Meson Exchange Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 EFT Contact Terms and Pion Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Benchmark Basis for Experimental Constraints . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 NPDGamma Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Neutron-Proton Continuum and Bound States . . . . . . . . . . . . . . . . . . . . . . . 15

3.1 NPDGamma Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 SNS Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Proton Beam Accumulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Supermirror Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 FnPB Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.6 Chopped Spectrum at Upstream Beam Monitor . . . . . . . . . . . . . . . . . . . . . . 25

3.7 Beam Monitor Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.8 Polarizing Bender . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.9 RF Spin Rotator Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.10 Spin Rotator Sequencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.11 Gamma Detector Array Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.12 Detector With lH2 Cryostat/Target and SR Coil Model . . . . . . . . . . . . . . . 38

3.13 Target Vessel and Ortho/Para Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.1 Gamma Detector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 8-Pulse Gamma Detector Readout Sequence . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.3 Prompt vs. Delayed Energy Discrepancy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4 Dedicated Target Decay Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.5 Resolved Prompt vs. Delayed Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.6 Variation in Detector Phosphorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

viii

Figure Page

4.7 30 Hz Signal Phase Portrait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.8 Accelerator Dropped Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.9 Chopper Phasing Oscilloscope View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.1 28Al De-excitation Gamma Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2 Prompt Energy Seen in CsI Array From Capture on Aluminum . . . . . . . 59

5.3 Verification of Neutron Cross-Sections in Al . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.4 MC Simulation Geometry Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.5 Energy Seen by CsI Array vs. Capture Position . . . . . . . . . . . . . . . . . . . . . . 62

5.6 Energy Seen by CsI Array vs. Capture Position with 100% Ortho-

hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.7 Energy Seen by CsI Array vs. Capture Position with 100% Parahydrogen 64

6.1 Θ for Hydrogen Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.2 Θ for 2016 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.3 Symmetric Component Fourier Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.4 Asymmetric Component Fourier Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.5 Analyzer Function for Hydrogen Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.6 Analyzer Function for 2016 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.7 ζ and Θ− ·X(τ) for 2016 Measurements in Fourier Space . . . . . . . . . . . . . 78

6.8 ζ for Hydrogen Measurements in Fourier Space . . . . . . . . . . . . . . . . . . . . . . . 79

6.9 α ∗ γ Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.10 Pedestal Drift Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.11 An Example of Geometric Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.1 Normalization Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.2 η Normalization Integral Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7.3 Threshold on Beam Monitor Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

ix

Figure Page

7.4 Conditional Beam Monitor Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

7.5 Threshold on SR RMS Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.6 Beam Asymmetry Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.7 Pair Asymmetry Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

7.8 Diagonalized Grand Fit χ2 Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

8.1 Thermal Equilibrium Parahydrogen Fraction . . . . . . . . . . . . . . . . . . . . . . . . . 105

8.2 Chlorine Asymmetry Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

8.3 Pair Asymmetry vs. M1 Asymmetry Regression . . . . . . . . . . . . . . . . . . . . . . 108

8.4 Fit of Composite Target Geometric Factors to Regression Slopes . . . . . . 109

9.1 DDH Parameter Space Constraints Including This Work . . . . . . . . . . . . . . 112

9.2 h1π From Experiment and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

x

Chapter 1

INTRODUCTION

This work focuses on the measurement and analysis of the spin-correlated photon

directional asymmetry in the ~np → dγ radiative capture of polarized, cold neutrons

on a liquid parahydrogen target in the NPDGamma experiment. The parity violating

component of this asymmetry, denoted as Aγ,PV , can be unambiguously related to

the strength of the ∆I = 1 hadronic weak interaction due to pion exchange, and is

primarily sensitive to neutral weak currents. Since the first measurements in the work

of Cavaignac et al. (1977), measurement of the parity-violating asymmetry has gone

without an improvement in precision for four decades. Their work placed an upper

limit of

Aγ,PV (~np) = (0.6± 2.1)× 10−7,

and measurements by the NPDGamma collaboration (Gericke et al. 2011) at Los

Alamos National Laboratory yielded

Aγ,PV = (−1.2± 2.1± 0.2)× 10−7

for the results of the first phase of the experiment. The goal of the second phase is

to reach an uncertainty in Aγ,PV of ∼ 1× 10−8 from measurements taken at the Oak

Ridge National Laboratory spallation neutron source in order to obtain a level of pre-

cision that begins to challenge theoretical predictions. The NPDGamma experiment

recently concluded measurements, and this work focuses on the analysis of the data.

In Chapter 2, a theoretical and experimental background will be developed to

motivate and support the following work, including a conceptual description of the

1

experiment. The experimental apparatus will be described in Chapter 3, as a neces-

sary foundation for discussing measurements and data reduction. Chapter 4 describes

measurements taken and strategies for determining Aγ in the presence of background

signals. The GEANT4-based Monte-Carlo created for the analysis in this work is

described in Chapter 5. Chapters 6 and 7 go into detail about employed methods of

reducing and selecting data into a determination of Aγ while minimizing systematic

effects. Chapter 8 describes the determination of those systematic effects. Finally, a

conclusion is given in Chapter 9 along with results of the described analysis and an

outlook for the impact of those results on the physics community.

2

Chapter 2

PARITY VIOLATION AS A PROBE OF FUNDAMENTAL PHYSICS

Lee and Yang (1956) hypothesized that, unlike the strong and electromagnetic in-

teractions, weak interactions may not conserve the parity of a system, where parity

refers to the symmetry (or antisymmetry) of the state under inversion of all spatial

coordinates. This hypothesis was inspired (at least in part) by the so-called τ − θ

puzzle, which was the observation of the precisely identical masses of two apparently

different particles. The two particles were deduced to be different due to considera-

tions of angular momentum and conservation of parity in their decays. In light of this

puzzle, Lee and Yang examined existing experimental evidence to see if parity non-

conservation could be ruled out as a possibility in the weak interaction, and found

that such a violation could not. Their 1956 paper proposed that experimentalists

should actively seek out proof of parity non-conservation in weak interactions. (Par-

ity non-conservation is referred to throughout this thesis as parity violation, where PV

and PC are taken to mean “parity-violating” and “parity-conserving”, respectively.)

Months later, Wu et al. (1957) found evidence of parity violation in the decays of

60Co.

The standard model (SM) of particle physics describes interactions of fundamen-

tal quarks and leptons arising from a mix of local (gauge) symmetry requirements

within the Lagrangian. In group-theoretical terms, the symmetries are described as

SU(3) × SU(2)L × U(1), with representations of the groups corresponding respec-

tively to the strong interaction color charge, weak isospin, and weak hypercharge.

The SU(3) symmetry applies only to quark fields giving rise to gluon interactions,

while the subscript on SU(2)L indicates that the symmetry only applies to left-handed

3

fermions. Because angular momentum is an axial vector, a parity transformation ef-

fectively maps left- and right-handed particles onto each other, and it is therefore the

explicit handedness of the SU(2) symmetry that gives rise to a maximal violation of

parity conservation by the associated vector bosons. Of course, nature does not allow

such an elegant symmetry of physics to go unspoiled, and within the SM we find

that the Higgs field, which exhibits a finite vacuum expectation value, dynamically

breaks the SU(2)L×U(1) symmetry, ultimately yielding a pair of massive, electrically

charged W± bosons, the neutral Z boson, and the neutral, massless photon from the

electroweak sector.

The SU(3) theory of quantum chromodynamics (QCD) at low energies gives rise

to the confinement of quarks in color singlets, i.e. hadrons. Confinement is believed

to arise from the effective anti-screening of color charge due to gluon-gluon interac-

tions. This anti-screening also makes the ground state of QCD unreachable by the

standard method of finding solutions to the interacting theory by treating interac-

tions as a perturbation of the free, non-interacting theory. Therefore, connecting the

high-energy theory of QCD to the reality of the structure of every-day matter is very

difficult. Limited contact has been seen by the success of lattice QCD, where numer-

ical calculations are made in discrete spacetime (i.e. on the lattice), in such areas

as predicting the masses of hadrons. Though weak interactions between fermions of

the SM are quite well understood, in hadronic systems at low energies they become

inextricable from non-perturbative strong interactions.

Parity violation, then, becomes a signature for isolating weak interactions in

hadronic systems. Constructing pseudoscalar products of cartesian vectors, such

as the ~σ · ~r beta emission asymmetry observed by Wu et al., targets interferences

between strong (or electromagnetic) and weak amplitudes. However, significant dif-

ficulties arise in observing hadronic parity violation since the natural scale of the

4

strong/weak interference is GFF2π ∼ 10−7 (Haxton and Holstein 2013). Nevertheless,

hadronic PV observables provide the opportunity to probe non-perturbative QCD,

and measurements of PV effects can serve as inputs to effective Lagrangians and help

to provide model-independent predictions.

2.1 NN Weak Interaction

The theoretical interpretation of observed parity violation in non-leptonic flavor-

changing decays of mesons and baryons has revealed puzzles that remain unresolved.

For example, anomalously large PV asymmetries in radiative decays of hyperons, as

well as the well-known ∆I = 1/2 rule (a phenomenological preference of the I = 1/2

over I = 3/2 isospin channels) in strangeness-changing (∆S = 1) decays, remain

unexplained by SM symmetries (Ramsey-Musolf and Page 2006). Whether such

anomalies are particular to strange quark dynamics, or even perhaps new physics

which fail to live up to the symmetries of the SM, is still unknown. Suppressing the

role of the strange quark by further exploration of hadronic weak interactions (HWIs)

in strangeness-conserving (∆S = 0) processes may provide additional insight. The

most accessible approach is to study nucleon-nucleon (NN) and nuclear interactions.

In nuclei, significant enhancement of PV effects can be observed. Treating the HWI

as a perturbation to the strong interaction, near degeneracies in nuclear states with

opposite parity can give rise to contributions of the form

� =〈Ψ′|HW |Ψ〉

∆E. (2.1)

However, observations of parity violation in complex nuclear systems that exhibit such

near degeneracies are theoretically difficult to interpret (with few exceptions), being

significantly affected by nuclear structure effects. To minimize theoretical ambiguity,

observables in two-body or at least few-body systems are sought out despite the

5

π, ρ, ω

PC(Strong)

PV(Weak)

N

N N

NDDH

Figure 2.1: DDH meson exchange model - Desplanques et al. (1980) modeled thenucleon-nucleon hadronic weak interaction by exchange of the three lightest availablemesons, the π, ρ, and ω. At one nucleon vertex, a strong (PC) interaction emits ameson which is absorbed by the second nucleon in a weak (PV) interaction.

experimental challenges.

In 1980, Desplanques, Donoghue, and Holstein (DDH) developed a framework

for analyzing PV NN observables (Desplanques et al.) which remains the default

benchmark. DDH provide a quark-model based solution where the HWI is assumed

to be mediated by the exchange of a meson (Figure 2.1). The three lightest available

mesons are included in the model, and the model is parameterized by a combination

of the exchanged mesons and the isospin change, leading to a total of six couplings,

h1π, h0,1,2ρ , h

0,1ω ,

where the subscript indicates the exchanged meson and the superscript indicates the

change in isospin. The “best value” predictions and reasonable ranges provided by

DDH are listed in Table 2.1, along with slightly newer predictions by Dubovik and

Zenkin (1986); Feldman et al. (1991). The reasonable ranges are intended to cover

theoretical uncertainties, but are unfortunately quite large. Because PV observables

from the exchange of neutral pseudoscalar mesons would also be CP violating (Barton

1961), such mesons are excluded from consideration. A seventh coupling, termed h1′ρ ,

6

Coupling DDH range DDH ”best” DZ FCDH

h1π 0.0→ 11 4.6 1.1 2.7

h0ρ −31→ 11 -11 -8.4 -3.8

h1ρ −0.4→ 0.0 -0.2 0.4 -0.4

h2ρ −11→ −7.6 -9.5 -6.8 -6.8

h0ω −10→ 5.7 -1.9 -3.8 -4.9

h1ω −1.9→ −0.8 -1.1 -2.3 -2.3

Table 2.1: DDH couplings and predictions - Listed here are the DDH meson-nucleon coupling parameters along with predicted values. DDH give reasonable rangesfor each parameter as well as a “best value”, also known as a “best guess”. Addi-tionally, slightly more recent estimates from Dubovik and Zenkin (DZ) and Feldmanet al. (FCDH) are listed.

N

N N

N

π

N

N N

Na) b)

Figure 2.2: EFT contact terms and pion exchange - In a pionful low-energyEFT, a) the dynamics of quarks and heavy mesons are absorbed into the contactterms, and b) pions are included as dynamical degrees of freedom.

exists in the original DDH work; however that coupling has since been determined

to be negligible (Holstein 1981). (Notably, however, Phillips et al. argue that a 1/Nc

QCD expansion indicates that h1′ρ should be no more suppressed than h

1π.)

In more recent years, developments in PV effective field theories (EFTs) have

allowed a more systematic approach to the analysis of low-energy measurements of

NN parity violation (Zhu et al. 2005; Ramsey-Musolf and Page 2006; Liu 2007).

7

EFT Lagrangians take advantage of the separation of scales at low energies and are

expressed as expansions in the ratio of scales. A complete set of terms that obey

the symmetries of the underlying theories make up the effective theory, where the

coupling constants that absorb the dynamics of high-energy scales can be determined

phenomenologically. Where the dynamics of the pion can be effectively integrated out,

a set of local contact terms remain in PV EFTs as illustrated by the left-hand diagram

in Figure 2.2. In systems where the dynamics of the pion are important, “hybrid”

EFTs obtain an additional degree of freedom with an explicit dynamical pion, as

illustrated by the right-hand diagram in Figure 2.2; such a degree of freedom also

makes it possible to systematically address two-pion exchange. The “hybrid” (pionful)

formulations then express the NN PV observables in terms of five contact couplings

equivalent to the dimensionless Danilov (1965; 1971) parameters that correspond to

the possible S − P transitions at low energy, as well as an additional parameter C̃π6

for the dynamical pion, which is proportional to the DDH h1π coupling.

2.2 Experimental Status

Starting with the work of Tanner (1957) in search of parity violation in (p, α) reso-

nances of 19F, many have followed the findings of Wu et al. with PV searches in other

systems. Though the Tanner experiment lacked the sensitivity to observe PV effects,

a number of experiments since have measured non-zero effects, and their results have

begun to paint a picture of the HWI. In this section, a number of experiments with

theoretical analyses that are considered to be on firm ground will be briefly reviewed

within the framework of DDH, beginning with an overview of past measurements,

and followed by a summary considering the combined influence of their results on the

DDH parameter space.

PV observables from strict two-body interactions are of particular interest. Two-

8

body PV observables are very elusive, however, as their natural size tends to be

O(10−7). Nevertheless, non-zero effects have been observed, namely in the analyz-

ing power for scattering of longitudinally-polarized protons on an unpolarized target,

AL(~pp). AL(~pp) has been measured at a number of energies (Eversheim et al. 1991;

Nagle et al. 1978; Balzer et al. 1980; Berdoz et al. 2003), yielding complementary con-

straints within the DDH model. The measurements at different energies are analyzed

together, placing key constraints on linear combinations of h0,1,2ρ and h0,1ω . (The ~pp

results have been summarized by Haxton and Holstein, which also incorporated most

of the other measurements mentioned in this section.)

Additionally, a pair of measurements of the circular polarization of photons emit-

ted in the np → dγ reaction, Pγ(np), was made at the Leningrad WWR-M reactor

facility (Lobashov et al. 1972; Knyaz’kov et al. 1984). However, the first was deter-

mined to be in error, while the second only placed an upper limit on Pγ(n) of O(10−7).

Measurements of Pγ(np) are primarily sensitive to h0,2ρ .

Finally, the PV directional asymmetry of photons emitted in the ~np → dγ reac-

tion, Aγ,PV (~np), has been measured in two experiments conducted several decades

apart. The Aγ,PV (~np) observable is dominated by the long-range coupling h1π. The

first measurement of Aγ,PV (~np) was made at the Institut Laue-Langevin (ILL) reactor

by Cavaignac et al. (1977). The second measurement of Aγ,PV (~np) was made by the

NPDGamma collaboration (Gericke et al. 2011) at the Los Alamos Neutron Science

Center (LANSCE) spallation source; this latter work was the precursor to measure-

ments at the Oak Ridge National Lab (ORNL) spallation neutron source (SNS) upon

which this work is based. The results of these two experiments place the upper limits

Aγ,PV (~np)|ILL = (0.6± 2.1)× 10−7,

Aγ,PV (~np)|LANL = (−1.2± 2.1± 0.2)× 10−7.(2.2)

The next section will cover the Aγ,PV measurement in greater detail.

9

Due to the difficulty in detecting PV observables in the two-body systems, larger

systems have been studied, some of which are considered to have reliable theoreti-

cal interpretation. For example, the analyzing power for the scattering of polarized

protons from an alpha target, AL(~pα), has been measured by Lang et al. (1985) at

46 MeV with a non-zero result. While uncertainties in the theoretical analysis of such

a measurement exist, that analysis is nonetheless considered to be on firm ground,

and provides an important constraint on a linear combination of h1π, h0,1ρ , and h

0ω.

Additionally, measurements involving flourine isotopes have been interpreted in the

DDH model with theoretical uncertainties that are considered to be minimal, due to

the ability to measure the necessary nuclear matrix elements from beta decay rates in

isobaric analog nuclei. Searches for circular polarization in photons emitted from the

decay of an excited state of 18F, Pγ(18F), were undertaken by several groups (Barnes

et al. 1978; Ahrens et al. 1982; Bini et al. 1985; Page et al. 1987). Measurements

of this kind are sensitive to isovector couplings (primarily h1π) and are therefore very

interesting results. The measurements, however, while having reached significant sen-

sitivities, did not observe parity violation. Finally, parity violation has been observed

in the directional asymmetry in the emission of photons from an excited state of 19F,

Aγ(19F), by two groups (Adelberger et al. 1983; Elsener et al. 1987). The Aγ(

19F )

observable is sensitive to couplings similar to those of AL(~pα) measurements.

Figure 2.3 shows the effect of the most constraining classes of experiments on a

convenient basis of isoscalar and isovector couplings chosen by Haxton and Wieman

(2001). The one-standard-deviation (1σ) constraints are shown with slight expansion

due to allowing uncorrelated variations of h1ρ, h2ρ, h

0ω, and h

1ω within the DDH reason-

able ranges, similar to the approach taken by Haxton and Wieman (2001); Haxton

and Holstein (2013). Additionally, a relatively recent lattice QCD result is shown.

The result by Wasem (2012) shows uncertainties that are a combination of statistical

10

1ω-0.18h

1ρ-0.12h

1πh

0.2− 0 0.2 0.4 0.6 0.8 1 1.2 1.46−10×

)0 ω

+0.

7h0 ρ

-(h

0.5−

0

0.5

1

1.5

2

2.5

3

3.56−10×

)αp(LAp)p(LAF)18(γPF)19(γA

LQCD (Wasem)DDHDZFCDH

Figure 2.3: Benchmark basis for experimental constraints - Shown here is aplot in the style of Haxton and Wieman; Haxton and Holstein showing the 1σ con-straints placed by several classes of experiments considered to be on firm theoreticalground on a convenient DDH parameter basis. Additionally, theoretical predictionsfrom Table 2.1 are shown as points, and a relatively recent lattice QCD result is givenin dashed lines.

11

and systematic. Wasem does not include renormalization of the bare PV operators,

EFT extrapolation to a physical pion mass (mπ ∼ 389 MeV is used), or disconnected

diagrams. However, the author expects systematic errors that are small compared

to the statistical uncertainties. There is disagreement in the theoretical literature

about whether the isovector couplings, particularly h1π, should be suppressed. The

Pγ(18F ) constraint shown in Figure 2.3 shows an upper limit that some consider dif-

ficult to accommodate theoretically. At the same time, recent work by Phillips et al.

(2015), for example, argues that a 1/Nc expansion of QCD indicates a suppressed

h1π . (0.8± 0.3)× 10−7, which tends to agree with the Pγ(18F) results. On the other

hand, Lobov (2002) give an estimate of h1π = 3.4× 10−7 from QCD sum rules that is

relatively intermediate with respect to predictions by Desplanques et al. and Phillips

et al..

Other experimental efforts require some consideration as well. As far as current

efforts go, the n3He experiment has recently finished taking data at the ORNL SNS,

and analysis is ongoing. The n3He experiment measures the PV directional asym-

metry of outgoing particles in the reaction ~n +3 He → p + t + K.E. (Gericke 2016).

Additionally, a recent upper bound on PV neutron spin rotation (NSR) in 4He has

been set by Snow et al. (2011) at NIST, and the group intends to improve the ex-

perimental sensitivity in the near future. Both experiments provide opportunities

to constrain the HWI through coupling combinations independent of those shown in

Figure 2.3. Notably, PV nuclear anapole moment measurements of 133Cs (Wood et al.

1997) and 205Tl (Vetter et al. 1995) are in stark disagreement with the bounds found

by the experiments shown in Figure 2.3, as well as with each other. Those results

have not been included here due to their difficult theoretical interpretation.

12

n p

θγ

d

n p

θγ

d

Figure 2.4: NPDGamma asymmetry - An effective parity transformation ismade by alternating the spin of the neutron beam. For θγ the angle between theneutron spin and the emitted photon momentum, the differential cross section sees aspin-correlated modulation of magnitude Aγ,PV cos θγ.

2.3 The NPDGamma Experiment

This thesis is particularly concerned with the determination of the Aγ(~np) asym-

metry (henceforth simply Aγ), by analysis of recent data from the NPDGamma ex-

periment. Aγ (illustrated in Figure 2.4) is taken to be a general spin-correlated

asymmetry in the direction of photons emitted from ~np capture. For clarity, Aγ,PV

and Aγ,PC are used to denote the PV and PC components of the asymmetry. The dif-

ferential cross section for the emission of a photon into solid angle dΩ can be written

as

dσ

dΩ∝ 1 + Aγ,PV k̂γ · σ̂n + Aγ,PC k̂γ ·

(σ̂n × k̂n

), (2.3)

where the PV part comes from a pseudoscalar combination of cartesian vectors, and

the PC part comes from a scalar combination. Equation 2.3 serves to explicitly

define the two asymmetries. The goal of the NPDGamma experiment is to measure

Aγ,PV down to a sensitivity of 1 × 10−8, representing an order of magnitude better

13

sensitivity than has been achieved. Though measurement of parity violation is the

primary motivation, the PC component will also be extracted. To isolate the physics

asymmetries and suppress instrumental effects, the asymmetries are extracted by

rapidly alternating the spin orientation of a polarized neutron beam incident on a

proton target. The photons emitted from the reaction are detected and their intensity-

spin correlation as a function of dΩ is measured. From that intensity distribution,

the orthogonal PV and PC correlations are extracted. In practice, the finite detector

size must be incorporated, and false asymmetries must be carefully addressed. The

experimental setup and the data reduction approach used in this work are described

in chapters 3 and 6, respectively.

In order to understand the relationship of Aγ,PV to the meson exchange picture,

let us work from experiment to theory. Considering isospin as a valid symmetry,

the neutron and proton are different states of the same particle. From Fermi-Dirac

statistics, the deuteron must have a wavefunction that is antisymmetric under nucleon

exchange. Furthermore, the deuteron is an isospin singlet since pp and nn bound

systems are not found. Particle exchange symmetry, then, allows only S states in a

spin triplet configuration, and P states in a spin singlet configuration. Because the

3S1, I = 0 state is energetically favorable, the spin triplet state is the ground state

of the deuteron. The parity of the ground state, being determined entirely by the

orbital angular momentum in the NN system, is (−1)0 = +1, which is even parity.

Treating the weak interaction at low energies as a perturbation to the strong

interaction, as is naturally done by assuming definite parity of the ground state, an

admixture of opposite-parity (irregular) P states into the (regular) ground state arises.

Admixtures also arise for the S-wave scattering states, as shown in Figure 2.5 (in the

style of Byrne 2013). In the figure, unhindered electric and magnetic matrix elements

are represented by arrows, where the regular transition occurs from the 1S0 partial

14

1S0 I=1 3P0 I=11P1 I=03P1 I=13S1 I=0

3S1 I=0 3P1 I=1 1P1 I=0

m(0)e(1)

e(0)

Figure 2.5: Neutron-proton continuum and bound states - HWIs contributeadmixture of opposite-parity states onto low-energy S states. The unhindered tran-sitions are shown with arrows with e(J) and m(J) indicating electric and magnetictransitions starting from a J total spin state.

wave. According to Gari and Schlitter (1975), the PV asymmetry comes about from

interference between the m(0) regular transition and the e(1) irregular transitions:

Aγ,PV = −√

2e(1)

m(0). (2.4)

(Alternatively, circular polarization in photons emitted from unpolarized neutron

capture comes from interference between m(0) and e(0) transitions.) Thus, we can

see that Aγ,PV is sensitive to admixtures of3P1 states with I = 1 onto the scattering

and bound 3S1, I = 0 states, meaning that Aγ,PV is sensitive to ∆I = 1 weak

interactions.

If we consider the low-energy charged weak Hamiltonian in current-current form,

we have

H cw =GF√

2J+µ J

µ+ + h.c., (2.5)

where

J+µ = cos θC ūγµ (1 + γ5) d+ sin(θC)ūγµ (1 + γ5) s. (2.6)

15

For ∆S = 0 interactions, a ∆I = 0, 2 component appears multiplied by cos2 θC ,

while a ∆I = 1 component appears multiplied by sin2 θC . Thus, the Cabibbo angle

suppresses the charged current in the Aγ,PV observable. The neutral weak current

gives no such suppression, so the NPDGamma asymmetry is expected to be primarily

sensitive to neutral currents. The ∆I = 0 admixture dependence also indicates that

the asymmetry is dominated by the exchange of long-range pions. The calculated

relationship between the NPDGamma asymmetry and the DDH couplings is (Gericke

et al. 2011)

Aγ,PV = −0.1069h1π − 0.0014h1ρ + 0.0044h1ω, (2.7)

confirming that Aγ,PV is dominated by pion exchange.

16

Chapter 3

THE NPDGAMMA EXPERIMENTAL APPARATUS

The NPDGamma experiment consists of a dedicated apparatus operated for a

high-statistics result at the ORNL SNS. As the most intense pulsed-mode spallation

neutron source, the ORNL SNS delivers cold neutrons on the Fundamental neutron

Physics Beamline (FnPB) at a rate high enough to reach or exceed the goal of an

unprecedented 10−8 measurement of the σ̂n · k̂γ parity-violating correlation in the

~np→ dγ reaction: a measurement that has been heavily statistics limited for decades.

The FnPB was designed to maximize cold neutron fluence and remove line-of-sight

between the experiment room and the neutron moderator. By removing line-of-sight,

fast background radiation is minimized (Fomin et al. 2014). The apparatus, illustrated

in Figure 3.1, polarizes the incoming neutron pulses and alternatingly flips their spin

on a pulse-by-pulse basis. This alternating spin sequence allows the measurement

Spin rotatorPolarizerFrom spallationsource and LH2moderator

n p d

Chopper1

Chopper2 Shutter

Guide

Lead shieldingParahydrogentarget

Ortho/paramonitor

Beam monitor

"Racetrack" holding field coils

CsI crystal detectors

ŷ

ẑ

Figure 3.1: NPDGamma experimental apparatus - This figure gives a cartoonoverview of the components of the NPDGamma apparatus. The green bar illustratesthe neutron beam and intensity as it travels from left to right in the ẑ direction. Thespins are polarized up in the ŷ direction, leaving the x̂ direction at beam left into thepage.

17

to be insensitive to detector gain, gain drifts, and slow background variations. The

majority of the neutrons capture on a liquid parahydrogen target, and the emitted

gammas are detected by an array of 48 thallium-doped CsI scintillation detectors.

These detectors are arranged symmetrically about the beam axis, and cover a solid

angle of approximately 3π sr. The symmetry of the detectors allows the cancellation

of beam power fluctuations that would otherwise complicate error analysis. The

asymmetry of the target is determined by the correlation of power deposited into the

CsI detectors with the spin orientation.

The apparatus was operated for hydrogen target measurements from 2012-2014. In

2015, it was determined that additional measurements of backgrounds were required,

and the apparatus was reinstalled for measurements in the first half of 2016. In

this thesis, these two distinct instances of the experiment are typically referred to as

hydrogen measurements and 2016 background measurements, respectively.

3.1 ORNL Spallation Neutron Source

The SNS is a pulsed neutron source that uses a proton beam to release neutrons

from Hg nuclei in a process known as spallation. Of critical importance in spallation

sources is the production of large fluxes of cold, thermal, and epithermal neutrons

while maximizing the ability to use neutron Time-Of-Flight (TOF) information to

separate energies. The spallation process is driven by 1 GeV protons impacting the

mercury target, producing ∼ 30 fast neutrons per incident proton. The fast neutrons

are then moderated (slowed) by a hydrogenous medium with a particular composition

and temperature (depending on the beamline) to energies of order meV for neutron

scattering applications and fundamental neutron studies.

The proton beam (Figure 3.2) starts with H− ions selected from a plasma (Stockli

et al. 2010), which are then injected into a 335 m-long linac at 402.5 MHz. The protons

18

from linac

accumulation ring

to spallation target

mer

ge

Figure 3.2: SNS accelerator - The SNS proton accelerator consists of a 1 GeV linacwhich produces bunches that “wrap” around an accumulation ring. The accumulatedproton bunch is then extracted to the mercury spallation target. The above figure isa cartoon of the physical layout from an overhead perspective.

are then accelerated to 1 GeV. A chopper selects a 695 ns macro pulse of protons at

1.059 MHz (Jones 2016). The chopper configuration is designed to fascilitate the

“wrapping” of macro pulses around an accumulator ring. The negative charge of the

accelerated bunch allows a dipole magnet to merge the incoming linac pulse into the

positively charged stored bunch as shown in Figure 3.3. At the point that the two

bunches merge, the protons pass through a carbon foil that strips the electrons from

the H− ion. The accumulator ring stores and shapes the proton bunch, retains the

695 ns envelope, and accumulates protons over 1060 macro pulses (∼1 ms fill time).

The ring is filled and subsequently extracted into a spallation target at 60 Hz.

The spallation target is ≈1.4 m3 of mercury circulating in a loop at ≈325 kg s−1 in

a stainless steel vessel (Fomin et al. 2014). The flowing mercury along with flowing

water in an outer vessel cools the target. The cooling is necessary because & 850 kW

of sustained power is deposited into the mercury target by the accelerated protons.

19

stored

bunch

H - bunch

merged bunch

dipole magnet

foil

Figure 3.3: Proton beam accumulation - The H− bunch from the SNS linacmerges with the accumulation ring using a dipole magnet and a carbon stripping foil.

An array of moderators sit above and below the spallation target. These moderators

are viewed by the neutron beamlines.

3.1.1 Fundamental Neutron Physics Beamline

The FnPB views the bottom downstream 20 K supercritical parahydrogen neutron

moderator through a 10 cm (width) by 12 cm (height) curved window. The moderator

has an average thickness of 55 mm, and is surrounded by a 20 mm light-water premod-

erator coupled to a beryllium reflector, which serves to contain neutrons and increase

the flux into the beamline at the expense of a longer time response. Parahydrogen

moderators are known as non-thermalizing leakage moderators because their moderat-

ing properties and cross section tend to disappear below energies where the 14.5 meV

para-ortho upconversion is the primary energy loss mechanism. Below ≈50 meV, nu-

clear spin coherence begins to remove the upconversion moderating mechanism (Kai

et al. 2004). This type of moderator has the advantage of producing high peak intensi-

ties for cold neutrons. While the moderator is designed to maintain reasonable timing

20

characteristics, the sharp bunches delivered to the spallation target are expanded out

to tens of microseconds by the time the cold neutrons escape the moderator (Iverson

2016).

Viewing the moderator is a cold neutron guide that serves multiple purposes

beyond transporting cold neutrons to the experiment. The guide is 10 cm (width)

by 12 cm (height) rectangular, consisting of neutron optics which have the ability to

totally reflect if the transferred neutron momentum is below a threshold. The guide

is also curved, with a radius and length suited for removing line of sight and higher

energy neutrons / gamma radiation.

To understand the neutron optics, for unbound neutrons the time-independent

Schrödinger equation can be rewritten as a Helmholtz equation,

∇2Ψ(~r) + k2(~r)Ψ(~r) = 0. (3.1)

A solution to this equation is

k = k0n(~r) (3.2)

where k0 is the wave number of the neutron in free space, and

n(~r) =√

1− V (~r)/E, (3.3)

as discussed in depth in Byrne (2013). For materials presenting positive bulk nuclear

potentials to low-energy neutrons, refractive indices less than that of free space are

typically seen, providing the opportunity for total external reflection of neutrons: a

useful feature for guiding the particles.

For neutron wavelengths long compared to the interaction between neutron and

nuclei within a medium, the neutron wavefunction satisfies equation 3.1 with V (~r) =

VF , a uniform nuclear potential derived from the Fermi contact pseudopotential given

by

VF =2π~2Nbmn

, (3.4)

21

n1n2

substrate

Figure 3.4: Supermirror (SM) coating - A SM consists of a multilayer coatingof alternating refractive indices that decrease in thickness deeper into the coating.This produces a superposition of Bragg reflection peaks which are further broadenedby random variation in the layer thicknesses.

where N is the mean number of scattering nuclei per unit volume, b is the mean

scattering length observed under the assumption of an infinitely massive nucleus, and

mn is the rest mass of the neutron. A neutron in the zero-energy limit, as is applicable

for a cold neutron source, behaves as if interacting with a continuous medium. Since

scattering lengths are known experimentally to be typically positive, refractive indices

will usually be less than one. The result is that a cold neutron incident upon such a

medium at glancing angles less than

θc = sin−1(√

VF/E)

'√VF/E

(3.5)

will be totally externally reflected.

For natural nickel, a particularly good cold neutron reflector,

θc,Ni = 1.73 mrad Å−1 × λ0,

22

where λ0 is the free neutron wavelength (Fomin et al. 2014). In order to accept a

larger phase space, the neutron guide improves upon this benchmark limit of total

external reflection by using multiple layers of alternating materials on its surface pro-

ducing carefully-designed Bragg scattering. The layers are of varying thickness in an

arrangement known as a supermirror (SM), designed to overlap multiple Bragg peaks

that are themselves broadened by randomization of the layer thickness, effectively

increasing θc (Figure 3.4). SMs are characterized by their effective θc in a ratio to

that of single-layer natural nickel in a value known as m. The FnPB uses SM coatings

within the guides that have m values up to 3.8.

3.2 Beam Choppers

The NPDGamma experiment operates by alternating the spin orientation of the

pulsed neutron beam on a pulse-by-pulse basis. In order to do so, the experiment

uses an RF spin rotator (section 3.6), which is configured to efficiently flip the spin

of the pulse for a single neutron wavelength at any given instant in time. As such,

the neutron beam at any given time must have a narrow spectrum of wavelengths.

Though parahydrogen moderators are non-thermalizing, such moderators still pro-

duce a neutron energy distribution that is nearly Maxwellian, with a higher effective

temperature (Brun 1997). Given the distribution, a long-wavelength tail exists (Fig-

ure 3.5) that will be overlapped down the beamline by faster neutrons from the next

spallation pulse.

On the short-wavelength end of the spectrum, neutrons with wavelengths shorter

than ∼0.4 Å will rapidly depolarize by up converting the molecular parahydrogen in

the capture target. The neutrons in this short-wavelength range come primarily from

leakage of ”slowing-down” neutrons in the moderator (Byrne 2013; Iverson 2016).

These higher-energy neutrons, then, should also be removed from the beam.

23

Figure 3.5: FnPB spectrum - The neutron spectrum is shown in blue, alongwith a calculation in red. The long-wavelength tail that comes from a near Maxwell-Boltzmann distribution of neutron energies must be truncated to avoid overlap withsubsequent pulses. On the short-wavelength end of the spectrum, the faster neutronsare also truncated to avoid depolarization from up converting parahydrogen in thetarget.

In order to truncate the neutron spectrum, a pair of choppers synchronized to

the 60 Hz pulses are located on the beamline at 5.5 m and 7.5 m downstream of the

moderator (Fomin et al. 2014). The choppers consist of rotating carbon fiber disks

that are coated in a material containing a concentration of 10B of at least 0.13 g cm−2.

The upstream and downstream choppers have angles cut out of them that are 131◦

and 167◦ respectively. The distance from the chopper axes to the center of the neutron

beam is 25.0 cm.

The choppers are phased appropriately to work together to eliminate fast neutrons

and slow neutron overlap. The neutron spectrum seen by the upstream beam monitor

24

wavelength (Å)0 5 10 15 20 25 30 35 40

Main chopped spectrum ~3-6 Å

Wraparound neutrons

Figure 3.6: Chopped spectrum at upstream beam monitor - Shown here isthe neutron spectrum seen by the upstream 3He beam monitor. Due to the 1/v lawfor the capture within the beam monitor, the spectrum seen in this plot is artificiallyweighted by the wavelength.

described in section 3.3 is shown in Figure 3.6. As shown, small windows of long-

wavelength overlap, or “wraparound” neutrons can still be seen, though at very small

levels.

3.3 Beam Monitors

Of significant importance to the experiment is the ability to determine the relative

neutron beam flux (where flux refers to the count per unit time over the entire area of

the beam) into and out of the target. For that purpose, current-mode neutron detec-

tors (or beam monitors) were commissioned and installed upstream and downstream

of the experiment. These detectors have been used to perform neutron polarimetry

(Musgrave 2013), studies of orthohydrogen concentration within the hydrogen target

(Barrón-Palos et al. 2011; Grammer 2015), a new parahydrogen cross-section mea-

surement (Grammer et al. 2015), and analysis of neutron beam flux modulation into

25

Figure 3.7: Beam monitor concept -The NPDGamma neutron beam monitorscontain helium and nitrogen gas to pro-duce ionization from cold neutrons. Thecartoon to the right shows a side-on crosssection of the detector. Three parallel pla-nar electrodes along with the aluminumhousing define the electric field inside theionization chamber. Two of the electrodesare held at positive high voltage, and thecenter electrode is a pseudoground inputto the preamplifier. The aluminum hous-ing is also held at ground, though it is notread out and current to the housing is lost.Ionization comes from the conversion ofneutrons to t+p+K.E., which ionizes he-lium (and nitrogen) gas for downstream(upstream) monitors.

+ +

Signal

Beam in

t p

the hydrogen and background targets for the purpose of NPDGamma asymmetry

determination.

Several such beam monitors were used throughout different stages of the NPD-

Gamma experiment, but within this document monitors known as M1 and M4 are of

interest, which were used as the upstream and downstream beam monitors, respec-

tively. Each monitor is composed of an aluminum ionization chamber approximately

4 cm thick with a closely-integrated preamplifier, and contain some level of 3He gas

for the conversion of neutrons into charged particles via the reaction

n+3 He→ p+ t+ 764 keV,

which dominates the cross-section for low-energy (below eV) incident neutrons due

to a nearby resonance of 4He and the suppression of gamma production (Gillis 2006).

The conceptual operation of the beam monitors can be seen in Figure 3.7. Three

parallel planar electrodes, along with the aluminum chamber, define the electric field

within the gas volume. 3He gas at a partial pressure of 0.03 atm, which absorbs

about 3.7% of 4 Å neutrons, is contained in M1. The overall He pressure in M1

26

is increased to 0.5 atm with 4He, and another 0.5 atm of N2 facilitates ionization

and dielectric strength (Gillis 2006). M4 contains primarily 3He gas, which tends to

absorb a significant portion of the remaining neutrons since no neutrons are needed

downstream (Musgrave 2013).

3.4 Supermirror Polarizer

As discussed in 3.1.1, a convenient way of guiding neutrons is through reflection

at material boundaries. Total external reflection occurs at or below a critical glancing

angle θc, which is enhanced by layering alternating materials to generate reflections

caused by interference from the material boundaries at different depths. This multi-

layer coating, when created in such a way as to spread out the Bragg scattering and

effectively extend θc, constitutes a SM coating.

In equation 3.4, the potential due to magnetic interactions is ignored. Such scat-

tering is incoherent in paramagnetic materials due to the random orientation of atomic

magnetic moments. However, in ferromagnetic materials, magnetic domains arise be-

low the Curie temperature that produce magnetic fields much larger than that of any

individual atom (Byrne 2013). This gives rise to optical birefringence with respect to

neutron spin, made clear if the neutron refractive index is modified for ferromagnetic

materials:

n± =

√1− VF ± µnB

E, (3.6)

where µn is the neutron magnetic moment, B is the magnitude of the magnetic

field within the ferromagnetic domain, and the upper and lower signs represent the

refractive indices for neutron spin antialigned and aligned with the domain.

Combining the concepts of SM coatings and birefringence leads to the possibility

of a neutron reflector with the ability to select a certain neutron spin orientation

within a range of neutron momentum transfer if the SM substrate is loaded with

27

Figure 3.8: Polarizing bender - The NPDGamma SMP is a polarizing benderconsisting of an array of curved polarizing blades. Neutrons with the desired spinorientation travel paths between the blades, reflecting along the surfaces. Neutronswith the opposite spin are absorbed into the borofloat glass substrate. The lengthand curvature of the SMP is such that no line-of-sight exists from one end to theother.

a neutron absorbing isotope. If the SM layers are created from alternating layers

of ferrous material (with saturated magnetization aligned by an external field) and

(typically) silicon compounds, the coating can be tuned such that neutrons with one

spin orientation see alternating refractive indices, exhibiting reflection coefficients

near unity, while neutrons with the opposite spin orientation see very small changes

in refractive index, exhibiting correspondingly small reflection coefficients (Petukhov

et al. 2016). Such a mirror is known as a supermirror polarizer (SMP).

The SMP used on the FnPB for NPDGamma was comissioned by Swiss Neutron-

ics, and is a polarizing bender (Figure 3.8) made up of an array of 45 40 cm-long

thin blades each with a radius of curvature of 9.6 m. Each blade consists of Fe/Si

SM layer pairs on top of 0.3 mm borofloat glass with enriched 10B (Balascuta et al.

28

2012; Fry 2015). This SMP has a 10 cm-by-12 cm active cross section (matching that

of the beamline), and the blades are oriented such that the neutrons are polarized

in the ŷ direction. The radius of curvature and the length dictate that no neutron

can pass through the bender without interacting with a polarizing mirror surface.

To saturate the Fe layers, the SMP is surrounded by 12 pairs of NdFeB permanent

magnets, producing an applied field within the SMP in excess of 300 G. Outside of

the SMP, a compensation magnet was installed specifically to cancel the magnetic

field gradients at the experiment due to the SMP magnets (Balascuta et al. 2012).

The performance of the polarizer is good, measured at an average of 94% polariza-

tion at the target for the neutron wavelengths used for asymmetry analysis (Musgrave

2014). The polarization was measured a number of times throughout the experiment,

and the results are consistent.

3.5 Magnetic Holding Field

As shown in Figure 3.1, after exiting the SMP, the neutrons enter a magnetic

holding field defined by a set of racetrack coils. There are four such coils stacked

vertically to produce a field in the ŷ direction. The purpose of this field is two-fold:

to maintain polarization of the beam as the neutrons traverse the distance to the

target, and to provide an appropriate Larmor precession for the RF spin rotator

described in section 3.6. The optimal holding field was determined to be about 9.4 G.

3.6 Spin Rotator

The pulse-by-pulse alternating neutron spin flip is achieved in this experiment

through the application of nuclear magnetic resonance in a device referred to here as

a resonant RF spin rotator (SR) as termed by Seo et al. (2008). The SR consists of

a magnet (section 3.5) to produce a uniform, time-independent magnetic field ~B0 in

29

ŷ

ẑ

Figure 3.9: RF spin rotator concept - Magnetic fields involved in the spin rota-tion are the holding field caused by the red racetrack coils, and the oscillating fieldof the illustrated coil.

the direction of the incident neutron polarization surrounding a coil driven by an RF

signal (in this case at∼30 kHz) that produces a linear oscillating field orthogonal to ~B0

(see Figure 3.9 for visualization). The time-independent field establishes a resonance

with respect to the frequency of the oscillating field for flipping the neutron spin.

The conceptual operation of the SR is most easily understood from a semi-

classical approach. Consider a neutron propagating in the ẑ direction through a

time-independent field in the same direction as the neutron polarization, ŷ, as the

particle begins to propagate through the coil. Also assume for now that the linear

oscillating field produced by the coil is instead a field with constant magnitude that

rotates at a given rate in the ẑ, x̂ plane. Throughout the propagation, ~B0 defines

(along with the gyromagnetic ratio of the neutron, γn) a Larmor precession of the

neutron at frequency

ωL = γnB0. (3.7)

30

As the neutron begins to propagate through the rotating field, consider a frame of

reference that rotates along ŷ at frequency ωL. If the angular frequency of the rotating

field matches the Larmor frequency, the effective total magnetic field in this frame

of reference is a constant vector in the plane orthogonal to ŷ. The effect is that the

expectation value of the neutron spin precesses about this vector at a rate dependent

on the magnitude of the rotating field. If the field magnitude is tuned such that

the neutron spin rotates 180◦ by the time the neutron exits the coil, the spin of the

neutron will be efficiently flipped.

The probability of spin transition, derived quantum mechanically in Byrne (2013),

is

W (t, ω) =(γnB1)

2 sin2[t2

√(ω − ωL)2 + (γnB1)2

](ω − ωL)2 + (γnB1)2

, (3.8)

where t is the time of propagation through the oscillating coil, ω is the frequency of

the rotating field, and B1 is the magnitude. This has the form of a Breit-Wigner

resonance multiplied by a function oscillating in time. If we assume that the rotating

field is perfectly on resonance (ω = ωL), perfect spin-flip efficiency can be obtained

for

t =nπ

γnB1, n odd. (3.9)

In the actual SR, the field within the coil is, as stated, a linear oscillating field. Such

a field can be considered a superposition of two rotating fields, one rotating at ω

and the other at −ω. Since the former is on resonance, and the latter is very far off

resonance for realistic B0 and B1, equation 3.8 holds approximately true for the actual

linear oscillating field. The degree to which the effective resonance changes under the

assumed equivalence of a rotating and linear oscillating field is called the Bloch-Siegert

shift, and becomes important in experiments that take advantage of the resonance

to measure magnetic moments. In this experiment, however, the actual value of the

31

(s)t0 0.02 0.04 0.06 0.08 0.1 0.12

curr

ent (

arb)

0.04−

0.03−

0.02−

0.01−

0

0.01

0.02

0.03

0.04

0 0.02 0.04 0.06 0.08 0.1 0.12

flux

(ar

b)

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Figure 3.10: Spin rotator (SR) sequencing - Shown in blue is the measuredcurrent delivered to the RF SR. The ramping is a 1/TOF function for optimal spin-flip efficiency as the wavelength varies. In red, the approximate neutron flux at the SRis extrapolated by shifting the neutron capture signal for the purpose of visualizingalignment between the neutron flux and SR operation.

resonance frequency is not important, and parameters are simply tuned to maximize

the transition probability in equation 3.8.

Furthermore, at least for the case of a rotating field, the kinetic energy of the

neutron that undergoes such a rotation remains unchanged in the case where the

spatial boundaries into and out of the rotating field are infinitely sharp. This has

been shown to be the case by Golub et al. (1994), even though the potential energy

of the system changes from a spin flip due to interaction with the time-independent

field.

Because the propagation time through the SR coil depends on the neutron energy,

the SR is driven at a time-dependent amplitude to efficiently flip the full chopped

neutron spectrum. The propagation time is proportional to the TOF from the moder-

32

ator, so to meet the condition of equation 3.9, the amplitude has the form of 1/TOF.

The measured current delivered to the RF SR for a set of eight consecutive pulses

during hydrogen measurements can be seen in Figure 3.10, along with an overlay of

the neutron flux. In the figure, the ↓↑↑↓↑↓↓↑ spin sequence used for hydrogen mea-

surements is exhibited, which has the effect of cancelling up to second-order drifts in

the signal. For 2016 background measurements, this sequence was changed to a 30 Hz

alternating sequence.

For this experiment, two different oscillating coils were used, one for the hydrogen

measurements, and one when the experiment was set back up for background mea-

surements in 2016. Each coil is contained in a 6061 Al alloy housing with 0.5 mm

beam windows for hydrogen measurements, and 0.031” for 2016 measurements. Po-

larimetry was performed to determine the spin-flip efficiency for both measurements,

yielding a value ≈ 97% for hydrogen measurements (Musgrave 2014), and nearly

100% for 2016 measurements.

3.7 Gamma Detector Array

Gamma rays emitted from the capture of neutrons were detected by using an array

of 48 thallium-doped CsI scintillation detectors. Each detector is made up of a pair

of two CsI (Tl) crystals with a total volume of 152 x 152 x 152 mm3, as described

by Gericke et al. (2005). This volume enables the capture of 84% of the energy of an

average 2.2 MeV γ-ray incident on the center of the volume, with 11% leaking out

of the rear face, 3% backscattered from the front face, and the remaining 2% from

the sides. The detectors are arranged in 4 rings of 12, forming an approximately

circular-cylindrical array covering a solid angle ≈ 3π sr as seen in Figure 3.11.

Each scintillator volume comprised of 2 individual crystals is viewed by a single

Vacuum PhotoDiode (VPD). VPDs were chosen for their large detection area, linear

33

Beamn

36-4724-3512-230-11

011

Figure 3.11: Gamma detector array layout - Illustrated here is the basic layoutand geometry of the CsI gamma detector array. The center-of-capture for the capturetarget is approximately centered in the array, and the polarized neutron beam entersfrom the left. The detectors are numbered in the scheme indicated above, and thecolors of the CsI blocks are illustrative of the effect of an up-down PV asymmetry onthe power deposited into the crystals.

response, and insensitivity to stray RF fields. High-voltage batteries hold the VPD

cathodes at a bias ≈− 300 V. The VPD anode currents are amplified by solid state

electronics that drive coaxial transmission lines carrying the signal away from the

array. Aluminum housings encase each crystal volume, VPD, and amplifier; the

housings are electrically isolated from the support structure and each other to avoid

ground loops. The housings are supported by an aluminum frame covered in 6Li2CO3-

loaded silicon-matrix sheets. The same sheets are used to shield the inside of the array

from scattered neutrons.

The signals that reach the electronics rack where the data acquisition system

(DAQ) resides are then further amplified by active, 2nd-order, low-pass Bessel filters

with a cutoff frequency ≈5 kHz. The signals then feed into a variable-gain amplifier

before being digitized by the DAQ in order to utilize the digitizer’s full bit depth.

34

3.8 Data Acquisition Systems

Aside from using different SR coils, the difference between the hydrogen measure-

ments and the background measurements taken in 2016 is primarily in the data ac-

quisition system (DAQ). For hydrogen measurements, a set of 16-bit flash ADC VME

modules were used to digitize signals and pass them on through the VME backplane

to a CPU module that would reduce the data and pass them on. In the processes

of planning the reinstallation of the NPDGamma experiment to measure background

asymmetries, time constraints made reuse of the n3He DAQ desirable, which was at

the time in active use and could remain at the FnPB for the NPDGamma background

measurements once n3He was removed. The n3He system satisfied the requirements

of NPDGamma and provided far less deadtime due to readout. Therefore, 2016 back-

ground measurements were acquired by using 24-bit ∆Σ ADCs with an effective bit

depth comparable to the ADCs used for hydrogen measurements.

In both cases, two electrically-isolated yet synchronized DAQs were in operation

at the same time. One DAQ is known as “clean”, containing only signals from the

gamma detectors which are insensitive to SR influence down to far below the target

10−8 statistical uncertainty. The other DAQ is considered “dirty”, being used to

directly measure current delivered to the SR coil, as well as other signals to be syn-

chronized with gamma measurements such as beam monitors. The clean and dirty

DAQs are only allowed to be connected by optically-isolated digital signals, which

allows synchronization and data export without the risk of contaminating the clean

DAQ with SR-related signals.

The SNS facility provides what are known as T0 signals, synchronized to the

extraction of proton bunches into the spallation target. The T0 signals are therefore

synchronized to the arrival of chopped neutrons at the experiment. A set of electronics

35

gate the T0 signals in order to define a “run”, which are each about 7 min long. Many

such runs are carried out back-to-back for long periods of time. The T0 signals are

precisely delayed to coincide with the arrival of neutrons, and logically duplicated

to the clean and dirty DAQs to trigger acquisition of 16 ms of data, leaving 2/3 ms

before the next trigger for transferring data and avoiding corruption issues. The runs

are stored in files referenced by unique consecutive numbers starting at zero. The

same T0 signals are duplicated at the dirty DAQ and used to trigger the driving of

the SR coil.

3.8.1 Hydrogen Target DAQ

At the heart of the DAQ system used for hydrogen measurements is a set of 16-bit

flash ADCs by Alphi Technology Corp housed in VME crates, one for the clean DAQ

and one for the dirty. The clean and dirty ADC modules are fed external 50 kHz

and 62.5 kHz clocks, respectively. Since the dirty DAQ samples the SR current which

is primarily 30 kHz, it is clocked slightly faster to avoid aliasing. For the case of

gamma signals, which are already limited to 5 kHz, oversampling at 5× the Nyquist

frequency pushes roughly 80% of the digitization noise beyond the desired band. A

clock generator module for each DAQ takes T0 triggers and produces 800 and 1000

clock edges for the clean and dirty DAQs, respectively. Once eight such sample sets

are acquired, the ADC modules place an IRQ (interrupt request) on the VME bus to

be read out.

An Acromag CPU module for each VME crate listens for the ADC IRQ and

initiates a transfer for all channels over the backplane. This process takes enough

time that an entire 9th T0 is suppressed as a “readout pulse”. The CPUs on the

VME crates bin the samples into 40 time bins per T0 (except for the SR signal which

is left unbinned). The reduced data for both DAQs is then pushed over optical links

36

to a workstation for monitoring and to be organized into files for transfer to long-term

storage.

3.8.2 n3He Delta-Sigma DAQ

The company D-TACQ was commissioned to provide custom firmware for their

DAQ appliances used for the n3He experiment. These appliances carry 24-bit ∆Σ

ADCs and were used for NPDGamma background target measurements in the first

half of 2016. The custom firmware allows the appliances to be used in a similar way

to the DAQ for hydrogen measurements, while providing the same data structure

without a missing readout pulse. To achieve this, the digital filtering required for

∆Σ operation was reset on each T0. The appliances generate their own internal

programmable clocks distributed to all channels. The clean and dirty DAQs for 2016

measurements were again electrically isolated.

3.9 lH2 Cryostat

For the np → dγ reaction, a liquid molecular parahydrogen target is optimal

because such a target does not depolarize cold neutrons below 14.5 meV. The pri-

mary target for the NPDGamma experiment is a 16 L volume of liquid hydrogen with

a maximum parahydrogen concentration of 99.985%. The target is contained and

cooled by a cryostat made of 6061 Al alloy to ∼ 15.5 K. To reach and maintain a

near-thermal equilibrium para concentration, the hydrogen is filled and continuously

circulated through a catalyst to facilitate ortho to para downconversion. The hydro-

gen pressure vessel is surrounded by 6LiF-loaded polymer-matrix neutron absorber,

thermal shielding, and a vacuum chamber. Surrounding the vacuum chamber is the

∼ 3π CsI gamma detector array, as shown in Figure 3.12.

The hydrogen pressure vessel is a cylindrical volume with elliptically domed up-

37

AD

CB

Figure 3.12: Detector with lH2 cryostat/target and SR coil model cutaway- Shown here is a cutaway representation of the geometry created for the GEANT4MC simulation in the hydrogen-target configuration. The beam enters from right toleft, first through the RF SR coil (A). It then enters the main vacuum chamber (B)of the lH2 cryostat through a double window with an intermediate vacuum volume,where the cylindrical extrusion of the vacuum chamber is centered in the CsI array(C). The incident and scattered neutron beam is controlled by LiF absorber sheetsarranged to limit gamma-emitting capture to the hydrogen contained in the pressurevessel (D) and small amounts of aluminum in the flight path.

and down-stream walls, and has a thickness at the center of the upstream wall of

0.063”, which the beam incident on the hydrogen must pass through. The vessel

has a length of approximately 30 cm, and an ID of 10.5”. The thickness of the

cylindrical side wall and downstream wall is 0.12” and 0.13”, respectively. The vessel

has ports at the top and bottom of the downstream wall for vent operation and

circulation through the ortho/para converter (OPC), as shown in Figure 3.13. A

99.999% Al, high-conductivity thermal bus connects the pressure vessel to a feedback-

controlled temperature. The lines connected to the vent and OPC are stainless steel

with relatively low thermal conductivity to allow temperature gradients.

In order to maintain a high fractional parahydrogen concentration, liquid hydrogen

38

Tliq.

A

C

E

B

D

TOPC

T evap.

Figure 3.13: Target vessel and ortho/para conversion - A simplified schematicof the target is shown on the left, and engineering drawings of the same componentsare shown on the right. In the schematic, each feedback-controlled fixed temperatureis labeled with a dot. Volume A is the hydrogen target which is connected to fill/ventline B. Hydrogen vaporizes above the target volume and is reliquified in liquifactionchamber C, which is thermally bound to A by the five-nines Al thermal bus D. Liquidhydrogen flows down into OPC chamber E, and then back into A.

above the vent port is slowly vaporized and subsequently liquified over the OPC,

enforcing continuous circulation. The OPC is made of Fe(OH)3 powder and exhibits

high magnetic field gradients for the hydrogen molecules that flow through it, enabling

a spin flip of one of the ortho molecule nuclei. The estimated time for recirculation

of the target is about one day (Santra et al. 2010). A schematic of the components

involved in the circulation can be seen in Figure 3.13.

A number of studies of transmission through the target were performed throughout

the experiment using M1 and M4, which yield information about the O/P concen-

tration within the target. Firstly, exponential convergence of O/P concentration can

be seen in the transmission through the target within the first few days after the

vessel is filled from room temperature gas (as shown in FIG. 4 of Grammer et al.

(2015)). Secondly, flow rates were changed at certain points of operation by altering

temperatures indicated in Figure 3.13 and observing power delivered to heaters used

39

to control the temperature. In principle, differing flow rates will allow the target to

reach different equilibrium levels of parahydrogen due to the opposition of occasional

up conversion in the vent tube and in the walls. However, no statistically signifi-

cant changes were detected, allowing only upper limits to be established. The O/P

concentration is believed to be very close to thermal equilibrium.

40

Chapter 4

ASYMMETRY MEASUREMENTS

Measurements made with the NPDGamma apparatus for the purpose of determining

the asymmetry Aγ are described in this chapter along with general measurement

strategies, and features in the data pertinent to the data reduction (Chapter 6) and

selection (Chapter 7). To start, a general strategy for determining the asymmetry is

given.

4.1 General Strategy

The apparatus with the hydrogen target (described in section 3.9) installed pro-

duces a signal in the CsI detectors due to deposition from gammas of the 2.2 MeV

deuteron binding energy. Additional background is also deposited from radiative cap-

ture on, and radioactive decay of, apparatus materials in the beam path and in the

path of scattered neutron flux. The prompt background from radiative capture is

nearly perfectly correlated in time with the signal, and reasonably correlated in the

space of gamma detector number. Furthermore, because of the current-mode oper-

ation of the gamma detector array, the gamma energy cannot be used to select the

np → dγ reaction. The fractional prompt background power deposition into the de-

tectors, for all significant sources, must be determined along with their asymmetries.

The fractional contribution is determined by Monte-Carlo (MC) and radioactivity

of the materials following a long beam-on-target history. A number of background

target configurations are defined in order to determine or limit their contribution to

the asymmetry seen by the gamma detectors.

For each target configuration, raw asymmetries for each detector are determined

41

(for derivation, see section 6.2). These asymmetries have contributions from multiple

materials in general. Each contribution is the product of the physics asymmetry for

that material multiplied by polarization and geometric factors. Geometric factors

include the finite structure of the beam, effective solid angle of the detector, spatial

distribution of the material in question, an other effects. The geometric factors and

depolarization in the target are determined via MC simulation. The incident po-

larization is measured periodically. The validity of this approach will be tested by

applying this method to the measurement of an asymmetry for chlorine, which is very

large and easily measured due to significant enhancement.

In order to estimate the statistical variances in the determination of raw asym-

metries, the variances are determined internally by effectively performing many mea-

surements and examining the distribution. For calculation of Aγ, raw asymmetries

for all detectors and target configurations are combined with measured and calculated

polarization and geometric factors in a linear set of equations, in an application of

maximum likelihood with all physics asymmetries as parameters. Statistical variances

are propagated from raw asymmetries to the uncertainty in Aγ.

4.2 Overview of Hydrogen Measurements

Production measurements of the asymmetry Aγ with the hydrogen target in place

began at the end of November 2012 with a proton accelerator beam power of 850 kW,

and ended at the end of March 2014 with a beam power that ramped up to over 1 MW.

In that time, approximately 200 days of accumulated usable beam time were recorded

in the data stream. 50,620 runs were collected, of which 47,159 were chosen for the

analysis in this thesis. The runs are organized into groups of data that are referred to

in this thesis as batches. The hydrogen target remained operational throughout this

time, except when the vessel was vented and subsequently refilled over the significant

42

t (ms)20− 0 20 40 60 80 100 120 140 160 180

ampl

itude

(arb

)

5−10

4−10

3−10

2−10

A

B

C

D

E

Figure 4.1: Gamma detector response - Plot of the average digitized waveformfor a typical detector during a special 1 Hz operation of the accelerator. Feature A isa flash of photons from the accelerator preceding the arrival of neutrons. Feature Bis known as the leading chopper edge, and C is a pair of Al Bragg edges. Feature Dis phosphorescence from the CsI following the trailing cho