Doctorate Dissertation
博士論文

Precise Neutron Lifetime Measurement Using Pulsed
Neutron Beams(パルス中性子ビームを用いた中性子寿命の精密測定)

A Dissertation Submitted for Degree of Doctor of Philosophy
December 2018
平成 30 年 12 月博士（理学）申請
Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科物理学専攻

Naoki Nagakura
長倉直樹

Abstract
The neutron beta-decay lifetime (∼ 880 s) is an important parameter in the weak interaction of theStandard Model, cosmology, and astrophysics. For example, the neutron lifetime is a parameter
which can be used to determine the Vud parameter of the Cabibbo-Kobayashi-Maskawa quark mixing
matrix. The neutron lifetime is also one of the input parameters for the Big Bang Nucleosynthesis,
which predicts light element synthesis in the early universe.
The neutron lifetime has been previously measured by mainly two independent methods. One
is to measure the number of protons from neutron beta-decay, and the other is to store ultra cold
neutrons (UCNs) and count the number of remaining UCNs after a certain period of time. However,experimental measurements of the two methods are significantly diﬀerent (4.0σ or 8.4 s). Therefore,
we conduct a new type of experiment to resolve this problem. We set our eventual goal precision as
1 second on the neutron lifetime, which is comparable to the current best precision measurement.
The experiment is carried out at the polarized beam branch of beamline five, Materials andLife Science Experimental Facility, Japan Proton Accelerator Research Complex. The polarization
beam branch enters a spin flip chopper (SFC), which is composed of radio-frequency coils andmagnetic super mirrors. The magnetic super mirror can selectively reflect neutrons depending on
the neutron polarization direction, which makes it possible to create a neutron bunch with arbitrary
length.
A time projection chamber (TPC) made of polyether ether ketone was developed for a beta-decay
counter to realize low background condition. Furthermore, the inside walls are completely coveredby lithium fluoride plates to absorb scattered neutrons without prompt γ-ray emission. A small
amount of 3 He gas, which typically amounts to 100 mPa pressure, is injected into the TPC. The
neutron flux can be evaluated by counting the number of 3 He(n, p)3 H events in the TPC. Since thelength of each neutron bunch is about half of the TPC length, the TPC can detect both the betadecays and 3 He(n, p)3 H reactions with a 4π solid angle acceptance and the good signal-to-noise
ratio.
The detector response was simulated using the Geant4-based Monte Carlo simulation software.
The result is used to evaluate the signal selection eﬃciencies and expected background amountin the signal region. The full detector setup is implemented in the system. Using the simulation
result, the diﬀerence of the signal selection eﬃciencies between beta-decay and 3 He(n, p)3 H wascorrected. We started data acquisition in May 2014, and we have continuously taken the data every
year by 2018. During the data acquisition, 6.0 × 1011 neutrons entered the TPC in total, and the
all-combined data gives a statistical error of about a few seconds on the neutron lifetime. The
analysis result for the data taken through March 2018 was 898.8 ± 4.7 (stat.) +7.7
−8.9 (sys.) s. Several
IIIIV
upgrade plans to reduce both the statistical and systematic uncertainties are ongoing, such as SFC
upgrade and low-pressure TPC operation.

Contents
1 Introduction
1.1 Physics motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Light element production in Big Bang Nucleosynthesis model . . . . . . .
1.1.2 Vud determination for testing the CKM matrix unitarity . . . . . . . . . . .
1.2 Previous neutron lifetime measurements . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 UCN storage method . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 In-flight method (proton counting) . . . . . . . . . . . . . . . . . . . . . .
1.2.3 In-flight method (electron counting) . . . . . . . . . . . . . . . . . . . . .
1.3 This experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
1
5
6
7
8
10
12
12

2 Experimental setup
2.1 Facilities and experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 J-PARC facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Polarized beam branch . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Beamline setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Spin flip chopper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Radio-frequency coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Magnetic super mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Neutron time-of-flight distribution . . . . . . . . . . . . . . . . . . . . . .
2.3 Beam flux monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Neutron beam shutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Veto counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Shield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Time projection chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.1 Material selection for low-background condition . . . . . . . . . . . . . .
2.7.2 Operation gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.3 LiF plate covering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.4 Basic performance of the TPC . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Preamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Temperature monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11 Calibration system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15
15
15
15
16
17
17
19
19
22
22
23
23
26
29
29
30
30
32
35
35
38

V

VI

CONTENTS
2.11.1 Energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.2 Drift velocity calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.3 Dead time calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.12 Gas handling system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13 Mass spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38
39
40
42
43

3 Data acquisition cycle and data quality
3.1 Acquired physics data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Data acquisition cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Device conditions during the measurement . . . . . . . . . . . . . . . . . . . . . .
3.4 Gain deterioration with the elapsed time . . . . . . . . . . . . . . . . . . . . . . .

47
47
47
48
49

4 Simulation
4.1 Overview of simulation process . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Beam profile measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Simulated events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Neutron beta-decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 3 He(n, p)3 H reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Neutron scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Cosmic rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.5 Photoabsorption of 55 Fe X-rays . . . . . . . . . . . . . . . . . . . . . . .
4.3.6 Prompt γ-rays from LiF plate . . . . . . . . . . . . . . . . . . . . . . . .
4.3.7 Prompt γ-ray from SFC . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.8 3 H beta-decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.9 12 C(n, γ)13 C reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Recombination eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Diﬀusion eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.3 Attenuation eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.4 Space charge eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.5 Charge-inducing process . . . . . . . . . . . . . . . . . . . . . . . . . . .

51
51
53
53
53
55
55
55
55
57
57
57
57
58
58
59
59
59
62

5 Analysis
5.1 Expected background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Types of backgrounds for 3 He(n, p)3 H . . . . . . . . . . . . . . . . . . .
5.1.2 Types of backgrounds for neutron beta decay . . . . . . . . . . . . . . . .
5.1.3 Event rates of signal and background . . . . . . . . . . . . . . . . . . . .
5.2 Definition of analysis parameters . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Data analysis algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Time-of-flight subtraction method . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Energy separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Purity cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.4 Track size separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63
63
63
64
65
65
67
67
69
70
72

CONTENTS

VII

5.3.5 Scattering event analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.6 Low-gain measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.7 Cross section calculation . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.8 Pileup correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
He number density determination . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Evaluation of injected 3 He pressure . . . . . . . . . . . . . . . . . . . . .
5.4.2 Evaluation of 3 He pressure in operation He gas . . . . . . . . . . . . . . .

72
73
75
76
78
79
79

6 Results
6.1 Uncertainties for the neutron beta-decay events (Sβ ) . . . . . . . . . . . . . . . . .
6.2 Uncertainties for the neutron beta-decay selection eﬃciency (εβ ) . . . . . . . . . .
6.3 Uncertainties for the 3 He number density (ρ) . . . . . . . . . . . . . . . . . . . . .
6.4 Analysis results of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Combined result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83
83
85
88
88
91

7 Summary and discussion
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Upgrade plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95
95
96

5.4

A Mathematical definition of analysis parameters
99
A.1 Waveform parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
A.2 Event parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
B Thermometer specifications

101

C Gain reduction model in a wire chamber due to the space charge eﬀect103

Acknowledgments

107

List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9

Baryon-to-photon ratio v.s. He/H abundance (Yp ) with in-flight and UCN lifetime
results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Abundance of light elements after the Big Bang according to the standard big bang
nucleosynthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nucleosynthesis process creating 4 He nuclei from protons and neutrons. . . . . . .
Relation between the |Vud | value and the ratio of the axial vector to vector couplings
constant (λ) as computed using the neutron lifetime result. . . . . . . . . . . . . .
Results of previous neutron lifetime measurements. . . . . . . . . . . . . . . . . .
Schematic drawing of the experimental setup for the UCN storage method. . . . . .
Schematic drawing of the experimental setup for the in-flight method. . . . . . . .
Schematic view of the Kossakowski et al. experiment in 1989. . . . . . . . . . . .
Principle of this experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1
2.2
2.3
2.4
2.5
2.6
2.7

Bird’s eye view of J-PARC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic view of the polarized beam branch. . . . . . . . . . . . . . . . . . . . .
Principle of the SFC operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Picture of the radio-frequency coil. . . . . . . . . . . . . . . . . . . . . . . . . . .
Picture of the magnetic super mirror. . . . . . . . . . . . . . . . . . . . . . . . . .
Time-of-flight distribution of 3 He(n, p)3 H events in the TPC. . . . . . . . . . . .
Definition of the fiducial time along with the positional relation of a neutron bunchin the TPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Picture of the neutron beam monitor. . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Pulse height distribution of the neutron beam monitor. . . . . . . . . . . . . . . . .
2.10 Picture of a neutron shutter system. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11 Picture of the cosmic rays veto counters. . . . . . . . . . . . . . . . . . . . . . . .
2.12 Picture of lead shield surrounding the TPC. . . . . . . . . . . . . . . . . . . . . .
2.13 Picture of the TPC taken from the downstream side. . . . . . . . . . . . . . . . . .
2.14 Wire structure of the MWPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.15 Equipotential lines of the TPC drift region in the x-y plane calculated by Garfield
software. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 Equipotential lines of the MWPC in the x-y plane. . . . . . . . . . . . . . . . . . .
2.17 Background-subtracted energy spectra for G10 and PEEK measured by a Germanium detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
IX

2
3
5
6
7
9
10
11
12
16
17
18
19
19
20
21
22
23
24
25
25
26
27
27
27
29

X

LIST OF FIGURES
2.18 Avalanche multiplication factor as a function of the anode wire voltage. . . . . . . 31
2.19 Drift velocity of electrons in the TPC as a function of the reduced drift field strength. 31
2.20 Anode wire trigger eﬃciency for the minimum ionization particles. . . . . . . . . . 32
2.21 Typical event display of the beta-decay and 3 He(n, p)3 H events. . . . . . . . . . . 33
2.22 Picture of a preamplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.23 Preamplifier circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.24 Typical preamplifier output waveform. . . . . . . . . . . . . . . . . . . . . . . . . 34
2.25 Installing position of the eight LakeShore thermometers inside the vacuum chamber. 35
2.26 Temperature inside the TPC during the lifetime measurement. . . . . . . . . . . . 36
2.27 Schematic diagram of the DAQ circuit for the physics data acquisition. . . . . . . . 37
2.28 Schematic view of the calibration measurement setup. . . . . . . . . . . . . . . . . 38
2.29 Typical transition of the energy peak position after gas filling. . . . . . . . . . . . . 39
2.30 Cross section of the TPC for a cosmic-ray event describing the drift length correction. 40
2.31 Drift velocity distribution as a function of the number of hit anode wires. . . . . . . 41
2.32 Live time ratio of the data acquisition system in the shutter open mode. . . . . . . . 42
2.33 Schematic diagram of the gas handling system. . . . . . . . . . . . . . . . . . . . 44
2.34 Picture of the mass spectrometer at the University of Tokyo. . . . . . . . . . . . . 45
3.1
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

4.9
5.1
5.2
5.3
5.4
5.5

Growth of the attenuation coeﬃcient in the TPC as a function of the elapsed day
after the gas filling time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50Simulation flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic view of the detector setup constructed at the Geant4-based Monte Carlosimulation system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutron beam profile observed from the downstream side. . . . . . . . . . . . . .
Kinetic energy distribution of an electron from neutron beta-decay. . . . . . . . . .
Comparison of theoretical and experimental angular distributions of neutrons witha CO2 gas molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Recombination ratio of an electron-ion pair as a function of electric field in the TPC
gas composition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of the diﬀusion ratio parameter for experiment and Monte Carlo simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of the maximum energy deposit distribution without space charge
correction and with space charge correction based on an analytical gain reduction
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Amplitude ratio of induced waveform for wires near the avalanche anode wire
evaluated by the Garfield simulation. . . . . . . . . . . . . . . . . . . . . . . . . .

52

Waveform parameter definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Track parameter definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis flow to select the beta-decay events and the 3 He(n, p)3 H events. . . . . .
Schematic drawing of the time-of-flight distribution for signal and background
events in the shutter-open and shutter-closed mode. . . . . . . . . . . . . . . . . .
Maximum energy deposit distribution. . . . . . . . . . . . . . . . . . . . . . . . .

66
67
68

52
53
54
56
58
60

61
62

69
70

LIST OF FIGURES
5.6
5.7
5.8
5.9

Total energy deposit distribution in linear scale and logarithmic scale. . . . . . . .
Track length locality distribution in linear scale and logarithmic scale. . . . . . . .
Distribution of the reaction x position of the 3 He(n, p)3 H events. . . . . . . . . . .
Distribution of the distance between track vertex and TPC center for the signal andthe background events in a linear scale and a logarithmic scale. . . . . . . . . . . .
5.10 Total energy deposit distribution under the low-gain condition. . . . . . . . . . . .
5.11 Ratio of 14 N(n, p)14 C and 3 He(n, p)3 H events as a function of time. . . . . . . . .
5.12 Typical event display of a pileup event. . . . . . . . . . . . . . . . . . . . . . . . .
5.13 Examples of recognized tracks in the x-y plane event displays. . . . . . . . . . . .
5.14 Schematic drawing of the volume expansion method. . . . . . . . . . . . . . . . .
5.15 3 He(n, p)3 H event flux as a function of injected 3 He pressure. . . . . . . . . . . .
5.16 Results of the 3 He/4 He ratio measurements using the mass spectrometer method
and flux method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3
6.4
6.5
6.6
6.7
6.8
6.9

Signal selection eﬃciencies for the beta-decay events and the 3 He(n, p)3 H events
as a function of the reaction z point. . . . . . . . . . . . . . . . . . . . . . . . . .
Electron drift time and drift velocity distribution of the cosmic rays events as afunction of the ionization y position in the TPC. . . . . . . . . . . . . . . . . . . .
Average energy to create an electron-ion pair (w value) for an electron in CO2 gas.
Average energy to create an electron-ion pair (w value) for a proton in water vapor.
Breakdown of the uncertainties given for Fill96. . . . . . . . . . . . . . . . . . . .
Statistical uncertainty for each gas fill data. . . . . . . . . . . . . . . . . . . . . .
Systematic uncertainty for each gas fill data. . . . . . . . . . . . . . . . . . . . . .
Result of the neutron lifetime for each gas fill data and their averaged value. . . . .
Comparison of our result with other neutron lifetime measurements. . . . . . . . .

7.1
7.2

Expected statistical uncertainty as a function of the total data acquisition time. . . .
Picture of a new preamplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1
6.2

XI
71
73
74
74
75
76
77
79
80
81
81
84
86
87
87
90
91
92
92
93
96
97

C.1 Proposed model function of the gain reduction factor as a function of the multiplication factor in the TPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
C.2 Picture of the multi wire drift chamber. . . . . . . . . . . . . . . . . . . . . . . . . 104
C.3 Measured gain reduction factor along with the proposed best fit model curve. . . . 105
C.4 Energy deposit distributions without and including the gain reduction correction. . 105

List of Tables
1.1

Comparison of our experiment and the Kossakowski et al. experiment. . . . . . . .

2.1

2.6
2.7
2.8
2.9

The characteristics of the three beam branches in the BL05 at the design power of
MLF (1 MW). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specification of the magnetic super mirror in the SFC. . . . . . . . . . . . . . . .
Basic parameters of the TPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Physical properties of PEEK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scattering and capture cross section for a neutron with a nucleus in the TPC operationgas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specification of the Finesse ADC module. . . . . . . . . . . . . . . . . . . . . . .
Specification of the Finesse TDC module. . . . . . . . . . . . . . . . . . . . . . .
Specification of the Mensor pressure gauge. . . . . . . . . . . . . . . . . . . . . .
Specification of the Pfeiﬀer pressure gauge. . . . . . . . . . . . . . . . . . . . . .

3.1
3.2
3.3

Physics data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of data acquisition cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of experimental setup condition. . . . . . . . . . . . . . . . . . . . . . . . . .

47
48
49

4.1

Cross sections and γ-ray energies for a CO2 molecule to capture a neutron. . . . .

57

5.1
5.2

Trigger event rate of signal and background in the fiducial time window at Fill94(300 kW accelerator operation). . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multi track recognition eﬃciencies for the simulation data. . . . . . . . . . . . . .

65
78

6.1
6.2
6.3
6.4
6.5
6.6

Summary of the Sβ uncertainty: Fill66 . . . . . . . . . . . . . . . . . . . . . . . .
Summary of the S3 He uncertainty: Fill66 . . . . . . . . . . . . . . . . . . . . . . .
Summary of the εβ uncertainty: Fill66 . . . . . . . . . . . . . . . . . . . . . . . .
Summary of the ε3 He uncertainty: Fill66 . . . . . . . . . . . . . . . . . . . . . . .
Summary of the ρ uncertainty: Fill66 . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of the lifetime value combined with the same year gas data. . . . . . .

89
89
89
90
90
91

7.1
7.2

Expected neutron flux in the TPC for two prospective upgrade setups. . . . . . . .
Specification comparison of the current and new preamplifier. . . . . . . . . . . .

97
97

2.2
2.3
2.4
2.5

13
16
20
28
29
30
37
37
43
43

B.1 Specification of the Automatic Systems Laboratories platinum thermometer. . . . . 101
XIII

XIV

LIST OF TABLES

B.2 Specification of the LakeShore platinum thermometer. . . . . . . . . . . . . . . . 101

Chapter 1
Introduction
A free neutron decays into a proton, an electron, and an anti-neutrino through the beta-decay process.
The experiment to measure the neutron decay lifetime (τn ) is conducted at Japan Proton Accelerator
Research Complex (J-PARC). This chapter describes the research background and the motivation
to precisely measure τn .

1.1 Physics motivation
Neutron beta-decay process can be described as the transformation of a d quark to a u quark. It is oneof the fundamental processes in the weak interaction because of its simplicity. The experimental
measurement of the decay lifetime has an crucial impact on particle physics, astrophysics, andcosmology. In this section, the physics motivation to measure τn is discussed.

1.1.1 Light element production in Big Bang Nucleosynthesis model
According to the Big Bang Nucleosynthesis (BBN) model, nucleosynthesis processes is known
to have taken place between about 10 s and 20 min after the Big Bang. Light elements, such ashydrogen, helium, and lithium, were created during the BBN process. Elements heavier than lithium
have not yet formed at this stage. There is currently good agreement between the observed and thetheoretically calculated values of the light element abundance, which is one of the strong evidences
supporting the Big Bang model. For example, the helium-to-proton ratio can be calculated using
the baryon-to-photon ratio and the neutron lifetime. The predicted abundance agrees well with theobserved value by Peimbert et al. in 2016 as shown in Figure 1.1.
According to the BBN theory, time development of the light element composition after the Big
Bang can be calculated as shown in Figure 1.2 [1]. From the perspective of nucleosynthesis, thetime development of each stage in the early universe is described as below.
• t <1 s, T ∼ a few MeV
The energies of nuclei were high and the proton and neutron ratio was maintained in a thermal
equilibrium state as follows.
p + e− ↔ n + νe ,(1.1)
1CHAPTER 1. INTRODUCTION

Ratio of He/H Abundance (Yp)

2

0.26

Planck:2015

Izotov:2013

0.255
0.25

In-flight: 888.0 ± 2.0 sec

Aver2015
PDG:2018
Peimbert:2016

0.245
0.24
0.235
0.2

UCN storage: 879.6 ± 0.6 sec

0.4

×10−9
0.6
0.8
Baryon to photon ratio

Figure 1.1: Baryon-to-photon ratio v.s. He/H abundance (Yp ) with in-flight and UCN lifetime
results. Yp result comes from Peimbert2016 [2], Aver2015 [3], and Izotov2014 [4]. Baryon-tophoton ratio was observed by Planck2015 [5]. The BBN prediction band shows one standard
deviation uncertainty [6]. The two types of methods of τn measurement are described in Section
1.2.

1.1. PHYSICS MOTIVATION

37

Big Bang Nucleosynthesis as a Probe of New Physics

0.1

1

1

10−6

t/sec
100
1000

H

D b.n.

ν dec.

104

105

106

Yp

N

10−2
10−4

10

SBBN f.o.

n/p dec.

D/H

e± ann.

3

He/H
T/H

10−8

7

10−10

Be/H

7

Li/H

6

Li/H

10−12
10−14
1000

100
T /keV

10

1

1: Time ofandlight
temperature
evolution
all standard
big according
bang nucleosynthesis(SBBN)- big bang
Figure 1.2: Figure
Abundanceelements
afterofthe
Big Bang
to the standard
relevant
abundances.
verticalarrow [1].
indicates
momentat represents
T9 ≃ 0.85 atnucleosynthesis
by nuclear
M. Pospelov
and J.The
Pradler
in 2010
The theverticalaxis
the fraction
which
most
of
the
heliumnucleiaresynthesized.
Thegrayverticalbands
indicate
mainof total mass.
BBN stages. From left to right: neutrino decoupling, electron-positron annihilation and n/p
freeze-out, D bottleneck, and freeze-out of all nuclear reactions. Protons (H) and neutrons(N) are given relative to nb whereas Yp denotes the 4 He mass fraction.
Below we discuss the fusion of the light elements and compare their SBBN predictions withobservations.
1.1.1 O(0.1) abundances: 4 He. The beauty of the SBBN prediction for 4 He lies in
its simplicity. Only a few factors that determine it. The rates for weak scattering processes
that inter-convert n ↔ p at high plasma temperatures scale as G2F T 5 , where GF is the
Fermi constant. As the Universe cools, these rates drop below the T 2 -proportional Hubble
rate H(T ) Eq. (6). The neutron-to-proton transitions slow down, and the ratio of theirrespective number densities cannot follow its chemical-equilibrium exponential dependence,n/p|eq ≃ exp(−∆mnp /T ). Around T ≃ 0.7 MeV this dependence freezes out to n/p ≃1/6 but continues to decrease slowly due to residual scattering and β-decays of neutrons.
The formation of D during this intermission period is delayed by its photo-dissociation
process that occurs eﬃciently because of the overwhelmingly large number of photons [see

4

CHAPTER 1. INTRODUCTION

p + ν e ↔ n + e+ .

(1.2)

Protons and neutrons at this stage followed the Boltzmann probability distribution which canbe expressed as()
E−µf (E) ∼ exp −
,
(1.3)
kB T
where E is the particle energy, µ is the chemical potential, kB is the Boltzmann constant,and T is the temperature of the state. The chemical potentials of a proton and a neutron
are cancelled out with each other. The ratio of the numbers of neutrons to protons (Nn /Np )becomes()
Nnmn − mp∼ 1,(1.4)∼ exp −Np
kB T
where mn and mp represent the neutron and proton masses, respectively. Since the energy
at this stage was still much higher than the mass diﬀerence between a neutron and a proton,
their numbers were maintained to be almost the same.
• t ∼1 s, T ∼1 MeV
The reactions of Eq. (1.1) and (1.2) ceased to occur. At this moment, the Nn /Np ratio wasfixed by the freeze-out temperature Tfr ∼ 1 MeV as follows.
()
Nnmn − mp1∼ exp −∼ .
Np
kB Tfr6(1.5)• 1< t <100 s, 0.1 MeV< T <1 MeVDuring this stage, a fraction of the neutron decayed into a proton through the beta-decay
process as expressed in Eq. (1.6), which was the only reaction to aﬀect the Nn /Np ratio. At
the end of this stage, the ratio decreased to 1/7.
n → p + e− + ν e .

(1.6)• 100 s < t <1000 s, 0.05 MeV< T <0.1 MeVProtons and neutrons lost kinetic energies and were bound with each other to create deutrons
or heavier nuclei based on the chain processes described in Figure 1.3. Since there exists nostable nuclei with mass numbers of 5 and 8, nuclei heavier than lithium were not created in
the BBN process.
• t ∼1000 s, T∼ a few tens of keV
The nucleosynthesis process ceased to occur at this stage, and the nuclei ratio became constant
except for free neutrons. Remaining neutrons underwent beta-decays and turned into protons.

1.1. PHYSICS MOTIVATION

5
p

p

n

D
3He

n
3H

n

p
4He

Figure 1.3: Nucleosynthesis process creating 4 He nuclei from protons and neutrons.

1.1.2 Vud determination for testing the CKM matrix unitarity
In the Standard Model, the Cabibbo-Kobayashi-Maskawa (CKM) matrix plays a crucial role todescribe the quark mixing. The matrix is written as
Vud Vus Vub
VCKM =  Vcd Vcs Vcb  .
(1.7)
Vtd Vts Vtb
This matrix has four free real parameters, and is unitary according to the Standard Model. Therefore,
the experimental measurement to check the unitarity of the matrix is one of the fundamental tests of
the Standard Model. At present experimental results are consistent with the matrix being unitarity.
For example, the unitarity test of the first quark generation is confirmed with a precision of 0.06%
as
1 − (|Vud |2 + |Vus |2 + |Vub |2 ) = (6.1 ± 6.4) × 10−4 .
(1.8)
The uncertainty is dominated by the experimental accuracy of the Vud measurement. Thus it isrequired to improve the precision of the Vud measurement for further sensitivity.
There are several independent methods to obtain Vud . The method with nuclear super-allowed
beta-decay reactions gives the best precision of |Vud | = 0.97420(21) [7]. However, the method
has theoretical uncertainties originating from the nuclear structure. On the other hand, Vud can bealso determined using neutron beta-decays. It is the simplest beta-decay reaction, and there is no
theoretical uncertainty originating from the nuclear structure when determining Vud . To evaluate
Vud using neutron beta-decays, the ratio of axial vector to vector coupling constant λ is needed, in
addition to τn . The equation is expressed as
G2µ |Vud |2 5
1=
me (1 + 3λ2 )(1 + ∆RC )f,
τn
2π 3

(1.9)

CHAPTER 1. INTRODUCTION

ud

|V |

6

0.98

0.975

UC

In-

N

be

am

Unitarity

life

tim
e:

life

tim

e:

88

87

9.6

8.0

±0

.6

±2

.2

PDG average lambda

0.97

0.965
1.265

1.27
1.275
1.28
ratio of the axial-vector and vector couplings (|λ|)

Figure 1.4: Relation between the |Vud | value and the ratio of the axial vector to vector couplings
constant (λ) as computed using the neutron lifetime result. The result of λ = −0.12724 ± 0.00023[6] and the unitarity line of Vud [6] are also shown.
where f = 1.6887 is a phase space factor, ∆RC is the electroweak radiative corrections, Gµ =
1.16637(1) × 10−5 GeV is the Fermi constant evaluated by muon decay [8]. The current Vud value
obtained by τn and λ is shown in Figure 1.4, which is 0.9700 < |Vud | < 0.9760 [7]. The result takes
into account the discrepancy of the results of neutron beta-decay lifetime (see Section 1.2). The
precision is significantly limited by the experimental uncertainties of both τn and λ. By improving
the experimental precision of τn , we open the prospect for a more precise determination of the Vudelement.

1.2 Previous neutron lifetime measurements
Since the discovery of a neutron by J. Chadwick in 1932 [9], various experiments have been
conducted to measure its decay lifetime. Figure 1.5 shows the experimental results of the lifetime
used by the Particle Data Group [6]. The lifetime has been measured mainly by two independent
methods: (1) the UCN storage method, and (2) the in-flight method. The average result of the UCN
method gives (879.6 ± 0.6) s, while that of the in-flight method gives (888.0 ± 2.0) s. There exists

lifetime [s]1.2. PREVIOUS NEUTRON LIFETIME MEASUREMENTS

7

in-flight method: 888.0 ± 2.0 sec

890

885

880

UCN storage method: 879.6 ± 0.6 sec

1995

2000

2005

2010

2015

year
Figure 1.5: Results of previous neutron lifetime measurements [6]. The average of the in-flightmethod (red) is (888.0 ± 2.2) s, while that of the UCN storage method (blue) is (879.6 ± 0.6) s.
There exists a 8.4 s (4.0σ) discrepancy between the results of the two methods.
a significant discrepancy of 8.4 s (corresponding to 4.0σ) between the results of the two methods.
This may shake the confidence of the BBN theory, and prevent the further precise unitarity test of
the CKM matrix. As a result, the discrepancy becomes one of the serious issues not only in particle
physics but in astrophysics and cosmology. In order to resolve this problem, it is desired to evaluate
the result using a diﬀerent experimental method as well as to improve the measurement accuracy.

1.2.1 UCN storage method
In the UCN storage method, neutrons are cooled down into ultra cold neutrons (UCNs), whichhave velocities of a few m/s and the energies of a few hundred neV. One important characteristicof UCNs is that it feels an averaged potential (the Fermi potential) from the material of the storage
chamber and can be reflected, thus allowing UCNs to be stored. The neutron lifetime can beevaluated by counting the number of surviving UCNs after a certain amount of time. One of theexperiments using this principle was conducted between 2008 and 2010 in Institut Laue-Langevinby S. Arzumanov [10]. The schematic drawing of the experimental setup is shown in Figure 1.6.
In this setup, UCNs were stored in a stainless steel chamber. The UCN decay rate (λtot ) camefrom both beta-decays (λβ ) and the wall loss eﬀect due to the interaction between UCNs and thewall material (λloss ):λtot = λβ + λloss .
(1.10)The total decay rate λtot was measured by a proportional gas counter containing 3 He gas. In theexperiment mentioned above, λtot was measured in two diﬀerent geometries, for the purpose ofchanging the UCN collision frequency with the chamber wall. The total decay rate of each geometry

8

CHAPTER 1. INTRODUCTION

is expressed as
(1)
λtot

=

(2)

λtot =(1)(1)
log Ni − log Nf(1)
λβ + λloss =,Tf − Ti(2)(2)
log Ni − log Nf(2)λβ + λloss =,Tf − Ti(1.11)(1.12)

where the superscript (1) and (2) represent the two geometries of the chamber. The wall loss eﬀect
can be estimated using the counts of the thermal neutron detector J as
( (1) )J(1)
σie + σcap
λloss
εth
(
)
,
×
(1.13)
=
(1)
(1)
(1)
σie
λtot
Ni − Nf
(
(2)

λloss
(2)
λtot

= (

εucn
J (2)
εth

)

(2)
(2)
Ni − Nf)×

σie + σcap.
σie(1.14)

εucn
In these equations, εth and εucn are the detection eﬃciencies of the thermal neutron counter andthe UCN counter, respectively. σie and σcap are neutron cross sections of the chamber material for
inelastic scattering and capturing, respectively. Taking the ratio,
(2)

ξ≡

λloss
(1)

=

J (2) λtot (Ni

(2)

(2)

− Nf )

(2)

(1)

(1)

− Nf )λloss

J (1) λtot (Ni

τn =

1
ξ−1
= (1)
.
(2)
λβ
ξλtot − λtot

Finally, τn can be expressed as(1).

(1.15)(1.16)The recent measurement of this method gives the result of (880.2 ± 1.2) s [10].

1.2.2 In-flight method (proton counting)In this method, a neutron beam entered a decay volume, and protons from the neutron beta-decays
were trapped in the volume using a Penning trap technique. After the neutron beam irradiation, thetrapped protons were guided into the proton detector and the number is counted. The experimentusing this method was conducted by A. T. Yue et al. at National Institute of Standards and Technology
Center for Neutron Research (NCNR) [11]. The experimental setup is shown in Figure 1.7.
The number of detected protons (Np ) is
∫
∫
εp L
dv
(1.17)Np =da I(v) ,τn Av

1.2. PREVIOUS NEUTRON LIFETIME MEASUREMENTS

80

9S. Arzumanov et al. / Physics Letters B 745 (2015) 79–89

Measurements
trap; these two oof UCN collisions
surface exposed t
inside the copperwith the height olayer of fluid fluor
per cylinder is co
the UCN filling int
ters (2), (3), as w
detector shutter (stored UCNs fromter of 35 cm is in
the time intervalter (3) are closed
the cleaning interfor t clean = 200 s,
polyethylene disk
the polyethylene
continues during
Fig. 1. A scheme of the experimental set-up for the neutron lifetime measurement.
age interval, theFigure 1.6: Schematic
drawing of the experimental setup for the UCN storage method conducted by
1 – the entrance neutron guide, 2 – the UCN source shutter, 3 – the input shutter,
flow down into t
S. Arzumanov4et– al.
in fluorine
2015 [10].
UCNs
stored inthe stainlesstrapcoil,which
was installed
fluid
polymer,
5 –werethe copper
cylinder,6 – the steel
cooling
7 – thet reg = 150 s. Thenin the copper cylinder(5). disk,
The numberof remaining
UCNs werecountedby tube,the UCN(19).
polyethylene
8 – thermal
neutron counters,
9 – thepumping
10 – detector
theagain, however thecooler tube, 11 – the valve of the He filling line, 12 – the tube of the high-vacuum
total UCN loss pro
line, 13 – the vacuum set-up chamber, 14 – copper stripes, 15 – the additionalsurface above the trap bottom and the entrance shutter, 16 – the entrance planeinterval, is calcula
shutter, 17 – the pumping tube for the chamber bottom, 18 – the detector shutter,N 1 (t 1 ) and N 1 (t 2 )19 – the UCN detector, 20 – a horizontal cross section of the set-up with blocks oftime. In the geompolyethylene reflector for thermal neutrons.
ume is increased
100 µm and a wid
inelastic scattering on the trap walls, was performed in 2008–2010
the thickness of 1
at the high-flux neutron reactor of Institut Max von Laue–Paul
trap bottom; an aLangevin (ILL, Grenoble, France) [12]. Preliminary results, which
above the plane s
accounted for some systematic corrections, were published earlier
foils are covered w
in conference proceedings [13,14]. In the present work, particusult, the total surf
lar attention is devoted to analyzing all methodical effects of the
The intervals t
method.
geometry no. 1 a
A scheme of the installation is shown in Fig. 1. A storage trap
the storage interv

10

CHAPTER 1. INTRODUCTION

Figure 1.7: Schematic drawing of the experimental setup for the in-flight method conducted by A.
T. Yue in 2005 [11]. Protons from neutron beta-decays were trapped in the electrodes and guided
towards the proton detector. The neutron beam flux was measured by counting the 6 Li(n, α)3 H
FIG. 2: An illustration of the experimental method for measuring the lifetime by counting neutrons
events.
and trapped protons.

where A is the cross section of the decay volume, I(v) is the total neutron fluence for a neutron
velocityv, L is the
decay
volumelength,and εpandis thedetectioneﬃciency ofofthe
themeanprotonnumber
detector.
measurementof thedecay
detection
volume,accuratemeasurement
On the other hand, the neutron fluence in the decay volume can be estimated by counting thewithin the decay detection volume. Each of these diﬃculties is directly addressed
6 of neutrons
Li(n, α)3 H reaction using a diﬀerent detector
in this experiment in a manner similar∫ to that∫ of previous experiments utilizing the in-beamtechnique [8, 28–30]. Nneutron =daεneutron (v)σ(v)I(v)dv(1.18)
Adv∫
An illustration of the experimental method∫ is shownin Fig. 2.dvThe technique of trap= εion (v0 )v0da
σ(v0 )I(v) ,(1.19)
v by Byrne et al. and isping protons to increase the signal-to-background
A wasdvfirst proposed
described
detail31].α)A3 H
trapping
regionof length
L 2200intercepts
the detection
entire6
whereσ(v0 ) isinthe
crosselsewheresection of[28,Li(n,at neutron
velocityof v0 =
m/s. The63
eﬃciency
ions fromLi(n,H canofbethis
evaluated
neutronofbeam.
Withintheα)volumeregion,asneutron decay is observed by detecting
decay protons with an eﬃciency ϵp . ∫The∫ neutronΩ(x,beamy) is characterized by a velocity deεion (v0 ) = 2σ(v0 )dx dyρ(x, y)ϕ(x, y),(1.20)
pendent fluence rate I(v). The mean number of neutrons
in the trap at any time is given
4πby Ω(x, y), ρ(x, y), and ϕ(x, y) respectively
where! represent the solid angle of the detector, the 6 Li
1
number density, and the neutron fluencein the, plane perpendicular to the beam(3)axis.
Nndistribution= L daI(v)A
Finally, τn can be expressed as the ratio of the numberof vthese two kinds of events as
where A is the trap cross-sectional area having non zero fluence. Thus, the rate at which
ε (v )v N
decay events are detected, Ṅp , is τn = ion 0 0 neutron ,(1.21)
εproton !
L Nproton
1
−1
Ṅ
ϵ
da
I(v)
.
(4)
p = τ
pL
and the result was τn = (887.7 ± 1.2 (stat.) ± 1.9 (sys.))s [12].
v
A
After leaving the trap, the neutron beam passes through a detector whose eﬃciency for1.2.3 In-flight method (electron counting)detecting a low energy neutron is proportional to 1/v. Following the usual convention in

In 1989,
Kossakowski
et al. we
conducted
a lifetime
measurement
at Institut
Laue-Langevinreactorthermalneutron physics,
define theeﬃciency
for the neutron
detector,ϵo , as the ratiousing a diﬀerent method from those described above [13]. The schematic view of the experimentalof thereaction
product
the neutron
rateformed
incidenta 6 LiF by
depositfor neutrons
1.8.rate
Thetoneutron
beam wasintoonbunches
a rotating
drum and a
setup
is shown
in Figure8

to the decay electrons, the products of the 3He(n, p)t reaction in the drift chamber.
For this purpose a small, well defined quantity of 3He is admixed to the countergas (see sect. 5). The decay electron and (n, p) events can be well discriminated
due to their very different ionization power in the detector gas. By this method theneutron decay and neutron density are measured simultaneously in the same detector
1.2. PREVIOUS
NEUTRON LIFETIME MEASUREMENTS
and provide a direct measure for the neutron lifetime.
secondary n- guide11

gas container (4He + 3He + CO 2)......................

:

E P---:t-

1e-: ••••••••••••••••••(6Li F):t.:drift chamber

sense wires (MWPC)

1m
Fig. 2. Schematic view of the experimental setup. Only a part of the radiation shielding is shown.

Figure 1.8: Schematic view of the Kossakowski et al. experiment in 1989 [13]. The neutron
beam was formed into bunches by the rotating chopper drum and the crystal monochromator. The
electrons from neutron beta-decays were detected by the TPC.
crystal monochromator, and electrons from neutron beta-decays were detected by a TPC filled with
He and CO2 gas. The number of beta-decay events Sβ is expressed as
Sβ = N (1 − exp(−t/τn ))
t
∼ N ,
τn

(1.22)(1.23)

where N is the number of total neutrons passing through the TPC and t is the time during whicha neutron bunch exists in the TPC sensitive volume. A small amount of 3 He gas was also injected
inside the TPC for the neutron flux measurement. The number of 3 He(n, p)3 H events in the TPC
can be expressed using the cross section σ and the 3 He density ρ as
S3 He = N (1 − exp(−ρσvt)),∼ N ρσvt(1.24)(1.25)

where v is the neutron velocity. As a result, τn is obtained as the ratio of beta-decay events and3
He(n, p)3 H events in the TPC with the selection eﬃciency correction (εβ and ε3 He ) asτn =1 S3 He /ε3 He.
ρσv Sβ /εβ(1.26)The result of this experiment was τn = (878 ± 27(stat.) ± 14(sys.) ) s [13]. The main uncertainty
comes from low statistics of the beta-decay events. The result is not currently used to determine theaverage of the neutron lifetime by the Particle Data Group [6].

12

CHAPTER 1. INTRODUCTION
absorberpolarized
neutron beam

ﬂipperTime Projection Chambermagnetic mirror

3He+4He+CO2〜1 m

Spin Flip Chopper

Figure 1.9: Principle of this experiment. The polarized neutron beams are formed into bunches by
the SFC, and the number of beta-decay and the 3 He(n, p)3 H events are counted by the TPC.

1.3 This experiment
As described in the previous section, there is a significant discrepancy of the neutron lifetime
between the results of the UCN storage method and the in-flight method. An independent τnmeasurement using a diﬀerent technique is a crucial key to resolve this problem. Therefore, we areconducting the neutron lifetime experiment at J-PARC using the electron-counting method.

1.3.1 Principle
The principle of this experiment is shown in Figure 1.9. This experiment utilizes pulsed neutron
beams in the beamline 5 (BL05), at Materials and Life Science Experimental Facility (MLF) of
J-PARC. A polarized neutron beam at the beamline first enters a spin flip chopper (SFC), and theneutron beam is formed into bunches. The bunched neutron beams enter the TPC, and the numbersof both beta-decays and 3 He(n, p)3 H events are counted simultaneously. As described in Section
1.2.3, τn can be expressed as Eq. (1.26). Here, it is assumed that σ is inversely proportional to theneutron velocity (1/v law) [14], thus σv = σ0 v0 , where σ0 =(5333 ± 7) barn is the 3 He(n, p)3 H
cross section for a neutron with a velocity of v0 = 2200 m/s [15]. Using this relation,τn =1 S3 He /ε3 He.
ρσ0 v0 Sβ /εβ(1.27)

The advantages of our experiment compared to previous types of measurements can be summarized as follows.
• Forming neutron bunches by the SFC

1.3. THIS EXPERIMENT

13

Table 1.1: Comparison of our experiment and the Kossakowski et al. experiment [13] [16]. The
values with * will be improved in the future.
Year
Facility
Neutron source
Neutron wavelength
Neutron flux at detector [n/s]Beta-decay event rate
Pulse repetition rate
Beam size
TPC dimension
TPC operation gas (4 He:CO2 :3 He)
Data acquisition time
Statistical uncertainty

Kossakowski et al. experiment
1989
Institut Laue-Langevinreactor4.73 Å
2 × 105
0.1 cps110 Hzϕ20∼30 mm × 230 mm
190 mm × 190 mm × 700 mm
88 kPa : 7 kPa : 10 mPa
34 hours
3.1%

our experiment
2014∼
J-PARC
accelerator2∼8 Å
1 × 105 ∗0.08 cps ∗25 Hz
ϕ20∼30 mm × 400 mm
300 mm × 300 mm × 960 mm
85 kPa : 15 kPa : ∼100 mPa
4 × 103 hours ∗0.49% ∗

• Utilizing the intense pulsed neutron beams at J-PARC• Measuring the neutron fluence within the same detector
In this experiment, the pulsed neutron beam is formed into bunches, and the signal event is counted
only in the time window when each of neutron bunches is completely inside the TPC sensitive
region. This eliminates the uncertainty coming from neutron interaction with the material, whichcurrently becomes one of the main uncertainties in the UCN storage type of measurement. For thebunch formation, the high-intensity pulsed neutron beam is entirely favorable from the perspective of
beam flux. Moreover, the neutron fluence and neutron beta-decays can be measured simultaneously
by a single detector (TPC). As a result, the interdetector calibration between the beta-decay counterand the flux monitor does not produce any systematic uncertainties. This is a great advantage of
our experiment compared to the previous proton-counting measurement.
The previous neutron lifetime measurement by Kossakowski et al. utilized the same experimental
principle as ours. However, the precision was significantly limited due to the low statistics of thebeta-decay events. Since the pulsed neutron beams are used, our experiment has suﬃcient potential
to exceed the measurement precision of the previous experiment. Table 1.1 compares our experimentand Kossakowski et al. experiment. After the SFC upgrade as described in Section 7.2, 100-days
data taking is expected to yield 1 second statistical uncertainty at the design MLF operation powerof 1 MW.

Outline of this thesis
Chapter 1 gives an introduction of the neutron lifetime experiment. The physics motivation for the
lifetime measurement are discussed in this section. In addition, the advantage of our experimentcompared to the previous lifetime measurements are also introduced in this section. Chapter 2
describes the experimental setup of the beamline. The performance and the calibration method as

14

CHAPTER 1. INTRODUCTION

well as its specification are described. In Chapter 3, the acquired data set, the data acquisition cycle,
and the data quality are explained. The detail of the Monte Carlo simulation is described in Chapter
4. In the particle simulation section, detail processes of the simulated events are discussed. In
the detector simulation section, the physics model implementation to reproduce the detector output
is introduced. Chapter 5 explains the data analysis algorithm. This chapter mainly focuses on
the background subtraction method to evaluate the signal events. At last, the 3 He number density
measurement is also discussed. The Results of the data analysis are shown in Chapter 6. The
systematic uncertainties of the neutron lifetime is also listed in this section. Finally, Chapter 7
summarizes our experiment, with some upgrade plans for improving the measurement precision in
the future.

Contribution to this experiment
From the time I joined the lifetime experiment at J-PARC in 2015, I have significantly contributed
to both hardware and software work, in addition to taking the physics data. From the perspectiveof hardware, I developed a helium control gas sample, whose 3 He to 4 He ratio was precisely
controlled, using the gas handling system at J-PARC, which resulted in reducing the systematic
uncertainty of the neutron lifetime. I also developed a small prototype TPC and constructed ageneral energy calibration model using the Tandem accelerator at the University of Tsukuba. The
model is currently implemented in the Monte Carlo simulation. Regarding the software, based on
the careful observation of the TPC event display, I discovered a new type of background which had
not been taken into account at the time. I also invented a novel track detection algorithm using
the image recognition technique, which greatly reduced the uncertainty related to the pileup event.
Moreover, I implemented several physics processes in the Monte Carlo simulation to reproduce theexperimental distribution.
With the contribution described above, I have led my collaboration group since 2016, and playeda central role in analyzing the data from 2014 to 2018.

Chapter 2
Experimental setup
This chapter describes the experimental setup of the neutron lifetime measurement at Japan Proton
Accelerator Research Complex (J-PARC). The detailed experimental setup for each gas fill data is
discussed in Section 3.3.

2.1 Facilities and experimental setup
2.1.1 J-PARC facilities
J-PARC is a high-intensity proton accelerator facilities at Tokai, Ibaraki Prefecture, which is jointly
managed by JAEA (Japan Atomic Energy Agency) and KEK (High Energy Accelerator Research
Organization). A proton beam is accelerated by three types of accelerators, up to 400 MeV by the
Linac, 3 GeV by the Rapid Cycle Synchrotron, and 50 GeV by the Main Ring. Figure 2.1 shows abird’s eye view of J-PARC with the three accelerators emphasized. A fraction of the proton beamfrom the Rapid Cycle Synchrotron enters the Materials and Life Science Experimental Facility(MLF). Here, proton beams with a current of 333 µA interact with carbon graphite and mercury
targets to produce pulsed muons and neutrons, respectively, as a result of nuclear spallation reaction.
The repetition frequency of the spallation is 25 Hz. The resulting neutrons are cooled down to a
few tens of meV by a liquid-hydrogen moderator surrounding the mercury target.
The neutron lifetime experiment is conducted at the BL05 Neutron Optics and Fundamental
Physics beamline (NOP beamline), which is out of the 21 neutron beamlines at MLF. This beamline is constructed for precise measurements of fundamental physics using pulsed neutron beams.
In addition to the lifetime experiment, measurements of neutron scattering and interference areundergoing at this beamline.

2.1.2 Polarized beam branch
Neutron beams at BL05 are divided by super mirrors into three beam branches: polarized, nonpolarized, and low-divergence beam branches. The specifications of the three beam branches
are listed in Table 2.1. The neutron lifetime experiment is conducted using the polarized beam
branch in order to form a neutron bunch from the polarized neuron pulse beam (see Section 2.2).
15

16

CHAPTER 2. EXPERIMENTAL SETUP

Figure 2.1: Bird’s eye view of J-PARC [17]. Proton beams are accelerated by three types ofaccelerators: 400 MeV linear accelerator, 3 GeV rapid cycle synchrotron, 50 GeV main ring.
Table 2.1: The characteristics of the three beam branches in the BL05 at the design power of MLF(1 MW) [18] [19].
Branch nameNon-polarized
Polarized
Low-divergence

Beam size(ver.× hor.[mm2 ])50×40
120×6080×40

Beam flux[n/(cm2 · s)](3.8 ± 0.3) × 108(4.0 ± 0.3) × 107(5.4 ± 0.5) × 104

Divergence(ver.×hor.[mrad2 ])m=2
23 × 9.4
0.23×0.23

Luminance(n/(cm2 · str · s))—(1.8 ± 0.1) × 1011
(1.0 ± 0.1) × 1012

Polarization ratio—
0.94∼0.97—

The magnetic super mirrors selectively guide neutrons to the beam branch depending on theirpolarization direction, and the polarization is 94∼97% [18]. The neutron flux is expected to be(4.0 ± 0.3) × 107 neutrons/(cm2 ·s) at the designed MLF operation power of 1 MW [19].

2.1.3 Beamline setup
Figure 2.2 shows a schematic view of the polarized beam branch. The z-axis is defined as theneutron momentum direction, y-axis as the vertical direction, and the x-axis to satisfy the righthanded system. The pulsed neutron beams at this beam branch first enter the SFC. Here, eachneutron pulse is formed into five bunches. A TPC filled with He and CO2 gas is located at about
20 m downstream from the neutron source. It detects both neutron beta-decays and 3 He(n, p)3 H
reaction simultaneously. Iron and lead shields surrounding the TPC significantly suppress the event
rate of environmental background inside the TPC. The TPC is also surrounded by 14 sets of plastic
scintillators, thus almost every cosmic ray event passing through the TPC can be identified andrejected from the beta-decay event. The neutron beam can be switched on and oﬀ by a 5 mm-thick
LiF plate.

2.2. SPIN FLIP CHOPPER

17

Neutron Flow
Spin Flip Chopper(1)Time Projection Chamber

(15)
(14)

(2)
(3)
(5)

X
(4)
Y

(13)

(7)
(6)
(8)

(9)

(10)

(11)

(12)

Z

Figure 2.2: Schematic view of the polarized beam branch [20]: (1) exit of polarized beam branch,(2) exit of non-polarized beam branch, (3) exit of low-divergence beam branch, (4) lead shield, (5)magnetic super mirror, (6) radio-frequency coil, (7) (8) lead shield, (9) neutron shutter (5 mm-thickLiF), (10) iron shield, (11) plastic scintillator, (12) lead shield, (13) TPC, (14) beam dump, (15)vacuum chamber.

2.2 Spin flip chopper
In this experiment, the SFC is utilized to form neutron bunches from a polarized neutron beam. It
is composed of two radio-frequency (RF) coils and three magnetic super mirrors, surrounded bya lead shield. A magnetic field of 1 mT is applied in the vertical direction throughout the SFC tomaintain the neutron polarization. The polarization direction can be flipped after passing througheach of the RF coil when an alternative current is applied. At the magnetic super mirror, only a
non-flipped neutron can be reflected and guided downstream. By controlling the applied current of
the two RF coils, as described in Figure 2.3, a neutron bunch with an arbitrary length can be formed
from the neutron pulse.

2.2.1 Radio-frequency coilFigure 2.4 shows the picture of a radio-frequency coil. It has a 50 mm diameter and a 40 mm length
in total. A guide magnetic field By is applied in the vertical direction. The coil gives an alternating
magnetic field in the z direction, the amplitude of which is expressed as Bz . The neutron polarized
in the y direction starts a precessional motion in the RF coil due to the alternating magnetic field.

18

CHAPTER 2. EXPERIMENTAL SETUP

polarized neutron

absorber

RF coilB

magneticsuper mirror

to detector

B

Figure 2.3: Principle of the SFC operation. The neutron beam can pass through the SFC when no
current is applied at the RF coil (left), and is absorbed when an alternative current is applied (right).

The flipping probability of the neutron polarization direction P can be expressed as


(

P =
Bz2 +

Bz2

)2 sin 2ℏw
By − 2|µ
n|

|µn |
ℏ

√


(
)2
ℏw
Bz2 + By −t ,2|µn |(2.1)

where ℏ is a Planck’s constant, µn is a magnetic moment of a neutron, and ω is an angular speed of
the alternating magnetic field. The parameter t is the time in which a neutron exists in the RF coil,which is typically 10 µs at this beamline. One of the resonance conditions, at which the flipping
probability becomes one, is expressed asℏω,
2|µn |()
1|µn |Bz t =
n+
π.
ℏ
2
By =

This condition is realized at By = 1 mT, Bz = 0.3 mT, and ω = 2π × 29 kHz.

(2.2)
(2.3)

2.2. SPIN FLIP CHOPPER

Figure 2.4: Picture of the radio-frequency coil
[21].

19

Figure 2.5: Picture of the magnetic super mirror[21].

2.2.2 Magnetic super mirror
Cold neutrons at the polarized beam branch have a de Brogile wavelength of a few angstrom on
average, which is the same order of an atomic distance. Cold neutrons therefore feel an averagepotential from a material. Nickel, which is known to have a large potential, can reflect a cold
neutron with an incident angle smaller than about 0.1◦ . A super mirror is developed to achieve alarger reflection angle, and has recently been widely used in many applications. It is composed of
two kinds of substances with diﬀerent potential, typically Ni and Ti. They are alternately stacked,
the thicknesses of which are gradually changed. This realizes reflection of a neutron with a large
incident angle due to Bragg reflection.
A magnetic super mirror is composed of many layers of ferromagnetic and non-ferromagnetic
substances. Since a magnetic field is applied, the potential a neutron feels in the ferromagnetic
substance changes. Therefore, only neutrons with a certain polarization direction can be selectively
reflected at the mirror. This means the magnetic super mirror works as a spin polarizer for a neutron.
A picture and a specification of the mirror used in this experiment is shown in Figure 2.5 and Table
2.2. The mirror reflects a neutron with its incident angle up to 5 times larger than a pure Ni material(m value is 5).

2.2.3 Neutron time-of-flight distribution
During a normal operation of the SFC, the current applied to the two RF coils is adjusted to form
5 neutron bunches per pulse. The length of each bunch is about 40 cm, which is much shorter thanthat of the TPC in the z direction (∼ 100 cm). The distribution of time of flight (TOF), definedas the time length from the neutron pulse generation to the trigger timing of the TPC, is shown in20

CHAPTER 2. EXPERIMENTAL SETUP

normalized counts / bin

Table 2.2: Specification of the magnetic super mirror in the SFC [21].
Ferromagnetic substanceFe
Non-ferromagnetic substance SiGe3
Magnetic field
35 mT
Dimensions
140 mm × 35 mm × 0.7 mm
Number of layers
7445
m value
5

open
close

10−2

fiducial
sideband

10−3

10−4
0

10

20

30

40

time of flight (ms)Figure 2.6: Time-of-flight distribution of 3 He(n, p)3 H events in the TPC. The red and blue
histograms represent the shutter-open and shutter-closed data, respectively. Each of the five green
bands represents the fiducial time, in which a neutron bunch is completely inside the TPC sensitive
region. The light blue band represents the sideband region, during which no neutron bunch is inside
the TPC.

Figure 2.6 for 3 He(n, p)3 H events. Five peaks originating from the neutron bunches are clearlyseen in the figure. The “fiducial time” is defined as the time during which each neutron bunch iscrossing on the center line of the TPC, as described in Fig 2.7. During the fiducial time, since
all neutrons in a bunch are completely contained in the TPC, 4π solid angle acceptances for bothbeta-decays and 3 He(n, p)3 H are guaranteed. The fiducial times are expressed as green bands inthe figure. The sum of the five fiducial times is 2.35 ms per pulse, corresponding to 5.8% of thetotal measuring time. The “sideband time”, during which no neutron bunches exist inside the TPC,
is determined as 4 ms ≦ TOF ≦ 10 ms, corresponding to 15% of the total measuring time.

21

event rate

2.2. SPIN FLIP CHOPPER

Time of ﬂight

40 cm〜100 cmﬁducial time

ﬁducial time
start

ﬁducial time
end

Figure 2.7: Definition of the fiducial time along with the positional relation of a neutron bunch in
the TPC. The fiducial time is defined as the time during which the neutron bunch crossing on thecenter line of the TPC.

22

CHAPTER 2. EXPERIMENTAL SETUP

Figure 2.8: Picture of the neutron beam monitor [22].

2.3 Beam flux monitor
A neutron flux monitor manufactured by CANBERRA is set at the exit of the SFC. A picture of theflux monitor is shown in Figure 2.8. Argon, methane, and a small amount of 3 He gas are containedin the monitor, and the 3 He(n, p)3 H event inside the monitor is detected. An area of the sensitive
region is 10 cm × 4.2 cm, and its detection eﬃciency is measured to be about 10−5 for a thermal
neutron. The stability of the monitor against temperature and high voltage shifting was previously
studied [22], and it was found to satisfy our requirement of monitoring the neutron flux with a
precision of 0.1%.
The output pulse height of the beam monitor is taken by an ADC throughout the lifetime
measurement. The pulse height distribution is shown in Figure 2.9. A threshold level is set at 66%of the energy peak position, which is indicated as a red line in the figure. The number of events atthe beam monitor is used to correct for the beam flux fluctuation at the beam line. The algorithm tocorrect for the flux fluctuation is described in Section 5.3.1.

2.4 Neutron beam shutter
A neutron shutter, composed of 5 mm-thick LiF plate, is set just upstream of the TPC in the vacuum
chamber. The suppression ratio of this shutter is estimated to be 5 × 10−4 . The shutter can beswitched on and oﬀ by a remote control system; thus both the shutter-open and shutter-closed data
can be obtained. Figure 2.10 shows a mechanism to control the neutron shutter. Two 60 mm × 60
mm LiF plates are attached on a plastic plate, which can be rotated by a rotary stage. The right one
is used to stop the neutron beam in the shutter-closed mode, while the right one, with a 30 mm ×
30 mm hole, in the shutter-open mode.
In the lifetime measurement, the shutter-open and shutter-closed data is taken alternately, inorder to estimate the background event rate in the TPC. For the calibration measurement, theneutron shutter is set at the closed mode. The detail of the algorithm to subtract the background
event in the TPC is introduced in Section 5.3.1

# of events

2.5. VETO COUNTER

23

400

300

200

100

0
0

100

200

300

400

500

600

pulse height [ch]Figure 2.9: Pulse height distribution of the beam monitor. The main peak is fit by a gaussianfunction, and the energy threshold is set at 66% of the peak position (drawn as a red line in the
figure). The small peak at 500 ch comes from the pileup event. The small peak at around 500 ch
comes from neutron capturing process by boron nuclei (10 B(n, α)7 Li), which are expected to becontained in the inner wall of the beam monitor.

2.5 Veto counter
In order to identify cosmic rays event in the TPC, 12 mm-thick plastic scintillators are installedaround the TPC. Every scintillation light is converted into an electric signal by a photomultiplierand read out independently. As shown in Figure 2.11, each side of the TPC, except for the bottomside, is surrounded by two superposed scintillation counters. Furthermore, one more set of counters
are used in the front and back sides to avoid neutron beam ports of the TPC. Fourteen scintillation
counters are installed in total, and a cosmic ray trigger is produced when any of the 7 sets of counters
coincide. The event rate of the cosmic ray trigger is about 1 kcps, while that of the coincidence ofthe cosmic ray trigger and any of the 24 anode wires is about 50 cps. The detection eﬃciency for a
cosmic ray event was measured to be 96% [20].

2.6 Shield
A vacuum chamber containing the TPC is completely surrounded by a lead shield as shown in
Figure 2.12. The lead shield is put into an iron case, and the thickness is 10 cm for the front sideand 5 cm for the other five sides, respectively. It is installed to suppress environmental γ-rays andprompt γ-rays mainly originating from the SFC and the neutron target. The performance of theshield is measured by a NaI scintillation counter; with this shield, the event rate of environmental
γ-rays is measured to be decreased by 2% [20].

24

CHAPTER 2. EXPERIMENTAL SETUP

Figure 2.10: Picture of a neutron shutter system. Two LiF plates, the size of which is 60 mm × 60
mm × 5 mm, are attached to a rotary stage. The left plate has a 30 mm × 30 mm hole, which isused in the shutter-open mode. The right plate is used in the shutter-closed mode. The two states
can be switchable from the remote control system by rotating a plastic plate.

2.6. SHIELD

25

Figure 2.11: Picture of the cosmic rays veto counters [21]. Fourteen plastic scintillators (shown as
black plates in the figure) cover the TPC except for the bottom side.

Figure 2.12: Picture of lead shield surrounding the TPC [21]. The thickness is 10 cm for the front
side and 5 cm for the other five sides, respectively.

26

CHAPTER 2. EXPERIMENTAL SETUP

Figure 2.13: Picture of the TPC taken from the downstream side.

2.7 Time projection chamber

In this experiment, a TPC with a two-dimensional multi wire proportional chamber (MWPC) is
specially developed to detect both neutron beta-decays and 3 He(n, p)3 H. A picture of the TPC
is shown in Figure 2.13. The dimensions are 30 cm × 30 cm × 100 cm, and He and CO2 gases
are filled as operation gas. The detailed specifications of the TPC are listed in Table 2.3. Ionizedelectrons from beta-decays or 3 He(n, p)3 H reaction drift upwards by a uniform electric field of 300
V/cm, and it causes an avalanche multiplication at the MWPC region located at the top of the TPC.
The MWPC is composed of three wire layers, and the geometrical structure is shown in Figure
2.14. In the middle layer, 24 anode wires having 20 µm diameters and 24 field wires having 50µm diameters are aligned alternately with a interval of 6 mm. In the above and below layers, 162
cathode wires having 50 µm-diameters are aligned perpendicular to the anode and field wires, andevery 4 cathode wires in the same layer are electrically connected and read out as a single channel.
The equipotential lines of the TPC and MWPC calculated by Garfield software [23] are shown in
Figure 2.15 and 2.16, respectively.

27

Y

Z

2.7. TIME PROJECTION CHAMBER

Z

X
6 mm

Y
X

6 mm

6 mm

6 mm

anode wire (φ20 um)
ﬁeld wire (φ50 um)
cathode wire (φ50 um)

y [mm]

Figure 2.14: Wire structure of the MWPC. The diameter of anode wires, field wires, and cathodeCE OF THE BACKGROUND
wires are 20 µm, 50SUPPRESSIONµm, and 50 µm, respectively.93Cathode wires are aligned in the top and bottom
layers, and anode and field wires are aligned alternately at 6 mm intervals in the middle layers.

300

200

100

0

-100

-200

-300
-300

-200

-100

0

100

200

300
x [mm]

otograph of
5 Fe stage.

Figure2.15:
Equipotential
linesofofthe
theelectric
TPC infield
the ofFigure
6.16:
A XY image
x-y
calculated by Garfield software [23].
the plane
drift region.
The figure is taken from H. Otono’s Ph.D. dissertation [21].
ative permittivity of the 6 Li plate is measured as ϵr = 3.0 by

nd that of the PEEK is ϵr = 3.2 from its specification sheet.
ld is confirmed to be uniform by a calculation as shown in

under 50 kPa, 75 kPa and 100 kPa are measured by using

Figure 2.16: Equipotential lines of the MWPC in
the x-y plane calculated by Garfield software [23].

28

CHAPTER 2. EXPERIMENTAL SETUP
Table 2.3: Basic parameters of the TPC [20].
Dimensions
300 mm × 300 mm × 960 mm
Anode wire (24 ch)
ϕ20 µm, 1720 V
Field wire (24 ch)
ϕ50 µm, 0 V
Cathode wire (40 ch× 2) ϕ50 µm, 0 V
Electric field
300 V/cm (vertical direction)
Drift velocity
1.0 µ/sMultiplication factor
5 × 104
4
Gas composition
He (85 kPa), CO2 (15 kPa), 3 He (100 mPa)
The TPC has the following characteristics specialized for this experiment.
• Low background condition
Since the probability for a neutron to undergo beta-decays inside the TPC is about 10−6 ,the event rate of neutron beta-decays corresponds to only 1 cps at 200 kW operation. The
event rate of background events, such as cosmic rays, environmental radiation, and prompt
γ-ray emission from neutron capture reaction, should be significantly suppressed to realize
extremely low background condition for counting neutron beta-decays. It is shielded by leadand iron shields, and plastic scintillators surrounding the TPC are used to identify a cosmic
ray event passing through the TPC. Furthermore, the material used to construct the TPC are
carefully selected to reduce the environmental radiation.
• 3 He density control
In this experiment, an incident neutron flux is evaluated by counting 3 He(n, p)3 H events in
the TPC. Since the 3 He number density is used for this evaluation, the 3 He pressure in the
TPC is required to be precisely controlled during the measurement. Once operation gas is
injected in the TPC, therefore, it is kept sealed during the measurement. The TPC condition
gradually changes, such as the deterioration of the multiplication factor and the increase of an
attenuation eﬀect for drift electrons. The time transition of these eﬀects should be monitored
throughout the measurement.
• No magnetic field
The TPC in this experiment does not need to measure the momentum of a charged particle,
as is often the case with a TPC used in a collider-type experiment. As a result, no magnetic
field is applied in the TPC.
• Low scattering cross section for neutrons
A neutron scattered by operation gas molecules causes interaction with a TPC wall material
to produce prompt γ-rays. Because such a process becomes a background for beta-decays,
the operation gas is selected to make the scattering probability in the TPC as low as possible.
In addition, the inside walls of the TPC are covered by the LiF plates. 6 Li nuclei in the plate
can capture neutrons without almost no prompt γ-rays emission, which greatly contributes toreducing the background event for neutron beta-decays.

86
CHAPTER 6. TIME PROJECTION CHAMBER29
2.7. TIME PROJECTION CHAMBER

Figure 2.17: Background-subtracted energy spectra for G10 (left) and PEEK (right) measured by aGermanium
detector.
The verticalaxis ofis normalized
by the 6.4:
measuringtime. The
two figures
are
FigureA energy
spectrumof theFigure
6.3:
A energy
spectrumthetaken from H.detector
Otono’s Ph.D.
dissertation[21].
germanium detector with PEEK. The
germanium
with G10.
The backbackground was subtracted.
ground was subtracted.
Table 2.4: Physical properties of PEEK [24] [25].
Density
1.3 g/cm3
the frame as
described
Melting
point in the next section.
335 ◦ C
Water absorption
afterother24 hours
at 40% relative
humidity
0.15%as pre-amplifier,
The radioisotopes
in thecomponentsof the
TPC suchFlexural modulus
3.8 GPa
resistor, capacitor and 6 Li plate, are also confirmed to be satisfied
the requirements.
Heat distortion temperature
165◦ C
Volume resistivity> 1016 Ω · cm

6.1.3

Design of TPC

2.7.1 Material selection for low-background condition
The TPC consists of a drift part and a MWPC part. The electrons ionized by aMaterial constructing the TPC is required to have small amount of radioactive sources in order

passing
chargedparticle flux
insidedrift partmove ethelunderthe (PEEK),
electric polyphenylene
field which
to suppress
the backgroundfor thebeta-decay.
Polyethelketonesulfide,phenol formaldehyde
resin(PF), epoxy
glassonlaminate(G10), andisgeneratedby a positive
voltageappliedthe bottomof Alumina,
the driftwerepartlisted
andas
candidates for the TPC material. An energy spectrum of γ-rays from each material was measured
energized wires as shown in Figure 6.5. Resistors are installed between the wires
by a Germanium detector. The spectra for G10 and PEEK are shown in Figure 2.17. Since PEEK
anduniform field.
Wholeis shownare
in contained
Figure 6.6.
is an makeorganicathermoplastic
polymer,no picture
natural impurities
and has little radioactive
sources.
additionconsists
to radioactivity,
the cost, thewires.
water-absorbing
ratio,
the arebending
modulus,
andThe InMWPCof three-layered
The anode
wires
parallelto theother factors were carefully investigated, and as a result PEEK is selected as the material of theneutronand thephysicalcathodewires areperpendicular
toTablethe beam.
Considering
TPC [21].beam
The detailed
propertiesof PEEK
are listed in
2.4. The
event rate ofradioactivity
from
the
TPC
made
of
PEEK
is
estimated
to
be
(2.2
±
1.5)
cps
[20].
the energy loss of the minimum ionization under 100 kPa (He : CO2 = 85 : 15), thepitch of anode wire set to be 12 mm enables to collect at least one ionized electron

2.7.2
Operation
gas
at
99.9%
by using Geant4.
Field wires are located between the anode wires fortheconfinementof TPC,the electricfield.
gap
betweenanode andis
As operation
gas of the
He and CO
used asionization
gas theand quenchinggas,cathoderespectively.
2 are The
The totwobe
gases
are known
to haverelatively small
and capture
sections
for cana neutronset
6 mm
for axial
symmetry.
The scatteringcross sectionof thecrosselectricfield
beas listed in Table 2.5. Helium gas of 85 kPa and CO2 gas of 15 kPa are injected in the TPC as theshowningas.
Figure6.7 amountand thespecification
Table
6.4.added to the3operation
A smallof detailHe gas,ranging from is
50describedmPa to 200inmPa,
is alsoTwo 6-mm thick PEEK frames are used for the MWPC part. One has theanode/field wires and the top of the cathode wires on both sides; the other has thebottom of the cathode wires on one side. The wires are soldered to the circuit on
the kapton film pasted on the PEEK frame as shown in Figure 6.8. The position

30

CHAPTER 2. EXPERIMENTAL SETUP

Table 2.5: Scattering and capture cross section for a neutron with a nucleus in the TPC operationgas. [26]. The absorption cross section is expressed for a 2200 m/s neutron.
Isotope Natural abundance Scattering [barn] Absorption [barn]
3
He
1.4×10−665333(7)
4
He
0.9999986
1.34
0
12
C
0.989
5.559
0.00353
13
C
0.011
4.84
0.00137
16
O
0.997624.232
0.000117O0.00038
4.2
0.236
18
O
0.002
4.29
0.00016
operation gas for the flux measurement by counting the 3 He(n, p)3 H events in the TPC.

2.7.3 LiF plate covering
According to the cross section calculation, neutrons in the TPC are scattered by gas moleculeswith a probability of the order of 1%. Scattered neutrons cause interaction with the TPC walland produces prompt γ-rays. The γ-rays generate a Compton electrons inside the TPC sensitive
region with a probability of about 0.1%. As a result, this background is expected to occur for
every 105 incident neutrons in the TPC, which is larger than the neutron beta decay probability(L/v/τn = 1 m/1000 m/s/1000 s = 10−6 ). For suppressing this background, the internal walls of
the TPC are completely surrounded by LiF plates, so that no other material can capture scatteredneutrons. It is created by mixing LiF and polytetra fluoro ethylene (PTFE) as a sintered body, withthe weight composition of 30% and 70%, respectively. 6 Li-enriched (90% type and 95% type) Li
is used in order to capture a neutron through 6 Li(n, α)3 H reaction. More than 99.99% of the cold
neutron captured by the LiF plate causes this reaction, thus no γ-rays are emitted, although about
0.01% of them are captured with prompt γ-rays. A 200 µm-thick PTFE sheet is attached on thesurface of the LiF plates to prevent α rays or tritium ions from emitting inside the TPC sensitive
region. With these plates surrounding the TPC wall, the prompt γ-ray production can be suppressedto 10−4 . The background amount decreased, therefore, to an order of 10−3 for the beta-decay event.

2.7.4 Basic performance of the TPC
The basic performance of the TPC was previously studied using the calibration data [20]. Figure
2.18 shows the avalanche multiplication factor of the TPC as a function of the anode wire voltage.
The multiplication factor of about 104 can be obtained in the 50 kPa, 75 kPa, and 100 kPa operation
gas pressure. The drift velocity in the TPC is measured using the cosmic rays events passing
vertically through the TPC as described in Figure 2.19. The trigger eﬃciencies of the anode wires
were also evaluated by the cosmic rays events. A trigger eﬃciency of 97% is achieved around the
TPC center in the 100 kPa operation gas condition. Because of the non-uniformity of the electricfield around the anode wires, the deterioration of the trigger eﬃciencies near the TPC edges isobserved.

separation between the neutron decay and the 1.0-keV 12 C(n, γ)13 C reaction.
The reductionof the uncertainty on ϵcarbon is discussed in Section 5.5
together2.7. TIME PROJECTION CHAMBER
31
with the long-term stability.
30

Multiplication Gain ( ×104 )20

Discharge limit

102
1
50 kPa 75 kPa 100 kPa

He/CO2 = 85/15
4 ×10-1
1200 1300 1400 1500 1600 1700 1800 1900 2000

Sense Wire HV (V)Figure 2.18: Avalanche multiplication factor as a function of the anode wire voltage [20]. The
results with an operation gas pressure of 50 kPa, 75 kPa, and 100 kPa are plotted while the gas
is maintained
as He:CO
2 =85:15. The discharge limit line is empirically obtained.
Figure composition
6: Multiplication
gain
dependenceof the MWPC on voltage for sense wires andtotal pressure values. The gas mixture was fixed at He/CO2 = 85/15. Discharge limit was

Drift Velocity (cm/µs)

empirically obtained.
2

100 kPa
75 kPa
50 kPaMagboltz

He/CO2 = 85/15

5.4. Detection eﬃciency
for minimum ionizing particles
1.5
The detection eﬃciency
for the minimum ionizing particles with minimum1path length on the sense
0.5 wires was measured using the cosmic rays. At thenormal position of the 0TPC, the required direction was achieved only by
0

1

2

3

4

5

6

Reduced Drift Field E/p (V/cm/kPa)
horizontal cosmic rays, but the
numbers were not suﬃciently high. In order

2.19: Drift velocityof electrons
in the
TPC as a functionof the reduced
field strength
to use Figure
perpendicular
cosmicrays
instead,we rotatedthedrift
TPC
by 90◦ around[20]. The velocity calculated by the Magboltz software [27] is also drawn.

Figure5: Driftdependence
on reduced
fieldalmostand gaspressures,
E
the
beam
axis velocity
in the vacuum
vessel,which drift
has ansquarecrosswheresectionand p are the electric field and total pressure, respectively. The gas mixture was fixed at

24
He/CO2 = 85/15. The band shows the calculated
values with the Magboltz simulation
including an uncertainty of temperature[24].

32

CHAPTER 2. EXPERIMENTAL SETUP
He/CO = 85/15
2

1.05

100 kPaMIP Efficiency

1.00
0.95
0.90
0.85

50 kPa

0.80
0.75
0.70
0.65

0

5

10

15

20

25

Sense Wire Channel Number

Figure 2.20: Anode wire trigger eﬃciency for the minimum ionization particles [20]. Under the
100 kPa gas condition, the averaged wire eﬃciency of 97% is achieved in the TPC center region.

Figure 8: Detection eﬃciency for the minimum ionisation particles with minimum path
length on The
sense
wires.
The gasmixturefixed
2 = 85/15.
three
dimensionalchargedtrack in was
the TPC
canatbeHe/CO
reconstructedusing the anode and5.5.

cathode wire waveforms. The typical event displays of the beta-decay and 3 He(n, p)3 H events areshown in Figure 2.21. The energy deposit distributions in the three planes (x-y, y-z, and z-x planes)
are drawn. Noteperformancethat the absolute y positionof the track cannot be determined because the trigger
Long-term
stability
timing is not recorded. The clear track can be seen for the beta-decay events, while the large energy
deposit is localized for the 3 He(n, p)3 H events.

Since the gas is sealed during operation of the TPC, the attachment of
the ionized electrons in the drift cage is caused by contaminations due tooutgassing. The 55 Fe source on the rotation stage provides two drift lengths,
2.8 Preamplifier
which yields an attachment coeﬃcient, C [m−1 ]. A large attachment coeﬃEvery waveform of anode, field, and cathode wires, is amplified by a charge-sensitive preamplifier
cient means
degradation of the energy resolution.
shown in Figure 2.22. All of the preamplifiers are installed at the top of the TPC. The circuit diagramof the preamplifier is shown in Figure 2.23. The amplification factor can be varied by changing the

The
rate
to thepressure
achieved
the evacR0 outgassing
and R1 resistances.
Twowastypes relatedof preamplifierswith diﬀerent
amplification
factorsduring
are used inthis experiment. For cathode wires in the low plane and anode wires, R0 = ∞ (disconnected) anduationR1before
thegas filling,Pvac, andto3.6
×V/pC.
10−4ForPa
wasreached= 0 Ω, andthe amplification
factoris observed
be 1.3
cathodewires
in the highafter anplane and field wires, R0 = 300 Ω and R1 = 1 kΩ, and the amplification factor is observed to be
0.23 V/pC.
linearity of the preamplifier
outputIn
withthis
respect
to the input charge
confirmed
evacuationof Theapproximately
2 weeks.
condition,
the isoutgassing
rate
up to an output voltage of 3.3 V. A typical output waveform of the preamplifier is shown in Figure
2.24.
was 4.4
Pa/day. Figure 9 shows the long-term evolution of the attachment

coeﬃcient for the two diﬀerent Pvac . The TPC achieved C < 0.25 m−1 for
5 days of continuous operation, which resulted in an energy threshold of

2.8. PREAMPLIFIER

33

Figure 2.21: Typical event display of the beta-decay (top) and 3 He(n, p)3 H (bottom) events.

Figure 2.22: Picture of a preamplifier [21].

34

CHAPTER 2. EXPERIMENTAL SETUP

C1

C3
R4

R2

R5

R1

input

R0

OPA
656

R3

output

OPA
656

C2

voltage [ADC channel]

Figure 2.23: Preamplifier circuit. The multiplication factor is adjustable by changing R0 and R1
values.

80
60
40
20
0
0

200

400

600

800

1000

time [× 0.1 µs]

Figure 2.24: Typical preamplifier output waveform. The trigger timing is adjusted to be 30 µs in
the time window.

2.9. TEMPERATURE MONITORING

35

Figure 2.25: Installing position of the eight LakeShore thermometers inside the vacuum chamber.

2.9 Temperature monitoring
The temperature around the TPC is monitored by platinum thermometers, by measuring the resistivity of the platinum using a four-terminal method. Fourteen thermometers with two diﬀerent
types of systems, manufactured by Automatic Systems Laboratories and LakeShore, are used tomonitor the TPC temperature. Their measuring uncertainties are 60 mK at 298 K and 105 mk at
300 K, respectively. The detailed specifications of the two types of thermometer systems are listed
in Appendix B. Figure 2.25 shows the position of the eight LakeShore thermometers inside thevacuum chamber. As shown in Figure 2.26, the temperature inside the TPC during the lifetime
measurement increases with the elapsed time. This is due to the heat produced by the preamplifiers,
and a temperature increase of typically 5 to 10 degrees is observed.

2.10 Data acquisition system
The schematic diagram of the fast data (TPC signal, veto counters, kicker pulse signal) acquisition
system in this experiment is shown in Figure 2.27. Signals of the TPC and the cosmic ray vetocounters are recorded by the Front-end INstrumentation Entity for Sub-detector Specific Electronics(FINESSE) modules in the COmmon Pipelined Platform for Electronics Readout (COPPER) Lite
system [28]. On 5 COPPER Lite boards, 16 FINESSE ADC modules and 2 FINESSE TDC modules
are implemented. The detailed specifications of the ADC and TDC modules are listed in Table

CHAPTER 2. EXPERIMENTAL SETUP
Temperature [K]

36

CH 1
CH 2

320

CH 3
CH 5
CH 6

315

CH 7
CH 8

310

305

300

05/28
09:00

05/29
09:00

05/30
09:00

05/31
09:00

06/01
09:00

06/02
09:00
DAQ Time

Figure 2.26: Temperature inside the TPC during the lifetime measurement. CH6, CH7, and CH8
thermometers are installed close to the preamplifiers, which shows higher temperatures than others.
2.6 and 2.7, respectively. Waveforms of 24 anode wires, 24 field wires, 40×2 cathode wires are
digitized by the ADC module. The signal timing of TPC wires, veto counters, and a kicker pulse,which represents the time of producing the neutron beam, are respectively digitized by the TDC
modules. The digitized data by the ADC and TDC is sent to a computer through ethernet cables.
The trigger signal for taking the fast data is sent to the five COPPER Lite boards when any of 24
anode wires in the TPC exceeds a threshold voltage of 20 mV. The threshold level corresponds to a
200 eV energy deposit in the TPC. Once a trigger signal is accepted, each of the five COPPER Liteboards independently sends all of the digitized data to the computer. During the data transfer time,
which is typically 100 µs, the COPPER Lite modules output a busy signal and additional trigger
signal is rejected. The trigger signal is also vetoed for 70 µs when any of 7 sets veto counters
coincided with the TPC signal, in order to avoid triggering cosmic ray events. At the 300 kW
accelerator operation, the typical trigger event rates are 10 cps in the shutter-open mode, and 5 cps
in the shutter-closed mode, respectively. For the drift velocity calibration, cosmic rays data is taken
as a data acquisition cycle, in which the coincidence of TPC signal and any of 7 sets veto counters
signal is required as a data acquisition trigger (see Section 3.2 for the data acquisition cycle and its
trigger rate).
Aside from fast data acquisition, the TPC condition, such as gas pressure, temperature, and wireand electrode voltages are monitored on a continuous basis during the lifetime measurement. The
TPC gas pressure is measured every 7 seconds by a transducer pressure gauge (Mensor gauge) withan accuracy of 0.01%. As described in Section 2.9, the TPC temperature is monitored by fourteen
thermometers, whose data is recorded and sent to a computer every 11 seconds. The high voltages
applied for the anode wires and the drift field electrode are also monitored during the measurement,

2.10. DATA ACQUISITION SYSTEM

24 ch OR37

Gate Generator

veto

Gate Generator

Gate Generator

vetotriggergate

Anode Wire 24 ch
Field Wire 24 ch

FADC

Cathode Wire 80 ch
Clock

Cosmic Ray
Veto Countercoincidence
7 ch

Kicker Pulse

start

7 ch OR
stop
stop

14 ch

TDC

stop
busy
digitalanalogCopper Lite

Figure 2.27: Schematic diagram of the DAQ circuit for the physics data acquisition. ADC and TDC
operating in the COPPER Lite system [28] are used for taking the data. Wire waveforms of the
TPC are recorded by the flash-ADC (FADC), and timing of waveforms, kicker pulse, and cosmic
ray veto counters are recorded by the TDC.

Table 2.6: Specification of the Finesse ADC module.
Model
GNV-440 FINESSE 8CH ADC BOARD
Resolution
12 bits
Sampling clock frequency 10 MHz (external input)
Dynamic range
2 V peak to peak
Data size
10 bitInput channel
8Dimensions
76 mm × 186 mm

Table 2.7: Specification of the Finesse TDC module.
Model
FINESSE 32CH MULTI HIT TDC V2
Sampling clock frequency 125 MHz
Dynamic range±131 µs from trigger timing
Input channel
32
Dimensions
76 mm × 186 mm

38

CHAPTER 2. EXPERIMENTAL SETUP

Figure 2.28: Schematic view of the calibration measurement setup. The calibration source (55 Fe) is
attached to a rotary stage, enabling to change the height of the source. The drift length of electronsis 75 mm for Fe (up) mode and 225 mm for Fe (down) mode.
and an alert signal is produced when each of the voltage fell below a threshold voltage.

2.11 Calibration system
This section describes the energy, drift velocity, and dead time calibration system for the TPC.

2.11.1 Energy calibration
The multiplication factor of the TPC during the measurement is monitored using a 55 Fe X-ray
source. The Kα and Kβ X-ray, the energies of which are 5.86 keV and 6.45 keV, respectively[29], are emitted from the 55 Fe source. The X-ray causes a photoelectric eﬀect with the TPC gas
molecules, and the total energy is observed as the kinetic energy of a photoelectron by the TPC.
The source is attached to a rotary stage located close to the TPC side wall, making it possible toselectively change the height of the source position. The drift length of an electron is 75 mm in the
Fe (up) mode, while 225 mm in the Fe (down) mode as shown in Figure 2.28. The X-ray is limited
within 20 mrad in the vertical direction by a collimator.
A set of Fe (up) and Fe (down) data is taken every hour during the measurement, in order tomonitor the multiplication factor of the TPC. A typical transition of the energy peak position for
Fe (up) and Fe (down) mode is shown in Figure 2.29. The gas deterioration from outgas causes an
exponential reduction of the multiplication factor. Once the operation gas is pumped out for a whileand new gas is filled in the TPC, the energy peak position completely recovers. By comparing theenergy peak position between the two setups, the attenuation eﬀect for an electron to drift 150 mm
can be evaluated as a function of time. The attenuation length λ can be expressed as
λ=225 mm − 75 mm,
log(Eup /Edown )(2.4)

peak position [ADC channel]

2.11. CALIBRATION SYSTEM

39

Fe (up)1100

Fe (down)

1000

900

06/01
09:00

06/02
09:00

06/03
09:00

Time
Figure 2.29: Typical transition of the energy peak position after gas filling. The red and blue points
show the result at Fe (up) and Fe (down) modes, respectively. Each of the data points is fit by an
exponentially-decaying function.

where Eup and Edown represent the peak positions in the Fe (up) and Fe (down) modes, respectively.
The average attenuation length evaluated using Eq. (2.4) is about 2000 mm, corresponding to 7%
attenuation for an electron to drift 150 mm. Using this result, the energy calibration is conducted
as a function of time, correcting for the attenuation eﬀect. The attenuation becomes significant one
week after filling the gas, thus the operation gas is changed on a weekly basis in average during thebeam time.

2.11.2 Drift velocity calibration
The drift velocity of an electron inside the TPC is evaluated using cosmic ray events passing
vertically through the TPC. Such an event has a diﬀerent rise time of waveforms among anodewires, originating from the drift time of an electron. The diﬀerence between the fastest and theslowest rise time Tdrift corresponds to the drift time of the TPC length in the y direction (h ∼ 30 cm).
However, the eﬀective length becomes h − ∆h, where the correction length ∆h can be expressedusing the number of hit anode wires (n) as ∆h = h/n (see Figure 2.30). With this correction, the40

CHAPTER 2. EXPERIMENTAL SETUP

number of hit anode wires
n=8

anode wirehΔh=h/ncosmic ray
Figure 2.30: Cross section of the TPC for a cosmic-ray event describing the drift length correctionof Eq. (2.6). The maximum drift length of electrons among the anode wires (the rightest anodewires among 8 hit anode wires in the figure) becomes h − ∆h, where ∆h is expressed as h/n.
drift velocity vn can be expressed asvn =hTdrift()∆h(h − ∆h) 1 + h−∆h=Tdrift)(h/n= v0 1 +h − h/nv0=
1 − 1/n

(2.5)
(2.6)
(2.7)
(2.8)

Hence, by fitting vn as a function of n using the function in Eq. (2.8), the modified drift velocityof an electron v0 can be evaluated as shown in Figure 2.31. Since the drift velocity depends on theoperation gas composition, the drift velocity calibration is conducted for each gas. The typical drift
velocities v0 are evaluated to be 1.0 cm/µs.

2.11.3 Dead time calibration
As described in Sec 2.10, the data acquisition system vetoes the trigger signal under two conditions:(A) the data transfer time (typically 100 µs per trigger), (B) veto counters signal coincides with thatof anode wires (70 µs). During this dead time, no event in the TPC is recorded even if it happens,vn [cm/us]

2.11. CALIBRATION SYSTEM

41

2.5
2
1.5
1
0.5
0
0

2

4

6

8

10

12 14 16 18 20 22
Number of hit anode wires (n)Figure 2.31: Drift velocity (vn ) distribution as a function of the number of hit anode wires (n). The
points are fit by the v0 /(1 − 1/n) function to evaluate the modified drift velocity (v0 ).
which aﬀects the event rate of the signal and background events. Thus an accurate calibration
process for dead time is necessary to evaluate the accurate event rate of signal and background
events. The calibration is processed as a function of TOF, because both (A) and (B) components
have TOF dependence.
The dead time calibration is conducted according to the following procedure. Let’s assume irepresents a neutron pulse identification number (1 ≦ i ≦ N ; N is the number of total neutron
pulses).
1. The dead time flag of i-th neutron pulse di (tTOF ) is 1 when the veto function works at the
TOF of tTOF . That is to say,{1 (tstart≦ tTOF ≦ tendii )di (tTOF ) =,0 (otherwise)
where tstartand tend
represent the start and end timing of the dead time in the i-th neutroniipulse, respectively.
2. The dead time ratio D (tTOF ) is evaluated as
1 ∑di (tTOF ).
N i=1

(2.9)

L (tTOF ) = 1 − D (tTOF ).

(2.10)N

D (tTOF ) =3. The live time ratio L (tTOF ) as defined as

42

CHAPTER 2. EXPERIMENTAL SETUP

Live time ratio

1
0.8
0.6
0.4
0.2
0
0

10

20

30

40

Time of flight [ms]Figure 2.32: Live time ratio (L) of the data acquisition system in the shutter open mode. Hollows
originating from neutron bunches (15 ms < tTOF < 35 ms) and the neutron beam production(tTOF ∼0 ms) are observed.
4. The corrected event rate at tTOF , expressed as R (tTOF ), is obtained by multiplying the inverseof L (tTOF ) by the observed event rate R0 (tTOF ) as
R (tTOF ) = R0 (tTOF ) ×

1.
L (tTOF )(2.11)

Figure 2.32 shows the L (tTOF ) distribution in the shutter-open mode. Since a lot of background
events are produced as prompt γ-rays the moment when a neutron beam is generated, L (tTOF ∼0ms) becomes smaller. Several hollows originating from 5 neutron bunches, at around 15 ms< tTOF < 35 ms, are also observed in the plot. The average of the live time ratio is about 93%.

2.12 Gas handling system
The operation gas described in Section 2.7.2 is injected into the TPC through the SUS-based gas
handling system located at the BL05 beamline. The schematic diagram of the gas handling system
is shown in Figure 2.33. Every region and valve in the system is named as I1, I2,..., and V1, V2,...,
respectively. The vacuum chamber housing the TPC is expressed as ITPC in the figure. Helium
and CO2 gas cylinders are connected with the I1 region, while a 3 He gas cylinder is stored at the I6
region. Two Mensor pressure gauges are connected at Im region, whose full scales are 120 kPa and
35 kPa, respectively. The Pfeiﬀer pressure gauge, the full scale of which is 1.3 kPa, is connectedwith I6 region for low-pressure measurement. The detailed specification of the pressure gauges islisted in Table 2.8 and 2.9. The Automatic Systems Laboratories platinum thermometer is attached
to a surface of I1 SUS tube to measure gas temperature. A rotary pump and a turbo molecular pump(TMP) are attached to the I1 region to pump out the gas.

2.13. MASS SPECTROMETER

43

Table 2.8: Specification of the Mensor pressure gauge.
Model
Mensor CPG2500
Full scale
120 kPa(chA), 35 kPa(chB)
Precision
Max(0.01% of measured value, 6 Pa) for chA, 3.5 Pa for chB
Sensor volume
5 cc
Sensor temperature 5 K larger than environmental temperature
Table 2.9: Specification of the Pfeiﬀer pressure gauge.
model
690A11TRA
full scale 1333 Pa
precision 0.06% of measuring pressure + 25 mPa
As the operation gas, 3 He, 4 He, and CO2 gases are injected into the TPC in this order throughthis gas handling system. At first, 3 He gas is expanded from I6 to Im, and after measuring thepressure (a few kPa) by the Mensor gauge, it is expanded to ITPC. Next, 4 He gas is made to flow
directory into the TPC, with V1, V9 and VTPC valves open and others closed. After waiting 10
minutes for the gas to approach equilibrium, the 4 He pressure is measured by Mensor gauge, andCO2 gas is injected into the TPC by the same procedure. It took approximately one hour to fill thethree gases into the TPC.

2.13 Mass spectrometer
The isotopic contamination in a helium gas cylinder is required to be measured for evaluating 3 He
number density in the TPC. The contamination ratio for a typical helium gas cylinder is known
to be 0.1 ppm, which corresponds to about 10% of the total 3 He number density in the TPC.
The contamination ratio is precisely measured by a dual-type mass spectrometer (VG5400) at the
University of Tokyo [30]. A picture of the mass spectrometer is shown in Figure 2.34. A sampled
gas from a helium gas cylinder is attenuated to an order of 10−5 Pa and injected into the ion source
region. The gas is ionized and accelerated, and 3 He and 4 He ions are separated by the bending
region where a magnetic field is applied in the vertical direction. As ion detectors, the spectrometerhas a Faraday cup for a 4 He ion and a multiplication counter for a 3 He ion, respectively. The
number of both 3 He and 4 He ions can be counted simultaneously. The detail of the 3 He/4 He ratio
measurement is described at Section 5.4.

44

CHAPTER 2. EXPERIMENTAL SETUP

Baratron690A
Mensor
CPG2500
Baratron627B

Ib
TPC
ITPC

VTPC

I8

Im

He gasV2

CO2 gas

V5
V3
M4

V7

M5

V8

V2

I3

V9

TMP

V1

V10

I1

M3

I2

I4
I5

1300.00

V6

I7

I6
M6
M7

Swagelok
3/8' valve SS-6BG
1/4' valve SS-4H

Figure 2.33: Schematic diagram of the gas handling system. Helium, CO2 and 3 He gases are
injected into the TPC using this system.

2.13. MASS SPECTROMETER

45

Figure 2.34: Picture of the mass spectrometer [30] at the University of Tokyo. As indicated by thetwo arrows, the 3 He and 4 He ions can be separated by the magnet and counted simultaneously.

Chapter 3
Data acquisition cycle and data quality
This chapter describes the data acquisition cycle for the lifetime measurement from 2014 to 2018.
During the four years, some of the experimental setup changed as described in Section 3.3. The
data quality analysis in comparison with the diﬀerent hardware condition is of great significance toguarantee our analysis, which is discussed in the last part of this chapter.

3.1 Acquired physics data
We started taking the physics data to evaluate τn in 2014, and continued until 2018. Table 3.1 shows
the acquired data set. We took the data with 20 sets of operation gas conditions. The detailed
measurement condition of each gas ID is described in Table 3.3. The accelerator operation power
decreased from 500 kW to 200 kW in 2015 due to a target problem in MLF. In total, we obtained
960 hours (40 days) beam-incident data, and 6.0 × 1011 neutrons entered the TPC. The first result of
this experiment was presented by S. Ieki using the data between 2014 and 2016 [31]. All-combined
neutron beam fluence in Table 3.1 is 3.6 times more than the data used in the first result.

3.2 Data acquisition cycle
The data acquisition cycle during the lifetime measurement is listed in Table 3.2. The data with
the neutron beams is taken in two multiplication gain modes. At the normal-gain mode, 1720 V isapplied and the avalanche multiplication gain corresponds to 104 . At the low-gain mode, 1200 V isapplied and the avalanche gain is 102 .

Table 3.1: Physics data set
PeriodStart
2014A
2014/5/27
2015A
2015/4/26
2016A
2016/4/16
2017A
2017/5/28
2017B
2017/11/21
CombinedEnd
2014/6/3
2015/5/4
2016/6/14
2017/6/28
2018/3/22

Gas ID
42
53
63-66
83-89
94-101

Operation power [kW] Open [hour]
300
34
500
16
200
224
150
172
300, 400
514
960

47

Open [run]
126
57
825
517
1644
3169

Closed [run]
119
59
788
517
1509
2992

Calibration [run]
349
105
1222
792
2404
4872

Neutrons entering TPC [×1011 ]
0.2
0.2
1.2
0.6
3.9
6.0 × 1011

48

CHAPTER 3. DATA ACQUISITION CYCLE AND DATA QUALITY
Table 3.2: List of data acquisition cycleGainnormallow

ModeTime [s]open1000 or 1200
closed1000 or 800
Fe (up)100
Fe (down)
100
cosmic100
open1000 or 300
closed1000 or 300

Neutron shutter
open
closedclosedclosedclosedopen
closedTrigger condition
TPC hit without cosmic veto counters hit
TPC hit without cosmic veto counters hit
TPC hit without cosmic veto counters hit
TPC hit without cosmic veto counters hit
TPC and cosmic veto counters hit coincidence
TPC hit without cosmic veto counters hit
TPC hit without cosmic veto counters hit

Trigger rate [cps]
10
5
40
40
50
4
0.2

The purpose of taking each data in Table 3.2 is described in the following.
• Normal gain / shutter open
measuring the neutron beta-decay and 3 He(n, p)3 H events for evaluating τn .
• Normal gain / shutter closed
evaluating the background flux without the presence of the neutron beam.
• Normal gain / Fe (up), Fe (down)
detecting 5.9 keV monochromatic X-rays for the TPC energy calibration. The source position
is changed in two ways for monitoring the attenuation eﬀect.
• Normal gain / cosmic
detecting cosmic rays for the drift velocity calibration inside the TPC.
• Low gain / shutter open
measuring the 14 N(n, p)14 C background amount with respect to the 3 He(n, p)3 H event. In
this mode, the 14 N(n, p)14 C and 3 He(n, p)3 H peaks can be clearly separated in the energy
deposit distribution.
• Low gain / shutter closed
evaluating the background event in the low-gain measurement.

3.3 Device conditions during the measurement
During the four-years data taking time, the hardware conditions was changed as described in Table
3.3. The hardware setup conditions were changed mainly at the interval of the data acquisition
period. For example, the TPC alignment is found to be oﬀ the correct position after 2017. This isbecause the TPC was temporarily taken out from the beamline for the performance measurement,
and realigned at the beamline in the year. The TPC position directly aﬀects the beam profile
distribution in the TPC, which leads to the variation of the event selection eﬃciencies.

3.4. GAIN DETERIORATION WITH THE ELAPSED TIME

49

Table 3.3: List of experimental setup condition. A single capital letter in the table means the setup
had not changed during the period.
Fill number
42
53
63 64 65 66 83
84
86 87 88 89 94
95
Year
2014A 2015A
2016A
2017A
Beam power [kW]
300
500
200
150
300
Target type#2
G1 helium cylinder
#6
#7
#8
#10
Calibration source#1#2
Beam monitor position
A
B
C
D
E
LiF guide positionA
B
CD
TPC alignment
A
B
Proton bunch mode
double bunch
BL06-side Fe shieldno shield
shieldLow-divergence beam branch?
closedVacuum condition
not badgoodbad
DAQ time (open, closed) [s]1000, 1000
1200, 800
1200, 800
1000, 1000
TDC module
old
new

96

97 98
2017B

99 100

101

400
#8
#11

single bunch
almost open
not badmix
1200, 800

3.4 Gain deterioration with the elapsed time
The attenuation eﬀect of a drifting electron in the TPC is estimated using the calibration source data
as described in Section 2.11.1. As Figure 3.1 shows, the attenuation coeﬃcient gradually grows
with the elapsed time after the gas filling time, due to outgas from the material inside the vacuum
chamber. The attenuation eﬀect is empirically known to be in equilibrium at a coeﬃcient of about
1.5 m−1 .

CHAPTER 3. DATA ACQUISITION CYCLE AND DATA QUALITY

attenuation coefficient [m-1]50

Fill42Fill530.6

Fill63
Fill64
Fill650.4

Fill660.2

attenuation coefficient [m-1]

0
0

4

6

8

10

elapsed day

1.5

1

Fill83Fill84Fill860.5

Fill87
Fill8800attenuation coefficient [m-1]2

Fill89

0.5

1

1.5

2

2.5

3

elapsed day

0.8
0.6

Fill94Fill950.4

Fill96
Fill97
Fill980.2

Fill99Fill100

00Fill101

1

2

3

4

5

6

7

8

elapsed day

Figure 3.1: Growth of the attenuation coeﬃcient in the TPC as a function of the elapsed day after
the gas filling time: (top) 2014A∼2016A, (middle) 2017A, (bottom) 2017B.

Chapter 4
Simulation
This chapter describes the detail of the simulation framework. The Monte Carlo simulation of ourdetector system is constructed based on the Geant4 simulation framework [32] [33] [34]. In thissimulation, the output waveforms of the anode, field and cathode wires are simulated. The event
selection procedure, described in Chapter 5, is applied to the waveforms in order to evaluate signal
selection eﬃciencies for evaluating the εβ and ε3 He parameters in Equation (1.27). The result isalso used to estimate the background amount in the signal region.

4.1 Overview of simulation process
Figure 4.1 shows the overall procedure of the Monte Carlo simulation. It is divided into two
processes: the particle simulation and the detector response simulation processes. At the particle
simulation framework, the detector setup at the BL05 polarization beam branch is implemented,
such as plastic scintillation counters, the lead shield, the beam pipes, and the LiF plates. The
TPC structure made of PEEK and LiF plates is also faithfully reproduced. A schematic view ofthe setup construction in the simulation framework is shown in Figure 4.2. Particle transportationand ionization process in the TPC is simulated by the Geant4 simulation, and the corresponding
energy deposit from a charged particle is calculated as a function of its position. Note that thetime information is not used at the simulation procedure. The physics model of Bertini Cascade“FTFP_BERT_PEN” (Fritiof with Precompound, Bertini Cascade, Penelope model) is used for theinteraction model.
The energy deposit calculated at the particle simulation process is converted into the wire
waveforms in the detector simulation process. In this process, the induced current and the spacecharge eﬀect at the avalanche multiplication as well as recombination and attenuation during the drift
are implemented. A template waveform and the noise level are evaluated based on the experimental
waveforms. The event selection algorithm, which is the same as the one used in the experimental
data, is applied to the simulated waveforms.
51

52

CHAPTER 4. SIMULATION••

detector geometry
physics list••

Particle Simulation(Geant4)

Particle interaction- absorption- scatter- ionization

Deposit energy,
Point, Time

template waveformnoise waveform

Detector Simulation

Analysis
Waveform

Detector response- diﬀusion- induced current- attenuation

Figure 4.1: Simulation flow.

(a) Overall detector setup.

(b) TPC structure.

Figure 4.2: Schematic view of the detector setup constructed at the Geant4-based Monte Carlosimulation system: (a) overall detector setup, (b) TPC structure.

vertical [mm]4.2. BEAM PROFILE MEASUREMENT

53

30
2500

20
2000

10
0

1500

−10

1000

−20

500

−30
−30

−20

−10

0

10

20

30

0

horizontal [mm]Figure 4.3: Neutron beam profile observed from the downstream side. It is measured by a neutron
position detector at the TPC position.

4.2 Beam profile measurement
The neutron beam profile is measured by a two-dimensional neutron position detector. As a neutron
position detector, a ZnS/6 LiF scintillator is attached at a position-sensitive photomultiplier (model
R3292) manufactured by Hamamatsu Photonics. The detector has a sensitive region of 60 cm2 , andthe spatial resolution is less than 1 mm2 [35]. The position dependence of the detection eﬃciency
is evaluated in advance at an interval of 5 mm, and it is found to be at most 10% in the region within
15 cm from the center of the detector.
The neutron position detector is set at the position of the TPC, and the two-dimensional beam
distribution is measured. The eﬃciency-corrected beam profile is shown in Figure 4.3. During
the measurement, the SFC operated as usual, thus making 5 neutron bunches per pulse, so as toreproduce the lifetime measurement condition. The standard deviation of the distribution is 5.8 mm
and 7.6 mm in the x and y direction, respectively. The result of this beam profile measurement isused as an input of the interaction point as described in Section 4.3.

4.3 Simulated events
4.3.1 Neutron beta-decay
Since a neutron beta-decay process is a three-body decay, each of decay products has a continuous
energy spectrum. The maximum kinetic energies of the electron and the proton are 782 keV and
751 eV, respectively. Neglecting the masses of the electron and the anti-neutrino, the kinetic energy

Cummulative probability

CHAPTER 4. SIMULATION

Probability

54

0.002

0.0015
0.001

1

0.5

0.0005
0
0

200

400

600

Electron kinetic energy [keV]

0
0

200

400

600

Electron kinetic energy [keV]

Figure 4.4: Kinetic energy distribution of an electron from neutron beta-decay. The left plot
represents the probability density and the right plot represents the cumulative probability.
distribution of an electron Ke is expressed as√dΓ∝ (Ke − Qe )2 Ke2 − m2e Ke ,
dKe

(4.1)

where Qe is the Q-value of the electron energy, and me is the mass of an electron. The kinetic
energy distribution and its cumulative distribution are plotted in Figure 4.4.
The momentum direction of the electron has a slight dependence with respect to the neutron’spolarization direction θ asdΓJ⃗ · P⃗e
∝1+A
,
(4.2)
dΩ
Ee
where J⃗ is a spin of the neutron beam, Pe and Ee are the momentum and the energy of the electron,
respectively. The parameter A (= −0.1184 ± 0.0010) [6] is the neutron beta-decay asymmetry
parameter. There also exists an electron-neutrino angular correlation, which can be expressed asP⃗e · P⃗ν
dΓ
∝1+a
,
dΩ
Ee Eν

(4.3)

where Pe and Ee are momentum and energy of the anti-neutrino. The parameter a is the electronneutrino angular coeﬃcient, which is currently evaluated to be −0.1059 ± 0.0028 [6]. The momentum of the proton can be determined to satisfy the momentum conservation law.
The decay point in the x-y plane is randomly selected from the result of a beam profile measurement (see Section 4.2). The z position is determined in order to reproduce the experimental
distribution after the event selection using the time of flight (see Section 5.3.1).

4.3. SIMULATED EVENTS

4.3.2

3

55

He(n, p)3 H reaction

A 3 He nucleus in the TPC captures a neutron and emits a tritium and a proton with a Q-value of764 keV. According to the masses of the two nuclei, the kinetic energies of a 3 H and a proton are
191 keV and 572 keV, respectively. The two nuclei are emitted in the opposite direction with eachother. The range of the two nuclei is a few cm in the usual operation gas composition. The x, y,
and z coordinates of 3 He(n, p)3 H reaction points are randomly selected from the same distribution
as that of the neutron beta-decay simulation.

4.3.3 Neutron scattering
The neutron scattering cross sections with TPC operation gas molecules are listed in Table 2.5.
Since a wavelength of a neutron at BL05 beamline (λ ∼ 1 Å) is the same order of the atomic
distance of a CO2 molecule, coherent scattering cannot be neglected. Generally speaking, thescattering cross section between a neutron and a molecule is expressed as a function of the zenith
angle θ as1σ(θ) =
4π
xij ≡

(

M
M +1

)2 ∑ ∑

4πrij
θ
sin ,
λ
2

i

j

√

σi σj

sin xij
,
xij

(4.4)
(4.5)

where i and j are the index of each atom, rij is the distance between i and j atoms, σi andσj are coherent scattering cross sections of i and j nuclei, respectively, λ is a neutron de Brogile
wavelength, and M is the mass ratio of the molecule to a neutron [36]. The comparison of theoreticaland experimental angular distributions of neutrons with a CO2 gas molecule was studied by N. Z.
Alcock and D. G. Hurst in 1949 as shown in Figure 4.5 [37]. The scattering process is simulatedusing this formula for a neutron with 5 diﬀerent velocities (400, 600, 800, 1000, and 1200 m/s).
The five velocities approximately represent the velocities of 5 respective neutron bunches.

4.3.4 Cosmic rays
In the cosmic rays simulation, a charged muon is made incident on the upper side of the TPC. The
flux ratio of charged muons is set to be Fµ+ /Fµ− ∼ 1.3 to reproduce the observed data [6]. The
incident angle is implemented to follow the cos2 θ distribution with respect to a zenith angle.

4.3.5 Photoabsorption of 55 Fe X-rays
The photoabsorption process of 55 Fe X-ray is used for the energy calibration. It is simulated byemitting X-rays from the 55 Fe source position. The X-ray energy is selected to be 5.86 keV (89%)
or 6.45 keV (11%) [29]. The incident angle of the X-ray is limited to reproduce the collimator usedin the experiment. The absorption probability of X-rays in the TPC is evaluated to be 18%.

a pattern due to the form of the molecule.
The quantum-mechanicallycorrect method of calculating
the scattering requires a separate calculation for each possible

CCORDING
A collisionsofthe nuclear radiusrotational transition of the molecule (inelastic, elastic, and
CHAPTER
4.
SIMULATION
tion. The inelastic
superelastic}, and the summation of intensities after allowing
an approximately
for Doppler effect and the motion of the center of mass. 'responding to the
For a heavy molecule this requires a very large computational
Previous invest
effort and has not been attempted. The curves drawn innuclei of neutronsFigs. 2 and 3 were obtained by a semiclassical calculation inout by Grahame
which the neutron is represented by a wave, but the molecule
results indicate
is replaced by a rigid system of point scatterers. The method
magnitude of theassumes elastic scattering only and is the same as the normal'
sorption, but Gra
procedure for x-ray scattering, with the atomic structure
no inelastic
almostfactors replaced by constants. No account has been taken ofof 3 and 7 Mev,
paramagnetism in the oxygen molecule, s but small corrections
neutrons between
The availability
CARSON DIOXIDE GAS
spread of only +EXPERIMENTAL POINTS WITH STANOAROOEVIAT ION 5
in whic
scattering
THEORETICAL CURVE GIVEN SY
O Kv
X*"tribution in energ
@or 2
* 40
SIHf g I4 O 40I4
14.5-Mev neutron
X* I04
4CIN, 4* 24 a lO-240M2
tritium gas targe
4*4T IO-24IX42
CORRECTEO
FOR OOPPLER EFFECT AND
trostatic generato
GONVKRTKO TO LABORATORYSYSTEMA lead sphereenergy loss by tsmall central sp
could be placed.
elastic scattering
many neutrons a
are elastically sca
compared withthreshold detecto
foils which were r
0o
IOo
70o
%P
40
5%
60
57
8
SCATTERING ANGLE(0)when placed inwrapped helically&IG. 3. Angular distribution of 0.07-ev neutrons scattered from carbon
dioxide gas. angular distributions of neutrons withAa threshold dFigure 4.5: Comparison of theoretical and experimental
56

II

WHEIIK

X

o

f

~

& I

4

~ IO

o

CO2 gas molecule, taken from the work by N. Z. Alcock and D. G. Hurst in 1949 [37]. According
to the paper, the most likely cause of the small intensity at the small angle region is inter-molecularinterference because the carbon dioxide used in the experiment was near a liquid form.

4.3. SIMULATED EVENTS

57

Table 4.1: Cross sections and γ-ray energies for a CO2 molecule to capture a neutron [40].
Reaction

Cross section [mb]C(n, γ)13 C

3.89 ± 0.06

O(n, γ)17 O

0.189 ± 0.008

12

16

Probability [%]
67.8
32.2
0.161
81.7
18.3

Eγ1 [keV]
4945
1262
1857
10888
3272

Eγ2 [keV]
3684
3089
2184
871

Eγ3 [keV]
871-

4.3.6 Prompt γ-rays from LiF plate
Prompt γ-rays are produced from a LiF plate in the TPC by capturing a scattered neutron. The
capture point distribution is evaluated by simulating the neutron scattering process using Eq. 4.4[31]. A single or multiple γ-rays are emitted from the capture point according to a decay cascade
database [38]. The produced γ-ray undergoes Compton scattering mainly with the TPC wall, andthe probability is evaluated to be 1.3%.

4.3.7 Prompt γ-ray from SFC
A process of producing prompt γ-rays produced at the SFC is simulated by the Phits simulation[39], in which the SFC and the beam bender at the BL05 beamline is implemented. The energy,
momentum, and position of the γ-ray at the position of the neutron shutter are recorded. Making
the data as an input, the TPC output is simulated using the Geant4 simulation. The interaction
probability between the γ-ray and the TPC is about 2%.

4.3.8

3

H beta-decay

A neutron beam is captured by a beam dump made of LiF plate, at which the 6 Li(n, α)3 H reaction
occurs. A fraction of the tritium produced by the reaction is expected to leak out into the TPC anddiﬀuse through the entire TPC volume. A tritium nucleus undergoes beta-decay process and decays
into a 3 He, an electron, and an anti-neutrino, with a half lifetime of 12.3 years. The process issimulated by emitting the three decay objects from a randomly selected point in the TPC sensitive
region.

4.3.9

12

C(n, γ)13 C reaction

A CO2 molecule in the TPC causes 12 C(n, γ)13 C and 16 O(n, γ)17 O reactions and emits γ-rays.
The γ-ray energy and cross section are determined based on database values [40] as listed in Table
4.1. The reaction points are randomly selected from the same distribution as that of the neutron
beta-decay simulation. The γ-ray is emitted isotropically and the angular correlation between
multiple γ-rays is neglected.

6.4. PERFORMANCE FOR THE PARTICLE DETECT

1
0.9

Experiment : Recombination at the time of ionization
100kPa (He:CO = 85:15)
2

0.8
0.7
0.6

Attenuation Efficiency

CHAPTER 4. SIMULATION

Recombination Effect

58

1

0.8
0.7
0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0
0

50

100

150

200

250

300

Ex

0.9

0
0

350

50

Electric field [V/cm]

Figure 4.6: Recombination ratio of an electron-ion pair as a function of electric field in the TPC
gas composition (85 kPa He and 15 kPa CO2 ) [21].

Figure 6.26: The recombination eﬃciency with drift filed.
4.4 Detector simulation

Figure 6.27:
ciency with dri

In this section, implemented model to describe physical procedures in the TPC is described in this6.29 shows the time variation of the attenuation eﬀect.
section.

F
attenuation eﬃciency less than 4%, a continuous operatio

4.4.1 Recombination eﬀect
A fraction of an electron-ion pair produced from a charged particle is recombined into an ordinary
natural atom. The recombination aﬀects the number of drifting electrons, resulting in the decreaseof the deposit energy measured by the anode wires. For the purpose of evaluating the recombination
ratio, the 55 Fe X-ray was emitted directory towards the MWPC region, at which the electric field is
too strong for the recombination process to occur. By comparing the observed energy at this source
position and that in the normal source position, the recombination ratio can be evaluated. Figure
4.6 shows the recombination ratio as a function of an electric field in the TPC [21]. At our normal
operation field of 300 V/cm, the ratio was found to be 12%. In the detector simulation process, thenumber of ionized electrons are decreased by this factor.

4.4. DETECTOR SIMULATION

59

4.4.2 Diﬀusion eﬀect
Drift electrons disperse randomly due to the multiple collisions between gas molecules in the TPC.
It directly aﬀects the resolution of the track reconstruction, which is important to separate somebackgrounds from the signal events. Assume that ionized electrons are produced at one point x = 0
at the time of t = 0, which can be expressed as N (x, t = 0) ∝ δ(x), the electron density N (x, t)
can be described using a diﬀusion coeﬃcient D as)(1x2
N (x, t) ∝ √ exp −
.
(4.6)
4Dt
Dt
The diﬀusion coeﬃcient D describes how widely a drift electron disperses. Since the energy deposit
from the Fe X-rays is localized in the TPC (typically a few mm), the spread of ionized electrons in
the anode wires are used to optimize the diﬀusion coeﬃcient. Following parameters are introduced
to describe the spread of ionized electron:
maxch ≡ arg max ∆Ech ,

(4.7)

ch

CHARGE_DIV ≡max{∆Emaxch−1 , ∆Emaxch+1 },∆Emaxch(4.8)

where ∆Ei represents the observed energy at the i-th anode wire. The CHARGE_DIV parameter
becomes larger when the diﬀusion eﬀect increases. The diﬀusion coeﬃcient used in the simulation
is determined to reproduce the experimental CHARGE_DIV distribution as shown in Figure 4.7.
Noise and background cause the significant excesses in low CHARGE_DIV regions. In this analysis,
the region of interest to optimize the diﬀusion coeﬃcient is set to the CHARGE_DIV > 0.3 region.

4.4.3 Attenuation eﬀect
A fraction of a drifting electron is captured by an impurity gas molecule in the TPC gas, such as awater molecule. During the lifetime measurement, water vapor gradually comes out from the wallof the TPC and the vacuum chamber. The eﬀect significantly deteriorates the multiplication factorof the anode wires, resulting in the decrease of the observed energy deposit. During the lifetime
measurement, the attenuation eﬀect can be quantitatively monitored by the Fe (up) and Fe (down)
data using Eq. (2.4). In the Monte Carlo simulation, the attenuation length evaluated at the middle
time of the total measurement is implemented as an input parameter.

4.4.4 Space charge eﬀect
The avalanche multiplication process for 3 He(n, p)3 H suﬀers the self-induced space charge eﬀect
due to high-density electrons around a wire. As a result, the linearity of the detected energy withrespect to the deposit energy deteriorates. In this experiment, the significant space charge eﬀect
occurs for the 3 He(n, p)3 H events because of the high-density energy deposit. The 3 He(n, p)3 H
events is separated from beta-decays based on the energy deposit, thus the eﬀect is required tobe corrected. An analytical model to describe the saturation due to the space charge eﬀect was

60

CHAPTER 4. SIMULATION
Fe (down) comparison
Event ratio

Event ratio

Fe (up) comparison
0.05

Ex Fe (up)0.04

MC Fe (up) Best fit

Region of interest

0.03

0.05
Ex Fe (down)

0.04

0.02

0.01

0.01

0.2

0.4

0.6

Region of interest

0.03

0.02

0

MC Fe (down) Best fit

0.8
1
CHARGE_DIV

0.2

0.4

0.6

0.8
1
CHARGE_DIV

Figure 4.7: Comparison of the diﬀusion ratio parameter (CHARGE_DIV) for experiment and Monte
Carlo simulation. The left and right distributions are the result of Fe (up) and Fe (down) modes,
respectively. Noise and background cause the significant excesses in low CHARGE_DIV regions.
In this analysis, the region of interest is set to CHARGE_DIV > 0.3.

experimentally verified [41] and implemented in the Monte Carlo simulation. According to themodel, the gain reduction factor s (s < 1) can be expressed as
(
)
dE
G0
log 1 + f
dl
,
s=
dE
f
G0
dl

(4.9)

where dEis the energy deposit density per anode wire length, G0 is a multiplication factor withoutdl
the space charge eﬀect, and f is a parameter to determine the amplitude of the saturation eﬀect.
The experimental verification of the gain reduction model is described in Appendix C.
Comparison of the energy deposit distribution between the experimental data and the Monte
Carlo simulation is shown in Figure 4.8. The Monte Carlo simulation without the saturation modelis plotted in the left figure, while the simulation with the model in the right figure. The Monte
Carlo simulation implementing the gain reduction model describes the measured energy deposit
distribution, although there exists a significant discrepancy for the 3 He(n, p)3 H event in the highenergy region. The discrepancy is neglected in the analysis because it is much higher than theseparation threshold (see Section 5.3.2).

MC beta decay
MC 3He(n,p)3H
EX

15000

61

# of events# of events

4.4. DETECTOR SIMULATION

MC beta decay
MC 3He(n,p)3H
EX

15000

10000

10000

5000

5000

0
0

100 200 300 400 500

MAXENERGY [keV]

0
0

100

200

300

400

500

MAXENERGY [keV]

Figure 4.8: Comparison of the maximum energy deposit (MAXENERGY) distribution without
space charge correction (left) and with space charge correction based on an analytical gain reduction
model [41] (right). The Monte Carlo simulation implementing the gain reduction model describes
the measured energy deposit distribution, although there exists a significant discrepancy for the
3
He(n, p)3 H event in the high energy region.

62

CHAPTER 4. SIMULATION
0.6%

Field

Anode

2.1%

11%

100%

11%

2.1%

0.6%

Avalanchee-Figure 4.9: Amplitude ratio of induced waveform for wires near the avalanche anode wire evaluatedby the ANSYS [43] and Garfield [23] software.

4.4.5 Charge-inducing process
A wire signal waveform is induced by a motion of ions produced from an avalanche multiplication.
Furthermore, the motion also induces reverse-phase waveforms at the grounded wires (the fieldand cathode wires) and anode wires at which no avalanche multiplication has occurred. In thisexperiment, the field wires as well as the anode wires are used to measure the energy deposit ofcharged particles, therefore the amplitude of the induced charge is an important parameter for theenergy calibration. It can be determined using Ramo’s theorem [42]. According to the theorem,
the induced current i at an electrode is expressed asi = q⃗v · E⃗w ,(4.10)

where q is the electric charge, ⃗v is the velocity vector of the charge, E⃗w is the weighted field of
the electrode. The weighted field can be obtained by giving unit potential to the electrode andgrounding the other electrodes. The calculation is conducted using ANSYS [43] and Garfield [23]software. As shown in Figure 4.9, the amplitude is evaluated as a function of the distance between
the target wire and the point where the avalanche multiplication has occurred. The software is notable to calculate the induced signal of the cathode wires due to memory shortage. Therefore, in thedetector simulation process, the induced waveforms of the cathode wires are generated to reproduce
experimental pulse height distributions.

Chapter 5
Analysis
This chapter introduces the analysis procedure to evaluate the number of signal events (Sβ and S3 He )and the number density of 3 He (ρ). The analysis parameters used in the analysis are defined in
Section 5.2.

5.1 Expected background
The Expected background events for Sβ and S3 He detected at the TPC are described in this section.

5.1.1 Types of backgrounds for 3 He(n, p)3 H• 14 N neutron capture (hereinafter called Bnitro )Although nitrogen is not originally injected into the TPC as operation gas, it gradually comesout from the wall of the TPC or the vacuum chamber. A neutron is captured by a 14 N nucleus
of a nitrogen molecule and undergoes 14 N(n, p)14 C reaction in the TPC. The Q-value of thereaction is 626 keV, and the cross section is (1.83 ± 0.03) barn [15].
• 17 O neutron capture (Boxy )A neutron is captured by a 17 O nucleus, which exists as an isotope of an oxygen in CO2 gas.
The natural abundance of 17 O is (3.8 ± 0.3)% [15]. The Q-value is 1818 keV and its crosssection is (0.235 ± 0.010) barn [15].
• 3 He(n, p)3 H from scattered neutrons (Bscat3He )Neutrons are scattered by gas molecules in the TPC with a probability of about 1%, and theneutrons cause the 3 He(n, p)3 H reaction. A fraction of the event occurs near the TPC walland has small energy deposit in the TPC, which leads to deteriorate the detection eﬃciency
for the 3 He(n, p)3 H reaction. In order to avoid the deterioration, the 3 He(n, p)3 H reaction
from scattered neutrons is treated as a background in the analysis.
63

64

CHAPTER 5. ANALYSIS

5.1.2 Types of backgrounds for neutron beta decay• 12 C neutron capture (hereinafter called BCO2 )A 12 C or 16 O nucleus in a CO2 gas molecule captures a neutron and undergoes the 12 C(n, γ)13 C
or 16 O(n, γ)17 O reactions, respectively. The cross sections of the two reactions are(3.53 ± 0.07) barn and (0.190 ± 0.019) barn, respectively [15]. After capturing, the nucleus in an excited state returns to a ground state with prompt γ-rays while the nucleus itself
recoils towards the opposite direction. The typical recoil energy is a few keV, which is highenough to be detected by the TPC.
• γ-ray produced inside the TPC (Bintγ )A scattered neutron interacts with a LiF plate in the TPC and produces prompt γ-rays from (n,γ) reaction, such as 6 Li(n, γ)7 Li and 19 F(n, γ)20 F. The γ-rays undergo Compton scatteringwith the TPC gas or wall material and produces an electron inside the TPC sensitive region.
• Beta-decays from scattered neutrons (Bscatβ )A scattered neutron undergoes beta-decay in the TPC. This event is treated as a backgroundin the same way as Bscat3He for consistency.
• 3 H beta-decay (Btrit )A neutron beam passing through the TPC is captured by a beam dump made of a LiF plate
mainly through the 6 Li(n, α)3 H reaction. Some tritium nuclei are expected to be emitted
from the plate and dispersed in the TPC gas. A tritium nucleus decays into a 3 He, an electron,
and an anti-neutrino through the beta-decay process with a half-life of 12.3 year and a Q-valueof 18.6 keV. During the measurement, the increase of the point-like events can be observedin the sideband region [31]. The events are uniformly distributed in the TPC.
• γ-ray produced outside of the TPC (Bextγ )At the SFC, prompt γ-rays synchronized with the neutron pulses are produced due to theneutron absorption at, for example, the magnetic super mirror. Some γ-rays pass throughthe beam pipe and cannot be absorbed by the lead shield. A fraction of the γ-ray undergoes
Compton scattering and produces an electron in the TPC. This background has the time-offlight distribution roughly synchronized with that of the neutron pulses.
• TPC material radioactivation (Brad )When a neutron beam is made incident in the TPC, the material inside the TPC becomesradioactivated by capturing a neutron. For example, a LiF plate captures a neutron beam andproduces radioactive isotopes, such as 8 Li and 20 F, which undergo beta-decay with lifetimesof (839.9 ± 0.9) ms and (11.00 ± 0.02) s, respectively [40]. These lifetimes are much larger
than the pulse repetition interval (40 ms), while much shorter than the data acquisition period(∼1000 s). Consequently, (1) this background is not observed in the shutter-closed mode,but only in the shutter-open mode, and (2) the background has the constant time-of-flight
distribution in the shutter-open mode.
• Environmental background (Benv )A constant background existing both in the shutter-open and shutter-closed modes is classified

5.2. DEFINITION OF ANALYSIS PARAMETERS

65

Table 5.1: Trigger event rate of signal and background in the fiducial time window at Fill94 (300
kW accelerator operation).
Event
Event rate [cps]
Sβ
1.2
BCO2
3.5
Bintγ
0.05
Bscatβ0.003
Btrit
0.0∼ 0.2 increase with time
Bextγ
0∼1 dependent on time of flight
Brad
0.06
Benv
5.7
S3 He
27
Bnitro0∼0.1 increase with time
Boxy
0.2
Bscat3He
0.06
as this type of background. One example is natural radiation, such as beta-decay or electron
capture of a 40 K nucleus. Furthermore, when a cosmic ray passing through a gap of the vetocounters creates an energy deposit in the TPC, such an event cannot be vetoed by our trigger
system and is counted as this type of background.

5.1.3 Event rates of signal and background
The trigger event rates of signal and background described above are listed in Table 5.1. Note thatthe event rates of Btrit and Bnitro increases with the elapsed time after the gas filling time.

5.2 Definition of analysis parameters
Definitions of parameters used in this analysis are described in this section. The mathematicalexpression of the definitions is described in Appendix A.
The following parameters for the waveforms of anode, field, and cathode wires are defined asshown in Figure 5.1. The parameters defined in every event are introduced in the following, someof which are described in Figure 5.2.
• TOTALENERGY
Total energy deposit detected by the all anode wires.
• MAXENERGY
Maximum energy deposit per wire among all the field wires. It is used to describe how
localized the energy deposit is in the TPC.
• LOCALITY
Ratio of the maximum energy deposit to the total energy deposit among all the anode wires

66

CHAPTER 5. ANALYSISADC channel
integral range
28us - 70us
pulse
heightintegralthreshold
30 ch (15 mV)

pedestal

0 us

100 ustime

rise time

Figure 5.1: Waveform parameter definitions. The detailed definition is described in Appendix A.
• MINRISE
Trigger timing of the TPC (corresponds to the time when the first wire waveform exceeds thethreshold level).
• HITNUM
Number of wires detecting energy deposit above the threshold level among all the field wires.
It describes the track length in the field wire direction.
• DTIME
Track length in the y direction as a unit of drift time measured by the anode wires.
• CENTER
Track center position weighted by the energy deposit of wires. It expresses the reaction pointin the 3 He(n, p)3 H event. CENTER_A, CENTER_F, and CENTER_CH correspond to thecenter position measured by the anode wires, the field wires, and cathode high-gain wires,
respectively• DTC (Distance between Track and TPC Center in Anode wires)
The distance between the center wire and the most closest wires detecting energy deposit.
DTC_A and DTC_CH correspond to the distance measured by the anode wires and cathodehigh-gain wires, respectively.
• DVC (Distance between track Vertex and TPC Center in Anode wires)
Distance between the track origin point and TPC center as a unit of wire interval. DVC_A
and DVC_CH correspond to the distance measured by the anode wires and cathode high-gain5.3. DATA ANALYSIS ALGORITHM

67

anode wire

high-gain cathode wire

17

18

19

20

CENTER̲CH

DTIME̲A

X

13
12

X

Y

DVC̲A
CENTER̲A

11

HITNUM̲A=4

14

16

DVC̲CHZHITNUM̲CH=5

DTIME̲CH

Y

Z

Figure 5.2: Track parameter definitions. The detailed definition is described in Appendix A.
wires, respectively. DTC and DVC parameters are closely correlated to the track origin point
and are useful to separate the background event originating from the TPC wall.

5.3 Data analysis algorithm
An analysis algorithm to extract the number of signal events (Sβ and S3 He ) from the acquired data
is introduced in this section. The section describes the overall procedure of the analysis, and thedetails are described in the following sections. The overall analysis algorithm is described in Figure5.3. Each of the detailed procedures is explained according to the sequence in the figure.

5.3.1 Time-of-flight subtraction method
The TOF subtraction process is conducted at first for the obtained data, at which the backgroundhaving diﬀerent TOF structure can be subtracted, such as Bextγ , Brad , and Benv . Figure 5.4 showsa schematic drawing of the TOF distribution for the signal (beta-decay) and background eventsin the TPC. The variable N is defined as the number of observed events in the TPC, where thesuperscript “open” or “close” represents the shutter mode, and the subscript “f” and “s” represents
the “fiducial” and “sideband” time in the TOF distribution. The background events having diﬀerent

68

CHAPTER 5. ANALYSIS

S3He, Boxy, Bnitro, Bscat3He, Sβ, Bintγ, Bscatβ, Btrit, BCO2, Bextγ, Brad, Benv
TOF subtraction

Bextγ, Brad, Benv
S3He, Boxy, Bnitro, Bscat3He, Sβ, Bintγ, Bscatβ, Btrit, BCO2

Energy separation

S3He, Boxy, Bnitro, Bscat3He

Sβ, Bintγ, Bscatβ, Btrit

S3He, Boxy, Bnitro, Bscat3He

Sβ, Bintγ, Bscatβ, Btrit

BCO2

Purity cut

Track size

Btrit
Sβ, Bintγ, Bscatβ
Scattering event
analysis

S3He, Boxy, Bnitro

Bscat3He

Bintγ, Bscatβ
Sβ

Low gainmeasurement

S3He, Boxy
Cross section
calculation

S3He

BnitroBoxy

Figure 5.3: Analysis flow to select the beta-decay events (Sβ ) and the 3 He(n, p)3 H events (S3 He ).

5.3. DATA ANALYSIS ALGORITHM

69

Signals (Sβ, SHe)

TPC material radiation (Brad)

Beam-induced backgrounds(Bnitro, Boxy, Bintγ, Bscatβ, Bscat3He, Btrit, BCO2)

Environmental backgrounds (Benv)

γ-rays from upstream (Bextγ)

Shutter-closed

Sideband

Fiducial

Ts

Tf

open

Ns

Number of events

Number of events

Shutter-open

Sideband

Fiducial

Time of Flight

open

Time of FlightclosedNfNsclosedNf

Figure 5.4: Schematic drawing of the time-of-flight distribution for signal and background eventsin the shutter-open (left) and shutter-closed (right) mode. The backgrounds with diﬀerent time-offlight structure from signals can be subtracted using the two distributions. Note that there are fivesets of fiducial time per pulse in the actual measurement setup, although only one is shown in the
figure.
TOF structure than that of signal events can be subtracted in this process. Both Bextγ and Benv
backgrounds can be subtracted using the shutter-closed data. The Brad background can be estimatedusing the sideband data in the shutter-open mode because it has a uniform TOF distribution. For
comparing the shutter-open and shutter-closed events, the total counts of the beam monitor (BMopen
and BMclosed ) are used. This normalization can correct for the neutron flux fluctuation during themeasurement. On the other hand, for comparing the fiducial and sideband events, each of the time
width per neutron pulse (Tf = 2.35 ms and Ts = 6.00 ms) is used as the normalization factor. As
a result, the amount of these three types of backgrounds can be subtracted from Nfopen as
Nfopen − (Bextγ + Benv ) − Brad()
BM openBM
Tf
open
closedopen
closed
×
− Ns
×
−
Ns
.
= Nf
− Nf
BM closed
Ts
BM closed

(5.1)

open

(5.2)

5.3.2 Energy separation
The acquired data after the TOF subtraction is divided into three categories based on the deposit
energy in the TPC. First, high energy events are defined as those with MAXENERGY of larger than

70

CHAPTER 5. ANALYSISCounts20000

MC beta104

MC offaxis beta
MC LiF
MC CO215000

103

MC 3heMC offaxis 3heEX data

10000

102

5000

10

0

100

200

300

MAXENERGY [keV]

1
0

100

200

300

MAXENERGY [keV]

Figure 5.5: Maximum energy deposit (MAXENERGY) distribution in linear scale (left) and logarithmic scale (right). The clear separation of the beta-decay events and the 3 He(n, p)3 H events ataround 30 keV is seen.
25 keV. Here, Sβ -like events (Sβ , BCO2 , Bintγ , Bscatβ , and Btrit ) and S3 He -like events (SHe , Bnitro ,Bscat3He , and Boxy ) are separated as shown in Figure 5.5. Next, the events having TOTALENERGY
less than 5 keV are treated as very low energy events and separated from the beta-decay events asshown in Figure 5.6. In this process, 99.9% of the BCO2 background can be subtracted because theenergy deposit in the TPC is extremely low (typically a few keV in the TPC). The remaining 0.1%
events still exists in the beta-decay region, which is treated as the uncertainty for the beta-decay
event (see Section 6.1).

5.3.3 Purity cut
Several purity cuts are applied for both Sβ -like and S3 He -like events to increase the signal-to-noise
ratio. The purity cuts are introduced in the following.
• Beta-decays– Trigger cut
The trigger timing is later than 25 µs (MINRISE > 25 µs).
The cut requires no events before trigger timing.
– Anode any hit cut
Reconstructed track center position of anode wires exists in the sensitive area (0 wire <CENTER_A < 23 wire).
The cut requires detection of the energy deposit by any anode wire.

5.3. DATA ANALYSIS ALGORITHM

71

MC beta
MC offaxis beta

600

MC LiF500

MC betaCountsCounts700

MC offaxis beta
MC LiF

MC CO2MC CO2EX dataEX data

102

400
300
200
100
−10

10

0

10
20
30
40
TOTALENERGY [keV]

−10

0

10
20
30
40
TOTALENERGY [keV]

Figure 5.6: Total energy deposit (TOTALENERGY) distribution in linear scale (left) and logarithmic
scale (right). The cut threshold energy is set at 5 keV. The shortage of the BCO2 background in theexperimental data supposedly originates from the TPC ineﬃciency at the low energy region.

72

CHAPTER 5. ANALYSIS– Drift cut
Track length in the y direction is shorter than 190 mm (DTIME < 190 mm).
The cut rejects events whose track passing vertically through the TPC, such as cosmic
rays.
– TPC passing cut
Track does not pass through the TPC in the z direction ( (CENTER_CH-20)2 +(DVC_CH20)2 < (8 wires)2 ).
The cut rejects events whose track passing parallel to the beam direction in the TPC.
• 3 He(n, p)3 H– Trigger cut
Same as the one for beta-decays.
– Anode any hit cut
Same as the one for beta-decays.
– Basic cut
The cut requires the energy deposit detection by at least one fired field wires. Furthermore, the reconstructed track center position by the field wires is required to exist in the
TPC sensitive area (HITNUM > 0 & 0 wire < CENTER_F < 23 wire).

5.3.4 Track size separation
A track size selection is introduced to separate the Btrit background from the rest of Sβ events.
The maximum kinetic energy of an electron is 18.6 keV, flying a few mm in the TPC gas. As aresult, the energy deposit is extremely localized in the TPC, and only a single anode wire detects
the energy deposit. The track localization in the TPC is expressed by the LOCALITY parameter.
Figure 5.7 shows the LOCALITY distribution for the experimental data, the Sβ events, and the Btrit
background. The separation threshold value is optimized to be 0.8. According to the Monte Carlosimulation, the ineﬃciency of this selection for the beta-decay events is 0.6%.

5.3.5 Scattering event analysis
In the scattering event analysis procedure, the amount of gas-induced backgrounds for 3 He(n, p)3 H(Bscat3He ) and beta-decay (Bintγ and Bscatβ ) is estimated by the Monte Carlo simulation. The
3
He(n, p)3 H reaction from a scattered neutron can be identified using the reaction point in the TPC.
As a parameter to describe the position, a weighted mean position of the field wires (CENTER_F)
is used. The Bscat3He background has a broad distribution, while S3 He has a localized distribution
around the center. As shown in Figure 5.8, the simulated Bscat3He and S3 He distributions arenormalized by the numbers of events in the inner (5 wires <CENTER_F<18 wires) and outer(CENTER_F < 5 wires or CENTER_F > 18 wires) regions in the experimental data. The ratio of
the two normalized events, which is 0.3%. The Bscatβ distribution is also normalized using thisscattering probability.

# of events

0.003

73

# of events

5.3. DATA ANALYSIS ALGORITHM

Open fiducial
MC Beta
MC 3H

0.002

Open fiducial

10−3

MC Beta
MC 3H

10−4
0.001

0

10−5

0.5

1
LOCALITY

10−6
0

0.5

1
LOCALITY

Figure 5.7: Track length locality (LOCALITY) distribution in linear scale (left) and logarithmic
scale (right). The cut threshold energy is set at 0.8. The experimental fiducial distribution in the
shutter open mode is also shown as black points. The distributions of the Monte Carlo simulation
are arbitrary normalized.
The amount of Bintγ is estimated using the DTC_A parameter, which represents the initial
ionization point in the TPC in the anode wire direction. An electron track starts at around the beam
position for Sβ , thus the Sβ event exists at the inner region DTC_A < 4 wires. The Bintγ background,on the other hand, has a flat DTC_A distribution because an electron track mainly originates fromthe TPC wall. The simulated Bintγ distribution is normalized by the number events in the outerregion (DTC_A ≧ 4 wires). Figure 5.9 shows the DVC_A distribution, in which the signal region isdefined as DVC_A < 4 wires. The amount of the gas-induced background is evaluated to be about
5% for Sβ in the signal region.

5.3.6 Low-gain measurement
After sealing the vacuum chamber, the nitrogen pressure gradually increases due to outgas from thematerial, such as PEEK. A 14 N nucleus captures a neutron and undergoes a 14 N(n, p)14 C reaction
with a Q-value of 626 keV. Unfortunately, the TPC does not have enough energy resolution to
separate the event from the 3 He(n, p)3 H events (Q=764 keV). For the purpose of separating the twokinds of events, the applied voltage of the anode wires is decreased to 1200 V (see Table 3.2) so thatthe multiplication factor decreases by 2 orders of magnitude. Under this condition, the beta-decay
signal could not be detected. The low-gain data is taken usually every other day (each one is called
as a data cycle) during the lifetime measurement.
Figure 5.10 shows the TOTALENERGY distribution of the all data cycles under the low-gain
condition. The clear separation of 14 N and 3 He(n, p)3 H is seen. The double-gaussian fitting is

74

CHAPTER 5. ANALYSIS# of events

105
MC 3He410

MC scatter 3He

103

EX

102
10
1
10−1
0

5

10

15

20

CENTER_F

Counts8000

MC beta
MC offaxis beta

7000

MC LiFEX data

6000

CountsFigure 5.8: Distribution of the reaction x position (CENTER_F) of the 3 He(n, p)3 H events. The
experimental data (black points) are fit by the Monte Carlo simulation result of 3 He(n, p)3 H reaction
from scattered neutrons (blue) and 3 He(n, p)3 H reaction from non-scattered neutrons (red).

MC beta
MC offaxis beta
MC LiFEX data

3

10

5000
102

4000
3000

10

2000
1000
0

5

10

DVC_A [ch]

1
0

5

10

DVC_A [ch]Figure 5.9: Distribution of the distance between track vertex and TPC center (DVC_A) for Sβ ,Bintγ , and Bscatβ in a linear scale (left) and a logarithmic scale (right).

# of events

5.3. DATA ANALYSIS ALGORITHM

75

103
102
10
1
0

200

400

600
800
1000
TOTALENERGY [keV]

Figure 5.10: Total energy deposit (TOTALENERGY) distribution under the low-gain condition(anode voltage at 1200 V). The two peak corresponds to the 14 N(n, p)14 C (Q=626 keV) and3
He(n, p)3 H (Q=764 keV) events. The cut threshold drawn as a blue line is set at a local minimumof the distribution. The deviation of the low-energy 3 He(n, p)3 H peak from the gaussian function
is expected to be due to the space charge eﬀect around the anode wires.

conducted for the distribution, and the cut threshold is set at the local minimum position. The
numbers of both the 14 N(n, p)14 C and the 3 He(n, p)3 H events are counted for each data cycle.
The contamination from the 3 He(n, p)3 H peak to the 14 N(n, p)14 C peak is corrected based on thefitting result. Note that the fitting for the 14 N(n, p)14 C distribution does not work well for each data
cycle because of the poor statistics. Figure 5.11 shows the time variation of the contamination. The
data is fit by a straight line, and it is found to have (0.430 ± 0.031) Pa/day increase in average. The
result is used to correct for the number of 3 He(n, p)3 H events counted in the high-gain mode. Since
the rate of increase depends heavily on how good the vacuum condition has been before injecting
the operation gas, the contamination analysis is conducted individually for each gas condition.

5.3.7 Cross section calculation
A 17 O nucleus in a CO2 molecule captures a neutron in the TPC and undergoes the 17 O(n, α)14 C
reaction. Since the TPC does not have enough energy resolution to separate this event from S3 He ,the contamination from the Boxy events is corrected based on its reaction probability. It is calculatedusing the cross section and the natural abundance of 17 O. Assuming the natural abundance ratio of17
O (R17 O =0.038%) for the CO2 gas and the 100% detection eﬃciency of the TPC, the number of

3

0.02

2.5
0.015

2
1.5

0.01

N2 pressure [Pa]CHAPTER 5. ANALYSIS

14N/(3He+14N)

76

1
0.005
0.5
0

05/28
09:00

05/29
09:00

05/30
09:00

05/31
09:00

06/01
09:00

06/02
09:00

0

Figure 5.11: Ratio of 14 N(n, p)14 C and 3 He(n, p)3 H events as a function of time. The data points
are plotted for each data cycle. The corresponding nitrogen pressure is also shown on the right axis.
The data is fit by a straight line (χ2 /ndf = 3.66/4 = 0.92), and the pink band represents the 1σ
standard deviation of the fitting line. The rate of increase is evaluated to be (0.430 ± 0.031) Pa/day.
17

O(n, α)14 C events with respect to that of 3 He(n, p)3 H (N17 O /N3 He ) in the TPC is calculated as
N17 O
σ17 O × ρ17 O
=
,
N3 He
σ3 He × ρ3 He
σ17 O × 2PCO2 × R17 O=.
σ3 He × P3 He

(5.3)
(5.4)

Under the normal gas conditions, PCO2 = 15 kPa and P3 He = 100 mPa, and according to Table of
Isotopes, σ17 O = (0.235 ± 0.010) barn and σ3 He = (5333 ± 7) barn [15]. Substituting these values,
N17 O /N3 He = (0.502 ± 0.025)% is obtained, where the uncertainty is dominated by that of σ17 O .
The value is used to subtract the 17 O(n, α)14 C contamination.

5.3.8 Pileup correction
In the waveform integration range of 40 µs, it is possible that the TPC accidentally detects morethan one events for a single trigger, resulting in multiple signals being recorded. Such events arecalled as pileup events, which may aﬀect the signal selection eﬃciency. A typical event display of
a pileup event is shown in Figure 5.12. The image recognition algorithm is applied to the acquired
data for the purpose of counting the number of observed tracks in the TPC. The event is rejectedfrom the analysis when multiple tracks are identified. After this selection, the pileup correction
amount is estimated using the Monte Carlo simulation, by taking into account all of the possible
pileup event combinations.

5.3. DATA ANALYSIS ALGORITHM

77

Figure 5.12: Typical event display of a pileup event. The energy deposit is shown with colors.

78

CHAPTER 5. ANALYSIS
Table 5.2: Multi track recognition eﬃciencies for the simulation data.
Event
Trigger Following
Sβ
Sβ
Sβ
Sβ
Bextγ
Sβ
Bintγ
Bextγ
Sβ
Bintγ
Sβ

Multi track recognition eﬃciency
x-y plane z-y plane both in x-y and z-y planes
0.04
0.006
0.002
0.58
0.73
0.50
0.60
0.73
0.50
0.60
0.59
0.47
0.61
0.80
0.55
0.53
0.56
0.42

For identifying a charged track in the TPC, the technique of image recognition using OpenCV
library [44] is applied. Based on the two-dimensional event displays constructed using the anodeand cathode high gain wire waveforms, the observed track number and respective position arerecognized. The image recognition algorithm is described in the following.
1. Create two-dimensional event displays of the TPC in the x-y and z-y planes. The waveform
voltages are shown with colors in the event displays.
2. Transform the x-y and z-y color event displays into binary images at a certain threshold.
3. Identify bounded regions surrounding pixels whose values are one.
4. Create a box which completely contains each polygon so that its size becomes minimum.
5. Identify the box as a track when the area size exceeds the threshold.
Free parameters in the algorithm, such as the binary threshold and the area size threshold,are optimized using the experimental event displays. Figure 5.13 shows some examples of therecognized tracks in the x-y plane event displays. A track detection eﬃciency of 99.9% can beachieved for the single beta-decay event. As the figure shows, the algorithm can detect multiple
tracks when they are spatially separated in the event display, although the overlapped pile up event
cannot be separated. Double tracks are detected with an eﬃciency of about 60% for the pileup
beta-decay events. To achieve the higher pileup detection eﬃciency, new types of track separation
algorithm, such as Hough transform, are desired.
The algorithm performance is estimated using the Monte Carlo simulation, in which two waveforms are superimposed with a random delay time to reproduce the pileup event. Table 5.2 lists
the recognition eﬃciencies of the algorithm for the simulation data. In our analysis, the event isrejected from the signal events when more than one tracks are recognized both in the x-y and z-yevent displays. About half of the pileup events can be rejected using the recognition algorithm,
although 99.8% of the single beta-decay events survives.

5.4

3

He number density determination

The 3 He pressure in the TPC is required to be measured with an accuracy of 0.1% for evaluating thetotal neutron fluence in the TPC. However, the typical 3 He pressure is about 100 mPa, which cannot

5.4. 3 HE NUMBER DENSITY DETERMINATION

79

single track event

double track event

Figure 5.13: Examples of recognized tracks in the x-y plane event displays for the single track
events (top) and the double track events (bottom). The recognized track is expressed as a red box.
The algorithm can detect multiple tracks when they are completely separated in the event display.
However, when they are partially overlapped with each other, the algorithm cannot separate them.
be directly measured by a pressure gauge with the accuracy. We therefore independently evaluatedthe number density of 3 He (1) injected from a 3 He cylinder and (2) contained in the operation helium
gas, and summed them to evaluate the total number density in the TPC. Each method is describedin the following.

5.4.1 Evaluation of injected 3 He pressure
As described in Section 2.12, 3 He gas is expanded from the Im (Vbuﬀer ) region to the Im, I1, I8,
and ITPC regions (VTPC ). The schematic drawing of the expansion method is shown in Figure
5.14. The 3 He pressure in Vbuﬀer is about 1 kPa, which can be directly measured with about 0.01%
accuracy. The volume ratio of Vbuﬀer and VTPC is measured in advance with about 0.01% accuracy
using 4 He gas. Assuming the helium gas to be an ideal gas, the injected 3 He pressure in the TPC
is calculated with about 0.1% accuracy using Boyle’s Law. In this estimation, the eﬀect of thediscrepancy between an ideal gas and a real gas is also considered (see Section 6.3).

5.4.2 Evaluation of 3 He pressure in operation He gas
The 4 He cylinder used in this experiment is known to contain about 0.1 ppm 3 He gas. Assuming
85 kPa 4 He pressure in the TPC, the contaminated 3 He pressure corresponds to 85 kPa × 0.1 ppm= 8.5 mPa. Since we inject about 100 mPa 3 He directly from the 3 He cylinder, the contamination

80

CHAPTER 5. ANALYSIS~ 100 mPa

~ 1 kPa

pressuregaugepressuregauge

VbuﬀerVTPC

releaseVbuﬀer

VTPC~ 40 cm3~ 6 105 cm3

Figure 5.14: Schematic drawing of the volume expansion method. A 3 He gas at 1 kPa 3 He is stored
in a buﬀer region (40 cm3 ), and is expanded to the TPC volume (∼ 6 × 105 cm3 ).
is not negligible and should be measured accurately. We used 4 cylinders, and the contamination
amount is evaluated for each cylinder using two independent methods as described in the following.
• Mass spectrometer method
One method is to analyze the 3 He/4 He ratio of the cylinder gas using a mass spectrometer at
the University of Tokyo [30]. The mass spectrometer is calibrated by a standard helium gas
sample known as Helium Standard of Japan (HESJ) [45], whose 3 He/4 He ratio is evaluatedby our group to be (27.36 ± 0.11) ppm [46]. The calibration measurement is conducted
for at least two cycles to monitor the spectrometer operation. The precision of the 3 He/4 He
ratio measurement is a few percent, which is currently limited by the spectrometer output
fluctuation.
• Flux method
The other method is to extrapolate the proportional relationship between the 3 He(n, p)3 H
event rate and the 3 He pressure in the TPC. Multiple gas data with diﬀerent injected 3 Hepressures are combined to evaluate the coeﬃcient of proportion. Figure 5.15 shows thecorrelation between the 3 He(n, p)3 H event rate and the injected 3 He pressure in the TPC. The
contamination 3 He pressure from the 4 He cylinder can be expressed as the intercept point inthe x axis. The extrapolation is independently conducted for each cylinder.
Figure 5.16 shows the evaluated 3 He ratio in each 4 He cylinder. The results of both methods are
consistent with each other (χ2 /NDF = 1.14), although the mass spectrometer method currently
gives better precision. The result of the mass spectrometer measurement is used to evaluate thetotal 3 He pressure in the TPC.

3Hecount/BMcount

5.4. 3 HE NUMBER DENSITY DETERMINATION

81

G1#7 [3He from G1 = (9.9± 1.3)mPa,(0.116± 0.015)ppm]
G1#8 [3He from G1 = (9.6± 0.6)mPa,(0.113± 0.007)ppm]

0.3

G1#10 [3He from G1 = (8.1± 0.5)mPa,(0.095± 0.006)ppm]
G1#11 [3He from G1 = (9.8± 0.3)mPa,(0.115± 0.004)ppm]

0.2

0.1

0
−50

0

50

100

150

inject 3He pressure [mPa]

3He ratio [ppm]Figure 5.15: 3 He(n, p)3 H event flux as a function of injected 3 He pressure. Each point corresponds
to a single gas data. The intercept point in the x axis indicates the 3 He pressure from the 4 He
cylinder.

Mass spectrometer method

0.13

Flux method

0.12
0.11
0.1
0.09
7

8

9

10

11

bombe ID
Figure 5.16: Results of the 3 He/4 He ratio measurements using the mass spectrometer method (red)and flux method (blue). They are consistent with each other within their respective uncertainties(χ2 /NDF = 1.14).

Chapter 6
Results
The corrections and uncertainties for each parameter in Eq. (1.27) are described in this chapter. The
analysis result of τn is also discussed.

6.1 Uncertainties for the neutron beta-decay events (Sβ )• Upstream γ-ray correction from LiF plates
The γ-rays coming from the SFC undergoes Compton scattering in the TPC, which becomesa background for beta-decay (Bextγ ) as described in Section 5.1. Although this backgroundcan be subtracted for the most part by the TOF subtraction algorithm (see Section 5.3.1), a
fraction of the γ-ray is expected to be stopped by a neutron shutter, or 5 mm-thick LiF plate,in the shutter-closed mode. Therefore, the background rate in the shutter-closed mode is not
same as that in the shutter-open mode any more. The eﬀect is estimated using Phits [39] andGeant4 [32] [33] [34]: The position, momentum, and energy distribution of γ-rays at the LiF
plate position is evaluated by the Phits simulation, while the interaction between the γ-ray
and the LiF plate is estimated by the Geant4 simulation.

• SFC S/N
Although neutron bunches are formed by the SFC as described in Figure 2.7, neutrons also
exist outside of the bunch region with an average contrast ratio of 1/422, because of theimperfectness of the spin flipping and reflection at the SFC. The event selection eﬃciency
decreases for neutron beta-decays that decay close to the upstream or downstream edge of the
TPC. The acceptance depends on the track length of the event, thus the eﬀects for beta-decay
and 3 He(n, p)3 H do not cancel as shown in Figure 6.1. As the figure shows, The selection
eﬃciencies degrade at around z = ±500 mm, which corresponds to the edge of the TPC
sensitive area.
83

Selection efficiency

84

CHAPTER 6. RESULTS

beta decay1

10−1

10−−2800

−600

−400

−200

0

200

400
600
800
Reaction z point [mm]

200

400

Selection efficiency

3He capture1

10−1

10−−2800

−600

−400

−200

0

600

800

Reaction z point [mm]Figure 6.1: Signal selection eﬃciencies for the beta-decay events (top) and the 3 He(n, p)3 H events(bottom) as a function of the reaction z point. The red line shows the average eﬃciency between-280 mm < z < 280 mm. The decrease of the selection eﬃciencies starts at around the z = ±500mm region.

6.2. UNCERTAINTIES FOR THE NEUTRON BETA-DECAY SELECTION EFFICIENCY (εβ ) 85

6.2 Uncertainties for the neutron beta-decay selection eﬃciency(εβ )• Drift distortion
Due to the asymmetrical structure of the TPC in the y direction, the drift velocity has asignificant non-uniform dependence along the y direction. It gives a systematic uncertainty
for the beta-decay selection eﬃciency because the drift time parameter is used as a purity
cut. The non-uniformity is measured using the cosmic rays events assuming that each of
their tracks forms a straight line. The drift time is defined as the time width from the vetoscintillator hit to the waveform rise time. The ionization y position of channel i anode wire(yi ) is defined asi − MINHIT − 1
yi = yMWPC − LTPC ×,(6.1)
HITNUM − 2
where yMWPC =150 mm is the MWPC y position and LTPC =300 mm is the TPC y length. The
drift velocity can be evaluated by diﬀerentiating the drift time. Figure 6.2 shows the drift timeand drift velocity distribution as a function of the y position in the TPC. The non-uniformityof the drift velocity along with the y direction is observed. The drift velocity distortion(dv/dy) is evaluated to be 0.011 µs, which gives a drift velocity distortion of 20% between
the upper and lower region of the TPC. The systematic uncertainty of the drift distortion eﬀect
is estimated by implementing this distortion in the detector simulation.
• Proton w value
It is experimentally known that the w value, the average energy to create an electron-ion pair,is independent of the kinetic energy above a few MeV for an α particle and a few keV for anelectron [47]. In the Monte Carlo simulation, the w value is implemented as the mean value
in CO2 and He gases, independent of the electron energy. However, in the low energy region,
it is reported that the w values for charged particles increase, such as an electron in CO2 gas[48] and a proton in water vapor [49] as shown in Figure 6.3 and 6.4, respectively. In the gas
composition of the TPC, it is possible that the w value increase causes a significant eﬀect on
protons from neutron beta-decays, because the proton has a kinetic energy of less than 1 keV.
The accurate w value dependence on the kinetic energy of a charged particle is unknown in
the low energy region. The upper limit of this eﬀect is estimated by the special beta-decay
simulation in which a proton kinetic energy is set to be zero. This is equivalent to setting
infinite w value for a proton, thus giving the upper limit of this eﬀect.
• Neutron polarization
Although the neutron beam is polarized at the SFC position, the polarization condition at the
TPC position is totally unknown. A polarized neutron beam undergoes an asymmetric betadecay with respect to the polarization direction as described in Section 4.3.1. For example,
when the neutron beams are polarized in the vertical direction, the drift length of electrons
from beta-decay would change and the attenuation eﬀect would produce a systematic eﬀect forthe detection eﬃciency. However, the polarization of the neutron beams at the TPC position is
yet to be measured. In order to estimate the upper limit of this eﬀect, the detection eﬃciency

CHAPTER 6. RESULTS

Drift time [us]

86

30
3

10

20
102

10

−0150

10

−100

−50

0

50

100

150

1

Drift velocity [cm/us]

Ionization y position [mm]
3
103

2
102

1
10

0
−150

−100

−50

0

50

100

150

1

Ionization y position [mm]Figure 6.2: Electron drift time (top) and drift velocity (bottom) distribution of the cosmic rays
events as a function of the ionization y position in the TPC. The bottom plot is obtained by taking
the derivative of the y position in the top plot with respect to the drift time. The non-uniformity ofthe drift velocity along with the y direction is observed.

W VALUES OF PROTONS IN WATER
6.2. UNCERTAINTIES FOR THE NEUTRON BETA-DECAY SELECTION EFFICIENCY(εβ ) 87

while for those in liquid water, the data calculated byMonte Carlo simulation were used.
RESULTS AND DISCUSSION

Figure 2 shows the experimental and theoretical W
values of protons in water vapour determined in thiswork. For comparison, the W values of protons in liquidwater are added in Figure 2. It can be seen from Figure
2 that above 20 keV, the W values are nearly independent of energy. In this energy region, the experimental values for water vapour are about 16% higher
than the theoretical ones obtained with the stopping
cross sections of ICRU. Better agreement is found if the
stopping cross sections of Uehara et al (6) are used. This

E. Waibel, B. Grosswendt / Energy loss of electrons in CO,

I ; Ske V

!"#

!$#

!##
0.95

.()+,-

%#

a

&#

e!

may be put down to the fact thatthe stopping cross sections S(T)ionisation, excitation, and charg
as used in this work to calcula
quence that the inaccuracies of
not propagate into the ratio !ip(
In the energy region below
stopping cross sections of ICRU
deviation between theoreticalvalues. The deviation increases
This is probably due to the ina
cross sections of ICRU which fo
dence predicted by the free-electing to this model, the electronic
are linearly proportional to theever, several theoretical and ex
revealed that the stopping crossecules with rather tightly bodecrease much more strongly tha
jectile velocity.
Figure 2 also shows that abov
cal W values in liquid water ancoincide while below 100 keV,cantly lower than the latter. T
phase dependence found for theof electrons. Above 500 eV, thein water vapour are about 16%
liquid water calculated by M
However, the agreement of theof protons in the two water phthe inaccuracies of the cross sec
electron energy spectra used in

P

IO3

IO2

10'

7

eV

10’

c

Fig. 4. W values for electrons completely stopped in carbon
dioxide as a function of the electron energy T: (+) present
experimental
results, (0) experimental
data from Combecher[8], (0) experimental
data of Smith and Booz [2], (A) present

Figure6.3: Averageenergy to create an) fitting function of eq. (S), ( -+ )Monte Carlo results, (high energy
accordingto ICRU
electron-ion
pairW(wvalue)
for[lo].an electron
in CO2 gas. The horizontal axis showsthekinetic
energyof thewassentedin fig. 6;
experimental
and electron.
calculated
B, It
agree
quite
well
thoughthecalculatedaregenerally
somewhatstudied by E. Waibel and B. Grosswendt inhigher. B, and B, are equal for energies above 1 keV,
1991(+), electron(◦), (□)
are independent
but at[48]:decreasingenergy,the energy relatedexcoefficient B, must be higher than B, due to the fact
perimental
results, (△) Monte Carlosimuthat the mean energy of the backscatteredelectrons islation,(-)
fittingfunction.
obviously lower associated with increasing W. The ratioof the calculated B, and B, values increases slightly
from 1.33 at 50 eV to 1.62 at 5 keV, that of B,/B,
from 1.46 to 1.62.
If one compares these new backscatter coefficientswith those for other low-Z materials it can be seen thatthey are very similar to those for N,, 0,, and air ofGrosswendt and Waibel[29] and for air of Berger et al.
[32] and are somewhat smaller than those published by
Ohlenschlaeger et al. [33] for N,, O,, and CO.
4.3. Eiectron ranges

CONCLUSION

At low energies, the theoretic
using the stopping cross sections
II
0.5
1
ably higher than the experime
1. 5
reason for this deviation is pro
zhof the T0.5 dependence of the sto
Fig. 5. Ratio of the #energy transfer E(zp) in a medium of mass
protons in water vapour below 1
!
!#
!##
!#"
!#!
per area zp and the!#$%mean numberof ionizations
N(zp) northeoretical results of this work, tmalized to the W value as a function '()*+,of the distancez
in water vapour are higher thannormalized to the practical range R, with the primary electron
the low energy region, whereas
energy T as a parameter:(0) w of table 1, (other symbols)
Figure2. W values of protons in water vapour and liquid water:
values almost coincide. On thepresent Monte Carlo calculation.
( — ) theoretical W values of protons in liquid water calculated energy W values of electrons(. . .)create
theoretical anusing the6.4:
stoppingAveragecross sections energyof ICRU (5), to
Figurefound to be higher than those in
W values of protons in water vapour calculated using the stop(wetvalue)fora proton
W values inthis contrast may arise from t
ping
sectionspair
Ueharaal (6), (---) theoreticalarea (zp)electron-ion
and crossperforming
aofdiffusion
correction
accordof protons inwatervapour[30],calculatedusing
cross sections interaction cross sections used f
ing to Grosswendt
andWaibelbut also
bytheusing
(5)
water
vapor.
The
horizontal
axis
showsW values. Therefore, further in(!) experimental
resultstransfer
for protons
of ICRU
the numerical
distributionsof the energy
and in water
respect to the examination
vapour.
the ionization
number from
the MonteCarlosimulathe kinetic
energyof theproton.
It waswith
sections, are envisaged.
0.9

20 1

"#

$#

tion.
The upper part of fig. 7 shows the practical mass
REFERENCES
range (Rp); of the energy transfer obtained by calcula-studied by G. Willems et al. in 2002 [49]:(◦) experimental result, (—), (· · · ), and (–1. Waibel, E. and Willems, G. Ionisation Ranges and W Values for Low Energy Protons in Tissue-eq–) theoreticalwith diﬀerent crossDosim. 13, 79–81curves(1985).
2. Waibel, E. and Willems, G. W Values for Low-energy Protons in Methane-based Tissue-equivalen
sectionmodels.
Phys. Med. Biol. 37, 249–259 (1992).

‘onm

‘,,;F
10'

l-

As stated in section 2, electron ranges can be determined from the energy transfer and ionization number distributions along the primary beam direction. Thiswas done here not only by using the experimental
ionization measurements in dependence on mass per

349

Downloaded from https://academic.oup.com/rpd/article-abstract/99/1-4/347/1687812
by University of Tokyo Library user
on 03 September 2018

lo2

Fig. 6. Energy dependence

lo3

ev

104

of the backscatter coefficients BI
for ionization,
B, energy imparted and B, the particle number for electrons stopped in CO, gas, (+ ) experimental
resultsof B,; (x) B,, (0) B,, (v) B, from Monte Carlo calculations.

88

CHAPTER 6. RESULTS
for neutron beta-decay is studied in the Monte Carlo simulation by changing the polarization
direction, and it is found to have negligible eﬀect on our analysis.

6.3 Uncertainties for the 3He number density (ρ)• Chamber deformation by pressure
The TPC volume is precisely measured by the volume expansion method as described in
Section 5.4.1. However, during the volume ratio measurement, the 4 He pressure filling the
TPC volume is a few hundred Pa, resulting in a deformation of the vacuum chamber due tothe atmospheric pressure surrounding the chamber. This means the TPC volume is slightly
diﬀerent between he volume ratio measurement and the lifetime measurement, which changes
the 3 He number density in the TPC. The deformation can be calculated using the Young’s
modulus parameter of the chamber material (aluminum and stainless steel). The deformation∆y of a rectangular plate with a Young’s modulus E, a thickness t, applied pressure P , anda short side length b, is expressed as∆y = βP

b4
,
Et3

(6.2)

where β is a function of the ratio of the short to the long side length of the plate [50]. In ourcase, the atmospheric pressure causes the volume deviation of 2300 cm3 at most, or 0.3% of
the total volume.
• Virial coeﬃcient
For the 3 He density calculation, the He and CO2 gases are assumed to be ideal gases and thegas state equation is used. For a real gas, however, molecules attract each other, which istaken into account in the van der Waals equation:(a )P + 2 (V − b) = RT.
(6.3)
V
In this equation, V is a normalized volume. The equation can be rewritten as
PVBC= 1 + + 2 + ···
RT
V
V

(6.4)

Assuming B = (127 ± 13) cm3 /mol for CO2 gas at T =30◦ [51], and B = (11.79 ± 0.06)
cm3 /mol for He gas at T =25◦ [52], the deviation from an ideal gas is expected to be about
0.5%.

6.4 Analysis results of parameters
The analysis results of parameters in Eq. (1.27) is shown in Table 6.1 for Sβ , Table 6.2 for S3 He ,Table 6.3 for εβ , Table 6.4 for ε3 He , and Table 6.5 for ρ, respectively. The amount of each uncertainty
is plotted in Figure 6.5.

6.4. ANALYSIS RESULTS OF PARAMETERS

89

Table 6.1: Summary of the Sβ uncertainty: Fill66
Term

Value

Correction

Uncertainty

Correction[%]Uncertainty[%]Sβ before correction

14175
13685
13685
13685
13669
13669
13665
13670
13670

0
-490
0
0
-16
0
-3
5

±206 (stat.)±204 (stat.)
±3
± 18

0.000
-3.5860.000
0.000-0.1180.000-0.0250.034±1.505 (stat.)±1.491 (stat.)±0.020±0.128Gas background
Upstream γ-ray correction from LiF
LiF γ-ray spectrum
SFC S/N
CO2 recoil
3 He event contamination

PileupSβ corrected

+16
−0
+0
−39
+3
−0

±8
± 290 (stat.) +26−43 (sys.)+0.118−0.000+0.000−0.283+0.025−0.000±0.060±2.118 (stat.) +0.187−0.317 (sys.)

Table 6.2: Summary of the S3 He uncertainty: Fill66
Term

Value

Correction

Uncertainty

Correction[%]Uncertainty[%]

S3 He before corrected

346777345936345864345449343596341844341724341724

0
-841
-72
-415
-1853
-1751
-120

±593 (stat.)±60 (stat.)0.000-0.246-0.021-0.122-0.542-0.513-0.035±0.174 (stat.)±0.018 (stat.)

Scatter event
Beta decay event contamination
SFC S/N
14 N(n, p)14 C contamination
17 O(n, α)14 C contamination

Pileup
S3 He corrected

+72
−0
+415
−0

± 191
± 88
+120
−0
± 596 (stat.) +486
−210 (sys.)+0.021−0.000+0.122−0.000±0.056±0.026+0.035−0.000±0.175 (stat.) +0.142−0.061 (sys.)

Table 6.3: Summary of the εβ uncertainty: Fill66
Term

Value

Correction

Uncertainty

Correction[%]Uncertainty[%]

MC statistic

0.9414
0.9414
0.9414
0.9414
0.9414
0.9414
0.9414
0.9414
0.94140.9396
0.93960.00000.00000.00000.00000.00000.00000.00000.00000.0000-0.0018±0.0007 (stat.)

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
-0.191±0.079 (stat.)

Waveform shape
Low energy cut
High energy cut
Drift distortion
Anode wire eﬃciency
Beam shift
Proton w value
Neutron polarization
Multi track rejection
εβ corrected+0.0004−0.0006+0.0010−0.0017+0.0024−0.0035± 0.0010+0.0000−0.0000± 0.0009± 0.0011± 0.0002+0.0018−0.0000±0.0007 (stat.) +0.0037−0.0043 (sys.)+0.046−0.063+0.107−0.179+0.261−0.371±0.110+0.001−0.001±0.099±0.113±0.023+0.191−0.000±0.079 (stat.) +0.391−0.457 (sys.)

90

CHAPTER 6. RESULTS
Table 6.4: Summary of the ε3 He uncertainty: Fill66

Term

Value

Correction

Uncertainty

Correction[%]Uncertainty[%]

MC statistics

0.99990.99990.99990.00000.0000±0.0000 (stat.)± 0.0000± 0.0000 (stat.) +0.0000−0.0000 (sys.)

0.000
0.000

±0.003 (stat.)±0.000±0.003 (stat.) +0.000−0.000 (sys.)

Energy cut
ε3 He corrected

Table 6.5: Summary of the ρ uncertainty: Fill66
Term
Inject 3 He amount
Virial coeﬃcient
Thermal transpiration
3 He gas isotopic purity
3 He gas chemical purity
3 He from G1 4 He gas

Chamber deformation (pressure)
Chamber deformation (temperature)
Preamplifier heat generation

Correction

Uncertainty

Correction[%]Uncertainty[%]

0.00
3.72
-0.98
0.00
0.00
202.04
-3.51
-0.49
0.00

± 6.57± 0.01± 0.100.000
0.163-0.043
0.000
0.000
8.835
-0.154-0.0210.000±0.287±0.000±0.004

+0.00
−1.04
+0.00
−0.12

± 6.07± 3.51± 0.49± 0.49± 0.00 (stat.) +9.64−9.69 (sys.)+0.000−0.046+0.000−0.005±0.265±0.154±0.021±0.022±0.000 (stat.) +0.421−0.424 (sys.)

Sβ
S3He
εβ
ε3He
ρ
σ0

0.005
0.004
0.003
0.002

injectvirialthermalisopurity
chemipurity
g1hedeform_pres
deform_temp
heat_generation
cross_section

drift
wireeff
beamshift
protonw
polarization
multitrackenergycut

pileup3He
waveformshape
lowenergy
highenergy

co2contami
he3contami
pileupbeta
betacontami
sfcsn3He
nitrogenoxygen0sfcsnbeta
lifspectle

0.001
upgamma

uncertainty

ρ correctedValue2086.04
2089.76
2088.78
2088.78
2088.782290.822287.312286.822286.822286.82

Figure 6.5: Breakdown of the uncertainties given for Fill96.

uncertainty

6.5. COMBINED RESULT

91

0.06

0.04

0.02

0 42 53 63 64 65 66 83 84 86 87 88 89 94 95 96 97 98 99 100101
fillnum
Figure 6.6: Statistical uncertainty for each gas fill data.

6.5 Combined result
The statistical and systematic uncertainties of the neutron lifetime for each gas fill data are shown in
Figure 6.6 and Figure 6.7, respectively. The neutron lifetime evaluated for each gas fill condition isplotted in Figure 6.8. The averaged result combining the same year is listed in Table 6.6. They are
consistent with each other, and the overall averaged value is 898.8 ± 4.7 (stat.) +7.7
−8.9 (sys.) s. Our
result is shown in Figure 6.9 along with previous measurements by others.
Table 6.6: Comparison of the lifetime value combined with the same year gas data.
Year
Measured neutron lifetime [s]2014A 942.1 ± 24.9 (stat.) +14.0−8.3 (sys.)
2015A 896.4 ± 18.9 (stat.) +5.9
−5.7 (sys.)
2016A 887.9 ± 10.5 (stat.) +6.3
−6.1 (sys.)+8.3
2017A 911.3 ± 21.3 (stat.) −10.7 (sys.)
2017B 899.0 ± 5.7 (stat.) +7.9
−9.9 (sys.)

92

CHAPTER 6. RESULTS

uncertainty

Low uncertainty

0.015

High uncertainty

0.01

0.005

0 42 53 63 64 65 66 83 84 86 87 88 89 94 95 96 97 98 99 100101
fillnum

lifetime [s]Figure 6.7: Systematic uncertainty for each gas fill data.

Statistical error

1000

Systematic error

900

800
42 53 63 64 65 66 83 84 86 87 88 89 94 95 96 97 98 99 100101

fill number
Figure 6.8: Result of the neutron lifetime for each gas fill data and their averaged value. Our overall
2
averaged lifetime, shown as a blue line, is 898.8 ± 4.7 (stat.) +7.7
−8.9 (sys.) s (χ /ndf = 12.9/19 =0.68).

lifetime [s]6.5. COMBINED RESULT

900

93

・In-ﬂight method

・UCN storage method

Our result

890

880
2000

2010

year

Figure 6.9: Comparison of our result with other neutron lifetime measurements [6].

Chapter 7
Summary and discussion
7.1 Summary
The precise neutron lifetime measurement was conducted using the pulsed neutron beams at JPARC. The spin flip chopper is developed to form the neutron bunches from the pulsed beams.
The signal events are counted only when each of the neutron bunches is completely inside the TPC
sensitive region. As a result, the 4π solid angle acceptance is guaranteed for the signal events inaddition to suppressing the background. As a detector, the time projection chamber made of the
low radiation material is also developed. It is filled with helium, CO2 , and a small amount of 3 Hegases. It detects both the neutron beta-decay events and the 3 He(n, p)3 H events at the same time.
The neutron lifetime is expressed using the numbers of these two kinds of events. Furthermore,
The Monte Carlo simulation of the TPC is developed. Implementing the accurate physics models
to describe the detector response, the simulation can reproduce the experimental distribution well.
The signal selection eﬃciencies are evaluated using this simulation with an uncertainty of below
0.5%.
We started the data taking at 2014 and continued by 2018. Combining the four years’ data, thetotal data taking time with the neutron beams is 40 days, and 6.0×1011 neutrons entered the TPC. The
averaged result of the measured neutron lifetime is 898.8 ± 4.7 (stat.) +7.7
−8.9 (sys.) s. This is the first
result of the neutron lifetime measurement that obtained a 1% level of the precision using the pulsed
neutron beams. Although our result is closer to the averaged result of the in-flight method, it is also
consistent with the averaged result of the UCN storage method. We do not yet know what causes
the discrepancy between the in-flight method and the UCN storage method: whether it is simply
caused by missing some systematic eﬀects or it indicates new physics beyond our understanding.
By resolving this problem, the future potential of improving the Vud precision can be proposed aswell as increasing the reliability of the BBN model. Our result is not precise enough to give any
indication of the discrepancy puzzle, hence further precise measurement is significantly required.
We have to improve both the statistical and systematic uncertainties to achieve our eventual goal
precision of 1 second. Several upgrade plans are proposed and ongoing in our goal.
95

CHAPTER 7. SUMMARY AND DISCUSSION

Uncertainty [%]96

10Fill42150 kW

Fill53200 kW

Fill63
Fill66300 kW

Fill83500 kW

Fill891000 kW

1

10−1

103

102
1

10

104

# of cycles
102

Data acquisition time [day]Figure 7.1: Expected statistical uncertainty as a function of the total data acquisition time. The color
represents the accelerator operation power, and some of the experimental results are also expressedas points in the figure.

7.2 Upgrade plans• SFC upgrade
After the increase of the accelerator operation power, the neutron flux in the TPC is expected
to be 2.5 × 107 neutrons/s for the 1 MW power operation. As shown in Figure 7.1, 600
days of data taking is required to achieve 0.1% statistical uncertainty by scaling our results
statistically. Therefore, it would be preferable to increase the neutron beam flux in the TPC
by several times. The current beam size, 2.5 cm × 2 cm, is significantly limited by thebeam transportation system, such as magnetic super mirrors and flipper coils in the SFC. It isplanned to increase the sizes of these devices so that the beam size in the TPC would be 3 cm
× 10 cm. Two upgrade plans are currently proposed as summarized in Table 7.1. After these
improvements, the total neutron flux in the TPC is expected to be 1.33×108 for the 1MW
accelerator operation, which is 5.3 times larger than the current one. Under this operation
condition, we can achieve a statistical uncertainty of 0.1% by taking data for 100 days.
• Low-pressure operation
In the current analysis, the gas-induced background is one of the main backgrounds forbeta-decays, which exists about a few percent for beta-decay in the signal region. Since thisbackground comes from a neutron scattering with gas molecules in the TPC, the amount is
expected to decrease when the operation gas pressure is reduced below 100 kPa. For thispurpose, it is planned to operate the TPC with the low-pressure gas condition. We already7.2. UPGRADE PLANS

97

Table 7.1: Expected neutron flux in the TPC for two prospective upgrade setups. The neutron flux
is normalized by the accelerator design operation power of 1 MW.
Setup
Collimator size Vertical mirror
0 (default)
25×20 mm2
no1
100×30 mm2
yes
2
100×30 mm2
yes

Reflection mirror
140×30×0.7 mm3
200×100×0.3 mm3200×100×0.3 mm3Coil
35×35 mm2
35×35 mm2
> 40×40 mm2

Neutron flux at TPC
2.50×107 /s
3.96×107 /s
1.33×108 /s

Ratio
1
1.58
5.32

Figure 7.2: Picture of a new preamplifier. Input wire signals of 24 channels are amplified per board.
took the data in the 50 kPa gas condition while the composition ratio was maintained. Dueto the heat generation from the preamplifiers, we found the gas temperature was increased
by at most 20◦ during the measurement, which is higher than a 15◦ increase at 100 kPa
condition. Under the further low-pressure condition, the temperature would increase more,which gives a large temperature gradient in the TPC. It gives a non-uniform 3 He distribution
inside the TPC, which aﬀects the estimation of the 3 He number density. In order to reduce thisnon-uniformity, a new type of preamplifier with low power-consumption, the specification ofwhich is listed in Table 7.2, is currently developed in our group (see Figure 7.2).
Table 7.2: Specification comparison of the current and new preamplifier.
ChannelPower consumption
Gain
Equivalent noise charge

Current preamplifier
1 ch/chip
500 mW/ch
1 V/pC∼8000

New preamplifier
24 ch/board
9 mW/ch
0.8 V/pC∼3000• Thinning of the neutron shutter
The neutron beam in the TPC can be switched on and oﬀ by the 5 mm-thick LiF shutter as

98

CHAPTER 7. SUMMARY AND DISCUSSION
described in Section 2.4. Some of the backgrounds for the beta-decay events can be subtractedusing the shutter-closed data (see Section 5.3.1). However, γ-rays from the upstream of the
TPC undergo Compton scattering in the shutter with a probability of 4.8%, which causes thebias of the background subtraction between the shutter-open and shutter-closed data. The
systematic uncertainty due to the eﬀect is 0.35% for the number of beta-decayevents. The
scattering probability can be reduced by lowering the composition ratio of the polytetra fluoro
ethylene (PTFE) in the shutter. As as alternative, as a result of simply thinning the shutter
thickness by half, the systematic uncertainty can be suppressed to be 0.1% level.
• 3 He density estimation
The 3 He amount injected into the TPC is evaluated with a precision of 0.3%, which iscurrently one of the largest systematic uncertainties. The uncertainty mainly originates fromthe resolution of the pressure gauge. By using a new pressure gauge of Mensor CPT9000,
which has a larger dynamic range (500 kPa) and better resolution (0.08%), the uncertainty canbe suppressed. Furthermore, the procedure to inject 3 He gas into the TPC can be simplified
in order to reduce the uncertainty propagation. After the improvement, the uncertainty of theinjected 3 He number density is expected to be 0.11%.

Appendix A
Mathematical definition of analysis
parameters
Mathematical definitions for the analysis parameters introduced in Section 5.2 are expressed in thisappendix.

A.1 Waveform parameters• PED
A pedestal (an average voltage) level between 0 µs to 28 µs.
• PH
Waveform pulse height (maximum voltage from PED level).
• HIT
A binary parameter expressing the existence of energy deposit of the wire. The HIT parameter
becomes true when PH is higher than a threshold level, and false otherwise. The thresholdlevel was set as 15 mV for anode and field, and low-gain cathode wires. For high-gain wires,we use 17.5 mV.
• RISETIME
A time at which the waveform exceeds the threshold level for the first time.
• INT
Integral of the waveform from PED level. The integral region was determined so as tocompletely contain a signal waveform. Since the drift velocity depends on the TPC gas
pressure, the region was optimized as 28µ s to 70µ s.
99

100

APPENDIX A. MATHEMATICAL DEFINITION OF ANALYSIS PARAMETERS

A.2 Event parameters• TOTALENERGY =∑INTi .

i∈anode & HITi =true

Total energy deposit in the TPC• MAXENERGY = max{PHi |i ∈ field}.
Maximum energy deposit in the TPC∑• LOCALITY = max{PHi |i ∈ anode}/INTii∈anode & HITi =true• MINRISE = min{RISETIMEi |i ∈ anode & HITi = true}.
Trigger timing of the TPC∑• HITNUM =1.
i∈field & HITi =true

Number of wires detecting energy deposit• DTIME = max{RISETIMEi |i ∈ anode & HITi = true}−min{RISETIMEi |i ∈ anode & HITi =true} × vdrift .
Track length in y direction as a unit of time
)
) (
(
∑
∑
INTi .
i × INTi /• CENTER_A =i∈anode & HITi =truei∈anode&HITi =true

Track center position weighted by the energy deposit of wires• MINHIT_A = min{i|i ∈ anode & HITi = true}.
The most left side (the x coordinate is minimum) wire number detecting energy deposit.
• MAXHIT_A = max{i|i ∈ anode & HITi = true}.
The most right side (the x coordinate is maximum) wire number detecting energy deposit.
• DTC_A = min{|i − 12| | i ∈ anode & HITi = true}.
The distance between the center wire and the most closest wires detecting energy deposit.
• DVC_A = min{WIRENUM_A/2 − MINHIT_A, MAXHIT_A − WIRENUM_A/2},
where WIRENUM_A=24, WIRENUM_F=24, WIRENUM_CH=40, and WIRENUM_CL=40.
The distance between the center wire and the wire detecting the track origin point.

Appendix B
Thermometer specifications
The detailed specifications of the two types of thermometers (manufactured by LakeShore andAutomatic Systems Laboratories) are listed in Table B.1 and Table B.2.
Table B.1: Specification of the Automatic Systems Laboratories platinum thermometer.
Monitor model
F201
Monitor manufacture Automatic Systems Laboratories
Platinum manufacture Netsushin and Chino
Platinum resistance100 Ω
Uncertainty
60 mK at 298 K

Table B.2: Specification of the LakeShore platinum thermometer.
Monitor model
218
Monitor manufacture LakeShore
Platinum manufacture LakeShore
Platinum resistance100 Ω
Uncertainty
105 mK at 300 K

101

Appendix C
Gain reduction model in a wire chamber
due to the space charge eﬀect
In this experiment, the multiplication factor of the TPC is relatively high (∼ 104 ) in order to achieve
the high detection eﬃciency for the neutron beta-decay events. As a result, the linearity of thedetected energy is distorted for the 3 He(n, p)3 H events because of a large number of space charges
around the anode wires. An analytical model to describe the gain reduction is proposed [21] [41],which expresses the gain reduction factor s (0 < s ≤ 1) as()
dE
log 1 + f G0
dl
s=
,
(C.1)
dE
f G0
dl
where G0 is the multiplication factor without the space charge eﬀect, and dE/dl is the energy deposit
density per anode wire length. In this model, the microscopic behaviour of the space charges is
described by a single free parameter f . The f parameter, depending on the anode wire radius andthe operation gas composition, determines the absolute saturation scale. The s value as a functionof G0 is drawn in Figure C.1.
For the purpose of experimentally verifying the model, a small multi wire drift chamber wasdeveloped as shown in Figure C.2 [41]. The proton beams at the Tandetron accelerator in the
University of Tsukuba [53] were irradiated into the drift chamber. The gain reduction (s) for the
proton beams was measured by comparing the detected energy with the energy deposit calculatedby the Monte Carlo simulation. The model was investigated by changing (1) the anode wire voltage
and (2) the proton beam angle with respect to the anode wires. The observed dependence of s wasconsistent with the proposed model in Eq. (C.1) as shown in Figure C.3. The optimum parameter−3
to reproduce the experimental gain reduction was evaluated to be f = (1.8+0.5
mm/MeV.
−0.4 ) × 10
Figure C.4 shows the energy deposit distribution before and after the correction using the model.
This gain reduction model is implemented in the Monte Carlo simulation for the neutron lifetime
measurement. For the purpose of updating the model, it is planned to measure the saturation eﬀect
with diﬀerent ion beams and gas compositions.

103

s

104APPENDIX C. GAIN REDUCTION MODEL IN A WIRE CHAMBER DUE TO THE SPACE CHARGE EFFECT

f=5× 10-4 mm/MeV
f=5× 10-3 mm/MeV

1

f=5× 10-2 mm/MeV

0.5

0

103

104

105

106
G0

Figure C.1: Proposed model function of the gain reduction factor (s) as a function of the multiplication factor (G0 ) [41]. In this plot, the typical energy deposit density dE/dl = 20 keV/mm isassumed.

Figure C.2: Picture of the multi wire drift chamber. The chamber is composed of epoxy glass
laminate (G10). The dimensions of the sensitive region are 13 cm × 13 cm × 6 cm.

gain reduction factor (s)

105

1.5

EX
model best fit
uncertainty

1

0.5

0

40

50

60

70

80
90
MWDC angle (φ) [deg]EX (w/o correction)
EX (w correction)

0.2

MC truth0.15

EX (w/o correction)
EX (w correction)

0.2

MC truth0.15

φ = 90°

0.1
0.05
0

normalized events

normalized events

Figure C.3: Measured gain reduction factor along with the proposed best fit model curve [41]. The
horizontal axis represents the proton beam angle with respect to the anode wires.

φ = 60°

0.1
0.05

50

100
150
deposit energy [keV]

0

50

100
150
deposit energy [keV]

Figure C.4: Energy deposit distributions without and including the gain reduction correction [41].
The proton beam angles with respect to the anode wires were set at 90◦ (left) and 60◦ (right). The
respective energy deposit distribution calculated by the Monte Carlo simulation is also drawn as a
red histogram.

Acknowledgments
First of all, I would like to express my greatest appreciation to my supervising advisor Prof.
Satoru Yamashita. He gave me the precious opportunity to join such an exciting and interesting
experiment. Whenever I was at a standstill in my research, I always received accurate and essential
advice from him. In addition, he actively gave me many opportunities to participate in various
kinds of conferences, seminars, and schools. It greatly heightened my interest and motivation for
physics. It was a wonderful and fruitful experience for me to be able to do the research with him
for five years.
I am grateful to all the members of the neutron lifetime experiment. They always gave melots of beneficial advice for my analysis, measurements, and presentations, which supported andencouraged me so much. Prof. Kenji Mishima devoted a considerable amount of his time to guide
me in my research. We had many chances of discussing variety field of physics, and His extensive
knowledge always taught me the fun to seek truths in physics. Prof. Masaaki Kitaguchi and Prof.
Tamaki Yoshioka always gave me accurate advice in our weekly group meetings. I also would like toexpress my appreciation to all the other Neutron Optics and Fundamental Physics (NOP) members.
It was a lot of fun to discuss neutron physics at conferences, seminars, and J-PARC dormitories. I
hope all of them would enjoy their respective research and accomplish great achievements in thefield.
I also would like to thank all the members of Yamashita laboratory. I especially had theimmense support from Mr. Takahito Yamada and Dr. Sei Ieki, who are also collaborators of theneutron lifetime experiment. I spent a significant percentage of my research life with them, and theytaught me all of the experiment, such as neutron physics, the data analysis, and the Monte Carlosimulation. I could not enjoyed my research so much without their kind and continuous support.
In addition, I am deeply grateful to Mr. Yu Kato and Mr. Kazuki Fujii for improving ourselves
through the experiment at the University of Tsukuba. Although it was not always an easy way due
to a lot of troubles, it is definitely one of my best memories in my research life. Dr. Tomohiko
Tanabe helped me a lot to finish this thesis by proofreading all the sentences in this thesis. Thanks
to his appropriate and kind advice, I was able to keep my motivation up to writing the thesis. My
gratitude also goes to all the other Yamashita laboratory members, Dr. Masakazu Kurata, Dr. Ryo
Katayama, Dr. Nao Higashi, Mr. Harumichi Yokoyama, Mr. Takuaki Mori, Mr. Kento Kasuya, Mr.
Shohei Fujikura, Mr. Takanori Mogi, and Mr. Shogo Kajiwara. Their earnest and energetic attitudes
toward research are good stimuli for me, and they all gave me great advice for my research.
I would like to appreciate Sekiba laboratory members at the University of Tsukuba. We
started collaboration experiment in 2016, and Dr. Daiichiro Sekiba provided us great opportunities
107

108

ACKNOWLEDGMENTS

to conduct the experiment using the tandem accelerator. Furthermore, his advice based on his
experience led me to the success of our collaborative experiment. I also enjoyed discussion
and device development with other Sekiba laboratory members, Dr. Isao Harayama, Ms. Yumi
Watahiki, Mr. Yuki Sugisawa, and Mr. Junichi Kikuda. It was great experience to have discussion
with researchers in other fields.
I also enjoy my student life with all the ICEPP members. In particular, I would like to express
my respectful gratitude to the ICEPP secretaries for supporting my research life. During my five
years at ICEPP, I was able to focus on my research thank to their huge support.
I would like to thank Dr. Takuya Okudaira. I appreciate his feedback on my thesis despite hisbusy schedule. We enjoyed discussion every time participating in the international conferences,which always gave me a positive impact on my research.
I am also specially grateful to Mr. Tatsuya Kawaguchi and Mr. Yuichiro Tsuchiya for giving me
a lot of technique related to the image recognition algorithm. I would not have finished the analysis
without their persevering support.
In my research life, Dr. Jacqueline Yan gave me so many considerable support. She always
provided useful comments and advice to my presentations as well as my thesis. In addition, shehelped me to get the modules and the devices necessary for our experiment. We also enjoyed various
kinds of meaningful seminars.
Finally, the deepest appreciation goes to my family for supporting me all my life.

Bibliography[1] M. Pospelov and J. Pradler. Big Bang Nucleosynthesis as a Probe of New Physics. Annual
Review of Nuclear and Particle Science, Vol. 60, pp. 539–568, 2010.
[2] A. Peimbert, M. Peimbert, and V. Luridiana. The primordial helium abundance and the numberof neutrino families. Revista Mexicana de Astronomia y Astrofisica, Vol. 52, pp. 419–424,
2016.
[3] E. Aver, K. A. Olive, and E. D. Skillman. The eﬀects of He I λ 10830 on helium abundance
determinations. Journal of Cosmology and Astroparticle Physics, Vol. 2015, No. 07, p. 011,
2015.
[4] Y. I. Izotov, T. X. Thuan, and N. G. Guseva. A new determination of the primordial He
abundance using the He I λ10830Å emission line: cosmological implications. Monthly
Notices of the Royal Astronomical Society, Vol. 445, No. 1, pp. 778–793, 2014.
[5] PAR Ade et al. Planck 2015 results: XIII. Cosmological parameters. Astronomy and Astrophysics, Vol. 594, pp. 1–63, 2016.
[6] M. Tanabashi et al. (Particle Data Group). Review of particle physics. Phys. Rev. D, Vol. 98,
p. 030001, Aug 2018.
[7] J. C. Hardy and I. S. Towner. Nuclear beta decays and CKM unitarity. In 13th Conference on
the Intersections of Particle and Nuclear Physics (CIPANP 2018) Palm Springs, California,
USA, May 29-June 3, 2018, 2018.
[8] A. Czarnecki, W. J. Marciano, and A. Sirlin. Precision measurements and CKM unitarity.
Physical Review, Vol. D70, p. 093006, 2004.
[9] J. Chadwick. The existence of a neutron. Proceedings of the Royal Society of London A:
Mathematical, Physical and Engineering Sciences, Vol. 136, No. 830, pp. 692–708, 1932.
[10] S. Arzumanov et al. A measurement of the neutron lifetime using the method of storage ofultracold neutrons and detection of inelastically up-scattered neutrons. Physics Letters, Vol.
B745, pp. 79–89, 2015.
[11] J. S. Nico et al. Measurement of the neutron lifetime by counting trapped protons in a cold
neutron beam. Physcal Review C, Vol. 71, p. 055502, 2005.
109

110

BIBLIOGRAPHY[12] A. T. Yue et al. Improved Determination of the Neutron Lifetime. Physical Review Letters,Vol. 111, No. 22, p. 222501, 2013.
[13] R. Kossakowski et al. Neutron lifetime measurement with a helium-filled time projection
chamber. Nuclear Physics A, Vol. 503, No. 2, pp. 473 – 500, 1989.
[14] J. Als-Nielsen and O. Dietrich. Slow Neutron Cross Sections for He3 , B, and Au. Phys. Rev.,
Vol. 133, pp. B925–B929, Feb 1964.
[15] R. B. Firestone and V. S. Shirley. Table of Isotopes. Wiley-Interscience, 1.0 edition, March
1996.
[16] P. Grivot et al. A helium-filled time projection chamber for a neutron lifetime measurement.
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with
Materials and Atoms, Vol. 34, No. 1, pp. 127 – 134, 1988.
[17] J-PARC oﬃcial website. http://j-parc.jp/.
[18] T. Ino et al. Measurement of the neutron beam polarization of BL05/NOP beamline at JPARC. Physica B: Condensed Matter, Vol. 406, No. 12, pp. 2424 – 2428, 2011. Proceedingsof the 8th International Workshop on Polarised Neutrons for Condensed Matter Investigation.
[19] K. Mishima. J-PARC 中性子基礎物理ビームライン（BL05/NOP）. Neutron network news
(Hamon), Vol. 25, No. 2, pp. 156–160, 2015.
[20] Y. Arimoto et al. Development of time projection chamber for precise neutron lifetime
measurement using pulsed cold neutron beams. Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol.
799, pp. 187 – 196, 2015.
[21] H. Otono. New detector system for the precise neutron lifetime measurement using pulsed cold
neutron beams. Ph.D. dissertation, The University of Tokyo, December 2011.
[22] T. Ino et al. Precision neutron flux measurement with a neutron beam monitor. Journal of
Physics: Conference Series, Vol. 528, No. 1, p. 012039, 2014.
[23] Garfield oﬃcial website. http://garfield.web.cern.ch/garfield.
[24] A. R. Siddiq and A. R. Kennedy. Porous poly-ether ether ketone (PEEK) manufactured by anovel powder route using near-spherical salt bead porogens: Characterisation and mechanicalproperties. Materials Science and Engineering: C, Vol. 47, pp. 180 – 188, 2015.
[25] Y. Lee. Physical properties of poly(ether ether ketone). Ph.D. dissertation, University of
Massachusetts Amherst, 1988.
[26] Neutron scattering lengths and cross sections. http://www.ncnr.nist.gov/resources/n-lengths/.

BIBLIOGRAPHY

111[27] Magboltz oﬃcial website. http://magboltz.web.cern.ch/magboltz/.
[28] Y. Igarashi et al. A common data acquisition system for high-intensity beam experiments.
Nuclear Science, IEEE Transactions, Vol. 52, No. 6, 2 2005.
[29] Japan Radioisotope Association. アイトソープ手帳 11 版. Maruzen Publishing, 2012.
[30] H. Sumino, K. Nagao, and K. Notsuji. Highly sensitive and precise measurement of helium isotopes using a mass spectrometer with double collector system. Journal of the Mass
Spectrometry Society of Japan, Vol. 49, No. 2, pp. 61–68, 2001.
[31] S. Ieki. Measurement of the Neutron Lifetime by Counting the Beta Decay at J-PARC. Ph.D.
dissertation, The University of Tokyo, December 2017.
[32] S. Agostinelli et al. Geant4―a simulation toolkit. Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol.
506, No. 3, pp. 250 – 303, 2003.
[33] R. Grossman, D. Hanley, and Xiao Qin. Caching and migration for multilevel persistent object
stores. In Proceedings of IEEE 14th Symposium on Mass Storage Systems, pp. 127–135, Sept
1995.
[34] J. Allison et al. Recent developments in Geant4. Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol.
835, pp. 186 – 225, 2016.
[35] K. Hirota et al. Development of a neutron detector based on a position-sensitive photomultiplier. Physical Chemistry Chemical Physics, Vol. 7, pp. 1836–1838, 2005.
[36] N. Z. Alcock and D. G. Hurst. Neutron diﬀraction by the gases N2 , CF4 , and CH4 . PhysicalReview, Vol. 83, pp. 1100–1105, Sep 1951.
[37] N. Z. Alcock and D. G. Hurst. Neutron diﬀraction by gases. Physical Review, Vol. 75, pp.
1609–1610, May 1949.
[38] Prompt gamma-ray neutron activation analysis.
pgaa7/index.html.

https://www-nds.iaea.org/pgaa/[39] Phits oﬃcial website. https://phits.jaea.go.jp/indexj.html.
[40] Nuclear data evaluation project. http://www.tunl.duke.edu/nucldata/.
[41] N. Nagakura et al. Experimental verification of a gain reduction model for the space charge
eﬀect in a wire chamber. Progress of Theoretical and Experimental Physics, Vol. 2018, No. 1,
p. 013C01, 2018.
[42] S. Ramo. Currents induced by electron motion. Proceedings of the Institute of Radio Engineers,Vol. 27, No. 9, pp. 584–585, Sept 1939.

112

BIBLIOGRAPHY[43] ANSYS oﬃcial website. https://www.ansys.jp/index.html.
[44] G. Bradski. The OpenCV Library. Dr. Dobb’s Journal of Software Tools, 2000.
[45] J. Matsuda et al. The 3He/4He ratio of the new internal He standard of Japan (HESJ).
Geochemical journal GJ, Vol. 36, pp. 191–195, 01 2002.
[46] K. Mishima et al. Accurate Determination of the Absolute 3He/4He Ratio of a SynthesizedHelium Standard Gas (Helium Standard of Japan, HESJ): Toward Revision of the Atmospheric
3He/4He Ratio. Geochemistry, Geophysics, Geosystems, Vol. 19, No. 10, pp. 3995–4005,
2018.
[47] W. Blum, W. Riegler, and L. Rolandi. Particle Detection with Drift Chambers. Springer, 2008.
[48] E. Waibel and B. Grosswendt. Degradation of low-energy electrons in carbon dioxide: energy
loss and ionization. Nuclear Instruments and Methods in Physics Research Section B, Vol. 53,
No. 3, pp. 239–250, 1991.
[49] G. Willems, W. Y. Baek, and B. Grosswendt. Energy dependence of w values of protons inwater. Radiation Protection Dosimetry, Vol. 99, No. 1-4, pp. 347–350, 2002.
[50] Japan Ship and Boat Manufacturers’ Association. 通信教育造船科講座テキスト「船殻設計」学習指導書. 2000.
[51] D. Cook. The second virial coeﬃcient of carbon dioxide at low temperatures. Canadian
Journal of Chemistry, Vol. 35, No. 3, pp. 268–275, 1957.
[52] G. S. Kell, G. E. McLaurin, and E. Whalley. Second virial coeﬃcient of helium from 0
to 500◦ C by the two-temperature gas-expansion method. The Journal of Chemical Physics,
Vol. 68, No. 5, pp. 2199–2205, 1978.
[53] D. Sekiba et al. Installation of high-resolution ERDA in UTTAC at the University of Tsukuba:
Determination of the energy resolution and the detection limit for hydrogen. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials andAtoms, Vol. 401, pp. 29 – 32, 2017.