学位論文

Measurement of the Neutron Lifetime
by Counting the Beta Decay at J-PARC(J-PARC におけるベータ崩壊の計数による中性子寿命の測定)

平成 29 年 12 月博士（理学）申請

東京大学大学院理学系研究科
物理学専攻
家城 斉

Measurement of the Neutron Lifetime
by Counting the Beta Decay at J-PARC
Ph.D dissertation

Sei Ieki

Department of Physics,
School of Science, The University of Tokyo
7-3-1, Hongo, Bunkyo-ku, 113-0033, Tokyo, Japan
December, 2017

Abstract
The neutron decays into the proton, the electron and the neutrino with lifetime of about
15 minutes. The neutron decay is simple picture of semi-leptonic process mediating W
boson and the neutron lifetime is studied as a tool to probe the theory of weak interaction,cosmology and production of light nuclei in the early universe.
For the precise measurement of the neutron lifetime, key issues arise from statistics andaccurate measurement of absolute flux and that of neutron decay. The lifetime experiments
are classified into two methods, depend on the way to count neutron decay. In the in-flightmethod, neutron decay in-flight is counted by detecting the decay products, while the bottle
method store neutrons and count the remaining after a certain storage time. There havebeen recent interests in improving the uncertainty on the neutron lifetime to below 0.1 %,because there are 3.8 σ deviation between two methods, although the reported values are
consistent within each method.
In order to achieve high precision, we perform the measurement with intense neutron
beam at Japan Proton Accelerator Research Complex (J-PARC), Materials and Life Science
Experimental Facility (MLF), beamline 05. While most of the lifetime experiments wereconducted with reactor based sources, we have an advantage to increase the beam flux
based on the high intensity proton beam at J-PARC. A distinguishing feature of our setup
is that the source of backgrounds are reduced by material selection of the time projection
chamber (TPC). The neutron beam is formed into bunches by originally developed spin
flip chopper, that also contribute to improve the signal-to-noise ratio. Our experiment isconceptually based on the in-flight method with a He-filled TPC proposed by ILL-ISL-LAPP
collaboration [6], which have an advantage to cancel the uncertainties in the diﬀerent beam
flux and neutron velocity since neutron decay and beam flux are measured by the samedetector, simultaneously.
We carried out engineering data taking in 2014 and 2015, that correspond to two measurement series with a new gas mixture for each run, and established the procedure ofanalysis. In 2016, the first physics data set was obtained at 170 kW operation. The neutrons with the velocity range of 500 ∼ 1200 m/s are provided and 6.37 × 104 events of neutron
decay have been detected in about 1 m of decay volume. Combined with the engineering
data, the accumulated data correspond to 12 days of the beam time, and we present our
first result of the neutron lifetime as
τn = 899 ± 10 (stat.) ± 911 (syst.) sec.
Major systematical uncertainties are originated from the process to evaluate the number ofneutron decays and detection eﬃciencies. In this thesis, the investigation of backgrounds
and the analytic methods are explained in detail.

Contents
I

Neutron lifetime

1

1 Introduction
1.1 Discovery of neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Neutron lifetime physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Probablity of neutron decay . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Big Bang nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 CKM matrix unitarity . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Previous neutron lifetime experiments . . . . . . . . . . . . . . . . . . . . . .
1.3.1 In-flight method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Bottle method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Reported values of the neutron lifetime . . . . . . . . . . . . . . . . .

1
1
2
3
5
7
8
9
12
15

II

17

NOP experiment

2 Neutron lifetime measurement at J-PARC
17
2.1 J-PARC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 NOP beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Experimental setup
23
3.1 Overview of the setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Spin flip chopper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Radio frequency flipper coil . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.2 Magnetic supper mirror . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Beam entrance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Time projection chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1 Drift cage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4.2 Multi wire proportional chamber . . . . . . . . . . . . . . . . . . . . 34
3.5 Chamber gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.1 Measurement of 3 He density . . . . . . . . . . . . . . . . . . . . . . . 38
3.6 Cosmic ray veto counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
ii

CONTENTS
3.7 Calibration source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 TPC performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Readout electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.10 Summary of the features of experimental setup . . . . . . . . . . . . . . . . .

43
44
47
50

4 Neutron interactions
52
4.1 (n, γ) reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 (n, p) and (n, α) reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3 Neutron scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 3 H decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 Categorization of signals and backgrounds . . . . . . . . . . . . . . . . . . . 57
5 Simulation
59
5.1 Overview of simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1.1 List of the MC samples . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2 Production of ionized particles . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.1 GEANT4 physics model . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.2 Beam structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2.3 Capture reactions of scattered neutron . . . . . . . . . . . . . . . . . 63
5.2.4 Energy spectrum of prompt γ rays from the LiF tile . . . . . . . . . . 63
5.2.5 Neutron polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.6 Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3 Statistics of ionized partilces . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.1 Diﬀusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3.2 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3.3 Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3.4 Amplification and avalanche-induced electric field . . . . . . . . . . . 67
5.3.5 Space charge eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.6 Production of waveform . . . . . . . . . . . . . . . . . . . . . . . . . 68

III

Analysis70

6 Signal estimation
70
6.1 Overview of the analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2 Separation of neutron decay and 3 He(n, p)3 H reaction . . . . . . . . . . . . . 72
6.3 Background reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.3.1 Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.3.2 Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.4 Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.4.1 Corrections for the 3 He(n, p)3 H candidates . . . . . . . . . . . . . . . 82
iii

CONTENTS

6.5

6.4.2 Corrections for the neutron decay candidates . . . . . . . . . . . . . .
Summary of the number of signal events . . . . . . . . . . . . . . . . . . . .

86
90

7 Eﬃciency
92
7.1 Evaluation of signal eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2 Uncertainties of the cut parameters . . . . . . . . . . . . . . . . . . . . . . . 93
7.3 Uncertainties of cut eﬃciencies . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4 Summary of eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

IVConclusion

99

8 Conclusion and future prospects
99
8.1 Upgrade plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A Radiative neutron decay

104

B Beam structure105
B.1 RPMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
B.2 Measurement of the eﬃciency of RPMT . . . . . . . . . . . . . . . . . . . . 106
B.3 Measurement of the beam structure . . . . . . . . . . . . . . . . . . . . . . . 108
C γ ray spectrum of LiF tile109
C.1 Measurement of γ ray spectrum . . . . . . . . . . . . . . . . . . . . . . . . . 109
C.2 Reconstruction of the intensity of γ rays . . . . . . . . . . . . . . . . . . . . 110
D Mass spectrometry113
D.1 Noble gas analyzing system . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

iv

Part I
Neutron lifetime

Chapter 1
Introduction
1.1

Discovery of neutron

In 1932, the neutron is discovered by J. Chardwick [1]. The discovery leads to deeper
understanding of nuclear structure and neutron correlated parameters. So far, atomic nuclei
were considered as a composition of protons and electrons. In 1930, Walther Bothe andHerbert Becker reported the observation of non-ionizing radiation with strong penetrating
power. In Bothe’s experiment, 9 Be was exposed to α particles from polonium, resulted in
the following reaction.
9

Be +4 He →12 C + n

In the previous assumption, the observed electric neutral radiation was considered as a highenergy γ ray. However, the energy of the radiation was estimated to be about 50 MeV byCurie-Joliot and M. Joliot and by Webster, that was diﬃcult to account for the interactionof a beryllium nucleus and an α particle.

Figure 1.1: Illustration of experimental setup of Chadwick’s experiment [1].

1Chapter 1. Introduction

The contradictions were resolved by Chadwick. In Chadwick’s experiment, beryllium
was irradiated by α ray which were emitted from polonium source and mysterious neutral
radiations were generated (Fig. 1.1). By putting a target in the path of the radiations,charged particles were recoiled from the target. Then, charged particles were detected
via ionization in a gas chamber to reconstruct the velocity. The velocity reached at least
3 × 107 m/s, that could not be explained by γ rays while if the recoil particle is assumed as
the proton, it satisfies the conservation law.
The mass of mysterious radiation was also calculated by conducting the measurementswith several target materials. The estimated value was 1.0081 u and that was very close to
the proton mass. Combined with its penetrating power, the mysterious radiation must be
neutral and it was concluded as a new particle, the neutron.

1.2

Neutron lifetime physics

Some motivations arise to measure the neutron lifetime since it has important implications
in particle physics and in cosmology.
• Big Bang nucleosynthesis• CKM matrix unitarity• Solar burning
Dominant decay mode of neutron isn → p + e− + ν¯e + 782 keV.

(1.1)

Neutron decay relates to parameters such as the mass diﬀerence between neutron and

u

u

d
d

d

u
W

⌫¯e

e

Figure 1.2: Dominant decay mode of neutron.

2Chapter 1. Introduction

proton. They diﬀer only 1293 keV, result in about 15 minutes of long lifetime of neutron.
The energy of neutron is mainly shared with the electron and the antineutrino, where theend point of electron is 782 keV and the energy of proton is only 0.75 keV at maximum.
On the other hand, radiative beta decay and two-body decay are known as the otherdecay modes of the neutron [3, 15].
n → p + e− + ν¯e + γ
n → H o + ν¯e(BR ∼ 3 × 10−3 )(BR ∼ 4 × 10−6 )

(1.2)
(1.3)

They have little contribution to neutron lifetime measurements because of the small branching ratio. In this thesis, the uncertainty derived from these decay are not taken into consideration.

1.2.1

Probablity of neutron decay

As the neutrino is included into the theory, the neutron decay is explained by Enrico Fermi
in 1934. It successfully demonstrates the probability of transition and that is now referred
to as Fermi’s Golden Rule. The neutron lifetime is equal to the inverse of the probabilityof transition.
2π|Mif |2 ρfℏ
2π 2=g |⟨ψf |H|ψi ⟩|2 ρf ,ℏ

W = τn−1 =(1.4)

where W is the transition probability, Mif is matrix element for the interaction, g is strengthof coupling and ρf is density of final states. The final state wavefunctions are given as follows:{ψe (r) = √1V e−ipe ·r/ℏ,ψν (r) = √1V e−ipν ·r/ℏ
it is assumed that ψe (r = 0) = ψν (r = 0) = √1V . Then, Eq. (1.4) is modified withτn−1 =

2π g 2|Mif |2 ρf .
ℏ V2

(1.5)

To focus on the density states, it is proportional to the number of unit cells in phase space
occupied. We define dN as the number of ways that the total energy can be divided between
the electron and the neutrino.
dne dnνdpe dpν
(V )(V )= 4πp2e dpe 3 4πp2ν dpν 3 .
h
h

dN =

3

(1.6)
(1.7)

Chapter 1. Introduction

According to the conservation law,EνE0 − Ee=,cc
16π 2 V 2=
(E0 − Ee )2 p2e dpe ,h6 c 3

pν =
dN
dE0

(1.8)
(1.9)

where E0 is equal to the Q-value. By introducing Fermi function F (Zd , pe ) which is accountfor the nuclear coulomb interaction with the emitted particle, ρf is given as follows.
ρf

∫
V2
=
F (Zd , pe )(E0 − Ee )2 p2e dpe
4π 4 ℏ6 c3
m5e c4 V 2=
f (Zd , Q),
4π 4 ℏ6(1.10)

here d represents the daughter particle and f is called f function. Finally, Eq. (1.5) is combined with Eq. (1.10), we obtain the probability of transition expressed as the proportional
function of vector and axial-vector couplings, gV and gA .
m5e c4 2
g |Mif |2 f (Zd , Q)
2π 3 ℏ7
g 2 + 3gA2
= V
f (Zd , Q),Kτn−1 =(1.11)(1.12)

where K is equal to 2π 3 ℏ7 /m5e c4 . When radiative correction and nucleus independent correction are taken into account, one obtains,
gV2 (1 + ∆VR )(1 + 3λ2 )f (1 + δR ),K

τn−1 =(1.13)

where λ that is the ratio of gV to gA .
Correlation coeﬃcients
The neutron decay is related with some coeﬃcients appear in Eq. (1.14),{p⃗e · p⃗νp⃗ep⃗νp⃗e × p⃗ν }1+a+ σ⃗n · (A
+B
+D
) .
Ee Eν
Ee
Eν
Ee Eν

dW ∝ (gV2 + 3gA2 )F (Ee )• Electron-antineutrino asymmetry:a=

1 − |λ|2.
1 + 3|λ|24(1.14)

Chapter 1. Introduction• Spin-electron asymmetry:|λ|2 + |λ| cos ϕ.
1 + 3|λ|2

A = −2• Spin-antineutrino asymmetry:
B = −2|λ|2 − |λ| cos ϕ.
1 + 3|λ|2• Triple correlation:
D=2|λ| sin ϕ.
1 + 3|λ|2A
Electron

Neutron spin

B
Neutrino

ProtonFigure 1.3: Drawing of the neutron decay correlation coeﬃcients.

1.2.2

Big Bang nucleosynthesis

A motivation to improve the precision of the neutron lifetime is that it is one of important
input parameters for Big Bang nucleosynthesis (BBN). BBN theory describes the formationof light elements, and the uncertainty of the prediction is limited by the precision of neutron
5

Chapter 1. Introduction

lifetime. After 1 sec of the Big Ban, the universe expands and cools down. Depending on thetemperature variation, the thermodynamics condition which decides the ratio of the numberof neutrons to that of protons is changed. Because the reaction rates are expressed as thefunction of neutron abundance, the neutron lifetime determines primordial 4 He abundance.
The time after the Big Ban is roughly divided according to the temperature, as follows.
1. Thermal equilibrium (T > 1 MeV)
In the high temperature universe, the expansion rate superior to cooling, and following
thermal equilibrium are satisfied.
• p + e− ↔ n + ν• n + e+ ↔ p + ν• n ↔ p + e− + ν̄The n/p ratio is given as Boltzmann distribution.
n/p = e−∆m/kB T ,here ∆m is the mass diﬀerence between the neutron and the proton, kB is the Boltzmann constant and T is temperature. The n/p ratio is estimated to be 1/6.
2. Freeze-out (T ∼ 0.1 MeV)
The thermal equilibrium is no longer hold when the Hubble expansion rate exceed theweak reaction rate. The n/p ratio is fixed before the freeze-out and it is reduced to
1/7 due to neutron decay. The temperature of freeze-out TF depends on the neutron
lifetime, for example, if the neutron has longer lifetime, the freeze-out would occur at
higher temperature and it also aﬀects the equilibrium of the n/p ratio.
3. Nucleosynthesis (T < 0.1 MeV)As the number of photons are reduced, it allows to proceed the exothermic reactions
as below, then deutron and 4 He formations are started.
• p+n→d+γ• d + n → 3H + γ• 3 H + p → 4 He + γ• d + p → 3 He + γ• 3 He + n → 4 He + γ• d + d → 3 He + n• 3 He + d → 4 He + p• d + d → 3H + p• 3 H + d → 4 He + n• d + d → 4 He + γ
6Chapter 1. Introduction

1.2.3

CKM matrix unitarity

The Cabbibo-Kobayashi-Maskawa (CKM) matrix represents the coupling constant of weakinteraction that change one flavor of quark into another.
 ′   dVud Vus Vubd s′  =  Vcd Vcs Vcb   s (1.15)′bb
Vtd Vts Vtb
Previously, the CKM matrix unitarity have been tested by nuclear superallowed beta decays,
neutron decay and pion beta decay. Neutron decay have an advantage in the independenceof nuclear structure, while it has to be taken into account the contributions from not only
vector but also axial-vector. Since Vud and the weak coupling constant from purely leptonic
muon decay GF are connected with gV (= GF Vud ), Vud is derived from Eq. (1.13),
2
Vud
=

K
G2F (1 + ∆VR )(1 + 3λ2 )f (1 + δR )τn.

(1.16)The CKM unitarity can be tested by the conjunction of three matrix elements and theunitarity is established if the condition of Eq. (1.17) is satisfied.
2
2
Vud
+ Vus
+ Vub2 = 1(1.17)

Vus is obtained by the measurement of semi-leptonic kaon decays, while Vub has little contribution to the unitarity test because of its small value.
|Vus | = 0.2196 ± 0.0023|Vub | = 0.0036 ± 0.0010
Vud is responsible for the accuracy of the test, and therefore precise measurement of theneutron lifetime is important. However, currently uncertainty is governed by the precisionof ∆VR .
The results from three methods are shown in Tab. 1.1. The most precise value is given
by nuclear superallowed beta decays and it is consistent with the neutron decay method
despite of its large error. When the measurement of supperallowed beta decay is referred
to, the unitarity is not satisfied by 2.3 standard deviations. On the other hand, the neutron
decay method do not have enough precision to give the conclusion of unitarity. For thatreasons, improvement of uncertainties in both experiment and theory are needed.

7

Chapter 1. Introduction
Method|Vud |
Nuclear0.9740(5)Neutron decay 0.9745(16)Pion decay
0.9670(16)Σi Vui2
0.9968(14)0.9978(33)0.9833(311)|Vud|

Table 1.1: Reported values of Vud [14].

0.98

Bo
t
87 tle M
9.6
eth±
0.7 od:
se
c

0.978
0.976

Super allow decay

0.974
88

0.972

Be
am
8.0 Meth±o
2.0 d:
sec

Unitarity

0.97
Perkeo II 2012

0.968
0.966

0.964
1.264 1.266 1.268 1.27 1.272 1.274 1.276 1.278 1.28 1.282
λFigure 1.4: Vud vs. λ.

1.3Previous neutron lifetime experiments

The neutron lifetime is measured by the ratio of neutron flux to number of neutron decay.
In order to achieve precise measurement, key issues arise as following.
• High statistics of neutron.
• Precise measurement of the absolute neutron flux.
• Low background condition for counting the neutron decay.
There are two possible directions to count the neutron decay. One is called in-flight method,where neutron decay is identified by detecting the decay products. The in-flight method
have an advantage in statistics, but some diﬃculties arise in the measurement of beam fluxand identification of the decay products. The other is bottle method, the neutron lifetime is8Chapter 1. Introduction

measured by counting the remaining neutrons which have been stored in a bottle. Signal-tonoise ratio is much preferable in bottle method, while possibilities of non-beta decay losses
are pointed out.
We will introduce both methods in the following section, and our experiment is conceptually based on the in-flight method with a He-filled TPC proposed by ILL-ISL-LAPP
collaboration [6], that is also explained in the following.
MethodIn-flight
BottleFeaturesIssuesProton counting
Absolute flux
Electron counting
High background rate
Material bottle
Wall loss and energy spectrum of UCN
Magnetic trap
Complicated orbits and spin flips
Table 1.2: Methods and issues.

1.3.1

In-flight method

For the measurement of neutron lifetime, beam flux and neutron decay have to be evaluated.
The transition of neutron density is given by exponential expression.
N (t) = N (0) e−t/τn ,(1.18)

where N (t) is the number of neutron at a certain time t and τn is the neutron lifetime. The
number of neutron decay Nβ is calculated with beam flux ϕ and it is well approximated as
the function proportional to t/τn because τn is much longer than t.
Nβ ∼

ϕt
.
τn

(1.19)In the measurement of neutron flux, there are diﬃculties arise from its electric neutrality.
Generally, neutron flux is measured by detecting neutron capture reaction, for example,
3
He(n, p)3 H reaction is used for on-line counting.
Nn = ϕ e−ρσvn t ∼ ϕρσvn t,(1.20)

where Nn is number of 3 He(n, p)3 H reactions, ρ is 3 He density, σ is the capture cross section
and vn is the velocity of neutron. The cross section of 3 He(n, p)3 H reaction with the neutron
velocity at 2200 m/s is well known as 5333(7) barn [4]. Since the cross section of capture
reaction for slow neutron is proportional to the inverse neutron velocity, σvn is expected tobe constant value.
σvn = σ0 v0 = const.
9

Chapter 1. Introduction

Including the detection eﬃciencies ϵβ and ϵn , Nn is divided by Nβ to obtain the neutron
lifetime,τn =1 Nn /ϵn.
ρσ0 v0 Nβ /ϵβ(1.21)

Neutron capture reactions in 3 He and 10 B are widely used in on-line beam flux measurements, while Au and Co are applied for oﬀ-line measurements. Neutron decay measurements
have been performed by three kinds of approaches in the previous beam experiments. One
is to detect the decay electron and a serious problem arise from high background condition.
For the reduction of backgrounds, chopped neutron beam is generally used. The other ways
are detection of decay proton, and coincidence measurement of electrons and protons. In
these approaches, signal-to-noise ratio is much improved but there are uncertainties originated from separate measurement of beam flux and the neutron decay. In the following, we
will focus on two experiments, one detected the decay protons and the other measured theelectrons with a He-filled TPC.
Measurement by counting the trapped protons
Precise measurement with a quasi-Penning trap was performed by J. S. Nico et al. in 1980
at ILL reactor [18]. The cold neutrons were provided by the research reactor and the decay
protons were counted. The setup is shown in Fig. 1.5. There are three steps to detect the

Figure 1.5: Illustration of the quasi-Penning trap and Si detectors [18].

decay protons, trapping the protons, counting the protons, and cleaning the trap. Firstly,
potential well with depth of 0.8 keV was formed by 4.6 T magnetic field and 16 electrodes.
The maximum cyclotron radius of the proton was small enough for the confinement. Afterthe trapping time, decay protons were accelerated toward Si detector and collected. The
10

Chapter 1. Introduction

technique of detecting the proton is bit complicated due to low energy of protons whichhave end point of 0.75 keV, so that acceleration is needed to increase the energy.
The backgrounds condition is favorable to count the neutron decay, however the precisionof the measurement was limited by the evaluation of neutron flux. Neutrons were counted
by using a target which is surrounded by four Si semiconductor detectors. The reaction
products of 6 Li(n, α)3 H were detected and flux was calculated based on the 1/v law. As theresult, the neutron lifetime was presented as τn = 886.6 ± 1.2 (stat.) ± 3.2 (syst.) sec. The
systematics errors includes ones derived from neutron counting, beam halo, proton trapping
and proton counting. Ones of the most responsible are areal density of 6 LiF deposit andthe capture cross section of 6 Li(n, α)3 H.
Electron counting measurement with a He-filled TPC
The electron counting experiment was performed by ILL-ISN-LAPP collaboration, which
proposed the neutron lifetime measurement with He-filled time projection chamber (TPC)[6]. Characteristic approach in this experiment is that beam flux and neutron decay were
measured in the same volume of detector simultaneously.
The experiment was carried out at the research reactor at ILL (H14-PN7) and the setup
is illustrated in Fig. 1.6. In the upstream, monochromatic neutron packets were formed bychopper drum and they were delivered to TPC that contained small amount of 3 He. Beam

Figure 1.6: Experimental setup of the neutron lifetime experiment by ILL-ISL-LAPP collaboration [6].
flux was determined by counting 3 He(n, p)3 H reaction. The measured neutron velocity was
11Chapter 1. Introduction

837 m/s, that the probability of neutron decay in flight length of 70 cm correspond to orderof 10−6 . The intensity was 2000 neutrons per packet of 20 cm length and 4 cm2 cross section.
Long track of ionized particles were generated by the decay electrons and the ionized particles
drift toward multi wire proportional chamber which enable to detect in a 4π geometry.
The final result is τn = 878 ± 27 (stat.) ± 14 (syst.) sec. Statistical error dominates theuncertainty because of the shortage of beam time. As for the systematical errors, thesignificant backgrounds were derived from neutron scattering followed by capture reactions.
Although chamber was coated with 6 LiF, further suppression of γ rays was necessary. It wasalso pointed out that major part of backgrounds were originated from point-like ionization
events that limited the eﬃciency of neutron decay. Possible sources of the backgrounds
would be the neutron capture reaction in CO2 gas and the decay electron from 3 H that
could be provided by 6 Li(n, α)3 H and 3 He(n, p)3 H.

1.3.2

Bottle method

The other concept of the neutron lifetime measurement is to obtain the exponential decay
curve. In the bottle method, techniques to store ultra cold neutron (UCN) in a bottle havebeen developed and the surviving neutrons are counted. Equation (1.18) can be expressed
as following.
τn−1 =ln (N (t1 )/N (t2 )),t2 − t1(1.22)

where N (t) is the number of neutrons in the bottle at a storage time t (t1 < t2 ). There isno need for worry about the eﬃciency of neutron detector and the neutron loss rate duringtransportation, because the lifetime in Eq. (1.22) concern only the ratio of the number ofneutrons. Besides, recent improvements of storage techniques are remarkable and statistical
disadvantage have being overcome.
Important systematical uncertainties are caused by losses of neutrons which are notrelated to the decay. The measured neutron lifetime τm is given by−1−1τm= τn + Σ τloss.

(1.23)

Therefore, the precision of measurement is determined by the treatment of undesired losses.
Measurement using gravitationally trapped UCN
The most precise neutron lifetime measurement was performed by PNPI group at ILL in
Grenoble, France [20]. The distinguishing features of the experiment are that the UCN isgravitationally trapped and the energy spectrum of UCN is measurable. The measurement
proceeds as follows. The first process is to fill the UCN into the trap which is illustrated
with dashed line in Fig. 1.7. In the filling process, the trap window was set at the down
12

Chapter 1. Introduction

position and UCN is guided from inlet valve (2). During the storage time, trap window
was positioned to up, and then rotated to the UCN detector (12) in the counting process.
Since the maximum energy of storable UCN is determined by the height of the trap window
respect to the bottom of the trap, it can work as a spectrometer.

Figure 1.7: Schematic view of the gravitational UCN storage system [20]. 1: input neutron
guide, 2: inlet valve, 3: selector valve, 4: aluminum foil, 5: “dirty” vacuum volume, 6:“clean” vacuum volume, 7: cooling coils for the thermal shields, 8: UCN storage trap,
9: cryostat, 10: mechanics for trap rotation, 11: stepping motor, 12: UCN detector, 13:detector shield, and 14: vaporizer.
A problem concerning the uncertainty in the bottle method is neutron losses caused byinteractions of wall. In order to achieve an ideally homogeneous surface, the trap surface wascoated with a material named perfluoropolyether (PFPE), which is also known as fomblin
oil. Because it contains only carbon, oxygen and fluorine, the probability of neutron capture
is lowered. PFPE was deposited on the surface by evaporation in vacuum and the uncovered
part of the surface was less than 10−6 . On the other hand, studies reported that unexpected
neutron loss due to quasi-elastic scattering emerged. When neutrons were scattered by thewall, neutrons were escaped from the trap according to the momentum transfer. And also it
was investigated that the neutron losses were insignificant under -120 ◦ C and the experiment
was performed at -160 ◦ C.
The result of the measurement is τn = 878.5 ± 0.7 (stat.) ± 0.3 (syst.) sec. Still statisticalerror dominates the uncertainty of the measurement, while the probability of neutron losses
from the trap accounted for only 1 % of the probability of neutron decay. In detail, the13Chapter 1. Introduction

largest systematical error was derived from the calculation of eﬀective frequency of collision
which depends on the size of the trap and the energy of UCN. Next one was the shape ofthe function responsible for the UCN losses from reflection, and small uncertainty was givenby the energy spectrum of UCN.
Experiments using magnetic storage ring
The lifetime measurement with NEutron STOrage Ring (NESTOR) was performed again
at ILL reactor [21, 22]. A strong point of the measurement is that since neutrons wereconfined by magnetic barriers, they were free from wall loss. If the magnetic field B holdthe following condition, neutrons are harmonically confined in a sextupole.
U = −µn · B ∝ r2 ,(1.24)∂B= cr,
F = −∇U = µn(1.25)∂r
where U is potential of magnetic field, F is the corresponding force and µn is the magnetic
moment of the neutron. The setup and magnetic field are illustrated in Figs. 1.8 and 1.9.

Figure 1.8: Schematic view of the magnetic
sextupole trap [22].
Figure 1.9: Cross section of an ideal sextupole[22]. Dashed line: magnetic field, dotted line:
equal magnetic potential.
In this method, we should take the eﬀect of the Lamor precession into consideration
because there is a possibility of neutron loss arise from the change of the magnetic moment
orientation respect to the magnetic field. The problem would be avoided if the frequency ofmagnetic field ωB is small enough compared to the Lamor frequency ωL .
ωL = −

|Ḃ|
2µn B
>>
= ωB
ℏ
B
14

(1.26)

Chapter 1. Introduction
The obtained neutron lifetime is τn = 876.7 ± 10 sec. Because of the possible neutron
loss due to dynamics, an exponential fit was applied except the beginning of storage. The
main component of error comes from low statistics.

1.3.3

Reported values of the neutron lifetime

As it is detailed in the previous sections, the neutron lifetime have been measured with two
methods. The individual neutron lifetime values are shown in Fig. 1.10 and the averaged
values are
In-flight method : τn = 888.0 ± 2.0 sec
Bottle method : τn = 879.6 ± 0.7 sec
7 values in the Fig. 1.10 are averaged and one obtains [5],PDG2017 : τn = 880.2 ± 1.0 sec
The results within each method showing good agreement but diﬀer between in-flight method
and bottle method. Therefore, there have been recent interest in improving the uncertainty
on the neutron lifetime to below 0.1 %. The main sources of systematical uncertainties
in in-flight method are derived from the measurement of beam flux and high backgroundcondition. While unexpected neutron losses are severe problem in bottle method. The
measurement reached closer to the lifetime was carried out with gravitational trap andincreasing number of measurements with gravitational trap and magnetic trap have been
performed.

15nτ [sec]Chapter 1. Introduction

894
892
890
888
886
884
882
880
878
876
1990

1995

2000

2005

2010

2015
[year]

Figure 1.10: Previous results of the neutron lifetime measured by in-flight method (red) andby bottle method (blue) [23–29].

16

Part IINOP experimentChapter 2
Neutron lifetime measurement at
J-PARCIn this thesis, we report the neutron lifetime with accelerator based intense neutron beam at
Japan Proton Accelerator Research Complex (J-PARC). We approach precise measurementwith statistical advantage and the achievement of low background condition.
First, the experimental setup is described in chapter 2 and 3. The performance ofneutron beam is descried in this chapter, and the construction of TPC and optical devices
are explained in chapter 3.
In chapter 4, we focus on important neutron interactions, and categorize signals andbackgrounds. The development of Monte Carlo (MC) simulation is described in chapter 5.
Then, analytic approach is detailed in chapter 6 and 7. These are the main topics inthis thesis. Engineering data was taken in 2014 and 2015 (series 1, 2), and we confirmed
the performance of apparatuses and established the method of analysis. Our first physics
data have been taken in 2016 (series 3∼6). In total, we have 6 series of measurements witha new gas mixture for each measurement. The evaluation of the number of signal eventsare described in chapter 6, and eﬃciency of measurement are given in chapter 7. Finally,
conclusions are given in chapter 8.

2.1

J-PARCAt J-PARC, a series of three accelerators provide world-class high energy proton beam tothe experimental facilities (Fig. 2.1). A proton beam is accelerated by a 400 MeV linear
accelerator (LINAC), a 3 GeV rapid cycling synchrotron (RCS) and a main ring (MR)which currently running at 30 GeV. The proton beam is extracted from MR and deliver to amercury target at Materials and Life Science Experimental Facility (MLF). As the result of
spallation reaction, high intensity pulsed neutron beam is produced with a repetition rateof 25 Hz.
17

Chapter 2. Neutron lifetime measurement at J-PARC

Figure 2.1: Bird’s eye view of J-PARC [30].

Moderator
The neutrons are decelerated to cold region by a coupled hydrogen moderator and delivered
to BL05, “Neutron Optics and Physics (NOP)” beamline. The coupled moderator havestrong point in neutron flux, while time structure is broader than ones provided by a decoupled moderator. The neutron velocity is in the range between 500 m/s to 1200 m/s witha maxwellian distribution.
Time-integrated thermal neutron flux [n/s·cm2 ]Peak neutron flux at 10 meV [n/eV·s·cm2 ]Pulse width in FWHM at 10 meV [ s]µ

4.6 × 108
6.0 × 1012
92

Table 2.1: Performance of neutron beam at 10 m from the coupled moderator at the 1 MW
operation [30].

18Chapter 2. Neutron lifetime measurement at J-PARC

Figure 2.2: Neutron instruments at MLF [30].

19Chapter 2. Neutron lifetime measurement at J-PARC

2.2

NOP beamline

Figure 2.3 is the picture of NOP beamline. Supermirror guides and benders are aligned in 7.2∼ 12.0 m downstream of the exit of moderator and neutrons with diﬀerent spin polarizationand velocity are divided into three branches, the polarized beam branch, the unpolarized
beam branch, the low-divergence beam branch (Figs. 2.4 and 2.5). Each beam branch
is used according to the experimental requirement. The neutron lifetime experiment iscarried out at the polarized beam branch. On the other hand, the experiments approachingfundamental physics of slow neutron such as electric dipole moment and T-violation are
conducted at the other beam branches. Also, a doppler shifter for UCN production isdeveloped.
A beam shutter which is made of 2 m thick iron is in 2.5 ∼ 4.5 m downstream of themoderator. When the beam shutter is closed, neutron beam is completely shut out. At
usual operation, beam shutter is open during the data acquisition while the passage ofneutron into detector is controlled by LiF shutter as described in Sec. 3.3. The beam
performance at the 1 MW operation is shown in Tab. 2.2.

Figure 2.3: BL05 NOP beamline.

20Chapter 2. Neutron lifetime measurement at J-PARC

Figure 2.4: Overview of the NOP beamline [31].

Figure 2.5: Illustration of the beam branches. (A) entrance of the beam benders, (B) exitof the polarized beam branch, (C) exit of the unpolarized beam branch, and (D) exit of the
low-divergence beam branch.

21

Chapter 2. Neutron lifetime measurement at J-PARC

Polarized beam branch
Polarized neutron beam is produced by using mirrors whose reflectivity depend on theneutron spin. Then, the polarized neutron beam is delivered to the experimental setup of
the lifetime measurement. We have achieved the polarization eﬃciency of 96 % [33].
Unpolarized beam branchThis beam branch provide most intense neutron beam and is adopted for an experimentsearch for unknown medium range force, but it is currently used for the development of
doppler shifter.
Low-divergence beam branch
An experiment for neutron interferometer is assigned to this beam branch. There is aninterest in gravitational phase shift and Ahoronov-Casher eﬀect. Successive performanceof multilayer interferometer with spatially separated paths for the steady beam have been
demonstrated [34].

Cross section [mm2 ]Neutron intensity [n/s·cm2 ]Beam divergence [ str]µ

Polarized beam Unpolarized beam
80 × 50
55 × 457
3.9 × 10
9.4 × 107
1.9 × 102
1.0 × 102

Low-divergence beam
80 × 20
5.4 × 104
5.4 × 10−2

Table 2.2: Beam performance at 16 m position (see Fig. 2.4) at the 1 MW operation [30].

22Chapter 3
Experimental setup
Low background condition have been achieved by employing low radiative material for TPC
and also large contribution from the development of spin flip chopper (SFC). The detail of
our experimental setup including the formation of bunched neutron, TPC and trigger system
are described in this chapter. The comparison of key features between NOP experiment andthe experiment described in [6] is summarized in the end.

3.1

Overview of the setup

The overview of the setup is shown in Fig. 3.1. In the polarized beam branch, neutron beampass through SFC to form neutron bunches. By making the time structure of neutron intensity, prompt γ rays are eﬀectively discriminated. Then, bunched neutrons are transported to
TPC which have been originally developed to suppress (n, γ) reactions. TPC is surroundedby lead shields and veto scintillators are installed outside of the lead shield. Further, theoutermost is covered with iron shields in order to prevent environmental backgrounds.

3.2

Spin flip chopper

The polarized neutrons are delivered to SFC which consist of two radio frequency flipper
coils and three magnetic supper mirrors. A single unit of SFC consist of a coil and two
mirrors, and two sets of SFCs are used to provide outstanding performance. The spin ofneutron is flipped by the flipper coils, and then neutrons are selectively reflected by the
mirrors depends on the polarization. By the combination of coils and mirrors, neutrons are
guided to TPC or beam dump and the time structure of neutron intensity is constructed.

23

Chapter 3. Experimental setup

(1)

BL06

(2)

(3) (4) (5)

(6)

(7)

Shield of BL06

BL05(a) (b) (c)

(d)

(e)

Spin Flip
Chopper(B) (C)

(A)
(X)

(Y)

TPC

(D)

x
z

(Z)

Shield of

1m

BL04

BL04

Figure 3.1: Overview of SFC and TPC. (X) polarized beam branch, (Y) unpolarized beam
branch, and (Z) low-divergence beam branch. (a) short-pass wavelength neutron filter, (b)a guid coil, (c) first and second RFF coils, (d) magnetic supper mirrors, and (e) a neutron
beam monitor. (A) beam dump, (B) lead shields, (C) iron shields, and (D) LiF beamcollimators. (1) a Zr foil, (2) a LiF shutter, (3) cosmic veto counters, (4) lead shields, (5) avacuum chamber, (6) a TPC, (7) a LiF beam catcher, and (8) a turbo molecular pump.

2350

(C)

(B)

(D)

(E)

40

20

0

340

(A)

(H)

(F)
(G)

Figure 3.2: Illustration of SFC, viewed in xz plane. Polarized neutron is provided from theleft side. (A) first RFF coil, (B) first and second mirrors, (C) a LiF shutter, (D) second
RFF coil, (E) third mirror, (F) a guide coil, (G) boron gum, and (H) lead shields.

24Chapter 3. Experimental setup

3.2.1

Radio frequency flipper coil

The radio frequency flipper (RFF) coil is nuclear magnetic resonance device which includes
a solenoid coil and a guide coil (Fig. 3.3). The spin of neutron is rotated on the basis of
Larmor precession. When the external magnetic field is applied perpendicular to the spinof neutron, a torque is exerted on the spin angular momentum. The flipping probability, P
is given by Eq. (3.1).
√
(
)
2
Bxz
ℏω
2 |µn |l2 + (B −
sin
)2 ,
P = 2
Bxz
(3.1)
y
ℏω 2
ℏv
2|µ
|
)
Bxz + (By − 2|µnn|where Bxz and By are the magnitude of the magnetic field applied by the solenoid coil andthe guide coil, respectively. µn denotes the magnetic momentum of the neutron, ω is thefrequency of the oscillation of Bxz , l is the length of RFF and v is the neutron velocity. The
magnitude of the magnetic field applied by the guid coil is 1 mT.
When a current is supplied to RFF, the solenoid coil makes oscillating magnetic filed. If
Bxz and ω satisfy the following conditions, P takes the maximum value.
By =ℏω
2|µn ||µn |Bxz l
1= (n + π),
ℏv
2

(3.2)
(3.3)

here n is positive integers. By turning the current on and oﬀ, the length of the bunch isadjusted to be about a half the length of TPC. The specification of RFF is given in Tab.
3.1.

Figure 3.3: Radio frequency flipper coil.

25

Chapter 3. Experimental setup
Diameter [mm]Length [mm]Frequency of the magnetic field [kHz]Magnitude of the magnetic field [mT]

50
40
29
0.3

Table 3.1: Specifications of the solenoid coil.

3.2.2

Magnetic supper mirror

The magnetic supper mirror have two kinds of layers, one consist of ferromagnetic material
and another is made of non-magnetic material. The mirrors are placed in the magnetic
field which is strong enough to magnetize the ferromagnetic material. In the slow neutron
physics, neutron have wave properties and it can be reflected by making use of Bragg’s law.
2dn sin θ = mλ,(3.4)

where dn is the thickness of nth layer, θ is the incident angle, λ is the wavelength of theneutron and m is positive integers. As it is indicated in Eq. (3.4), the reflectivity depends on
the thickness of layers. It means that neutrons with continuous distribution of wavelength
can be reflected by changing the thickness gradually (Fig. 3.4).
Spin parallel

B

Spin antiparallel
1 = 2d1 sin ✓2 = 2d2 sin ✓3 = 2d3 sin ✓✓Ferromagneticd1

Non-magnetic

d2

d3

x
z

Figure 3.4: Basis of Bragg diﬀraction. The magnetic supper mirror is viewed in xz plane andthe magnetic field is applied vertical to the paper surface. The neutron with spin parallel tothe magnetic field (red) is reflected, while one with spin antiparallel (blue) penetrates themirror.

26

Chapter 3. Experimental setup

Further, the reflectivity also depends on the neutron spin. Here we define the neutron
with spin parallel (antiparallel) to the magnetic field as n∥ (n⊥ ). The magnetic potential ofneutron is written as following.
{
Vnucl + |µn |B (n∥ )Vmag =(3.5),
Vnucl − |µn |B (n⊥ )where Vmag represents the magnetic potential, Vnucl is the nuclear potential, µn is the magnetic momentum of neutron and B is the magnitude of the magnetic field. While n∥ isreflected toward TPC because it satisfies the Bragg condition, n⊥ just go through the mirrors. Note that the neutron beam is inclined from the direction of the exit of SFC and thatprevents γ rays to be detected. The specification of mirror is summarized in Tab. 3.2.

Figure 3.5: Magnetic supper mirror. A case is surrounded by magnets and five mirrors arealigned inside.

Ferromagnetic material
Non-magnetic material
Thickness of layers [nm]m-value
Mirror size [mm3 ]Number of mirrors
Magnetic field [mT]

Fe
SiGe3
1.9 ∼ 605
140 × 35 × 0.7
535

Table 3.2: Specification of the magnetic super mirror.
Figure 3.6 shows the performance of SFC. The neutron intensity diﬀerence is defined as
the signal-to-noise ratio of SFC and we have achieved the signal-to-noise ratio to be about27

Chapter 3. Experimental setup
400. At 300 kW operation, we obtained 2.9 × 107 neutron/sec at the exit of the polarized
beam branch. When neutron beam is formed into five bunches with a length of 40 cm, beam
flux was measured to be 1.7 × 105 neutron/sec inside TPC.

Figure 3.6: Neutron flux measured by TPC vs. TOF. The ratio of flux measured with SFC
switched on and oﬀ is 1 to 400.

3.3

Beam entrance

The passage of neutron from the exit of SFC to the beam entrance of vacuum vessel is
described in this section. Beam flux is monitored at the exit of SFC as it is shown in Fig.
3.1 (e). The beam monitor is used to compensate the fluctuation of beam flux and thathave to be measured with an accuracy of 0.1 %. The beam monitor contains small amountof 3 He gas and is operated on the basis of proportional counter (Fig. 3.7). The gas gain
have dependence on the high voltage, the temperature, beam flux and detection eﬃciency.
The details were studied in [32] and an important problem was pointed out that there are
more than 10 % of position dependence on detection eﬃciency. To avoid ambiguities inneutron flux measurement, the monitor is fixed to the incident neutron beam during thedata acquisition. While the fluctuation derived from other factors were measured to besmall enough and required stability of measurement is satisfied. The specification of thebeam monitor is shown in Tab. 3.3.

28

Chapter 3. Experimental setup
Material
Active volume [mm3 ]Gas mixture
Thermal neutron detection eﬃciency

A5 aluminum
100 × 42 × 40
Ar (1.3 bar) + CH4 (10 %) + 3 He
∼ 4 × 10−5

Table 3.3: Specification of beam monitor manufactured by Canberra Industries Inc. [32]µNeutrons enter to the vacuum chamber from a 50 m thick Zr foil. Zr is adopted as
entrance window because of the high mechanical strength and low neutron capture crosssection. The passage to TPC is controlled by operating LiF shutter which consist of a LiF
tile and stepping motor (Fig. 3.8). Two kinds of data, “Beam ON” and “Beam OFF”, wastaken by changing the shutter position and that is detailed in chapter 6. Note that when
LiF shutter is closed, SFC is still irradiated and γ rays are continuously detected by TPC.

Figure 3.7:
Neutron beam monitor
MNH10/4.2F, product by Canberra Indus- Figure 3.8: LiF shutter on the stepping motor.
tries Inc.

3.4

Time projection chamber

In order to measure the neutron lifetime with high precision, it is very important to reduce
the source of backgrounds, especially γ rays. The material of TPC was selected with greatcare, and also the materials placed inside of the vacuum vessel are selected to prevent
radioactive contamination. The schematic view of TPC is shown in Figs. 3.9 and 3.10. The
vacuum vessel contains drift cage, LiF tiles, MWPC and calibration source.
29

Chapter 3. Experimental setup

Figure 3.9: Schematic view of TPC in yz plane.

MWPC plane

5.9 keV X-ray

Preamplifiers

55

Fe source& collimator

Rotation stage

Signal readout
Beam entrance / exit

Drift

6

Resistor chain

Li tilesAluminized PET film

Drift HVy

Drift wires

x

50cm

Figure 3.10: Schematic view of TPC in xy plane, viewed from downstream [36].

30Chapter 3. Experimental setup

3.4.1

Drift cage

The schematic view of drift cage is shown in Fig. 3.11. We had five candidates for the TPC
material as below [44].

Cathode wires (top)Sense/field wires
Cathode wires (bottom)

6

Li tilesBeam catcher

eDriftdirection

Drift wires

Neutron beam bunch
Beam axis
Drift cathodeFigure 3.11: Schematic view of the drift cage [36].

• G10• Poly ethel ethel ketone (PEEK)• Poly phenylene sulfide (PPS)• Phenol formaldehyde resin (PF)• Alumina
Generally, G10 is used as a gas detector material. It is made of continuous glass woven
fabric base impregnated with an epoxy resin binder. The radioisotope contamination havebeen tested by making a trial production and γ ray spectrum was measured by using agermanium detector. As the result, it was found that G10 includes the Uranium-Thorium
series radioisotopes. Although G10 was removed from the candidates, significant isotope
peak was not detected from PEEK. The γ ray spectra are shown in Fig. 3.12 and note thatbackgrounds were already subtracted.
31

Chapter 3. Experimental setup

Figure 3.12: γ ray spectra of G10 (left) and PEEK (right), normalized by the measurement
time and size of the samples [44].
PEEK is the product of a thermoplastic resin by Yasojima Proceed Co. Ltd. There arelittle possibility of radioactive contamination in the manufacturing process because the main
components of PEEK are carbon, hydrogen and oxygen. Followings are the characteristics
of PEEK whose product name is called PEEK450G [50]. As it satisfies our demand forconstruction and low background level, PEEK was selected as the material for our TPC.
This is the first attempt to use PEEK as the material for a gas chamber.
• Low level of radioactivity• Low outgassing and metal ion elution• Machinable, weldable and bendable• Mechanical strength for wire tension• High insulation capacity• Heat tolerance for soldering
LiF tiles
LiF tiles are fitted into the drift cage from inside and also they are used for beam catcher
and shutter. The LiF tile is made by baking the 6 Li-enriched LiF powder (2.6 g/cm3 ) with
polytetrafluoroethylene (PTFE, 2.2 g/cm3 ) at weight ratio of 3:7. The specification of the
LiF tile is indicated in Tabs. 3.5 and 3.6. Each tile is covered with 100 m thick PTFE
sheets to absorb the α ray emitted from 6 Li(n, α)3 H reaction. Since LiF tiles are installed tothe place visible from the inside of TPC, neutrons scattered only once or less will certainly
hit the LiF tiles (Fig. 3.14). The neutron absorption length of the LiF tile is about 0.5 mm
and 99.95 % of neutrons are absorbed in 5 mm thick LiF tile.

µ32

Chapter 3. Experimental setup
G10 PEEK
Density [g/cc]
1.8
1.3
Bending elastic modulus [GPa] 20
3.6
Melt point [◦ C]
334
Water absorbing ratio [%]
0.10
0.14
11
Volume resistance [Ω·m]101014
Cost [1000JPY/kg]
3.3
45

PPS
1.4
3.9
278
0.04
1014
8

PF
1.4
0.15
130
0.3
1012
5

Alumina
3.9
350
1500
0
1015
100

Table 3.4: Physical properties of the materials [50].

Figure 3.13: LiF tile.

Figure 3.14: Inside of TPC viewed from upstream.

Size [mm3 ]300 × 300 × 5
3Density [g/cm ]2.3
Relative permittivity
3.0
Table 3.5: Specification of the LiF tile.

33

Chapter 3. Experimental setup
Mole fraction [%]
Li
17.3
7
Li
0.9
C
21.2
F
60.6

6

Table 3.6: Mole fraction of the LiF tile.

3.4.2

Multi wire proportional chamber

In this section, the properties of multi wire proportional chamber (MWPC) includes wires
and preamplifiers are detailed.
Wires
There are four kinds of wires aligned in three xz planes with diﬀerent y positions. As it isshown in Fig. 3.15, anode wires and field wires are arranged in parallel with the z axis andalternately aligned in the same xz plane. In the upward and downward of anode wires, there
are cathode wires arranged in the x direction. While anode wires and downward cathodewires are connected to high gain preamplifiers, field wires and upward cathode wires areoperated with low gain preamplifiers as it is described in the next section.
There are 28 anode wires and 27 field wires, but only 24 wires of each in the central
region are read out. Four consecutive cathode wires are connected to single readout channel
and there are 40 channels in each cathode plane. Totally, 128 channels are read out andrecored as waveforms. The properties of wires are summarized in Tab. 3.7. One of theimportant diﬀerence between [6] and our experiment is that field wires are read out in oursystem. High voltage (1720 V) is applied to anode wires, while field wires with 0 V are
supportive of the electric field to prevent distortion.

Number of wires
Number of channels
Pitch [mm]Diameter [ m]Material
Preamplifier

µ

Anode
28
24
12
20
W-Au
High gain

Field
Cathode high
27
160
24
40
12
6
50
50
Be-Cu
Be-Cu
Low gainHigh gain

Table 3.7: Properties of wires

34

Cathode low
160
40
6
50
Be-Cu
Low gainChapter 3. Experimental setup

6mm

z

6mm

Anode
Field
CathodexyCathode low

Cathode high

6mm
6mm

x

Figure 3.15: Wire geometry of MWPC.
1

Preamplifiers
The charge pulses from wires are integrated by preamplifiers and converted into a voltage.
Figure 3.17 shows the circuit diagram of preamplifier. By adjusting the resistance of R0 andR1, it is possible to operate the preamplifier with diﬀerent gain. In the low gain operation,
R0 and R1 are set to 300 Ω and 1 kΩ, and about a quarter of the original charge is amplified.
On the other hand, R0 and R1 are set to 0 Ω in the high gain operation so as to amplify
total amount of the original charge.
In the design of preamplifier, high gain and low gain diﬀer by a factor of approximately 4.
However, it is found that the diﬀerence of gain was 5.5 in the measurement. That is because
the operational amplifier in the circuit was operated without satisfying the condition ofvirtual grounding, due to insuﬃcient resistance of R0.

35

Chapter 3. Experimental setup

Figure 3.16: Preamplifier.

Figure 3.17: Circuit diagram of the preamplifier.

Electric field
The ionized particles drift toward MWPC in the applied electric field. In the region ofincreasingly high electric field, multiplication starts and charges are collected by anodewires. The electric field is formed as following. At the bottom of TPC, LiF tiles are covered
with 12 m thick aluminized PET film which is applied -9000 V, while MWPC plane isconnected to the ground. As shown in Fig. 3.11, drift wires are coiled around the corners ofdrift cage, that help to make uniform field. Another PET film covers the top of TPC thatthe electric field prevents to trigger cosmic rays generated in the upward of TPC. Besides,
it works to avoid charge up.

µ

Figure 3.18: Electric field of the drift region
Figure 3.19: Electric field around the anodein xy plane, viewed from upstream.
wires.
36

Chapter 3. Experimental setup

Figure 3.19 shows the electric field calculated by using Garfield, under the condition of
100 kPa and 300 V/cm. In designing, the position dependence of electric field was estimatedto be less than 1 %. However, we observed that the drift velocity depends on the position iny direction. A possible reason of the electric field distortion is dielectric material containedin PEEK and LiF tile. The measured relative permittivity of PEEK and LiF tile resultin 3.2 and 3.0, respectively. The non-uniformity of the electric field is estimated to be notmore than 10 % and that is explained in Sec. 7.2.

3.5

Chamber gas

In general, argon and isobutane are widely used as the fill gas of a MWPC because of its
high gain and lower cost. For the requirement of our experiment, the fill gas should have
low neutron scattering cross section. Therefore argon and hydrogen were removed from thecandidates and we employed a mixture of 4 He 85 % + CO2 15 %. 4 He have a low neutron
scattering cross section of 1.34 barn and do not absorb neutron. Although the quenchinggas, CO2 , have about 4 times larger neutron scattering cross section, this is comparatively
low probability of scattering. The components of commercial product of 4 He gas named
G1He, and that of CO2 gas named G1CO2 are summarized in Tabs. 3.8 and 3.9. According
to the mass spectrometry, about 0.1 ppm of 3 He is contained in the 4 He gas and that will
be corrected in the evaluation of number density of 3 He (see appendix D).
Component Quality standard
He [%]
99.9995
O2 [ppm]< 0.5
N2 [ppm]< 5
CO [ppm]< 0.5
CO2 [ppm]< 0.5
THC [ppm]< 0.5
Table 3.8: Component of 4 He gas, commercial product by Tomoe shokai Co., Ltd.
Component
Purity [vol. %]Moisture [vol. %]Sulfide [wt. ppm]
Carbonhydrate [vol. ppm]
H2 , N2 , O2 , Ar [vol. %]Quality standard> 99.9990< 0.0010< 0.03< 1< 0.0010

Table 3.9: Component of CO2 gas, commercial product by Tomoe shokai Co., Ltd.

37

Chapter 3. Experimental setup

3.5.1

Measurement of 3 He density

We introduce about 1 ppm of 3 He gas into TPC by making use of thermometers and threekinds of pressure gauges with diﬀerent measurable range (Tab. 3.10). Because 3 He density
is very small and such a small pressure can not be measured directory, the gas mixture is
introduced by a slightly elaborate procedure as described below.
To prevent the possibility of biasing in the evaluation of signal events, we employ blind
analysis and 3 He density is disclosed after these analysis have been fixed.
Pressure gauge
A
B
C

Full scale [kPa] Accuracy [%]
120.
0.01
35.
0.01
1.333
0.05

Table 3.10: Specification of pressure gauges.

Basis of the measurement
Number density of 3 He is measured by introducing the gas into vessels with diﬀerent volume
V1 and V2 . Assume that V1 is small and V2 as TPC, and they are connected by a valve (Fig.
3.20). Firstly, 3 He is introduced into V1 with high pressure and we measure the pressure P1
and temperature T1 . Equation (3.6) is obtained on the basis on ideal gas law:P1 V1 = nRT1 .

(3.6)

P1 can be measured precisely since the precision of pressure gauge is proportional to thepressure. Subsequently, the valve is opened to diﬀuse the gas into V2 , then pressure P2 andtemperature T2 are measured. 3 He density ρ is calculated as following.
P2 (V1 + V2 ) = nRT2 ,
P1
V1
ρ=
,
RT1 V1 + V2

(3.7)
(3.8)

where n is the amount of 3 He and R is the gas constant. Thus, ρ is derived from threeparameters, P1 , T1 , and ratio of V1 and V2 . The volume ratio have been measured ahead of
the neutron lifetime measurement.

38

Chapter 3. Experimental setup

Pressuregauge

V1

Pressuregauge

V2

Figure 3.20: Basis of gas introduction.
expanded to larger volume (V2 ).

Release3

V1

V2

He gas is introduced to small volume (V1 ) and1

Procedure of gas introduction

In the procedure of gas introduction, 3 He is introduced at first and then 4 He and CO2 follows.
Figure 3.21 shows the gas introduction system, where pipes and valves are indicated with “I”
and “V”. Pipes are connected with each other and hermetically sealed by valves. Pressuregauges A and B are connected with V8 and, gauge C is connected with V5 . 3 He gas is
introduced from I6 and diluted by diﬀusing many times as below.
1. I6 → I6 + I5
2. I6 + I5 → I5
3. I5 → I5 + I4 + I1 + Im
4. I5 + I4 + I1 + Im → Im
5. Im → Im + I1 + I7 + I8 + ITPC
Series
1
2
3
4
5
6

4

He [×1025 atom/m3 ] CO2 [×1024 atom/m3 ]2.0124(7)3.55(2)
1.9880(7)3.50(2)2.0292(7)3.59(2)2.0137(7)3.56(2)2.0106(7)3.53(2)2.0009(7)3.50(2)

3

He [×1019 atom/m3 ]2.24(1)
1.867(5)2.127(7)3.96(1)
0.993(4)2.089(7)Table 3.11: Number density of injected gases.

39

Chapter 3. Experimental setup

Baratron627B
Baratron690A
Mensor
CPG2500

22L
BufferBottleSampling
Bottle
I7
V1

Msample4

He gasV2

CO2 gas
V6

V5

V3

V7

I1

M4

M5
V8

V2

TPC
VTPC

I8

I5
3
He
I6 Buffer
Bottle

I2

V9

ITPC

I4
1300.0

Im

M6
M3
V10

M7

TMP
I3

Swagelok
V# 3/8' valve "SS-6BG-TW"
M# 1/4' valve "SS-4H"

1L
BufferBottle3

He gasFigure 3.21: Illustration of the gas introduction system. The pressure gauges A and B
correspond to two channels of Mensor CPG2500, and the gauge C is Baratron690A.

Systematical uncertainties of 3 He density
The systematical uncertainties in the measurement of 3 He density are mainly derived fromthe precision of instruments and deformation of vessel. Besides, the deviation from ideal
gas law slightly aﬀect the measurement and these are summarized in Tab. 3.12.

40

Chapter 3. Experimental setup
SeriesVolume expansion
Heat generation by preamplifier
Contamination from G1He
Deformation of vessel
Impurity of pure 3 He
Virial coeﬃcient
Thermal transpiration
Total

1
2
3
0.46
0.28
0.31
0.35
0.29
0.27
0.18
0.18
0.16
0.16
0.15
0.15
0.066 0.066 0.066
0.0004 0.0005 0.0005
0.0001 0.0001 0.0001
0.6
0.5
0.4

4
5
6
0.27
0.41
0.31
0.33
0.30
0.30
0.086
0.61
0.28
0.15
0.15
0.15
0.066 0.066 0.066
0.0005 0.0005 0.0005
0.0001 0.0001 0.0001
0.5
0.7
0.5

Table 3.12: Systematical errors of 3 He density in percentage.

3.6

Cosmic ray veto counter

The aluminum vessel is surrounded by scintillation counters to veto cosmic ray backgrounds
as shown in Fig. 3.22. Single counter consists of a few number of plastic scintillators and aphoto multiplier. Scintillators are covered with reflectors and light shielding, and wavelength
shift fiber are inserted. Each side of the TPC is covered with two counters and veto signal
is generated by taking the coincidence. Figure 3.23 shows a counter which is put in thefront and back of the TPC. It has a trench with 20 mm pitch to pass the beam. From theoutside, the trench is covered with a couple of small square counter.

Figure 3.22: Cosmic ray veto counters.

41

Chapter 3. Experimental setup

Figure 3.23: Drawing of the cosmic ray veto counter (Front and Back).
PositionATop
99.52 ±0.06
Front
Back
Right
100.00 ±0.06
Left99.69 ±0.06
XFront97.95 ±0.06
XBack
98.58 ±0.06

B99.57 ± 0.02
99.60 ± 0.02
99.76 ± 0.02
99.65 ± 0.02
99.46 ± 0.02-

C
99.19 ± 0.04
98.83 ± 0.04
98.92 ± 0.04
98.74 ± 0.04
97.66 ± 0.04-

D
99.73 ± 0.04
99.64 ± 0.04
99.73 ± 0.04
99.73 ± 0.04
99.82 ± 0.04-

E
99.12 ±0.04
98.34 ±0.04
98.93 ±0.04-

Table 3.13: Detection eﬃciency of veto counters [44]. Position A∼E are shown in Fig. 3.23.

Usually veto counters are used to remove cosmic ray events, while cosmic ray measurements are included in the data acquisition cycles in order to evaluate the wire eﬃciency
and to estimate the accuracy of energy calibration. In that case, veto counters are used togenerate trigger signal.

42

Chapter 3. Experimental setup

3.7

Calibration source

Energy deposit is calibrated by using 55 Fe checking source which emit X-ray (5.9 keV). The
checking source is set on the rotating table and diﬀerent y position, y = 75, 0, and -75 mm,
can be selected (Figs. 3.24 and 3.25). Here, center of TPC is defined as standard y position.
As it is shown in Fig. 3.14, there are windows in the side wall.

Figure 3.24: Checking source on the rotating Figure 3.25: Side view of TPC. The source isfixed to y = 0 mm.
table.
When checking source is fixed to y = 0 mm (Fig. 3.25), windows are covered with LiF
tiles. While rotating table is set to y = 75 or -75 mm, the X-ray is emitted from the windowand energy deposit caused by photoelectric eﬀect is detected. The obtained energy resolution
was 22.9 % FWHM at 5.9 keV, under 100 kPa operation.
The transition of pulse height is shown in Fig. 3.26. Comparing the measurement with
diﬀerent y position, the eﬀect of attenuation appears as it is proportional to the drift length.
The energy deposit from y = 75 or -75 mm at a certain time can be obtained by fitting thetransition. The fit function is given as
t−t0

f = A (1 − Be− τ ) e−l(t−t0 ) ,(3.9)

where t is a certain time of the measurement, t0 is the time when gas have been filled and l isthe drift length which is equal to 75 mm (225 mm) when the calibration source is positioned
at y = 75 mm (-75 mm). A, B and τ are constants in charge of the eﬀect of outgas andrecombination.
Since magnetic field is not applied to the TPC, the important point of our experimentis that what is indicated in y direction is only relative position of energy deposit. For thatreason, we assume that all ionized particles are generated at the standard y position andenergy calibration have been performed by interpolating these two fits in Fig. 3.26.
43

Chapter 3. Experimental setup

The uncertainty of energy calibration would be maximized when ionized particles are
generated near the MWPC or bottom of the TPC.
Anode pulse height [ch]Log(Near/Far) aph [ch]Attenuation vs time
1110
1100
1090
1080
1070

0.06

0.05

0.04

0.03

1060
0.02

1050
1040

0.01

1030
06/04

06/05

06/06

06/07

06/08

06/09

06/10

06/11

06/12

0

06/13 06/14
Date [month/day]

06/04 06/05

06/06 06/07

Calibrated adc aph [ch]

1110

1100

1100

1090

1090

TPC performance

1080

1080

Multiple gain

Gain growing vs ti

1120

1110

3.8

06/10

Combined calibrated ADC aph [ch]Position Calibrated ADC vs time
Figure 3.26: Transition of pulse height.
The calibration source was positioned at y = 75 mm
1130(red) and y = -75 mm (blue).
1120

06/08 06/09

1070

1070

1060

1060

To measure the multiple gain, the checking source was placed just above the MWPC.
In such1050
1050
a setup, ionized particles 06/04
were06/05detectedwithout
drifting
in
the
TPC.
AssumingW-valueof 0906/07 0906/08 0906/09 0906/10 090
06/06 06/07 06/08 06/09 06/10 06/11 06/12 06/13 06/14
06/04 0906/05 0906/06
Date [month/day]4
4
He (42 eV), multiplication gain was calculated to be 4 × 10 . Because we have developed
TPC with such a high gain, low level threshold equivalent to 0.2 keV is applicable.
Drift velocity
Drift velocity is estimated by using cosmic ray events. If we require a series of hits in anodewires and the track to be penetrated in y direction, the absolute y position of the ionizedparticles can be determined with a certain accuracy because the angle of cosmic ray can be
restricted by the number of hit wires. Assuming that there are hits with two anode wires,Fig. 3.27 shows the ideal case (left) and worse case (right) to calculate the drift velocity.
Since actual drift length l1 is equal to the height of TPC, the drift velocity can be calculated
accurately. In the worse case, l2 is shorter than the height of TPC and the time diﬀerenceof hits also become shorter. Therefore, the drift velocity is mistaken as faster.
Consequently, the drift velocity is given as a function of number of hit wires and moreaccurate result can be obtained with larger number of hits. Standard velocity is calculated
by extrapolation, resulted in about 1 cm/ s with 100 kPa operation (Fig. 3.28).

µ44Chapter 3. Experimental setup

l1

l2

✓1

✓2

Drift velocity [cm/µs]

Figure 3.27: Ideal case (left) and worse case (right) to calculate the drift velocity by using
cosmic ray. TPC is viewed in xy plane and hit anode wires are indicated with red.

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

Figure 3.28: Drift velocity calculated with diﬀerent number of hit anode wires.

45

Chapter 3. Experimental setup

Anode wire detection eﬃciency

Efficiency [%]In order to estimate the detection eﬃciencies of anode wires, cosmic ray events are triggeredby veto counters and the track penetrating the TPC in y direction are selected. The eﬃciencyof each anode wire was determined by the hit ratio of the events in which both side of wires
have hits and we obtained the averaged wire eﬃciency to be more than 99 % at 100 kPa.
100

99.5

99

98.5

98

97.5

97

2

4

6

8

10

12

14

16

18

20
22
Anode wire

Figure 3.29: Detection eﬃciencies of anode wires.

Background rate
After the installation of veto counters and shields, the rate of environmental background ismeasured to be 7.7 cps. The environmental γ rays and cosmic rays account for 1.3 cps and2.0 cps, respectively. The remaining backgrounds are derived from radioisotope inside TPC
and vacuum vessel.
Stability of operation
Since the gas introduction, three things might be changed with elapsed time. One is temperature, that would rise to a few degree Celsius and gives uncertainties of number density of3
He. Another thing is radioactivation around the TPC. The backgrounds correspond to neutron capture reactions would increase proportional to the beam flux. They are consideredin Sec. 6.3.2.
The other is the deterioration of vacuum condition. Because the aluminum vessel havebeen sealed during the data acquisition, outgas will increase. Increasing amount of outgas
lower the multiple gain and also reduce the accuracy of the energy calibration. This is oneof the most significant problems aﬀect the stability of operation. Hydrogen and oxygen
are contained in the outgas and large electron aﬃnities are given to them. The eﬀect of46

Chapter 3. Experimental setup

Attenulation Coefficienct [m-1 ]attenuation appears in the diﬀerence of pulse height measured with the source fixed at
diﬀerent y position (Fig. 3.30).
0.5

0.4

0.3

0.2

0.1

0

0

2

4

6

8

10
Elapsed time [day]Figure 3.30: Transition of the attenuation coeﬃcient. The operation was suspended in theblank space because of the maintenance of the accelerator.

The amount of outgas depends on the vacuuming before starting data acquisition. Whengas introduction was started with the vacuum condition of 3.6 × 10−4 Pa, outgassing wasmeasured to be 4.4 Pa/day. After 5 days of operation, the uncertainties in multiple gain
and drift velocity were estimated to be 10 % and 1 %, respectively. In order to avoid theuncertainty in the energy calibration, continuous data cumulation is restricted to about 10
days at longest.

3.9

Readout electronics

Our readout system consist of a common pipelined platform for electronics readout (COPPER) with digitization daughter cards called FINESSE, front-end instrumentation entities
for sub-detector specific electronics. Both of FINESSE and COPPER are products developed by KEK [37].
Readout system proceed as follows (Fig. 3.31). Trigger signal is emitted when any anodesignal exceed the threshold. Firstly, waveforms from 128 channels are sent to flash ADC
type FINESSE cards which digitizes waveforms with 20 MHz clock and 12 bit dynamic range.
A FINESSE card have 8 channels so that there are 16 cards for ADC and two cards for
TDC. A set of four FINESSE cards is on a COPPER board, and each card is consecutively
read out with the transmission rate of 1 Gbps. In total, five COPPER boards are used.
Finally, waveforms are recored from 30 sec before to 70 sec after the trigger signal with

µ

µ

47

Chapter 3. Experimental setup

2048 channel resolution. Synchronized with the readout of ADC, the time-of-flight (TOF)
and the beam monitor count are also transmitted. The time diﬀerence between the collisionof latest proton pulse on the mercury target and trigger signal is recorded by TDC whichhave 1.25 MHz clock and 16 bit dynamic range.

Figure 3.31: Block diagram of the readout electronics [31].

COPPER
Number of boards
Number of FINESSE cards on a COPPER board
FINESSE 8 ch FADC
Number of cards
Clock
Dynamic range
ChannelData size
FINESSE 32 ch multi hit TDC V2
Number of cards
Clock
Channel5416
1 ∼ 65 MHz
100 sec (12 bit)
8 ch
2 kbyte/chµ21.25 MHz (16 bit)
32 ch

Table 3.14: Specification of readout system.

48

Chapter 3. Experimental setup

Figure 3.32: GNV-440 FINESSE 8ch ADC board (12bit/65MSPS).

Trigger selection
We conduct four kinds of measurements and trigger condition is selected depend on the
purpose.
• Beam ON (LiF shutter open)• Beam OFF (LiF shutter closed)• Calibration• Cosmic ray
In the measurement of cosmic ray, trigger signal is generated by the coincidence of scintillation counters. Otherwise, scintillation counters veto cosmic rays and the first fired anodewire creates the trigger signal.
Dead timeµ

A veto signal is emitted if scintillation counters are triggered or TPC emit the trigger signal
to record an event. The readout system is vetoed for 70 s in the former case. According tovetoed time, dead time is calculated to correct the number of triggered events.
As it is shown in Fig. 3.31, we record the TOF of kicker pulse, veto start and veto stop.
The number of times to take a certain TOF is counted by referring the kicker pulse, and thatcan be expressed as a step function of TOF, A(t). While vetoed time B(t) is defined as the49

Alive rate

Chapter 3. Experimental setup

1

0.8

0.6

0.4

0.2

0
0

5

10

15

20

25

30

35

40
TOF [ms]

Figure 3.33: Alive rate vs. TOF.

period from veto start to veto stop. B(t) is divided by A(t) and we obtain the correction
for dead time. Alive rate is calculated as the complement of dead time rate and that isshown in Fig. 3.33. When alive rate is equal to 1, that means no correction is required. A
fluctuation of alive rate can be seen in the region of TOF > 15 ms, because of the increaseof trigger signal caused by the arrival of neutron bunches.

3.10

Summary of the features of experimental setup

The features of experimental setup are summarized in Tab. 3.15, compared with the experiment by ILL-ISN-LAPP collaboration [6]. One of the points is the source of neutron. In
the experiment described in [6], high flux neutron was provided from the research reactor
and rotating chopper dram was used to make monochromatic neutrons. On the other hand,
rapid-cycling synchrotron (RCS) at J-PARC delivers proton beam to targets producing theintense cold neutron. In the configuration shown in the table, the neutron decay rate iscomparable.
Another point is the rate of backgrounds. We have reduced radiative sources by selecting
the material inside TPC and possible backgrounds are taken into consideration with greatcare as described in the following chapter. The other distinctive features of our experiment
are low gain operation and high detection eﬃciency which have been achieved by adopting
the lower threshold. Low gain operation is possible for our TPC, that contribute to estimate
neutron capture reactions in 14 N and 17 O. Further, operation with lower pressure is underinvestigation and it will help to reduce beam induced backgrounds.

50

Chapter 3. Experimental setup

NOP
Beam profile
SourceAccelerator based
Repetition rate [Hz]25
Pulse per repetition
5
Pulse length [cm]40
Beam size [mm2 ]20 × 20
Beam divergence [mrad]± 4.2
Neutron velocity [m/s]
500 ∼ 1200
0.059
Duty factor for fiducial time (=F)
Neutron flux inside the TPC [1/s]
1.3 × 105
TPC
Drift cage [mm3 ]290 × 295 × 960
3
MWPC cell size [mm ]12 × 12Gas pressure [kPa]100
Gas mixture [He : CO2 ]85 : 15
3
He abundance [ppm]∼1
Event rate
Neutron decay rate [1/F·s]
0.092
Environmental background [1/s]8
Neutron induced background [1/s]2

ILL-ISN-LAPP collaboration
Reactor based110
1
23 ∼ 25
15 × 25
± 8.7
837
0.044
2.2 × 105
190 × 190 × 700
10 × 1095
93 : 7
0.7
0.10
80
20

Table 3.15: Comparison of setup between the experiment described in [6] and NOP experiment, assuming 220 kW beam power at J-PARC.

51

Chapter 4
Neutron interactions
Neutron interactions induce backgrounds and that have significant influence to the systematical errors in the neutron lifetime. This chapter introduce the neutron interactions andbriefly sort out how to deal with the backgrounds. Categorization of signals and backgrounds
are summarized in the end of this chapter.

4.1(n, γ) reactions

Beam correlated backgrounds are dominated by (n, γ) reactions. Since possible energy of γ
ray is a few MeV at most, the energy deposit of γ rays are detected as the result of photoelectric eﬀect or compton scattering. The discrimination of γ rays is a serious problem tocount the decay electrons and the backgrounds can be avoided by using material with low
absorption cross section.
In our experimental setup, mainly four places are exposed to the neutron beam. One is
the magnetic super mirror whose main component is 28 Si. The other three places are insideof TPC, the beam catcher and the LiF shutter at the entrance of TPC. These places arecovered with the LiF tiles which consist of 6 Li, 7 Li, 12 C and 19 F. Also, it has to be taken
into account that neutrons are absorbed by CO2 gas. The characteristics of (n, γ) reactions
whose short descriptions are given as below are linked with the analytic approach and thatis detailed in chapter 6. Note that in most cases more than one γ ray will be emitted.
• 6 Li(n, γ) and 28 Si(n, γ)
Only prompt γ rays are emitted from the absorption reactions in 6 Li and 28 Si. The
time structure of neutron decay and that of prompt γ rays generated in the upstream
are diﬀerent from each other, so that the backgrounds are easily removed by TOF
method. However, γ rays from LiF tiles are not discriminated by TOF method andthey are corrected in Sec. 6.4.
• 7 Li(n, γ) and 19 F(n, γ)
52Chapter 4. Neutron interactions
As the results of neutron absorption reactions in 7 Li and 19 F, not only prompt γ rays
but also the decay electrons are emitted after the long lifetime. Subtraction procedure
is applicable to remove the background and that is described in Sec. 6.3.2.
• 12 C(n, γ) and 16 O(n, γ)
Point-like backgrounds are generated by 12 C and 16 O which are derived from CO2 gas.
The reaction probabilities are about 3 times larger than that of neutron decay in ourconfiguration of gas mixture. The energy deposit from γ rays are not always detected,
though the kinetic energy of the recoil atoms are about 1 keV and that is suﬃciently
large to be triggered. Detailed description of analysis is given in Sec. 6.3.1.

4.2(n, p) and (n, α) reactions

In the measurement of beam flux, main source of backgrounds are derived from neutron
capture reactions. As for capture reactions of slow neutron, it is well known that the crosssection is proportional to the inverse of the neutron velocity. In NOP experiment, thevelocity of chopped neutrons are in the range between 500 m/s to 1200 m/s and they are
suﬃciently slow for satisfying the 1/v law. Following backgrounds are result from neutron
capture reactions.
• 6 Li(n, α)3 HThis reaction have the order of magnitude larger cross section than that of (n, γ)
reactions in the LiF tiles. Because of that, 6 Li is commonly used to prevent thegeneration of γ rays. However, large amount of 3 H is generated and that would
produce another background, the decay electron. That is detailed in Sec. 4.4.
• 14 N(n, p)14 C
14N is derived from the outgas and it gradually increases with the elapsed time. The
common feature of 14 N(n, p)14 C and 3 He(n, p)3 H is that they have large and local
energy deposit. Therefore, 14 N(n, p)14 C can not be separated from 3 He(n, p)3 H atusual operation. In order to evaluate the amount of 14 N, we insert the measurementswith low gain operation. That is described in Sec. 6.4.1• 17 O(n, α)14 C
17
O is mainly coming from quenching gas. This reaction can not be distinguishedfrom 3 He(n, p)3 H as it is the same with the capture reaction in 14 N. The number of
17
O(n, α)14 C events will be estimated in Sec. 6.4.1.
53

Chapter 4. Neutron interactions

4.3

Neutron scattering

Neutron scattering is often followed by (n, γ) reactions in the LiF tile. In order to separate
signal and backgrounds, we make a demand for signal events not to include neutron scattering so that once neutron is scattered, it is treated as the background. From this definition,
one of the significant features of signal is provided that the starting point of the track insignal events are limited to the on-axis region. Here we define the on-axis region as the
cross section of the beam which correspond to 2 × 2 cm2 in xy plane. Therefore, it is important to take scattering probabilities and kinematics under advisement. Since scattering
itself can not be measured directly, the cross sections and momentum are calculated basedon [38,39] and the theoretical treatment of neutron scattering caused by 4 He and CO2 gases
are considered.
In the cold neutron physics, the wavelength of neutron is long compared with the interval
between atoms, that result in the neutron show a wave nature. For the accurate treatmentof neutron scattering, the thermal motions and the structure of gas molecules have to betaken into account. To avoid enormous cost of calculation, semiclassical approximation was
introduced in [38], where a neutron is represented by a wave and the molecule is replaced
by a rigid system of point scatterers. The diﬀerential cross section of neutron scattering isderived from Eq. (4.1).
σ(θ) =

1 sin xij
1
M 2∑∑
(
)
(σj σi ) 2,
4π M + 1
xij
i
j

(4.1)

where θ is the scattering angle in the center of mass system, M is the ratio of the masses ofthe molecules and neutron, and σi is the total bound scattering cross section of the nucleus
i if i = j, otherwise it is the coherent cross section. And xij is given by
xij = (4πrij /λ) sin (θ/2),(4.2)

where rij is the distance between the atoms i and j, and λ is the wavelength. Note that thiscalculation is performed in the center of mass system and transformed to the laboratory
system. The initial neutron velocities are derived from the standard velocity of neutrons ineach bunch, while a maxwellian distribution at room temperature have been adopted to therelative velocity of the gas molecules.
The result of calculation is shown in Tab. 4.1. The scattering cross section of CO2 isabout 10 times larger compared with that of 4 He, though considering the number density of
the gas moleclues, the probability of neutron scattering in each gas is comparable. Figure
4.1 shows relation between the neutron velocity after scattering and the scattered angle.

54

Chapter 4. Neutron interactions
σCO scat.
×50
10−6
0.8

2

cosθ

cosθ

σ4He scat.
45

0.6

0.0035
0.6

40

0.4

0.2

30

0

0.003

0.4

35

0.2

0.004
0.8

0.0025

0

25

−0.2

20

−0.2

−0.4

15

−0.4

−0.6

10

−0.6

−0.8

5

−0.8

0.002
0.0015
0.001

−1
0

500

1000

1500

2000

2500

3000

−1
0

3500
4000
vn [m/s]

0.0005

500

1000

1500

2500

3000

0
3500
4000
vn [m/s]σCO scat.

σ4He scat.
×50
10−6
0.8

2

cosθ

cosθ

2000

45

0.6

0.0035
0.6

40

0.4

0.2

30

0

0.003

0.4

35

0.2

0.004
0.8

0.0025

0

25

−0.2

20

−0.2

−0.4

15

−0.4

−0.6

10

−0.6

5

−0.8

0.002
0.0015
0.001

−0.8
−1
0

500

1000

1500

2000

2500

3000

−1
0

3500
4000
vn [m/s]

0.0005

500

1000

1500

2500

3000

0
3500
4000
vn [m/s]σCO scat.

σ4He scat.
×50
10−6
0.8

2

cosθ

cosθ

2000

45

0.6

0.0035
0.6

40

0.4

0.2

30

0

0.003

0.4

35

0.2

0.004
0.8

0.0025

0

25

−0.2

20

−0.2

−0.4

15

−0.4

−0.6

10

−0.6

−0.8

5

−0.8

0.002
0.0015
0.001

−1
0

500

1000

1500

2000

2500

3000

−1
0

3500
4000
vn [m/s]

0.0005

500

1000

1500

×50
10−6
0.8

45

2500

3000

0
3500
4000
vn [m/s]

0.6

2

cosθ

cosθ

2000

σCO scat.

σ4He scat.

0.0035
0.6

40

0.4

0.2

30

0

0.003

0.4

35

0.2

0.004
0.8

0.0025

0

25

−0.2

20

−0.2

−0.4

15

−0.4

−0.6

10

−0.6

−0.8

5

−0.8

0.002
0.0015
0.001

−1
0

500

1000

1500

2000

2500

3000

−1
0

3500
4000
vn [m/s]

0.0005

500

1000

1500

2500

3000

0
3500
4000
vn [m/s]σCO scat.

σ4He scat.
×50
10−6
0.8

45

0.6

40

0.4

35

0.2

30

0

25

2

cosθ

cosθ

2000

0.004
0.8
0.0035
0.6
0.003

0.4
0.2

0.0025

0

−0.2

20

−0.2

−0.4

15

−0.4

−0.6

10

−0.6

5

−0.8

0.002
0.0015
0.001

−0.8
−1
0

500

1000

1500

2000

2500

3000

3500
4000
vn [m/s]−100.0005

500

1000

1500

2000

2500

3000

0
3500
4000
vn [m/s]

Figure 4.1: Cosine of scattered angle vs. neutron velocity after scattered by 4 He (left)
and CO2 (right). The standard neutron velocity in each bunch was assumed for the initial
neutron velocity at 304 K. From the top, the initial velocity is 598, 709, 843, 997 and1177 m/s.
55

Chapter 4. Neutron interactions
vn [m/s] σ4 He [barn] σCO2 [barn]
598
1.97
16.6
709
1.71
18.7
843
1.51
21.2
997
1.34
24.0
1177
1.22
27.0
Table 4.1: Theoretically calculated neutron scattering cross sections at 304 K. Here, vn isthe initial neutron velocity.

4.4

3

H decay3

H decay is not a direct reaction of neutron but neutron is related to the production of 3 H
via 6 Li(n, α)3 H and 3 He(n, p)3 H reactions. 3 H decay is expressed as follows:3

H → 3 He + e − + ν¯e + 18.6 keV.

(4.3)

Even though 3 H have long lifetime (τ = 12 y), considerable amount of 3 H are generated
because the LiF tiles are incessantly exposed to neutrons and the decay electron from 3 H
can not be ignored. Some studies about the diﬀusion of 3 H from LiF are given in [40, 41].
By clarifying the following features, we have concluded the existence of the decay electronfrom 3 H. Firstly, point-like backgrounds have been detected across the TPC. Secondly, therate of the background is proportional to the beam flux and it gradually increases with theamount of irradiation. When irradiation is interrupted, the rate also becomes constant.
Thirdly, the source of the background is limited in the downstream of the Zn foil, and thelifetime of the background is more than one week. Fourthly, the rate of the backgroundhave been reset by the operation of a new gas filling.
The background can be extracted by applying a cut, where we introduce a parameter“ph/int” and the definition is described in Sec. 6.3.1. Figure 4.2 shows the energy depositof the background. Although the sensitivity of the cut is limited to energy deposit less than
15 keV, due to saturation of pulse height. The broad distribution of energy deposit appears
in the MC sample of 3 H decay as shown in Fig. 4.3, and that can not be explained by
the interactions of other materials surrounding TPC. Consequently, the background is well
suppressed by the cut as demonstrated in Fig. 4.4.

56

Chapter 4. Neutron interactions

350

240
220

300

200
180

250

160
200

140
120

150

100
80

100

60
40

50

20
0
0

5

10

15

20

0
0

25
30
Energy deposit [keV]

5

10

15

20

25
30
Energy deposit [keV]5count [cps]count [cps]Figure 4.2: Energy deposit of the point-like Figure 4.3: Energy deposit of the MC sample
background events extracted from data.
of 3 H decay.

4.5
4
3.5

0.7
0.6
0.5

3
0.4

2.5

0.3

2
1.5

0.2

1
0.1

0.5
0

May/28 May/29 May/30 May/31 Jun/01 Jun/02
09:00
09:00
09:00
09:00
09:00
09:00

0

Jun/03
09:00
Date

May/28 May/29 May/30 May/31 Jun/01 Jun/02
09:00
09:00
09:00
09:00
09:00
09:00

Jun/0309:00
Date

Figure 4.4: Transition of the count rate of neutron decay candidates with 3 H suppressioncut (left) and the count rate of the background extracted by 3 H suppression cut (right).
The accelerator was operated with constant beam power during the measurement.
Assuming that 100 % detection eﬃciency of the TPC at 150 kW operation, the generationof H is expected to be 9 × 104 cps and it is estimated that 1/200 of them are released to be
detected.
3

4.5

Categorization of signals and backgrounds

In the previous sections, we enumerated possible neutron interactions with materials surrounding TPC. Signals and backgrounds are categorized as summarized in Tab. 4.2. MC
simulation of these reactions will be detailed in chapter 5. The analysis have been developed
to adopt each background and that will be explained in chapter 6.

57

Chapter 4. Neutron interactions

Neutron decay
SignalNeutron decay without scattering
Neutron decay after scattering
Background(n, γ) reactions
6
Li(n, α)3 H

3Beam flux
He(n, p) H without scattering3
He(n, p)3 H after scattering
14
N(n, p)14 C
17O(n, α)14 C
3

Table 4.2: Categorization of signals and backgrounds.

58

Chapter 5
Simulation
Signal eﬃciency and the amount of neutron induced backgrounds are estimated by using MC
simulation. The reproducibilities of the cut parameters are matters of critical importance.

5.1

Overview of simulation

The construction process is separated into two parts. In the former, the distribution ofenergy deposit inside the TPC is calculated based on GEANT4 simulation [42]. General
physics process in gas detector such as diﬀusion, recombination and attenuation are considered in the latter. As the result of process, we obtain waveforms of all wires as it is thesame with the measurement.
Part1 : Production of ionized particles• Physics model and cross section• Beam structure• Energy spectrum of prompt γ ray• Neutron polarization• Ionization
Part2 : Statistics of ionized partilces• Diﬀusion• Recombination• Attenuation
59

Chapter 5. Simulation• Induced electrical field• Space charge eﬀect• Production of waveform

5.1.1

List of the MC samples

The list of MC samples is tabulated as below. It is not eﬃcient to trace all the tracks
of neutrons because the probability of neutron decay is very low (10−6 ) and the cost of
calculation become too large. To avoid such situation, the position of neutron interactions
were determined beforehand as described in Sec. 5.2.2. Then, GEANT4 simulation isstarted by tracing the reaction products. The statistics of MC sample is about 10 times
larger than that of data.
SampleInitial particles
Neutron decay (signal)
neutron
Neutron decay (background)neutron3
He(n, p)3 H (signal)
p and 3 H
3He(n, p)3 H (background)p and 3 H
LiF capture
photonCO2 capture
recoil atom and photon
Cosmic rayµ±55
Fe source
photonTable 5.1: List of the MC samples.

5.2

Production of ionized particles

In the former part of the simulation, geometrical tracking was performed with considerationof the capture reactions and the inelastic reactions, based on GEANT4 physics model.
Finally, whole energy deposit from the reaction products are recorded. Full structure of thedetectors and shields have been implemented to the simulation.

5.2.1

GEANT4 physics model

In the GEANT4 simulation, it is possible to customize the library to optimize calculationaccording to particles and range of energy. We employ two kinds of physics lists called
60

Chapter 5. Simulation“QGSP BERT HP” and “FTFP BERT PEN” where neutron capture reaction and inelastic
interaction are taken into account.
QGSP BERT HP
The physics lists of this library use the “NeutronHP” model which dedicate to the neutroninteractions in the energy range of below 20 MeV. The neutron capture reactions and theabsorption reactions can be simulated. Note that this library was used only when we tracescattered neutrons and that is described in Sec. 5.2.3.
FTFP BERT PEN
FTFP BERT PEN is suitable for the calculation of low energy electrons and photons which
are dominant particles produced in the ionization chamber. Most of our simulation is started
with the generation of reaction products, and therefore FTFP BERT PEN was selected. It
should be noted that the calculation concerned with the angular distribution of neutron
decay products, the neutron scattering and the energy spectrum of prompt γ rays from the
LiF tile were originally implemented to deal with the interactions of cold neutron in correctmanner. As for the neutron decay described in G4NeutronBetaDecayChannel.hh, the decay
products were incorrectly emitted on the same plane, so that we corrected the relative
relationship of angles in the program. In the neutron scattering, G4NeutronHPElastic.hh
deal with only the scattering by free atoms at a given temperature. For the proper treatmentof low energy neutron scattering, thermal motion and structure of the gas molecules haveto be considered. We calculated the scattering cross section on the basis of [38] and input
to the simulation (see Sec. 4.3).

5.2.2

Beam structure

The reproduction of the beam structure is significant for the evaluation of those backgrounds
induced from neutron scattering since the key features of signal are provided by identifying
the starting point of the track. Three dimensional position is reproduced as following. Theenergy deposit of 3 He(n, p)3 H reaction is very localized so that it provides good informationof the passage of neutrons as shown in Fig. 5.1, and the position in z direction versus TOF
of 3 He(n, p)3 H reaction was input from data. While the xy distribution of the neutron was
acquired from additional measurement which was arranged ahead of the physics data taking
and the result was also input to the simulation (Fig. 5.2). The detail of measurement is
described in appendix B.
In the passage of the decay volume (68 cm), the eﬀect of diﬀusion in xy direction wasmeasured to be not more than 1 mm and that is smaller than wire pitch (12 mm). In
the simulation, it is assumed that the neutron pass along the z axis without changing the61Chapter 5. Simulationz [cm]

xy distribution. In this way, three dimensional interaction points of neutron have been
determined to generate the reaction products.

Figure 5.1: The center of energy deposit in z direction vs TOF, provided by extracting
He(n, p)3 H events.

3

Figure 5.2: Beam distribution in the xy plane, measured with RPMT.

62

Chapter 5. Simulation

5.2.3

Capture reactions of scattered neutron

In order to simulate the reactions result from neutron scattering, we have to figure out theposition of neutron scattering and that of capture reactions. The simulation was processedin two steps. Firstly, the position of scattering was determined. According to the mean
free path, which was obtained from the cross section (see Sec. 4.3), scattering position in z
direction can be calculated. To beware that xy distribution of the scattering coincide with
Fig. 5.2. The momentum distribution of the scattered neutron is acquired from Fig.4.1 andthe preparation to simulate the track of scattered neutron have done.
Secondly, another simulation was carried out to calculate the position of neutron capture reactions. Based on previously calculated momentum and the position of scattering,
scattered neutron was emitted and then 6 Li(n, α)3 H and 3 He(n, p)3 H events were identified
by tagging both of physics process and the reaction products. In this way, the position of
capture reaction was projected into two kinds of maps, one for the capture reaction in the
LiF tiles and another for 3 He(n, p)3 H reaction. The maps are shown in Fig. 5.3. Because of
the long mean free path of the neutron decay and 3 He(n, p)3 H reaction compared with the
decay volume, it is assumed that position of these two reactions have similar distribution.

Figure 5.3: Position of 3 He(n, p)3 H reaction after neutron scattering (left) and that of
6
Li(n, α)3 H reaction (right), shown in xz plane.

5.2.4

Energy spectrum of prompt γ rays from the LiF tile

The energy spectrum of prompt γ rays from the LiF tile depend on the component of
LiF tile and neutron velocity, so that it is preferable to obtain the spectrum from data.
The measurement was conducted with the cooperation of the neighboring beamline, BL04
[54–56]. The LiF tile which have been used in the NOP experiment was brought to theBL04 and irradiated to measure the energy spectrum. The γ rays were detected by a set of63Chapter 5. Simulation

germanium photon detectors and the intensity of γ rays was reconstructed as shown in Fig.
5.4. The detail of measurement is given in appendix C.

10− 1

10− 2

10− 3
0

1000

2000

3000

4000

5000

6000

7000
[keV]

Figure 5.4: Energy spectrum of γ rays emitted from the LiF tile. Intense peaks found at
477 keV, 6768 keV and 7245 keV are derived from 6 Li.

5.2.5

Neutron polarization

The angular distribution of the decay electron depend on the polarization of neutron andit may slightly contribute to the detection eﬃciency. The probability to emit the electronwith an angle θ with respect to the neutron spin is written as follows [8].
W (Ee , θ) ∝ 1 + βP A cos θ,(5.1)

where A is the angular correction between the neutron spin and the electron, and A has
been measured to be -0.1184(10) [5]. β is the speed of the electron relative to the speed oflight, P is the neutron polarization and Ee is the energy of the electron.
Although polarized neutron beam is provided in the upstream, the magnetic field is
required to keep the polarization and that is limited to around SFC. The neutron spin might
be aﬀected by the geomagnetism, and therefore the polarization is not sure. However, it
should be noted that our TPC is able to detect ionization tracks in a 4π geometry. For thesereasons, the eﬀect of polarization is considered to be very small and we deal with depolarized
neutron in the simulation. The uncertainty in the detection eﬃciency was estimated with
the MC sample of polarized neutron decay, which was prepared only for this estimation,
resulted in 0.13 %.
64

Chapter 5. Simulation

5.2.6

Ionization

Charged particle leave the trace of passage when it passes through a gas chamber. This is
the result of ionization that ionized particles are left by the collision between the charged
particles and gas molecules. Ionized particles drift toward to MWPC according to theelectric field, and the energy deposit which is proportional to original ionization is detected
after amplification. The amount of ionized particles depend on W -value which is the eﬀective
average energy for the production and diﬀers by the gas molecule as shown in Tab. 5.2. Wβof 4 He and CO2 were weighted based on the partial pressure, and we apply 40.9 eV in thesimulation.

Gas
4
He
CO2

Wα [eV] Wβ [eV]
46.0
42.3
34.3
32.8

I [eV]
24.58
13.81

Table 5.2: W -value of TPC gas [44]. Wα and Wβ are average energy required to produce
an α particle and an electron, respectively. I is the minimum ionization potential.

For a charged particle with low energy, it is known that W -value is increased and therefore the energy deposit of the proton in the neutron decay might be overestimated in thesimulation. The lower limit of the detection eﬃciency can be estimated by simulating thesituation that only the energy deposit from the decay electron could be detected. The
uncertainty was calculated to be 0.35 %. The same thing can be said about 12 C(n, γ)13 C
reaction and 16 C(n, γ)17 O reaction, because only small portion of energy is shared with therecoil atom (E13 C = 1.01 keV and E17 O = 0.54 keV) [45]. Although the energy deposit of 13 C
and that of 17 O would be slightly enlarged and they are more likely to be detected in our
simulation, 99.9 % of them are discriminated by applying a cut.

5.3

Statistics of ionized partilces

In this section, the latter half of the simulation is detailed. After ionized particles havebeen traced, they will be converted into waveforms and the main point of this section is tocalculate the gain and the attenuation of charges as they drift toward MWPC.
65

Chapter 5. Simulation

5.3.1

Diﬀusion

During the drift in the electric field, electrons are diﬀused by collisions with gas molecules.
The proportion of the electrons in the dx is given by Eq. (5.2).
dNN
σx( x2 )
1
= √
exp −
dx,
4Dt
4πDt
√
=
2Dt,

(5.2)
(5.3)

where x denote the distance from the origin after time t, D is diﬀusion coeﬃcient which isdetermined to reproduced the measurement, and σx is the diﬀusion width. In the simulation,t is calculated by the y positions of the ionized particles and eventually primary electrons
are diﬀused at a distance of σx .

5.3.2

Recombination

Recombination aﬀect to diminish the ion pairs. There are some possibilities for a positiveion and an electron to be neutralized. For example, one would be recombined with ionizedparticles or extracting an electron at the walls. While stronger electric field help to suppress
these eﬀect, the electric field of 300 V/cm have been applied in our experiment and themeasurement of the probability of recombination resulted in 12 %. The detail is studied
in [44]. The eﬀect of recombination is implemented in the simulation as the expression
confirming poisson distribution, where the mean value is proportional to the number oforiginal ion pairs.

5.3.3

Attenuation

The electrons are attached to gas molecules, result in the reduction of detected electrons.
This influence of attenuation depends on the number of collisions with gas molecules. Therefore, as it is empirically tested that attenuation is enhanced by the amount of outgas, slower
drift velocity, higher gas pressure and longer drift length (Fig. 3.30). The eﬀect of attenuation can be expressed by poisson distribution in which the mean value is proportional tothe drift length.
∆y∆N = N (1 − e− λ ) ∼ N

∆y
,
λ

(5.4)

where ∆N is the amount of reduced charge, N is the number of original ion pairs, ∆y isdrift length and λ is the inverse of attenuation coeﬃcient.
66

Chapter 5. Simulation

5.3.4

Amplification and avalanche-induced electric field

In the basic operation of proportional wire, electrical field is expressed as
q 1
E=
,
(5.5)
2πϵ0 rwhere q is the charge density, ϵ0 is the dielectric constant for the gas and r is the distancefrom center of the wire. Electric field is rapidly increased as an electron approaches to anodewires and it will obtain enough energy to induce secondary ionization. In this way, avalanche
is started and detected energy is proportional to the amount of collected electrons.

Figure 5.5: Time development of an avalanche in a proportional counter [35]. A pair of
ionized particle is created (a). Secondary ionization is induced on the way toward to theanode wire (b) and laterally diﬀused (c). As the development of an avalanche, the wireis surrounded by electrons (d). The electrons are rapidly collected and positive ions are
attracted to the cathode wire (e).
With continuous development of avalanche, it induces electric field. The eﬀect is not
limited in the single wire but also extend to neighboring wires and inverse pulses are produced. The avalanche-induced electric field was simulated by using ANSYS ver 15.0 [46]and Garfield [47]. First, three dimensional electric field was calculated based on the finite element method (FEM) by using ANSYS. To reduce the calculation costs, the repeat
structure of the wires was simplified to unit structure. The result was input to Garfield
and multiplication of charge was simulated. Based on the Shockley-Ramo theorem [49], thecurrent which is induced by the movement of charge is expressed as follows.
i = qvEv ,(5.6)

here v is the velocity of charged particle and Ev is the magnitude of electric field parallel tov. There is no diﬀerence in the time structure between the induced current and the original
current. Consequently, the eﬀect can be taken into account by calculating the ratio of theinduced current and scale factor was introduced to the simulation.
67

Chapter 5. Simulation

5.3.5

Space charge eﬀect

The influence of space charge eﬀect is observed when high density of positive charge cover
the wire. It can be seen in 3 He(n, p)3 H reaction because the energy deposit of the proton
is large and localized. The wire is surrounded by positive ions, result in the decline of theelectric field. It means that the wire is not maintaining the proportionality and the energy
deposit will be underestimated. The electric field will recovered after all ions are collected in
the cathode wire and it takes about a few s. This eﬀect is taken into account by applying
following model of saturation [36].

µs=log (1 + f (ϕ)∆EG0 ),f (ϕ)∆EG0(5.7)

Saturation

where f (ϕ) represent the amplitude of saturation, ϕ is the angle of the track to x axis, ∆E
is deposited energy in the wire, G0 is multiplication factor for the condition without spacecharge eﬀect. The reduction of s means the suppression of the amplification. Figure 5.6
shows the saturation factor s measured by using 241 Am source. Data was fitted by arbitraryscale to obtain the parameter f and ∆E.

1.4
1.2
1
0.8
0.6
0.4

f ∆E = (2.94 ± 0.52)×10-4

0.2
0
10

102

103

104

105

Gain

Figure 5.6: Measurement of the saturation factor s as a function of gain by using 241 Am
source [36]. The vertical scale was normalized to s(G0 = 0) → 1.

5.3.6

Production of waveformIn the previous section, we considered when and how many charges have been collected ineach wire and we obtained the charge density which is formulated as a function of time.
Besides, the template waveform was measured with the checking source (Fig. 5.7).
68Chapter 5. Simulation

A waveform is produced by convoluting the charge density function with the template
waveform:{
0(0 ≤ t ≤ 298)
F (t) = ∫ t−299
,
(5.8)
N
(τ
)T
(t
−
τ
)dτ
(299
≤
t
≤
1000)
e
0
where F (t) is the produced waveform at time t, Ne (t) is the function of charge density,
T (t) is the template waveform. Finally, the pedestal noise is added to obtain the detected
waveform.

1000

800

600

400

200

0
0

100

200

300

400

500

600

700

800

900
1000
[µs/10ch]

Figure 5.7: Template waveform measured by using the X-ray source.

69

Part III
Analysis

Chapter 6
Signal estimation
In this chapter, the evaluation of number of signal events are described. Our basic concept ofsignal estimation is that the backgrounds are removed from all events rather than extracting
the signal events. By this means, we have to solve three issues to count the neutron decay
and the 3 He(n, p)3 H reaction.
• Separate neutron decay and 3 He(n, p)3 H reaction.
• Remove backgrounds as many as possible.
• Correct remaining backgrounds.
The critical points in the analysis are the improvement of signal-to-noise ratio and correct
treatment of the uncertainties.

6.1

Overview of the analysis

We will follow the procedure shown in Fig. 6.1 to evaluate signal events. The first process of
the analysis is to separate all events into the neutron decay candidates and the 3 He(n, p)3 H
candidates. A parameter is defined to discriminate signal events as detailed in Sec. 6.2.
Next is to remove the backgrounds. The methods of background reduction significantly
aﬀect both of statistical and systematical errors. The backgrounds are removed from thesignal candidates depending on their features, step by step. This process is described in Sec.
6.3. Finally, some corrections are applied to estimate remaining backgrounds which can not
be measured directory. These are performed by using MC simulation as demonstrated inSec. 6.4.

70

Chapter 6. Signal estimation

All events

Separation

Cut

Subtraction

Correction

3He(n, p)3H

Neutron decay

Figure 6.1: Analysis flow of the signal evaluation.

Data set
The configurations of engineering data and physics data are summarized in Tab. 6.1. The
accumulated data correspond to 12 days of beam time.
Series1 (May 2014)
2 (Apr. 2015)
3 (Apr. 2016)
4 (Apr. 2016)
5 (May 2016)
6 (Jun. 2016)

Beam power [kW]
240
430
170
170
170
160

DAQ [day]
1.4
0.7
0.8
3.0
2.8
3.0

3

He density [×1019 atom/m3 ]2.24(1)
1.867(5)2.127(7)3.96(1)
0.993(4)2.089(7)Table 6.1: Acquired data set.

71

Chapter 6. Signal estimation

Data have been accumulated with following cycle, basically with high gain operation((a)∼(d)). In order to estimate the amount of 14 N derived from the outgas, low gain
measurement ((e), (f)) was inserted about four times per gas filling.
(a) Beam ON(b) Beam OFF(c) 55 Fe source(d) Cosmic ray(e) Beam ON with low gain operation(f) Beam OFF with low gain operation

6.2

Separation of neutron decay and 3He(n, p)3H reaction

At first, we have to separate the neutron decay candidates and the 3 He(n, p)3 H candidates
because both reactions are measured in the same volume of detector. The characteristic of
the neutron decay is long track of the electron starting from the on-axis region. On the other
hand, large and local energy deposit of the proton is detected in the 3 He(n, p)3 H reaction.
Therefore, the diﬀerent ionization power provide the discrimination with good performance.
The waveforms of anode wires and cathode wires were recorded in the experiment by
ILL-ISN-LAPP collaboration, while the field wires are also read out in our experiment andthat help to increase the accuracy of separation. Here, we define the maximum single pulse
height among all field wires as the parameter to separate the candidates. This parameter isable to reflect the amount of energy deposit and its reach. The performance is demonstrated
in Fig. 6.2.
There are two kinds of uncertainties arise from this procedure. One is 3 He(n, p)3 H
contamination in the neutron decay candidates. That is more serious than reverse contamination since the identification of the neutron decay is more complex. Furthermore, theprobability of 3 He(n, p)3 H reaction with the 3 He admixture of 1 ppm at atmospheric pressure
is about 25 times larger than that of the neutron decay. For these reasons, the threshold of
25 keV was adopted to minimize 3 He(n, p)3 H contamination. The detail discussion is given
in Sec. 6.4.
Another uncertainty comes up to the signal eﬃciency due to the ambiguity of the parameter and that is estimated in chapter 7.
72

# of events# of events

Chapter 6. Signal estimation

8000
7000

103

6000
5000
4000

102
3000
2000
1000
0
0

10
50

100

150
200
250
300
Maximum pulse height in field wires [keV]

0

10

20

30

40

50
60
70
80
90
100
Maximum pulse height in field wires [keV]

Figure 6.2: Maximum pulse height in the field wires. Left : Signal candidates are separated
at 25 keV, which is indicated with green line. Right : Enlarged view of the left figure withlogarithmic scale.

6.3

Background reduction

The backgrounds should be removed or corrected, otherwise the number of signal eventswould be overestimated. Although we can rely on a statistical subtraction of the residual
backgrounds, we should not depend on it too much because it is not eﬀective way to reduce
statistical error, and therefore some cuts are applied before the subtraction. In the following,
we will categorize the backgrounds and then focus on the practical approach.
Categorization of the backgrounds
The backgrounds can be separated based on the time structure and its sources (Figs.
6.3∼6.5). Firstly, the backgrounds are categorized into ones which are induced from neutron reactions and others. The ratio of latter backgrounds can be estimated by comparing“Beam ON” and “Beam OFF”.
• Beam ON
This measurement have been operated with the LiF shutter open and the neutrons
beam pass through the TPC.
• Beam OFF
The LiF shutter is closed, and neutrons are shut out by 6 Li(n, α)3 H reaction.
Secondly, the backgrounds with diﬀerent TOF structure are removed by subtracting “Sideband” from “Fiducial”.
• Fiducial
Fiducial time is defined as the time when a bunch is completely contained within 14 cm
inner side than the edge of the drift cage. Because SFC is adjusted to shape bunches
73

Chapter 6. Signal estimation

with the interval of 3.2 m, next bunch is not yet formed in the upstream during thefiducial time.
• Sideband
Sideband region is decided not to include the neutron bunches inside TPC, nor the
events which are generated at the moment that proton beam hit the mercury target.

A

B C

TOF

TOF

Figure 6.3: Drawing of TOF spectra of Beam ON (top) and Beam OFF (bottom). Signal
events (red), the beam induced background (blue), the prompt γ rays from upstream (green),
the environmental backgrounds (orange) and the radioactivation backgrounds (magenta) areillustrated. The time range from B to C roughly indicate the fiducial time.

74

Chapter 6. Signal estimation

A

B

C

Figure 6.4: Passage of the neutron beam, which is indicated with red line, at a certain TOF
of Beam ON. A, B and C are indicated in Fig. 6.3. The intense beam is emphasized withbold red line.

Figure 6.5: Passage of the neutron beam of Beam OFF. The neutrons are intercepted by
the LiF shutter.

75

Chapter 6. Signal estimation

The definitions of Beam ON, Beam OFF, Fiducial and Sideband are represented by
Fig. 6.6. Red and black histograms correspond to Beam ON and Beam OFF. Fiducial andSideband are defined as shown with yellow bands and a green band, respectively. Beam OFF
is subtracted from Beam ON, that result in the blue histogram with five peaks. The numberof peaks indicate the number of bunches. Before the arrival of bunches, other five peaks
are found in red and black histograms. These are caused by prompt γ rays and eﬀectively
removed by subtraction.

z

Figure 6.6: TOF of Beam ON (red), Beam OFF (black), and Beam OFF subtracted by
Beam ON (blue).

Figure 6.7: Definition of the fiducial time.

76

Chapter 6. Signal estimation

The passage of neutron bunch in the TPC is indicated in the center of energy depositin z direction versus TOF (Fig. 5.1), and the fiducial region is determined as illustrated inFig. 6.7. Although the fiducial time per kicker pulse corresponds to only about 2.3 ms, itmuch increases the signal-to-noise ratio. On the other hand, we have 6 ms of sideband per
kicker pulse. Note that the slow neutrons, which have been generated by previous kicker
pulse, continuously distribute in the outside of bunches due to the failure performance of
SFC.
In this way, all events are categorized into a (Beam ON, Fiducial), b (Beam ON,
Sideband), c (Beam OFF, Fiducial), d (Beam OFF, Sideband) and e others. e is
not taken into account in the analysis. The backgrounds which are independent from theneutron interactions can be removed by Eq. (6.1).

O

O

O

O
O

O O O O( a − b)−( c − d)

O

(6.1)

Before we perform the subtraction, Beam OFF and sideband events are normalized tocompensate the diﬀerence of beam flux and time width. After that, the remaining neutron
induced backgrounds are corrected in Sec. 6.4.

6.3.1

Cut

Eﬃcient reduction of backgrounds is achieved by introducing parameters to reflect theirdiﬀerentiation. Some parameters are described in the following. At first, a reference time isA

Pulse height A
Integral A

Pedestal A

B
Threshold B
Pedestal B
tTrig. B

Trig. A

30μsecFigure 6.8: Definition of parameters. First and second triggered channels are illustrated.

defined as the time when the first anode wire exceed the threshold. Then, the time window
77

Chapter 6. Signal estimation

µ

µ

µ

with a width of 100 sec is adjusted to set the reference time to be 30 sec. Pedestal iscalculated from the average of the pulse height within the range from 0 to 28 sec, and
it is employed as the reference point of the pulse height. The energy deposit is obtainedby integrating the pulse height after 30 sec. By using the X-ray events (5.9 keV) as thestandard of the energy calibration, both of pulse height and integral are converted into
energy.
Following cuts are applied to improve the purity of the neutron decay candidates.

µ• Fiducial TOF Cut
The prompt γ rays from the magnetic super mirrors are greatly suppressed by limiting
the TOF.
• Drift length ≤ 190 mm
Cosmic rays are not completely rejected by the veto scintillators because some ofthem pass through the gap between scintillators. Characterized by the long track goes
through the TPC, the cosmic rays penetrate in y direction are well discriminated byadopting this cut. Drift length is calculated by the maximum time diﬀerence among
triggered anode wires and the drift velocity.
• Energy deposit in the anode wires > 5 keV
Point-like energy deposit are detected along with the beam axis, due to the neutron
capture reactions in CO2 gas. These events are discriminated by requiring the energy
deposit to be more than 5 keV.
• ph/int < 0.8
The 3 H decay background is removed by introducing the parameter “ph/int” whichreflect the waveform features. ph/int is defined as the ratio of the maximum single
pulse height to total energy deposit. When low energy deposit is detected, the pulse
height will fit within the dynamic range of ADC. In this case, the waveform keep thesame shape with the template (Fig. 5.7) and its height is proportional to the energy
deposit. These events distribute ph/int of around 1.0 and this is just the case of the3
H background. As for the neutron decay, ph/int is likely to be small because theelectrons trigger many anode wires and the energy deposit come to large comparedwith the maximum pulse height. Although the background with the energy morethan 15 keV are not removed by this cut due to saturation of ADC, they are able tobe subtracted.
The performance of each cut is shown in Figs. 6.9 ∼ 6.14. For example, Fig. 6.9 shows thedrift length of data. The red histogram is “Beam ON, Fiducial” and that includes signal
events. Other histograms are “Beam ON, Sideband” (magenta), “Beam OFF, Fiducial”(blue) and “Beam OFF, Sideband” (cyan), where histograms are normalized by the beam
monitor counts and TOF. The thresholds are indicated by green lines. All of four histograms
78

Chapter 6. Signal estimation

are perfectly overlapping in the one side of the threshold. Obviously, this cut serve to reducethe background and also it is indicated that subtraction can fulfill its role. The remaining
cosmic ray will be subtracted in Sec. 6.3.2.

1800
4000

1600

3500

1400

3000

1200

2500

1000

2000

800

1500

600

1000

400

500

200

0
0

50

100

0
0

150
200
250
Track length in y direction [mm]

50

100

150
200
250
Track length in y direction [mm]Figure 6.9: Comparison of the drift length Figure 6.10: Comparison of the drift length
among data before subtraction. Histograms between arbitrary scaled MC samples of theare normalized by the beam monitor counts neutron decay (red) and cosmic ray (blue).
and TOF.
800

500

700
400
600
500

300

400
200

300
200

100
100
0
0

5

10

15

20

25

30

35

0
0

40
45
50
Enegy deposit [keV]

5

10

15

20

25

30

35

40
45
50
Enegy deposit [keV]

Figure 6.11: Comparison of the energy deposit Figure 6.12: Comparison of the energy deposit
among data before subtraction. Histograms between arbitrary scaled MC samples of theare normalized by the beam monitor counts neutron decay (red) and the neutron capture
and TOF.
reaction in CO2 (blue).

79Chapter 6. Signal estimation

1800
2500
1600
1400

2000

1200
1500

1000
800

1000
600
400

500

200
0
0

0.2

0.4

0
0

0.6
0.8
1
1.2
Ratio of pulse height to energy deposit

0.2

0.4

0.6
0.8
1
1.2
Ratio of pulse height to energy deposit

Figure 6.13: Comparison of ph/int among Figure 6.14: Comparison of ph/int between
data before subtraction. Histograms are nor- arbitrary scaled MC samples of the neutron
malized by the beam monitor counts and decay (red) and the 3 H decay (blue).
TOF.

6.3.2

Subtraction

The backgrounds with following characteristics are removed by the subtraction, “Fiducial Sideband” and “Beam ON - Beam OFF”.
• Constant in time structure• Not related to neutron reactions
Ones of former are the radioactivation backgrounds, such as 20 F decay (τ = 11.07 s) and 8 Li
decay (τ = 839.9 ms), result from (n, γ) reactions:
F →
8
Li →

20

Ne + e − + ν¯e + 7.02 MeV,
8
Be + e − + ν¯e + 16.0 MeV.

20

(6.2)
(6.3)

The rate can be consider to constant in time because they have long lifetime compared withthe cycle of kicker pulse (40 ms). These backgrounds are removed by subtracting Sideband
from Fiducial.
The other backgrounds are cosmic ray and the 3 H decay. Though some of them would
be left behind due to the ineﬃciency of the cuts, they are well removed by subtracting
Beam OFF from Beam ON. Figures 6.15 ∼ 6.17 show the results of subtraction and thesimulation is normalized by the statistics of data. Compared with Figs. 6.9, 6.11 and 6.13,
it is clear that the neutron decay is hardly eliminated and cuts are appropriate to increase
the signal-to-noise ratio.
80Chapter 6. Signal estimation

1800
1600
1400
1200
1000
800
600
400
200
0
0

50

100

150
200
250
Track length in y direction [mm]Figure 6.15: Comparison of the drift length between data after subtraction (black) and MC
sample of the neutron decay (red) which is normalized by the statistics of data.

500

400

300

200

100

0
0

5

10

15

20

25

30

35

40
45
50
Enegy deposit [keV]

Figure 6.16: Comparison of the energy deposit between data after subtraction (black) andMC sample of the neutron decay(red) which is normalized by the statistics of data.

81

Chapter 6. Signal estimation

1800
1600
1400
1200
1000
800
600
400
200
0
0

0.2

0.4

0.6
0.8
1
1.2
Ratio of pulse height to energy deposit

Figure 6.17: Comparison of ph/int between data after subtraction (black) and MC sampleof the neutron decay (red) which is normalized by the statistics of data.

There would be an uncertainty arise from diﬀerent LiF shutter condition of Beam ON and
Beam OFF. When the shutter is open, more γ rays could pass through the shutter comparedwith the case of Beam OFF, and the γ rays might remain in the neutron decay candidates
after the subtraction. The remaining γ rays are estimated by using Particle and Heavy
Ion Transport code System (PHITS) [48] and GEANT simulation, and the uncertainty areincluded in the neutron lifetime.

6.4

Corrections

The remaining backgrounds are derived from the neutron interactions as described in chapter
4. We will enumerate possible backgrounds and make a correction respectively.

6.4.1
3

Corrections for the 3 He(n, p)3 H candidates

He(n, p)3 H candidates include followings.
• 3 He(n, p)3 H without neutron scattering (signal)• 3 He(n, p)3 H after neutron scattering (background)• 14 N(n, p)14 C
82

Chapter 6. Signal estimation• 17 O(n, α)14 C• Neutron decay• Pileup of events
3

He(n, p)3 H after neutron scattering

We will remove 3 He(n, p)3 H events which accompanied with neutron scattering. Note that
14
N(n, p)14 C and 17 O(n, α)14 C reactions are not distinguishable from 3 He(n, p)3 H in highgain operation and they are not yet separated from signal events at this point. The key
feature of the signal events is that the starting point of the track is concentrated in the
on-axis region. In other words, only the backgrounds are distributed in the oﬀ-axis region.
The origin of the proton from 3 He(n, p)3 H is suitably reconstructed by a parameter “fce”
which is defined as the center of energy deposit in the field wires as shown in Fig. 6.18.
Where a single unit of fce corresponds to 12 mm. The MC sample of the background is scaled
so as to oﬀset the number of events in the oﬀ-axis region of the data, and the total numberof background events have been estimated. In this estimation, the on-axis region is definedas 7≤fce<16 and it suﬃciently covers the beam cross section. While the oﬀ-axis region isthe complement of the on-axis region. Consequently, signal candidates are evaluated bysubtracting the background from data.
×10

3

5

160

10

140
104

120
100

3

10

80
60

102

40
20
0
0

10
2

4

6

8

10

12

14

16
18
20
22
24
Energy center of field wire

0

2

4

6

8

10

12

14

16
18
20
22
24
Energy center of field wire

Figure 6.18: The center of energy deposit in the field wires, displayed with linear (logarithmic) scale in the left (right). Red and blue histograms correspond to the MC samples ofsignal events and neutron scattering background events. The center of TPC in x directionis fce = 11.5.
It is important to note that the number of backgrounds in the on-axis region was notderived from data driven approach. It just relies on the MC simulation resulted fromtheoretically calculated cross section, however the systematical uncertainty arise from thereproducibility of the MC sample of the background is not taken into account in this thesis.
With advanced understanding of the backgrounds, the problem would be eliminated by83Chapter 6. Signal estimation

including the scattered events as the signal. The probability of the neutron scattering isestimated from the ratio of the number of background events to that of signal.
Neutron decay# of events

In the separation of signal candidates explained in Sec. 6.2, a certain percentage of theneutron decay events exceed the threshold and mistaken as 3 He(n, p)3 H candidates (Fig.
6.19). The ratio of leakage is calculated by applying the 3 He(n, p)3 H selection cuts to theMC sample of neutron decay. By combining with the measured neutron decay events, theneutron decay contamination can be evaluated. The correction is inversely proportional tothe amount of 3 He.

104

3

10

102

10

1
0

5

10

15

20

25
30
35
40
45
50
Maximum pulse height of field wires [keV]

Figure 6.19: Maximum pulse heigh of the field wires in the neutron decay. The cut thresholdis indicated with green line.

Pileupµ

A single event is recorded by TDC with the time window of 100 sec, and multiple reactions
would be detected by a certain probability. Since we calculate the dead time based on thenumber of triggers, signal events have to be counted similarly. For that reason, we definethat when multiple reactions are detected in a single event, only the first one is counted.
In this definition, we have to correct the events which were not triggered by 3 He(n, p)3 H
reaction, and the possible combinations of the reactions are categorized as below.
(a) A background event followed by the 3 He(n, p)3 H reaction.
(b) Pileup of high energy backgrounds.
84

Chapter 6. Signal estimation(c) Combinations of a high energy background and a neutron decay candidate.
The high energy backgrounds include 3 He(n, p)3 H reaction after neutron scattering and a
portion of cosmic rays. (b) and (c) do not contain signal events and therefore account for
only 0.0003 % of the 3 He(n, p)3 H candidates. Some of them might have been removed byprevious procedures. Eventually, the correction is dominated by (a), result in about 0.07 %of the candidates.
14

N(n, p)14 C reaction

The measurements with low gain operation were conducted to estimate the contaminationof 14 N. Low gain measurements were inserted about 4 times in each gas mixture. Figure 6.20
shows the energy deposit of the low gain measurement. The peak of 3 He (764 keV) and thatof 14 N (626 keV) are fitted by double-gaussian function (blue), while another peak can befound in higher energy region, that includes 17 O(n, α)14 C reaction and pileup of 3 He(n, p)3 H(red). Compared with 3 He, the amount of 14 N is obtained by using the ratio of the numberof events and the capture cross sections. As shown in Fig. 6.21, the amount of 14 N at a
certain time is calculated by interpolating the transition of the ratio. The contaminationof 14 N(n, p)14 C reaction result in about a few percent of the 3 He(n, p)3 H candidates. Notethat what aﬀect to the uncertainty of the lifetime is the overlap of two peaks, that is taken
as the statistical uncertainty of 14 N and not more than 0.1 %.

103

102

10

1
0

200 400 600 800 1000 1200 1400 1600 1800 2000
keV

Figure 6.20: Energy deposit of the low gain measurement.

85

14

3

N/ He

Chapter 6. Signal estimation

0.01
0.008
0.006
0.004
0.002
0

5

10

Elapsed time [day]Elapsed Time [Day]Figure 6.21: Transition of the ratio of neutron capture events, 14 N/3 He.

17

O(n, α)14 C reaction

As it is indicated in Fig. 6.20, 17 O(n, α)14 C reaction was observed with low gain operation.
The energy deposit of the capture reaction is 1844 keV, that is about twice the energy
deposit of 3 He(n, p)3 H reaction. We identified single tracks with such a high energy deposit
and its rate agreed with the expectation. Thus we concluded the existence of 17 O(n, α)14 C
contamination and they were corrected by using the capture cross section (0.236 barn) andthe natural abundance of 17 O in CO2 gas (0.038 %). Under the condition of 4 He 85 kPa +CO2 15 kPa, the partial pressure of 17 O is to be 11.4 Pa. The contribution of the correction
accounts for about 0.5 %.

6.4.2

Corrections for the neutron decay candidates

The neutron decay candidates include followings.
• Neutron decay without neutron scattering (signal)• Neutron decay after neutron scattering (background)• (n, γ) reactions from the LiF tiles• 3 He(n, p)3 H• Pileup of events
86Chapter 6. Signal estimation

Gas induced backgrounds
Here we will deal with the backgrounds derived from neutron scattering. As mentioned
in the previous section, the oﬀ-axis region is occupied by the backgrounds so that theidentification of the starting point is also essential to count the neutron decay, and we
introduce two parameters. One works as to separate the backgrounds and another indicatesthe starting point of the track. The former parameter, “XValue” is defined as the distance
between the nearest hit anode wire to the beam axis. If a neutron was scattered to the oﬀaxis region and its energy deposit was limited to there, it is easily eliminated by requiring
XValue to be less than 3.
The latter parameter, “DC” is defined as the distance between the beam axis to theedge of the track which is closer to the beam axis. The definition of DC is illustrated in Fig.
6.22, viewing the xy plane of the TPC. The neutrons go through the center of TPC andthree arrows indicate the electron tracks which start from red points. The center of TPC inx direction is shown as green dotted line. DC corresponds to the distance between the redpoint to the green line. The backgrounds are dominated by the ones derived from LiF tiles
and they are more likely to take larger value of DC. Therefore, the signal-to-noise ratio canbe improved by applying DC to be less than 3 (Fig.6.23). Since a unit length of XValueis made to be 12 mm and that is the same with DC, both of the regions, “XValue≤3” and“DC≤3”, fully cover the beam cross section.

Figure 6.22: Drawing of the definition of DC. The TPC is viewed in xy plane and theelectron tracks are illustrated as blue arrows. The red points and the green dotted line
indicate the origin of the tracks and the beam axis.

The number of signal events have been estimated by using three kinds of MC samples,the signal neutron decay, the background neutron decay and the prompt γ rays from LiF
tiles. Each MC sample is scaled so as to satisfy the following constraints.
87

Chapter 6. Signal estimation• The total number of events of all MC samples are equal to that of data.
• In XValue>3, the sum of two background samples is equal to data.
• The ratio of the background neutron decay to the signal neutron decay is equal to theprobability of scattering.
The probability of the neutron scattering have been calculated in the previous section. After
subtracting the backgrounds from data, the number of signal events is obtained by applying
the cut, DC≤3.

104

12000

10000

3

10
8000

102

6000

4000
10
2000

0

2

4

6

8

10

1

12
XValue

0

2

4

6

8

10

12
XValue

0

2

4

6

8

10

12
DC

104

9000
8000

3

7000

10

6000
5000

102

4000
3000
10

2000
1000
0

2

4

6

8

10

1

12
DC

Figure 6.23: XValue (top) and DC (bottom) of the data and the MC samples. Red, green andblue histograms correspond to MC samples of the signal neutron decay, (n, γ) backgroundand the neutron decay background followed with scattering. Each parameter is displayedwith linear and logarithmic scale on the left and right.

88Chapter 6. Signal estimation
3

He(n, p)3 H reaction

He(n, p)3 H reaction is rarely mistaken as neutron decay because we have adjusted thethreshold to minimize the contamination and almost no correction is required. Figure 6.24
shows the distribution of the separation parameter.

# of events

3

102

10

1

0

5

10

15

20

25
30
35
40
45
50
Maximum pulse height in field wires [keV]

Figure 6.24: Maximum pulse heigh of the field wires in 3 He(n, p)3 H reaction. The cut
threshold is indicated with green line.

PileupAs it is the same with 3 He(n, p)3 H candidates, only the event which was triggered by theneutron decay have to be counted. Followings are the combinations of events to be corrected.
(A) A low energy background followed by signal neutron decay.
(B) Pileup of low energy backgrounds.
(C) Signal neutron decay followed by a 3 He(n, p)3 H candidate.
Low energy backgrounds are the events such as neutron decay after scattering, (n, γ) backgrounds in the LiF tiles, the neutron capture in CO2 and cosmic ray. (C) should be counted
as the neutron decay but previously categorized as 3 He(n, p)3 H candidates and have been
removed in Sec. 6.4.1. That account for 0.2 % of the neutron decay candidates. In the caseof (A), CO2 is important background since it has high rate and less likely to be eliminated bydetected with neutron decay. (B) have negligible influence, and finally correction of pileup
result in 0.08 % of the neutron decay candidates.
89

Chapter 6. Signal estimation

6.5

Summary of the number of signal events

We have started first physics data taking in 2016. Combined with engineering data, weprepared six gas mixtures and accumulated 6.37 × 104 events of neutron decay (Tab. 6.2).
The uncertainties of number of signal events were evaluated as summarized in Tabs. 6.3 and6.4. The precision of the number of signal events is restricted by statistics of neutron decay.
The systematical uncertainties of the neutron decay events have significance influence andmainly they are related with γ ray backgrounds, the neutron capture reaction in CO2 andpileup of events.
Series
1
2
3
4
5
6
Total

Nβ
8.5(3)×103
8.5(2)×103
3.6(2)×103
1.49(4)×104
1.38(4)×104
1.44(4)×104
6.37(8)×104

Nn2.436(6)×105
2.003(6)×105
9.47(3)×104
6.92(1)×105
1.810(5)×105
3.580(7)×105
1.770(3)×106

Table 6.2: Number of signal events.

Series1
Systematical errors
Neutron decay contamination 0.03
Pileup0.08
14
14N(n, p) C contamination
0.047
17
O(n, α)14 C contamination
0.025
Subtotal
0.10
Statistical error of data
0.21
Total
0.23

2
0.05
0.11
0.066
0.028
0.14
0.24
0.28

3

4

0.03 0.02
0.07 0.07
0.076 0.019
0.026 0.014
0.11 0.08
0.34 0.13
0.36 0.15

5

6

0.08
0.07
0.12
0.050
0.16
0.25
0.30

0.05
0.07
0.060
0.026
0.11
0.18
0.21

Table 6.3: Uncertainties of the number of 3 He(n, p)3 H events in percentage.

90

Chapter 6. Signal estimation

SeriesSystematical errors
LiF shutter condition
γ spectrum of LiF tile
PileupCO2 contamination
3
He contamination
S/N of SFC
Subtotal
Statistical error of data
Total

1

2

3

4

5

6

1.3
0.23
0.29
0.27
0.06
0.020
1.3
2.7
3.0

0.12
0.024
0.45
0.25
0.05
0.016
0.5
2.2
2.2

0.12
0.22
0.19
0.30
0.00
0.026
0.4
5.1
5.1

0.59
0.065
0.35
0.23
0.00
0.051
0.7
2.5
2.6

0.43
0.16
0.10
0.30
0.01
0.017
0.6
2.6
2.7

0.33
0.037
0.18
0.27
0.00
0.022
0.5
2.6
2.6

Table 6.4: Uncertainties of the number of neutron decay events in percentage.

91

Chapter 7
Eﬃciency
7.1

Evaluation of signal eﬃciency

Signal eﬃciency is evaluated by applying the cuts to the MC samples. In this process, wehave to take care of followings.
• The uncertainty of each cut parameter has to be estimated correctly.
• Considering the uncertainty of the parameter, threshold should be set within small
fluctuation of eﬃciency to keep the precision of evaluation.
• Suppression of the statistical error is also critical role of the cuts.
Followings are the cuts introduced in chapter 6.
Cut
Noise suppression
Fiducial TOF
Signal separation
Cosmic ray suppression
Discrimination of energy deposit3
H suppression
On-axis track selection

Source of uncertainty
Negligible
Negligible
Energy calibration
Drift velocity
Energy calibration
Deviation of ph/int
Beam distribution

Table 7.1: Cuts for the neutron decay.

92Chapter 7. Eﬃciency
Cut
Noise suppression
Fiducial TOF
Signal separation

Source of uncertainty
Negligible
Negligible
Energy calibration

Table 7.2: Cuts for the 3 He(n, p)3 H reaction.

7.2

Uncertainties of the cut parameters

At first, we will deal with the sources of uncertainties in cut parameters, these are the drift
velocity, the energy calibration, deviation of ph/int and reproducibility of beam distribution.
Drift velocity
It was found out that the drift velocity depends on the position in y direction. That would
be caused by non-uniformity of the electrical field, and generate large uncertainty of drift
length. In order to measure the position dependence, the absolute y positions of the ionizedparticles were determined as it is explained in Sec. 3.8, and the result is shown in Fig.
7.1. The velocity standard is equal to the velocity at the center of TPC, and the maximum
deviation is given when ionized particles drift from distant position. The uncertainty of drift
velocity was estimated to be less than 10 %. Therefore, the loose threshold was applied tosuppress the ambiguity in the cut eﬃciency.

Drift velocity [cm/µs]

2

1.5

1

0.5

0

5

10

15

20

25

30

Depth [cm]Figure 7.1: Drift velocity vs. y position, measured with cosmic ray events.

93

Chapter 7. Eﬃciency

Energy calibration

100
90

Anode energy deposit [keV]

Anode energy deposit [keV]

As it is explained in Sec. 3.7, energy deposit is calibrated by using the X-ray source. There
are two possible reasons which lower the precision of calibration. One is the position ofenergy deposit. If ionized particles have been generated in a distant place from standard
y position, the uncertainty of the energy calibration would be enlarged. Another thing is
the transition of the gain due to increasing of outgas. If the vacuum condition is bad, thegain will be immediately lowered and outgas enhance the position dependence of energy
calibration over time. The reproducibility of energy calibration is estimated by comparing
data and the MC sample of cosmic ray for the most probable value of energy deposit (Fig.
7.2). The uncertainty of energy calibration resulted in 5 ∼ 9 %.

103

80
70
60

102

50
40

102
90
80
70
10

60
50
40

30

30

10

20

1

20

10
0
0

100

10
50

100

150

200

250

300

350

400

450
500
Range [mm]

0
0

1

50

100

150

200

250

300

350

400

450
500
Range [mm]

10

20

30

40

50

60

70
80
90
100
Anode energy deposit [keV]

100
90
104

80
70
60

103

50
40
30

102

20
10
0
0

100

200

300

400

500
Range [mm]0Figure 7.2: Comparison of data and MC sample of cosmic ray. Energy deposit vs. track
length of data (top left) and that of MC sample (top right). The track length of data (black)and MC sample (red) are shown in bottom left, and the energy deposit of data (black) andMC sample (red) are shown in bottom right.

94

Chapter 7. Eﬃciency

Deviation of ph/int
The ph/int works to remove the event which have low energy deposit (< 15 keV) and the
waveform is similar to the template. In the case of photoelectric events generated by Xray from the calibration source, the energy deposit is 5.9 keV and they are suitable for
evaluating the ambiguity of ph/int. The uncertainty of ph/int was evaluated from thestandard deviation of the X-ray events, resulted in 0.033 which correspond to 4 % of theuncertainty of the threshold.
105

104

104

103

103

102

102

10

10

1

1
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2
ph/int

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2
ph/intFigure 7.3: Deviation of ph/int measured with the X-ray source positioned y = 75 mm (left)
and y = -75 mm (right).

Reproducibility of the beam distribution
To reproduce the beam distribution, another measurement was conducted and the data
was input to the MC simulation (see appendix B). We consider two possible sources of
uncertainties, one is the resolution of detector and another is the precision of detectoralignment. Each uncertainty is estimated to be 1 mm in x direction and we concluded thatthe irreproducibility of the beam distribution is not more than 2 mm.

7.3

Uncertainties of cut eﬃciencies

Based on the ambiguities of parameters, the thresholds were determined to minimize thestatistical errors and the systematical errors. Except for the parameter “DC”, the systematical errors arise from cuts are estimated by the fluctuation of the cut eﬃciencies. The
performance of the cuts are shown in Figs 7.4 ∼ 7.9. The uncertainties of the parameters
are indicated with yellow bands and the thresholds are shown with green lines.

95

0.05

Cut efficiency

Statistical error

Chapter 7. Eﬃciency

0.045
0.04

1
0.9
0.8

0.035

0.7

0.03

0.6

0.025

0.5

0.02

0.4

0.015

0.3

0.01

0.2

0.005

0.1

0
0

5

10

15

20

25

30

35

0
0

40
45
50
Enegy deposit [keV]

5

10

15

20

25

30

35

40
45
50
Enegy deposit [keV]

0.05

Cut efficiency

Statistical error

Figure 7.4: Statistical error vs. Anode energy Figure 7.5: Cut eﬃciency vs. Anode energy
deposit.
deposit.

0.045
0.04

0.8

0.035

0.7

0.03

0.6

0.025

0.5

0.02

0.4

0.015

0.3

0.01

0.2

0.005
0
0

0.1
50

100

0
0

150
200
250
Track length in y direction [mm]Figure 7.6: Statistical error vs. Drift length.
0.05
0.045
0.04

50

100

150
200
250
Track length in y direction [mm]Figure 7.7: Cut eﬃciency vs. Drift length.
Cut efficiency

Statistical error

1
0.9

1
0.98
0.96

0.035
0.03

0.94

0.025

0.92

0.02
0.9

0.015
0.01

0.88

0.005
0
0

0.86
0.2

0.4

0.6
0.8
1
1.2
Ratio of pulse height to energy deposit0

Figure 7.8: Statistical error vs. ph/int.

0.2

0.4

0.6
0.8
1
1.2
Ratio of pulse height to energy deposit

Figure 7.9: Cut eﬃciency vs. ph/int.
96

Chapter 7. Eﬃciency# of events

In order to estimate the uncertainty derived from DC, MC simulation was re-weighted
to shift the beam distribution in x direction by 2 mm (Fig.7.10). We calculate the neutron
decay candidates with and without shifting the beam distribution and the uncertainty of cut
eﬃciency is obtained by the diﬀerence of the number of candidates. The threshold of DC
is suﬃciently outside of the beam crossing, therefore the uncertainty of the cut eﬃciency
resulted in not more than 0.03 %.

7000
6000
5000
4000
3000
2000
1000
0

− 40

− 20

0

20

40
x [mm]

Figure 7.10: Beam distribution in x direction. Each histogram represents the original
distribution (black), shifted by +2 mm (red) and shifted by -2 mm (blue).

7.4

Summary of eﬃciency

The uncertainties of eﬃciency is summarized in Tabs. 7.4 and 7.5. In addition to theuncertainties explained in the previous section, the eﬀect of neutron polarization and W value are included. The largest error is generated by the separation of neutron decay and3He(n, p)3 H reaction. The amount of energy deposit is the only parameter used to separate
the candidates, therefore the systematical error is originated from energy calibration. The
separation could be improved by adopting additional parameters such as length or shape ofthe track.
The estimation of number of signal events depends on the identification of the originof the track, the ambiguity of eﬃciency is avoided by loose threshold. Further, lower limitof the energy deposit is set to suppress the neutron capture reactions in CO2 , and theuncertainty is not remarkable because the threshold is set within small fluctuation of theeﬃciency. As for the evaluation of 3 He(n, p)3 H reaction, we have achieved high eﬃciency of97

Chapter 7. Eﬃciency

almost 100 %, besides its uncertainty is less than 0.01 %.
Series123456ϵβ [%]
ϵn [%]
94.1(6) 99.986(4)94.2(5) 99.997(4)94.3(5) 99.978(6)94.0(6) 99.987(4)94.1(9) 99.995(13)93.9(8) 99.999(8)Table 7.3: Eﬃciencies of signals.
SeriesStatistic of MC
Signal separation
Cosmic ray suppresion
Discrimination of energy deposit3
H suppression
On-axis track selection
Neutron polarization
W -value
Total

1
0.08
0.45
0.18
0.07
0.05
0.09
0.13
0.35
0.63

2
0.08
0.31
0.18
0.07
0.05
0.02
0.13
0.35
0.53

3
0.08
0.88
0.19
0.16
0.07
0.12
0.13
0.35
1.00

4
0.08
0.57
0.18
0.12
0.05
0.04
0.13
0.35
0.72

5
0.08
0.88
0.20
0.18
0.05
0.02
0.13
0.35
0.97

6
0.08
0.74
0.17
0.16
0.06
0.03
0.13
0.35
0.87

Table 7.4: Uncertainties of the eﬃciency of neutron decay in percentage.
SeriesStatistic of MC
Signal separation
Total

1
0.004
0.000
0.004

2
3
0.002 0.005
0.004 0.004
0.004 0.006

4
0.004
0.000
0.004

5
0.002
0.013
0.013

6
0.001
0.008
0.008

Table 7.5: Uncertainties of the eﬃciency of 3 He(n, p)3 H reaction in percentage.

98

Part IV
Conclusion

Chapter 8
Conclusion and future prospects
Precise measurement of the neutron lifetime is the key to increase the accuracy of theprediction of Big Bang cosmology and the light nuclei production in the early universe, since
the neutron lifetime has direct influence to determine the relative abundance of primordial
helium and also the time scale of thermal equilibrium of the weak interactions.
We measured the neutron lifetime with accelerator based neutron beam at J-PARC.
A distinctive feature of our experiment is the low level background condition that havebeen achieved by originally developed TPC and SFC. Radioactive backgrounds and neutron
correlated backgrounds are mitigated with material selection of the drift cage. SFC is thenew optical device to switch the neutron beam and is able to adjust the length of neutron
bunches, that much contribute to discriminate prompt γ rays produced in the upstream.
In addition, our approach is diﬀerent from the bottle experiments in the point of view ofsystematical uncertainty since neutron decay is counted by detecting the electron.
In 2014 and 2015, engineering data was taken so as to establish the analytic method. Our
first physics data have been taken in 2016, and the blind analysis was performed to avoid
the possibility of biasing. Physics data is combined with engineering data and accumulated
data correspond to 12 days of data acquisition at averaged beam power of 170 kW. We
present our first result of measurement as below.
τn = 899 ± 10 (stat.) ± 911 (syst.) sec (Combined)

99

Chapter 8. Conclusion and future prospects
Series1 (May 2014)
2 (Apr. 2015)
3 (Apr. 2016)
4 (Apr. 2016)
5 (May 2016)
6 (Jun. 2016)

Beam power [kW] DAQ [day]
240
1.4
430
0.7
170
0.8
170
3.0
170
2.8
160
3.0

τn [sec]
952 ± 26 (stat.) ± 15
15 (syst.)
908 ± 20 (stat.) ± 87 (syst.)
901 ± 46 (stat.) ± 118 (syst.)
890 ± 22 (stat.) ± 109 (syst.)
881 ± 24 (stat.) ± 129 (syst.)
870 ± 23 (stat.) ± 108 (syst.)

Table 8.1: Summary of the results of the neutron lifetime measurement.

The backgrounds originated from neutron interactions were studied in detail and they
were removed by data driven approach, as much as possible. MC simulation was used
to estimate the eﬃciency and the backgrounds induced by neutron scattering. In orderto reconstruct the measurement, we conducted additional measurements as described inappendix B and C, and the results were input to the simulation. In addition, uncertainties
in cut eﬃciency were avoided by applying the loose threshold.
Statistical and systematical errors account for about 1 % respectively, and systematicalerrors are summarized in Tab. 8.2. It is practically possible to improve the statisticalaccuracy by long-term operation at 500 kW. Besides, we have plans to upgrade the setup
and that is explained in the latter part of this chapter.
Systematical errors can be classified into (a) ones that can be reduced by increasing
the statistics of data, (b) another would be decreased by statistics of simulation, (c) others
have to be measured more precisely, and (d) the others are improved by making advanceson analytic methods. In the following, we explain how to reduce systematical errors with
examples.
(a) Statistics of data
In the estimation of number of signal events, uncertainties are derived from the backgrounds, such as 14 N(n, p)14 C and pileup. The uncertainties in these corrections aregoverned by the measurement of event rate, therefore they can be reduced when statistics are increased. We have the upgrade plan to increase the beam flux.
(b) Statistics of simulation
Important uncertainties are derived from γ ray and are dominated by the statistics ofsimulation, because γ ray have low probability of interaction. The uncertainties would
be reduced by increasing the statistics of simulation and improvement in analysis isalso substantial.
(c) Cross sections of neutron capture reactions
Since the number of neutron capture reactions in 3 He and CO2 were calculated by100

Chapter 8. Conclusion and future prospects

using the capture cross sections, the uncertainties were determined by the precision ofcross sections and they have to be measured more precisely.
(d) Methods of analyses
There are still room for improvement in analytic methods. For example, the largest
influence to the uncertainty of cut eﬃciency is generated by the separation of theneutron decay and 3 He(n, p)3 H reaction. Separation is performed by using only theenergy deposit and that would be improved by introducing a parameter to enhance
topological diﬀerences of the tracks. The other important uncertainties are originatedfrom γ rays and they would be eﬀectively discriminated by identifying the starting
point of the decay electron in z direction.

Series
1
Nβ
1.3
Nn
0.10
ϵβ
0.63
ϵn
0.004
ρ
0.6
σ0
0.13

2
0.5
0.14
0.53
0.004
0.5
0.13

3
0.4
0.11
1.00
0.006
0.4
0.13

4
0.7
0.08
0.72
0.004
0.5
0.13

5
0.6
0.16
0.97
0.013
0.7
0.13

6
0.5
0.11
0.87
0.008
0.5
0.13

Table 8.2: Systematical errors of the neutron lifetime in percentage.

8.1

Upgrade plans

As the future prospects, we have plans to improve the precision of measurement. One
is to operate with lower gas pressure, that is eﬀective for reducing the neutron induced
backgrounds, and another is the enlargement of the setup to increase the beam flux.
Operation of TPC with lower gas pressure to reduce neutron induced backgrounds
Some of the backgrounds were caused by neutron scattering and the contamination accountfor a few percent of the neutron decay events. In order to avoid the ambiguity of simulationand to perform the measurement with data driven approach, the probability of scattering has
to be reduced and we have been studying the performance of TPC operated with decreased
pressure. While we have reported the measurement with 100 kPa in this thesis, anotherconfiguration of 50 kPa have been demonstrated and the measured probability of scattering
is roughly proportional to the gas pressure.
101

Chapter 8. Conclusion and future prospects

For the practical operation, mainly we have two problems to be solved. One is heatgeneration of the preamplifiers, that would locally increase the temperature around thepreamplifiers. As the result, the uncertainty would be generated by the non-uniformity of3
He gas density. We have been developing a new preamplifier with higher gain and lower
heat generation. Another problem is the reduction of detection eﬃciency, since MWPC has
to be operated with lower voltage to avoid an electric discharge. On the other hand, we
observed the reduction of the eﬀect of attenuation. The drift velocity become 1.5 times
faster and that contribute to reduce chances of interactions with gases. Besides, that might
help to conduct longer operation with a gas filling.
Modification of SFC and collimators to increase the neutron beam intensity
In the present experimental setup, we can achieve the statistical accuracy of below 0.1 %by accumulating data correspond to 100 days at 1 MW operation, while the upgrade of the
setup is planed to move forward. Firstly, larger collimaters and larger mirrors of SFC aredesigned to expand the beam cross section, because there are losses of neutron due to small
acceptance of the setup. Secondly, TPC is also enlarged to adopt the larger beam crosssection.

Collimater
B4 C collimater size [mm2 ]LiF collimater size [mm2 ]MirrorMirror size [mm3 ]Number of 1st and 2nd mirrors
Number of 3rd mirror

Present

Upgrade plan

40 × 40
25 × 20

100 × 30
100 × 30

140 × 30 × 0.7 200 × 100 × 0.3
5
8
5
10

Table 8.3: Upgrade plans of the setup. B4 C collimater and LiF collimater are positioned
1185 mm and 1570 mm downstream of the target.

The improvement of the beam flux have been estimated by using PHITS simulation, andthe result is shown in Tab. 8.4 and Fig. 8.1. When enlarged collimaters and mirrors are
adopted, we expect to obtain 23.5 times higher beam flux and the statistical accuracy of onorder of 0.1 % will be achieved by 5 days of DAQ time at the 500 kW operation.

102

Chapter 8. Conclusion and future prospects

Beam flux [neutron/s·MW]
Present
5.96(29) × 106
Enlarged mirrors
1.49(05) × 107
Enlarged mirrors and collimaters1.40(02) × 108
Table 8.4: Upgrade plans and expected beam flux.

Figure 8.1: Improvement of the statistical error.

103

Appendix A
Radiative neutron decay
Radiative neutron decay shares second largest branching ratio among the decay modes ofneutron. Depend on the way of bremsstrahlung, three kinds of Feynman diagrams are
possible as shown in Fig. A.1.

p

n

p

n

p

n

1

⌫e

⌫e

⌫e

e

e

e

1

1

1

1

Figure A.1: Feynman diagrams of radiative neutron decay. The electron bremsstrahlung(left), the proton bremsstrahlung (center) and bremsstrahlung from weak vertex (right).
1

Each branching ratio is determined by the photon energy, in other words, the ratio is
determined by the energy of the electron and that of the proton. The leading order isthe electron bremsstrahlung and the proton bremsstrahlung, while the former is dominantbecause of the mass diﬀerence (me ≪ mp ). The influence of radiative decay appears in theradiative correction of the CKM matrix element, Vud .

104

Appendix B
Beam structure
To reconstruct beam structure is an important issue because our estimation of the numberof signal events rely on finding the origin of the track. We conducted the measurement of
the beam structure by using RPMT, which is a two dimensional detector and also possible
to measure the TOF. And the eﬃciency of RPMT was measured at the low-divergence beam
branch.

B.1

RPMT

A helium filled beam monitor is widely used to measure the neutron flux since it has highdetection eﬃciency of neutron but lack of position sensitively. In the measurement of beam
structure, RPMT is used to obtain positional resolution, while the beam monitor is used
to refer the beam flux. RPMT consists of a position-sensitive PMT (PSPMT), a neutron
scintillator and readout system. The schematic of setup is illustrated in Fig. B.1. The
scintillator was put on the PSPMT without using grease between the optical contact of the
PMT and the scintillator. Because the scintillator includes 6 Li, the α particle is emitted as
the result of 6 Li(n, α)3 H reaction. Besides, the scintillator contains ZnS so that scintillation
light is generated by α particle and that is detected after amplified with a 12-stage dynode.
Anode wires are crossed in x and y directions and the current is read out from both ends
of wires. The current of each anode wire is divided into I1 and I2 by resisters. Eventually,four signal lines of X1 , X2 , Y1 and Y2 are read out and the position of incident neutron isreconstructed by the ratio of current, I1 /(I1 + I2 ).

105

Appendix B. Beam structure

Figure B.1: Schematic diagram of RPMT [52].

PSPMT
Diameter [mm]Spacial resolution [mm]Eﬀective area [mm2 ]Scintillator
Material
Thickness [mm]Light yield [photons/n]

127
0.5 ∼ 0.8
60 × 60
ZnS(Ag)/6 LiF
0.25
> 104

Table B.1: Specification of the RPMT [52, 53].

B.2

Measurement of the eﬃciency of RPMTThe position dependence of detection eﬃciency was measured at the low-divergence beam
branch. The setup is shown in Figs. B.2 and B.3. The beam monitor was fixed at the exit of
the low-divergence beam branch and the neutron beam was collimated by using 2 × 2 mm2
cadmium foil to avoid saturation of RPMT. Just behind the slit, the RPMT was fixed on
the XY stage and the stage was moved so as to scan the RPMT surface. The alignment of
RPMT and beam monitor is better than 1 mm and that is small enough compared with thespacing of the anode wires of MWPC. Although, the detection eﬃciency depend on positionof hit and the neutron velocity, it was not yet corrected in the Fig. 5.2.
106

Appendix B. Beam structure

Neutron beam

RPMTz [mm]

327

Slit

Beam monitor

280

250

0

y [mm]

Figure B.2: Illustration of the side view of Figure B.3: Top view of the setup for the meathe setup for the measurement of RPMT eﬃ- surement of RPMT eﬃciency.
ciency.

120

300

25

100

250

20
200

80
15

150

60
10

40

20

5

0
0

0

20

40

60

80

100

120
x [mm]

Figure B.4: Eﬃciency of the RPMT.

100

50

0
0

5

10

15

20

25

30

35
40
TOF [ms]

Figure B.5: TOF spectrum measured with the
RPMT.

107

Appendix B. Beam structure

B.3

Measurement of the beam structure

In the measurement of the beam structure, the RPMT was moved to the polarization beam
branch and set inside the aluminum vessel (Fig. B.6). It should be noted that measurement
was performed without vacuuming because the RPMT can not be used in such a condition.
The light receiving face of the RPMT was positioned 8.5 cm downstream from the edge of
TPC. In this measurement, the RPMT was not moved but the slit was moved with XY
stage to scan whole surface of the exit of SFC. The result of measurement is given in Fig.
5.2.

Beam monitor

Slit

RPMT

8.5cm

Figure B.6: Setup of the measurement of the beam structure.

108

Appendix C
γ ray spectrum of LiF tile
The energy spectrum of γ rays from the LiF tile was measured at beamline 04 (ANNRI).
The measurement was conducted to reconstruct (n, γ) events and the result was input toMC simulation.

C.1

Measurement of γ ray spectrum

ANNRI is the experimental facility with Ge detector array and is possible to measure neutron
capture cross section accurately. The detail of experiment can be found in [54–56]. The
schematic view of the setup is given in Figs. C.1 and C.2. The neutrons are moderated withcoupled hydrogen moderator and go through the T0 chopper, neutron filter, disk choppers
and collimators. The sample and Ge spectrometer are placed at 21.5 m downstream of themoderator.

Figure C.1: Size view of the beamline 04 [56]. The neutron beam goes through the T0
chopper, neutron filter, disk choppers and collimators.

109

Appendix C. γ ray spectrum of LiF tile

Ge
LiF
Pb
LiH
BGO
Al

  

≈

~157mm≈Figure C.2: Schematic diagram of Ge spectrometer [56]. A sample is set in the center of the
Ge detectors. Coaxial-Ge detectors are shown in red and cluster-Ge detectors are shown inlight blue.
The LiF tile which is actually installed to our TPC was brought to ANNRI and thetile was irradiated with the neutron beam. The energy spectrum of γ rays was measured
by cluster-Ge detectors which were viewing the tile from top and bottom. TOF was also
obtained in the measurement. There are coaxial-Ge detectors surrounding the sample but
they were not used in the measurement. The specification of Ge detector is given in Tab.
C.1.
Cluster-Ge detector
Coaxial-Ge detector
Energy resolution (at 1.33 MeV)
Peak eﬃciency (at 1.33 MeV)

2 × 7 ch
8 ch
2.5 keV
3.64 × 0.11 %Table C.1: Specification of the Ge detector.

C.2

Reconstruction of the intensity of γ rays

The measurements were performed with and without setting the LiF tile, and the observed
γ ray spectra are shown in Fig. C.3. In the reconstruction of the γ ray energy spectrum,
110Appendix C. γ ray spectrum of LiF tile

the MC samples which include detector energy resolution were used. At first, the spectrum
which was measured without the LiF tile was subtracted from the one measured with the LiF
tile. Then, we estimated the intensity of each peak from one with higher energy. Each MC
sample was scaled to conform the area of the peak with 5 σ, and removed from data. This
procedure was repeated until all peaks were to be subtracted. In 19 F(n, γ) reaction, somepeaks were too small to estimate so that the relative intensity was calculated based on thereference value, and one of the intense peak of 1387 keV was employed as the standard. The
detected spectrum was reconstructed as shown in Fig. C.4. Finally, we obtained intensityof γ rays emitted from the LiF tile, that is given in Fig. 5.4.
It should be noted that there were two unexpected peaks found at 140 keV and 198 keV.
According to the level of scheme, the γ ray with such energy would not be emitted fromthe component of the LiF tile. In the case of peak with 198 keV, the lifetime was estimatedto be about 20.4 ms and we concluded that the γ ray was derived from 71 Ge. On the other
hand, we also analyzed the TOF of another peak and found that it was not prompt γ ray.
Because the time structure of the background is diﬀerent from that of signal events, thebackground does not matter to the evaluation of signal events.

105

104

103

102

10

1000

2000

3000

4000

5000

6000

7000

8000
keV

Figure C.3: Energy spectrum of γ rays measured with LiF tile (red) and without LiF tile
(blue).

111

Appendix C. γ ray spectrum of LiF tile

104

103

102

10

1

1000

2000

3000

4000

5000

6000

7000

8000
keV

Figure C.4: Energy spectrum of γ rays of the data after subtracting the background (black)and the reconstructed spectrum by using MC samples (red).

112Appendix D
Mass spectrometry
We use G1He gas which is the commercial product by Tomoe shokai Co., Ltd. and mainly
consist of 4 He. In order to determine 3 He density precisely, we have to take into accountthe isotopic contamination of 3 He in G1He. The helium isotopic ratio (3 He/4 He) was measured by using mass spectrometry and the total amount of 3 He introduced to the TPC wascorrected.

D.1

Noble gas analyzing system

After data acquisition have been finished, the TPC gas was sampled from the valve at thedownstream of aluminum vessel and the measurement of 3 He/4 He ratio with mass spectrometry was conducted with cooperation of isotope geochemistry and cosmochemistry laboratory, at the University of Tokyo. The mass spectrometer has double collector system and it
can determine the 3 He/4 He ratio with a precision of ± 10 % under the condition of partialpressure of 3 He in the range of 0.5 to 5 × 10−14 Torr.
The noble gas analyzing system consist of gas extraction part, gas purification part,separation part and mass spectrometry part. The measurement is performed as below.
Firstly, the gas sample is introduced from the left side of the Fig. D.1 and purification
proceed by using Ti-Zr getters (Ti1 and Ti2) and charcoal traps (CH1 and CH2). In thisprocess, released noble gases such as argon, krypton and xenon are adsorbed by CH1. Whilehelium and neon are purified with Ti2, CH2 and a SORB-AC getter pump. Then, neon isseparated by a cryogenically cooled trap (Cryo-trap) and helium is guided into the modifiedVG(5400) to measure the 3 He/4 He ratio.
In the mass spectrometry part, both of 3 He beam and 4 He beam are measured simultaneously. Figure D.2 shows the picture of the setup. The ion beams are bended in thepassage of the magnetic field, where the radius of curvature depend on the mass to charge
ratio. Finally, 3 He beam and 4 He beam are detected by the ion-counting system and theHigh-Faraday cup, seperately.
113

Appendix D. Mass spectrometry

Figure D.1: Schematic diagram of the noble gas analyzing system [57].

Samplegas

IonsourceMagnet
4He

Magnetic ﬁeld

3He

Collector
Faraday cupIon counterFigure D.2: Setup of the mass spectrometry.

114

Appendix D. Mass spectrometry
In order to determine the absolute ratio of 3 He/4 He, a standard helium gas with wellknown isotopic ratio is needed. Historically, atmospheric helium has been used as a primary
standard but it is not preferable because its 3 He/4 He ratio would be changed, and large
amount of gas have to be introduced to the measurement system due to low density of 3 He
in the air.
An artificial gas mixture named HESJ (He Standard of Japan) was prepared to be used
as an internal standard of 3 He/4 He ratio and we adopted HESJ in the measurement [58].
The sample gas and HESJ were measured alternately. Finally, the 3 He/4 He ratio of thesample was determined as it is summarized in Tab. D.1. According to the result, 3 He
density was corrected in Sec. 3.5.1.
Bottle# Series
61
7
2, 3, 4
8
5, 6

G1He/HESJ (×10−3 )3.21(7)4.05(6)3.70(11)

Table D.1: Ratio of 3 He/4 He of G1He to that of HESJ.

115

Acknowledgements
I would like to thank all the people who supported me throughout the years of after graduated. This work could not be accomplished without anyone’s help.
First of all, I wish to express great appreciation to my supervisor, Satoru Yamashita,
who always give me critical advices and initiate the way to find the issues to be addressed.
I think I could have been working on because he kindly respected my opinion and increase
my eagerness to study more. Many things that I have learned from him were not limited inexperimental physics and that really help me in my daily life. I am glad to be a member of
Yamashita group.
I would like to thank Kenji Mishima, for the great contribution to practical work andinformative discussions. He have been engaging in not only the conduction of the experiment
but also data analysis, therefore our experiment would not progress without him. It is hard
to conclude the discussions even if our collaboration is not so large, and I would like to thank
Masaaki Kitaguchi who encourage active and approachable discussions. When I suggested
new things, he always discussed with patience to reach the best conclusions.
I would like take this opportunity to express my sincere gratitude to Hirohiko M. Shimizu,
Takashi Ino, Hirochika Sumino, Yoshihisa Iwashita, Tamaki Yoshioka, Katsuya Hirota, Tatsusi Shima, Daiichiro Sekiba, Kaoru Taketani, Yoshichika Seki, and all those who havecontinuously supported for the construction of apparatuses, commissioning and all of works
to conduct NOP experiment.
I would like to send many thanks to Takahito Yamada who has substantial contribution
to the development of data acquisition system. He gave me a lot of knowledge concerning
computing and gas chamber physics, and enthusiastically guided me. During the work in
Tokai, I worked with many colleagues and I often worked with Tatsuhiko Tomita. Since I
was the later student to join NOP experiment, he politely answers my questions and helped
me with conducting the measurement. Besides, I thank him for his friendly atmospherethat relieve me so much. I would like to thank Ryuunosuke Kitahara who taught me about
SPC and the analysis of 14 N background in detail. I am grateful to Naoki Nagakura andNaoyuki Sumi. I learned many things from fruitful discussions and I believe each of themwill play a vital role in the next measurement. Concerning with the upgrade of the setup,
Mami Yokohashi and Aya Morishita played important roles. They made strenuous eﬀorts
in the designing of the setup and simulation studies, and that encouraged me a lot. I also
116

worked with Jun Koga and Hideaki Uehara, who are thoughtful and attentive students. It
was very fun to have dinner together and I hope to work with them in the future.
I especially would like to thank the member of Yamashita group, Tomohiko Tanabe,
Masakazu Kurata, Takuro Murase, Ryo Katayama, Nao Higashi, Harumichi Yokoyama,
Takuaki Mori, Kento Kasuya, Shohei Fujikura, Yu Kato and Kazuki Fujii. And also, I
really appreciate Hidetoshi Otono and Hideyuki Oide who have been great mentors to me.
Their contributions are indispensable for not only this work but also the development of
the basis of another work. Although they had already graduated when I joined Yamashitagroup, they gave me a lot of advices from far away and my framework of studying have been
constructed based on their previous works.
I would like to express appreciation to ICEPP secretaries and the members of the user’soﬃce at J-PARC, who supported me with managements.
Special thanks are to all of those whose names are not written but enriched my life invarious aspects and shared precious time outside the laboratory.
Finally, I really thank my parents, my sister and my brothers.

117

List of Figures
1.1

Illustration of experimental setup of Chadwick’s experiment [1]. . . . . . . .

1

1.2

Dominant decay mode of neutron. . . . . . . . . . . . . . . . . . . . . . . . .

2

1.3

Drawing of the neutron decay correlation coeﬃcients. . . . . . . . . . . . . .

5

1.4

Vud vs. λ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

1.5

Illustration of the quasi-Penning trap and Si detectors [18]. . . . . . . . . . .

10

1.6

Experimental setup of the neutron lifetime experiment by ILL-ISL-LAPP
collaboration [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.7

Schematic view of the gravitational UCN storage system [20]. 1: input neutron guide, 2: inlet valve, 3: selector valve, 4: aluminum foil, 5: “dirty”
vacuum volume, 6: “clean” vacuum volume, 7: cooling coils for the thermal
shields, 8: UCN storage trap, 9: cryostat, 10: mechanics for trap rotation,
11: stepping motor, 12: UCN detector, 13: detector shield, and 14: vaporizer. 13

1.8

Schematic view of the magnetic sextupole trap [22]. . . . . . . . . . . . . . .

14

1.9

Cross section of an ideal sextupole [22]. Dashed line: magnetic field, dotted
line: equal magnetic potential. . . . . . . . . . . . . . . . . . . . . . . . . . .

14

1.10 Previous results of the neutron lifetime measured by in-flight method (red)and by bottle method (blue) [23–29]. . . . . . . . . . . . . . . . . . . . . . .

16

2.1

Bird’s eye view of J-PARC [30]. . . . . . . . . . . . . . . . . . . . . . . . . .

18

2.2

Neutron instruments at MLF [30]. . . . . . . . . . . . . . . . . . . . . . . . .

19

2.3

BL05 NOP beamline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

2.4

Overview of the NOP beamline [31]. . . . . . . . . . . . . . . . . . . . . . . .

21

2.5

Illustration of the beam branches. (A) entrance of the beam benders, (B)exit of the polarized beam branch, (C) exit of the unpolarized beam branch,and (D) exit of the low-divergence beam branch. . . . . . . . . . . . . . . . .

21

118

LIST OF FIGURES

3.1

Overview of SFC and TPC. (X) polarized beam branch, (Y) unpolarized
beam branch, and (Z) low-divergence beam branch. (a) short-pass wavelength
neutron filter, (b) a guid coil, (c) first and second RFF coils, (d) magnetic
supper mirrors, and (e) a neutron beam monitor. (A) beam dump, (B) leadshields, (C) iron shields, and (D) LiF beam collimators. (1) a Zr foil, (2) a
LiF shutter, (3) cosmic veto counters, (4) lead shields, (5) a vacuum chamber,(6) a TPC, (7) a LiF beam catcher, and (8) a turbo molecular pump. . . . .
3.2 Illustration of SFC, viewed in xz plane. Polarized neutron is provided fromthe left side. (A) first RFF coil, (B) first and second mirrors, (C) a LiF
shutter, (D) second RFF coil, (E) third mirror, (F) a guide coil, (G) boron
gum, and (H) lead shields. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Radio frequency flipper coil. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Basis of Bragg diﬀraction. The magnetic supper mirror is viewed in xz plane
and the magnetic field is applied vertical to the paper surface. The neutron
with spin parallel to the magnetic field (red) is reflected, while one with spin
antiparallel (blue) penetrates the mirror. . . . . . . . . . . . . . . . . . . .
3.5 Magnetic supper mirror. A case is surrounded by magnets and five mirrors
are aligned inside. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Neutron flux measured by TPC vs. TOF. The ratio of flux measured with
SFC switched on and oﬀ is 1 to 400. . . . . . . . . . . . . . . . . . . . . . .
3.7 Neutron beam monitor MNH10/4.2F, product by Canberra Industries Inc. .
3.8 LiF shutter on the stepping motor. . . . . . . . . . . . . . . . . . . . . . . .
3.9 Schematic view of TPC in yz plane. . . . . . . . . . . . . . . . . . . . . . . .
3.10 Schematic view of TPC in xy plane, viewed from downstream [36]. . . . . . .
3.11 Schematic view of the drift cage [36]. . . . . . . . . . . . . . . . . . . . . . .
3.12 γ ray spectra of G10 (left) and PEEK (right), normalized by the measurement
time and size of the samples [44]. . . . . . . . . . . . . . . . . . . . . . . . .
3.13 LiF tile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 Inside of TPC viewed from upstream. . . . . . . . . . . . . . . . . . . . . . .
3.15 Wire geometry of MWPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.16 Preamplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 Circuit diagram of the preamplifier. . . . . . . . . . . . . . . . . . . . . . . .
3.18 Electric field of the drift region in xy plane, viewed from upstream. . . . . .
3.19 Electric field around the anode wires. . . . . . . . . . . . . . . . . . . . . . .
3.20 Basis of gas introduction. 3 He gas is introduced to small volume (V1 ) andexpanded to larger volume (V2 ). . . . . . . . . . . . . . . . . . . . . . . . .
3.21 Illustration of the gas introduction system. The pressure gauges A and B
correspond to two channels of Mensor CPG2500, and the gauge C is Baratron690A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.22 Cosmic ray veto counters. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.23 Drawing of the cosmic ray veto counter (Front and Back). . . . . . . . . . .
119

24

24
25

26
27
28
29
29
30
30
31
32
33
33
35
36
36
36
36
39

40
41
42

LIST OF FIGURES

3.24 Checking source on the rotating table. . . . . . . . . . . . . . . . . . . . . .
3.25 Side view of TPC. The source is fixed to y = 0 mm. . . . . . . . . . . . . . .
3.26 Transition of pulse height. The calibration source was positioned at y = 75 mm(red) and y = -75 mm (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.27 Ideal case (left) and worse case (right) to calculate the drift velocity by using
cosmic ray. TPC is viewed in xy plane and hit anode wires are indicated with
red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.28 Drift velocity calculated with diﬀerent number of hit anode wires. . . . . . .
3.29 Detection eﬃciencies of anode wires. . . . . . . . . . . . . . . . . . . . . . .
3.30 Transition of the attenuation coeﬃcient. The operation was suspended in theblank space because of the maintenance of the accelerator. . . . . . . . . . .
3.31 Block diagram of the readout electronics [31]. . . . . . . . . . . . . . . . . .
3.32 GNV-440 FINESSE 8ch ADC board (12bit/65MSPS). . . . . . . . . . . . . .
3.33 Alive rate vs. TOF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1

4.2
4.3
4.4

5.1
5.2
5.3
5.4
5.5

5.6
5.7

Cosine of scattered angle vs. neutron velocity after scattered by 4 He (left)
and CO2 (right). The standard neutron velocity in each bunch was assumed
for the initial neutron velocity at 304 K. From the top, the initial velocity is598, 709, 843, 997 and 1177 m/s. . . . . . . . . . . . . . . . . . . . . . . . . .
Energy deposit of the point-like background events extracted from data. . . .
Energy deposit of the MC sample of 3 H decay. . . . . . . . . . . . . . . . . .
Transition of the count rate of neutron decay candidates with 3 H suppressioncut (left) and the count rate of the background extracted by 3 H suppressioncut (right). The accelerator was operated with constant beam power during
the measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The center of energy deposit in z direction vs TOF, provided by extracting
3
He(n, p)3 H events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beam distribution in the xy plane, measured with RPMT. . . . . . . . . . .
Position of 3 He(n, p)3 H reaction after neutron scattering (left) and that of
6
Li(n, α)3 H reaction (right), shown in xz plane. . . . . . . . . . . . . . . . .
Energy spectrum of γ rays emitted from the LiF tile. Intense peaks found at
477 keV, 6768 keV and 7245 keV are derived from 6 Li. . . . . . . . . . . . .
Time development of an avalanche in a proportional counter [35]. A pair of
ionized particle is created (a). Secondary ionization is induced on the way
toward to the anode wire (b) and laterally diﬀused (c). As the developmentof an avalanche, the wire is surrounded by electrons (d). The electrons are
rapidly collected and positive ions are attracted to the cathode wire (e). . .
Measurement of the saturation factor s as a function of gain by using 241 Am
source [36]. The vertical scale was normalized to s(G0 = 0) → 1. . . . . . .
Template waveform measured by using the X-ray source. . . . . . . . . . . .
120

43
43
44

45
45
46
47
48
49
50

55
57
57

57
62
62
63
64

67
68
69

LIST OF FIGURES

6.1
6.2

Analysis flow of the signal evaluation. . . . . . . . . . . . . . . . . . . . . . .
Maximum pulse height in the field wires. Left : Signal candidates are separated at 25 keV, which is indicated with green line. Right : Enlarged view ofthe left figure with logarithmic scale. . . . . . . . . . . . . . . . . . . . . . .
6.3 Drawing of TOF spectra of Beam ON (top) and Beam OFF (bottom). Signal
events (red), the beam induced background (blue), the prompt γ rays fromupstream (green), the environmental backgrounds (orange) and the radioactivation backgrounds (magenta) are illustrated. The time range from B to C
roughly indicate the fiducial time. . . . . . . . . . . . . . . . . . . . . . . .
6.4 Passage of the neutron beam, which is indicated with red line, at a certain
TOF of Beam ON. A, B and C are indicated in Fig. 6.3. The intense beam
is emphasized with bold red line. . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Passage of the neutron beam of Beam OFF. The neutrons are intercepted by
the LiF shutter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 TOF of Beam ON (red), Beam OFF (black), and Beam OFF subtracted by
Beam ON (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Definition of the fiducial time. . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Definition of parameters. First and second triggered channels are illustrated.
6.9 Comparison of the drift length among data before subtraction. Histograms
are normalized by the beam monitor counts and TOF. . . . . . . . . . . . .
6.10 Comparison of the drift length between arbitrary scaled MC samples of theneutron decay (red) and cosmic ray (blue). . . . . . . . . . . . . . . . . . . .
6.11 Comparison of the energy deposit among data before subtraction. Histograms
are normalized by the beam monitor counts and TOF. . . . . . . . . . . . .
6.12 Comparison of the energy deposit between arbitrary scaled MC samples of
the neutron decay (red) and the neutron capture reaction in CO2 (blue). . .
6.13 Comparison of ph/int among data before subtraction. Histograms are normalized by the beam monitor counts and TOF. . . . . . . . . . . . . . . . .
6.14 Comparison of ph/int between arbitrary scaled MC samples of the neutron
decay (red) and the 3 H decay (blue). . . . . . . . . . . . . . . . . . . . . . .
6.15 Comparison of the drift length between data after subtraction (black) andMC sample of the neutron decay (red) which is normalized by the statistics
of data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.16 Comparison of the energy deposit between data after subtraction (black) andMC sample of the neutron decay(red) which is normalized by the statistics
of data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.17 Comparison of ph/int between data after subtraction (black) and MC sampleof the neutron decay (red) which is normalized by the statistics of data. . . .
121

71

73

74

75
75
76
76
77
79
79
79
79
80
80

81

81
82

LIST OF FIGURES

6.18 The center of energy deposit in the field wires, displayed with linear (logarithmic) scale in the left (right). Red and blue histograms correspond to theMC samples of signal events and neutron scattering background events. The
center of TPC in x direction is fce = 11.5. . . . . . . . . . . . . . . . . . . . .
6.19 Maximum pulse heigh of the field wires in the neutron decay. The cut threshold is indicated with green line. . . . . . . . . . . . . . . . . . . . . . . . . .
6.20 Energy deposit of the low gain measurement. . . . . . . . . . . . . . . . . . .
6.21 Transition of the ratio of neutron capture events, 14 N/3 He. . . . . . . . . . .
6.22 Drawing of the definition of DC. The TPC is viewed in xy plane and theelectron tracks are illustrated as blue arrows. The red points and the green
dotted line indicate the origin of the tracks and the beam axis. . . . . . . .
6.23 XValue (top) and DC (bottom) of the data and the MC samples. Red,
green and blue histograms correspond to MC samples of the signal neutron
decay, (n, γ) background and the neutron decay background followed with
scattering. Each parameter is displayed with linear and logarithmic scale on
the left and right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.24 Maximum pulse heigh of the field wires in 3 He(n, p)3 H reaction. The cut
threshold is indicated with green line. . . . . . . . . . . . . . . . . . . . . . .
7.1
7.2

Drift velocity vs. y position, measured with cosmic ray events. . . . . . . . .
Comparison of data and MC sample of cosmic ray. Energy deposit vs. track
length of data (top left) and that of MC sample (top right). The track lengthof data (black) and MC sample (red) are shown in bottom left, and the energy
deposit of data (black) and MC sample (red) are shown in bottom right. . .
7.3 Deviation of ph/int measured with the X-ray source positioned y = 75 mm(left) and y = -75 mm (right). . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Statistical error vs. Anode energy deposit. . . . . . . . . . . . . . . . . . . .
7.5 Cut eﬃciency vs. Anode energy deposit. . . . . . . . . . . . . . . . . . . . .
7.6 Statistical error vs. Drift length. . . . . . . . . . . . . . . . . . . . . . . . . .
7.7 Cut eﬃciency vs. Drift length. . . . . . . . . . . . . . . . . . . . . . . . . . .
7.8 Statistical error vs. ph/int. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.9 Cut eﬃciency vs. ph/int. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.10 Beam distribution in x direction. Each histogram represents the original
distribution (black), shifted by +2 mm (red) and shifted by -2 mm (blue). . .
8.1

83
84
85
86

87

88
89
93

94
95
96
96
96
96
96
96
97

Improvement of the statistical error. . . . . . . . . . . . . . . . . . . . . . . . 103

A.1 Feynman diagrams of radiative neutron decay. The electron bremsstrahlung(left), the proton bremsstrahlung (center) and bremsstrahlung from weakvertex (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
B.1 Schematic diagram of RPMT [52]. . . . . . . . . . . . . . . . . . . . . . . . . 106
122

LIST OF FIGURES

B.2 Illustration of the side view of the setup for the measurement of RPMT
eﬃciency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
B.3 Top view of the setup for the measurement of RPMT eﬃciency. . . . . . . . 107
B.4 Eﬃciency of the RPMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
B.5 TOF spectrum measured with the RPMT. . . . . . . . . . . . . . . . . . . . 107
B.6 Setup of the measurement of the beam structure. . . . . . . . . . . . . . . . 108
C.1 Size view of the beamline 04 [56]. The neutron beam goes through the T0
chopper, neutron filter, disk choppers and collimators. . . . . . . . . . . . . 109
C.2 Schematic diagram of Ge spectrometer [56]. A sample is set in the centerof the Ge detectors. Coaxial-Ge detectors are shown in red and cluster-Ge
detectors are shown in light blue. . . . . . . . . . . . . . . . . . . . . . . . . 110
C.3 Energy spectrum of γ rays measured with LiF tile (red) and without LiF tile
(blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
C.4 Energy spectrum of γ rays of the data after subtracting the background(black) and the reconstructed spectrum by using MC samples (red). . . . . 112
D.1 Schematic diagram of the noble gas analyzing system [57]. . . . . . . . . . . 114
D.2 Setup of the mass spectrometry. . . . . . . . . . . . . . . . . . . . . . . . . . 114

123

List of Tables
1.1
1.2

Reported values of Vud [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods and issues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

Performance of neutron beam at 10 m from the coupled moderator at the
1 MW operation [30]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Beam performance at 16 m position (see Fig. 2.4) at the 1 MW operation [30]. 22

2.2

8
9

3.1 Specifications of the solenoid coil. . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Specification of the magnetic super mirror. . . . . . . . . . . . . . . . . . . . 27
3.3 Specification of beam monitor manufactured by Canberra Industries Inc. [32] 29
3.4 Physical properties of the materials [50]. . . . . . . . . . . . . . . . . . . . . 33
3.5 Specification of the LiF tile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6 Mole fraction of the LiF tile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.7 Properties of wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.8 Component of 4 He gas, commercial product by Tomoe shokai Co., Ltd. . . . 37
3.9 Component of CO2 gas, commercial product by Tomoe shokai Co., Ltd. . . . 37
3.10 Specification of pressure gauges. . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.11 Number density of injected gases. . . . . . . . . . . . . . . . . . . . . . . . . 39
3.12 Systematical errors of 3 He density in percentage. . . . . . . . . . . . . . . . . 41
3.13 Detection eﬃciency of veto counters [44]. Position A∼E are shown in Fig. 3.23. 42
3.14 Specification of readout system. . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.15 Comparison of setup between the experiment described in [6] and NOP experiment, assuming 220 kW beam power at J-PARC. . . . . . . . . . . . . . 51
4.1
4.2
5.1
5.2

Theoretically calculated neutron scattering cross sections at 304 K. Here, vn
is the initial neutron velocity. . . . . . . . . . . . . . . . . . . . . . . . . . .
Categorization of signals and backgrounds. . . . . . . . . . . . . . . . . . . .
List of the MC samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
W -value of TPC gas [44]. Wα and Wβ are average energy required to produce
an α particle and an electron, respectively. I is the minimum ionization
potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
124

56
58
60

65

LIST OF TABLES

6.1
6.2
6.3
6.4

Acquired data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Number of signal events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Uncertainties of the number of 3 He(n, p)3 H events in percentage. . . . . . . .
Uncertainties of the number of neutron decay events in percentage. . . . . .

71
90
90
91

7.1
7.2
7.3
7.4
7.5

Cuts for the neutron decay. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cuts for the 3 He(n, p)3 H reaction. . . . . . . . . . . . . . . . . . . . . . . . .
Eﬃciencies of signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Uncertainties of the eﬃciency of neutron decay in percentage. . . . . . . . .
Uncertainties of the eﬃciency of 3 He(n, p)3 H reaction in percentage. . . . .

92
93
98
98
98

8.1
8.2
8.3

Summary of the results of the neutron lifetime measurement. . . . . . . . . . 100
Systematical errors of the neutron lifetime in percentage. . . . . . . . . . . . 101
Upgrade plans of the setup. B4 C collimater and LiF collimater are positioned
1185 mm and 1570 mm downstream of the target. . . . . . . . . . . . . . . . 102
Upgrade plans and expected beam flux. . . . . . . . . . . . . . . . . . . . . . 103

8.4

B.1 Specification of the RPMT [52, 53]. . . . . . . . . . . . . . . . . . . . . . . . 106
C.1 Specification of the Ge detector. . . . . . . . . . . . . . . . . . . . . . . . . . 110
D.1 Ratio of 3 He/4 He of G1He to that of HESJ. . . . . . . . . . . . . . . . . . . 115

125

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