Ph.D. Thesis

New detector system for the
precise neutron lifetime
measurement using pulsed cold
neutron beams

Hidetoshi Otono

Department of Physics, Graduate School of Science,
The University of Tokyo
December 2011

Abstract
The values of the neutron lifetime τn and the baryon density of the universe η are
key parameters for Big Bang nucleosynthesis. Recently, the measurement of thecosmic microwave background radiation at the Wilkinson Microwave Anisotropy
Probe has become increasingly sensitive to η, which motivates a neutron lifetime
measurement with improved accuracy.
Since the ﬁrst observation of the neutron decay in 1948, various methods for themeasurement of the neutron lifetime using nuclear reactors have been developed,
resulting in the world average 881.5 ± 1.5 s given by the Particle Data Group.
The proposed method in this thesis employs an accelerator for the ﬁrst time in all
neutron lifetime measurements, making use of the world’s most intensive pulsed
neutron source at the J-PARC accelerator complex in Tokai, Ibaraki, Japan. In thismethod, pulsed monochromatic bunch passes through a time projection chamber(TPC), which detects the electron from the neutron decay. The neutron ﬂux canalso be measured via the 3 He(n, p)3 H reaction by mixing a small amount of 3 He
in the same detector.
A measurement accuracy of a level 0.1% is needed to be competitive withthe world average. To achieve this, backgrounds to the neutron decay and the3
He(n, p)3 H reaction have to be physically reduced and statistically subtracted. In
this work, a low background TPC has been developed, making use of polyether
ether ketone (PEEK) as its main component, which contains no radioactive sources;
6
Li plates are installed in the inner wall of the TPC to capture scattered neutrons;
the TPC is surrounded by 4 π shielding to reduce environmental radiation. Consequently, the achievable signal-to-background ratio is estimated to be 1, corresponding to a statistical uncertainty of 0.8% for 150 days of beam time, assuming
the current beam power of 220 kW. In parallel, an analysis algorithm has been developed, which subtracts the remaining backgrounds using a data-driven approach
while retaining more than 99.9% detection eﬃciency for the neutron decay andthe 3 He(n, p)3 H reaction. As a result, all the systematic uncertainties arising fromthe particle detection are reduced to a level of 0.1%.

iii

Contents
Abstractiii

1 Introduction

1

2 Neutron decay

5

2.1

Low energy eﬀective theory of the weak interaction . . . . . . . . .

5

2.2

Big Bang nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . .

6

2.3

Experiments of the neutron lifetime . . . . . . . . . . . . . . . . . .

8

2.3.1

Methods for the measurement of the neutron lifetime . . . .

8

2.3.2

Penning trap method . . . . . . . . . . . . . . . . . . . . . . 10

2.3.3

Gravitational trap method . . . . . . . . . . . . . . . . . . . 12

2.3.4

Magnetic trap method . . . . . . . . . . . . . . . . . . . . . 13

2.4

Beam method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1

Principle of the Kossakowski’s experiment . . . . . . . . . . 14

2.4.2

Experimental setup for the Kossakowski’s experiment . . . . 15

2.4.3

Results of the Kossakowski’s experiment . . . . . . . . . . . 16

3 Experiment in this thesis

19

3.1

Approaches in this thesis . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2

Neutron Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3

3.4

3.2.1

MLF/J-PARC . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.2

Polarization branch on BL05 . . . . . . . . . . . . . . . . . . 25

Spin ﬂip chopper . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1

Overview of the SFC . . . . . . . . . . . . . . . . . . . . . . 27

3.3.2

Magnetic supper mirror . . . . . . . . . . . . . . . . . . . . 28

3.3.3

Radio-frequency ﬂipper . . . . . . . . . . . . . . . . . . . . . 29

3.3.4

Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Time projection chamber . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.1

Overview of the TPC . . . . . . . . . . . . . . . . . . . . . . 33

3.4.2

Pre-ampliﬁer . . . . . . . . . . . . . . . . . . . . . . . . . . 33v

vi

CONTENTS
3.4.3

Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4.4

Frontend electronics . . . . . . . . . . . . . . . . . . . . . . 36

3.5

Beam monitor and 6 Li shutter . . . . . . . . . . . . . . . . . . . . . 37

3.6

Shields for the environmental background . . . . . . . . . . . . . . . 37

3.7

3.6.1

Pb shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.6.2

Cosmic-ray veto counter . . . . . . . . . . . . . . . . . . . . 40

Shields for the beam-induced background . . . . . . . . . . . . . . . 41

4 Simulation
4.1

45Interaction of particles . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.1

Decay of neutron . . . . . . . . . . . . . . . . . . . . . . . . 46

4.1.2

Scattering of neutron . . . . . . . . . . . . . . . . . . . . . . 46

4.1.3

Capture of neutron . . . . . . . . . . . . . . . . . . . . . . . 48

4.1.4

Energy loss of charged particles . . . . . . . . . . . . . . . . 48

4.2

Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3

Drift and diﬀusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.4

Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.5

Signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Analysis algorithm

59

5.1

Overview of the analysis algorithm . . . . . . . . . . . . . . . . . . 59

5.2

Signal of the neutron decay . . . . . . . . . . . . . . . . . . . . . . 61

5.3

Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.4

5.5

5.3.1

Backgrounds to the beta decay . . . . . . . . . . . . . . . . 62

5.3.2

Backgrounds to the neutron capture in 3 He . . . . . . . . . . 65

Signal separation by using calorimetric approach . . . . . . . . . . . 66
5.4.1

Separation between Sβ and Sn . . . . . . . . . . . . . . . . . 66

5.4.2

Separation between Sβ and Bβenergy . . . . . . . . . . . . . . 68

Signal selection by using track ﬁnding . . . . . . . . . . . . . . . . . 70
5.5.1

Selection of the neutron decay . . . . . . . . . . . . . . . . . 70

5.5.2

Selection of the neutron decay under reduced pressure . . . . 73

5.5.3

Selection of the neutron capture in 3 He . . . . . . . . . . . . 74

5.5.4

Selection of the neutron capture in 3 He under reduced pressure 75

5.6

Subtraction by using 3 He-enriched measurement . . . . . . . . . . . 76

5.7

Subtraction by using TOF spectrum . . . . . . . . . . . . . . . . . 77

5.8

5.7.1

Neutron decay . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.7.2

Neutron capture in 3 He . . . . . . . . . . . . . . . . . . . . . 80

Subtraction by using reduced-pressure measurement . . . . . . . . . 80

CONTENTS

vii

6 Time projection chamber

83

6.1

6.2
6.3
6.4

Development of the TPC . . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.1 Material candidate . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.2 Study of the radioactive contamination by using germanium
detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.1.3 Design of TPC . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.4 Design of vacuum chamber . . . . . . . . . . . . . . . . . .
Installation of the 6 Li plate . . . . . . . . . . . . . . . . . . . . . .
Performance of the background suppression . . . . . . . . . . . . . .

Performance for the particle detection . . . . . . . . . . . . . . . . . 95
6.4.1 Setup for the measurement . . . . . . . . . . . . . . . . . . . 95
6.4.2 Detection for the neutron decay . . . . . . . . . . . . . . . . 96
6.4.3
6.4.4

Separation between the neutron decay and the neutron capture in 3 He . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Separation between the neutron decay and the neutron capture in CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7 Discussion
7.1
7.2
7.3

86
90
91
93

101

Uncertainty arising from the particle detection . . . . . . . . . . . . 101
Additional uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 102
Achievable sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 103

8 Conclusions

105

Acknowledgments

107

Chapter 1
Introduction
The neutron was discovered by Chadwick in 1932 [1, 2]. It decays into a proton,
an electron and an antineutrino with a lifetime of about 15 minutes. The neutron
lifetime plays a key role in Big Bang nucleosynthesis (BBN) as described in theAlpher-Bethe-Gamow paper in 1948 [3, 4], since the neutron lifetime has a direct
eﬀect on the abundance of the light elements. After the measurement of thebaryon density of the universe by the Wilkinson Microwave Anisotropy Probe(WMAP), the abundance of the light elements is uniquely determined, assuming
the BBN as described in Section 2.2. However, the measured abundance does notagree with the prediction, which has become a controversy among particle physics,
observational astronomy and cosmological theory. Thus the improvement of theaccuracy in the neutron lifetime measurement is desired more strongly than ever.
The experiment described in this thesis diﬀers in many important aspects ascompared to any other experiment included in the world average of neutron lifetime
given by the Particle Data Group [5]. In particular,• a pulsed neutron beam generated by an accelerator, J-PARC,• a new scheme of shaping the neutron beam by using a spin ﬂip chopper,• an innovative time projection chamber,are employed. This thesis focuses on the development of the TPC and the analysis
algorithm.
The ﬁrst observation of the neutron decay was done by Snell and Miller by theuse of a reactor in 1948 [6]. Since then, more than 20 major experiments havebeen done, using a variety of methods [7]. The currently-conducted experiments
can be classiﬁed into three types: the “penning trap method”, “gravitational trap
method” and the “magnetic trap method” as described in Section 2.3 and Table
1

2

CHAPTER 1. INTRODUCTION

1.1. The drawback of each method is the diﬃculty in evaluating a neutron ﬂux, awall loss, and a depolarization of the neutrons, respectively.
Methodpenning trap [8]SourcereactorNeutron energy
cold neutron
Measured target
protonAdvantage
low backgroundτn result [sec]886.6 ± 1.2 ± 3.2

gravitational trap [9]reactorultra cold neutron
neutronsmall correction
878.5 ± 0.7 ± 0.3

magnetic trap [10]reactorultra cold neutron
neutronno wall loss
878.2 ± 1.9

Table 1.1: Properties of methods for the various neutron lifetime measurement experiments.

The “beam method” as described in Section 2.4 and Table 1.2 was developed
by Kossakowski and his colleagues in 1989 [11], which is the preceding study of theexperiment in this thesis. Kossakowski et al. used a continuous cold neutrons at
a reactor in Institut Laue-Langevin (ILL), with an energy range of about 1 meV∼ 20 meV. A chopper shapes the beam into short bunches, which pass though atime projection chamber (TPC). In the TPC, the electron from the neutron decay
is detected, while the neutron ﬂux can be measured simultaneously in the samedetector due to a small amount of mixed 3 He which causes 3 He(n, p)3 H reaction.
The length of the bunch is adjusted to be shorter than that of the TPC, so thatthe ﬁducial volume of the measurement can be deﬁned accurately when the entire
bunch is inside the TPC. Since a detection coverage of 4π srad solid angle for bothreactions is guaranteed, it is possible to avoid systematic uncertainties caused by
the drawbacks of the currently-conducted experiments.
MethodSourceNeutron energy
Measured target
Advantage
τn result [sec]beam method [11]reactorcold neutron
electron
ﬂux monitoring, no wall loss, no depolarization
878 ± 27 ± 14

Table 1.2: Properties of the beam method for the neutron lifetime measurement experiments.

However the beam method have the following challenges:
1. How to obtain high statistics of pulsed monochromatic neutron,
2. How to reduce and shield the background to the neutron decay,

3
3. How to extract the neutron decay from the data,
4. How to subtract the background to the neutron decay.
In order to overcome these challenges, new approaches are proposed in thisthesis. The comparisons from the experiment by Kossakowski et al. are listed.
• Previous work
1. continuous neutron source + rotating drum + single crystal
2. radiation shield
3. use of the track pattern
4. use of the sideband region outside the ﬁducial region• The experiment in this thesis
1. pulsed neutron source (MLF/J-PARC) + spin ﬂip chopper
2. TPC made of no radioactive contamination with 4π radiation shields
3. use of calorimetric information
4. use of the data-driven approach
The detailed explanation is described in Section 3.1.

The contribution on this work
The author has developed the TPC and invented its analysis algorithm for themeasurement of the neutron lifetime. For this purpose, the simulation frameworkis also established in parallel. The beam line (BL05) at MLF in J-PARC, the spin
ﬂip chopper, and the 4π radiation shields are developed mainly by K. Mishima,
K. Taketani and H. Oide, respectively.

The organization of the thesis
The ﬁrst chapter of this thesis is serves as an introduction. In Chapter 2, a theoretical explanation for the neutron decay and the role of the neutron lifetime in the
Big Bang nucleosynthesis are described. Methods of past and current experiments
are also summarized. Chapter 3 is devoted to an overview of the experimental
setup developed in this thesis. Chapter 4 explains simulation framework developed for this experiment. In Chapter 5, the analysis algorithm for the neutron

4

CHAPTER 1. INTRODUCTION

lifetime is presented. In Chapter 6, features and performances of the TPC aresummarized. The discussions on the basis of the results are given in Chapter 7.
Finally the thesis is concluded in Chapter 8.

Chapter 2
Neutron decay
2.1

Low energy eﬀective theory of the weak interaction

The neutron lifetime τn is expressed as∫
1= P (Ee )dEe ,
τn

(2.1)

where P (Ee ) is a rate of emitting the electron with an energy of Ee . According
to Fermi’s golden rule, P (Ee )dEe can be expressed by using the transition matrix
Hβ and the density of available ﬁnal states dn/dE0 where E0 is a total energy ofthe electron and the antineutrino:
P (Ee )dEe =2πdn|Hβ |2
.
~
dE0

(2.2)

Let pe and pν be the momentum of the electron and antineutrino, respectively.
Then, the number of the states is described asdn
4πp2e dpe · 4πp2ν dpν=.
dE0(2π~)6 dE0(2.3)

By using the relativistic relationship between the energy and momentum, pe andpν can be transformed, which gives
1
1 √p2e dpe = 2 pe Ee dEe = 3 Ee Ee2 − m2e c4 dEe ,cc11p2ν dpν = 3 Eν2 dEν = 3 (E0 − Ee )2 dEe ,ccwhere the neutrino mass was neglected. Inserting them into Eq. (2.3), the equationis rewritten as√
Ee2 − m2e c4 (E0 − Ee )2dn
2 Ee= (4π)
dEe .
(2.4)
dE0
(2π~c)65

6

CHAPTER 2. NEUTRON DECAY
The transition matrix of weak interaction |Hβ |2 has two components: Fermi

transition which carries zero angular momentum |HF |2 and Gamow-Teller transition which carries one unit of angular momentum |HGT |2 . In the case of freeneutron decay, each transition matrix is calculated [12] as|HF |2 = 1,
|HGT |2 = 3.
By using strengths of each transition, CV and CA , |Hβ |2 = CV + 3CA can beobtained, which introduces√∫
Ee Ee2 − m2e c4 (E0 − Ee )2
1= (CV + 3CA )
dEe .
(2.5)
τn
2π 3 ~7 c6

2.2

Big Bang nucleosynthesis

Big Bang nucleosynthesis (BBN) applies the results from nuclear physics to theearly universe under high temperature and pressure, with the free parameters being
only the baryon-to-photon ratio of the universe η. The predicted abundance of lightelements is in good agreement with the observation of primordial population [3, 4],which is one of the evidence for the Big Bang theory.
Immediately after the Big Bang (t ∼ 10−4 s) the quark-gluon plasma was cooled
down to give rise to neutrons and protons. The temperature was high enoughfor the weak, strong and electromagnetic interactions to remain in equilibrium:n + e+ ↔ p + ν̄ and p + e− ↔ n + ν. At that time, the ratio of neutrons to protons
was given by the Boltzmann factor
n/p = exp (−∆/T ),(2.6)

where T is the temperature of the universe and ∆ is the diﬀerence between the
proton and the neutron mass. At t ∼ 1 s after the Big Bang, the temperaturereached T ∼ 1 MeV, at which point, the weak interaction fell out of the equilibriums. This is called nucleon freeze-out, during which the neutron lifetime plays asigniﬁcant role since the strength of the charged weak interaction is proportional
to the combination of the coupling constants CV and CA that appear in Eq. (2.5).
Subsequently, the neutron lifetime governs the change in the neutron to proton ratio until the universe was cool enough to form stable deuterium. Then all
neutrons in the universe were bound into light nuclei by t = 3 min.
Since nucleon freeze-out depends also on η, BBN can constrain η by using theprimordial element abundances as a function of the neutron lifetime. Recently,

2.2. BIG BANG NUCLEOSYNTHESIS

7

the data on cosmic microwave background (CMB) anisotropies by the WMAP
observatory have become increasingly sensitive to η [13]. Thus the comparison ofthese two independent measurements allow for a more stringent test of BBN.
Figure 2.1 shows the primordial element abundances versus the baryon density[14] which are based upon the world average of neutron. The thickness of the
bands represents 1σ uncertainties in the calculated abundance. The ratio of 4 He
to H is described as Y in the top ﬁgure and is expected from BBN to be Y =0.2486 ± 0.0002. On the other hand, the latest measurement of Y by [15] ﬁnds
Y = 0.2565 ± 0.0010 ± 0.0050. This value is more than 1σ away from the value
given by BBN, which is determined by the neutron lifetime.
If this deviation is real, then it may provide insight into new physics beyond theminimal BBN model [16], for example, inhomogeneous big bang nucleosynthesis,
which motivates a neutron lifetime measurement with improved accuracy.

Figure 2.1: The primordial element abundances versus the baryon density based on
Big Bang nucleosynthesis [14].

8

CHAPTER 2. NEUTRON DECAY

2.3

Experiments of the neutron lifetime

After the discovery of the neutron in 1932 [1, 2], Chadwick and Goldhaber began
measuring the mass of the neutron and conﬁrmed that it exceeds the mass of the
proton in 1935 [17, 18]. Thus they predicted a possible decay of the neutron into
a proton, an electron and an antineutrino. However, it took more than 10 years
to detect the decay since the neutron ﬂux from radioisotopes was not suﬃciently
high. The development of the nuclear reactor provided the prospect of signiﬁcantly
higher neutron ﬂux.

2.3.1

Methods for the measurement of the neutron lifetime

Neutrons are classiﬁed according to its energy and the featured categories in thisthesis are the following:• fast neutron
Fission neutrons from a reactor and spallation neutrons by an accelerator
belong to fast neutrons, whose energy is around 1 MeV.
• cold neutron
The neutrons decelerated by a moderator to a temperature of a several tensof degrees Kelvin belong to cold neutrons, whose energy is around 1 meV.
The wave nature of the neutron becomes apparent at this energy scale, whichallows for a use of optical devices, such as a spin ﬂip chopper as describedin Section 3.3.
• ultra cold neutron
The neutrons decelerated by a moderator such as superﬂuid helium by meansof phonon scattering belong to ultra cold neutron (UCN), whose energy isless than 220 neV. Since the kinetic energy of UCNs is lower than the Fermi
eﬀective potential of the matter, UCNs are reﬂected oﬀ the surface of matter.
The relationship among energy, velocity and wavelength of the neutron is summarized in Figure 2.2. Figure 2.3 and 2.4 show the energy spectra of electrons andprotons from the neutron decay. The end points of the energy are 0.754 keV and
782 keV, respectively.
By using the various energy of the neutron and the characteristic spectra of the
proton and the electron, various measurements for the neutron lifetime have been
done, which are summarized in Table 2.1. The transition of the world averagevalue given by the Particle Data Group is shown in Figure 2.5.

2.3. EXPERIMENTS OF THE NEUTRON LIFETIME

9Electron from neutron decay

1

10-1

Simulation : Energy spectrum

10
1

10-1
10-2

10-3

10-3

10-4

10-4

1

10

102

103

Electron Energy [keV]

Figure 2.3: A energy spectrum of electrons emitted from the neutron decay.

Proton from neutron decay (cumulative)
Proton from neutron decay

10-2

10-5

Cumulative probability

10Electron from neutron decay (cumulative)

Probability [1/meV]

Simulation : Energy spectrum

Cumulative probability

Probability [1/keV]

Figure 2.2: Classiﬁcation of neutrons according to its energy.

10-5
1

10

102

103

Proton Energy [eV]

Figure 2.4: A energy spectrum of protons emitted from the neutron decay.

10

CHAPTER 2. NEUTRON DECAY
The experiments currently in operation are classiﬁed into three methods: “pen-ning trap method”, “gravitational trap method” and “magnetic trap method”. In
the past 20 years the accuracy of the neutron lifetime has improved to 0.1%, resulting in the world average 881.5 ± 1.5 s given by the Particle Data Group [19].
However the included values are not consistent with each other, in particular, thepenning trap method by NIST group gives 886.3 ± 1.2 ± 3.2 s [8], while the gravitational method by PNPI group gives 878.5 ± 0.7 ± 0.3 s [9] as shown in Figure
2.6. In the following sections, each method is described.

Figure 2.5: History of the neutron
lifetime world average given by theParticle Data Group [5].

2.3.2

Figure 2.6: Weighted average of the neutron
lifetime combined by the Particle Data Group
in 2011 [19].

Penning trap method

The most accurate measurement in the penning trap method was obtained by
the Sussex-ILL-NIST series of experiments [8, 32] as shown in Figure 2.7. A cold
neutron beam passes through a decay volume, so that some neutrons decay andemit the proton, whose maximum energy is 754 eV. Thus the protons are stored in
the penning trap with a voltage of 800 V and are led to the detector after turningoﬀ the voltage. After the neutron beams exits the trap, it passes through a verythin 6 LiF on a silicon substrate, which causes 6 Li(n, α)3 H reaction. A set of four
detectors with well characterized detection solid angle is located beside the silicon
substrate. The eﬃciency for the alpha and triton is also obtained, thus the neutron
ﬂux can be measured.
The count rate of the neutron decay Sβ is given by
Sβ =  p N

L1
,
τn v

(2.7)

2.3. EXPERIMENTS OF THE NEUTRON LIFETIMEτn (sec)
1108 ± 216
1100 ± 165
1013 ± 26
919 ± 14875 ± 95903 ± 13891 ± 9877 ± 10870 ± 8887.6 ± 3.0∗878 ± 27 ± 14
888.4 ± 3.1 ± 1.1
882.6 ± 2.7∗
889.2 ± 3.0 ± 3.8∗
885.4 ± 0.9 ± 0.4∗
878.5 ± 0.7 ± 0.3∗
886.3 ± 1.2 ± 3.2∗
878.2 ± 1.9
880.7 ± 1.3 ± 1.2∗
881.5 ± 1.5

YearAuthers
1951
J. M. Robson
1959
N. D’Angelo
1959
A. N. Sosnovsky
1972
C. J. Cristensen
1980 Yu. Yu. Kosvintsev et al.
1986 Yu. Yu. Kosvintsev et al.
1988
P. E. Spivak
1989
F. Anton et al.
1989 A. G. Kharitonov et al.
1989
W. Mampe et al.
1989
R. Kossakowski et al.
1992 V. V. Nesvizhevsky et al.
1993
W. Mampe et al.
1996
J. Byrne et al.
2000
S. Arzumanov et al.
2005
A. Serebrov et al.
2005
J. S. Nico et al.
2009
V. Ezhov et al.
2010
A. Pichlmaier et al.
2011
Particle Data Group

Ref.
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[11]
[30]
[31]
[32]
[33]
[9]
[8]
[10]
[34]
[19]

11

MethodEnergy
beam
CN
beam
CN
beam
CN
beam
CN
gravitational trap UCN
gravitational trap UCN
beam
CNmagnetic trap
VCN
gravitational trap UCN
gravitational trap UCN
beam
CNgravitational trap UCN
gravitational trap UCN
penning trapCNgravitational trap UCN
gravitational trap UCN
penning trapCNmagnetic trap
UCN
gravitational trap UCN——

Table 2.1: Summary of the experiments of the neutron lifetime. The world averagegiven by the Particle Data Group combines the data with asterisk, which is also shownin Figure 2.6. CN, VCN and UCN stand for cold neutrons, cold neutrons and ultra cold
neutrons.

where p is the detection eﬃciency of the proton from the neutron decay, N is theneutron ﬂux, v is the neutron velocity and L1 is the length of the decay volume,
which is located between a red part and a green part in Figure 2.7.
The neutron ﬂux is independently monitored and the count rate Sn is given by
Sn = n N ρσL2 ,(2.8)

where n is a detection eﬃciency of the triton and alpha from the neutron capturein 6 Li, ρ and σ denote the density and the cross section of the absorber, and L2 isthe thickness of the foil. From Eq. (2.7) and Eq. (2.8), the lifetime is expressedas)(1
Sn /n L1
τn =
.
(2.9)
ρσv Sβ /p L2
The neutron beam normally contains a broad spectrum of velocities. However, theabsorption cross section of cold neutrons is approximately inversely proportional
to the neutron velocity [35, 36], hence σv can be treated as a constant∗ .
∗In a recent measurement, a capture cross section in 3 He is obtained as (849.77 ± 0.14 ±12

CHAPTER 2. NEUTRON DECAY
The largest systematic uncertainties come from the accuracy of the densities
6of Li. The uncertainty in the capture cross section of the 6 Li is also signiﬁcant.

Figure 2.7: A schematic view of the experimental setup by means of beam method by
the Sussex-ILL-NIST group [8].

2.3.3Gravitational trap method

The UCNs are reﬂected oﬀ a surface of the material by Fermi potentials (∼ 220
neV) and are trapped by gravity (102 neV/m). Thus the UCNs can be stored in amaterial bottle for a time comparable to the neutron lifetime. Then the surviving
neutrons are counted. The UCNs are observed by Luschikov in 1968 [38] andthe ﬁrst measurement of the neutron lifetime by means of the gravitational trap
method is done by Kosvintsev in 1980 [24]. The eﬀects of the wall loss such as
inelastic scattering has inﬂuence on the systematic uncertainty, which is causedby residual hydrogen atoms on the bottle, thus the study of the hydrogen-free oilsuch as fomblin oil are usually used to coat the wall. However it is diﬃcult toevaluate the reﬂectivity of the surface with high precision.
The lifetime measurement uses the number of neutrons measured at two diﬀerent storage times, S1 and S2 . Hence the ratio S1 /S2 is expressed with the neutron
life time τn and the wall loss τwall asln(S1 /S2 )
1
1
=
+
.
∆t
τn τwall(2.10)The most accurate experiment was developed by the PNPI group and operated
at the ILL as shown in Figure 2.8. They invented a new coating, a ﬂuorinatedpolyether similar to the fomblin oil that is evaporated onto a surface and forms astable coating at cryogenic temperatures, in this case -160 ◦ C. With this coating,1.02)E − 2 − (1.253 ± 0.00+0.008−0.049 ) barn, where E is an energy of neutrons in a unit of eV [37]. In
the case of cold neutrons, deviation from the 1/v law is less than 0.1%.
1

2.3. EXPERIMENTS OF THE NEUTRON LIFETIME

13

the inelastic scattering probability decreased by a factor of 10 smaller than that−1by the fomblin oil [7]. Consequently τwall
becomes 1% of τn−1 . The neutron lifetime
from this experiment was 878.5 ± 0.7 ± 0.3 s [9].

Figure 2.8: A schematic view of the experimental setup by means of the gravitational trap method by the PNPI group[9]: 1 input neutron guide for UCN, 2 inlet valve, 3 selector valve, 4 foil unit, 5 vacuum volume, 6 separate vacuum volume of
the cryostat, 7 cooling system for the thermal shields, 8 UCN storage trap with thedashed lines depicting a narrow cylindricaltrap, 9 cryostat, 10 trap rotation drive, 11
step motor, 12 UCN detector, 13 detector
shield, and 14 vaporizer.

2.3.4

Figure 2.9: A schematic view of the experimental setup by means of the magnetic
trap method by the ILL group [10].

Magnetic trap method

Neutrons have a magnetic dipole moment and can be trapped by magnetic-ﬁeld
gradients alone in order to avoid the loss when neutrons come in contact with thewall. The ﬁrst such measurement is done by Anton et al. in 1989 [27] using very
cold neutrons whose energy is between the cold neutron and the UCN. The magnetic dipole moment of the neutron is 60 neV/T, thus the gradient will provide aforce that returns one spin state toward the center. In principle polarized neutrons
can be trapped until they decay. However there is an important loss mechanisms:

14

CHAPTER 2. NEUTRON DECAY

the depolarization in the gradient ﬁeld.
The latest measurement was performed at ILL [10] with UCNs instead of very
cold neutrons as shown in Figure 2.9. While the measurement principle is similar
to the bottle method, UCNs do not interact with matter in the wall during thestorage interval. Neutrons enter the top of the bottle and go down to the mainpart formed with a cylindrical, 20-pole permanent magnet array. A result from thisexperiment has been presented at conferences: 878.2 ± 1.9 s but not yet published
as of this writing. The quoted uncertainty is statistical only.

2.4

Beam method

A beam method was invented by Robson in 1951 [20], which uses cold neutrons anddetects the decay products in ﬂight. However it has not been performed for over
20 years after the experiment by Kossakowski et al. [11], which is the preceding
study of the experiment in this thesis.

2.4.1

Principle of the Kossakowski’s experiment

The electron from the neutron decay is detected in a time projection chamber(TPC). The continuos neutron beam from the reactor at the ILL go through achopper, which forms monochromatic neutron bunches. Thus the spatial spreadof the bunches is limited during their ﬂight path in the TPC. Analyzing the events
while the neutrons are completely in the TPC, a detection of 4π solid angle isguaranteed. One should note that only the electron from the neutron decay whose
maximum energy is 782 keV can be detected by the TPC, but not the proton since
the energy of the proton is less than 0.754 keV.
A small amount of 3 He is mixed with the gases.

3

He has a large neutron

capture cross section of σ0 = 5333 ± 7 barn at v0 = 2200 m/s [39], and thereaction products are the proton and triton whose energy are 572 keV and 191
keV, respectively. Thus the decay and the ﬂux of neutrons can be simultaneously
counted in the TPC. In the case of using 3 He gas, the density ρ3 He can be controlled
by the pressure and conﬁrmed by the mass spectrometer. Inserting L1 = L2 into
Eq. (2.9), the lifetime is obtained as1τn =ρ3 He σ0 v0(

Sn /nSβ /β),where β is a detection eﬃciency for the electrons from the neutron decay.

(2.11)

2.4. BEAM METHOD

15

In this method, the determination of the 3 He density directly inﬂuences theaccuracy of the neutron lifetime, so that the gas composition must not change
during the measurement. Thus the TPC is placed in a vacuum chamber, which isthen ﬁlled with gas after vacuuming. The gases do not ﬂow during the experiment.

2.4.2

Experimental setup for the Kossakowski’s experiment

In Kossakowski’s experiment, a mechanically rotating drum with a hole and asingle crystal monochromator were employed as a chopper [40]. The rotating
drum made a pulse, but the neutrons in the pulse had various velocities, so thatits length did not remain constant as it got transported. Thus the monochromator
was located in the downstream of the drum and was reﬂects neutrons with a certain
velocity and then the bunch with a ﬁxed length went to the TPC [41]. A schematic
view is shown in Figure 2.10.

Figure 2.10: A schematic view of the experimental setup by Kossakowski et al. [11].

The selected velocity corresponds to 837 m/s, thus only a fraction of 10−6 ofthe neutrons decays within the TPC with a length of 700 mm, which corresponded
to 0.1 cps of the neutron decay rate. Since the detectable particle from the neutron
decay was only the electron, the background was mainly caused by environmental
radiation. For shielding, the TPC was housed in 50 cm thick concrete walls andsurrounded by 5 cm thick lead. Cosmic rays events were rejected by making use ofplastic scintillators. The neutron capture γ rays also became background, which
originated from the gases along the ﬂight path. The gases also scattered theneutron inside the TPC with a probability of about 1% per meter, the materials

16

CHAPTER 2. NEUTRON DECAY

Figure 2.11: Wavelength spectrum of the neutrons at diﬀerent points of the beam line.
(a) exit of main guide, (b) exit of chopper drum, (c) secondary beam. The ﬁrst and thesecond-order Bragg reﬂection lines are indicated (4.73 and 2.36 Å), which corresponds
to 837 m/s and 1674 m/s, respectively [11].

around the ﬂight path became a source origin. For shielding the scattered neutrons,
the TPC was placed in a 6 LiF coated plexiglas box. 6 Li has a large neutron capture
cross section and the branching ratio of the reaction with γ rays is 4 × 10−5 . The
gases for the ionization and multiplication were He and CO2 , whose scattering andcapture cross section are shown in Table 2.2.
3

He
4
He
CO2
Ar
C 2 H2
C2 D2
CH4
N2

σs (barn) σ2body (barn) σγ (barn)
6
5333
0
1.34
0
0
14.0
0
0.0039
0.683
0
0.675
175.1
0
0.672
26.4
0
0.008
333.6
0
1.33
23.0
3.66
0.160

Table 2.2: Cross sections for 2200 m/s neutrons in typical gases. The scattering crosssection σs does not consider the eﬀect of molecular gas scattering described in Section
4.1.2. σ2body denotes the capture without prompt γ rays and σγ denotes the capture
with prompt γ rays.

2.4.3

Results of the Kossakowski’s experiment

It took 34 hours to take the data for the ﬁrst result, 878 ± 27 ± 14 s, whose
uncertainties arised from following items:• Low statistics due to monochromator,

2.4. BEAM METHOD

17

The wavelength spectrum of the neutrons are shown in Figure 2.11. It isfound that almost the neutrons transmit the monochromator, while only afraction of the neutrons arrived into the TPC. The rate of the neutron decay(Sβ ) was 0.1 cps, which caused a large statistical uncertainty of 3.1%. The
rate of capture of neutron by 3 He (Sn ) was controlled by the gas pressure
and it was set at 1.8 cps.
• Remained background after shielding the radiation,
After shielding, the environmental background (Be ) and the beam induced
background (Bb ) remained 80 cps and 20 cps, which dominated the rate of
the neutron decay. In order to compare the rate of the neutron decay withthat of other background, it is useful to convert it to the case of a continuos
1 s∼ 2 cps. For this conversion, the duty cycle
beam as 0.1 cps × 400 µs×110
Hzof the beam pulse is used.
• Low detection eﬃciency due to the signal selection by using track pattern,
In order to increase the signal-to-background ratio, the background to theneutron decay was strictly reduced by using signal selection. The electrons
from the neutron decay originate along the beam axis, which corresponds
to the center of the TPC. Thus they rejected the events whose end pointsof tracks did not match the center of the TPC, then only the 8% of the
background was remained after the selection (B ). However the rejected
events included the electrons from the neutron decay, which are scatteredon the material of the TPC, for instance. As a result, the signal selection
criteria reduced the detection eﬃciency for the neutron decay to 87.2% (β ),which resulted in 1.1% of systematic uncertainty for the correction of thedetection eﬃciency.
In addition, the separation between the neutron decay and the 3 He reaction
due to the saturation eﬀect as described in Section 4.4, which reduced thedetection eﬃciency for the 3 He reaction to 99.6% (n ) and introduced 0.6%
of systematic uncertainty for the correction of the detection eﬃciency.
• Subtraction of the background by using sideband region.
The subtraction of the beam-induced background caused by scattered neutron by gas is diﬃcult for the subtraction since it is associated with theneutron decay. They assumed an isotropic beam-induced background to theneutron decay, and subtracted it by using the sideband region outside theﬁducial volume where the neutron decay did not occur. In their analysis

18

CHAPTER 2. NEUTRON DECAY
0.9% of the systematic uncertainty was ascribed.
As a result, the lifetime was obtained with 3.5% uncertainties.
Facility
Repetition rate
Pulse per repetition
Length of pulse
Velocity
Fiducial time
Beam cross-section
Divergence
TPC gasGas pressure
Dimensions of TPC
Neutron decay rate (Sβ )Neutron capture rate in 3 He (Sn )Environmental background (Be )Beam-induced background (Bb )Remained background after the selection (B )Eﬃciency for the neutron decay (β )Eﬃciency for the 3 He reaction (n )Beam time
Statistical uncertainty
Correction for β
Correction for n
Subtraction of Bb
Cross section of 3 He
Resultreactor in ILL
110 Hz1
230∼250 mm
837 m/s
400 µs15 mm × 25 mm±8.7mradHe : CO2 = 93 : 7
95 kPa
190 mm×190 mm×700 mm
0.1 cps
1.8 cps
80 cps
20 cps
8%
87.2%
99.4%
34 hour
3.1%
1.1%
0.6%
0.9%
0.17%
878 ± 27 ± 14 s

Table 2.3: Parameters of the experiment by Kossakowski et al. The neutron bunch after
the chopper, characteristics of the TPC, and systematic uncertainties are summarized.

Chapter 3
Experiment in this thesis
The key points of the experiment in this thesis are• monochromatic neutron bunches whose length is shorter than the TPC,
• coincident detection of the neutron decay and the neutron ﬂux in the TPC,
which were conceived by Kossakowski et al. In this chapter, the novel approach
undertaken in the experiment as well as the experimental setup are described.

3.1

Approaches in this thesis

In order to overcome their shortcomings as discussed in Section 2.4, new approaches
are proposed in this thesis as follows. Comparison between the Kossakowski’s
experiment and this work is summarized in Table 3.1. The whole setup of theexperiment is shown in Figure 3.1. The schematic view of the TPC is shown in
Figure 3.2.
• Pulsed neutron source / spin ﬂip chopper
In order to make a high intensity bunch, a pulsed neutron source is moresuitable than continuous neutrons extracted from reactors, since the neutron
pulse broadens according to its velocity proﬁle. In other words, neutrons
with a certain velocity can be selected by means of the time of ﬂight (TOF)with a chopper. Thus the bunch can remain undispersed after the chopper,
eliminating the need for a monochromator, so that the transportation eﬃciency of the neutron becomes better. For this purpose a “spin ﬂip chopper”
is newly employed instead of the rotating drum [42]. In the case of the pulsed
neutron source, the cycle of the chopper has to decrease with increasing timeof ﬂight for a constant length of the bunch, while the cycle rate of the rotating drum used by Kossakowski was kept constant. The SFC can change the19

20

CHAPTER 3. EXPERIMENT IN THIS THESIS
direction of the neutron in a certain region of TOF spectrum by means of
the radio frequency, so that it can control the length of the neutron bunch
and the repetition rate. The neutron beam and the SFC are described in
Section 3.2 and Section 3.3, respectively.
• 4π shielded TPC with no radioactive contamination
The TPC developed by Kossakowski et al. was not cared for the radioactive
contamination and was made of no special low-activity material. For theevaluation of the radioactive contamination, many materials are investigatedby a germanium detector; a TPC made of polyethel ethel ketone (PEEK) has
been developed as described in Section 6.1. In order to shield the scatteredneutrons 6 Li plates are installed inside the TPC as described in Section 6.2.
A lead box and plastic scintillators are designed to surround the TPC with 4π
solid angle coverage as described in Section 3.6. Moreover, shields around the
SFC and an iron wall are installed to reduce the background arising from theneutron beam as described in Section 3.7. Consequently, the background to
the neutron decay can be reduced to 1/10 compared with the TPC developed
by Kossakowski et al.
• High detection eﬃciency by use of calorimetric approach
In this thesis, the TPC employs a calorimetric approach, which achieves
more than 99.9% detection eﬃciencies of the neutron decay and the neutron
capture in 3 He as described in Section 5.4. Moreover the reduction of the
backgrounds makes it possible to loosen the selection for the neutron decay.
The ratio of remained background after the selection (B ) becomes 25%,
which increases the detection eﬃciency as described in Section 5.5. Thus
the systematic uncertainty for the correction of the detection eﬃciency is
reduced to 0.1%.
• Subtraction of beam-induced background by use of a data-driven approach.
Kossakowski et al. accounted 0.9% of systematic uncertainty for the estimation of the beam-induced background by means of the sideband region.
In this thesis, new sources of background are investigated at ﬁrst. Subsequently, the beam-induced background is classiﬁed in terms of its origin
and subtracted by using 3 He-enriched measurements, time of ﬂight spectra
and reduced-pressure measurements as described in Section 5.6, 5.7 and 5.8,
which reduces the systematic uncertainty to be less than 0.1%.

3.1. APPROACHES IN THIS THESIS

21(1) (2) (3) (4) (5) (6)(a) (b)(7)(8) (9)(10)(c)(e) (f) (g)(d)

Spin FlipChopper

(A)
(X)

(Y)

(B) (C)

(D)
1m

(Z)

Figure 3.1: A drawing of the experimental setup: (A) beam dump, (B) lead shield,(C) iron shield, (D) 6 LiF-PTFE beam collimator, (X) Polarization branch, (Y) Unpolarization branch, (Z) Low divergence branch, (a) short-pass wavelength neutron ﬁlter,(b) guide coil, (c) spin ﬂipper, (d) magnetic super mirrors, (e) spin ﬂipper, (f) magnetic
super mirrors, (g) neutron beam monitor, (1) Zr window, (2) neutron switching shutter,(3) electron suppression magnet, (4) cosmic veto counter, (5) lead shield, (6) vacuum
chamber, (7) TPC, (8) electron suppression magnet, (9) 6 LiF beam catcher, and (10)turbo molecular pump.

55Fe Source& Collimator

MWPC Plane

5.9keV X-ray

Preamp.

Source Rotation Stage

Signal Readout

Al. mylar Drift CathodeBeam Entrance

Drift

LiF Inner Shield

Resistor Chain
Drift HV

Drift Cage Wires

50cm

Figure 3.2: A schematic view of the time projection chamber (front view).

22

CHAPTER 3. EXPERIMENT IN THIS THESIS

Kossakowski
Facility
reactor in ILL
Repetition rate
110 HzPulse per repetition
1
Length of pulse
230∼250 mm
Velocity
837 m/s
Duty factor
4.4%
Beam cross-section
15 mm×25 mm
Divergence±8.7mradTPC gasHe : CO2 = 93 : 7
Gas pressure
95 kPaDimensions of TPC 190 mm × 190 mm × 700 mm
Sβ
0.1 cps
Sn
1.8 cps
Be
80 cpsBb
20 cps
B
8%
β
87.2%
n
99.4%

This work
J-PARC40 Hz
5∼6
400 mm
500 m/s ∼ 1200 m/s∼ 7%
20 mm × 20 mm±4.2 mrad
He : CO2 = 85 : 15
50 kPa ∼ 100 kPa
300 mm × 300 mm × 960 mm
0.1 cps1∼3 cps
8 cps
2 cps
25%
> 99.9%> 99.9%

Table 3.1: Comparison between the preceding study and this work assuming 220 kWof beam power at J-PARC. Parameters of the neutron bunch after the chopper, characteristics of the TPC, and the systematic uncertainties are summarized.

3.2. NEUTRON BEAM

3.2

23

Neutron Beam

The experiment in this thesis employs the Polarization beam branch at a beamline
for neutron fundamental physics (BL05), Material and Life Science Experimental Facility (MLF), Japan Proton Accelerator Research Complex (J-PARC). The
property of the pulsed proton provided by Rapid-cycling Synchrotron (RCS) in
J-PARC is described in Section 3.2.1. The property of the spallation neutron at
the target in MLF is also described. Section 3.2.2 describes the characteristics ofeach beam branch at BL05 in MLF.

3.2.1

MLF/J-PARC

J-PARC is constructed in JAEA Tokai site as a joint project of the Japan Atomic
Energy Agency (JAEA) and High Energy Accelerator Research Organization (KEK). At J-PARC, a proton linac and 3 GeV and 30 GeV proton synchrotrons will provide MW-class proton beams.
These high intensity proton beams are used to produce various secondary andsuccessive decay particle beams. There are 4 major experimental facilities: Neutrino Facility, Nuclear and Particle Physics Experimental Hall (Hadron Hall), Materials and Life Science Experimental Facility (MLF) and Transmutation Experimental Facility.

Figure 3.3: A bird’s view of the J-PARC accelerator [43].

24

CHAPTER 3. EXPERIMENT IN THIS THESISParameter
Designed injection energy from Linac
Achieved injection energy from Linac
Extraction energy
Designed beam power
Achieved beam power
Repetition rate

Value
400 MeV
181 MeV
3 GeV
1 MW
220 kW
25 Hz

Table 3.2: Parameters of RCS [43].

MLF is aimed at promoting materials science and life science using the intense
pulsed neutron and muon beams which are produced using pulsed 3 GeV protons
with a repetition rate of 25 Hz. The protons are provided by RCS, which accelerates proton beams from 181 MeV (in the ﬁrst stage) to 3 GeV. While the design
goal of the beam power is 1 MW, the achieved beam power in 2011 is about 220
kW.
The pulsed protons reach into a liquid mercury target at MLF. The resulting
spallation neutrons are slowed down in moderators to 1 meV ∼ 20 meV, so-called
cold neutrons, and have a velocity spectrum of 500 m/s ∼ 2000 m/s. There arethree types of moderators: coupled moderator, decouple moderator and poisoned
moderator. Among the moderators, the coupled moderator provides the mostintense neutron beam and is employed for the experiment in this thesis. All moderators circulate supercritical H2 at 20 K and 1.5 MPa and provide cold neutrons
to 23 beam ports. The cold neutrons under Maxwell-Boltzmann velocity distribution are provided to each beam line and are broaden in the experimental areas at
a distance of about 16m from the moderator.

Numberofbeam port
Coupled11
Decoupled
6
Poisoned (thicker side)
3
Poisoned (thinner side)
3
Type of moderator

Time-integrated
Peak Neutron
thermal neutron
ﬂux at 10 meV
ﬂux [1/s/cm2 /MW] [1/eV/s/cm2 /MW]
4.6 × 108
6.0 × 1012
8
0.95 × 10
3.0 × 1012
0.65 × 108
2.4 × 1012
80.38 × 10
1.4 × 1012

Pulse width
in FWHM
at 10 meV
92
33
22
14

Table 3.3: Designed values of the neutron source at 10m from the moderators assuming
1 MW of the beam power at J-PARC [43].

3.2. NEUTRON BEAM

3.2.2

25

Polarization branch on BL05

BL05 provides neutrons moderated at the coupled moderator and divides theminto three characteristic branches by the bender at a distance of 7.2 ∼ 12 mfrom the moderator. These branches are called as “Polarization beam branch”,“Unpolarization beam branch” and “Low-divergence beam branch”.
• The Polarization beam branch is designed for the measurement of lifetimeof the neutron and the angular correlation of the neutron decay. Magnetic
supper mirror, described in Section 3.3.2 in detail, is housed in the beam
bender; only the neutrons whose spin is parallel to the magnetic ﬁeld are
reﬂected to the downstream.
• The Unpolarization beam branch produces the highest energy and most intense neutron ﬂux of these branches with a super-mirror bender. This beam
branch is designed for experiments of neutron small angle scattering to search
for a new medium range force and also to produce ultra cold neutron by aDoppler shifter.
• The Low-divergence beam branch is designed for an experiment of a neutroninterferometer, which consists of two super-mirror surfaces.
At the distance of 11.75 m from the moderator, horizontal and vertical beamslits were installed to deﬁne the beam width and position at the ends of each beam
bender. After the slit, the neutrons pass through the boron-lining vacuum ductsurrounded by iron and concrete shielding. A drawing of the BL05 and each beam
branch are described in Figure 3.4 and Figure 3.5. The ﬂux and the TOF spectrumof the neutron beam are shown in Table 3.4 and Figure 3.6.
Position Cross Section [cm2 ] Divergence [µstr](A)
10.0 × 11.0
2.0 × 102(B)
10.0 × 4.0
1.9 × 102
(C)
5.0 × 4.0
1.0 × 102
(D)
10.0 × 1.0
5.4 × 10−2

Flux [1/s/cm2 /MW]
(7.3 ± 0.9) × 108(3.9 ± 0.3) × 107(9.4 ± 0.7) × 107(5.4 ± 0.5) × 104

Table 3.4: Measured ﬂuxes, divergences at each position in BL05 as described in Figure
3.4.

26

CHAPTER 3. EXPERIMENT IN THIS THESIS

(B)
(C)
(A)
(D)
7.2 m
12.0 m
16.0 mFigure 3.4: A drawing of the BL05; (A) Upstream of the beam benders, (B) Exit ofPolarization beam branch, (C) Exit of Unpolarization beam branch, and (D) Exit of
Low-divergence beam branch.

Figure 3.5: A schematic view of eachbeam branch at upstream of the beam benders in BL05.

Figure 3.6: Measured neutron ﬂux ofeach beam branch in BL05.

3.3. SPIN FLIP CHOPPER

3.3

27

Spin ﬂip chopper

In this section, the principle and the performance of the spin ﬂip chopper (SFC) aredescribed. The ﬂight path of the neutron depends on the spin state as described in
Section 3.3.1. The SFC has two components, a magnetic super mirror (MSM) anda radio frequency ﬂipper (RFF) in the guide coil, which are described in Section
3.3.2 and 3.3.3, respectively. The performance of the SFC is presented in Section
3.3.4.

3.3.1

Overview of the SFC

The overall view of the SFC is found in Figure 3.7. There are three MSM and
two RFF in the guide coil. The MSM is made of several hundred double layersof ferromagnetic-nonmagnetic material inside the permanent magnet. The MSM
reﬂects the neutron from the Polarization branch whose spin is parallel to themagnetic ﬁeld, while neutrons with an opposite spin are transmitted. The RFF
provides an AC magnetic ﬁeld inside the solenoid coil. If the strength and frequency of the AC magnetic ﬁeld satisfy the resonance condition with the guidecoil, the Larmor rotation starts inside the solenoid coil and the spin of the neutron
ﬂips.
Figure 3.8 (top) shows the neutrons from the polarized branch reﬂected at all
the MSM when the RFF is turned oﬀ. Figure 3.8 (bottom) shows the neutronstransmitted at the ﬁrst MSM when the RFF is turned on. Thus RFF can control
the length and the repetition of the neutrons which are transported into the TPC.
2350

(C)

(B)

(D)

(E)

40

20

0

340

(A)

(H)

(F)
(G)

Figure 3.7: A drawing of the SFC at Polarization branch in BL05: (A)a ﬁrst radio
frequency ﬂipper, (B) ﬁrst and second magnetic supper mirrors, (C) a 6 Li shutter, (D)a second radio frequency ﬂipper, (E) a third magnetic supper mirror, (F) a guide coil,(G) boron gum, and (H) lead shields.

28

CHAPTER 3. EXPERIMENT IN THIS THESIS

Figure 3.8: A schematic view of the SFC.

3.3.2

Magnetic supper mirror

Let us consider a thin-layer with the angle of the incident neutron θ as shown in
Figure 3.9. If the neutron energy perpendicular to the thin-layer is less than the
nuclear potential of the thin-layer, the incident neutrons are reﬂected. However,even one of the largest eﬀective potential is 220 neV for nickel, which corresponds
to the speed of neutron of 6.8 m/sec. Thus, in order to make it larger, Mezei
proposed a supper mirror alternately stacked two materials with diﬀerent eﬀective
potential by changing their thickness [44]. Consequently, the energetic neutrons
are reﬂected depending of the thickness by means of Bragg reﬂection. In the ﬁeldof neutron optics, when the eﬀective potential of the supper mirror is larger thanthat of the nickel by a factor of m, it is expressed as mQc . The performance of thesupper mirror with large m-value is sensitive to the roughness of the surface andit is diﬃcult to attain high reﬂectivity. The relationship between m-value and thenumber of the layer N is expressed as N ' 4m4 .
The “magnetic” supper mirror stacks the ferromagnetic and nonmagnetic material, which is placed in strong enough magnetic ﬁeld to induce magnetic-ﬁeld
saturation (Bs ) in the ferromagnetic material. The potential of the ferromagnetic
material is expressed as a sum of the nuclear potential Vnucl and the magnetic potential ±µn Bs . Thus the nonmagnetic material is selected as its nuclear potential
is equal to Vnucl − µn Bs . As a result, the neutrons whose spin is antiparallel to themagnetic ﬁeld does not feel the potential gap and transmit the layers. It means
the MSM works as a polarizer of the neutron spin.

3.3. SPIN FLIP CHOPPER

29

Figure 3.9: A schematic view of the cross section of the magnetic supper mirror.

For this experiment, the magnetic supper mirrors were fabricated with sputtering ion beam in Kyoto University Research Reactor Institute (KURRI) and thespeciﬁcation is summarized in Table 3.5. As shown in Figure 3.10, ﬁve of themirrors are housed in the permanent magnet.
ferromagnetic materialFenon-magnetic material
SiGe3
the number of layers
7445
thickness of the thinnest layer
1.9 nmthickness of the thickest layer
60 nm
critical angle of the mirror
5 Qc
size of the mirror
140 mm × 35 mm× 0.7 mm
gap between mirrors
2.9 mmthe number of mirrors
5magnetic ﬁeld
35 mT
Table 3.5: Speciﬁcation of the magnetic supper mirror.

3.3.3

Radio-frequency ﬂipper

The radio frequency ﬂipper (RFF) consists of the guide coil and the solenoid coil
as shown in Figure 3.11 and can be divided into three regions which are depicted
in Figure 3.12. The region 1 and region 3 correspond to the outside of the solenoid
coil and the constant magnetic ﬁeld By is provided by the guide coil. Inside thesolenoid coil, region 2, the constant magnetic ﬁeld By and the AC magnetic ﬁeld
Bz at a frequency ω are provided.
The neutrons are passing through the regions in order and the ﬂipping proba-

30

CHAPTER 3. EXPERIMENT IN THIS THESIS

Figure 3.10: A photograph of a magnetic
supper mirror (MSM).

Figure 3.11: A photograph of a radio
frequency ﬂipper (RFF).

Figure 3.12: An illustration of the Larmor precession inside the radio frequency ﬂipper.

3.3. SPIN FLIP CHOPPER

31

bility in the region 2 is described as
√
P =

+

Bz2
Bz2 + (By − 2|µ~n | ω)2
Bz2
Bz2 + (By + 2|µ~n | ω)2(

sin2  Bz2 + By −√sin2 

(Bz2 + By +~
ω
2|µn |~
ω2|µn |

)2

)2


t

t .

Assuming By  Bz , the probability equals to 1 in case of 2|µ~n | ω = By and Bz t =(n + 1/2)π, which is called as the resonance condition. The speciﬁcation in thisexperiment is summarized in Table 3.6.
Diameter of solenoid
Length of solenoid
Frequency of the magnetic ﬁeld of the solenoid coil
Amplitude of the magnetic ﬁeld of the solenoid coilStrength of magnetic ﬁeld of the guide coil

50 mm
40 mm
29 kHz0.3 mT
1 mT

Table 3.6: Speciﬁcation of a radio frequency ﬂipper.

3.3.4

Performance

In practice, some neutrons are reﬂected at the MSM when the RFF is turned on,since the following items are less than 1:• 1 − 0 : the polarization degree of the polarized branch,• 1 − R : the ﬂipping ratio by the RFF,
• 1 − M : the transmission of the undesirous neutron at the MSM.
0 , R and M are around 5 × 10−2 . In this experiment, two RFFs and three MSMs
are employed to improve the beam extinction while the RFF is in operation.
ΦBeam represents the spin component of the polarized branch. MR and MM
denote the transportation matrices of RFF and MSM, respectively. These areexpressed with 0 , R and M :( )1
ΦBeam =
,
0

(
MR =

)
R 1
,
1 R

(
MM =

1 0
0 M

)
.

(3.1)

32

CHAPTER 3. EXPERIMENT IN THIS THESIS

Neutron counts [a.u.]

Neutron counts [a.u.]

1
Experiment : Performance of SFC
Flipper OFF

10-1

Flipper ON

10-2

10-3

0.01
0.009
0.008

Experiment : Performance of SFC
Flipper OFF
Flipper ON

0.007
0.006
0.005

10-4

0.004
0.003

-5

10

0.002
10-6
0.001
-7

10

0

5

10

15

20

40

0
19.6 19.8 20 20.2 20.4 20.6 20.8 21 21.2 21.4

Time of flight [msec]

Time of flight [msec]

25

30

35

Figure 3.13: Performance of the Spin
Flip Chopper.

Figure 3.14: Magniﬁed view of Figure
3.13.

ΦON and ΦOF F are the spin component of the neutrons which go to the TPC when
the RFF turns on and turns oﬀ, respectively. These can be calculate as(1
0 3M

)

ΦON =

3
MM
ΦBeam =

ΦOF F =

2
MM MR MMMR ΦBeam =,(R (0 + R ) + 2MM (0 + R )).

From this equation, ΦOF F is expected to be suppressed down to O(2 ).
The performance of the SFC is shown in Figure 3.13 and Figure 3.14. The
contrast of ΦON /ΦOF F ∼ 400 is achieved. The raising and falling time is about
0.5 ms which corresponds to the length of the RFF, 5 cm. The minimum lengthof the bunch is 15 cm. These values are summarized in Table 3.8
Cross section of the bunch
2 cm × 2 cm
Minimum length of the bunch
15 cm
Rising slope of the bunch
5 cmΦON /ΦOF F
400
Table 3.7: The performance of the developed SFC.

3.4. TIME PROJECTION CHAMBER

3.4

33

Time projection chamberThis section describes the key points of the time projection chamber (TPC) for
the simulation (see Chapter 4) and the analysis algorithm (see Chapter 5).

3.4.1

Overview of the TPC

The TPC has a rectangle MWPC part above an open-topped cuboid drift part.
In this thesis, z-axis corresponds to direction of the neutron beam. Then y-axis
is perpendicular to the ground. Applying high voltage on the bottom of TPC,
ionized electrons along the trajectory of a charged particle inside the drift part
travel to MWPC part. The TPC is set in the vacuum chamber and the gases are
ﬁlled after the evacuation.
Sensitive region of the TPC
290 mm (x) × 300 mm (y) × 960 mm (z)Number of anode wire
24 (z direction)
Number of ﬁeld wire
24 (z direction)
Number of cathode wire
160 × 2 (x direction)
Gas mixture
He : CO2 = 85 : 15 with a few ppm of 3 He
Gain
50000
Drift velocity
10 mm/µs
Total pressure
50 kPa ∼ 100 kPa
High voltage for the drift
6 kV ∼ 9 kVHigh voltage for the ionization
1450 V ∼ 1720 V
Table 3.8: The basic parameter of the TPC.

The TPC in this thesis is completely diﬀerent from the TPC developed by
Kossakowski et al. in two ways:• made of PEEK which contains no radioactive contamination,• installed 6 Li plate for the capture of scattered neutron.
The detailed design and the performance are described in Chapter 6.

3.4.2

Pre-ampliﬁer

The collected charge on the wires is converted to the voltage signal by a charge
sensitive preampliﬁer. The gains, 1 V/pC and 0.1 V/pC, are designed for the neutron decay and the neutron capture in 3 He, respectively. The electric connection
with wires are summarized in Table 3.9.

34

CHAPTER 3. EXPERIMENT IN THIS THESIS

412.0

Top LiF Frame

MWPC Hanger

Anode/Cathode Frame (t6)Cathode Frame(t6)Field Cage Front Panel

Field Cage Frame (Top)418.0

Field Wire Land (t2)Field Cage Frame (Bottom)

400.0
550.0

Figure 3.15: A drawing of the front of the TPC (x-y plane).

1070.0Top LiF Frame
1032.0
Anode/Cathode Frame
Cathode Frame
Field Cage Frame (Top)289.0Side Bar
Corner Piller
MWPC Hanger
Field Cage Frame (Bottom)
Al Pedestal
980.0

1080.0Figure 3.16: A drawing of the side of the TPC (y-z plane).

3.4. TIME PROJECTION CHAMBER
Low gain ampliﬁer
Wire
anode / cathode (bottom)
Channel
24 ch / 40 ch
Gain
1 V/pC
Shaping time
0.5 µsec
Consumption power
500 mW/ch
ENC
8000

35
High gain ampliﬁer
ﬁeld / cathode (top)
24 ch / 40 ch
0.1 V/pC
0.5 µsec
500 mW/ch
80000

Table 3.9: Speciﬁcation detail of the pre-ampliﬁer and wire connections.

The circuit board with OPA656 produced by Texas Instruments is developed
by S. Satoh (KEK) and the values of discrete components are optimized for thisexperiment as shown in Figure 3.17. The current fed into the circuit is controlled
by R1 and R2 , which reduce the current to 1/10 in the low gain mode. The ﬁrst
time constant, 7.7 µsec, is set to maximize the signal-to-noise ratio and the signals
are shaped in the diﬀerentiating and integrating circuit of about 0.5 µsec time
constant.

Figure 3.17: A circuit of the ampliﬁer for this thesis. R0 = NoConnect and R1 = 0Ω
in high gain mode. R0 =1k Ω and R1 =10 kΩ in the low gain mode. C1 =1.5 pF, C2 =330
pF, C3 =47 pF, R2 =5.1 MΩ, R3 =1 kΩ, R4 =24 kΩ, and R5 =11 kΩ in common.

3.4.3

Trigger

An event for the acquisition is triggered when any signal of the anodes exceeds thethreshold which corresponds to 200 eV. A block diagram of the electronics is given
in Figure 3.18. In order to suppress the background due to cosmic ray, signal fromthe scintillators surrounded TPC vetoes the trigger for 50 µs. Subsequently the
waveforms of all wires and the time of ﬂight are recorded via FADC and TDC on

36

CHAPTER 3. EXPERIMENT IN THIS THESIS

Copper-Lite.

Figure 3.18: A circuit for the trigger and the data acquisition.

3.4.4

Frontend electronics

KEK online group has developed a general purpose pipeline readout board, COPPER(COmmonPipelined Platform for Electronics Readout), which has four daughter cards, collectively called FINESSE (Front-end INstrumentation Entity for Subdetector Speciﬁc Electronics). Many type of FINESSE such as 500 MHz FADC
have been also developed. The data from the FINESSEs is built on the COPPER
and transferred via an ethernet port. The acquisition dead-time is 300 µs/eventand the busy signal from the Copper-Lite is also considered.
Our using FINESSE and improvement of the FPGA are as follows:• 65 MHz 12 bit FADC
The default ﬁrmware does not support the self-trigger since the write operation starts at a falling edge of the trigger signal. Thus a ring buﬀer in
the FIFO is implemented, which enables to take the data before the trigger
signal.
• 1 GHz 16 bit multihit TDC
The dynamic rage of the default setting is 60 µs, however it is much shorter
than the beam interval of J-PARC, 40 ms. Therefore we implemented frequency divider and lengthen the dynamic range to 52 ms, which corresponds
to 1.25MHz.

3.5. BEAM MONITOR AND 6 LI SHUTTER

Number of FINESSE
Number of channel
clock
sampling point
data size
Improvement

65MHz 12bit FADC
16820 MHz
10 bit2 kbyte/ch
support for self-trigger

37
1GHz multihit TDC
132
1.25 MHz
16 bit< 1 kbyte
lengthen the dynamic range

Table 3.10: The speciﬁcations of the FADC and TDC.

Figure 3.19: A photograph of a beam
monitor.

3.5

Figure 3.20: A photograph of a 6 Li shutter.

Beam monitor and 6Li shutter

The neutrons captured in B4 C in the SFC generate γ rays. While almost all theγ rays are shielded by the surrounding lead, some of them emerge together with
the neutron from the exit of the SFC and becomes the background of the TPC.
The background is subtracted by use of a beam monitor and a 6 Li shutter locatedright downstream of the SFC. The pictures are shown in Figure 3.19 and 3.20.
The beam monitor (manufactured by Canberra Industries Inc., MNH10/4.2F)
contains small quantities of 3 He. The speciﬁcation is described in Table 3.11. The
6
Li shutter moves by a stepping motor inside a vacuum chamber, which has a
6
Li plate and an apertured 6 Li plate. The beam monitor can measure the relative
neutron ﬂux between two shutter conditions with an accuracy of 0.1% for 14 hours.

3.6

Shields for the environmental background

This section describes the designs of the shielding for the environmental radiation(Be ) which consist of the Pb shielding and cosmic-ray veto counter. Assuming 220

38

CHAPTER 3. EXPERIMENT IN THIS THESISGas
Ar : CH4 = 130 kPa : 13 kPa
Active size
100 mm × 42 mm × 40 mm
Detection eﬃciency
10−5Count rate stability± 0.005 on 72 hours
Background
1 cpm
Table 3.11: Speciﬁcation detail of a beam monitor.

kW of beam power at J-PARC and 7% of duty factor of the SFC, the rate of theneutron decay is expected to be 0.089 cps (Sβ ). In order to compare this number
with that of other background, it converted to the case of a continuos beam as
0.089 ×1
∼ 1.3 cps.
0.07

(3.2)

The rate of environmental background without shielding is measured as 123.7 cps
at the experimental area in MLF and becomes 30.7 cps after the signal selection
as described in Section 5.5. For achieving Sβ /Be ∼ 1, the hits of the TPC due tothe environmental radiation is reduced to 4% by the Pb shielding and the cosmic
ray veto counter.

3.6.1

Pb shielding

The environmental γ rays mainly originate from 40 K (1461keV) and 208 Tl (2615keV)in the ground. 222 Rn exists in air, whose decay products are also γ-ray sources;214

Pb (295keV, 352keV) and 214 Bi (609keV, 1765keV). Lead is used for the shielding of the environmental γ rays and is put into an iron case as shown in Figure
3.21. 10 cm thick lead shield is placed in 1 cm thick iron case for the upstreamside. For the other sides the thickness of the lead shield is 5 cm. The iron shields
a Pb-Kα X ray with a range of 70 keV to 90 keV due to the excitation and a β
ray from 210 Bi (Q=1.16MeV) which is a daughter nucleus of 210 Pb. For 1461 keV
γ ray from 40 K the penetrating eﬃciency is 2% according to a Geant4 simulation.
Figure 3.23 shows the assembled structure. The aperture ratio is about 1%
due to the two holes for the beam pipes. Figure 3.24 shows the performance of theshielding by using a 2-inch NaI detector. The environmental γ rays are suppressedby the shielding. Cosmic rays excite the iodine in NaI and cause a KX ray, thus itis vetoed by surrounding scintillators as described in the next section. As a result
the shielding eﬃciency is evaluated to be 2.0% and is in good agreement with the
expectation.

3.6. SHIELDS FOR THE ENVIRONMENTAL BACKGROUND

Figure 3.22: A drawing of the bottom of thefront of the Pb shielding.

Counts [cps/10keV]

Figure 3.21: A photograph of thebottom of the front of the Pb shielding.

39

Environmertal γ -ray background2

TPC shield w/ Pb/Fe

10

TPC shield w/ Pb/Fe and cosmic ray veto

10

I:KX

214

Bi
40

K

1

208

Tl

10-1
10-2
10-3
10-4
102

Figure 3.23: A photograph of the Pb
shielding.

103

Energy [keV]

Figure 3.24: A performance of the Pb
shielding.

40

CHAPTER 3. EXPERIMENT IN THIS THESIS

Outer size
1120 mm (x) × 1326 mm (y)× 1656 mm (z)Inner size
980 mm (x) × 1176 mm (y) × 1466 mm (z)Aperture ratio
1%
Penetrating eﬃciency at 1461 keV γ ray
2%
NaI count rate w/o the shielding
119 cps
NaI count rate w the shielding
5.0 cps
NaI count rate w cosmic ray veto
2.3 cps

Table 3.12: Speciﬁcation detail of the Pb shielding and summary of the performanceby using NaI detector.

3.6.2

Cosmic-ray veto counter

Scintillators for the cosmic-ray veto surround the lead shielding as shown in Figure 3.27, Extruded scintillators for the Telescope Array experiment are used. A
speciﬁcation is shown in Table 3.13.
Company
Product name
Size
Material
Wavelength of maximum scintillation
Scintillation eﬃciency
Decay time
Light attenuation length
Refractive index
Density

C. I. Industry
CIMS-G2
1500 mm × 250 mm × 12 mm
MS-IM-62-01
420 nm
60% Anthracene
3.0 ∼ 3.2 nsec
90 ∼ 110 cm
1.5 ∼ 1.58
1.04 cm3

Table 3.13: Speciﬁcation detail of the cosmic ray counter.

The scintillator has grooves at 10 mm intervals and a wavelength shifter, theY11 produced by Kuraray Co. Ltd. is installed. We use a tyvek sheet manufactured by DuPont Co. as a reﬂector and R329 manufactured by Hamamatsu
Photonics K. K. for the photon detector. These selections are conformed to theTelescope Array experiment.
The eﬃciency for the cosmic ray is evaluated by cubic scintillators, about 10 cm
on a side. While the maximum energy due to the environmental γ ray is less than
2.6 MeV, the cosmic ray can deposit more than 20 MeV in the cubic scintillators.
Thus only the cosmic ray can be triggered by means of energy threshold. The
eﬃciency map of each cosmic ray counter is taken and the minimum eﬃciency ismeasured to be 97.7%. In case of the assembled structure as shown in Figure 3.27,
the eﬃciency is evaluated to be 95.9%. This value includes the ineﬃcient region

3.7. SHIELDS FOR THE BEAM-INDUCED BACKGROUND

41

due to the hall for the beam pipes.
Position
Top
Front
Back
Right
Left
Xback
XFrontA [%]99.52 ± 0.06——
100.00− 0.06
99.69 ± 0.06
98.58 ± 0.06
97.95 ± 0.06

B [%]99.57 ± 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 [%]
E [%]
99.73 ± 0.04 99.12 ± 0.04
99.64 ± 0.04—
99.73 ± 0.04—
99.73 ± 0.04 98.34 ± 0.04
99.82 ± 0.04 98.93 ± 0.04————

Table 3.14: Detection eﬃciency of the cosmic ray veto counter at each position described in Figure 3.27.

3.7

Shields for the beam-induced background originated from the outside the TPC

This section describes shields for the beam-induced background originated fromoutside the TPC which consist of the SFC shielding and the Fe wall. A blue line
in Figure 3.29 shows the TOF spectrum of the beam-induced background with the6
Li shutter closed. and it is found that there are two component; the tail between
0∼5 ms and the bumps between 10∼40 ms.
The tail is derived from the fast neutron which is not stopped by the shielding at
a distance of 12∼16 m from the moderator. The Polarization beam branch selects
neutrons with one spin state for the SFC and the rest including fast neutrons areabsorbed by the concrete shielding located upstream of the SFC. However all theneutrons and prompt γ rays are not shielded, so that they become the backgroundto the neutron decay. In addition, BL04 which is constructed next to BL05 is alsoa background source for our experiment. For the shielding an L-Type iron wall 20
cm thick is set up as shown in Figure 3.29.
The bumps between 10∼40 ms are derived from the neutrons passing throughthe SFC. While the SFC shapes a desirable neutron bunch, some neutrons arecaptured on the supper mirror or scattered by the air. Consequently the structureof the bunches is clearly seen and the timing of the peaks corresponds to thetime when the neutron bunch reﬂect on the third magnetic mirror from upstream.
Thus the SFC is housed in the boron-lining lead box for the shielding as shownin Figure 3.7. A red line in Figure 3.29 shows the TOF spectrum after shielding.
The beam-induced background is reduced to be 2 cps (Bb ).

42

CHAPTER 3. EXPERIMENT IN THIS THESIS

Figure 3.25: A drawing of the front of the cosmic-ray veto counter. Detection eﬃciencies at positions A, B, C, D, and E are summarized in Table 3.14. A measurement setup
is shown in Figure 3.26.

3.7. SHIELDS FOR THE BEAM-INDUCED BACKGROUNDCounts [1/sec]

Figure 3.26: A setup for the measurement of detection eﬃciency of the cosmicray veto counters.

43

Figure 3.27: A photograph of the cosmic
ray veto counters.

6

Experiment : TOF spectrum with Li shutter closed

102

w/o SFC shielding and Fe wall
w/ SFC shielding and Fe wall

10

1

0

5

10

15

20

25

30

35

40

Time of flight [msec]

Figure 3.28: A TOF spectrum of the beam-induced background with no shielding(blue) and with SFC shielding and Fe wall (red) The neutron beam is chopped by the
SFC and stopped by the 6 Li shutter.

44

CHAPTER 3. EXPERIMENT IN THIS THESIS

Figure 3.29: A drawing of the Fe shielding and SFC shielding.

Chapter 4
Simulation
This chapter describes the Monte Carlo (MC) simulation for the neutron decay,
which includes the behavior of the particles and the response of the TPC. The
simulation is applied to the neutron decay, the neutron capture in 3 He and various
backgrounds as discussed in Chapter 5. The procedure of the simulation is asfollows.
• Calculate the interaction of the particles using GEANT4• Ionize atoms along the trajectory of the charged particle• Drift the ionized electrons• Cause the multiplication on the wire
• Process the signal
In particular, the interaction of the neutron and multiplication on the wire has
been developed for this experiment, as described in Section 4.1 and Section 4.4,
respectively.

4.1

Interaction of particles

The Monte Carlo (MC) simulation for the time projection chamber was codedusing GEANT4 release 9.2.p01. An example of MC simulation for the neutron decay
is shown in Figure 4.1. The vacuum chamber, the lead shielding and cosmic vetocounters are also implemented.
GEANT4 has selectable physics model, however the behavior of the neutron is
not fully reproduced. Thus the items as described as follows are independently
developed for the experiment in this thesis.
45

46

CHAPTER 4. SIMULATION• Angular correlation of the neutron decay• Angle and energy of the scattered neutron• Energy spectrum of the prompt γ ray due to the capture of the neutron

The components are described in 4.1.1, 4.1.2 and 4.1.3, respectively.

4.1.1

Decay of neutron

Figure 4.1: Implemented geometry on GEANT4. The yellow line represents the electronfrom the neutron decay inside the TPC. The electron moves from left to right.

The proﬁle of the neutron beam is shown in Figure 4.2, in which the TPC is
located from -480 mm to 480 mm. The divergence and attenuation of the beam areconsidered as described in Section 3.2.2. The attenuation length depends on thegas scattering and the velocity of the neutron, which is calculated in the Section
4.1.2. The neutron decay implemented in G4NeutronBetaDecayChannel.hh, emits
the decay products incorrectly on the same plane. Thus the progr am is modiﬁed
to model the three-body decay correctly.

4.1.2

Scattering of neutron

Scattering of the neutron with an energy less than 20 MeV is implemented in
G4NeutronHPElastic.hh, which describes only the scattering by free atoms at agiven temperature. However in the case of the molecular gas scattering, coherent
scattering due to the structure of the molecule has to be considered [45, 46, 47].
The eﬀects incorporated in the developed code is as follows.

Y direction [mm]4.1. INTERACTION OF PARTICLES

47

1

30

Simulation : Beam profile

0.9
0.8

20

0.7

10
0.6

0

0.5
0.4

-10
0.3

-20

0.2
0.1

-30
-1500 -1000 -500

0

500

1000

1500

0

Beam direction [mm]Figure 4.2: A simulated neutron distribution with scattering of gas on Y and Z axis.

• Coherent scattering from the atoms in the molecule
The neutron with an energy less than 1 eV is assumed to be S-wave, andtherefore the scattering of the neutron by a point-like nucleus at rest isspherically symmetric and independent of the velocity. The energy of theneutron provided in MLF/J-PARC corresponds to a wavelength of 0.2 nm ∼0.8 nm, which is comparable to the distance between C and O in the CO2 (∼0.1 nm). Thus the coherent scattering due to the structure of the moleculeis signiﬁcant. The calculation is performed by using the Semiclassical model
based on the Born approximation developed by N. Z. Alcock et al. [48].
4πrThe cross section σ(θ, φ) is described with xij = λ ij sin( 2θ ), where rij isthe distance between atoms and λ is the wavelength of the neutron. The
equation is obtained as follows.
σ(θ, φ) = −M 2∑∑
sin xij
1()(σi σj )1/2,
4π M + 1
x
ij
i
j

(4.1)

where σi σj denotes the total scattering cross section in the case of i = j,otherwise it denotes the coherent scattering cross section. M represents themass of the molecule in a unit of amu. (M/M + 1)2 indicates the transformation from the center of mass frame to the laboratory frame.
• Thermal motion of the gas molecule
While the velocity of the neutron is 500 ∼ 2000 m/s, the average velocities ofthe He and CO2 at room temperature are 1400 m/s and 400 m/s, respectively.

48

CHAPTER 4. SIMULATION
vn and vgas represent the velocities of the neutron and the gas so that the
number of interaction is proportional to 1 − vn v·v2gas . Therefore the relativen√
2 , is expressed using the Boltzmann distribution
velocity, vrel = vn2 + vgas
as:∫2
−mvgasm 3/2
2v̄rel = vrel × 4πvgas() exp()dvgas .
(4.2)
2πkT
2kT
From this equation, the contribution of the thermal motion can be calculated.

The developed code is conﬁrmed to reproduce the scattering of the neutron
with the velocity of 3700 m/sec in the preceding experiment as shown in Figure
4.3 [48] In the preceding experiment, CO2 under 60 atm was employed so thatthe suppression can be seen in the small angle due to the screening eﬀect. Figure
4.4 represents the velocity dependence of the scattering angle. As the incident
neutron becomes slower, the forward scattering is enhanced in particular and thetotal cross section is increasing.
Thermal motion also has an inﬂuence on the velocity after the scattering, which
has to be considered since the neutron capture cross section of the atom such as
3

He is inversely proportional to the velocity [35, 36]. Figure 4.5 shows the resultsof the neutron with the velocity of 400∼2000 m/sec scattered by He, CO2 andCH4 at room temperature. These data are employed for the scattered neutron.

4.1.3

Capture of neutron

The capture of the neutron with an energy less than 20 MeV is implemented in
G4NeutronHPCapture.hh and G4NeutronHPInelastic.hh. The cross section andits 1/v dependence is incorporated, however the decay products wrongly emit
prompt γ rays. Thus the map of the capture position for the scattered neutronis recorded at ﬁrst, and the correct products without γ rays are subsequently
generated on the spot.
Figure 4.6 shows the map of the neutron capture in 3 He and 6 Li. The neutron isscattered from the beam axis discussed in Section 4.1.1. The velocity and angle ofthe neutron is calculated as described in Section 4.1.2. Figure 4.7 shows the energy
spectrum of the prompt γ ray from the 95% 6 Li-enriched plate, which consists of
LiF : PTFE = 30wt% : 70wt%. Each contribution is summarized in Table 4.1.

4.1.4

Energy loss of charged particles

Geant4 has selectable physics models based on diﬀerent principles. For electromagnetic processes for e− and γ in the low energy domain, Low-energy and Standard

3
Neutron (v=3700m/sec) scattered from CO

2

Theoretical curve based on semiclassical model

2.5

49

Neutron wavelength [nm]Enhancement factor

4.1. INTERACTION OF PARTICLES

Experimental data taken by N.Z.Alcock (1959)

2

1
3

0.9
vn=2000 m/s

0.8

2.5

0.7
0.6
2

0.5
Experiment in this manuscript

0.4

1.5

1.5

0.3
vn=500 m/s

0.2

1

0.1
0

0.5

1

1.5

2

2.5

Experiment by Alcock (vn=3700m/s)

30Scattering angle [radian]

0.5

1

1.5

2

2.5

1

3

Scattering angle [radian]Figure 4.3: The angular distribution of
the enhancement factor by an interferenceof CO2 molecule. The crossed points aremeasured values by Alcock et al. , and thesolid curve is the calculation by using thesemi-classical model.

6

Li
7
Li
C
F

cross section
39 mbarn
45 mbarn
3.5 mbarn
39 mbarnmole fraction
0.173
0.009
0.212
0.606

Figure 4.4: The enhancement factor dependence of the scattering angle and neutron wavelength. The green solid line describes the wavelength which Alcock et al.
was used for their measurement.

branching ratio
4.1 × 10−5
2.5 × 10−6
4.5 × 10−6
3.5 × 10−5

average number of γ ray
1.41
1.03
1.16
2.78

Table 4.1: Properties of the prompt γ rays from the 6 Li plate.

packages are prepared. Low-energy package consists of two diﬀerent approaches,
which are Library-based (Livermore) models and Penelope-like models. Livermore
models are based on publicly available evaluated data tables including elementsfrom Z = 1 to Z = 100 with a validity range of 250 eV ∼ 100 GeV. On the other
hand, Penelope is a Monte-Carlo code, which directly calculates atomic eﬀects as
ﬂorescence x ray. The validity range is also 250 eV ∼ 100GeV.
The comparison between two packages in release 9.1 are investigated in termsof energy deposition in homogeneous targets [49]. According to this work, theaccuracy achieved by simulations involving Library-based processes is comparable
to, or better than, the one resulting from Penelope processes. Thus the work inthis thesis adapt the Livermore package as below.

Neutron:1200m/sec , Target:He

Neutron:1200m/sec , Target:CO2

Neutron:1200m/sec , Target:CH4

Scattering angle [radian]

Scattering angle [radian]

CHAPTER 4. SIMULATION

Scattering angle [radian]

50

3
2.5
2
1.5

3
2.5
2
1.5

3
2.5
2
1.5

1

1

1

0.5

0.5

0.5

0
0

1500
2000
2500
3000
Velocity after scattering [m/sec]

500

1000

0
0

1500
2000
2500
3000
Velocity after scattering [m/sec]

500

1000

1500
2000
2500
3000
Velocity after scattering [m/sec]

Neutron:1000m/sec , Target:He

Neutron:1000m/sec , Target:CO2

Neutron:1000m/sec , Target:CH4
Scattering angle [radian]

1000

Scattering angle [radian]

500

Scattering angle [radian]

0
0

3
2.5
2
1.5

2
1.5

1

1

0.5

0.5

1000

00

1500
2000
2500
3000
Velocity after scattering [m/sec]

3
2.5
2
1.5

500

1000

00

1500
2000
2500
3000
Velocity after scattering [m/sec]

Neutron:800m/sec , Target:CO2
3
2.5
2
1.5

2
1.5

1

1

0.5

0.5

00

1500
2000
2500
3000
Velocity after scattering [m/sec]

3
2.5
2
1.5

1000

00

1500
2000
2500
3000
Velocity after scattering [m/sec]

Neutron:600m/sec , Target:CO2
Scattering angle [radian]

Neutron:600m/sec , Target:He

500

3
2.5
2
1.5

2
1.5

1

1

0.5

0.5

0
0

1500
2000
2500
3000
Velocity after scattering [m/sec]

3
2.5
2
1.5

1000

0
0

1500
2000
2500
3000
Velocity after scattering [m/sec]

Neutron:400m/sec , Target:CO2
Scattering angle [radian]

Neutron:400m/sec , Target:He

500

3
2.5
2
1.5

2
1.5

1

1

0.5

0.5

1000

1500
2000
2500
3000
Velocity after scattering [m/sec]

00

500

1000

1500
2000
2500
3000
Velocity after scattering [m/sec]

1500
2000
2500
3000
Velocity after scattering [m/sec]

3

1

500

1000

2.5

0.5
00

500

Neutron:400m/sec , Target:CH4
Scattering angle [radian]

1000

1500
2000
2500
3000
Velocity after scattering [m/sec]

3

1

500

1000

2.5

0.5
0
0

500

Neutron:600m/sec , Target:CH4
Scattering angle [radian]

1000

1500
2000
2500
3000
Velocity after scattering [m/sec]

3

1

500

1000

2.5

0.5
00

500

Neutron:800m/sec , Target:CH4
Scattering angle [radian]

500

Scattering angle [radian]

Scattering angle [radian]

2
1.5

3
2.5

1

Neutron:800m/sec , Target:He

Scattering angle [radian]

2.5

0.5
00

Scattering angle [radian]

3

00

500

1000

1500
2000
2500
3000
Velocity after scattering [m/sec]

Figure 4.5: Diﬀerential scattering cross sections with scattering angle and velocity
after scattering for 3 gases (He, CO2 , and CH4 ) and 5 diﬀerent initial velocities.

Y direction [mm]4.1. INTERACTION OF PARTICLES

51

200
150

Simulation : Capture position
3

He

100

6

Li

50
0
-50
-100
-150
-1500

-1000

-500

0

500

1000

1500

Beam direction [mm]CountsFigure 4.6: A scatter plot of positions of the neutron capture calculated by the simulation taking account of the gas scattering.

Simulation : Energy of prompt γ -rays from the Li board
6

1

10-1

10-2

10-3

10-4

0

1

2

3

4

5

6

7

8

Energy [MeV]

Figure 4.7: The prompt γ ray spectrum generated by neutron capture of 6 Li.

52

CHAPTER 4. SIMULATION
From

Low energy EM process
Particle
G4LowEnergyIonizatione−
G4LowEnergyBremsstrahlunge−Livermore
G4LowEnergyPhotoelectricγ
G4LowEnergyComptonγ
G4LowEnergyGammaConversionγ
G4LowEnergyRayleighγ
G4hLowEnergyIonisation
hadrons
Table 4.2: Libraries used in this simulation code.

4.2

Ionization

A charged particle that traverses the gas leaves a track of ionization along its
trajectory. The total amount of ionization is characterized by the energy W thatis spent, on the average, on the creation of one free electron. The energy W depends
on the gas mixture so that many measurements of W have been performed. As
shown in Figure 4.8 and 4.9, W values depend on the incident particle and its
energy at low energy, while they become constant for electrons with an energyof more than 1 keV and protons with an energy of more than 10 keV, which aresummarized in Table 4.3.

HeCO2Wα [eV]46.0
34.3

Wβ [eV]
42.3
32.8

I [eV]
24.58
13.81

Table 4.3: Average energy W spent for the creation of one ionization electron. Wα andWβ are from measurement using α or β sources, respectively. The minimum ionization
potential is also indicated.

Ionization process consists of two steps and the energy W is the inclusive value.
At ﬁrst, an incident charged particle ionizes atoms and the second step is caused byelectrons which are ejected from the ﬁrst ionization. Since GEANT4 also simulatesalso secondary electrons, the distribution of ionization electron can be obtained byusing Poisson statistics.

4.3

Drift and diﬀusion

The ionization electrons drift in the electric ﬁeld as they are diﬀused by the gas
molecules. The drift part of the TPC is designed to make a uniform electric ﬁeld

4.4. MULTIPLICATION

Figure 4.8: W value of CO2 for the electron as a incident particle [50].

53

Figure 4.9: W value of CO2 for the proton as a incident particle [51].

and it is conﬁrmed that the variation of drift velocity is within 1%. The diﬀusion
width is measured to be less than 1mm. Thus in this simulation the drift velocity
is treated as uniform and the diﬀusion is neglected.

4.4

Multiplication

The multiplication on the wire is formulated by H. Oide [52], which takes into
account the space-charge eﬀect. As an ionized electron drifts towards the anodewire, it travels in an increasing electric ﬁeld, which causes avalanche multiplication.
A gain factor G is exponentially increasing with the anode voltage V as shown in
Figure 6.22. Since V has a linear relationship with electric ﬁeld on the wire E(r0 )where r0 is a radius of the wires, G ∝ exp(E(r0 )) can be obtained.
G depends on the number of electrons collected on the wire, which are createdby the incident charged particle. Let us call Gi the gain factor for the i-th electron
arriving at the wire, so that Gi ∝ exp(Ei (r0 )) can be assumed, where Ei (r0 )denotes the electric ﬁeld E(r0 ) at the time of i-th avalanche multiplication.
The TPC detects the neutron decay and the neutron capture in 3 He. In the former case the multiplied signal is proportional to the number of electrons collected.

54

CHAPTER 4. SIMULATION

However, in the latter case, the number of the initial ionized electrons is so muchthat the created ions during the avalanche multiplication induce a space-charge
eﬀect around the wire, which causes a saturation of the multiplied signal.
Since a mobility of the ions are smaller than that of the electron by three ordersof magnitude, the ions can be considered not to move during the whole multiplication. Assuming the electric ﬁeld decreases proportionally with the created ions,
Ei (r0 ) is calculated asEi (r0 ) = E0 (r0 ) − α

i−1
∑

Gj ,

(4.3)

j=0

where α is a constant determined by the angle θ between the anode wire and a direction of the incident charge particle. By using the relationship Gi ∝ exp(Ei (r0 )),Gi+1= exp(Ei+1 (r0 ) − Ei (r0 )) = exp(−αGi )
Gi

(4.4)

can be introduced. Using αGi  1,Gi '

G01 + iαG0(4.5)

is a good approximation. Inserting it into Eq (4.4), both sides of the equation areequivalent at a level of O(α). Assuming the number of the collected electrons is
n, the eﬀect of the saturation s(θ) can be computed as the accumulation of each
multiplication:1 ∑ln(1 + nαG0 )s(θ) ≡Gi =.
nG0 i=0
nαG0
n−1

(4.6)

Figure 4.10 shows a setup using 5.5-MeV α rays emitted from the 241 Am tomeasure the saturation eﬀect. The energy deposit (∆E) varies across the wires
and the results are summarized in Fig 4.11. The saturation eﬀect increases withthe angle because the multiplication region is localized and with the deposit energy
because the multiplied ions are accumulated. From this measurement, nα can beobtained as
a∆E
nα =
−1
{ 1 + b tan θa = (1.39 ± 0.06) × 10−3
b = 2.5 ± 0.4,
where a and b are constants. In the MC simulation, the saturation eﬀect is implemented by using this formula and the position dependence is also considered.

55

Saturation effect4.5. SIGNAL PROCESSING

1
Experiment : 241Am°

0.9

0 , 3.9MeV°

45 , 0.7MeV

0.8°

45 , 0.8MeV°

0.7

45 , 1.0MeV°

45 , 1.4MeV°

0.6

90 , 0.6MeV°

90 , 0.8MeV

0.5°

90 , 1.1MeV°

0.4

90 , 1.3MeV°

90 , 1.5MeV

0.3
0.2
0.1
0

103

104

105
Gain

Figure 4.10: A schematic view of themeasurement of the saturation eﬀect byusing 5.5-MeV α rays emitted from the241 Am. Anode wires are shown in dottedlines.

4.5

Figure 4.11: Evaluated curves for thesaturation eﬀect obtained by ﬁtting themeasured value.

Signal processing

As described in Section 3.4.2, the collected charge on the wire is converted to
the voltage signal by a charge sensitive preampliﬁer. Then all the waveforms arerecorded via FADCs on Copper-Lite.
Figure 4.12 (top) shows the event display of the MC simulation. The data
format is same as the experimental data, which is also described in Figure 4.12
(bottom).

56

CHAPTER 4. SIMULATION

Figure 4.12: Views of the event display drawing a track event made by the simulation(top) and obtained by TPC (bottom).

Conc.
H—
1
H
99.985
2
H
0.015
He
—
3
He 0.00014
4He 99.99986
Li
—
6
Li
7.5
7
Li
92.5
B
—
10
B
20
11
B
80
C
—
12
C
98.9
13
C
1.1
N
14
N
99.63
15
N
0.37
O
—
16
O
99.762
17
O
0.038
18
O
0.2
F 100

σs (barn) σ2body (barn) E2body (keV) σγ (barn) Eγ (MeV) Erecoil (keV)
τn
82.02
0
—
0.3326
—
—
—
82.03
0
—
0.3326
2.22
1.32
—
7.64
0
—
0.000519
6.25
6.96
12.32a1.34—
0.00747———65333.(7.)
764
—
—
—
—
1.34
0
—
0
—
—
—
1.37
—
70.5
—
—
—
0.97
940.(4.)
4783
0.039
—
—
—
1.4
0
—
0.0454
—
—
840ms
5.24
0
—
767.(8.)
—
—
3.1
0
—
3835.(9.)
—
—
—
5.77
0
—
0.0055——20.2ms5.551
0—0.0035
—
—
—
5.559
0
—
0.00353
4.95
1.01
—
4.84
0
—
0.00137
8.17
2.56
5.7 × 103 year
11.51
—
—
—
—
—
11.53
1.83
626
0.0798
10.8
4.20
—
5.21
0
—
0.000024
8.87
7.1sec4.232
0—0.00019
—
—
—
4.232
0
—
0.0001
3.27
0.339
—
4.2
0
—
0.236
4.37
0.570
—
4.29
0
—
0.00016
4.18
delay
26.5sec
4.018
0—0.009611.2sec

4.5. SIGNAL PROCESSING
57

Table 4.4: Table of the parameters related with the neutron capture or scattering.

Al
Cr
50
Cr
52
Cr
53
Cr
54
Cr
Fe
54
Fe
56
Fe
57
Fe
58
Fe
Ni
58
Ni
60
Ni
61
Ni
62
Ni
64
Ni
Zr
90
Zr
91
Zr
92
Zr
94
Zr
96
Zr

Conc. σs (barn) σ2body (barn)
100
1.503
—
—
3.49
—
4.35
2.54
—
83.79
3.042
—
9.5
8.15
—
2.36
2.6
—
—
11.62
—
5.8
2.2
—
91.7
12.42
—
2.2
1
—
0.3
28.(26.)
—
—
18.5
—
68.27
26.1
—
26.1
0.99
—
1.13
9.2
—
3.59
9.5
—
0.91
0.017
—
—
6.46
—
51.45
5.1
—
11.32
9.7
—
17.19
6.9
—
17.28
8.4
—
2.76
3.8
—

E2body (keV) σγ (barn) Eγ (MeV) Erecoil (keV)
τn
—
0.231
—
—
2.24sec
—
3.05
—
—
—
—
15.8
—
—
27.7day
—
0.76
—
—
—
—
18.1(1.5)
—
—
—
—
0.36
—
—
3.50min
—
2.56
—
—
—
—
2.25
—
—
2.74a
—
2.59
—
—
—
—
2.48
—
—
—
—
1.28
—
—
44.5day
—
4.49
—
—
—
—
4.6
—
—
7.6 × 104 a
—
2.9
—
—
—
—
2.5
—
—
—
—
14.5
—
—
100.1a—1.52——
2.52hour
—
0.185
—
—
—
—
0.011
—
—
—
—
1.17
—
—
—
—
0.22
—
—
1.53 × 106 a—
0.0499——64.0day—
0.0229——16.7hour58
CHAPTER 4. SIMULATION

Table 4.5: Table of the parameters related with the neutron capture or scattering.

Chapter 5
Analysis algorithm for themeasurement of the neutron
lifetime
In this chapter, a newly developed analysis algorithm for the measurement of theneutron lifetime is discussed. The experiment in this thesis classiﬁes the backgrounds according to the physics processes and evaluates them quantitively. Then
• 99.9% detection eﬃciency by use of calorimetric approach,• subtraction of the background by using data-driven approach,have been developed.

5.1

Overview of the analysis algorithm

For the measurement of the neutron decay, the counts of the neutron decay (Sβ )and the neutron capture in 3 He (Sn ) have to be extracted from the analyzed data.
In Table 5.1, a developed analysis algorithm is described. Assuming the datataking under 100 kPa with a 3 He pressure of 0.1 Pa (N 100kPa/0.1Pa ), it includes
various backgrounds. The backgrounds are categorized according to methods ofthe subtraction as described in Section 5.3: Bβenergy , Bβn , Bβtof , Bβgas , Bnenergy , Bntof
and Bngas .
In this algorithm, three other conditions of the ﬁlling gas are employed as shownin Table 5.2. N 100kPa/1.0Pa is a 3 He-enriched measurement with a 3 He pressure of
1.0 Pa. N 50kPa/0.1Pa and N 50kPa/1.0Pa are taken under reduced pressures, 50 kPa.
In the ﬁrst step, Sβ , Sn and Bβenergy are discriminated by using a calorimetricapproach with more than 99.9% detection eﬃciency for both reactions as described59

60

CHAPTER 5. ANALYSIS ALGORITHM
Data (N 100kPa/0.1Pa )Approach

N 100kPa/0.1Pa = Sβ + Bβenergy + Bβn + Bβtof + Bβgas + Sn + Bntof + Bngas↓

calorimetry
100kPa/0.1Pa

Nβ↓= Sβ + Bβn + Bβtof + Bβgas

Nn100kPa = Sn + Bntof + Bngas↓

Signal selection
0 100kPa/0.1Pa

Nβ

↓
0

0

0

0

= Sβ + Bβn + Bβtof + Bβgas

0

0

↓
↓
↓

3

He-enrichedmeasurement(N 100kPa/1.0Pa )00Nβ100kPa= Sβ + Bβtof + Bβgas
0↓

TOF spectra0

reduced-pressure
measurement(N 50kPa/0.1Pa , N 50kPa/1.0Pa )

0

0

0

↓
↓
↓
↓
↓
↓
↓

0

0

0

Nn100kPa = Sn + Bntof + Bngas

0

0

0

Nβ100kPa= Sβ + Bβgas
00

Nn100kPa= Sn + Bngas
00

↓
↓
↓

↓
↓
↓

0

0

Sβ

Sn

Table 5.1: Analysis algorithm for the neutron lifetime.

in Section 5.4. In the second step, the signal selections are applied for the reduction of the background as described in Section 5.5. An inﬂuence on the detection
eﬃciency of the TPC under the reduced pressure is also discussed. The resulting
candidate of the neutron decay includes the background due to the neutron capture00
in 3 He (Bβn ). An amount of Bβn depends on the pressure of 3 He and is evaluatedby 3 He-enriched measurement (N 100kPa,1Pa ) in the third step, which is described in
Section 5.6. In the fourth step, the backgrounds due to radioactivation, environmental radiation and prompt γ ray originated from outside the TPC (Bβtof , Bntof )are subtracted by using TOF spectrum as described in Section 5.7. Finally, the00remaining backgrounds depends on the total pressure of the gas (Bβgas , Bngas ), sothat the reduced-pressure measurements (N 50kPa,0.1Pa , N 50kPa,1Pa ) are employed as
described in Section 5.8.
00Consequently Sβ and Sn are extracted from the analyzed data with more than
99.9% detection eﬃciencies for both reactions and the neutron lifetime is calculated

5.2. SIGNAL OF THE NEUTRON DECAY
4

100kPa/0.1Pa

N
N 100kPa/1.0Pa
N 50kPa/0.1Pa
N 50kPa/1.0PaHe
CO285 kPa
15 kPa
85 kPa
15 kPa42.5 kPa 7.5 kPa
42.5 kPa 7.5 kPa

61
3

He
0.1 Pa
1.0 Pa
0.1 Pa
1.0 PaTable 5.2: Measurements under various gas pressure for the subtraction of the background by using data-driven approach.

as
1
τn =
ρ3 He σ0 v0(0

Sn /n0Sβ /β),(5.1)

which is discussed in Section 2.4.

5.2

Signal of the neutron decay

If the SFC is not active, all the neutrons are reﬂected on the supper mirror and go
into the TPC, which yields 1.2 × 106 neutron/s with a power of 220 kW. Figure
5.1 and Table 5.3 show the condition of the SFC which enables to maximize therate of neutron decay. In the following, the ﬁducial volume with a length of 800
mm are assumed. The length of the bunch corresponds to a half of the ﬁducial
volume (400 mm). The interval between the bunches are set to be equal to the
distance between the window and the beam dump (2826 mm). On this condition,
13.9% of the neutrons pass the TPC and the sum of the ﬁducial time per cycle
t1 corresponds to 2.8 ms. Consequently the rate of the neutron decay becomes
1.2 × 106 × 7.3 × 10−8 = 8.9 × 10−2 decay/s. A subset of the time when the neutron
does not exist inside the TPC, t0 , is set to be 6 ms as shown in Figure 5.1, which
is used for the subtraction by use of the TOF spectrum.

5.3

Backgrounds

Backgrounds to the neutron decay are divided into four categories: Bβenergy , Bβn ,Bβtof and Bβgas . Backgrounds to the neutron capture in 3 He are divided into three
categories: Bnenergy , Bntof and Bngas .
In the following, 400-mm bunches with a velocity of 1000 m/s inside the 2826mm vacuum chamber. which corresponds to 400 µs of the ﬁducial time. The ratioof the event in the ﬁducial time is calculated as 400mm/2826mm = 0.14.

CHAPTER 5. ANALYSIS ALGORITHM

Neutron counts [a.u.]62

1Experiment : Performance of SFC @ 220kW
Flipper OFF : 1.2×106neutron/sec

10-1

Flipper ON : 8.9×10-2decay/sec
-2

10

t0

10-3
10-4
10-5
10-6
10-7
0

5

10

15

20

25

30

35

40

Time of flight [msec]

Figure 5.1: TOF spectrum assuming 6 of 400 mm-bunches per 1 pulse and 2826 mmof the interval of bunches. 2826 mm corresponds to the distance between the window ofthe vacuum chamber and the beam dump.

Velocity [m/sec]
1250
1085
941
816
708
615
total

Neutron ratio[10−2 ] Fiducial time [ms/cycle]
1.4
0.32
2.4
0.36
3.1
0.42
3.0
0.49
2.3
0.56
1.6
0.65
13.9
2.8 (≡ t1 )Decay ratio[10−8 ]
0.50
0.98
1.5
1.7
1.4
1.2
7.3

Table 5.3: Neutron decay ratio inside the 800mm of the ﬁducial volume assuming 6 of
400 mm-bunches per 1 pulse and 2826 mm of the interval of bunches.

5.3.1

Backgrounds to the beta decay

Backgrounds are categorized according to methods of the subtraction. Bβenergy (B0 )can be discriminated by the calorimetric approach. Bβn (B1 ) can be subtracted
by using measurements under diﬀerent pressure of 3 He. Bβtof can be subtracted
by using TOF spectrum and consists of B2 ∼ B5 . Bβgas is subtracted by using
measurements under reduced pressures and consists of B6 ∼ B8 .
• SβThe neutron with a lifetime of 881.5 s decays at a rate of 1.1 × 10−6 permeter and 4.3 × 10−7 of the neutrons decays in the ﬁducial time. In the
TOF spectrum, the detected neutron decay increases as the bunch comes in5.3. BACKGROUNDS

63

the TPC and becomes constant while the bunch is fully inside the ﬁducial
volume. It then decreases as the bunch gets out of the TPC. A schematic
TOF spectrum is shown in Figure 5.20.
• Bβenergy– B0 : Recoiled nucleus due to prompt γ rays
The neutron is captured in CO2 inside the TPC with a probability of
3.4 × 10−6 per meter and prompt γ rays are emitted, which recoils thenucleus with an energy of 1 keV.
• Bβn
– B1 : Oﬀ-axis neutron capture in 3 He
The neutron is scattered by He and CO2 inside the TPC with a probability of 3.3 × 10−2 per meter. Some scattered neutron are captured in
3
He on the way to the 6 Li plates. In particular, the neutron captured
in 3 He near the 6 Li plates becomes background to the neutron decay,
since decay product, a proton or a triton, goes into the 6 Li plates anddeposit only a portion of Q-value in side the TPC.
• Bβtof– B2 : Prompt γ rays outside the TPC
On the Polarization beam branch in the BL05/MLF, only the cold neutron can be transferred by the supper mirror at a distance of 7.2∼12 mfrom the target. The rest is captured in the iron and concrete shielding
at a distance of 12∼16 m from the target and emit prompt γ rays, whichcauses the spectrum to decrease exponentially with time. As shown in
Figure 3.28, the rate of B2 between 15∼34 ms is 1.0 cps; the rate of B2
between 34∼40 ms is 0.8 cps.
– B3 : Radioactivation inside the TPC
Radioactive atoms generated by the neutron capture and their decay
products become the background to the neutron decay. In the 6 Li
plate, 20 F (τ = 11.2s) is the most dominant component following by
8
Li (τ = 840ms). Both have lifetime longer than the beam interval of
40 ms, thus the time structure of this background is almost ﬂat.
– B4 : Radioactivation outside the TPC
Outside the TPC, Pb and Fe in the shields and Si in the supper mirror

64

CHAPTER 5. ANALYSIS ALGORITHM
are radioactivated. Their lifetime is also longer than 40 ms, thus thetime structure is almost ﬂat.
– B5 : Environmental radiation
Environmental radiation consists of naturally-occurring radioisotopes,
cosmic rays and radioisotopes inside the TPC itself, whose time structure is ﬂat. In this section, the rate of the environmental radiation isassumed as 1.4 cps, which can be obtained in Section 6.3.
• Bβgas– B6 : Prompt γ rays from 6 Li plate
The neutron is scattered by He and CO2 inside the TPC with a probability of 3.3 × 10−2 per meter and captured in the 6 Li plates. The
branching fraction to prompt γ rays is about 8.3 × 10−4 and an average
number of the prompt γ rays is 2.0. A Compton electron due to prompt
γ rays reaches the TPC with a probability of 9.5 × 10−3 , which resultsin the background in the ﬁducial time with a rate of 2.0 × 10−8 perneutron. The time structure is the same as that of the neutron decay
signal.
– B7 : Prompt γ rays from CO2
The neutron is captured in CO2 inside the TPC with a probabilityof 3.4 × 10−6 per meter, which emit 1.5 of the prompt γ rays on anaverage. A Compton electron due to prompt γ rays reaches the TPC
with a probability of 1.5 × 10−3 , which results in the background in theﬁducial time with a rate of 3.0 × 10−9 per neutron. The time structureis the same as that of the neutron decay signal.
– B8 : Oﬀ-axis neutron decay
Some scattered neutron decay in its ﬂight on the way to 6 Li plates witha probability of 2.2 × 10−7 . which results in the background in theﬁducial time with a rate of 3.3 × 10−9 per neutron. The time structureis the same as that of the neutron decay signal.

The event probability of each signal in the ﬁducial time is described in Table
5.4. Not all process is applicable and the relevant factor are listed. Ps is thescattering probability per meter, Pγ is the emission probability of the prompt γray, Nγ is the average number of the prompt γ ray, Pβ is the emission probabilityof β ray including the neutron decay, Ptime is the ratio of the event in the ﬁducial
time and PT P C is the hit probability of the TPC in the ﬁducial time.

5.3. BACKGROUNDS

Sβ
B0
B1
B2
B3
B4
B5
B6
B7
B8

L
Ps
2.82
—
2.82
—
2.82 3.3 × 10−2——
2.82 3.3 × 10−2————
2.82 3.3 × 10−2
2.82—
2.82 3.3 × 10−265Pγ—
3.4 × 10−6
—
—
—
—
—
8.3 × 10−5
3.4 × 10−6—NγPβ
— 1.1 × 10−6——
— 2.2 × 10−7——
— 6.5 × 10−6
— 5.0 × 10−10——
2.0 9.5 × 10−3
1.5 1.5 × 10−3
— 2.2 × 10−7

Ptime
0.14
0.14
0.14
—
0.01
0.01
—
0.14
0.14
0.14

PT P C
4.3 × 10−7
1.3 × 10−8
3.3 × 10−9—
2.1 × 10−9
5.0 × 10−12—
2.0 × 10−8
3.0 × 10−9
3.3 × 10−9

Table 5.4: The probabilities of each step of the generation of the background due tothe gas inside TPC.

5.3.2

Backgrounds to the neutron capture in 3 He

Backgrounds to the neutron capture in 3 He are also categorized according to methods of the subtraction.
• Sn : Neutron capture in 3 He
The neutron is captured in 3 He which subsequently decays into a proton andtriton (σ=5333 barn, Q-value=782 keV) The rate with a 3 He partial pressureof 4.0 mPa at 276 degrees Kelvin corresponds to that of the neutron decay.
• Bnenergy : Neutron capture in N2 inside the TPC
The neutron is captured in N2 and decays into a proton and 14 C (σ=1.83
barn, Q-value=626 keV). The contamination of the nitrogen is caused byoutgassing or air leak, thus this reaction increases over time. The rate withbarn× 2) at 276 degrees
a N2 partial pressure of 5.8 Pa (= 4.0 mPa× 5333
1.83 barn
Kelvin corresponds to that of the neutron decay. The time structure is thesame as that of the neutron capture in 3 He.

• Bntof : Environmental radiation
The ﬂat background stems from natural α-activity on the surface of thedetector such as radon. The half-life of the radon is 3.8 day, thus this reaction
decreases over time.
• Bngas : Scattered neutron capture in 3 He inside the TPC
The neutron is scattered by He and CO2 inside the TPC with a probabilityof 3.3×10−2 per meter and some scattered neutron are captured in 3 He. The
time structure is the same as that of the neutron decay signal.

66

CHAPTER 5. ANALYSIS ALGORITHM
In particular Bnenergy is caused by N2 contained in the outgas and the reaction

Counts [a.u.]of 14 N(n, p)14 C cannot be discriminated from the neutron capture in 3 He with theenergy resolution of the TPC as shown in Figure 5.2. Thus we have no choice tothoroughly remove the N2 gas from the vacuum chamber to reduce the 14 N(n, p)14 C
reaction to less than 0.1% of the 3 He(n, p)3 H reaction.

Simulation : N2 reaction

105

3

He reaction
N2 reaction
Total energy spectrum

104
103
102

10

1
300

400

500

600

700

800

900 1000 1100

Deposit Energy [keV]

Figure 5.2: The expected pulse height spectrum of 3 He reaction candidates. The redcross is the 3 He spectrum measured by the TPC with an anode voltage of 1100V. The
blue cross is the expected N2 spectrum obtained by linear scaling of the Q-value as 10%of 3 He events.

5.4

Signal separation by using calorimetric approach

5.4.1

Separation between Sβ and Sn

An electron from the neutron decay has an energy up to 782 keV and the energy ofthe proton is less than 0.754 keV. On the other hand, the neutron capture in 3 Hegenerates the proton and triton with energies of 579 keV and 191 keV, respectively.
Figure 5.3 and 5.4 show the rate of energy loss per unit length (dE/dx) and rangeof the electron and proton in the gas inside the TPC (He : CO2 = 85kPa : 15kPa).
It is found that the dE/dx of the electron is smaller than that of the proton by
two orders of magnitude. According to the Bethe-Bloch formula, dE/dx decreases
as β −2 with increasing energy and it reaches 0.8 keV/cm.
The energy deposit varies substantially depending on the initial energy of theelectron. Figure 5.5 and Table 5.5 show the relationship between the energy of

2

Range

104

104

dE/dx

105

67

105
Proton : 100kPa (He:CO =85:15)
2

Range

104

104

dE/dx

103

103

103

103

102

102

102

102

10

10

10

10

1

1

1

1

10

103

102

102

10

Electron Energy [keV]

Figure 5.3: Flight range and dE/dx forelectron with its energy.

dE/dx [keV/cm]

105
Electron : 100kPa (He:CO =85:15)

Range [cm]105

dE/dx [keV/cm]

Range [cm]5.4. SIGNAL SEPARATION BY USING CALORIMETRIC APPROACH

103

Proton Energy [keV]

Figure 5.4: Flight range and dE/dx for
proton with its energy.

the electron and the energy deposit inside the TPC (300mm × 290mm × 960mm),
assuming the neutron decays in the ﬁducial volume (20mm × 20mm × 800mm).

3

Entries 1000000

103

782keV : End point of the electron energy

2.5
2

102

10

Log (Deposit energy [keV])At low energy the energy deposit inside the TPC is increasing until the range oftrajectory excesses the TPC size. Then it is decreasing with a progressive reduction
in dE/dx.

1.5
1
10782keV

0.5
0
0

0.5

1

1.5

2

2.5

3

1

Log (Electron energy [keV])
10

Figure 5.5: The relation between electron initial energy and the energy deposit on the
TPC under 100 kPa.

The neutron capture in 3 He is also shown (blue, Figure 5.6),
Figure 5.6 shows the energy spectra of the neutron decay (red), the neutron

68

CHAPTER 5. ANALYSIS ALGORITHM

Electron energy
Terminal position
Deposit energy

0∼60 keV
inside the TPC
0∼60 keV

60∼200 keV
inside/outside the TPC
12∼200 keV

200∼782 keVoutside the TPC
8∼30 keV

Table 5.5: Energy, terminated position and deposit energy in TPC for electrons produced by the neutron decays on the beam axis under 100 kPa.

capture in 3 He (blue) and the neutron capture in CO2 (green). The neutron capture in 3 He has a broad energy spectrum due to the saturation eﬀect as describedin Section 4.4. This simulation assumes the gain of MWPC as 50000 in Eq. 4.6.
Figure 5.7 shows the separation between the neutron decay and the neutron capture in 3 He by means of the maximum energy deposit among the ﬁeld wires, sincea Bragg peak of the protons and tritons from the 3 He reaction is much higher
than that of the electrons. The selection in terms of the range of the trajectory is
also eﬀective for the separation. By requiring the events with a range of less than
10cm (red, Figure 5.7), the extraction of the 3 He reaction can be fully achieved byusing a threshold of 35 keV. Thus the analyzed data (N 100kPa/0.1Pa ) is divided into
100kPa/0.1Pa
candidates of the neutron decay (Nβ) and candidates of the neutron cap100kPa/0.1Pa). However the candidates of the neutron decay include
ture in 3 He (Nnoﬀ-axis neutron capture in 3 He (pink, Figure 5.7), which is subtracted by using
3
He-enriched measurement as described in Section 5.6.

5.4.2

Separation between Sβ and Bβenergy

A nucleus in the gases captures the neutron and the emitted prompt γ ray recoils
E2
the nucleus with an energy of 2Mγ , where Eγ is the energy of prompt γ ray and
M is the mass of the recoil nucleus. This event occurs along the neutron beamaxis, thus can not be distinguished from the neutron decay. Table 5.6 summarizes
the recoil energy Erecoil for the prompt γ ray and the maximum energy Eγ for
typical nuclei. The natural abundance and the neutron capture cross section are
also shown.
Among the using gas, the cross sections of helium and oxygen are negligibly
small, however 12 C has also large neutron capture cross section and corresponds to
2.5 times larger than the neutron decay rate. The recoil energy is 1.01 keV, thus
more than 99.9% of the electrons from the neutron decay can be be distinguishedby means of the energy spectrum. In addition, carbon contains 13 C at a rate of
1.1% and its recoil energy is 2.56 keV. To avoid the inﬂuence on the neutron decay,
13
C-free CO2 is needed.

Counts [a.u.]Counts [a.u.]

5.4. SIGNAL SEPARATION BY USING CALORIMETRIC APPROACH

Simulation : Deposit energy in TPC

102
10

Sβ

: On-axis neutron decaySn: On-axis neutron capture in 3He

energyBβ

69

Simulation : Max energy deposit w/ range selection

102

Sβ : On-axis neutron decay
Sn : On-axis neutron capture in 3He

103

Bnβ : Off-axis neutron capture in He: Neutron capture in 12CO2

1

1
10-1

10-1

35keV

10-2

10-2

10-3

10-3

10-4

10-4

10-5
0
0

0.5

1

1.5

2

2.5

0.5

1

1.5

2

2.5

3

log (Energy [keV])
103log (Energy [keV])
10

Figure 5.6: Energy spectrum of the deposit energy inside the TPC by neutron
decay (red), neutron capture in 3 He (blue),
and CO2 (green) under 100 kPa.

Figure 5.7: Simulated maximum energy depositions among the wires after
the range selection by on-axis neutron decay (red), on-axis neutron capture in 3He(blue) and oﬀ-axis neutron capture in 3He(pink) under 100 kPa.

The separation between Sβ and Bβenergy depends on the ﬂuctuation of the number of initial ionized electrons, which is determined by W value as Section 4.2.
However it is deteriorated by a recombination eﬀect at the time of ionization (R),an attenuation eﬃciency during the drift (A(y)) and a non-uniformity of the gain(G). The output of the TPC caused by deposit energy E is described as following
equation.
Output ∝E× (1 − R) × {1 − A(y)} × G.
W

(5.2)

Figure 5.8 shows more than 99.9% electrons from the neutron decay under 50

1

H
2
H
4
He
12
C
13
C
16
O
17
O

Natural abundance
σγEγ [MeV]99.9850.33262.22
0.015
0.000529
6.25
99.99986
0—98.9
0.00353
4.95
1.1
0.001378.17
99.7620.0001
3.27
0.00380.236
4.37

Erecoil [keV]
1.32
6.96
—
1.01
2.56
0.339
0.570

Table 5.6: Neutron capture cross sections, energy of emitted gamma, and their recoil
energies for isotopes.

70

CHAPTER 5. ANALYSIS ALGORITHM

kPa and 100 kPa can be separated from Bβenergy with an energy threshold of 1.4
keV, if the performance of the TPC satisﬁed the requirement as shown in Table
5.7.

Counts1032

10energySimulation : Separation between S and Bββ
Sβ 100kPa (He:CO =85:15)
2
Sβ 50kPa (He:CO =85:15)
2

energyBβ101

1.4keV-1

10

Recombination

13 %Attenuation4%

Non-uniformity of gain 9 %

10-2
10-3
10-4
10-5
0

1

2

3

4
5
6
Deposit Energy [keV]

Figure 5.8: A separation between the electron from the neutron decay and the neutron
capture in CO2 . Assumed detector performance of the TPC is also shown.

Recombination at the time of ionization < 13%
Attenuation during the drift of 150 mm < 4%
Non-uniformity of the gain
< 9%
Table 5.7: Requirement for the performance of the TPC in order to separate theneutron decay (Sβ ) and the recoiled nucleus (Bβenergy ).

5.5

Signal selection by using track ﬁnding

In order to select the neutron decay and the neutron capture in 3 He, a new variable
X and a weighted center in x axis are introduced, respectively, which do notdecrease the detection eﬃciency for both reactions under the reduced pressure.

5.5.1

Selection of the neutron decay

For the reduction of the background to the neutron decay, the signal selection
criteria are as follows:• the deposit energy is larger than that of the recoiled nucleus (1.4 keV),5.5. SIGNAL SELECTION BY USING TRACK FINDING

71• the trajectory has a intersection with ﬁducial volume.
Even after the selection, more than 99.9% detection eﬃciency for the neutron
decay is performed. The ﬁrst criterion is for the discrimination of B0 and thesecond criterion is explained in the following sentence.
By using the topological diﬀerence between the neutron decay and the background, an eﬀective subtraction of the background is performed. For instance, theprompt γ rays from the 6 Li plates knock out the electrons on material of the TPC
itself, thus they originate on the inside wall of the TPC. On the other hand, theneutron decay occurs along the beam axis.
One should note that the end points of the tracks do not necessarily correspondto the center of the TPC, since the probability of the backscattering on the 6 Li
plate is more than 1% as shown in Figure 5.9. In particular, more than 0.1%

Back scattering probability [%]electrons come back to the ﬁducial volume. The TPC reconstructs the tracks byorthogonal wires and has diﬃculty separating close tracks.

6

Simulation : Scattering on LiF plate10

whole events
back to the fiducial volume

1

10-1
0

100 200 300 400 500 600 700 800 900 1000
Electron Energy [keV]

Figure 5.9: A probability of the back scattering on the wall inside the TPC. All
scattering events are shown in a red line and those which go back to the ﬁducial volume
are shown in a blue line.

Thus a new variable X is introduced as follows:
1. deﬁne the region of neutron bunch on the beam axis,
2. search fa pair of anode and cathode wires (which are orthogonal by design)
whose pulses have temporal overlap,
3. calculate the closest distance from the beam axis.

72

CHAPTER 5. ANALYSIS ALGORITHM

The procedure is also described in Figure 5.10. Since the distance is calculated
for not only the end points but also for all the hits, a robust analysis can be
performed as shown in Figure 5.11 in case the track reconstruction get worse dueto the backscattering.

Figure 5.10: A schematic view of trajectory in TPC (XY image).

Figure 5.11: A schematic view of a trajectory in TPC (YZ image) in case of neutron
decay (left) and background (right). A distance between a red circle and a green line
corresponds to X value.

Figure 5.12 shows the X distribution for the neutron decay and Bβgas . The
distribution of the neutron decay is localized as X < 4 wires. The backgrounddue to the γ ray from CO2 (B7 ) has the same distribution as the neutron decay,
since it is associated with the recoil atom along the beam axis. On the other
hand, the background due to the γ ray from the 6 Li plates (B6 ) and the oﬀ-axis
neutron decay (B8 ) have broad distributions in X which are smeared along the size

10-6
Simulation : Neutron decay candidates
Sβ : On-axis neutron decay
B6 : Prompt γ -ray from Li plate
6

-7

10

Ratio

Probability [1/wire]

5.5. SIGNAL SELECTION BY USING TRACK FINDING

73

0.06
Simulation : B’β / Sβ
gas

B’β

0.05

B’6 : Prompt γ -ray from 6Li plate
B’7 : Prompt γ -ray from CO

B7 : Prompt γ -ray from CO

2

2

0.04

B8 : Off-axis neutron decay

B’8 : Off-axis neutron decay

10-8
0.03
-9

10

0.02
10-10

0.01

10-11
0

2

4

6

8

10

12

14

0

200

400

600

Figure 5.12: The simulated X distribution of signal and backgrounds.

800 1000 1200 1400
Velocity [m/sec]

X [wire]Figure 5.13: The ratio of signal to backgrounds with X less than 4 wires.

of the TPC. The background ratios due to the scattered neutron have a velocity
dependence as shown in Figure 5.13, since the scattering cross section, angle andvelocity of the scattered neutron are correlated with the incident velocity. The
results for the selection are summarized in Table 5.8,

B0
B1
B2
B3
B4
B5
B6
B7
B8

B/S
Recoiled nucleus due to prompt γ rays
3.0
3Oﬀ-axis neutron capture in He
7.7 × 10−3
Prompt γ rays outside the TPC
1.0
Radioactivation inside the TPC
4.9 × 10−3
Radioactivation outside the TPC
1.2 × 10−5
Environmental radiation
3.4
6
Prompt γ rays from Li plate
4.7 × 10−3
Prompt γ rays from CO2
7.0 × 10−3Oﬀ-axis neutron decay
7.7 × 10−3

B 0 /S
3.0
2.0 × 10−4
0.25
1.9 × 10−3
3.0 × 10−6
1.1
2.0 × 10−2
7.0 × 10−3
5.1 × 10−3

Table 5.8: Probabilities for each step of background generating due to the gases inside
the TPC.

5.5.2

Selection of the neutron decay under reduced pressure

The energy loss in the gas decreases under the reduced pressure, so that variationof the detection eﬃciency has to be considered. In this simulation, the measured
detection eﬃciencies by using cosmic ray as described in Section 6.4 are applied.

CHAPTER 5. ANALYSIS ALGORITHM

1Simulation : On-axis neutron decay
100kPa50kPa

10-1

Probability [1/wire]

Probability [1/wire]

74

gas

Simulation : B6 + B7 + B8 (B

β

1

)

100kPa50kPa

100kPa : 0.677 ± 0.003
50kPa : 0.670 ± 0.003

-1

10
10-2

10-3
0

2

4

6

8

10

12

14

10-2
0

2

4

6

8

X [wire]Figure 5.14: The simulated X distribution of signal with gas pressure of 100 kPa(red) and 50 kPa (blue).

10

12

14
X [wire]Figure 5.15: The X distribution of signal
with gas pressure of 100 kPa (red) and 50
kPa (blue).

Figure 5.14 shows the X distribution of the neutron decay under 100 kPa and 50
kPa. It is found that both distributions are localized within less than 4 wires.
Figure 5.15 shows the X distribution of the summation of Bβgas under 100 kPa
and 50 kPa. The ratios in X < 4 wires are 67.7% and 67.0%, respectively, andthe diﬀerence is 1.0 ± 0.6%. Since the total background ratios are about 3% under
100 kPa as shown in Figure 5.13, the diﬀerence of the detection eﬃciency has a
3% × 1% ∼ 0.03% eﬀect on the counting rate, which is negligible.

5.5.3

Selection of the neutron capture in 3 He

As same as in the neutron decay, the track pattern of the on-axis neutron capture in
3
He is diﬀerent from that of the oﬀ-axis neutron capture in 3 He. For the selectionof the on-axis neutron capture in 3 He, a weighted center of the energy deposit
can be used because the decay products, triton and proton, are stopped in thegas and are not scattered in their ﬂight. Figure 5.16 shows the distribution of
the weighted center and the background ratio is 0.28% in the case of 1000m/sec
neutron. The velocity dependence is shown in Figure 5.17. The distribution of theoﬀ-axis neutron capture in 3 He is described by use of the angular distribution of
the scattered neutron P (θ, φ) as∫
P (x) =P (θ, φ)dydz,
D cos θ sin φRatioProbability [1/wire]

5.5. SIGNAL SELECTION BY USING TRACK FINDING

10-4
3

Simulation : He reaction candidates

10-5

Sn : On-axis neutron capture in 3He
gas
Bn : Off-axis neutron capture in 3He

10-6

0.01

0.009

gas

Simulation : B’n

/ Sn

0.008
0.007

-7

10

0.006

-8

10

0.005

10-9

0.004

10-10

0.003
0.002

10-11
10-12
0

75

0.001
0
2

4

6

8 10 12 14 16 18 20 22 24

200

400

600

800 1000 1200 1400
Velocity [m/sec]

Weighted center [wire]

Figure 5.16: The weighted mean centerof 3 He events.

Figure 5.17: The ratio of oﬀ-axis to onaxis 3 He events whose weighted mean is in
the central region.

where D is a plane inside the TPC which is perpendicular to the x axis. Since theangular distribution is analytically calculated.

5.5.4

Selection of the neutron capture in 3 He under reduced pressure

Figure 5.18 shows the distribution of the weighted center of the on-axis neutron
capture in 3 He under 100 kPa and 50 kPa. The energy loss in the gas decreases
under the reduced pressure, so that the ranges of the decay products become
longer. However it is found that the distribution under 50 kPa is also localized aswell as that under 100 kPa
Figure 5.19 shows the distribution of the weighted center of the oﬀ-axis neutron
capture in 3 He under 100 kPa and 50 kPa. The ratios within the dashed line
are 55% and 52%, respectively, and the diﬀerence is about 6 ± 4%. Since thebackground ratios are less than 0.4% under 100 kPa as shown in Figure 5.17,
the diﬀerence of the detection eﬃciency has a 0.4% × 6% ∼ 0.02% eﬀect on the
counting rate, which is negligible.

CHAPTER 5. ANALYSIS ALGORITHM

Probability [1/wire]

Probability [1/wire]

76

Simulation : On-axis neutron capture in 3He
100kPa50kPa

1Simulation : Off-axis neutron capture in 3He
100kPa

10-1

10-2

10-2

2

4

6

10-3
0

8 10 12 14 16 18 20 22 24

100kPa : 0.55 ± 0.01
50kPa : 0.52 ± 0.01

10-1

10-3
0

50kPa

1

2

4

6

8 10 12 14 16 18 20 22 24

Weighted center [wire]

Weighted center [wire]

Figure 5.18: The simulated weighted
center distribution of 3 He reaction withgas pressure of 100 kPa (red) and 50 kPa(blue).

Figure 5.19: The simulated weighted
center distribution of background to 3 He
reaction with gas pressure of 100 kPa (red)and 50 kPa (blue).

Subtraction by using 3He-enriched measurement

5.6

The oﬀ-axis neutron capture in 3 He (Bβn ) is included in the candidates of the
100kPa/0.1Pa
neutron decay (Nβ), which depends on the pressure of 3 He. Thus the
100kPa/1.0Pa
3He-enriched measurement (Nβ) is employed. Ratios of the 3 He pressuresand the neutron ﬂux between the measurements are denoted as k and α, so thateach counting rate is wrote down as
0 100kPa/0.1Pa

Nβ

0 100kPa/1.0Pa

Nβ

0

0

0

0

= Sβ + Bβgas + Bβtof + Bβn ,
0

0

0

0

= α(Sβ + Bβgas + Bβtof + kBβn ).

The neutron ﬂux is measured by the neutron monitor as described in Section 3.5. In
this calculation, k can be obtained as 1.0Pa/0.1Pa = 10. From the two equations,the candidates of the neutron decay without the oﬀ-axis neutron capture in 3 He
0
(Nβ100kPa) is calculated as
00 100kPa
β0

N

0

0 gas

= Sβ + Bβ

0 100kPa/0.1Pa

0 tof

+ Bβ

=

αkNβ

0 100kPa/0.1Pa

0 100kPa/1.0Pa− Nβα(k − 1)0 100kPa/1.0Pa

.

(5.3)

The measurement time for Nβ
and Nβare denoted as t100kPa/0.1Pa
and t100kPa/1.0Pa . The total measurement time is described as t100kPa = t100kPa/0.1Pa +5.7. SUBTRACTION BY USING TOF SPECTRUM

770t100kPa/1.0Pa . The uncertainty of the Nβ100kPa
is write down as following.
0√
0 100kPa/0.1Pa

α2 k 20∆Nβ100kPa
=
0

Nβ
0

t 100kPa/0.1Pa

0 100kPa/1.0Pa

Nβ+ t0 100kPa/1.0Pa

α(k − 1)

(5.4)

√
√
0 100kPa/0.1Pa
0 100kPa/1.0Pa
+ Nβ
αk Nβ
√
=
(5.5)
α(k − 1) t100kPa√
0Nβ100kPa
1 + αk=,(5.6)
1 − αkt100kPa√√
0 100kPa/0.1Pa
0 100kPa/1.0Pa: Nβ
is optimum.
where t100kPa/0.1Pa : t100kPa/1.0Pa = αk Nβ0 100kPa/0.1Pa

0In addition, Nβ100kPa ∼ Nβ

0 100kPa/1.0Pa∼ Nβ

is assumed. In case of α = 1

and k = 10,0∆Nβ100kPa
01.2=√
0 100kPa0
Nβ 0
N 100kPa t100kPa

(5.7)

β

can be obtained.

5.7

Subtraction by using TOF spectrum

By using the TOF spectrum, the inﬂuence of the radioactivation and the environmental radiation can be evaluated. Not only that, the 6 Li shutter as shown in
Section 3.5 enables to subtract the background due to the prompt γ ray from outside the TPC. The counting rates are classiﬁed by the region in the TOF spectrum
and the condition of the 6 Li shutter as shown in Table 5.9. t1 and t0 correspondto the ﬁducial time and a subset of the time when the neutron bunch is not in the
TPC, respectively. s1 and s0 denote the measurement with the 6 Li shutter opened
and closed.
Shutter opened
Shutter closed

Beam inside the TPC
0
N 100kPa (s1 , t1 )0
N 100kPa (s0 , t1 )No beam inside the TPC
0
N 100kPa (s1 , t0 )0N 100kPa (s0 , t0 )Table 5.9: Classiﬁcation by means of condition of the 6 Li shutter and the TOF spectrum.

5.7.1

Neutron decay

Assuming the SFC is set to produce one neutron bunch which arrives at the centerof the TPC at 20 ms, the top of Figure 5.20 depicts a time spectrum for the

78

CHAPTER 5. ANALYSIS ALGORITHM

neutron decay, with the 6 Li shutter opened. The TPC has a 4π acceptance for theneutron decay in the time interval between the dashed lines. On the other hand,the bottom of Figure 5.20 depicts the distribution, with the 6 Li shutter closed. t1
can be stretched for the statistics as long as possible and is denoted as t0 = k 0 t1 ,where k 0 is a constant. Each spectrum is described in terms of the individual signal
and background components as:
0

0

0

0

0

0

0

0

0

Nβ100kPa(s1 , t1 ) = Sβ + Bβgas + B2 (s1 , t1 ) + B3 (s1 ) + B4 (s1 ) + B5 (s1 ),
0
0

0

0

(s1 , t0 ) = B2 (s1 , t0 ) + k 0 B3 (s1 ) + k 0 B4 (s1 ) + k 0 B5 (s1 ),Nβ100kPa
0
0

0

0

0

0

0

(s0 , t1 ) = α0 {B2 (s0 , t1 ) + B4 (s0 ) + B5 (s0 )},Nβ100kPa000(s0 , t0 ) = α0 {B2 (s0 , t0 ) + k 0 B4 (s0 ) + k 0 B5 (s0 )},Nβ100kPa
0
where α0 is a ratio of the neutron ﬂux between the measurements. The radioactivation and environmental radiation are constant during the beam cycle of 40 ms,
thus the time expressions are omitted in B4 , B5 and B6 . B2 is scaled according to
the ﬂux, so that following equation can be obtained.
00

B (s0 , t1 )
B (s0 , t0 )α = 20= 20.
B2 (s1 , t1 )
B2 (s1 , t0 )0Finally the candidates of the neutron decay without Bβtof (Nβ100kPa) is calculated
00
as
0

0

0

Nβ100kPa= Sβ + Bβgas
00
1 0 100kPa
N 0(s1 , t0 )k0 β
00Nβ100kPa(s0 , t1 ) − k10 Nβ100kPa(s0 , t0 )
0
0
−
,
α0

0

= Nβ100kPa(s1 , t1 ) −0∆N

0 100kPa
β 00

= √

1

(√
0

Nβ100kPa(s1 , t1 ) +0

t0100kPa1+ 0
α√0 100kPa
β0

N

(5.8)

1 0 100kPa
N 0(s1 , t0 )k 02 β

)1 0 100kPa(s0 , t1 ) + 02 Nβ 0(s0 , t0 ) , (5.9)
kwhere t0100kPa denotes the summation of the measurement time with shutter opened
and the shutter closed. Assuming k 0 = 6.0ms/2.8ms as discussed in Section 5.2
and α0 = 1.0, the expected rates of each components are described in Table 5.10.
Substituting these values into Eq. (5.9), the statistical uncertainty is obtainedas0∆Nβ100kPa
00
1.0 × 101
= √0 100kPaNβ 00
t0100kPa(5.10)

Counts

5.7. SUBTRACTION BY USING TOF SPECTRUM

79

s1 : Shutter Open
B’2 : Prompt γ -ray outside the TPC

S’β : On-axis neutron decay
6

B’6 : Prompt γ -ray from Li plate
B’7 : Prompt γ -ray from CO

B’3 : Radioactivation inside the TPC

B’8 : Off-axis neutron decay

B’5 : Environmental radiation

B’4 : Radioactivation outside the TPC

2

N’β’(s , t1 )1N’β’(s1 , t0 )Counts02040Time of flight [msec]

s0 : Shutter Close

B’2 : Prompt γ -ray outside TPC
B’4 : Radioactivation outside TPC
B’5 : Environmental radiation

Nβ’(s0 , t1 )Nβ’(s , t0 )
0

0

20

40
Time of flight [msec]

Figure 5.20: A schematic drawing of signal and background in TOF with the shutter
open (top) and closed (bottom).

80

CHAPTER 5. ANALYSIS ALGORITHM
00Nβ100kPa(s1 , t1 ) Nβ100kPa(s1 , t0 )
0
0
0
−2
S
8.9 × 10—0−2
B2
1.7 × 10
3.0 × 10−20B3
4.4 × 10−4
9.5 × 10−4
0−2
B5
9.8 × 10
2.1 × 10−10 gas
Bβ2.7 × 10−3—
Total
2.1 × 10−1
2.4 × 10−100Nβ100kPa(s0 , t1 ) Nβ100kPa(s0 , t0 )
0
0
—
—
−2
1.7 × 10
3.0 × 10−2——
9.8 × 10−2
2.1 × 10−1——
1.2 × 10−1
2.4 × 10−1

Table 5.10: Expected amount of the neutron decay and backgrounds in the TOF
spectrum.

which corresponds to 0.48% of the statistical uncertainty for the 50 days of beamtime with 220 kW of beam power.

Neutron capture in 3 He

5.7.2

Figure 5.20 depicts a time spectrum for the candidates of the neutron capture in
3
He, with the shutter opened. The distribution with the shutter closed consistsof only the environmental radiation, thus the subtraction can be simpliﬁed andperformed in the same manner as the neutron decay:
0

0

0

0

Nn100kPa= Sn + Bngas = Nn100kPa (s1 , t1 ) −00

1 0 100kPaN(s1 , t0 ).
k0 n

The count rate of the neutron capture in 3 He is controlled by the pressure. In
the case of 0.1 Pa of the 3 He, the count rate is 25 times larger than that of theneutron decay. Thus the statistical uncertainty arising from the neutron capturein 3 He can be negligible.

5.8

Subtraction by using reduced-pressure measurement

All the remaining background at this stage is caused by the gas inside the TPC,
so that the amount of the background is proportional to the gas pressure. The
same procedures are applied to the data taking under 50 kPa (N 50kPa/0.1Pa andN 50kPa/1.0Pa ). The TPC performance under the reduced pressure is discussed in00Section 5.5.2 and 5.5.4. Consequently, Nβ50kPa
and Nn50kPa
can be obtained, which
00
00
are wrote down as
0

0

0

0

0

0

Nβ50kPa= α00 (Sβ + k 00 Bβgas ),00= α00 (Sn + k 00 Bngas ),Nn50kPa00

Counts

5.8. SUBTRACTION BY USING REDUCED-PRESSURE MEASUREMENT81

S’n
gas

B’n

s1 : Shutter Open3

: On-axis neutron capture in He
3: Off-axis neutron caputure in He

B’tof: Environmental radiationnN’n(s1 , t1 )N’n(s1 , t0 )

0

20

40
Time of flight [msec]

Figure 5.21: A schematic drawing of 3 He reaction candidates in TOF with shutter
open.

where α00 and k 00 are ratios of the neutron ﬂux and the total pressure between the0000measurements, respectively. By comparing Nβ100kPa
and Nn100kPa, Sβ and Sn are
00
00
extracted as
0

0

Sβ
0

Sn

Nβ50kPa− α00 k 00 Nβ100kPa
00
00
,
=
00
00
α (1 − k )Nn50kPa− α00 k 00 Nn100kPa
00
00
=
.
00
00
α (1 − k )Finally, SSnβ in the Eq. 5.1 can be obtained as000Nβ50kPa− α00 k 00 Nβ100kPa
00
00
Sn
=
.
0
0 50kPa
0
100kPaSβ
Nn00− α00 k 00 Nn00

In case of α = 1.0 and k = 1/2, t050kPa : t0100kPa = 2 : 1 is optimum, where t050kPa
denotes the total time for the measurement under 50 kPa. Thus∆τn √ ∆N 100kPa= 3 0 100kPa
τnN
0(5.11)

can be obtained. In 150 days an achievable statistical uncertainties are 0.82% witha power of 220 kW and 0.24% with a power of 1 MW as shown in Table 5.11.
In this section, the rate of the environmental background (B5 ) is assumed as
B50 /S = 1.1, which can be obtained in the next chapter. The statistical uncertainty

82

CHAPTER 5. ANALYSIS ALGORITHM
uncertainty [%]220 kW 1 MW
50 kPa 100 days
0.34
0.099
100 kPa 50 days
0.48
0.14
total
150 days
0.82
0.24

3
Simulation : Statistical uncertainty in 150 days

2.5

Statistical uncertainty [%]Statistical uncertainty [%]Table 5.11: Achievable statistical uncertainties.

This work (220 kW)

2

1.5

1.6
1.4

Simulation : Statistical uncertainty in 150 days
This work (B’ / S = 1.1)
5

1.2
1

1 MW equivalent

0.8

1
0.6
0.5

0
0

0.4
0.2
2

4

6

8

10

12
B’5 / S

0
0

1

2

3

4

5

6

7

8

9

10

Rate of increase in neutron flux

Figure 5.22: The achievable statisticaluncertainty as a function of an amountof the environmental background after thesignal selection (B50 ). A black circle describes the achieved B50 /Sβ0 ∼ 1 by the developed TPC in this thesis.

Figure 5.23: The achievable statistical uncertainty as a function of the beam
power of J-PARC. A black circle describes
the current beam power, 220 kW.

is depends on B50 /S as shown in Figure 5.22, thus the reduction of the environmental background is required. The developed TPC in this thesis is aiming to achieve
B50 /S ∼ 1.
Figure 5.23 shows a beam-power dependence of the statistical uncertainty,
which motivates high ﬂux of the neutron beams.

Chapter 6
Time projection chamber
In this chapter, the performance of the TPC is described. The requirement issummarized in Table 6.1.
Requirement
environmental background6
Li plate coverage
detection eﬃciency for Sβ and Sn

Value
B50 /S ∼ 1
100%> 99.9%

Table 6.1: Requirements for the TPC.

6.1

Development of the TPC without radioactive contamination

6.1.1

Material candidate

G10, which is commonly used for gas detectors, is made of continuous glass woven
fabric base impregnated with an epoxy resin binder. While G10 has high mechanical strength, a silica, the raw materials for glass contains the Uranium-Thorium
series radioisotopes. Ceramic made from alumina also contains 40 K in the K2 O
mixed for workability. Thus other materials, three plastics and one ceramic areinvestigated for radioactive contamination. These materials are selected by meansof the other aspects as shown in Table 6.2.
• Poly Ethel Ethel Ketone (PEEK)
A thermoplastic resin produced by Yasojima Proceed Co. Ltd whose product name is PEEK450G. PEEK consists of only C, H and O without natural
materials, thus the impurities cannot be mixed in. It has good fabrication
83

84

CHAPTER 6. TIME PROJECTION CHAMBER
accuracy by means of the extrusion method and weldability due to the thermoplastic property.
• Poly Phenylene Sulﬁde (PPS)A thermoplastic resin produced by Yasojima Proceed Co. Ltd whose productname is FORTRON. The PPS consists of only C, H, O and S also without
natural materials. The mechanical strength and water absorption are better
than PEEK.
• Phenol Formaldehyde resin (PF)A thermohardening resin produced by Yasojima Proceed Co. Ltd whose product name is PS1121. The PF consists of only C, H and O without the natural
materials and costs less than PEEK. However the mechanical strength is inferior to PEEK.
• Alumina
A special ceramic produced by Ariake Materials Co. Ltd whose product nameis MA995. The potassium content is reduced to 0.01wt%. Due to the sinterforming, the fabrication accuracy is worse than the above extruded plastics.
G10
density [g/cc]
1.8
bending elastic modulus [GPa] 20
melt point [◦ C]—
water-absorbing ratio [%]0.10
volume resistance [Ω·m]1011
cost [1000JPY/kg]
3.3

PEEK
1.3
3.6
334
0.14
1014
45

PPS
1.4
3.9
278
0.04
1014
8

PF Alumina
1.4
3.9
0.15
350
130
1500
0.3
0
12
10
1015
5
100

Table 6.2: Properties of the material candidates which are density, bending elastic
modulus, melt point, volume resistance and cost.

PEEK is selected by not only the low level of radioactivity as described in thenext subsection, but also its insulating capacity for the high voltage, mechanicalstrength for the wire tension, heat tolerance for soldering, water absorption for
vacuuming and cost as described in Table 6.2.

6.1.2

Study of the radioactive contamination by using germanium detector

According to the Geant4 simulation, the requirement for the material of the TPC
is calculated to be less than 0.01 Bq/cc. A germanium detector at Proton Beam

6.1. DEVELOPMENT OF THE TPC

Figure 6.1: (A) sample, (B) Germanium detector, (C) Acrylic, (D)Oxygen-free copper, (E) Lead, and(F) Switch.

85

Figure 6.2: The measured value of radioactive contents for each materials in unit is
Bq/cc.

Application Building in KEK is used for the measurement of the radioisotope.
Figure 6.1 shows a picture of the sample laid on the germanium detector. The
detector is surrounded by 1 cm thick acrylic plate, 1 cm thick oxygen-free copperand 10 cm thick lead. The energy spectrum of the measurement with no sample
is indicated in Figure 6.2 and its counting rate is 1.26 cps.
PEEK, PPS, PS , Alumina and G10 are investigated for the material of TPC.
In addition electronics such as pre-ampliﬁers, resistors, capacitors and cables arechecked. Stainless steel and aluminum for the vacuum chamber, lead and ironfor the shields and 6 Li plate for the neutron shielding are also tested. Figure 6.3
and 6.4 shows the energy spectrum of the G10 and PEEK after subtraction of
the background as shown in Figure 6.2 for instance. It is found that there is no
signiﬁcant peak in the spectrum of PEEK.
In order to convert from the counting rate of the germanium detector to Bq,
self-shielding have to be considered. An eﬃciency of the self-shielding  is empirically expressed in terms of the energy of γ ray, Eγ , asln  = a + b ln Eγ + c(ln Eγ )2 ,(6.1)

where a, b and c are calculated from the composition of each material. The results
are summarized in Table 6.3. For the material of the TPC, PEEK, PS and Alumina
satisfy the requirement. Among these candidates, PEEK has a better fabrication
accuracy than that of Alumina and a better bending elastic modulus than thatof PS. Thus PEEK is chosen for the material of the TPC. However due to thelower bending elastic modulus than that of G10, the wire tension make the PEEK
frame would distort, so that a pretension is applied while soldering the wires to

86

CHAPTER 6. TIME PROJECTION CHAMBER

Figure 6.3: A energy spectrum of thegermanium detector with G10. The background was subtracted.

Figure 6.4: A energy spectrum of thegermanium detector with PEEK. The
background was subtracted.

the frame as described in the next section.
The radioisotopes in the other components of the TPC such as pre-ampliﬁer,
resistor, capacitor and 6 Li plate, are also conﬁrmed to be satisﬁed the requirements.

6.1.3

Design of TPC

The TPC consists of a drift part and a MWPC part. The electrons ionized by apassing charged particle inside the drift part move under the electric ﬁeld whichis generated by a positive voltage applied on the bottom of the drift part andenergized wires as shown in Figure 6.5. Resistors are installed between the wires
and make a uniform ﬁeld. Whole picture is shown in Figure 6.6.
The MWPC consists of three-layered wires. The anode wires are parallel to theneutron beam and the cathode wires are perpendicular to the beam. Considering
the energy loss of the minimum ionization under 100 kPa (He : CO2 = 85 : 15), thepitch of anode wire set to be 12 mm enables to collect at least one ionized electron
at 99.9% by using Geant4. Field wires are located between the anode wires forthe conﬁnement of the electric ﬁeld. The gap between the anode and cathode is
set to be 6 mm for axial symmetry. The cross section of the electric ﬁeld can beshown in Figure 6.7 and the detail speciﬁcation is described in Table 6.4.
Two 6-mm thick PEEK frames are used for the MWPC part. One has theanode/ﬁeld wires and the top of the cathode wires on both sides; the other has thebottom of the cathode wires on one side. The wires are soldered to the circuit on
the kapton ﬁlm pasted on the PEEK frame as shown in Figure 6.8. The positionof wires are determined by grooves with a width of 100 µm as shown in Figure 6.9.
The anode plane consists of 24 sense wires (φ 20 µm) and 24 ﬁeld wires

212
IsotopePb
Eγ [keV]
239
PEEK
—
PPS
0.0016PS—
Alumina—G100.0480Pre-ampliﬁer—
Resistor—
Capacitor—
6
Li plate—
SUS3040.0012
Al
0.0028

Pb
295
—
—
—
—
0.0272
—
—
—
—
—
—

214

Ac
338
—
—
—
—
0.0424
—
—
—
—
—
—

228

208
214
212
Pb
Tl
Bi
Bi
352
583
609
727
—
—
—
—
—
—
0.0028 0.0080———
0.0080——(0.0026)—
0.0257 0.0135
0.0201 0.0480
—
—
—
—
—
—
—
—
—
—
—
—
—
(0.0006)————(0.0025)——(0.0011)
—
—

214

228
40
Tl
Ac
K
861
911
1461
—
—
—
—
—
0.0068————0.0020—0.0142 0.0412 0.022
—
—
—
—
—
—
—
—
—
—
—
—
—
—
0.0116——0.0072

208

Bi
1765
—
—
—
—
0.0267
—
—
—
—
—
—

214

6.1. DEVELOPMENT OF THE TPC

Table 6.3: Radioisotopes in the samples in Bq/cc unit.

87

88

CHAPTER 6. TIME PROJECTION CHAMBER

Figure 6.5: A photograph at the front of
the ﬁeld cage.

Figure 6.6: A photograph of a whole image of TPC without
6 Li plate.

Figure 6.7: A electric ﬁeld around the anode wire, calculated by Garﬁeld.

6.1. DEVELOPMENT OF THE TPC

89

cathode (top)anode / ﬁeld
diameter
φ 50 µm
φ 20 µm / φ 50 µm∆ra /ra0.02
0.02
material
Au-Be-Cu
Au-W / Au-Be-Cu
pitch
6 mm
6 mm
◦
Angle to the beam
90
0◦Applied voltage
0V
1720 V / 0 V
AMP modehighhigh / low

cathode (bottom)
φ 50 µm
0.02
Au-Be-Cu
6 mm
90◦
0V
low

Table 6.4: Speciﬁcation details of wires; cathode, anode, and ﬁeld.

(φ 50 µm) alternatively placed every 6 mm with applied voltages of 1720 V and
0 V, respectively. Each cathode plane consists of 6mm-spaced 160 cathode wires(φ 50 µm) and 4 cathode wires are linked up to an ampliﬁer.
The resistor of 1 MΩ connects the anode wire to a power supply so that only asmall fraction of the signal is lost into the power supply. In addition, the capacitorof 1 nF connects the anode wire for decoupling the ampliﬁer.
As described in Section 5.4.2, the non-uniformity of the gain at the anode wires
has to be suppressed less than 9%, which is inﬂuenced by a non-uniformity of thediameter of the anode wire ∆ra /ra , a displacement of the anode wire ∆x and a
deformation of the cathode wire ∆y as described in Table 6.5. In the case of thedeveloped TPC, ∆ra /ra < 0.02 and ∆x < 0.05 mm are obtained.
A deformation of the cathode wire depends on the tension T as in the following
equation:
∆y =

F L2
,
8T

(6.2)

where F is a electric force from the anode wire and L is a length of the cathodewire. In this experiment 20 g of the wire tension is required, which corresponds to
dG/G = 1%.
Imperfection
non-uniformity of the diameter of the anode wire
displacement of the anode wire
deformation of the cathode wire
total

dG/G
2.9∆ra /ra ∼ 6%
0.49∆x ∼ 2%
0.69∆y ∼ 1%
7%

Table 6.5: A relationship between imperfections of the wires and expected variationsof the gain, which is calculated according the work by G. A. Erskine [53]. ∆x and ∆yare in mm unit.

90

CHAPTER 6. TIME PROJECTION CHAMBER

Figure 6.9: A closeup view of the cross sectionof the MWPC part.
Wire tension [g]Figure 6.8: A closeup view of the
MWPC part.

60
50
40
30
20

Cathode plane (Top)10

Cathode plane (Bottom)

00Figure 6.10: A photograph ofthe tensioning device.

20

40

60

80

100
120
140
160
Cathode wire number [ch]Figure 6.11: A distribution of the tension on eachwire.

However the mechanical strength of PEEK is lower than G10, the frame bends
beneath the burden of the wire tension. Calculating the displacement under thedesirable tension, the suitable pre-tension is applied to the frame during the soldering as shown in Figure 6.10. Figure 6.11 shows a variation of the wire tension
and the minimum tension is 27.2 g, which is higher than designed value, 20 g.
The non-uniformity of the gain is expected to be less than 7% in total. The
measurement is shown in Figure 6.30.

6.1.4

Design of vacuum chamber

For the purpose of the determination of the 3 He density, the TPC is housed ina vacuum chamber and the gas is ﬁlled after the vacuuming. During the operation of the TPC, there is no gas ﬂow into the vacuum chamber. Figure 6.12
shows a stainless-steel vacuum chamber, which has three aluminum ﬂanges withfeedthroughs. The detail speciﬁcation is summarized in Table 6.6.
The stainless steel and the aluminium are also checked by the germanium
detector. As shown in Table 6.3, both materials contain 212 Pb and 40 K. While6.2. INSTALLATION OF THE 6 LI PLATE

91

Figure 6.12: A photograph of the vacuum chamber.

Speciﬁcation
Chamber material
Chamber outer size
Chamber inner size
Lid material
Upper lid size
Side lid size
Dry pump vacuum rate
Turbo pomp vacuum rate
Achieved vacuum（1 day）
Outgas rate（w/o baking）
Leak rate

Valuesstainless-steel (SUS304)
680 mm (x) × 730 mm (y) × 1230 mm (z)630 mm (x) × 680 mm (y) × 1180 mm (z)aluminium (A5052)
630 mm (x) × 25 mm (y) × 1180 mm (z)25 mm (x) × 680 mm (y) × 1180 mm (z)450 l/min (Adixen ACP28)
210 l/sec (PFEIFFER TMU261)
1 × 10−4 Pa
5 × 10−5 Pa/sec
4.4 Pa/day

Table 6.6: Speciﬁcation detail of the vacuum chamber.

the β ray from the radioisotope is mostly stopped inside the material, a Compton
electron induced by the γ ray from the radioisotope can hit the TPC. 212 Pb emits
239 keV γ ray with 88% branching ratio and 40 K emits 1461 keV γ ray with 11%
branching ratio. Table 6.7 summarizes the Geant4 simulation of the radioisotopes
contained in the vacuum chamber. As a result, the background rate is expected
to be 0.21 cps, which satisﬁes the requirement.

6.2

Installation of the 6Li plate

In the TPC, some of the incident neutrons are scattered by the gas and captured
in the material of the TPC with prompt γ ray. Thus the scattered neutrons have

92

CHAPTER 6. TIME PROJECTION CHAMBER

material
volume [cm3 ]
Bq
212
Pb
Hit probability
TPC hit [cps]Bq40
K
Hit probability
Expected TPC hit [cps]Total TPC hit [cps]Stainless-steel (SUS304) Aluminium (A5052)
1.3 × 104
2.2 × 104(1.6 ± 1.1) × 101(6.2 ± 0.9) × 101−3(1.5 ± 0.1) × 10
(1.7 ± 0.1) × 10−3
(2.4 ± 1.8) × 10−2
(10.5 ± 2.2) × 10−2
(1.5 ± 0.8) × 102(1.6 ± 1.1) × 102−4(2.7 ± 0.2) × 10
(2.3 ± 0.2) × 10−4
(4.1 ± 2.5) × 10−2
(3.7 ± 2.9) × 10−2
0.21 ± 0.05

Table 6.7: Radioactive contamination inside the materials of the vacuum chamber.

Figure 6.13: A photograph of 6 Li plate.

Figure 6.14: A photograph of the insideof TPC.

to be captured by some nuclei such as 3 He, 6 Li and 14 N, all of which causes twobody decays without γ-ray emission. The products of the two body decays arealso nuclei thus they can be easily stopped by a thin material.
In this experiment, 95% 6 Li-enriched plate which consists of LiF : PTFE =30wt% : 70wt% is produced for the scattered neutron as shown in Figure 6.13. As
shown in Table 4.1, more than 99.99% of the reaction in the plate is n +6 Li →3 H + α(Q=4.8 MeV) and 200 µm thick pure PTFE on the surface is suﬃcient to stop the
decay products. The plates are installed into the TPC and the coverage from thebeam axis is 100%. Figure 6.14 shows the picture inside the TPC and the bottom
is covered by 12 µm thick aluminized mylar, which prevents the buildup of static
electric charge. The slit on the left is used for the calibration. A 55 Fe stage on
a rotating table is set up beside the drift part. Figure 6.15 shows the 55 Fe stage
with a collimator (left) and the LiF (top and bottom). During calibration, 55 Fe
moves to a position lateral to the slit.
It is noteworthy that the 6 Li plate is a dielectric material and is installedy [mm]6.3. PERFORMANCE OF THE BACKGROUND SUPPRESSION

93

300

200

100

0

-100

-200

-300
-300

-200

-100

0

100

200

300
x [mm]

Figure 6.15: A photograph ofthe rotating table of 55 Fe stage.
Figure 6.16: A XY image of the electric ﬁeld of
the drift region.

inside the wire. Relative permittivity of the 6 Li plate is measured as r = 3.0 by
KEYCOM Corp. and that of the PEEK is r = 3.2 from its speciﬁcation sheet.
Thus the electric ﬁeld is conﬁrmed to be uniform by a calculation as shown in
Figure 6.16.
Drift velocities under 50 kPa, 75 kPa and 100 kPa are measured by using
electrons due to the environmental γ ray and can be calculated as shown in Figure
6.17. While the discharge voltage also decreases under reduced pressure, the drift
velocity is inversely proportional to the pressure. It is conﬁrmed that the drift
velocity of 1 cm/µs can be possible. Figure 6.18 shows the position dependence
under 100 kPa and 300 V/cm and the variation is less than 1%.

6.3

Performance of the background suppression

An environmental background of the TPC was 123.7 cps in the experimental areain the MLF. After housing in the lead shielding, the counting rate is decreased to58.4 cps and the surrounding cosmic ray counters reduces it to 7.7 cps. According
to the analysis algorithm as discussed in Section 5.4.2, the backgrounds for theneutron decay are events with an energy of more than 1.4 keV and with a hit in
the ﬁducial region. Thus the selections, the energy cut and the ﬁducial cut, areapplied and the eventual backgrounds can be obtained as 1.4 cps. Figure 6.19

CHAPTER 6. TIME PROJECTION CHAMBER

2.4
Experiment : Drift velocity

2.2

Drift velocity [cm/µsec]

Drift velocity [cm/µsec]

94

100kPa (He:CO = 85 :15)
2

2

75kPa (He:CO = 85 :15)

1.8

50kPa (He:CO = 85 :15)

2
2

1.6
1.4
1.2

1.02
1.01

300V/cm, 100kPa (He:CO =85:15)
2

0.99
0.98

1

0.97

0.8

0.96

0.6

Experiment : Drift velocity uniformity

1

0.95

0.4
0.94

0.2
0
0

0.93

50

100

150

200

250

300

350

Drift Field [V/cm]

Figure 6.17: The measured drift velocity
with diﬀerent drift ﬁelds. The red, green
and blue points show the gas pressure of100, 75 and 50 kPa, respectively.

0.92
0

5

10

15

20

25

30
35
40
Cathode wire [ch]Figure 6.18: The position dependence ofthe drift velocity.

shows the energy distribution and Figure 6.20 shows the X distribution. These
values are summarized in Table 6.8.
Assuming 220 kW of beam power at J-PARC and 7% of duty factor of the SFC
as discussed in Section 5.2, the rate of the neutron decay is expected to be 0.089
cps. Thus the signal-to-background ratio is calculated as
S/N =8.9 × 10−2
∼ 1.1.
1.4 × 7.0 × 10−2

(6.3)

As described in Section 3.6, the Pb shielding stop 98% of environmental γ
ray from the measurement of the NaI detector and the surrounding cosmic-ray
veto counters trigger 96% of the cosmic ray from the measurement of the cubic
scintillator. For further reduction of the background, an improvement of the Pb
shielding and the cosmic-ray veto counter is needed.

Environmental BG+ Pb shield+ Cosmic-ray veto

Total count[cps] Energy cut[cps]
123.7
100.1
58.4
44.2
7.7
4.3

Fiducial cut[cps]
30.7
13.9
1.4

Table 6.8: The measured event rate inside MLF, with a shield, and with cosmic-ray
veto (successive application).

103

95

Experiment : Environmental Background

Counts [a.u.]Counts [1/keV/sec]

6.4. PERFORMANCE FOR THE PARTICLE DETECTION

w/o Pb shield and w/o cosmic ray vetow/ Pb shield and w/o cosmic ray veto102

w/ Pb shield and w/ cosmic ray veto1
Experiment : Environmental Backgroundw/ Pb shield and w/ cosmic ray veto

10
1
10-1
1.4keV

10-1
10-2
10-3
1

10

102

10-2
0

Deposit Energy [keV]

2

4

6

8

10

12

14
X [wire]Figure 6.19: Energy spectrums of environmental background. A red, green andblue lines represent the spectrum with noshielding, only with Pb shielding and with
Pb shield and cosmic ray veto.

6.4

Figure 6.20: X distribution of the environmental background with Pb shielding
and cosmic ray veto.

Performance for the particle detection

In order to achieve more than 99.9% detection eﬃciency for the neutron decay andthe neutron capture in 3 He, the following items have to be satisﬁed:• Detection for more than 99.9% of the neutron decay and the neutron capturein 3 He,• Separation between the neutron decay and the neutron capture in 3 He,• Separation between the neutron decay and the neutron capture in CO2 .
In this section, these items are investigated.

6.4.1

Setup for the measurement

The performance of the TPC is evaluated by using 5.9-keV X rays from 55 Fe, cosmic
rays and neutrons as shown in Table 6.9 and Figure 6.21. For the measurement of
the detection eﬃciency of the anode wires by use of the cosmic rays, the TPC isrotated 90 degrees. The MWPC part of the TPC consists of two PEEK frame anda gap between the plates is 6 mm. 5.9-keV X rays from 55 Fe at position A in Figure
6.21 pass through the gap and converts into an electron inside the wire cell. Thus
it is possible to directly measure the gain of MWPC. The drift part has two slits at

96

CHAPTER 6. TIME PROJECTION CHAMBER

positions B and C, and another 55 Fe on the rotating table enables to evaluate therecombination at the time of ionization and the transportation eﬃciency during
the drift. The cosmic rays are triggered by two scintillators arranged one above theother (X and Y) and detection eﬃciencies of the anode wires are obtained. The
neutrons pass through an entrance of the TPC and make it possible to evaluate
the 3 He reaction.
A
B, C
D
E

55

Fe
Gain
Fe
Recombination and transportation eﬃciency
Cosmic ray
Detection eﬃciency
3
NeutronHe reaction
55

Table 6.9: Evaluated components, positions (Figure 6.21), and kind of sources tomeasure the detector performances.

Figure 6.21: A schematic drawing of the positions of the sources for the evaluations of
performances of the TPC.

6.4.2

Detection for the neutron decay

The pressure and voltage dependences of the gain of MWPC are shown in Figure 6.22. Although the gain at the discharge voltage decreases with decreasingpressure, the gain of 50000 can be performed under 50 kPa ∼ 100 kPa. Detection

90000Detection efficiency

Gain

6.4. PERFORMANCE FOR THE PARTICLE DETECTION

100kPa (He:CO =85:15)
2

80000

75kPa (He:CO =85:15)
2

70000

50kPa (He:CO =85:15)
2

60000

97

1.2
Experiment : Detection Efficiency
1.15

100kPa (He:CO =85:15)
2

50kPa (He:CO =85:15)

1.1

2

1.05
1

50000

0.95

40000

0.9

30000

0.85

20000

0.8

10000

0.75

0

1350 1400 1450 1500 1550 1600 1650 1700 1750 1800

Anode voltage [V]Figure 6.22: The measured gains with
diﬀerent anode voltages. The red, green
and blue points show the gas pressure of100, 75 and 50 kPa, respectively.

0.7
2

4

6

8

10

12

14

16 18 20 22
Anode wire [ch]Figure 6.23: The detection eﬃciencies
for each anode wire, measured with 1720
V for anode wires and 300 V/cm or thedrift part.

eﬃciencies of the anode wires are evaluated by cosmic rays entering at an angle ofless than 5◦ with respect to the cathodes. Figure 6.23 shows the detection eﬃciencies under 50 kPa and 100 kPa with the gain of 50000, which reﬂects the energy
loss in the gas. Applying this detection eﬃciency to Geant4 simulation, more than
99.9% detection eﬃciency is achieved even under 50 kPa as shown in Figure 5.14.

6.4.3

Separation between the neutron decay and the neutron capture in 3 He

As discussed in Section 4.4, the saturation eﬀect becomes apparent in the caseof the neutron capture in 3 He, since the energy loss of the reaction products, aproton and a triton, is suﬃcient to induce the space-charge eﬀect. Figure 6.24
shows the saturation eﬀect for the neutron capture in 3 He. It is found that an
output decreases with increasing pressure and gain. Thus the energy spectrumof the electrons from the neutron decay overlaps that of the neutron capture in3
He as shown in Figure 5.6. According to a Geant4 simulation as shown in Figure
5.7, these two reactions are separated if the maximum energy deposit among thewires of the neutron capture in 3 He is more than 35 keV. Figure 6.25 shows the
maximum energy deposit of the 3 He reaction candidates, which includes the onaxis and oﬀ-axis reaction (Sn , Bngas ) as discussed in Section 5.3.2. It is found that
99.9% of the 3 He reaction candidates deposits more than 35 keV as the maximum

3

CHAPTER 6. TIME PROJECTION CHAMBER

1200
Experiment : 3He reaction
100kPa (He:CO =85:15)
2

1000

75kPa (He:CO =85:15)
2

Counts

Output of He reaction [keV]98

Entries

6287

Experiment : Max energy deposit among the field wires

103

50kPa (He:CO =85:15)

3

On-axis He reaction candidates

2

800762keV
102

600

35keV

400

10
200

0

1350 1400 1450 1500 1550 1600 1650 1700 1750 1800
Anode voltage [V]11log (Energy [keV])
10

Figure 6.24: The measured pulse heightwith diﬀerent anode voltage and gas pressures.

Figure 6.25: The spectrum of the maximum energy deposit among the ﬁeld wires.

energy among the wires.
The separation is also conﬁrmed by using 3 He-enriched measurement, sinceeach spectrum can be independently extracted as discussed in Section 5.6. If thepressure decreases, the eﬀect of saturation and the energy loss of the electron
decreases, so that the separation remains even at reduced pressure.

6.4.4

Separation between the neutron decay and the neutron capture in CO2More than 99.9% of the neutron decay has to be separated from the recoiled
nucleus due to the neutron capture in CO2 as discussed in Section 5.4.2. However
the separation is deteriorated by the recombination at the time of ionization, theattenuation eﬃciency during the drift and the position dependence of the gain asshown in Table 5.7.
Recombination eﬀects and transportation eﬃciency can be evaluated by use of
Fe at positions A, B and C, which decrease with an increase of the electric ﬁeld
in the drift part as shown in Figure 6.26 and Figure 6.27. Under 300 V/cm, themeasured values are 12% and 2%, respectively.
55

In this experiment, the gases do not ﬂow during the experiment, so that H2 O
contained in outgassing is emitted from the TPC itself, which causes electron
attachment during the drift. Figure 6.28 shows the spectrum of a quadrupole
mass spectrometer under 3.6 × 10−4 Pa after evacuation for two weeks. Figure

10.9

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

0.8
0.7
0.6

Attenuation Efficiency

Recombination Effect

6.4. PERFORMANCE FOR THE PARTICLE DETECTION

1
100kPa (He:CO = 85:15)

0.7
0.6

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1
100

150

200

250

300

350

Electric field [V/cm]

Figure 6.26: The recombination eﬃciency with drift ﬁled.

2

0.8

0.5

50

Experiment : Attenuation during drift

0.9

0.5

0
0

99

0
0

50

100

150

200

250

300

350

Electric field [V/cm]

Figure 6.27: The transportation eﬃciency with drift ﬁled.

6.29 shows the time variation of the attenuation eﬀect. For the requirement, theattenuation eﬃciency less than 4%, a continuous operation for 4 days is possible.

Figure 6.28: A spectrum of the quadrupole mass spectrometer in the vacuum chamber
under 3.6 × 10−4 Pa.

Figure 6.30 shows a spectrum of the 5.9-keV X ray from 55 Fe after the correctionof the time variation of the attenuation eﬃciency; the energy resolution is obtained
as 9.9%. Eliminating contributions of the initial ionization, the recombination andthe attenuation, the non-uniformity of the gain can be calculated as 5.1%, which
also satisﬁes the requirement. Table 6.10 summarizes all the items.
In this condition, the ratios of the electrons with an energy of less than 1.4

CHAPTER 6. TIME PROJECTION CHAMBER

6000

0.12

Experiment : Time variation of attenuation efficency
Achieving vacuum : 3.6 × 10-4 Pa
Achieving vacuum : 2.9 × 10-3 PaCountsAttenuation efficiency

100

Experiment : Energy Resolution
Measured5000

55

Fe spectrum

Expected Non-uniformity of gain

0.1

σ/mean = 9.9%

4000

0.08
3000

0.06

1000

0.02

0
0

σ/mean = 5.1%

2000

0.04

0.5

1

1.5

2

2.5

3

3.5

4
4.5
5
Time [day]Figure 6.29: The time variation of theattenuation eﬃciency of the TPC with different achieving pressures.

0
3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

Deposit Energy [keV]

Figure 6.30: Energy resolution for the
5.9-keV X ray from 55 Fe (red) and an expected non-uniformity of the gain.

Recombination at the time of ionization
Attenuation eﬃciency during the drift of 150mm
Non-uniformity of the gain

requirement measurement
13%
12%
4%
4%
9%
5%

Table 6.10: Comparison between the requirement and the measurement for the items
which determine the separation between the neutron decay and the neutron capture in
CO2 .

keV under 50 kPa and 100 kPa are 0.06% and 0.03%, respectively. According to00Sβ0 = 2N50kP
a − N100kP a as discussed in Section 5.8, an uncertainty arising fromcorrection of the detection eﬃciency for the neutron decay becomes 0.1%.

Chapter 7
Discussion
An innovative TPC with no radioactive contamination and high detection eﬃciency has been developed. In this chapter, the expected sensitivity by use of thedeveloped TPC is described.

7.1

Uncertainty arising from the particle detection

As discussed in Section 6.4, the developed TPC has a capability to detect morethan 99.9% of the neutron decay and the neuron capture in 3 He, which are fully
separated by the calorimetric approach. In addition, the various backgrounds areproperly subtracted by the data-driven approach as described in Chapter 5. As aresult, the systematic uncertainty arising from the particle detection is reduced to
0.1%. In addition, the statistical uncertainty can reach 0.8% in 150 days with abeam power of 220 kW.
For the further improvement, intense neutron beams are desired as shown in
Figure 5.23. The conceivable approaches are as follows.
• Beam power of J-PARC
In spite of the designed beam power, 1 MW, the current beam power islimited under 300 kW, since the mercury target in MLF is damaged by the
impact of the proton pulse. The study to soften the impact is in progress,
so that it would be possible to increase the beam power in the near future.
• Beam loss in the Polarization beam branch
The intensity of the Polarization beam branch is about a third of that ofsimulation. The reason is not known exactly, however there is the potential
for an increase in the neutron ﬂux.
101

102

CHAPTER 7. DISCUSSION• Beam loss at the SFC
In spite of the cross section of the Polarization beam branch, 100 mm × 40
mm, only 20 mm × 20 mm of the neutrons can be reﬂected due to the size ofthe magnetic supper mirror. Thus sizable magnetic supper mirrors are now
developed.
If the neutron intensity becomes equivalent to that with a beam power of 1 MW,
the statistical uncertainty can reach 0.2% in 150 days.

7.2

Additional uncertainty

Additional systematic uncertainty are shown in Table 7.1, which are the determination of the counting rate of the neutron capture in 3 He as follows.
• Partial pressure of 3 He
By use of the mass spectrometer, the ratio of 3 He and 4 He can be obtainedby comparing it with a standard gas whose mixture ratio is pre-determined
at 0.5%. An air gauge currently in use has a 0.01% accuracy guarantee, sothat an accurate standard gas can be produced.
• Cross section of the neutron capture in 3 He
In the preceding measurement of the cross section, the monochromatic neutron by use of Bragg reﬂection in crystal is employed; however the result waslimited by the accuracy of the wavelength of the neutron [54]. BL08 in MLF
is designed to have the world best resolution of the wavelength, 0.03%, thus
it is possible to improve the cross section by using BL08.
• Non-uniformity of the temperature of the gas
According to P = ρRT (x), the temperature of the gas has inﬂuence on thedensity of 3 He, whose non-uniformity is measured to be 0.1%. In particular,
the pre-ampliﬁer on the MWPC part becomes a source of heat. Thus amicro-power pre-ampliﬁer has been developed with a group of liquid xenon
TPC mainly in KEK, which is expected to reduce the non-uniformity of thetemperature.
• N2 contamination
N2 causes the 14 N(n, p)14 C reaction as discussed in Section 5.3.2, which becomes the background to the 3 He(n, p)3 H. By using a gas chromatography,
the nitrogen pressure of 0.6 Pa is measured 5 days after ﬁlling the gas. Assuming 3 He partial pressure of 0.1 Pa, the 14 N(n, p)14 C reaction arises an7.3. ACHIEVABLE SENSITIVITY

103

uncertainty of 0.5%. Therefore sources of N2 contamination, such as outgassing or air leak, have to be identiﬁed and removed.
Item
uncertainty
3
Determination of the partial pressure of He
0.5%
3
Cross section of the neutron capture in He
0.13%
Non-uniformity of the temperature of the gas
0.1%
N2 outgassing
0.5%
Table 7.1: Additional uncertainty except for the particle detection.

7.3

Achievable sensitivity

In Table 7.2, an achievable sensitivity is summarized. Owing to the developmentof the TPC, the experiment is limited by uncertainties except for the particle
detection. As a result, for the 150 days the experiment in this thesis will reach
1.0% and 0.8% under 220 kW and 1 MW of the beam power, respectively.

104

CHAPTER 7. DISCUSSION

This work
Facility
J-PARC
Repetition rate
40 Hz
Pulse per repetition
6
Length of pulse
400 mmVelocity
500 m/s ∼ 1200 m/s
Duty factor∼ 7%
Beam cross-section
20 mm × 20 mm
Divergence±4.2 mrad
TPC gasHe : CO2 = 85 : 15
Pressure
50 kPa ∼ 100 kPa
Size of TPC
300 mm × 300 mm × 960 mm
Beam Power
220 kW
1 MW
Neutron decay (Sβ )0.1cps
0.5 cps
Neutron capture rate in 3 He (Sn )1∼3 cps1∼3 cpsEnvironmental background(Be )
8 cps
8 cps
Beam-induced background (Bb )2 cps
20 cpsβ> 99.9%> 99.9%n> 99.9%> 99.9%Beam time
150 days
150 days
Statistical uncertainty
0.8%
0.2%
Correction for β
0.1%
0.1%
Correction for n< 0.1%< 0.1%
Subtraction of Be< 0.1%< 0.1%
Subtraction of Bb< 0.1%< 0.1%
3
Determination of partial pressure of He
0.5%
0.5%
3
Cross section of the neutron capture in He
0.13%
0.13%
Non-uniformity of temperature of gas
0.1%
0.1%
N2 outgassing
0.5%
0.5%
Total uncertainty
1.0%
0.8%
Table 7.2: Expected accuracy of the experiment in this thesis. Parameters of the neutron bunch after the chopper, characteristics of the TPC, and systematic uncertainties
are summarized.

Chapter 8
Conclusions
The neutron lifetime is of growing importance in Big Bang nucleosynthesis (BBN)
after the observation of the baryon density of the universe by WMAP, since thedetailed veriﬁcation for the BBN may provide insight into new physics beyond theminimal BBN model. In that context a new experiment for the neutron lifetime
is proposed in this thesis and employs the world’s most intensive pulsed neutron
source, J-PARC. This will be the ﬁrst experiment for the neutron lifetime by meansof the accelerator.
A key principle of the experiment due to Kossakowski et al. is the coincident
measurement of the neutron decay and the neutron capture in 3 He in a time
projection chamber. For the coincident measurement, the neutrons have to be
shaped into a bunch whose length is shorter than the TPC. By analyzing theevent while the whole the bunch is inside the TPC, 4π acceptance for each event
is guaranteed.
The preceding study by Kossakowski background to was limited by the performance of the TPC which has a large amount of the background to the neutron
decay. Thus an innovative time projection chamber has been developed, which ismade from PEEK without radioactive contamination, installed 6 Li plate for the
scattered neutron inside the TPC and surrounded by 4π shielding for the environmental radiation. Consequently, the background to the neutron decay can be
reduced to 1/10 compared with the TPC developed by Kossakowski et al.
Meanwhile an analysis algorithm for the reduction of the systematic uncertainty
has been developed. Due to the calorimetric approach, more than 99.9% detection
eﬃciency for the neutron decay and neutron capture in 3 He is performed. Moreover
the remained backgrounds can be subtracted properly by the data-driven approach.
As a result, all the systematic uncertainties arising from the particle detection
are reduced to 0.1%. And then, for the 150 days the experiment in this thesis will
105

106

CHAPTER 8. CONCLUSIONS

reach 1.0% and 0.8% under 220 kW and 1 MW of the beam power respectively.
The dominant systematic uncertainty is due to the uncertainty of the 3 He density.
If the precise measurement of the 3 He density and the high intensity of the neutron
beam are realized, it is possible to achieve 0.1% accuracy in the neutron lifetime
measurement.

Acknowledgments
First of all, I am deeply grateful to my supervisor, Prof. Satoru Yamashita. He
guided me to the world of particle physics and supported the whole of my study.
Every time I stumbled on a diﬃculty, his kind and patient assistance helped mea lot. I have acquired an attitude to physics from him, which has aﬀected me somuch. It is a great fortune to spend my Ph.D. program as his student.
I would like to thank all the collaborators of the measurement of the neutron
lifetime and the Neutron Optics and Physics. In particular, it is my pleasure to
express my biggest thanks to Dr. Kenji Mishima, who has worked together fromthe beginning of the study in this thesis. His deep knowledge of neutron physics
is crucial for my achievement. Mr. Hideyuki Oide enriched my life during mystudy in so many aspects. We always had an enormous amount to discuss about
our research and visited many places in and outside Japan, which was very muchstimulating. I am very glad to have met him and am looking forward to working
on experiments together in the near future. I owe Dr. Tamaki Yoshioka, whom
I met on my ﬁrst night in Tokyo. Since then, his suggestions including private
advices supported me a lot.
I also would like to express my thanks to all the other members of the Yamashitagroup of ICEPP, Dr. Taikan Suehara, Dr. Tomohiko Tanabe, Dr. Takashi Kubota,
Dr. Yuichi Morita, Mr. Hitoshi Hano, Mr. Toru Suehiro, Mr. Takeshi Takahashi,
Mr. Takuro Murase, Mr. Ryo Katayama, Mr. Takahito Yamada, and Mr. Nao
Higashi. I enjoyed sharing a lot of time with them.
I deeply appreciate my mother Yukiko, my father Yoshitoshi, who gave me somany opportunities and encouragements throughout my life. Finally, I would liketo dedicate this thesis to my wife, Ryoko.

107

Bibliography[1] J. Chadwick. Possible existence of a neutron. Nature, 129(830):312, 1932.
[2] J. Chadwick. The existence of a neutron. Proceedings of the Royal Societyof London. Series A, 136(830):692–708, 1932.
[3] R. A. Alpher, H. Bethe, and G. Gamow. The origin of chemical elements.
Phys. Rev., 73:803–804, Apr 1948.
[4] G. Gamow. Expanding universe and the origin of elements. Phys. Rev.,
70:572–573, Oct 1946.
[5] K Nakamura et al. Review of particle physics. J. Phys., G37:075021, 2010.
[6] H. Snell and L. C. Miller. On the radioactive decay of the neutron. PhysicalReview, 74(9):1217, 1948.
[7] Fred E. Wietfeldt and Geoﬀrey L. Greene. Colloquium : The neutron lifetime.
Rev. Mod. Phys., 83:1173–1192, Nov 2011.
[8] J. S. Nico, M. S. Dewey, D. M. Gilliam, F. E. Wietfeldt, X. Fei, W. M. Snow,
G. L. Greene, J. Pauwels, R. Eykens, A. Lamberty, J. Van Gestel, and R. D.
Scott. Measurement of the neutron lifetime by counting trapped protons in acold neutron beam. Phys. Rev. C, 71:055502, May 2005.
[9] A. Serebrov, V. Varlamov, A. Kharitonov, A. Fomin, Yu. Pokotilovski, P. Geltenbort, J. Butterworth, I. Krasnoschekova, M. Lasakov, R. Tal’daev, A. Vassiljev, and O. Zherebtsov. Measurement of the neutron lifetime using a gravitational trap and a low-temperature fomblin coating. Physics Letters B,
605(1-2):72 – 78, 2005.
[10] V. Ezhov. Seventh International Workshop on Cold and Ultracold Neutrons,
St. Petersburg Russia, 2009.
109

110

BIBLIOGRAPHY[11] R. Kossakowski, P. Grivot, P. Liaud, K. Schreckenbach, and G. Azuelos.
Neutron lifetime measurement with a helium-ﬁlled time projection chamber.
Nuclear Physics A, 503(2):473 – 500, 1989.
[12] M Greiner. Gauge theory of weak interactions, 3rd edition , p272.
[13] E.L. and Wright. The WMAP data and results. New Astronomy Reviews,
47(11-12):877 – 881, 2003. Proceedings of the Workshop on The Cosmic
Microwave Background Radiation and its Polarization.
[14] Richard H Cyburt, Brian D Fields, and Keith A Olive. An update on the
big bang nucleosynthesis prediction for 7 li: the problem worsens. Journal of
Cosmology and Astroparticle Physics, 2008(11):012, 2008.
[15] Y. I. Izotov and T. X. Thuan. The primordial abundance of 4He: evidence
for non-standard big bang nucleosynthesis. Astrophys. J., 710:L67–L71, 2010.
[16] Robert A. Malaney and Grant J. Mathews. Probing the early universe: areview of primordial nucleosynthesis beyond the standard big bang. Physics
Reports, 229(4):145 – 219, 1993.
[17] J. Chadwick and M. Goldhaber. A nuclear photo-eﬀect: Disintegration of the
diplon by -rays. Nature, 134:237–238, 1934.
[18] J. Chadwick and M. Goldhaber. The nuclear photoelectric eﬀect. Proceedingsof the Royal Society of London. Series A - Mathematical and PhysicalSciences, 151(873):479–493, 1935.
[19] K. Nakamura et al. (Particle Data Group). Journal of Physics G37, 075021(2010) and 2011 partial update for the 2012 edition.
[20] J. M. Robson. The radioactive decay of the neutron. Phys. Rev., 83(2):349–
358, Jul 1951.
[21] N. D’Angelo. Cloud-chamber measurement of the half-life of the neutron.
Phys. Rev., 114(1):285–292, Apr 1959.
[22] A.N. Sosnovsky, P.E. Spivak, Yu.A. Prokoﬁev, I.E. Kutikov, and Yu.P. Dobrinin. Measurement of the neutron life-time. Nuclear Physics, 10:395 – 404,
1959.
[23] C. J. Christensen, A. Nielsen, A. Bahnsen, W. K. Brown, and B. M. Rustad.
Free-neutron beta-decay half-life. Phys. Rev. D, 5(7):1628–1640, Apr 1972.

BIBLIOGRAPHY

111[24] Yu.Yu. Kosvintsev, Yu.A. Kushnir, V.I. Morozov, and G.I. Terekhov. The useof ultracold neutrons for measurement of the neutron lifetime. JETP Letters,
31(4):236 – 240, 1980.
[25] Yu. Yu. Kosvintsev, V. I. Morozov, and G. I. Terekhov. Measurement of neutron lifetime through storage of ultracold neutrons. JETP Letters, 44(10):571– 574, 1986.
[26] P. E. Spivak. Zh. Eksp. Teor. Fiz., 94(1), 2009.
[27] F. Anton, W. Paul, W. Mampe, L. Paul, and S. Paul. Measurement of theneutron lifetime by magnetic storage of free neutrons. Nucl.Instrum.Meth.A,
284(1):101 – 107, 1989.
[28] A.G. Kharitonov, V.V. Nesvizhevsky, A.P. Serebrov, R.R. Taldaev, V.E. Varlamov, A.V. Vasilyev, V.P. Alﬁmenkov, V.I. Lushchikov, V.N. Shvetsov, and
A.V. Strelkov. Preliminary results of neutron lifetime measurements withgravitational ucn trap. Nucl.Instrum.Meth.A, 284(1):98 – 100, 1989.
[29] W. Mampe, P. Ageron, C. Bates, J. M. Pendlebury, and A. Steyerl. Neutron
lifetime measured with stored ultracold neutrons. Phys. Rev. Lett., 63:593–
596, Aug 1989.
[30] R.R. Tal’daev et al. V.V. Nesvizhevskii, A.P. Serebrov. Zh. Eksp. Teor. Fiz.,
102, 740, 1992.
[31] W.Mampe et al. JETP Lett. 57, 82., 1993.
[32] J. Byrne, P. G. Dawber, C. G. Habeck, S. J. Smidt, J. A. Spain, and A. P.
Williams. A revised value for the neutron lifetime measured using a penning
trap. EPL (Europhysics Letters), 33(3):187, 1996.
[33] S Arzumanov, L Bondarenko, S Chernyavsky, W Drexel, A Fomin, P Geltenbort, V Morozov, Yu Panin, J Pendlebury, and K Schreckenbach. Neutron
life time value measured by storing ultracold neutrons with detection of inelastically scattered neutrons. Physics Letters B, 483(1-3):15 – 22, 2000.
[34] A. Pichlmaier, V. Varlamov, K. Schreckenbach, and P. Geltenbort. Neutron
lifetime measurement with the UCN trap-in-trap MAMBO II. Phys.Lett.,
B693:221–226, 2010.

112

BIBLIOGRAPHY[35] Willis E. Lamb. Capture of neutrons by atoms in a crystal. Phys. Rev.,
55:190–197, Jan 1939.
[36] L. D. P. King and Louis Goldstein. The total cross section of the 3 He nucleus
for slow neutrons. Phys. Rev., 75:1366–1369, May 1949.
[37] C. D. Keith, Z. Chowdhuri, D. R. Rich, W. M. Snow, J. D. Bowman, S. L.
Penttilä, D. A. Smith, M. B. Leuschner, V. R. Pomeroy, G. L. Jones, andE. I. Sharapov. Neutron cross sections for 3 He at epithermal energies. Phys.
Rev. C, 69:034005, Mar 2004.
[38] V. I. Lushchikov, Yu. N. Pokotilovskii, A. V. Strelkov, and F. L. Shapiro.
Observation of ultracold neutrons. JETP Letters, 9(1):23 – 26, 1969.
[39] Neutron News, 3:29–37, 1992.
[40] A. Bussiére, P. Grivot, R. Kossakowski, P. Liaud, P. de Saintignon, and
K. Schreckenbach. A monochromatized chopped beam of cold neutrons forlow background experiments. Nucl.Instrum.Meth.A, 332(1-2):220 – 223, 1993.
[41] P. Grivot, R. Kossakowski, P. Liaud, K. Schreckenbach, G. Azuelos,
A. Bussiere, and P. de Saintignon. A helium-ﬁlled time projection chamber for a neutron lifetime measurement. Nucl.Instrum.Meth.A, 34(1):127 –
134, 1988.
[42] K. Taketani et al. A high S/N ratio spin ﬂip chopper system for a pulsed
neutron source. Nucl.Instrum.Meth.A, 634(1, Supplement):S134 – S137, 2011.
Proceedings of the International Workshop on Neutron Optics NOP2010.
[43] The web site of J-PARC. ”http://j-parc.jp/”.
[44] F. Mezei. Commun. Phys., pages 81–85, 1976.
[45] E. Fermi and L. Marshall. Interference phenomena of slow neutrons. Phys.
Rev., 71:666–677, May 1947.
[46] Edward Melkonian. Slow neutron velocity spectrometer studies of O2 , N2 , A,
H2 , H2 o and seven hydrocarbons. Phys. Rev., 76:1750–1759, Dec 1949.
[47] E. Melkonian, L. J. Rainwater, W. W. Havens, and J. R. Dunning. Slowneutron spectrometer studies of oxygen, nitrogen, and argon. Phys. Rev.,
73:1399–1400, Jun 1948.

BIBLIOGRAPHY

113[48] N. Z. Alcock and D. G. Hurst. Neutron diﬀraction by gases. Phys. Rev.,
75:1609–1610, May 1949.
[49] A. Lechner, M.G. Pia, and M. Sudhakar. Validation of Geant4 low energy
electromagnetic processes against precision measurements of electron energy
deposition. Nuclear Science, IEEE Transactions on, 56(2):398 –416, april
2009.
[50] E. Waibel and B. Grosswendt. Degradation of low-energy electrons in carbon
dioxide: energy loss and ionization. Nucl.Instrum.Meth.A, 53(3):239 – 250,
1991.
[51] B. Grosswendt and W.Y. Baek. The energy dependence of W values for
protons of energies up to 10 Mev. Radiation Protection Dosimetry, 61(13):267–274, 1995.
[52] H. Oide. wire chamber を用いた電離損失 energy 測定における空間電荷効果の取り扱いについて. The Autumn Meeting of the Physical Society of Japan,
2011.
[53] G.A. and Erskine. Electrostatic problems in multiwire proportional chambers.
Nucl.Instrum.Meth.A, 105(3):565 – 572, 1972.
[54] J. Als-Nielsen and O. Dietrich. Slow neutron cross sections for He3 , B, and
Au. Phys. Rev., 133:B925–B929, Feb 1964.