Development of A Gadolinium-doped Water Cherenkov Detector
for The Observation of Supernova Relic Neutrinos
Takaaki Mori
Graduation School of Natural Science and Technology,
The University of Okayama
February 18, 2015

Abstract
Supernova relic neutrinos (SRN) are the neutrinos which are produced from all the past supernova
explosions and are supposed to be flowing in the universe. No experiments have succeeded in detecting
SRN yet. Super-Kamiokande (SK) is a 50-kton water Cherenkov detector which has the best sensitivity
to SRN. A study of γ-rays produced in neutral-current neutrino-oxygen quasi-elastic interaction and in
the pion absorption by oxygen nucleus was essential for the background estimation to SRN. This study
has played a significant role in the result of SRN search in SK.
Although SK reaches an SRN flux approximately within a factor 2 above the theoretical expectations
by detecting positron via inverse beta decay (IBD) interaction (ν¯e +p → e+ +n), the present search is limited by the systematic error due to much background. In order to observe SRN by reducing background,a GADZOOKS! project is proposed. By dissolving gadolinium sulfate Gd2 (SO4 )3 into the SK purewater in the future, SK will be able to tag the neutron in coincidence of the positron and separate IBDfrom background events which associate no neutrons in most cases. A dedicated 200-ton detector, whichis named EGADS, has been built to prove the feasibility of a realistic Gd-doped water Cherenkov detector.
In this thesis, the construction, the operation, and the initial performance of EGADS will be described.
The delayed γ-ray signal from Gd neutron capture has been measured using an Am/Be neutron sourceat 115 and 230 ppm concentrations of Gd2 (SO4 )3 in EGADS. The γ-ray energy, the position and thetime of γ-ray production from Gd neutron capture are measured. The detection efficiency is defined as”neutron capture efficiency” times ”reconstruction efficiency”. The detection efficiencies for 115 ppm and
230 ppm concentrations of Gd2 (SO4 )3 were measured to be 22.7±0.7% and 35.2±1.0%, respectively. The
background efficiencies for a 400 µsec time window were also measured to be 1.2 ± 0.3% and 1.1 ± 0.3%
for each concentration. These results are found to be consistent with Monte Carlo simulation. We expectthat the higher concentration provides the better performance since the neutron capture efficiency islinearly proportional to the detection efficiency.
Further, in order to evaluate the performance of the neutron capture in the SK detector, the γ-ray
events from Gd neutron capture are observed in the SK detector by using the Am/Be neutron source anda 2-litter vessel filled with Gd2 (SO4 )3 solution. The reconstruction efficiency of γ-ray from Gd neutron
capture and the background efficiency for a 35 µsec time window were estimated to be 88.0 ± 2.0%, and(8 ± 2) × 10−3 %, respectively. We also estimated the performance of the Gd-doped SK detector. About
16 - 30 SRN events are expected for 10 years of measurement , and the cosmic-ray accidental backgroundis expected to be negligible.

Contents
1 Physics Background
1.1 Supernova Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Type II Supernova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Supernova Relic Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Supernova Relic Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 SRN Search Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Supernova Relic Neutrino Search at Super-Kamiokande . . . . . . . . . . . . . . . . . . .
1.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Study of γ-ray Production in Neutral-Current Neutrino-Oxygen Interaction . . . .
1.3.3 The γ-ray Production in Pion Absorption . . . . . . . . . . . . . . . . . . . . . . .
1.4 Super-Kamiokande Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Phase of Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 20-inch Photo-Multiplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.3 Water Purification System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.4 Air Purification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.5 Data Acquisition System in SK-IV . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
2
6
6
7
10
10
13
15
16
17
17
19
22
22

2 GADZOOKS!
2.1 Neutron Tagging using Gadolinium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Benefit of Neutron Tagging in Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . .
2.3 Gadolinium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Gd Compound and Material Soak Test . . . . . . . . . . . . . . . . . . . . . . . . .

24
24
26
27
29

3 R&D Detector for a Gd-doped Water Cherenkov Detector: EGADS
3.1 EGADS Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Progress of the R&D Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 200-ton Water Cherenkov Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 DAQ System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 15-ton Tank and Pre-Treatment System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Water Circulation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Water Transparency Measurement Device . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Measurement of Gadolinium Concentration . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Radioactive Contamination of Gd sulfate . . . . . . . . . . . . . . . . . . . . . . . . . . .

31
31
32
35
40
43
45
45
46
48

i

CONTENTS

March 16, 2015

4 Detector Calibration
4.1 Pre-calibration and PMT Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 HV Determination in the EGADS Detector . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Gain Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Global Gain Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Relative Gain Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Quantum Efficiency Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Auto-Xe Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49
49
52
53
54
55
55
57
61

5 Software Tool
5.1 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Gd Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62
62
63
67
69

6 Detection and Analysis of γ rays from Gadolinium Neutron Capture70
6.1 Measurement and Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.1.1 Am/Be Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.1.2 BGO Scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.1.3 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.1.4 Neutron-Nucleus Interactions at low energy region . . . . . . . . . . . . . . . . . . 76
6.2 Analysis of γ rays from Gd neutron capture . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.3 Evaluation of Detector Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.3.1 Neutron Capture Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.3.2 Analysis of Reconstruction Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.3.3 Systematic Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.4 Evaluation of the Performance in the Super-Kamiokande Detector . . . . . . . . . . . . . 95
6.4.1 Measurement and Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.4.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.4.3 Measurement of Energy Spectrum of Gd γ ray . . . . . . . . . . . . . . . . . . . . 97
6.4.4 Evaluation of the Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7 Conclusion and Future Prospects

109

ii

Chapter 1

Physics BackgroundOn the 23rd of February, 1987, the Kamiokande, IBM, and BAKSAN observed a neutrino burst fromSN 1987A (Figure 1.1). The SN 1987A occurred at a distance of about 51.4 kpc from Earth, the threeneutrino detectors detect the neutrino bursts approximately three hours earlier than the measurementby the optical detectors. Kamiokande detected 11 neutrinos, IBM detected 8 neutrinos, and BAKSAN
detected 5 neutrinos. This was the first detection of a neutrino bursts from supernova explosion inhistory, and it introduced a new field of research: neutrino astronomy. This detection proved that thefundamental model of core collapse supernova was correct.

Figure 1.1: Supernova 1987A.

1.1

Supernova Explosion

The mechanism of supernova explosion is explained in this section. Supernova explosions occur at the
final stages of the evolution of massive stars. As shown in Figure 1.2, supernovae are categorized into
different types based on their spectroscopic characteristics and properties of the light curve. Supernovae
can also be divided into two categories according to the mechanism of explosion. Type Ia supernovae
are believed due to the thermonuclear disruption of white dwarfs, and they are discovered in galaxies
containing very old stars. Type Ib, Ic and II supernovae are generated by the core collapse of massive

1

stars (M> 8M ). From the point of view of neutrino physics, core-collapse supernovae are the mostinteresting, because they releases all types of enormous neutrinos.

Figure 1.2: Classification of supernova type [1].

1.1.1Type II Supernova

Type II supernova is caused by the core collapse of the star whose mass is more than 8M , where
M is solar mass. These star forms the iron core and burns the silicon at T ' 3.4 × 109 K. If themass of the iron core exceeds the Chandrasekhar mass limit (1.4M ), the gravitational core collapse andphotodisintegration are caused within a 10 sec. If the neutron star is left, the released energy from theType II supernova is calculated as




M2
M2
∆E =
−G
− −G
(1.1)
R GS
R NS

2 
−1
M
R
= 2.7 × 1053
[erg],(1.2)
M
10km
where GS and NS stand for a giant star and a neutron star, and the first term is almost negligible. On theother hand, the energy from the photodisintegration is estimated 1.4M ×6×1023 ×3.2MeV ' 1×1051 erg.
The kinetic energy for the ejecta mass of Mej = 10M is on the order of Ekin = 1/2Mej × v2 ' 1051 erg,
assuming v ∼ 2000km/s. In short, neutrino emission from a core collapse carries 99 % of the released
energy. The total energy obtained by SN 1987A is consistent with the calculation by Eq. 1.2.
Time evolution of type II supernova
1. Photodisintegration and neutronization
At the last stage of massive star evolution, the gravitational force is balanced by the pressureof degenerate relativistic electrons. In the core where the temperature and density are high, thephotodisintegration of iron nuclei occurs in the interaction,
γ + 56 F e → 13α + 4n − 124.4 M eV,
2

(1.3)

and the electron capture also occurs.
e− + N (Z, A) → N (Z − 1, A + νe ) + νe

(1.4)

These lead to the reduction of the pressure support by the electrons and the trigger of a rapid corecollapse. In this step, only electron-neutrinos are released freely from the core, because their mean
free path is much longer than the radius of the core. However, the amount of released neutrinos isquite smaller than the one in the third step.
2. Neutrino trapping
The collapse in the inner part of the core is homologous. On the other hand, the material outsidea certain value of radius collapses supersonically in quasi-free fall, and its velocity is proportional
to the inverse square of the radius. Electron-neutrinos begins to be trapped via coherent scattering
off nuclei in the core when the density of the inner core exceeds the 1011 − 1012 g/cm3 . The radiusof this characteristic surface is calculated by the coherent scattering cross section and the density
at


Eν
Rν ≈ 1.0 × 107 cm.
(1.5)
10M eVThis surface is called a neutrinosphere. Neutrinos generated outside of the neutrinosphere can bereleased from the core. However, neutrinos generated inside can be diffused out like the photons
from the photosphere of normal stars.

Figure 1.3: Time evolution of stellar shell for the selected mass points with the numerical supernova
model from [2]. Mass 1.665 M is the first mass point. Solid lines are drawn for every fifth mass point.
The dashed lines are for two succeeding mass points (108 M and 109 M ) near the edge of the nascentneutron star and ejected matter.

3

3. Core bounce and neutrino emission
The homologous collapse continues until the density of the inner core reaches at the nuclear density∼ 1014 g/cm3 . Figure 1.3 shows the time evolution of stellar shell. The repulsive nuclear force stops
the collapse, and drives the shock wave towards to the outer core. As the propagation of shock wave
toward to outer core dissociating nuclei into free proton and neutron, enormous electron neutrinos
are produced via electron capture.
e− + p → n + νe
(1.6)
The cross section of coherent scattering is proportional to the square of nuclear mass (A), whichleads to the decouple of the previously trapped anti-electron neutrinos from the matter. This sudden
release of electron-neutrinos is called prompt electron-neutrino burst or neutronization burst. The
peak of neutrino luminosity exceeds 1053 erg/s. However, due to the short time scale (a few msec
scale), the total energy of the emitted neutrino is about 1051 erg. simultaneously, all types of neutrinos (νe , νµ , νtau ) are produced thermally in the hit post-bound region via following interactions,electron-positron annihilation,e− + e+ → ν + ν̄,(1.7)
and nucleon-nucleon bremsstrahlung.
N + N → N + N + ν + ν̄

(1.8)

And, electron-neutrinos and anti electron-neutrinos are produced by charged-current interactions,e− + p→ n + νe ,

(1.9)

+

→ p + ν¯e .

(1.10)e +n
4. Delayed explosion

Shock wave loses the energy by photodissociation of nuclei (∼ 1.7 × 1051 erg to disintegrate 0.1
M iron) and by emission of neutrinos behind the shock front.
5. Remnant of the starTime scale of thermal neutrino emission is 10 seconds, Finally, the protonneutron star cools andturns into a neutron star or black hole, which is determined by the its mass and initial metallicity.
General description of type II supernova
Hydrodynamic calculation with neutrino transport is used to obtain the neutrino flux from the Type II.
The core density is > 1013 g/cm3 , so the core is opaque to neutrino transport. The effective temperatureof the core surface is estimated by the radiation law as
"

∆E/τ
1
Tef f =
2
4πσRef(7/8)gνf#1/4,(1.11)

where σ is Stefan-Boltzman constant, gν is the number of neutrino species, R is few 10 km, and τ is thecooling time of the core whose order is 5-10 sec. The effective temperature is obtained ' 4 MeV andaverage neutrino energy εν ≡ 3.15Teff ' 10MeV. The total neutrino flux is Φν = ∆E/εν ' 2 × 1058 .
The neutrino flux from the supernova at the center of the galaxy is obtained byφν =Φν
' 1.6 × 1012 cm−2 [ν 0 s/cm2 ].
4πd2
4(1.12)

Figure 1.4: Time evolution of neutrino luminosity and averaged energy from [2]. Dashed line is νe , solidline is ν¯e and bold solid line is νx (νµ , ν¯µ , ντ , ν¯τ ).

From this flux, we expect the following events in a 1-kt water Cherenkov detector for a supernova at
galactic center (∼10 kpc): 170 events(ν¯e + p → e+ + n), 8 events(νe + e → νe + e− ).
Figure 1.4 indicates the hierarchy of neutrino energies as follows:hEνe i < hEν¯e i < hEν¯x i(1.13)The neutrino energy reflects the temperature of matter surrounding the neutrino sphere. Inside of theneutrinoshere, thermal equilibrium is established. The neutrinos emitted from the deeper and hotter part
have the higher energy. The neutrinosphere for νx (x=µ,τ ) and ν¯x is the smallest among the all neutrino
flavors, and the νx ’s interacts only via neutral current interactions. The neutrinosphere for ν¯e is smaller
than that for νe because the proto-neutron star is neutron rich.
The current supernova models expect energy hierarchy shown in Eq. (1.13). However, it is not easy
to derive the time integrated average energy without detailed calculation. As shown in Figure 1.5, theaverage energies for all neutrino flavors are estimated roughly in [2, 3] as follows:hEνe i' 13M eV

(1.14)hEν¯e i

' 16M eV

(1.15)

hEνx i' 23M eV

(1.16)

Energy spectrum of supernova neutrinos is usually estimated by the Fermi-Dirac (FD) distribution withthe zero potential [4].
120 E 2
1
dN
= L 4 4 E/T −µ+1 ,(1.17)dE
7π T ewhere T is the effective neutrino temperature (T ' hEi/3.1514) and L is the total neutrino luminosity.
Figure 1.6 shows the energy spectrum is anti-electron neutrino calculated by supernova simulation [2].

5Figure 1.5: Energy spectra of neutrinos from [3]. Solid, dashed, and long-dashed lines correspond to νe ,ν¯e , and νx , respectively.

The suppression at the low and high energy region compared with FD distribution can be seen, which isdue to compensation by using a ”pinched” FD distribution [6, 7].
1 E2
1
dN
=L
dE
F (η) T 4 eE/T −µ + 1(1.18)

where η is a pinching parameter and F (η) = dxx3 /(ee−η + 1) is a normalization factor. In this case, theaverage energy depends on both T and η, and up to second order, < E/T >∼ 3.1514+0.1250η +0.0429η 2 .

1.2

Supernova Relic Neutrinos

Enormous numbers of supernovae have exploded since the beginning of the universe. There are about
1021 stars, and 1017 stars have a mass greater than 8 M , and they are expected to finish as a supernova
explosion. The neutrinos emitted from all such supernova explosions constitute the Supernova Relic
Neutrino (SRN) flux. Measuring the overall flux and energy spectrum of SRN will enable us to investigate
the history of past supernova explosions. For example, the flux of SRN can provide information on thestar formation rate and supernova rate in galaxies.

1.2.1

Supernova Relic Neutrino Flux

The origin of Supernova Relic Neutrinos (SRN) is all supernovae from the big bang to the present day.
Since SRN is the superposition of all supernova neutrinos, its spectrum is calculated by
Z ZmaxdNν (Eν0 ) dt
Fν (Eν ) = c
RSN (z)| |dz,(1.19)dEν0
dz
0
where c is light speed, RSN is the supernova rate depending on the red shift parameter, Eν is detected
neutrino energy, and E0ν = Eν (1 + z) is the neutrino energy initially emitted. The relation between thecosmic time t and red shift z is calculated by Friedmann equation aspdz= −H0 (1 + z) Ωm (1 + z)3 + ΩΛ ),(1.20)
dt
6

Figure 1.6: Energy spectrum of ν¯e from the theoretical model from [2]. The chemical potential is set tozero for the FD distribution.

where H0 is Hubble constant value, and Ωm and ΩΛ are the fraction of the cosmic energy density inmatter and dark energy respectively.
There are many theoretical models estimating the SRN flux in a similar assumption. Even before the
1987A, SRN had been predicted, and its flux was calculated assuming the constant SFR without experimental data. After the 1987A, SRN flux is calculated more precisely. Figure 1.7 shows the theoretical
SRN spectrum from [9]. The expected SRN spectrum peaks in <10 MeV region due to the red shift.
Rate of Supernova
The supernova rate is considered to be proportional to the star formation rate (SFR), because the lifetimeof a massive star is much shorter than the lifetime of the universe.
The SFR is usually obtained by measurement of living massive stars [8]. In order to estimate the
SFR from the observables, distribution of stellar masses at formation has to be considered as initial massfunction. Figure 1.8 shows the SFR as a function of red shift. These results indicate that SFR increases
with the red shift z for 0 - 1 region. It means that supernova explosion occurred more frequently in theearly universe. For z ≤ 1, RSN can be described as
RSN (z) ∼= RSN (0)(1 + z)β ,(1.21)

where, RSN (0) is a normalization factor, and the best fit value for β is 3.28 up to the red shift z ∼ 1 [9].

1.2.2

SRN Search Experiment

The SRN search has been performed at several detectors in the world (Kamiokande[35], Mont Blanc[36],
SNO[37], and KamLAND[38]). However, still SRN has not yet been discovered. The upper limits on
SRN ν¯e flux by these experiments are shown in Table 1.1. SK currently has the best sensitivity to the
SRN signal in the world. The advantage of the scintillation detectors is the lower background by neutron
tagging, while a water Cherenkov detector is capable of large size detector because of cheap material.
7

Figure 1.7: Theoretical spectrum for SRN from [17].

Figure 1.8: Recent measurement of core-collapse supernova as the function of red shift, with the expectation from star formation rate data [5].

8Experiment
Kamiokande
Super-KamiokandeMont Blanc
SNO
KamLAND

channel
ν¯e
ν¯e
ν¯e
ν¯e
ν¯e

Energy window [MeV]
8-14
16-30
20-50
22.9-36.9>19

Flux [/cm2 /sec]∼ 102
2.8-3.0
8.2 × 103
72
50

Table 1.1: Flux upper limit for each experiment.
SNO
Sudbury Neutrino Observatory (SNO) is a Cherenkov detector in Canada, and is consisted of 1 kton
heavy water and 10,000 PMTs. From 1999 Nov. 2 until 2001 May 28 (306.4 days) corresponding to an
exposure of 0.65 kton yr. SNO searches νe of SRN primarily throughνe + d → p + p + e−

(1.22)SNO obtained that upper limit of SRN ν¯e flux is 70 cm−2 s−1 at the 90% confidence level in the energy
range 22.9-36.9 MeV.
Mont Blanc
This is 90 tons liquid scintillation detector, which has been operating since 1985 at the Mont Blanc
Laboratory. Mont Blanc obtained the ν¯e limit flux of 8.2 × 103 cm−2 sec−1 at the 90% confidence level by
IBD search. LSD search νe and ν¯e signal via the following process.
→12

N + e−(1.23)

N

→

12

+

(1.24)

ν¯e + 12 C→

12B + e+(1.25)→

12−(1.26)

νe + 12 C
12

C +e

and

12

B

C +e

KamLAND
KamLAND is 1 kton single volume liquid scintillation detector in the Kamioka mine, and detecting
anti-electron neutrino from the sun and other sources via inverse beta decay (IBD) interaction. This flux
limit was applied for the SRN flux, result in SRN is found to be 139 cm−2 s−1 , assuming LMA model [15].
The main background in the scintillation detector is 9 Li produced by cosmic muons, reactor neutrinos,and critical one is the atmospheric neutrinos.
Borexino
Borexino is 300 tons single volume liquid scintillation detector in Italy, and detecting anti-electron
neutrino from the sun and other sources via IBD interaction. The specification of this detector is a low
energy threshold: 60 keV, good energy resolution:4.5% at 1 MeV.

9

1.3

Supernova Relic Neutrino Search at Super-Kamiokande

The world’s best limit on the SRN flux comes from Super-Kamiokande (SK), a large water Cherenkov
detector located in the Kamioka mine in Japan [18]. SK searches for SRN events via a positron signal
produced by the inverse beta decay interaction, since its cross section is by far the largest of the possiblesupernova neutrino interactions with water.
ν¯e + p → e+ + n(1.27)

The cross section of neutrino interactions in 0 - 60 MeV range is shown in Figure 1.9. While SK does
have the world’s best limit, its current search for SRN is strongly constrained by background; the searchregion for SRN ν¯e has been confined to 16 - 30 MeV.

Figure 1.9: Cross section for the water target, which includes the response of the SK detector like energy
resolution and trigger effect. Figure is from [20].

The most important sources of background are atmospheric νµ and νe charged current interactionsand γ rays produced by neutral-current neutrino-Oxygen interactions. Figure 1.10 shows the visibleenergy spectrum in the final data samples for each Cherenkov angle region, and fitting result of the LMA
model is overlaid. Figures 1.11 and 1.12 show the exclusion contour.

1.3.1

Background

After all cuts for the SRN search are applied, remaining backgrounds are from atmospheric neutrino
interaction. The energy spectrum of these remaining background is shown in Figure 1.13. These backgrounds are categorized into four interactions as follows:• Decay electron from invisible muon
This is the largest remaining background. Atmospheric muon-neutrinos interact in the SK detector and induce the muon via charged current interaction. This muon is low energy, often below
Cherenkov threshold, in which case its decay electron cannot be removed, because the muon isinvisible. This background’s energy spectrum is well known Michel spectrum.
10Figure 1.10: SK-I/III final sample and LMA model best fit result for each Cherenkov angle region [18].
The SRN signal region is determined to be 38-50 degree region.

Figure 1.11: Exclusion contour showing the SRN event rate vs. neutrino temperature [18]. The redregion is corresponding the 90% CL result of SK. CGI is Cosmic Gas Infall model [12], HMA is Heavy
Metal Abundance model [13], CE is Chemical Evolution model [14]. LMA is Large Mixing Angle model[15]. FS is Failed Supernova model [16], and the 4 and 6 MeV are estimation of neutrino temperaturefrom [17].

11Figure 1.12: Exclusion contour neutrino showing luminosity vs. neutrino temperature [18]. green andblue is allowed region by IMB ad Kamiokande for 1987A respectively. The red shows the 90% C.L. result.
Dashed line is individual 90% C.L. result.

• Atmospheric neutrino (νe ,ν¯e )Atmospheric neutrinos interact with proton or neutron asνe + n →ν¯e + p→e− + p,(1.28)+(1.29)

e + n.

Since SK cannot distinguish the electron and position signal, atmospheric νe cannot be separated
from SRN ν¯e signals.
• Neutral-current neutrino-oxygen quasi-elastic interaction (NC QE)
This is quasi-elastic scattering on an oxygen nucleus, which residual nucleus becomes excited, andcan give off de-excitation γ rays, or cause other nuclear reactions. This background have an energy
spectrum that rises sharply at our lower energy bound, similar to SRNs. Most of them are removed
by Cherenkov angle reconstruction, but some still leak into our final sample and must be modeled.
With the lowering of the energy threshold from 18 MeV to 16 MeV, this background has become
especially relevant.
• Heavy particle production from atmospheric neutrino events
This background is a grouping of two different things, both heavier particles. First NC interactions
generate charged pion (only π + >200 MeV are generated here). The pion events >200 MeV mostly
deposit energy in the detector through Cherenkov radiation from the accelerated pion. As theenergy reconstruction assumes these are electrons, the reconstructed energy varies largely and isroughly flat.
Included with them, since the spectrum and Cherenkov angle distribution are relatively similar, aresurviving muons (from muon-neutrino interactions) above Cherenkov threshold.
12

Figure 1.13: Energy spectrum of remaining background after event selection.

Backgrounds were modeled using SKDETSIM which is the official SK MC using GEANT 3.21 forparticle tracking, and NEUT [21] to model neutrino interactions. The γ-ray production in neutrinoOxygen NCQE interaction and pion absorption was re-evaluated and was contributed to the SRN searchin SK.

1.3.2

Study of γ-ray Production in Neutral-Current Neutrino-Oxygen Interaction

The γ-ray production from neutral-current neutrino-Oxygen quasi-elastic (NC QE) interaction, one ofremaining background, is very important, and has to be understood because its spectrum is similar to the
SRN spectrum. Recently, the calculation of cross section of γ-ray production was performed [22, 23, 24].
The cross section of γ-ray production following a NC QE interaction, σγ , is written in the formσγ

= σ(ν + 16 O → ν + γ + Y + N )X=σ(ν + 16 O → ν + Xα + N ) × Br(Xα → γ + Y ),(1.30)(1.31)

αwhere N is knocked out nucleon, Xα is the residual nucleus in the state α, and Y is the system resulting
15
14
15
from the electromagnetic decay in the state Xα , e.g., 15
8 O, 7 N, 7 O + n, 6 C + p.
The cross section NC QE is calculated byX ZdσνA
M dσνN=d3 pdEPN (P, E),(1.32)
dΩdEν0EN dΩdEν0
N =p,npdσνNwhere EN = M2 + p, M being is nucleon mass, dΩdE
0 is elementary neutrino-nucleon cross section,
νPN (p, E) is the spectrum function that is the probability of removing nucleon of momentum p from thetarget leaving the residual nucleus with energy E + E0 − M, E0 being the target ground-state energy.
According to the shell model, nuclear dynamics can be described by a mean field. In the simplest
implementation of this model, protons in the 16 O nucleus occupy three 8 states, 1p1/2 , 1p3/2 , and 1s1/2 ,13

Figure 1.14: Cross section for γ-ray production following NC QE interaction of neutrino (solid line)
and anti-neutrino (long-dashed line) compared to the NC QE cross section of neutrino (dotted line) andanti-neutrino (short-dashed line). Only the photons of energy larger that 6 MeV are considered [22].

with removal energy 12.1, 18.4, and 42 MeV, respectively [25, 26, 27]. The p1/2 , p3/2 , and s1/2
spectroscopic strengths (Sα ) have been computed by integrating the oxygen spectral function of over theenergy ranges 11.0 ≤ E ≤ 14.0 MeV, 17.25 ≤ E ≤ 22.75 MeV, and 22.75 ≤ E ≤ 62.25 MeV, respectively.
Dividing these numbers by the degeneracy of the shell-model states, one obtains the quantities listed inTable 1.2. The same spectroscopic strengths have been used for protons and neutrons.
α

p1/2

p3/2

s1/2

Sα
Br(Xα → γ+Y)

0.632
0%

0.703
100%

0.422
16 ± 1 %Table 1.2: Spectroscopic strength of the 16
8 O hole states (Sα ) and their branching ratios for de-excitationby the Eγ > 6MeV photon emission [23].
The branching ratios Br(Xα → γ + Y ), necessary to calculate the cross section (σγ ), are also given
15
in Table 1.2. In the case of the p1/2 -proton (neutron) knockout, the residual nucleus is 15
7 N (8 O) groundstate. Hence, no γ rays are produced. As the p3/2 -proton (neutron) hole lies below the nucleon-emission
threshold, 10.2 MeV (7.30 MeV), they always de-excites to the ground state by the emission of 6.2 or 6.3
MeV γ rays. When a proton (neutron) is knocked out from the deepest s1/2 shell, the excitation energy
14
14
is high enough for many de-excitation channels to open, of which only two, 14
6 C + p and 7 N + n (6 C + p
and 11
6 C + α), yield photons of energy higher than 6 MeV. The theoretical estimate of the branching ratio
for these processes [23, 28, 29], being in total 16%, turns out to be in good agreement with the value
1615.6±1.3+0.6
O(p, 2p)15 N experiment (E148) carried out at the Research Center for−1.0 % measured by the
Nuclear Physics of the Osaka University [30].
Recently, T2K experiment measured the cross section of νµ + O → νµ + X + γ, for the first time [22].

141.3.3The γ-ray Production in Pion Absorption

The re-evaluation of the γ-ray background by pion absorption in NEUT was one of the key point to the
publication of SK SRN result [18]. NC interactions generate pion (ν + 16 O → ν + 16 O + π). The pion
interaction above 100 MeV is dominated by π + + 16 O → ∆. On the other hand, the pion interaction
below 100 MeV is dominated by pion absorption in Oxygen. The γ-ray produced by
π ± + 16 O → X + γ.

(1.33)The branching ratio of γ-ray emission in NEUT is not based on the experimental data. By referring to

Figure 1.15: Angular correlation for the 16 O(π + , 2p)14 N at the 115 MeV with 0 to 20 MeV excitationenergy in the residual nucleus 14 N [31].
the existing experimental data of 16 O(π + , 2p)14 N (Eπ =115 MeV) [31] and 16 O(π − , 2n)14 N [34], the γray emission process was checked. The first experiment measured the scattering angle of both scatteredprotons. Figure 1.15 shows the angular correlation of two protons. Since a peak was observed, thedominant interaction in Eπ < 200 MeV is the two nucleon emission. The three or four nucleon emissions
are also existing, but its cross section is very small, hence de-excitation γ rays comes mainly from
14
N .The γ-ray emission, electromagnetic interaction, has to be dominant below the proton separationenergy Sp =7.55 MeV (neutron separation energy Sn = 10.55 MeV). So, pion absorption γ-ray backgroundcan be removed from the SRN background.
In order to estimate specification of γ-ray emission, the second experiment 16 O(π − , 2n)14 N data [34]was referred. This experiment measured branching ratio of Br(3.945 MeV →2.313 MeV) = 4.8%, Br(5.106
MeV →2.313 MeV) = 0.2%. According to Table of Isotope, 2.313 MeV excited state of 14 N emits γ-ray
with 100% probability. This measurement obtained Br(2.313 MeV)=5.3%; hence, the probability of single
2.313 MeV γ ray can be calculated, 5.3-(0.2+4.8)=0.3%. Table 1.3 shows the implemented table of γ raybranching ratio in NEUT.

15

the number of γ
210Energy[MeV]Ratio[%]

2.795, 2.313
1.64, 2.313
0.717
2.313
3.684
3.865
4.44
5.106
5.27
6.131
0

0.2
4.8
1.3
0.3
1.9
1.0
4.0
0.7
0.5
1.7
83.6

Table 1.3: Branching ratio of γ ray emission in pion absorption in NEUT.

1.4

Super-Kamiokande Experiment

Super-Kamiokande (SK) is the water Cherenkov detector for the neutrino observation. SK has achieved
several physics discoveries: evidence of first neutrino oscillations through atmospheric neutrinos [39],observation of solar neutrino oscillation [40],[41], first indication of terrestrial matter effect (day/nighteffect) of solar neutrino [41], confirmation of atmospheric neutrino result as a far detector of long baseline
experiment (K2K experiment)[43],[44],[45]. And SK has found the lower lifetime limit of proton decay[46].
SK is located 1000 m depth underground in order to reduce cosmic ray muon background. Construction of the detector is started from 1991 and completed in 1995. SK is made up of a cylindricalstainless water tank, 39 m radius and 41.4 m height, filled with 50 ktons of pure water. The SK tank isa double structure of Inner detector (ID) and outer detector (OD). ID is the cylindrical water tank, 33.8
m radius and 36.2 m height, filled with 32.5 ktons of pure water. The purpose of OD is follows:• The veto counter for the cosmic ray background.
• The shields for the background such as γ rays by the radioactive source from the surround rock
ID and OD is separated by the structure called super module which supports the twelve 20-inch PMTs for
ID and two 8-inch PMTs for OD. The surface coverage of PMTs is approximately 42%, which coverage
is called photo coverage.
Detection of neutrinos
Neutrinos do not have the electric charge and through matter, so, it is difficult to detect them. However,neutrinos occasionally interact with matter and a charged particle is generated. The charged particle isdetected by the Cherenkov light. Cherenkov light is emitted when the speed of a charged particle exceeds
the speed of the light.
nm
Ethr = √(1.34)
n2 − 1
where n is reflective index (n=1.34), and m is the mass of a charged particle. Cherenkov photons are
emitted in a cone with opening angle defined bycosθ =

1.
nβ
16(1.35)

Figure 1.16: Overview of the Super-Kamiokande detector.

The number of photons emitted per unit wavelength per unit length of radiator is given by
d2 N
2πz 2 α
1
=
1
−
,
dλdx
λ2
β 2 n2 (λ)(1.36)

where z is particle charge in unit of e, α is the fine structure constant, and β is the velocity of electron
in unit of light speed in vacuum.

1.4.1

Phase of Super-Kamiokande

The operation of the detector is separated into 4 phases from SK-I to SK-IV. Table 1.4 shows thesummary of feature of each SK phase. The first operation from 1996, SK-I, began with 11,146 ID PMTs
and 1,885 OD PMTs. SK-I was operated for years to April 2001 stably, but it was suspended for thetrouble and the reconstruction of the detector. SK-II has started after partial reconstruction, at thecondition with reduced PMTs (5,182 ID PMTs and 1,885 OD PMTs). After full reconstruction, SK
begun the operation, as the SK-III. To avoid to repeat the trouble about the PMTs, the fiber reinforced
plastic and acrylic case was attached to PMTs in the full reconstruction. SK-IV is the phase for upgraded
DAQ and electronics which is explained in Sec. 1.4.5.

1.4.2

20-inch Photo-Multiplier

Cherenkov light is detected by PMTs. The 20-inch PMT was originally developed by Hamamatsu
photonics in cooperating with Kamiokande collaboration [47]. The pohoto-cathode of PMT is coatedwith Bialkali so that the sensitive region is 300 - 600 nm and quantum efficiency is maximum at 390 nm(Figure 1.19). The dynode structure was optimized to achieve high collection efficiency which results ina good 1 p.e. distribution and timing resolution. The specification of 20-inch PMTs is summarized in
the Table.1.5.
The inside of the PMTs is vacuum for preventing discharging and accelerating photo-electronics
effectively. Then, if the glass tube is broken, it causes a strong shock wave. In order to avoid cascading17

Figure 1.17: PMT support frame called super module for the top, barrel and bottom PMTs.

18

Figure 1.18: Schematic view of the 20-inch PMT.
Phase

SK-I

SK-II

SK-III

SK-IV

Start
End
Number of ID PMTs
Number of OD PMTs
Photo-cathode Coverage
Front-End Electronics
Trigger Type

Apr. 1996
Apr. 2001
11,146
1,885
40 %
ATM
HardwareOct. 2002
Oct. 2005
5,182
1,885
19%
ATM
HardwareJul. 2005
Aug. 2008
11,129
1,885
40%
ATM
HardwareSep. 2008
Current
11,129
1,885
40%
QBEE
SoftwareTable 1.4: Feature of each SK-phase.

of the implosions of PMTs in the detector, all of the ID PMT are covered by acrylic covers and fiber
reinforced plastic cases (Figure 1.20).

1.4.3

Water Purification System

The 50 kton of pure water used in SK are taken from underground water in Kamioka mine. The
impurities like small dust, ions, and bacteria not only shorten the light attenuation length, but also canbe a background source for low energy neutrino observation. Therefore, it is crucial to remove impurities
from the water as much as possible before filling the detector.
1. 1 µm Water filter : This filter removes the garbage of more than 1 µm in pure water. Furthermore,
the radio active source attached to that garbage.
2. Heat Exchanger : This device keeps water temperature around 13 degrees. The circulation pumpand PMTs mounted inside detector heats the water. Heated water induced the dark noise of PMTs,
convection in the detector and bacteria in the pure water. It is important to manage the watertemperature.
3. Ion Exchanger : This device removes the iron ions in the pure water such as Fe2+ , Ni2+ , Co2+ ,and 222 R and its Daughter nuclide 218 Po ions. CO2 is also removed in this step because CO2 isdissolved in the pure water as CO2 + H2 O → 2H+ + CO−2.
19

Figure 1.19: Cherenkov light spectrum and quantum efficiency of the PMT are plotted as the functionof wavelength.

Figure 1.20: The FRP and acrylic case to prevent the shock wave.

20

Product name
Photocathode are
Photocathode material
Collection efficiency
DynodeQuantum efficiency
Gain
Dark noise rate
Timing resolution
Drift time
WeightPressure tolerance

R3600
50 cm diameter
Bialkali(Sb-K-Cs)
70 %11 stage Venetian bind type
about 21 % (360-400nm)
107 (1700-2000V)
4.5 kHz2.2 ns RMS (1 p.e.)∼100 ns
13 kg
26kg/cm water proof

Table 1.5: Specification of 20-inch PMTs.

Figure 1.21: Overview of the water purification system.

4. UV sterilizer : The bacteria in the pure water is removed by irradiation of ultraviolet rays.
5. Rn less air dissolving system : Dissolve the Rn less air into the pure water to improve theremoval efficiency of the Rn air in the step of vacuum degasfilter system.
6. Reverse Osmosis Filter : Remove the an organic compound with more than 100 atomic number.
7. Vacuum Degasfilter system : Removing the gas in the water. Main target is Rn gas which isremoved with efficiency of ∼96%. Oxygen is also removed about ∼99%.
8. Cartridge Ion Exchanger : This is resin for high molecular. This removes the ions such as Na+ ,Cl− ,Ca+2 and others.
9. Ultra Filter : Remove small particles down to the 10 nm size.
10. Membrane Degasfilter : Remove the radon gas with efficiency of ∼83%.

21

The concentration of the Rn in the pure water is suppressed less than 10−3 Bq/m3 through this system.
Furthermore, transparency of pure water exceeds 130 m.

1.4.4

Air Purification

The ambient air in the mine contains a rich Rn gas emitted from the rock. The concentration of Rn gas
in the mine is ∼1500 Bq/m3 and ∼30 Bq/m3 during summer and winter seasons respectively. In order
to send fresh air into SK experimental area, the air purification system was installed at the entrance ofthe mine, which is consisted of air blower, air filters and a heat exchanger. As a result, Rn concentrationin experimental area is kept at 20-30 mBq/m3 . [48]Figure 1.22: Overview of the Rn reduced air system.

1.4.5

Data Acquisition System in SK-IV

The data acquisition system in SK-IV phase is explained here. As explained in Section 1.4.1, front-end
electronics were replaced to QBEE [49] from beginning of the SK-IV phase. Figure 1.23 shows the DAQ
block diagram for SK-IV. The data from the QBEE is sent to the front-end PCs as TCP packets, andsorted in time order. The merger PCs are merges and sorts the data sent from the front-end PCs via
10-Gigabit Ethernet, and scans the data by software trigger. Triggered events are sent to the Organizer
PCs and are sorted in time order again, and stored in the disk for further analysis.
SK has multiple trigger types. High energy (HE) trigger is for the high energy events like atmospheric neutrinos. Low energy (LE) trigger is for low energy events like supernova relic neutrinos andsolar neutrinos. Special high energy (SHE) trigger is issued when PMT hits exceeds the 70 hits whichcorresponds to ∼10 MeV. After (AFT) trigger is issued after SHE trigger, and it requires that OD trigger
is not issued. Super low energy (SLE) was introduced to take events for more low energy solar neutrinos.
Summary of trigger configuration in SK-IV is shown in Table 1.6.

22

Figure 1.23: Block diagram of DAQ in SK-IV phase.

SK-IV Triggers

Hits/200nsec threshold

Gate width ( µs )

OD
SLE
LE
HE
SHE
AFT

22
34
47
50
70 - 58
SHE, no OD-0.5 → 1.0-5 → 35-5 → 35-5 → 35
35 → 535

Table 1.6: Trigger configuration in SK-IV phase.

23Chapter 2

GADZOOKS!
2.1

Neutron Tagging using Gadolinium

GADZOOKS! [Gadolinium Anti-neutrino Detector Zealously Outperforming Old Kamiokande, Super!],a Gadolinium-doped water Cherenkov detector, has previously been proposed [50]. The addition of 0.1%
gadolinium (Gd) to the SK water is the key to reducing the SRN background, which should allow the
first detection of SRN. Neutrons produced by inverse beta decay (IBD) are thermalized in about 1 µsec
and captured by Gd.
n + Gd → Gd + γ 0 s (8M eV )(2.1)
Figure 2.1 shows the principle idea behind GADZOOKS!. Neutron capture on Gd emits about 3 - 4 γ-rays
with a total energy of 8 MeV. The coincident detection of the prompt positron and the delayed γ-ray
cascade makes it possible to uniquely identify anti-neutrino events and to lower the energy thresholdfor the SRN search down to 10 MeV, where more SRN events are expected (see Figure 1.7). Given thepredicted rates, this widening of the energy window should lead us to the first observation of SRN using
SK. With its large thermal neutron capture cross section (49000 barn), 0.1% Gd solution results in about
90% efficiency in neutron capture (Figure 2.2); the remaining 10% are captured by protons in the water(p + n → d + γ(2.2 MeV)).

Figure 2.1: The principle of delayed coincidence detection.

24

Figure 2.2: Neutron capture efficiency as a function of the concentration of Gd2 (SO4 )3 .

The SRN search is affected by background like spallation and solar neutrinos in the low energy region.
Figure 2.3 shows the event rate in the 22.5 kton fiducial volume in SK-IV after event selection. Its origin
is spallation events induced by cosmic rays, which remains after the present spallation cut. The coloredline is the expectation of the theoretical model of SRN in SK. The current background rate in final sample
is about 8 events per day. On the other hand, from theoretical models, the expected rate for ν¯e is 0.7 1.1 events per year. To reach SRN signals, the background rate must be suppressed by 2 × 10−4 times
from the current level.

Figure 2.3: The low energy event rate in SK. The color lines corresponds to various theoretical SRN
spectra [17]. Black dots are current SK-IV final data sample after the spallation cut.

25

2.2

Benefit of Neutron Tagging in Super-Kamiokande

The ability to identify anti-electron neutrinos using IBD will provide extra benefits to the SK analysis.
They are explained here.
Neutron tagging using GADZOOKS! improves the SK’s ability to measure the directionality of supernova detection. A supernova explosion emits both neutrinos and anti-neutrinos which have different
energy spectra and the time profiles. The discrimination of these neutrinos will improve the investigation of the explosion mechanism. Using the electron scattering (ν + e− ), the current SK can determine
the supernova direction with an uncertainty of ∼5 degrees. (SK is the only neutrino detector capableof measuring supernova directionality in the world.) By neutron tagging, SK can discriminate between
electron scattering and IBD interactions, and improve the accuracy to ∼3 degrees as shown in Figure
2.4. In addition, the γ rays and/or neutrons from neutral-current ν-Oxygen events would be much better

Figure 2.4: Simulation of angular distribution without neutron tagging (left) and with neutron tagging(right). Neutrino flux and spectrum from Livermore simulation [2].

identified. This is of key importance in measuring the νµ /ντ temperature [52].
If supernova is big and close to Earth. GADZOOKS! has a chance to detect neutrinos from supernova
even before the core collapse. Some candidates are Antares (170 pc), Betelgeuse (200 pc) and Gamma
Velorum (340 pc). About a week before an explosion, during the Si-burning phase, anti-electron neutrinos
are produced via electron-positron annihilations in the core. Although the luminosity of neutrinos is quite
low compared to the forthcoming core collapse (10−8 order), while the latter lasts just a few seconds, theSi burning phase lasts several days. The mean energy of neutrinos from Si burning is about 1 MeV. Mostof anti-neutrinos are invisible in SK, but the total 8 MeV γ ray from a Gd neutron capture detected andit results in the sudden and monotonical increase in single rate of PMT as shown in Figure 2.5. Table
2.1 shows the expected number of pre-supernova neutrinos in the current SK and GADZOOKS!. It is26

important to observe pre-supernova neutrinos, since we can study the mechanism of stellar evolution
at the Si-burning stage before the core collapse begins. In addition, the increase in the event rate is
obviously an indication of the beginning of a supernova explosion, and it can be used as alarm before
supernova neutrino bursts occur.

Figure 2.5: The number of IBD events from Betelgeuse before the day when the core collapse [53].

Detector

Target mass

Min. pre-collapse

Ev. 24-0h pre-collapse

Ev. 3-0h

Borexino
KamLAND
Super-KGADZOOKS!

0.3 kt1 kt
32 kt
22.5kt

2 MeV
2 MeV
5 MeV
3.8 (1.8) MeV

22
108
173
442 (1883)

13
65
158
345 (1130)

Table 2.1: Estimation of the number of detectable events by SK and GADZOOKS! from pre-supernova
candidate Betelgiuse, assuming it is 0.13 kpc away [54]. The number in parentheses is only neutron
signals in IBD interaction.
GADZOOKS! can suppress the background in the energy range below 10 MeV for reactor neutrino
observations. If all reactors in Japan are activated, GADZOOKS! can detect the reactor neutrinos atsame event rate as KamLAND. Neutron tagging can help in discriminating between neutrinos and antineutrinos in the GeV scale energy region for atmospheric neutrino physics. Neutron tagging also reduces
the background in proton decay searches by requiring final states with no neutrons.

2.3

Gadolinium

There are 7 isotopes of Gd in the natural world. The abundance ratio and cross section for neutron
capture of these isotopes are shown in Table 2.2. 155 Gd and 157 Gd have a resonance state in the thermalenergy region in the neutron capture reaction. A neutron captured Gd is excited and returns to theground state, then approximately 3 - 5 γ rays are emitted. The γ ray energy can be calculated by using

27

Figure 2.6: The cross section of the neutron capture on Gd [55]. The red and blue lines are the crosssection of neutron capture on 157 Gd and 155 Gd, respectively. The green line is the neutron-proton elastic
scattering. The yellow line is neutron capture on proton.

mass difference. For example, 155 Gd neutron captured emits the γ rays through the following process:n + 155 Gd → 156 Gd∗ → 156 Gd + γ 0 s(2.2)

Then, the total energy of emitted γ rays is
Eγ = M (155 Gd) + Mn − M (156 Gd) = 8.54[M eV ],(2.3)

where M(155 Gd) and M(156 Gd) are the mass of 155 Gd and 156 Gd respectively, Mn is the mass of neutron..
In the same way, the energy of the γ ray from the 157 Gd neutron capture is obtained as 7.94 MeV. SK
in SK-IV phase searches for SRN by using the 2.2 MeV γ ray from neutron capture on proton.
n + p → d + γ (2.2M eV )(2.4)

Atomic number

Abundance ratio [%]Cross section [barn]

152
154
155
156
157
158
160

0.2
2.18
14.80
20.47
15.65
24.84
21.86

735
85
60,9001.8
254,000
2.2
1.4

Table 2.2: Cross section and abundance ratio of each Gd isotope.

28

The detection efficiency for 2.2 MeV γ rays is 17.74% and the accidental background probability is 1.06%
per 500 µsec [19]. If a Gd-doped SK is realized, the higher efficiency for 8 MeV γ-ray energy of Gd
potentially enables us to obtain the first detection of SRN in SK.

2.3.1

Gd Compound and Material Soak Test

At the first, a Gd compound which is dissolved in the SK water had to be determined. To be a goodcandidate for GADZOOKS!, the compound must be water soluble, relatively transparent to Cherenkov
light, and not be too difficult to handle in large quantities, as about 100 tons (roughly half of which
is Gd) would be required for a 50 kton detector. We considered three easily dissolved candidate Gd
compounds, GdCl3 , Gd(NO3 )3 , Gd2 (SO4 )3 . However, we discovered that the chlorine in GdCl3 caused
unwanted corrosion, and strong light absorption by nitrate in Gd(NO3 )3 was found below 350 nm, cutting
off a significant part of the Cherenkov light spectrum. Consequently, Gd2 (SO4 )3 remained as the best
candidate. 0.2% Gd2 (SO4 )3 solution corresponds to about 0.1% Gd solution in terms of mass of Gd.
Soak test
Soak tests for all 32 component materials of the SK detector were conducted to evaluate any potential
corrosion and/or deterioration [56]. Each sample piece was placed into a polypropylene bottle filled eitherwith 0.2% Gd2 (SO4 )3 solution or pure water and stored at a variety of controlled temperatures.
The transparencies of the solutions were investigated using JASCO V-550 spectrophotometer. The
only material that made transparency worse was found to be a rubber, which is used for the PMT supporter in SK. The measured transparency is shown in Figure 2.7. This study, however, concluded that theeffect of Gd-loading on the SK detector materials is expected to be negligible and that water transparency
will remain high if the water temperature is kept at 15o C. This corresponds to the temperature of thesurrounding rock at the underground SK site.

Figure 2.7: Measured transparency as the function of the wavelength. The dip in transparency of Gd
solution around 250 nm is absorption by Gd. The 20-inch PMT is sensitive in 300 - 600 nm wavelength
as shown in Figure 1.19.

29

An estimation of the effect is explained here. The absorbance is defined by
A = −ln(T /T0 ),(2.5)

where T is the measured transparency of 0.2% Gd2 (SO4 )3 solution with a sample and T0 is pure water
without a sample. The effective transparency (µef f ) which includes the quantum efficiency (QE) of PMT
is calculated by
R 1( 2 QE(λ)µ(λ)dλ),(2.6)µef f = Rλ 1
( λ2 QE(λ)dλ)where µ is the transparency, and λ is wavelength. This µ is obtained usingµ(λ) =

A(λ)
1× ,0.02m R

(2.7)

where 0.02 m is the length of our quartz capsule, and R is the accelerated factor of this soak test comparedwith the SK water. The pure water in the SK detector is circulated within one month. Meanwhile, theduration of this soak test was 3 months, and the amount of the water and the surface area of the rubber
was taken into account (Table 2.3). So, R is given as R = 3 × 5.08/(5.25 × 10−3 ) = 2900. The attenuation
length can be calculated using Lλ = µ−1 , and so
Lef f =

1=∼ 100[m].
µef f

(2.8)

This is almost the same level as the current SK water. The effect of Gd2 (SO4 )3 in SK is estimated tobe small. The final evaluation will be performed by using a dedicated R&D system (EGADS) which is
explained in the next chapter.

Soak test
SK

Amount of water [g]Surface area of the rubber [mm2 ]Ratio[mm2 /g]

5 × 102
5 × 1010

2.54 × 103
2.63 × 108

5.08
5.25 × 10−3

Table 2.3: Condition of the soak test and SK.

30

Chapter 3

R&D Detector for a Gd-doped
Water Cherenkov Detector: EGADS
3.1

EGADS Experiment

The new experimental hall near the SK detector in the Kamioka mine was excavated and a dedicated
R&D facility was constructed in the hall in order to demonstrate the principle of GADZOOKS! (Figure3.1). This facility is named EGADS [Evaluation Gadolinium’s Action on Detector Systems]. As shown

Figure 3.1: Location map of the EGADS experimental hall in the Kamioka mine.

in Figure 3.2, the EGADS facility consists of a 200-ton water Cherenkov detector with the same 20-inch
PMT as used for SK, a pre-treatment system for dissolving Gd sulfate (Gd2 (SO4 )3 · H2 O) into the waterin the 15 ton tank, a main Gd-doped water circulation system, and a water transparency measurement
device (UDEAL). The following items are being tested with this facility:• Transparency of the Gd-doped water. As in SK, it is important to keep the transparency high toenable various physics analyses.
• Since current SK water system removes ions, it must be modified to purify without throwing the31Figure 3.2: The schematic view of the R&D detector for Gd-doped water Cherenkov detector.

Gd sulfate out.
• Effect of Gd on detector materials. We are looking for any Gd-related corrosion and/or deteriorationof SK materials.
• Behavior and handling of Gd sulfate in the water. Gd sulfate should be uniformly distributed in
the detector, and should be able to be removed quickly, economically, and completely wheneverdesired.
• Ambient neutron level in the tank. We need to check how Gd γ-ray events from non-IBD neutrons
may affect the solar neutrino measurements in the SK detector.
• Demonstration of delayed coincidence detection by the 200-ton detector,

3.1.1

Progress of the R&D Experiment

The general progress of EGADS is explained here.
• Step1
Before mounting PMTs in the 200-ton tank, the water purification system was checked with thepure water for 6 months to check for any effect on the stainless steel tank. The water transparency
was evaluated by UDEAL, and it achieved the same level of clean water as the SK water.
• Step2
We next tested and succeed in the dissolution of Gd sulfate in the pre-treatment system. In
2011-2012, we first operated the circulation system with Gd-doped water and worked to achieve
the best possible efficiency of Gd recovery while maintaining good transparency of the Gd-doped

32

Figure 3.3: The EGADS R&D phase.

water. Gd recovery was determined to be above 99.9% for each pass. The Gd sulfate concentration
was periodically measured with an atomic absorption spectrometer, and stayed constant even after
many cycles.
Figure 3.4 shows the attenuation length of the pure water and Gd-doped water as a function of
the light wavelength. The Gd-doped water quality was investigated using not only the UDEAL
measurement and its linear extrapolation but also a commercial JASCO V-550 spectrophotometer. This spectrophotometer can continuously measure the attenuation length in steps of 0.1
nm, even for wavelengths below 337 nm, thus extending our transparency measurements beyond
UDEAL’s sensitivity region. Figure 3.5 shows the Cherenkov spectrum after passing through 15
meters. This was calculated using (Cherenkov spectrum) × (Attenuation length of water/Gd) ×(Quantum ef f iciency of P M T ). The length of 15 m was determined from the average path length
between the positions where the Cherenkov light was generated and the position where the light
was detected by PMTs in the SK detector. The Cherenkov light left (called LL15 hereafter) was
70.2% for the EGADS Gd-doped water compared with the no water. This value was 86.2% of theCherenkov light left for the SK pure water. This transparency is sufficient to perform all the usualphysics (plus the new physics enabled by neutron tagging) in a Gd-doped SK detector.
• Step3
For the total evaluation of the Gd-doped water Cherenkov detector, the PMTs were mounted in
the 200-ton tank. (see Sec. 3.2).
• Step4
After PMT mounting, the pure water was circulated through the detector, and we confirmed thattransparency was as good as before the PMT mounting. During the circulation with pure water,
the detector calibration was conducted (see Sec. 4).
• Step5

33

Figure 3.4: Attenuation length of pure water and Gd-doped water circulated thorough EGADS systembefore PMT mounting.

Figure 3.5: The expectation of detected Cherenkov light spectrum.

34

After approximately half a year circulation with pure water, the dissolution of the Gd compound
was started with the 30 kg of Gd sulfate. However, after the second batch of 30 kg of Gd sulfate, thetransparency became far worse compared with the transparency during Step 2. This indicated thatsome material related to the PMTs affected the transparency. In fact, the rusty wire was found in
the detector, which is used to support the black sheet. Unfortunately, this wire does not comprise
SUS304 which is the material used in the SK detector. Therefore, we had to remove this materialand clean the inside of the detector. In this thesis, the data for two batches of 30 kg of Gd sulfate
are analyzed. This corresponds to Gd sulfate concentrations of 115 ppm and 230 ppm (see Sec. 6).

3.2

200-ton Water Cherenkov Detector

The Gd-doped water was circulated through the EGADS detector and its transparency was evaluated.
The diameter and height of the inner volume of the detector are 541.7 cm and 494.9 cm, respectively(Figure 3.6). There are five ports on the top of the detector for the detector calibration. The same 20
inch-PMTs as used for SK were mounted in the detector. These PMTs were previously used in K2K 1
kton detector. Of the 227 PMTs, about 151 PMTs were bare, but the other 76 PMTs were equippedwith blast-resistant FRP and acrylic cases (Figure 1.20). As shown in Figure 3.7, these shielded PMTs
were uniformly mounted in the detector, as we want to test different configurations to evaluate the effectof Gd. Beside the SK PMTs, 8 5-cm hybrid photodetectors (HPD) and 5 20-inch high quantum efficiency
PMTs (HQE PMT) were installed [58]. They are developed for the Hyper-Kamiokande [59]. The active
photocathode coverage is about 40%, which is the same as for SK. As in the SK detector, opaquepolyethylene telephthalate sheets were installed to cover the gaps between the PMTs. It suppresses low
energy-radioactivity events behind the PMTs and reflection on the wall of the detector.
This detector can work as a supernova neutrino detector. If a supernova occurs near Earth, a lot ofneutrino events are expected (Betelgeuse:∼90,000 events, Galactic Center:∼40 events).

Figure 3.6: (left) The side view of 200-tank. (right) Floor of 200-ton tank and the PMT support frame.
168 (24×7) PMTs are mounted to wall, 36 PMTs are mounted to top and floor respectively.

35

Figure 3.7: The expand view of the EGADS detector.

PMT mounting
The PMT mounting work was performed in the summer of 2013. An overview of the PMT mounting
work is shown in Figure 3.8. In advance of the mounting work, 240 70-m cables were placed between thedetector and front-end electronics.
The PMTs selected by pre-calibration (Section 4.1) were carried into the EGADS experimental roomand checked one by one in terms of the dark rate, signal shape, and photocathode flaws. Only good
PMTs were attached the support frame as shown in Figure 3.9. They were brought into the detector
and mounted to the support beam. A 70-m cable and PMT are connected, and the connection part is
attached to a heat shrink tube for the waterproofing. For this work, about 8 people joined per a day, andit took one and a half months for all the PMTs.
Compensation coil
Since a large PMT is even affected by the terrestrial magnetic field (∼0.4 Gauss), the magnetic fieldin the detector has to be compensated. The magnetic field transverse to PMT (B0 ) is especially critical,
and it is calculated as( q
Bx2 + By2 ,(Top/Bottom PMTs)
B0 =
(3.1)
p
2
2
(−Bx sinθ + By cosθ) + Bz , (Barrel PMTs).
where the definition of θ is shown in Figure 3.10.
In order to reduce the effect of the terrestrial magnetic field, a network of compensation coils surrounds
the entire detector volume (the coil is attached to the tank wall). The alignment of this compensationcoil was designed with a magnetic field simulation. After the construction of the 200-ton tank, the coilcurrent was tuned to compensate the magnetic field effectively. A comparison of the magnetic field isshown in Figure 3.11. About 20% of the usual uncompensated values are sufficient for the R&D.

36

Figure 3.8: The picture of PMT mounting work.

Figure 3.9: The support frame for the PMT for (left) barrel position, (right) top and bottom position.

37

B [mG]

B [mG]

Figure 3.10: (left) Measurement height for barrel PTMs. (right) Gauss meter used for the measurement.

500

600

500

400
400
Magetic field w/o Coil300
Position 1

Position 2

300

Magetic field w/ Coilw/o Coilw/ Coil

Position 3
Position 1

200

Position 2

200

Position 3

100

0
0

100

50

100

150

200

250

300

0
0

350
degree

5

10

15

20

25

30

35

40
Pmt ID

Figure 3.11: (left) Terrestrial magnetic field at the position of barrel PMTs with and without thecompensation coil. (right) Magnetic field at the positions of the bottom PMTs.

38

Dark rate
After the adjustment of the high voltage for all PMTs (Sec.4.2), the dark signals for each PMT was
measured. As shown in Figure 3.12, the dark rate of PMT attached FRP cover was relatively higher
because of light emission from the FRP. According to the investigation at SK, this light emission isconsidered to be due to the chemiluminescence. However, this level of dark noise does not affect on the
our measurements using the calibration source.

Figure 3.12: The distribution of dark rate for all PMTs. (upper) bare PMTs. (bottom) PMTs with FRP
case.

Cosmic muon measurement
The first EGADS measurement was the cosmic muon rate. Cosmic muon was observed by the self
trigger mode, and the muon candidates were selected using following procedure.
• Select the events with more than 50 hit PMTs in order to remove low energy background events.
The muon energy is enough so that almost all PMTs observe the Cherenkov lights from the muon.
• Checked the hit pattern with the event display to remove the flasher events from PMT. Figure 3.13
shows the typical cosmic ray event.
We obtained the muon rate as 0.041 ± 0.003Hz, and the validity was confirmed by comparing with the SK
measurement. The flux of cosmic rays at the EGADS detector was assumed to be 1.54 × 10−7 s−1 cm−2 ,which was measured by SK. The cosmic muon rate is 1.8 Hz at SK. 1.38 Hz of them comes through the
top side of the SK detector and 0.42 Hz comes from the side of the SK detector, then
• The muon rate from the top of the detector was estimated to be 0.035 Hz by using SK’s value andthe ratio of the surface area between the SK and EGADS detector (0.257%).
39

Figure 3.13: Event display of cosmic muon event in the EGADS detector. Each circle indicates the PMT
and the color corresponds to the charge.

• For muons coming from the side of the detector, the rate was estimated using 0.035 × Rbarrel/top ×
R0Egads/Sk = 0.07 Hz, where Rbarrel/top is the surface area ratio of the top and side (0.23), andR0Egads/Sk is the ratio of the top/side between SK and EGADS (0.83).
Finally, the total muon rate was estimated to be 0.0425 Hz. The calculated and estimated rate differs byapproximately 3.5% and agrees well within the error.

3.3

DAQ System

The data acquisition (DAQ) and high voltage (HV) systems were installed in the control room near
the EGADS water circulation system. A schematic view of the DAQ system is shown in Figure 3.14.
The EGADS DAQ system was constructed by reusing old SK front-end electronics (the so-called ATMs
[Analog Timing Modules]) [57], and equivalent in performance to SK-I/III’s original DAQ system. The
ATM was developed based on the TKO (Tristan KEK Online) standard for SK. Integrated charges andthe time information for each PMT are recorded and digitized by the ATM module with a 12-bit ADC(Analog to Digital Converter). One ATM board can treat 12 PMT signals, and thus 20 ATMs were used
for the normal PMTs.
Signals from 12 PMTs are fed to an ATM module to be processed. Every 16 events, the digitized datain the ATMs are sent to VME memory modules called SMP (Super Memory Partner), with a typical datatransfer speed of ∼2 MB/sec. The TRG module records the trigger types and trigger generation timings
with a 50 MHz clock, counts an event number with a 16-bit counter, and generates a global trigger signal
when any one of the trigger signals is issued.
The data stream in the online PC is described in the Figure 3.15. Data collected by ATM are stored
in the SMP and TRG module respectively. These data were read by a front-end Linux PC via the VME
control module Bit3. Three processes were running on the front-end PCs. These are called the collector,
sorter, and sender respectively. The collector process monitors the number of the events in the SMP
module. If the number exceeds the pre-fixed value, the collector process reads the data from the SMP
40

Figure 3.14: Schematic diagram of the EGADS DAQ system.

and saves it in the shared memory. The sorter process reads the data in the shared memory and sorts theevents in order of the event number and save it in the shared memory again. The sender process sends
the data to the back-end PC after receiving requests from the event builder process. The event builder
process merges the data from the front-end PCs of both the SMP and TRG side. After the merger of theevent information, it is saved in a file with a binary format.
The offline process checks the data file and flag file for the DAQ process. If the offline process finds
the flag file of the stop or start of DAQ, the data file is sent to a computer building outside of the mine.

Figure 3.15: Schematic diagram view of the read-out system.

41

ATM calibration data on Timing

TDC count [Ch]

ADC - Pedestal [Ch]ATM calibration data on Charge
4000

4000

3500

3500

Buffer A

3000

2500

Buffer B

2500

2000

2000

1500

1500

1000

1000

500

500

0

0

Buffer A

3000

Buffer B

100

200

300

400

500

0

600

0

Input charge[pC]

200

400

600

800

1000

Time[nsec]

Figure 3.16: The overlay of the ATM calibration data (left) ADC, and (right) TDC for all ATM channels.
Since ATM has the two buffers, calibration data was taken for both buffers, which are shown by the redand blue color line respectively.
HV
CAEN SY1527LC and AP1932 were used for all PMTs. This setup is managed by Linux PC via a
TCP/IP connection. The specifications are shown in Table 3.1, and the performance is equivalent toSK’s system.
Output outrage
Max output channel current
Voltage ripple
Voltage-output drop

3 kV
0.5 mA< 39 mV pp
100-900 V

Table 3.1: Specification of the HV system.

ATM calibration
To convert the ATM response into real information from the PMT, the calibration of the ATM was
performed for all channels of the ATM. The CTG module (Charge Timing Module) was used for the
ADC calibration of ATM, which emits the signal like typical shape from the PMTs. The signal from
CTG was sent to the backplane of the TKO crate via the 70-m cables, which is the same length as thecables connected to the PMTs. The TDC tester was used to perform timing calibration of the ATM.
Figure 3.16 shows the obtained data for all ATM channel and its buffers. These were implemented in theoffline program.

42

Trigger system
An overview of the trigger system is shown in Figure 3.17. If the input signal into the ATM exceeds thethreshold level, the signal (200 nsec width and -15 mV height ) called HITSUM is emitted from the front
panel of the ATM. The HITSUM signal was used to produce a trigger signal for DAQ. The HITSUM
signal from all ATM boards was summed up and, summed signal was sent to the discriminator module.
If this summed up HITSUM signal exceeds the threshold level, the trigger signal of DAQ is generated.

Figure 3.17: Trigger system.

3.4

15-ton Tank and Pre-Treatment System

A schematic view of the 15-ton tank and pre-treatment system are shown in Figure 3.18. Gd sulfate
powder was dissolved into water in the 15-ton tank to produce a 0.2% Gd sulfate solution. The built-in
stirrer in the 15-ton tank helps to dissolve the Gd sulfate powder completely and quickly.
The pre-treatment system is equipped with microfilters, a UV lamp to kill bacteria, and a special
resin (AJ4400) which passes Gd but removes uranium and thorium with more than 99% efficiency. The
water was then injected from the pre-treatment system into the main circulation system and sent to the
200-ton tank.

43

Figure 3.18: Schematic view of 15-ton ton tank and pre-treatment system.

Figure 3.19: The uranium concentration measurement with ICP/MS after the resin, which was initially
10 ppt.

44

3.5

Water Circulation System

The light attenuation length in water must be kept long for various physics goals in SK when Gd is
loaded. The main EGADS water system was named “selective filtration”, because multivalent ions suchas Gd3+ and (SO4 )2− are selected out. A schematic view of this system is shown in Figure 3.20. The
membrane pore size of the nanofilters (NF) is smaller than Gd and SO4 ions, and so such multivalentions are selected out at the NF. The Gd-rejected water is then sent through reverse osmosis (RO), where
only H2 O molecules can pass through the membrane. Pure water and Gd sulfate are reunited in thecollection buffer tank and sent back to the 200-ton detector.
An ion exchange resin is used in the Gd removal system currently installed in the EGADS experimental
hall. The Gd is removed by this system with an efficiency of more than 99%. In the near future, a more
economical removal system, likely employing a mechanical filter press and/or cascade filtration, will be
installed. This new system is currently in development at the University of California, Irvine, USA.

Figure 3.20: The schematic view of ”selective filtration” water circulation system.

3.6

Water Transparency Measurement Device

To monitor the quality of the water in the EGADS system, we used a custom-built water transparency measurement device called UDEAL [Underground Device Evaluating Attenuation Length], shown
schematically in Figure 3.21. The main pipe is 8.6 meters tall. The light intensity is measured as a function of the light travel distance by changing the water level from empty to full in the main pipe. The
UDEAL monitors the light attenuation with the several wave length, which is relevant to Cherenkov

45

region, (337, 375, 405, 445, 473, 532, and 595 nm). Light pulses from the lasers to each 30-cm integrating
sphere are collected by UV enhanced silicon photodiodes, and the ratio of the integrated intensity istaken as the measured value. The precision of the UDEAL measurement is about 1%, even for hard-tomeasure attenuation lengths above 100 meters. The water used for the measurement is obtained fromthe top, middle, and bottom of the 200-ton tank in order to evaluate uniformity of the transparency inthe detector volume. Each position is measured daily to check the quality of water along with the statusof the circulation system.

Figure 3.21: The schematic view of the water transparency measurement device: UDEAL.

3.7

Measurement of Gadolinium Concentration

Gd concentration was monitored by the Atomic Absorption Spectrometer (AAS). Its schematic view isshown in Figure 3.22.
Water samples are collected from 3 points in the detector by using the same pipe as UDEAL sampling.
By measuring the concentration at 3 different height positions, the homogeneity in the detector can beinvestigated. Figure 3.23 shows the monitoring of the Gd sulfate concentration in the detector. The
injection of Gd can be seen as jumps in the concentration. Since the load water is injected from thebottom of the tank, there is the delayed increase in the concentration of the center and top position. we
can now calculate the total uncertainty to be a precision of 0.05%.

46

Figure 3.22: Schematic view of AAS measurement system.

Figure 3.23: Monitoring of Gd sulfate concentration in the detector by the AAS measurement before the
PMT mounting.

47

3.8

Radioactive Contamination of Gd sulfate

It is important to keep radioactive contamination in the detector as low as possible. Measurement ofradioactive contamination in the Gd sulfate itself has been conducted with the Ge detectors at Canfranc
Underground Laboratory, Spain. The measurement results are shown in Table 3.2. Taking into accountthe dilution of the Gd sulfate in the SK detector and the removal of uranium by the AJ4400 resin, thebackground is estimated to be < 3 × 10−2 events/year at SK. The solar neutrino flux at SK is ∼10
events/day for the three lowest energy bins (kinetic energy range from 3.5 MeV to 5 MeV), whereas theradioactive background coming mainly from 208 Tl β-decay is estimated to be ∼ 5 × 103 events/day/kton.
Several purification processes and analysis methods are being studied to reduce this background.
chain

sub-chain

Typical rad.[mBq/kg]

238U

238 U
336Ra
238 U
336Ra
238 U
336Ra

50
5
10
100
< 30
300

238U
238U

Table 3.2: Typical values of radioactive contamination in the Gd sulfate.

48

Chapter 4

Detector Calibration
The EGADS calibration is explained in this chapter. It is important to understand the detector
performance in order to identify the γ ray from Gd neutron capture both precisely and reliably. The
detector calibration was finished during pure water circulation, and this calibration followed the wellestablished SK calibration [60].
The output charge of the i-th PMT (Qobs ) is defined as
Qi,obs ∝ Nphoton × QEi × Gaini (i = 0 − 227),(4.1)

where Nphoton is the number of photons which hit the photo-cathode, and QE (quantum efficiency) is
the probability of photo-electron emission when a photon hits the photo-cathode. In our definition, QE
includes the probability that a photo-electron reaches the dynode (the collection efficiency). All PMTs
should have a uniform response in order to achieve good precise energy reconstruction, and this can bedone by the adjustment of HV value. The gain is the amplification factor at the PMT dynode, which is
calculated as
Gain ∝ α × HVβ ,(4.2)
where α and β are the parameters for each PMT, and HV is the high voltage applied to each PMT.
Pre-calibration was conducted before mounting PMTs in the detector. After PMT installation, we
performed HV determination and measured the gain and QE, and calibrated the timing for each PMT.

4.1

Pre-calibration and PMT Selection

Before the PMT mounting, pre-calibration was conducted for 250 PMTs in order to measure thefollowing properties of each PMT and to select 227 good PMTs to be used for EGADS.
• Measure α and β for all PMTs, and adjust the HV value to obtain uniform response for all PMTs.
After PMT mounting, this HV value will be the standard value, and β is used for further adjustment.
• Evaluate the quality of all PMTs in terms of the dark rate and 1 photo-electron (p.e.) sensitivity,
because our 250 20-inch PMTs have been left unused for 7 years. It is necessary to evaluate thesensitivity of each PMT to a single p.e. since signals between one and a few p.e. are expected ineach PMT from γ-rays generated by Gd neutron capture in the EGADS detector.
Pre-calibration work was conducted in about 10 days 1 .
1 2011/7/9 - 2011/7/20

49

Setup
In order to reduce the effect of the cosmic rays and measure the performance of the PMTs precisely,
the pre-calibration was performed at a laboratory inside the Kamioka mine. Two light sources (Xe lamp
and LED) were used.
• The Xe lamp was used for measurement of multiple p.e. in order to adjust the response of the
PMTs. The Xe lamp is suitable for checking individual PMT because the light intensity of the Xelamp is very stable in the long term.
• The LED was used for measurement of 1 p.e.. It enables us to conduct high event rate measurements.
The occupancy of the PMT for 1 p.e. is very low, and so a high event rate measurement is needed.
The setup for pre-calibration is shown in Figure 4.1. The PMTs were installed in the µ-metal box one
by one to suppress the effect of a magnetic field. The magnetic field inside the µ-metal box was less than
40 mGauss.
A Xe lamp was placed inside the black box. Light from the lamp first went through a UV filter toobtain only UV region light since the scintillation ball is only sensitive to the only 275 - 400 nm region.
After the UV filter, light is divided and sent to the scintillation ball and the APD. For uniform lightemission, the scintillation ball consisted of 15 ppm of POPOP and 200 ppm of MgO. The APD was used
for the trigger signal of DAQ and for monitoring of the light intensity of the Xe lamp.
The LED installed in the µ-metal box flashed in synch with the trigger signal.

Figure 4.1: The schematic view of the pre-calibration setup.

HV Determination
At the beginning of pre-calibration, we had to determine the target value of the PMT response. At
first, 7 PMTs were randomly selected from our 250 PMTs, and were used as standard PMTs during
pre-calibration. The response of standard PMTs was measured by supplying HV used in the previous
experiment (K2K 1-kton detector). This HV value was set to gain of 1.2×107 . The obtained average valueof standard PMTs was used as the target value of pre-calibration. The determination of the operational
HV value is based on the previous operational HV value (H0 ). By taking output charge data at four
HV values around the H0 , the target value can be calculated by fitting the four data points using ananalytical formula y = αxβ , where α and β are constants for each PMT. An additional measurement was
conducted to confirm the result. This procedure was repeated to achieve 1% of the target value.
Figure 4.2 shows the distribution of the ratio of the target value and the response of all PMTs. Using
this calibration, the initial variance of 13% (RMS) was improved to 0.8% (RMS).
50

Figure 4.2: The distribution of the ratio of the PMT response against to the target value before (left)
and after (right).

Selection of PMTs
We selected 227 PMTs to be mounted in the detector using following properties.

# of PMTs• Dark rate
After the HV adjustment, the dark rate count at the 0.5-p.e. threshold was measured. Figure 4.3
shows the distribution of the measured dark rate.

Entries
Mean
RMS

250
14.28
8.393

10

1

0

20

40

60

80

100
120
Dark rate [kHz]Figure 4.3: The distribution of measured dark rate for 250 PMTs. The high dark rate PMTs were
rejected.

• 1 p.e. sensitivity
The parameter of sensitivity to the 1 p.e., Peak-to-valley (PV), was measured for each PMT. Thiswas obtained from the ratio of the number of events at the 1 p.e. peak and the dip between 0 p.e.
and 1 p.e., as shown in the left of Figure 4.4.
Finally, 227 PMTs with the better PV values and low dark rates were selected from 250 PMTs as
candidates for PMTs to be mounted in the detector.

51

# of PMTs

Entries
250
Mean
1.542
RMS
0.1561

30

20

10

0

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2
PV

Figure 4.4: (left) The 1 p.e. distribution and the fitting result of double-gaussian. The PV is the ratioof hp and hv . (right) The distribution of the PV value of 250 PMTs.

4.2

HV Determination in the EGADS Detector

After the PMT installation, the uniform response of each PMT was checked with the HV value obtained
during pre-calibration, and further adjustment of HV was done using the Xe lamp.
Setup
The setup of the Xe lamp was almost the same as that for pre-calibration. However, this calibration
data was taken by the EGADS as shown in Figure 4.5.

Figure 4.5: The schematic view the Xe measurement setup.

Analysis
All PMTs were divided into groups such that the distance from the scintillation ball to each PMT were
the same, as shown in Figure 4.6. The target response of PMTs was defined by taking the average ofeach group with the HV value obtained during pre-calibration.
The measurements were conducted three times by rotating the scintillation ball to cancel the azimuthal
asymmetry of the scintillation ball. After taking the average of three measurements, the HV value for all

52

PMTs was re-calculated to reduce the variations from the target value of each group. After re-adjustmentof the HV value, a uniformity of 0.36% RMS was obtained as shown in Figure 4.7. PMTs with an acrylic
cover were also adjusted to same target response as bare PMTs since the attenuation of light by theacrylic case was small (1 - 2%).

# of PMTs

Figure 4.6: The definition of group of PMTs for (left) the barrel PMTs (right) the top and bottom PMTs.

Entries

60

227

Mean

0.9999RMS

0.003662

40

20

0

0.96

0.98

1

1.02
1.04
Ratio to average of group

Figure 4.7: The ratio of PMT response to the mean value of each PMT group.

4.3

Gain Measurement

The measurement of the gain of all PMTs is explained here. The gain can be expressed as the productof the global gain of the detector and the relative gain of each PMT.
Gaini = (Global Gain) × (Relative Gaini ), (i = 1 − 227)
53

(4.3)

The global gain is the absolute amplification factor of all PMTs, and the relative gain is distributed at
the standard value 1.0. The global gain and relative gain were measured independently.

4.3.1

Global Gain Measurement

The absolute gain is the factor for converting the charge to the number of p.e. This value is obtainedby calculating the mean value of the 1 p.e. charge distribution. The setup is shown in Figure 4.8, andthe LED light source was used as well as for pre-calibration.

Figure 4.8: The schematic view of the LED calibration setup.

Events/Trg

eventsSince the ATM ADC modules takes signal above ATM threshold (0.25 p.e.) and can not measure the0 p.e. contribution completely, the absolute gain was obtained with the procedure used in SK calibration.
The left of Figure 4.9 shows the sum of the distribution of all PMT charges. In order to remove the dark

10-1

104

10

3

102

10-2
10

1
-3

10

0

2

4

6

8

10

10-1
-500 -400 -300 -200 -100

12
14
Charge [pC]0

100 200 300 400 500

T-Tof [nsec]

Figure 4.9: (left) The T-TOF distribution of the LED data. (right) The 1 p.e. distribution of the LED.
rate, this distribution was selected by the ”on-time” 100 nsec time window and subtraction of the 100
nsec ”off-time” event. On-time and off-time are defined as (-50)-50 nsec and (-400)-(-300) nsec in the
T-TOF distribution (the right of Figure 4.9).
Since contributions bellow the ATM threshold (1 mV) have to be taken into account, the distribution
obtained with half ATM threshold (50 mV) and double-gain HV was used. Furthermore, we used astraight line extrapolation into this low-charge region because it is impossible to obtain data in the54

region lower than 0.3 pC. These compensations near the ATM threshold are shown in Figure 4.10. The
average of the charge distribution was obtained as 2.43 pC/p.e.

Figure 4.10: The charge distribution near ATM threshold. The half threshold data and linear fittingcompensates below the ATM threshold.

4.3.2

Relative Gain Measurement

The relative gain was measured with two sets of laser diode calibration data (Figure 4.11, the setup is
explained in Section 4.5). One had a high light output (∼50 p.e./PMT) and other had a 1 p.e. level ineach PMT. From Eq.(4.1), the relative gain of the i-th PMT is calculated using
Qobs (i)∝ Relative gaini , (i = 1 − 227)
Nhit (i)(4.4)

By taking the ratio of these data, the relative gain was obtained. Using exactly same setup except lightintensity and taking ratio, this method is independent from the water transparency, geomagnetic field,
and so on. The distribution of the obtained relative gain is shown in Figure 4.12.

4.4

Quantum Efficiency Measurement

As explained in the beginning of this chapter, all PMT has the quantum efficiency (QE), it meansthat all photons hitting the surface of PMT are not converted to the p.e.. It is important for EGADS
observing very low amount of light to evaluate the individual difference of QE precisely because theenergy reconstruction of EGADS needs the number of hit PMTs.
From Eq. 4.1, the number of hits in each PMT is given as
N hiti ∝ Nphoton × QEi .
The relative QE can be obtained by counting the number of hit for each PMT.

55

(4.5)

Figure 4.11: The schematic view of the LD calibration setup.

Figure 4.12: The relative gain distribution.

56

Ni source
Ideally, the 1 p.e. events had to be used in this calibration. The γ rays from a Ni ball and a 252 Cf
source were used. The radioactive element 252 Cf source was was contained in a brass rod and it was
installed at the center of the Ni ball, which consisted of 25% NiO2 and 65% polythene. A picture of
the setup is shown in Figure 4.13. The 252 Cf source decays through α decay (∼96.9%) and spontaneous
fission (∼3.1%) with a multiplicity of 3.8 neutrons. The Ni source emits the ∼9 MeV γ rays through thereaction Ni (n, γ) Ni. This setup was also used for the QE calibration for SK. The Cherenkov light from

Figure 4.13: Picture of Ni ball.

the Ni γ rays reaches the 1 p.e. level for each PMT in the SK detector. The EGADS detector detected
the signal of 2 p.e. level due to the much smaller detector size. However, we used the Ni source which
produces Cherenkov light because QE depends on the wavelength of the incident photon.
Analysis
The relative QE for each PMT was estimated by comparing the number of detected photons with the MC
simulation having a uniform QE. The hit rate ratio between the data and MC is defined as the relativeQE.
To remove hits due to dark noise and only count hits from the Ni, on-time hits were subtracted by
off-time hits as well as the LED calibration (Section 4.3.1). The relative QE distribution is shown in
Figure 4.14. The relative QE was implemented on a database of the Monte Carlo simulation.

4.5

Timing Calibration

Timing calibration was carried out using a two dimensional TQ (Timing versus charge) distributions.
This timing calibration is essential for vertex reconstruction. Ideally, the timing response of each PMTshould be the same after subtracting the time-of-flight from the vertex position to each PMT which aphoton hits. However, there are differences in PMT responses due to the difference in the length of signal
cables and the response of electronics (The time-walk effect (Figure 4.15)). The timing information has
to be corrected, and thus the TQ distribution was made for each ATM channel.

57

# of PMTs

15

BarrelTOP

Bottom

10

5

0
85

90

95

100

105

110
115
relative QE

Figure 4.14: The QE distribution.

Figure 4.15: The schematic diagram of the time-walk. A higher charge signal is triggered earlier than alower charge signal even if the peak position is same.

58

Figure 4.16: Timing distribution as the function of the Qbin before the correlation by TQ distribution. Qbin is defined in linear-scale from 0 to 10 pC (Q/0.2 pC) and in log-scale from 10 to 3981 pC(50log(Q)/pC).

Setup
The setup is shown in Figure 4.11. The laser diode (LD) module emits the light with a wavelength of
410 mm. The emitted light from the LD module is injected into the diffuser ball installed at the centerof the detector.The diffuser ball contained 1500 ppm light MgO of 5.8 µm diameter, such that the lightscattering length was about 1 cm. For the constant trigger signal, the NIM signal from the LD module
was used, which was emitted simultaneously with light emission.
Analysis
The laser hits of each readout channel are divided into 150 bins of charge, called Qbin. Figure 4.16
shows the TQ distribution without any corrections. The timing distribution in each Qbin is fitted by aGaussian to minimize statistical fluctuations. Since there is a contribution of both direct and indirect
light, the timing distribution in each Qbin is slightly asymmetric and is not Gaussian. In order totake into account these contributions together, the timing distribution in each Qbin was fitted using an
asymmetric Gaussian, which provides the peak timing and standard deviations. The peak timing andstandard deviations for each Qbin were fitted using polynomial functions as a function of Qbin.
polN (x) ≡ p0 + p1 x + p2 x2 + · · · pN xN ,(4.6)

Qbin ≤ 10 : F1 (x) ≡ pol3(x),(4.7)

Qbin ≤ 50 : F2 (x) ≡ F1 (10) + (x − 10) · pol4(x − 10),

(4.8)

Qbin > 50 : F3 (x) ≡ F2 (50) + (x − 50) · pol6(x − 50).

(4.9)

pi value from the fitting was used for the correction of the timing information for each PMT. Figure
4.17 shows the TQ distribution after the correction. Figure 4.18 shows the timing resolution of EGADS,
which corresponds to the standard deviation of the timing peak at the each Qbin as a function of thecharge.

59

Figure 4.17: Timing distribution as the function of the Qbin after the correlation by TQ distribution.

σ t [nsec]

Timing resolution
6

5

4

3

2

1

0
1

10

102

Charge [p.e.]

Figure 4.18: Timing resolution as the function of charge of signal.

60

4.6

Auto-Xe Calibration

In order to check the detector stability and the water quality after the dilution of Gd, the auto-Xe
calibration system was operated continuously except during the calibration run. The calibration setup is
the same as for the Xe flash lamp calibration, but the scintillation ball was installed at a non-centeredcalibration hole so that the scintillation ball was never touched. Auto-calibration was operated from theperiod of pure water circulation, and it achieved a stability of 1%. Figure 4.19 shows the transition of
the total charge of PMTs mounted at each one of three height positions. This system can measure the

Figure 4.19: The transition of the total charge of PMTs mounted at barrel, top and bottom position. By
monitoring the fluctuation of the observed charge, the tendency can be checked for each of the positions
and the PMT configuration.

water effect with good precision.

61

Chapter 5

Software Tool
In this chapter, the reconstruction method and simulation tool are explained. The reconstruction toolfor vertex and energy was imported from at the SK. The geometric value in this analysis can bee seen in
Figure 5.1. The Z-axis was defined to run vertically with its zero being the center of the SK tank. The
X-axis and Y-axis were perpendicular to each other and to the Z-axis.

Figure 5.1: The definition of basic variables.

5.1

Vertex Reconstruction

The vertex position where a particle interacts with another particles is reconstructed from the timing
when PMTs detected the light and its the PMT positions. The particle resulting from an interaction
flies, but its position is able to be treated as a point because the flight distance is short (∼10 cm for a 20
MeV electron). The likelihood function is used to obtain the vertex position by using the likelihood ∆ti .
∆ti is calculated asnp∆ti = ti −(x − xi )2 − t0
(5.1)
c
62

= ti − tof − t0 ,(5.2)

Likelihood

where tof is the time-of-light from the vertex position to the hit PMTs, and t0 is the mean value of the

1

10-1

10-2

10

-3

10-4

0

50

100

150

200

250

T-Tof [nsec]

Figure 5.2: Likelihood function of BONSAI vertex fitter from Ni calibration data. The peaks around the
40 nsec and 110 nsec are caused by the after pulses.

ti . The likelihood function for vertex fitting is defined as
Likelihood =

N
hit
X

log P (∆ti (~x)),

(5.3)

i=1

where P (∆ti (~x)) is the probability density function of ti (x~i )−tof −t0 that can be seen in Figure 5.2. This
fitter is called BONSAI(Branch Optimization Navigating Successive Annealing Iteration)[61]. Sometimes
dark noise hits and/or reflection light produces the local maxima of a likelihood. To avoid such misreconstructions, the likelihood is maximized from the vertex search by the combination of all four PMTs.
Each of the four PMT combinations provides a unique vertex candidate from their timing constraints.
Thus, events with more than four hit PMTs are reconstructed. This is iterated to obtain a good vertex
position with a larger and more stable likelihood value.
Figure 5.3 shows the reconstructed vertex position from the Ni source position: R2 = x2 + y2 + z2 .
The vertex resolution was evaluated by the electron simulation, which can be seen in Figure 5.4.

5.2

Energy Reconstruction

The reconstruction of particle energy is explained here. The particle energy affects the intensity of
Cherenkov light. Therefore, by counting the number of hit PMTs, the particle energy can be investigated.
The reason why is the number of hits is used instead of the observed total charge is because it is unrelated
to the PMT gain. The energy reconstruction has to be done while suppressing the effect from several
factors such as dark noise. The parameter defined by the following equation is used and is called the63Hz / bin(Ni+ 252Cf)- 252Cf
252
Ni+ Cf
252
Cf
MC:Ni

500
400
300
200
100

0.0

0.5

1.0

1.5

2.0

2.5 2 3.0
R [m2]

Vertex resolution [cm]Figure 5.3: Reconstructed vertex distribution of the Ni data and MC.

wall cut 0cm

150

wall cut 50cm
wall cut 100cm
100

50
0

2

4

6

8

10

Total electron energy [MeV]

Figure 5.4: The vertex distribution as a function of electron energy. Color corresponds to each fiducial
volume cut. This cut removes the events which reconstructed within 0, 50, and 100 cm from the wall of
the detector.

64effective PMT hit Nef f .
"
N50
X

Nall
ri
Likelihood =(Xi − dark + tail ) ×× S(θi , φi ) × exp( ) × Gi
Nalive
λ
i=1

#
(5.4)

• N50 lThis is defined as the maximum number of hits found by sliding a 50 nsec time window in the T
Tof distribution.
• Xi : Multiple photo electron hit correction
This is a correction to compensate for the effect of multiple p.e. in the i-th hit PMT due to thefact that if an event occurs near the detector wall and is directed towards the same wall, and theCherenkov cone does not have much distance to expand then the observed number of hits becomes
smaller. The Xi is defined as(log xi1−1 /xi xi < 1,
(5.5)
Xi =
3.0
xi = 1,
where xi is the ratio of hit PMTs in a the 3×3 PMTs surrounding the i-th PMT to the total number
1of live PMTs in the same area. The log( 1−x) term is then the estimated number of photons perione PMT in that area and is determined from Poisson statistics.
• dark : Dark noise correction
The dark noise hit is estimated using
edark =

50nsec × Nalive × Rdark
,
N50

(5.6)

where Nalive is the number of all live PMTs and RdarK is the measured dark rate.
• tail : Correction for late hit
Reflected Cherenkov light arrives late to PMTs. It performs a late hit outside of a 50 nsec window.
To correct for such an effect, etail is calculated using
etail =

N100 − N50 − Nalive × Rdark × 50nsec
,
N50

(5.7)

where N100 is the maximum number of hits found in a 100 nsec time window.
all• NNalive: Correction for Dead PMT
Nall is the total number of PMTs.

• S(θi1,φi ) : Correction for photo-cathode coverage
This correction is for the direction-dependent photo-cathode coverage. It is the effective photocathode area as a function of the incident angle (θi , φi ). Figure 5.5 shows the S(θi , φi ) and thedefinition of the angle (θi , φi ).
• exp( rλi ) : Correction for water transparency
This is a correction is for the water transparency effect. However, this correction is negligible for
EGADS data. ri is the distance from the vertex position to a hit PMTi , λ is the water transparency.
• Gi : Correction for PMT gain
This factor is used to adjust the relative gain of the PMTs for a single p.e..
65Figure 5.5: The definition of the incident angle to PMT. Correction function of the photon incident angle
obtained from MC simulation.

2000

Neff

EventsAfter the determination, and event’s energy in term of MeV can be calculated as the function of
Nef f . The relation between Nef f and MeV is obtained by electron simulation, because the calibration
apparatus such as LINAC cannot be installed in the EGADS detector. Figure 5.6 shows the Nef f by the
1-9 MeV electron simulation.

1800

50

1600
1400

40

wall cut 0cm
wall cut 50cm
x2+y2+z2<20000 [cm2]

1200
1000

30

800
600

20

400
200
0

0

10

10

20

30

40

50

60

Neff

0

2

4

6

8

10

Electron energy [MeV]

Figure 5.6: (left) Neff distribution of 1-9 MeV electron simulation. (right) The mean Ne ff obtained by
Gaussian fit as the function of electron energy. Each color line corresponds to the each vertex cut.

66

5.3

Detector Simulation

The EGADS simulation tool was constructed based on the Gean4 toolkit[62], and is named EGSIM. The
dataset versions used in this thesis are shown in Table 5.1. EGSIM uses the default of physics process of
GEANT4
G4LEDATAG4LEVELGAMMADATA
G4NEUTRONXSDATA
G4PIIDATA
G4RADIOACTIVEDATA
G4REALSURFACEDATA
G4SAIDXSDATA

Geant4.9.6.p02
G4EMLOW6.32
PhotonEvaporation2.3
G4NEUTRONXS1.2
G4PII1.3
RadioactiveDecay3.6
RealSurface1.0
G4SAIDDATA1.1

Table 5.1: Data set of Geant4 for EGSIM.
Geant4 for the production of Cherenkov light in the detector, and it provides the Cherenkov angle, andwavelength, etc. For the refractive index related to Cherenkov generation which EGSIM uses is the sameas those of SK. The interaction length of absorption, Mie, and Rayleigh scattering also comes from thepure water models used in SK. The event simulation in Gd-doped water was conducted using the samewater parameter as that of pure water, because the calibration data in a small detector such as EGADS
has to be free from the water effect.
Figure 5.7 shows simulated Gd neutron capture events in the detector. The shape of photocathodeof a 20-inch PMT installed in EGSIM is substantially hemispherical. The output file of EGSIM has thesame format as the output file of the actual EGADS. Therefore, it is possible to use the same analysis
process.

Figure 5.7: The EGADS detector simulation based on the GEANT4, which shows a Gd γ ray event.

67

Detector Response
When a photon reaches the PMT surface, the response of the detector is simulated. In short, the i-th
PMT’s probability (Pi (λ, θ)) of the production of a p.e. from the photon arriving at each PMT surface
is estimated by
Pi (λ, θ) = QE(λ) × F(θ) × COREPMT × relative QE(i), (i = 1 − 227),(5.8)

Hz / binwhere QE(λ) is the quantum efficiency depending on the wavelength (λ) of the incident photon, which is
the typical value measured by HAMAMATSU (Figure 1.19). F(θ) is the correction factor of the incident
angle θ which is imported from SK calibration, and COREPMT is determined from the Neff distributionof Ni data in Figure 5.8. The relative QE(i) is also obtained from Ni calibration (Section 4.4). In orderto reduce the calculation time, the number of generated Cherenkov lights is suppressed by a factor of
QE(λ)/0.75, therefore, including the 0.75, this factor is compensated by QE.

120(Ni+ 252Cf)- 252Cf
252
Ni+ Cf
252
Cf
MC:Ni

100
80
60
40
20

10

20

30

40

50

60

Neff

Figure 5.8: Neff distribution. The black dot is Ni events after the subtraction of background events.

1 photo electron distribution and ATM threshold
1 photo electron distribution implemented in EGSIM is obtained from LED measurement (Section 4.3).
The ATM threshold effect was estimated by using the double gain and half threshold measurement.
Timing resolution
The timing resolution in the MC is the result obtained from the TQ calibration, which is explained in
Section 4.5.
After-pulse and pre-pulse
The characteristic peaks in the PMT hit timing distribution after the main peak is called the after-pulse.
A possible explanation of the cause of the after-pulse is that if a p.e. is back scattered at the first dynode,68

it takes some time before it loses its velocity against the electric field, and comes back to the first dynode,thus producing a delayed hit.
The dark noise coming from the PMT was also generated in simulations; however, it is assumed tobe the same rate for all PMTs and was adjusted to be 8 Hz (this is higher than SK’s value:∼5 kHz).

5.4

Gd Simulation

For the Gd(n,γ) reaction, EGSIM uses the default model of Geant4 and the model provided by the
GLG4SIM library. GLG4SIM was originally developed for the scintillation detector experiment, and it
treats the discrete γ-ray emission process [63]. The default Geant4 model takes it into account the nucleus
recoil. Meanwhile, GLG4SIM does not take into account it.

GEANT4+G4NDL4.2

1/N

1/N

0.35
GEANT4+GLG4Sim

0.20
GEANT4+G4NDL4.2

GEANT4+GLG4Sim

0.18

0.30

0.16
0.25

0.14
0.12

0.20

0.10
0.15

0.08
0.06

0.10

0.04
0.05
0.02
0.00

0.00

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0
γ Energy[MeV]

0

2

4

6

8
10
the number of γ

Figure 5.9: (left) The comparison of the total γ-ray energy (right) and the number of γ rays from theneutron capture Gd.

1/N

-3

×10
22
20
18
16
14
12
10
8
6
4
2
0
0

GEANT4+G4NDL4.2

10

20

GEANT4+GLG4Sim

30

40

50

Neff

Figure 5.10: The comparison of Neff distribution of Gd γ ray events.

69

Chapter 6

Detection and Analysis of γ raysfrom Gadolinium Neutron Capture
After the pure water circulation, Gd sulfate was dissolved into the water circulation system and injected
into the detector in 2014. In this chapter, the first detection of γ ray from Gd neutron capture wasdemonstrated and the evaluation of its performance are explained. In addition, the performance of Gd
neutron capture in the SK detector is also estimated from the test data taken in SK detector.

6.1

Measurement and Setup

The Gd γ-ray measurement was performed by using a neutron source. We adopted an Am/Be source
which emits the 4.43 MeV γ ray and neutron. The Am/Be source is attached to a piece of BGO crystal.
It emits scintillation light with the 4.4 MeV prompt γ ray. This setup mimics the IBD signal as shownin Figure 6.1. In this section, the Am/Be source and related apparatus for measurements are explained.

Figure 6.1: The schematic view of the Am/Be source and a BGO scintillator, which generates the aprompt scintillation light and a neutron.

706.1.1

Am/Be Source

The Am/Be source is made up of three layers. The thin layer of Am was sandwiched between the 0.1
mm thick Be film. The Am/Be source was placed inside a 1.2 cm×1.2 cm×1.2 cm stainless steel case.
Neutron emission occurs through the following interactions: an α particle from Am decay interacts withBe, and a neutron and carbon are produced. When the excited carbon decays to the ground state, theγ rays depending on the excited state are emitted. We found that 4.43 MeV γ ray and neutron were
emitted at the 87 Hz and that no γ ray were emitted at 76 Hz (Figure 6.2). The 76 Hz of neutron emission
does not make a prompt trigger, and so it is treated as background events originating from the Am/Be
source (see Sec. 6.2). This is called the source background in this thesis.
241

Am

α + Be
12

C

∗

→

237

N p + α (7.78M eV )

(6.1)

→

12

∗

C + n,

(6.2)

→

12

C + γ (4.43M eV )

12

C +n

(6.3)

Figure 6.2: The energy spectrum of Am/Be measurement without the BGO scintillator in the SK detector.

Neutron energy spectrum
The neutron energy from the Am/Be source depends on excited levels of 12 C and the neutron scattering
angle, we used measured spectrum continuous energy spectrum in the MC simulation. Figure 6.3 shows
the neutron energy spectrum from [65].
γ-ray energy spectrum
Figure 6.4 shows the measured γ-ray energy spectrum by a Ge detector. The peak near 4.5 MeV is thefull energy deposited by a 4.43 MeV γ ray. The peak of a single escape and double escape can be seen at
3.92 MeV (4.43−me c2 ) and 3.51 MeV (4.43−2 × me c2 ) respectively, where me is the electron mass.

71

counts
150

100

50

0

0

2

4

6

8

10

12

MeV

countsFigure 6.3: The energy spectrum of neutrons from the Am/Be source [65].

104

AmBe
Background

3

10

102

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

MeV

Figure 6.4: The γ-ray energy spectrum measured by a Ge detector. The red line is measurement of the
Am/Be. The black line is the background measurement.

72

6.1.2BGO Scintillator

The BGO scintillator described by Bi4 Ge3 O12 is the crystal having the large cross section for the γ-ray
capture. The characteristics of this crystal is shown in Table 6.1. It is very dense, low afterglow, lowhygroscopicity, has good position resolution, and is easy to forming. Therefore, the BGO scintillator isused in many fields: medicine, nuclear physics and high energy physics, etc.
Density
Decay constant
Wavelength
Refractive index

7.13 [g/cm3 ]300 [nsec]
480 [nm]
2.15

Table 6.1: Characteristics of the BGO scintillator

Events

The configuration of the Am/Be source and BGO crystal is shown in the left of Figure 6.5. The probability that the 4.43 MeV γ ray interacts with the BGO scintillator was estimated by Geant4 simulation
to be approximately 12%. The energy deposited in the BGO scintillator by a 4.43 MeV γ ray is shown on
the right of Figure 6.5. The energy of the recoil electron (T) through Comptom scattering is calculated

102

10
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Energy deposit [MeV]

Figure 6.5: (left) The setup of the Am/Be source mounted on a BGO scintillator. The BGO used inthis measurement is not a square, is one of the corner is cut. (right) The energy deposit in the BGO
scintillator by the 4.43 MeV γ ray.
using the relation
T =Eγ
mc2 (1 − cosθ)Eγ ,E
1 + mcγ2 (1 − cosθ)(6.4)

where m is electron mass, Eγ is the incident γ ray energy, and θ is the scattering angle.

6.1.3

Measurement

Before injection of Gd-doped water into the EGADS detector, several preparations were done. In order
to measure γ rays from Gd neutron capture, a dedicated trigger system was built. When the scintillation
light induced by the 4.43 MeV γ ray is detected as the prompt signal, a 500 µsec gate is opened to73

Figure 6.6: The schematic view of the trigger logic for the delayed coincidence detection.

Figure 6.7: (left) Photo of the BGO scintillator setup. The BGO scintillator and the Am/Be source
installed into acrylic case. (right) The black sheet used for the adjustment of the light intensity.
search for the delayed low-energy signal. A schematic view is shown in Figure 6.6. Since the prompt
scintillation lights induced by the 4.43 MeV γ ray was too bright in the EGADS detector, the delayed
events were affected by the prompt signal (afterglow and after pulse). In order to reduce the effect, we
assembled a BGO scintillator in the following way. The BGO scintillator was covered by a black sheet,and the Am/Be source was attached on the black sheet. A few holes was made in the black sheet, which
is designed to reduce the intensity of the prompt scintillation light. The contribution of the black sheet
is shown in Figure 6.8. With a black sheet, the number of hit PMTs induced by the prompt signal isreduced to be around 100. The unwanted afterglow hits without a black sheet in the delayed trigger (seenin about 60 hits) disappeared with a block sheet and only noise hits are seen.
The distribution of the time difference between the prompt and delayed events is shown in the rightfigure of Figure 6.9. Although afterglow is still observed in first few µsec, the distribution is flat and no
disturbing events are observed.
After the injection of Gd-doped water into the detector, the Am/Be measurement was performed inconcentration of 115 ppm and 230 ppm of Gd sulfate as shown in the Figure 6.10. After the injection of
Gd-doped water into the detector, it takes a few days for the Gd concentration to become homogeneous
74

Hz/bin

1.4

Prompt trigger
w/o Black sheet
w/ Bacl sheet

1.2
1
0.8
0.6
0.4

Events / # of prompt Trg.

0.2

Figure 6.8:
events.

0
0.025

20

40

60

80

100

120

140

160

180

200

220

240

Delayed trigger
w/o Black sheet
w/ Bacl sheet

0.02
0.015
0.01
0.005
0

20

40

60

80

100 120 140 160 180 200 220 240
nhits

The number of hit PMTs. Upper figure: the prompt events. Bottom figure: the delayed

10-1

10-2

10-3

10-4

0

50

100

150

200

250

300

350

400

450 500µsec

Figure 6.9: The difference of trigger time between the prompt and delayed events.

75

in the detector. We analyzed Am/Be data which were taken at a date when the Gd sulfate concentrations
measured at 3 positions (top, center and bottom) agreed with each other. Therefore, position dependenceof the neutron capture was not considered.

Figure 6.10: Gd concentration monitored by AAS after the PMT mounting. Upward arrow indicates thedates when the Am/Be data were taken.

As mentioned in Section 3.1.1, the water transparency deteriorated after the injection of Gd-doped
water. However, the effect on the data due to water transparency was very small in a small detector suchas EGADS. Actually, the effect is negligible in Figure 6.11 which shows the Neff distribution of the Ni
data. The Am/Be data taken when the LL15 is 40 - 50% should be free from the water transparency
effect. In this thesis, 33,729 and 43,887 prompt trigger events of Am/Be data were taken and analyzed
for concentration of 115 ppm and 230 ppm, respectively. The background events were taken by a periodic
trigger in normal Run mode which has the 400 nsec time window. 97,163 and 6,413 triggers are generated
and analyzed for concentration of 115 ppm and 230 ppm respectively.

6.1.4

Neutron-Nucleus Interactions at low energy region

Here is the summary of the low energy neutron-nucleus interactions.
1. Elastic scattering (n,n): The incident neutron energy is divided to the neutron and nucleus, but
the nucleus is not excited.
2. Inelastic scattering (n,n), (n,nγ), (n,2n): (n,2n) is dominant in more than 10 MeV region.
3. Neutron capture (n,γ): This interaction is the most general because thermal neutron (0.025 eV)
is captured by almost all nuclei. This interaction is caused at specific energy in the epithermal
neutron region for each nucleus. It is called a resonance capture.

76

120

run 4222

run 4718

100

80

60

40

20

0

10

20

30

40

50

60
Neff

Figure 6.11: Neff distribution of Ni data. Run4222 is taken in status that LL15 was taken at LL15=∼70%,
and Run4718 was taken at LL15=∼30%.

4. Emission of charged particles (e.g. (n,p), (n,d), (n,α), (n,t), (n,αp) ): With the exceptionof some thermal neutron case, this reaction is likely to occur if the light elements or fast neutron.
5. Nuclear fission (n,f ) : This is a phenomenon that the composite nucleus is split into two fission
products and one or several neutrons. Fission occurs by fast neutrons in many heavy nuclides. For
235
U, 239 Pu and 233 U, the fission occurs mainly with thermal neutrons.
The neutrons from the Am/Be source interact with hydrogen in water approximately by 30 times.
They are thermalized and captured by Gd.

6.2

Analysis of γ rays from Gd neutron capture

In this section, the analysis of Am/Be data is explained. First, the prompt 4.43 MeV γ-ray events
have to be selected. As shown in Figure 6.8, the prompt scintillation event induced by a 4.43 MeV γ ray
produces 80 - 140 PMT hits. By requiring 80 - 140 hits for the prompt event, the background events canbe suppressed.
The selection criteria for the delayed events are as follows:• Vertex position cut: The delayed events by a Gd γ ray should be reconstructed around the Am/Be
neutron source. So, only the events reconstructed at R2 < 2m2 are selected. Figure 6.13 shows
R2 = x2 + y2 + z2 distributions of the reconstructed vertex.
• ∆T cut: The neutron capture time (∆T) has to be exponentially distributed. On the other hand,the background events have to be distributed uniformly in ∆T. Events with ∆ a T<400µsec wereselected.

77

-3

20
18
16
14
12
10
8
6
4
2
0

Events / Neutron

Events / Neutron

-3

×10

Data-B.G
MC:Gd
MC:2.2 MeV
MC:Source BG

×10
25

Data-B.G
MC:Gd
MC:2.2 MeV
MC:Source BG

20
15
10
5

1

2

3

4

5

0

R2 [m2]

1

2

3

4

5

R2 [m2]

Figure 6.12: Reconstructed vertex position from the source position : R2 = x2 + y2 + z2 [m2 ] (left) 115
ppm, and (right) 230 ppm Gd sulfate concentrations.
• Vertex fit goodness: Vertex fit goodness is the parameter of the quality of vertex reconstruction. For example, an unwanted event produced by flasher light from PMTs is reconstructed withgoodness<0.3. The good events were selected by requiring the goodness>0.3.
• DirKS cut: DirKS was a parameter obtained Kolmogorov-Smirnov (KS) test for azimuthal angular.
The well-reconstructed events can be selected by DirKS<0.4. This parameter indicates that hit
PMTs are distributed uniformly around the reconstructed particle direction.
• Energy cut : Remove the low energy background by E<2 [MeV].
Figure 6.13 shows the energy spectrum of the delayed events after event selection. The source background is explained in the next sub-sub-section. The mean reconstructed energy from Gd γ rays wasmeasured to be 4.2 MeV by the Gaussian fit using the MC spectrum. This value is less than 8 MeV
estimated by Q value (Eq.(2.3)). In Gd neutron capture, 3 - 4 γ rays are emitted with a total energy of
8 MeV. However, γ rays below 1 MeV are invisible since only a γ ray above 1 MeV produce a Cherenkov
light in a water Cherenkov detector, The event display of the delayed events is shown in Figure 6.15.
Figure 6.14 shows the ∆T distribution and an exponential fitting result, which gives the mean capture
time for each concentration as follows:
184.6 ± 4.8µsec (115ppm)
∆T =
(6.5)
151.3 ± 2.6µsec (230ppm)
From these result, the neutron tagging by Gd have been demonstrated. Compared with the 2.2 MeV
γ ray from neutron capture on proton, the Gd neutron capture occurs near the source position with ashorter ∆T, and 8 MeV γ ray cascade is sufficiently high. So, it must provide better performance to the
SK detector.

78

-3

Events / Neutron

Events / Neutron

-3

×10
18

Data-B.G
MC:Gd
MC:2.2 MeV
MC:Source BG

16
14
12
10

×10
25

Data-B.G
MC:Gd
MC:2.2 MeV
MC:Source BG

20
15

8
10

6
4

5

2
0

2

4
6
8
10
Total electron energy [MeV]

0

2

4
6
8
10
Total electron energy [MeV]

Figure 6.13: Reconstructed energy distribution after event selection. (left) 115 ppm, (right) 230 ppm
Gd sulfate concentration. Horizontal axis is normalized by the number of prompt trigger (neutron).

-3

14
12

χ2 / ndf

50.96 / 47

const

0.01233 ± 0.00033

τ

Events / Neutron / 10 µs

Events / Neutron / 10 µs

-3

×10

184.6 ± 4.8

108

Data:Gd

6

MC:Gd

×10
25

χ2 / ndf

57.9 / 46

const

0.02251 ± 0.00045

τ

20

151.3 ± 2.6

Data:Gd

15

MC:Gd

10

4
5
2
0

50

100

150

200

250

300

350

400

450

500

∆ T (µs)

0

50

100

150

200

250

300

350

400

450

500

∆ T (µs)

Figure 6.14: The ∆T distribution of the data and MC (left) 115 ppm and (right) 230 ppm Gd sulfate
concentration. The data points indicates the component of only γ rays from Gd neutron capture. The
background data and the source background and the 2.2 MeV γ rays are already subtracted in this figures.

79

Figure 6.15: The event displays of delayed events of Am/Be data.

80

Source backgroundTo analyze the Am/Be data correctly, background events originating from the Am/Be source have to
be considered. These are two types of such background. The first type, denoted BG1 in Figure 6.16, isthe event which is a 4.43 MeV γ ray and the delayed neutron events accidentally detected in the delayedgate. Time integration from 0 to Tmax (gate length of 400 µsec) provides the probability as
Z Tmax
Pdetect =
dt Pγ (t) · Rγ · Iγ + (Pp (t) + PGd (t)) · In ,

(6.6)

0

where Pγ , Pp and PGd are the detection probability of the 4.43 MeV γ ray from the γ ray from neutron
captured proton and Gd, respectively, Rγ is the probability that the 4.43 MeV γ ray does not interact
with the BGO scintillator, and Iγ , In is the intensity of the 4.43 MeV γ ray and the neutron emission,respectively.
The second type of the source background, denoted BG2 in Figure 6.16, is the delayed neutron eventsoccurring together with the scintillation light in the delayed gate. This scintillation event is not a prompt
event but is an accidental event in the delayed gate. Since this event is identified by the off-line event
selection, the only neutron event remains. The event probability can be obtained by
Z T 0 Z Tmax 
Pdetect =dτ
dt PGd (t − τ ) + Pp (t − τ ) × (1 − Rγ ) × In ,
(6.7)
0

T0

where τ is the time of the scintillation event detected in the delayed gate.
Since the probability of the first type is higher than that of the second type, it is important to checkthe 4.43 MeV γ-ray events. Figure 6.17 shows the Nef f and vertex distribution of a 4.43 MeV γ ray.
This was taken in the pure water by the Am/Be source without the BGO scintillator.
MC model dependence
Figure 6.18 shows the energy distribution of the delayed events for the data and two MC models. As
discussed in Section 5.4, the GLG4sim model gives a lower energy peak than Geant4+G4NDL4.2. From
this comparison, it is difficult to say which model has to be used. In this thesis, this discrepancy between
the data and MC is treated as a systematic error.

6.3

Evaluation of Detector Performance

The performance of the detector: the signal detection efficiency and background efficiency were evaluated. The signal detection efficiency is defined by ”neutron capture efficiency” × ”reconstruction efficiency”. These efficiencies were independently evaluated by Am/Be data. The background efficiency isdefined as the ratio of the number of the reconstructed events to the number of prompt triggers.

6.3.1

Neutron Capture Efficiency

It is important to measure the neutron capture efficiency because it directly affects on the detection
efficiency. By counting the number of remaining events of the Am/Be data after event selection, thecapture efficiency was calculated. The event selection criteria are as follows:• Vertex cut:R2 < 2m2• ∆T < 450µsec

81Figure 6.16: The schematic diagram of the source background. The source background is the event
originates from Am/Be source, and is accidentally detected in the 500 µsec delayed gate. The source
background consists of the γ-rays from neutron capture on Gd and proton, and the 4.43 MeV γ ray.

82

-3

7

Am/Be-BG

Am/Be

MC:4.4 MeV

MC:2.2 MeV

1/N

1/N

-3

×10

BG

×10
7

6

6

5

5

4

4

3

3

2

2

1

1

0

5

10

15

20

25

30

35
Neff

Am/Be-BG

Am/Be

MC:4.4 MeV

MC:2.2 MeV

0.0

0.5

1.0

1.5

BG

2.0

2.5

3.0
R2 [m2]

Figure 6.17: (left) The Nef f distribution of the 4.43 MeV γ rays. (right) The vertex distribution of the
4.43 MeV γ rays.

-3

Events / Neutron

Events / Neutron

-3

×10
18
16

Data-B.G

14

MC:Gd

12

MC:GLG4sim

10

×10
25

Data-B.G
MC:Gd

20

MC:GLG4sim

15

8
10

6
4

5

2
0

2

4
6
8
10
Total electron energy [MeV]

0

2

4
6
8
10
Total electron energy [MeV]

Figure 6.18: The comparison of the energy distribution between the data and MC simulations. (left) 115
ppm, and (right) 230 ppm.

83

• Vertex fit goodness > 0.4• DirKS < 0.4• Neff > 25
The energy cut (Neff > 25) removes most of the 2.2 MeV γ-ray event due to neutron capture on proton.
Consequently, the capture efficiency due to Gd can be simply obtained. We defined Hitrate as
Hitrate =

N0
,
NTrg

(6.8)

where Ntrg is the number of prompt triggers, and N’ is the number of remaining Am/Be events after
event selection. Using the MC simulation, the cut efficiency of the Gd γ ray was also estimated as
Cut
EffGdγ
=

N0Gd
,
NGdγ

(6.9)

0
where NGd is the number of Gd γ ray events, and NGd
is after the all event selection. The Nef f

Events / Neutron

-3

×10
25

Data-B.G
MC:Gd
MC:2.2 MeV
MC:Source BG

20
15
10
5

0

10

20

30

40

50

Neff

Figure 6.19: The Nef f distribution of the Am/Be data.

distribution after the event selection is shown on the right of Figure 6.19. Even after the event selection,
the source background events still remain. So Hitrate can be calculated not only from the Gd γ ray but
also from the source background component (NSBG ).
Hitrate =GdNTrg × Effcapture × EffGdγ+ NSBG
NTrg(6.10)

where Effcapture is the capture efficiency by Gd, NSBG is the number of the source background. Since thesource background contains the Gd γ-ray events, NSBG depends on the capture efficiency and is wrote in
the form
NSBG

=

γ
NGd
SBG + NSBG

(6.11)=γ
Cut
NTrg × Effcapture × EffSBG+ NTrg × EffSBG,(6.12)

84

-3

Data

30

Events / Neutron

Events / Neutron

-3

×10

MC(shift)

MC

25
20
15

Data

MC(shift)

MC

25
20
15
10

10

5

5
0

× 10

0.55

0.60 0.65

0.70 0.75

0.80 0.85

0.90 0.95

1.00

Goodness

0
0.0

0.1

0.2

0.3

0.4

0.5

DirKS

Figure 6.20: The comparison of the variables used for the event selection. Green light color is the shifted
histogram so that chi-square between the data and MC is minimum. (left) vertex fit goodness, (right)
DirKS.

γ
Gd
and EffSBG
is the detection efficiency of the source background of the Gd γ ray and thewhere EffSBG
4.43 MeV γ ray, respectively. These are also evaluated by the MC. Finally, the capture efficiency can becalculated asγ
Hitrate − EffSBG
Effcapture =.
(6.13)
Gd + Eff Gd
EffCutSBG

Table 6.2 shows the measured capture efficiency and efficiency expected by the MC. To compensate theHit rate
Gd
EffCutγ
EffSBG
Gd
EffSBG
Capture Eff.
ResultMC

0.0115%0.0230%

shifted MC
0.07080.223
0.226
0.00190.00190.01240.012529.2%
28.9%
29.2 ± 0.5Stat. ± 0.3Sys. %32.1%

shifted MC
0.110
0.223
0.226
0.00190.00190.01240.012546.1%
45.6%
46.1 ± 0.7Stat. ± 0.5Sys. %47.4%

Table 6.2: Calculation of neutron capture efficiency.

discrepancy between the data and MC, the MC variables were shifted to data as shown in Figure 6.20.
γ
Gd
Gd
Using the shifted MC variables, the cut efficiencies (EffSBG, EffCut, EffSBG) were re-evaluated, and thecapture efficiency was recalculated as shown in Table 6.2. The differences in these estimations are taken
into account as a systematic error.

85

6.3.2Analysis of Reconstruction Efficiency

The signal efficiency has to be kept high. On the other hand, the background has to be suppressed asmuch as possible. The reconstruction efficiency of the Gd γ-ray signal and background efficiency were
measured using the following steps:
1. Pre-cut : Remove the clear background events and the poorly reconstruction events.
2. Likelihood cut : Using the likelihood, the signal and background events are separated efficiently.
Pre-cut
In the pre-cut selection, the loss of the signal has to be minimized, and unnecessary events such as theprompt events have to be discarded. The pre-cut criteria is as follows:• Volume cut: remove the events reconstructed outside of the detector.
• ∆T < 400 µsec
• Neff > 5
As described in the previous section, the Am/Be data consist of the Gd γ ray and the background
events. Therefore, the efficiency of Gd γ rays can be calculated using
Effpre==(NGdγ )pre−cut
NGdγ
NData − NBG+SBG,
NTrg × Effcapture(6.14)(6.15)

where NData is the number of Am/Be events after the pre-cut, and NBG+SBG is the number of background,the source background and 2.2 MeV γ ray events, NTrg is the number of prompt triggers, and Effcaptureis the capture efficiency by Gd. Figure 6.21 shows the Neff distribution after the pre-cut. The pre-cut
efficiencies for each Gd concentration were obtained as shown in Table 6.3.
Concentration

NData [1/NGdγ ]NBG+SBG [1/NGdγ ]Efficiency[%]

115 ppm
230 ppm

2.817
2.023

2.002
1.221

81.6±0.9Stat.
80.2±0.6Stat.

Table 6.3: Calculation of pre-cut efficiency of signal. NData and NBG+SBG are given in unit of NGdγ .
The background efficiencies are calculated using Effpre,BG = N0BG /NTrg,BG , where NTrg,BG is thenumber of prompt triggers for the background events and N0BG is the number of background events after
the pre-cut. The following is then obtained.

39.0 ± 0.2Stat. % (115ppm)
Effpre,BG =(6.16)
38.5 ± 0.8Stat. % (230ppm)
Likelihood cut
As the next step, the likelihood analysis was applied to the remaining events after the pre-cut. The
root-TMVA program [67] was used to fit the distributions of the variables and to compute the likelihood
distribution (L) in the formnYvar
LS(B) (i) =PS(B),k xk (i) ,(6.17)
k=1

86

Events / Neutron

-3

40

× 10

MC+Bkg
2.2 MeV + Source Bkg + Bkg

35

data
Gd γ

30
25
20
15
10
5
0
0

5

10

15

20

25

30

35

Neff

Figure 6.21: The Neff distribution after the pre-cut. Black histogram is the Am/Be data, red histogramis merged one of the MC and the background, green histogram is the background. Gd γ-ray signal isestimated by subtraction of the background events (2.2 MeV γ ray, source background and background)which corresponds to blue histogram.


where S (B) denotes the Signal (Background), and P xk (i) are PDFs of the variables xk (i). The
likelihood response (y L ) for each event (i) isy L (i) =LS (i).
LS (i) + LB (i)(6.18)

By inputting the variables, Eq.(6.18) provides the optimal good separation between the signal and thebackground. The likelihood functions for the 115 ppm and 230 ppm concentrations were produced in thefollowing situation• Signal : The MC of a Gd γ ray.
• Background : The background data taken periodic trigger in the normal run mode.
For making the likelihood function, we used six variables (xk )k=1,6 (Vertex position, Nef f , ∆T,
goodness, DirKS, and β14 1 ).
These are shown in Figure 6.3.2 and 6.24, and its correlation is shown in Figure 6.22. 2
1 β

14 is the parameter for the event isotropy.
N −1

βl =

N

X X
2
Pl (cosθij ),N (N − 1)(6.19)

i=1 j=i+1

where N is the number of hit PMTs, θ is the angle between i-th and j-th PMT, and Pl is the l-th Legendre polynominals.
In the case of β ∼ 0, θ distributes uniformly. On the contrary, β ∼ ±1 means that θ distributes locally. Gd emits 3 - 4
γ rays isotropically, and so β14 = β1 + 4β4 can be used to separate background events such as radioactivity backgroundemitting a single particle. This was originally developed by the SNO experiment [68].
2 Correlation coefficient showing the correlation between two random variables X and Y is defined bycov(X, Y ).
(6.20)σX σYThe correlation coefficient is symmetric in X and Y, lies within the interval [1,1], and quantifies by definition a linear
relationship. Thus ρ = 0 holds for independent variables, but the reverse is not true in general.
ρ(X, Y ) =87

Correlation Matrix (signal)

Correlation Matrix (background)Linear correlation coefficients in %
β14

-4

∆T

1

8

1

19

-1

100

100

-1

Linear correlation coefficients in %

100
80

β14

10

-3

∆T

-4

2

11

25

-6

100

-3

100

-6

60

-18

-29

6

100

19

DirKS

-12

4

100

6

8

goodness

-18

100

4

-29

1

40

20

R2

-2

1

3

100

DirKS

-1

-5

100

3

goodness

-6

100

-5

1

-3

25

0
-20

Nef
f

-18
goo

dne
s

-12

-18

1

-4

DirK
S

R2

∆T

β14

s

-20
-40

2

-3

-60
100

20
0

11

-40

Neff

80
60

40
R2

100

-60

-80

Neff

-100

100

-6

Nef
f

goo

dne
ss

-1

-2

-4

10

DirK
S

R2

∆T

β14

-80
-100

Figure 6.22: Correlation matrix of used variables of signal (left) and background (right).
Figure 6.25 shows the response of the likelihood (y L ) of the remaining events of the Am/Be data after
the pre-cut. The MC distribution, which is normalized by the number of neutrons, reproduces the Am/Be
data. As shown in Figure 6.26, the component of the Gd γ-ray events is obtained from the Am/Be databy subtraction of the background (2.2 MeV γ ray, source background, and background events). Figure
6.27 shows the signal efficiency and background efficiency as a function of the cut value of likelihood
response. In this analysis, the signal and background events are selected by choosing a cut value such√that the significance is maximized (Significance = S/ S + B, where S and B are the number of events ofthe signal and background respectively).
Concentration
0.0115%0.0230%Likelihood Cut value
SignalBackground
SignalBackground

0.27
0.41

Likelihood Eff.[%]95.4 ±0.5Stat.
3.2±0.1Stat.
95.1±0.4Stat.
2.9±0.4Stat.

pre-cut × Likelihood [%]77.8 ±0.4Stat.
1.2±0.04Stat.
76.3 ±0.3Stat.
1.1±0.13Stat.

Table 6.4: The likelihood cut and reconstruction efficiencies for signal and background event for a 400µsec time window.

The efficiencies of the signal and background are shown in Table 6.4. The reconstruction efficiency
can be obtained as (Pre-cut) × (Likelihood cut). The detection efficiency takes into account the neutron
capture, and it calculated as (reconstruction efficiency) × (capture efficiency). A summary of the efficiency
is shown in Figure 6.28. The 115 ppm and 230 ppm data were analyzed, and data points at 0.2%
Gd sulfate concentration were evaluated by the MC and background data in 230 ppm. So, the 0.2%
Gd sulfate concentration results depends on the background data in a 0.2% Gd sulfate concentration
situation; however, a higher concentration of Gd would provide not only better capture efficiency but
also better separation between the signal and the background because of a shorter ∆T. Table 6.5 gives
a comparison of the detection efficiency of the data and MC, and a consistent result was obtained. The

88

0.15
0.1
0.05
0

10

20

30

40

50

60

4
3
2
1
0

70

0.3 0.4 0.5 0.6 0.7 0.8 0.9

0

2

4

6

8

10

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.2

2
1
0

0.2

0.4

0.6

0.8

1

0.005
0.004
0.003
0.002
0.001
0

12

1.2

1.4

DirKS

0.006

0.4

3

TMVA Input Variables: β14(1/N) dN / 6.78

(1/N) dN / 0.225

1.2

0.6

4

1

TMVA Input Variables: ∆T

2
TMVA Input Variables: R

0.8

5goodness

Neff

1

6

U/O-flow (S,B): (0.0, 0.0)% / (0.4, 0.3)%

0.2

5

7

2.5
2
1.5
1
0.5
0

50 100 150 200 250 300 350 400

R2

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.25

6

(1/N) dN / 0.0228

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

BackgroundU/O-flow (S,B): (0.1, 0.0)% / (0.0, 0.0)%

0.3

TMVA Input Variables: DirKS(1/N) dN / 0.0533(1/N) dN / 1.2

Signal(1/N) dN / 0.0134

TMVA Input Variables: goodness

TMVA Input Variables: Neff

-0.5

0

0.5

1

1.5

2

β14

∆T

Figure 6.23: Used variables for the 115 ppm concentration. (red) Gd γ-ray MC, (blue) Background
data.

0.05
0

10

20

30

40

50

60

70

3
2
1
0

80

0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.2
0

2

4

6

8

10

12

1
0

0.2

0.4

0.6

0.8

(1/N) dN / 6.78

0.006
0.005
0.004
0.003
0.002
0.001
0

50 100 150 200 250 300 350 400

R2

1

1.2

TMVA Input Variables: β14

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.4

2

DirKS

0.007

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 0.223

1.2

0.6

4
3

1

TMVA Input Variables: ∆T

2
TMVA Input Variables: R

0.8

5goodness

Neff

1

U/O-flow (S,B): (0.0, 0.0)% / (0.3, 0.3)%

0.1

4

6

∆T

2.5
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.2)%

0.2
0.15

5

(1/N) dN / 0.0194

0.25

6

(1/N) dN / 0.0451

Background

0.3

TMVA Input Variables: DirKS

7
U/O-flow (S,B): (0.1, 0.0)% / (0.0, 0.0)%

SignalU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 1.22

0.35(1/N) dN / 0.0134

TMVA Input Variables: goodness

TMVA Input Variables: Neff

2
1.5
1
0.5
0

-0.5

0

0.5

1

1.5

β14

Figure 6.24: Used variables for the 230 ppm concentration. (red) Gd γ-ray MC, (blue) Background
data.

89

230ppm
Bkg data

Am/Be data
10(1/N) dN / dx

(1/N) dN / dx

115ppmSource Bkg MC

2.2 MeV γ MC

Gd γ MC

10

1

10-1

10-1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10-2

1

Bkg data

Source Bkg MC

2.2 MeV γ MC

Gd γ MC1

10-2

Am/Be data

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Likelihood response

Likelihood response

Figure 6.25: The distribution of likelihood response (y L ).

230ppm(1/N) dN / dx

(1/N) dN / dx

115ppmGd γ (MC)Gd γ (Data)
Bkg

10

1

1

10-1

10-1

10-2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10-2

1

Gd γ (MC)Gd γ (Data)
Bkg

10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Likelihood response

Likelihood response

Figure 6.26: The distribution of the likelihood response of the Gd γ ray events and MC and backgrounddata. Gd γ events was obtained by subtraction of the background from the Am/Be data.

90115ppm

230ppm120

Gd γ Eff. (MC)Gd γ Eff.

Efficiency [%]Efficiency [%]120
Background Eff.

100

Gd γ Eff. (MC)Gd γ Eff.

Background Eff.

100

80

80

60

60

40

40

20

20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

Likelihood response

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Likelihood response

Figure 6.27: The cut efficiencies as the function of the cut point of the likelihood response.

Figure 6.28: The efficiency of signal and background as the function of the Gd concentration.

91

error estimations will be discussed in the next section.
Concentration

Data

MC

115 ppm
230 ppm

22.7 ±0.3Stat. ± 0.7Sys. %35.2 ±0.4Stat. ± 0.9Sys. %

24.1%
36.2%

Table 6.5: The comparison of detection efficiency between the measured and expected value. The systematic errors are explained in Sec. 6.3.3.

6.3.3

Systematic Error

The systematic errors in the reconstruction efficiency are explained here. First, the systematic error in
the pre-cut for the background efficiency was evaluated. From Figure 6.29, we see that the neutron signal
230ppm10-2

Events / Neutron

Events / Neutron

115ppm

10-3

10-3

10-1

0

MC + Bkg.
2.2MeV
Bkg.

Am/Be data
Gd
Source Bkg.

10-1

MC + Bkg.
2.2MeV
Bkg.

Am/Be data
Gd
Source Bkg.

10-2

2

4

6

8

10 2

12

R [m2]

0

2

4

6

8

10 2

12

R [m2]

Figure 6.29: The distribution of reconstructed vertex:R2 = x2 + y2 + z2 [m2 ] of 230 ppm measurement
after the pre-cut.

is dominant near the source position. By comparing the number of events of the Am/Be data and thebackground data in the region R2 > 3.1m2 , the systematic error in the background data was calculated
from ErrBG = (Ndata − NMC )/NBG − 1, where Ndata is the number of Am/Be events, NBG is the numberof background events and NMC is the number of source events of MC. On the other hand, the systematic
error in the MC was estimated in the region R2 < 3.1m2 . This region (R2 < 3.1m2 ) was determined so√that significance (S/ S + B) was a maximum. Since the signal efficiency was obtained by Eq. (6.15), thetotal systematic error due to this cut was evaluated by the systematic error of the MC, the background,and the capture efficiency ass
NData
ErrSig = (× Errcapture )2 + Err2BG + Err2MC .
(6.21)
NTrg × Effcapture
Next, the systematic error in the likelihood cut is explained. This takes into account the uncertainties
of the variables and the Gd concentration. Figure 6.30 shows the distribution of the six variables used
for the likelihood analysis. After the correcting for the discrepancy between the data and the MC by
92

shifting the MC variables, the PDFs were re-generated, and the efficiencies were re-evaluated by same
method. The uncertainty of the AAS measurement was also taken into account (±5ppm). Using theMC of +5 ppm concentration, the Gd γ signal was extracted from the Am/Be data. The efficiency for+5 ppm concentration was evaluated using the PDFs of the normal concentration (115/230 ppm). Thisis the reason why the systematic error of the background efficiency is negligible. The systematic error
estimation is summarized in Table 6.6.
115 ppmSignal Background
1.6%
0.8%
0.8%
0.3%
1.9%
0.8%

230 ppmSignal Background
0.8%
0.5%
0.5%
0.5%
1.0%
0.5%

Variables error
Gd concentration
Likelihood cut

1.0%
1.5%
1.8%

0.7%
0.7%

1.3%
1.6%
2.1%

0.7%
0.7%

Reconstruction

2.1%

0.2%

1.8%

0.3%

Detection

0.7%

-

0.9%

-

MC error
Background error
Capture efficiency error
pre-cut

Table 6.6: The summary of systematic errors.

93

-3

MC+Bkg

40

shift

bkg

Events / Neutron

Events / Neutron

-3

×10

data

35
30
25
20

18

10
8

4

5

2
15

20

25

30

0

35
Neff

×10

MC+Bkgshift

bkg

Events / Neutron

Events / Neutron

0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
Goodness
-3

-3

30

data

12

6

10

bkg

shift

14

10

5

MC+Bkg

16

15

0
0

×10

data

25
20
15

×10

MC+Bkg

35

bkg

shift

data

30
25
20
15

10

10

5

5

0
0.0

0.1

0.2

0.3

0.4

0.5
DirKS

shift

bkg

data

0
0

Events / Neutron

Events / Neutron

16
14
12
10
8
6
4
2
0
0

2

3

4

5

6

7

8

9 10
R2 [m2]

-3

-3

×10

MC+Bkg1

50 100 150 200 250 300 350 400 450∆T [µsec]

24
22
20
18
16
14
12
10
8
6
4
2
0

×10

MC+Bkg-0.4 -0.2

0.0

shift

0.2

0.4

bkg

0.6

data

0.8

1.0
Beta14

Figure 6.30: The distribution of six variables (xk )k=1,6 used in likelihood analysis. Black histogram is the
Am/Be data. Red histogram is merged histogram of the MC and background data. Light blue histogramis the background. Green histogram is the merged histogram whose the shifted MC histogram to beconsistent with the black histogram.

94

6.4

Evaluation of the Performance in the Super-Kamiokande
Detector

In order to estimate the performance of the delayed coincidence detection in the SK detector, we used
a 2-litter vessel filled with 0.2% Gd sulfate solution (Figure 6.31) and observed the Gd γ-ray signal in
SK. The first such measurement was performed in the SK-III phase, and its analysis has been published[66]. At the time, GdCl3 was a leading candidate as a Gd compound, and the data was taken by oldelectronics.

6.4.1

Measurement and Setup

An Am/Be source and the Gd sulfate solution vessel were installed at (x,y,z) = (35 cm, -71 cm, 0 cm)
using a pulley and lifter with an accuracy of 1mm. Figure 6.32 shows a schematic view of the setup.
Since the SK detector is much bigger than the EGADS detector, the black sheet for the BGO scintillator
was not used for the light intensity adjustment.

Figure 6.31: Picture of a 2-litter vessel filled with 0.2% Gd sulfate solution and an Am/Be source.

Figure 6.32: Schematic view of Gd vessel measurement in the SK detector.

95

The trigger setup is explained in Figure 6.33. The prompt scintillation event was detected by the
SHE trigger. The threshold of the SHE is 70 hits in 200 nsec. After the SHE trigger, a 40 µsec time
window was opened and the events with 29 hits in 200 nsec were recorded as the SHE sub events. After
35 µsec from the SHE trigger, a 500 µsec gate was opened and recorded the events with 20 hits. These
events are called AFT events.
When Merger Process on the online machine receives an AFT event, the merger process doesn’t receive
the next AFT events for 1 sec. Thus, it is a dead time and results in a 36% loss of AFT events. Basically,
future GADZOOOKS! is free from this effect.
The background events were taken by a periodic trigger in normal Run mode which has a 1 msec time
window, so 11069 msec of equivalent data was analyzed.

Figure 6.33: The schematic diagram of the trigger system of data taking in the SK detector. The prompt
scintillation event is detected by the SHE trigger. The delayed Gd γ-ray event is detected as the SHE
sub event and AFT events.

6.4.2

Simulation

Simulation of this measurement was performed by two simulation tools: EGSIM and the official SK
MC called SKDETSIM. EGSIM simulated the neutron capture process by Gd and protons inside/outsideof the vessel. SKDETSIM treated the propagation of particles in the detector and the response of thedetector. The SK group developed SKDETSIM based on GEANT 3.21 to understand the process in the
SK detector based on the calibration data, and tuned the following factors.
Production of Cherenkov photons
The number of Cherenkov photons (dN) emitted by an electron per wavelength interval (dλ) per track
length (dx) is given by


1
1
dxdλ,
(6.22)
dN = 2πα 1 − 2 2
n β
λ2

96

where n is the refractive index of water (n = 1.334), α is the fine structure constant, and β is the velocityof the electron in units of the velocity of light in a vacuum. The opening angle θ of Cherenkov photons
is given by cosθ = 1/(nβ).
Propagation of photon in water
The velocity of Cherenkov photons depends on its wavelength and it is given as a group velocity (vg )of the wave packet bycvg =,(6.23)n(λ) − λ dn(λ)
dλwhere n(λ) is the refractive index of pure water as a function of the wavelength such asr
a1n(λ) =+ a2 + a3 λ2 + a4 λ3 + a5 λ6
2λ − λ2a(6.24)The parameters are
α1 = 5.7473534 × 10−3 ,λ2α = 0.018085,
α4 = 8.715348 × 10

−3,

(6.26)−3,(6.27)

α3 = 2.797222 × 10

α2 = 1.769238,

α5 = 1.413942 × 10,

(6.25)−2in units of µm. There are three processes: Rayleigh scattering, Mie scattering, and absorption are taken
into account in photon propagation. The attenuation length (Lattn. ) of light in water is then describedby1,(6.28)
Lattn. =αabs (λ) + αRay(λ) + αM ie (λ)
where αabs (λ), αRay(λ) and αM ie (λ) are coefficients for the absorption, Rayleigh scattering, and Mie
scattering, respectively, as α function of the wavelength of photons (λ). The fraction of these processes
depends on the wavelength and the purity of water which is given byA(λ ≤ 350nm)
 11 ,
A1
λ A4
+
A
(
)
,
(350nm < λ ≤ 415nm) ,αabs (λ) =(6.29)
42
λA3
 A1 + f (λ),(415nm
<
λ)
λ4


R1
R2
αRay (λ) =×1+,(6.30)λ4λ2
M1
αM ie (λ) =,(6.31)
λ4
where Ax ,Rx and Mx are tuned parameters, and f (λ) is obtained from [69]. The measurement was
performed by periodic laser injection calibration. When a photon arrives at the detector wall (the acrylic
cover, the PMT surface or the black sheet), reflection, absorption, and transmission are considered.

6.4.3

Measurement of Energy Spectrum of Gd γ ray

The prompt event of interest is that generated by a 4.43 MeV γ ray. The prompt events were selectedusing the following criteria:• Total charge selection to select 4.4 MeV γ ray. The peak around 1000 p.e. corresponds to the 4.43
MeV γ ray.
• Vertex cut: R2 < 2m297• Time difference from last trigger > 1 ms ( remove the effect of the previous event)

EventsFigure 6.34 shows the total charge distribution of a prompt event before and after event selection. From
this selection, the loss fraction of AFT events becomes 30%. The delayed events selection:

Raw

3000
After selection

2000

1000

0
0

500

1000

1500

2000

Total p.e.

Figure 6.34: The total charge of the prompt event. Red histogram corresponds to the events used in thisanalysis.

• ∆T Cut > 1.7 µsec to remove the after-pulse from PMTs
• Vertex cut : R2 < 2m2• Vertex fit goodness>0.4• DirKS < 0.4• N200 > 20
Figure 6.35-6.37 shows the distribution of the ∆T, the vertex position, and the energy spectrum for
AFT and SHE trigger events after event selection. In the same way as the EGADS analysis, the source
background was taken into account. The peak of the reconstructed Gd γ ray energy was around 4 MeV
as seen in EGADS data. Figure 6.38 shows the event display of Gd γ-ray events in SK.

98

Events / 5 µs

Gd γ MCAm/Be data

BKG data

2.2 MeV γ MC

Source BKG MC

300

200

100

0

50

100

150

200

250

300

350

400

450

500

∆ T[µs]400

Am/Be data

BKG data

2.2 MeV γ MC

Source BKG MC

EventsEventsFigure 6.35: The time difference between prompt and delayed trigger. At the ∆T=35 µsec, trigger typeis separated (SHE trigger:<35µsec, AFT trigger:>35µsec). Horizontal axis is normalized by the numberof AFT trigger.

Gd γ MC300

Am/Be data

BKG data

2.2 MeV γ MC

Source BKG MC

Gd γ MC

300
200
200
100
100

0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
5.02
2

R [m ]

0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
5.02
2

Figure 6.36: The R2 distribution (left) SHE sub events, (right) AFT events.

99

R [m ]

Events

EventsGd γ MCAm/Be data

BKG data

2.2 MeV γ MC

Source BKG MC

200

200

Gd γ MCAm/Be data

BKG data

2.2 MeV γ MC

Source BKG MC

150

100

100

50

0
0

1

2

3

4

5

6

7

8

9

10

Energy[MeV]

0
0

1

2

3

4

5

6

Figure 6.37: Energy spectrum (left) SHE sub event, (right) AFT event.

Figure 6.38: Event display of Gd γ ray event.

100

7

8

9

10

Energy[MeV]6.4.4

Evaluation of the Performance

Capture efficiency
The capture efficiency was estimated for SK-Gd data in the same way as for EGADS analysis (Eq.
(6.13)). Results are given in Table 6.7. Then, it is possible to measure the position dependence of theneutron capture efficiency due to the non-uniformity of Gd concentration in the SK detector. A neutron
travels about 15cm in the Gd solution. Thus, most neutrons leak from the 2-litter vessel.

Hit rate
Gd
EffCutγ
EffSBG
Gd
EffSBG
Capture Eff.
ResultMC

SHE sub
shifted MC
0.06450.47900.45230.00060.00050.00230.0022
13.3%
14.1%
13.3 ± 0.4Stat. ± 0.8Sys. %
12.9%

AFT
shifted MC
0.05400.54900.51740.00780.06810.03550.03347.9%
8.6%
7.9 ± 0.3Stat. ± 0.7Sys. %7.3%

Table 6.7: Summary of calculation of capture efficiencies for each of the trigger events.

Reconstruction efficiency
The reconstruction efficiency of the delayed neutron signal and background efficiency were estimatedin the same way as for the EGADS analysis. Likelihood analysis was applied after the pre-cut. The
followings shows the selection criteria for the pre-cut:• Vertex cut : R2 < 5[m2 ]• ∆T Cut
1.7 µsec < ∆T < 35 µsec (SHE sub events)
35 µsec < ∆T < 535 µsec (AFT events)• N200>20 : N200 is the maximum number of hits in a 200 nsec time window.
The Neff distribution is seen in Figure 6.39, and the signal efficiencies of the pre-cut can be obtainedusing Eq.(6.15). The results are summarized in Table 6.8. The background efficiencies are calculated by
Trigger
SHE sub
AFT

NData [1/NGdγ ]
1.093
2.629

NBG+SBG [1/NGdγ ]
0.181
1.705

pre-cut Efficiency[%]
91.1±2.0Stat.
92.4±2.8Stat.

Table 6.8: Calculation of pre-cut efficiency of signal.
Effpre,BG = N0BG /NBG , where NBG is the number of SHE triggers, and N0BG is the number of background
events after the pre-cut in each trigger. Then, the following is obtained.

0.22 ± 0.04Stat. % (SHE sub)Effpre.BG =(6.32)
2.58 ± 0.15Stat. % (AFT)101

Events / Neutron

-3

×10
7
6

MC+Bkgdata

2.2 MeV + Source Bkg + Bkg

Gd γ

5
4
3
2
1
0

1

2

3

4

5

6

7

8
EnergyFigure 6.39: The energy distribution after the pre-cut. The Gd γ-ray signal is estimated by subtraction of
background events (2.2 MeV γ ray, source background and background) which corresponds to the entriesof blue histogram.

For the likelihood analysis, the same variables were used as for the EGADS analysis, PDFs were generated
by using the MC of Gd γ ray and background data. Figure 6.40, 6.41 shows the distribution of thevariables for each of the trigger events.
Figure 6.42 and 6.43 show the likelihood response (y L ) and the efficiencies as a function of the cut
value of the likelihood responses. As for the EGADS analysis, the efficiencies were evaluated at the
maximum significance. These efficiencies are summarized in Table. 6.9.
Event type
SHE sub
AFT

Likelihood cut value
SignalBackground
SignalBackground

0.101
0.176

Likelihood Eff.[%]Precut×Likelihood[%]96.6±2.2Stat.
3.6±0.4Stat.
98.4±3.0Stat.
3.3±0.4Stat.

88.0±1.9Stat.
(8. ± 1Stat. ) × 10−390.9±2.7Stat.
(8. ± 1Stat. ) × 10−2

Table 6.9: The likelihood cut efficiency and reconstruction efficiency.

The expected values for the reconstruction efficiency are 88.4% and 89.4% for the SHE sub and AFT
events. Then, the consistent results were obtained from the Am/Be data.
The better performance was obtained than that for the EGADS data. This comes mainly from thelower background and lower mis-reconstruction probability in the SK detector. BONSAI uses the numberof PMT hits for vertex reconstruction. SK can provide more PMT hits than EGADS due to the large
detector size.
Systematic error
Since the background events in the SHE sub and AFT triggers are intrinsically common, the systematic
error in the pre-cut efficiency for the background was evaluated by comparing the SHE sub events and
102

1.4
1.2
1
0.8
0.6
0.4
0.2
0

2

3

4

5

6

7

8

14
12
10
8
6
4
2
0

9

8
7

U/O-flow (S,B): (0.0, 0.0)% / (0.3, 0.4)%

Background(1/N) dN / 0.0185

1.6

TMVA Input Variables: DirKS

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

SignalU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 0.14

1.8(1/N) dN / 0.00688

TMVA Input Variables: goodness

TMVA Input Variables: Neff

6
5
4
3
2
1
0

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

0.2

0.4

0.6

0.8

goodness

Neff

DirKS

TMVA Input Variables: ∆T

2
TMVA Input Variables: R-3

1

TMVA Input Variables: β14

0.04
0.02
0

0.035

0.025
0.02
0.015
0.01
0.005
0

10000 20000 30000 40000 50000

R

0.03

5

10

15

20

25

2

30

2.5
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 3.4)%

0.06

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.1
0.08

0.04

(1/N) dN / 0.0415(1/N) dN / 0.597

0.045

0.12

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 847

×10

2
1.5
1
0.5
0
-0.5

35

0

0.5

1

1.5

β14

∆T

Figure 6.40: Used variables for SHE sub event. (Blue) Gd γ MC, (Red) Background data.

1
0.8
0.6
0.4
0.2
0

2

3

4

5

6

7

8

8
6
4
2
0

9

0.02
0

10000 20000 30000 40000 50000

R

2
1
0

0.2

0.4

0.6

0.8

0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0

50 100 150 200 250 300 350 400 450 500

2

1

1.2

TMVA Input Variables: β14

0.02
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.04(1/N) dN / 7.84

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 846

0.08

4

DirKS

TMVA Input Variables: ∆T

0.06

5

goodness

2
TMVA Input
Variables: R
-3
×10
0.14

0.1

6

3

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

Neff

0.12

7

U/O-flow (S,B): (0.0, 0.0)% / (0.4, 0.2)%

1.2

10

8

∆T

2.5
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 1.8)%

1.4(1/N) dN / 0.0194

Background(1/N) dN / 0.0421

1.6

TMVA Input Variables: DirKS

12
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

SignalU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 0.135

1.8(1/N) dN / 0.00728

TMVA Input Variables: goodness

TMVA Input Variables: Neff

2
1.5
1
0.5
0
-0.5

0

0.5

1

1.5

β14

Figure 6.41: Used variables for AFT event. (Blue) Gd γ MC, (Red) Background data.

103

aft
Am/Be data

Bkg data

Source Bkg MC

2.2 MeV γ MC

(1/N) dN / dx

(1/N) dN / dx

she

Gd γ MC

10

10

1

1

10-1

10-1

10-2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10-2

1

Am/Be data

Bkg data

Source Bkg MC

2.2 MeV γ MC

Gd γ MC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Likelihood response

Likelihood response

Figure 6.42: The distribution of likelihood response (y L ).

she

aft

120

120
Gd γ Eff. (MC)Gd γ Eff.

Background Eff.

Gd γ Eff. (MC)

100

100

80

80

60

60

40

40

20

20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

Likelihood response

0.1

0.2

0.3

Gd γ Eff.

0.4

0.5

Background Eff.

0.6

0.7

0.8

0.9

1

Likelihood response

Figure 6.43: The cut efficiencies as the function of the cut point of the likelihood response for (left) SHE
sub and (right) AFT events.

104

SHE sub

AFT

10-1

10-4

10-4

Events / Neutron

10-3

Events / Neutron

10-1

MC + Bkg.
2.2MeV
Bkg.

Am/Be data
Gd
Source Bkg.

10-2

10-2

0

MC + Bkg.
2.2MeV
Bkg.

Am/Be data
Gd
Source Bkg.

10-3

1

2

3

4

0

5

R2 [m2]

1

2

3

4

5

R2 [m2]

Figure 6.44: The R2 distribution for (left) SHE sub, and (right) AFT events.
the AFT events. In other words, the efficiency of both events are consistent for the pre-cut selection,
except for the ∆T selection. After the correcting for the time window of each event (EffAFT = EffSHE ×(500µsec/35µsec)), the difference between them was treated as the systematic error.
The systematic error in the pre-cut for the signal was evaluated by same method as for EGADS
analysis; the number of remaining event after the pre-cut was compared with the MC, and the systematic
error was evaluated. Figure 6.4.4 shows the vertex distribution after pre-cut selection.
The systematic error of the likelihood cut was evaluated by the shifted MC variables shown in Figure
6.45, and these are summarized in Table 6.10. In this analysis, the Gd concentration uncertainty was notconsidered, since the Gd concentration was well measured.

MC error
Background error
Capture efficiency error
Pre-cut

SHE sub
Signal Background
0.9%
0.04%
0.04%
0.8%
0.6%
0.04%

Signal
0.9%
0.53%
0.7%
0.9 %

AFT
Background
0.53%
0.53%

Variables error
Gd concentration error
Likelihood cut

0.1%
0.1%

0.7%
0.7%

0.4%
0.4%

0.7%
0.7%

Reconstruction

0.6%

0.002%

0.9%

0.02%

Table 6.10: Systematic error estimation of likelihood analysis.

105

-3

MC+Bkgbkg

shift

Events / Neutron

Events / Neutron

-3

×10
7

data

6
5
4
3

×10

MC+Bkg

10

bkg

shift

data

8
6
4

2
2

1
0

1

2

3

4

5

6

7

0
0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
Goodness

8
Energy-3×10

MC+Bkgshift

bkg

Events / Neutron

Events / Neutron

-3

14

data

12
10
8
6
4
2
0

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
DirKS

×10
22
20
18
16
14
12
10
8
6
4
2
0
0.0

×10

MC+Bkg

shift

4.0

bkg

Events / Neutron

Events / Neutron

0.5

1.0

bkg

shift

1.5

2.0

2.5

3.0

data

3.5

4.0
R2 [m2]

-3

-3

4.5

MC+Bkg

data

3.5
3.0
2.5
2.0

9

×10

MC+Bkg

shift

bkg

0.2

0.4

data

8
7
6
5
4

1.5

3

1.0

2

0.5

1

0.0
0

0

5

10

15

20

25

30

35 40
∆T [µsec]

-0.2

0.0

0.6
0.8
Beta14

Figure 6.45: The variables used in the likelihood analysis for the SHE sub event of the SK+Gd vessel data.
Black histogram is the Am/Be data. Red histogram is merged histogram of the MC and backgrounddata. Light blue histogram is the background. Green histogram is the merged histogram whose shifted
MC histogram to be consistent with the black histogram.

106

Estimation of performance
In this thesis, the Am/Be data was analyzed, and this gave a consistent result with the MC for both
EGADS (full Gd-doped water Cherenkov detector) and SK (the detector for GADZOOKS!). Therefore,
using the MC simulation, the performance of GADZOOKS! was evaluated in the situation that neutrons
are generated from the center of the detector. In order to compensate for the small statistics of backgrounddata, the efficiency was evaluated as follows:• Applied the pre-cut and evaluate the efficiency. However, ∆T cut was not applied, and the fiducial
cut (22.5kton) was applied instead of the R2 cut for the background events.
• For background events, the ∆T cut of a 100 µsec time window and the R2 < 3m2 cut efficiencies
can be calculated by scaling: 100µsec/1msec× ( 43 π33 )/22.5kton.
• Evaluated the likelihood cut efficiency. To suppress the background efficiency as much as possible,
the events were selected out of a 0.9 likelihood response as shown in Figure 6.46.

Figure 6.46: The distribution of the likelihood response (y L ).
Finally, the detection efficiency and background efficiency were obtained as 73.9% and 1.4 × 10−4 %respectively for a 100 µsec time window and the 2.5 MeV threshold using a 90% neutron capture efficiency
on 0.2% Gd sulfate solution. A previous study [66] evaluated the detection and background efficiencies
as 66.7% and 2 × 10−2 % for the 3.0 MeV threshold and a 60 µsec window (for 2.5 MeV threshold, thebackground efficiency was 1 × 10−1 %). The estimated performance has been greatly improved by thisstudy with the likelihood analysis.
Figure 6.47 shows the expected SRN spectrum for 10 years of measurements in GADZOOKS! using
the obtained signal and background efficiencies. The expected number of SRN signals is approximately
16.5, 18.2, 30.1, and 36.2 events in the case of an effective neutrino temperature of 4 MeV, 6 MeV,
8 MeV, and 1987a of the SRN model [17], respectively, and the accidental background is negligible.
Since the expected atmospheric neutrino background is approximately 18.1 events, approximately 5 σlevel observations are expected, and this provides enough statistics to discuss the differences in the SRN
models.

107

Events/10years/2MeV

10

T=8MeV

T=4MeV

8

SRN+B.G.

6

4
Total Atmosphericν B.G.
2
Atmospheric ν eAccidental B.G.

Events/10years/2MeV

100

T=6MeV

T=SN1987a

8

6

4

2

0

10 15 20 25 30 35 40 45 5010 15

Energy [MeV]

20

25

30

35

40

45

50

Energy [MeV]

Figure 6.47: Expected SRN spectrum and background for 10 years observation in the Gd-doped SK detector for each neutrino temperature (T). (upper:right) T=4 MeV, (upper:left) T=6 MeV, (bottom:right)
T=8 MeV, (bottom:left) T=1987a from [17]. Green line is the expected accidental background. The
atmospheric neutrino background events were selected by requiring that one neutron is captured by Gd
through the interaction process.

108

Chapter 7

Conclusion and Future Prospects
In this thesis, the delayed coincident detection in a Gd-doped water Cherenkov detector has been
demonstrated.
The delayed γ-ray signal from Gd neutron capture has been measured using an Am/Be neutron sourceat 115 and 230 ppm concentrations of Gd2 (SO4 )3 in EGADS. The γ-ray energy, the position and the timeof γ-ray production from Gd neutron capture are measured. The detection efficiencies for 115 ppm and
230 ppm concentrations of Gd2 (SO4 )3 were measured to be 22.7±0.7% and 35.2±1.0%, respectively. The
background efficiencies for a 400 µsec time window were also measured to be 1.2±0.3% and 1.1±0.3% foreach concentration. For the SK detector, the signal reconstruction efficiency and background efficiency
were evaluated to be 88.0±2.0% and (8 ± 2) × 10−3 % (SHE sub events) by using the 2-litter vessel filledwith 0.2% Gd2 (SO4 )3 solution. The measured values were consistent with MC predictions. Finally, thisstudy has shown that Gd should give the sufficiently high detection efficiency of the delayed event andaccidental background can be also sufficiently suppressed compared with the search of 2.2 MeV γ rayfrom neutron capture on protons for the observation of SRN.
After refurbishing and cleaning inside the detector, the EGADS experiment resumed the circulation
with Gd-doped water. It will complete the study of the water transparency of Gd-doped water in near
future (in 2015). The Am/Be measurement will be also resumed, and Gd γ-ray data up to 0.2% Gd2 (SO4 )3concentration will be checked.
In the world, the big projects are processing to search for the SRN signals (Hyper-Kamiokande, SNO+,
LENA etc.). Any one of these would be a spectacular device for detecting SRN, but it will still take adecade until the SRN observation. However, GADZOOKS! may start the SRN observation by using theexisting SK detector, and a Gd-doped SK detector has a better chance for the first detection of the SRN
signals.
The other type of backgrounds has to be studied more carefully. In order to suppress the radioactivity
in Gd compound, the Rn measurement setup is being prepared in the EGADS experimental room, andseveral membranes will be tested by this setup. The measurement technique of Rn concentration in purewater has been established by SK, but the measurement for Gd-doped water is the first trial. Although
the theoretical calculation of γ ray production is explained in this thesis, better understanding on NC
QE γ ray is also necessary. At the present time, some experiments have started investigating it (T2K
NC QE γ ray measurement [71], and Research Center for Nuclear Physics E398 [72]).
In parallel, EGADS will be converted to an advanced-technology supernova neutrino detector byreplacing its front-end electronics with QBEE suitable for the very high data rates expected in the casefor a nearby supernova explosion. Such an explosion will overwhelm SK’s ability to record all events. In

109addition, a GPS time stamping and a real-time intelligent trigger system comprised of custom hardware
and software will be added, and they are designed to extract the most detailed, accurate supernova
neutrino data possible as rapidly as possible. Then, EGADS will be the only neutrino detector that has
the direction sensitivity and neutrino-antineutrino flavor sensitivity until realization of the Gd-doped SK
detector.

110

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