Journal of Nuclear and Radiochemical Sciences, Vol. 1, No. 2, pp. 63−68, 2000

63

Positron Annihilation in Liquid Scintillator for Electron Antineutrino Detection
Yasushi Kino,*,a Tsutomu Sekine,a Yasuyoshi Sato,a Hiroshi Kudo,a Fumihiko Suekane,bAtsuto Suzuki,b Yasuo Ito,c and Takenori SuzukidaDepartment of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
Research Center for Neutrino Science, Graduate School of Science, Tohoku University, Sendai 980-8578, Japanc
Research Center for Nuclear Science and Technology, The University of Tokyo, Tokai, Ibaraki 319-1195, Japand
Radiation Science Center, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801,
Japanb

Received: May 16, 2000; In Final Form: August 21, 2000
Positron annihilation processes in a liquid scintillator to be used for the detection of electron antineutrinos in the
KamLAND project were studied. The liquid scintillator was a mixture of isoparaffin, pseudocumene and 2,5diphenyloxazole. We measured positron annihilation lifetime (PAL) spectra which contained important timing
information on identification of the electron antineutrinos. The PAL spectra of a nitrogen-saturated liquid scintillator consisted of three lifetime components. Two fast components with the lifetime of 0.19 ± 0.05 ns and 0.48 ±0.05 ns correspond to the mixture of para-positronium annihilation and free positron annihilation. The delayedcomponent (3.41 ± 0.02 ns) with the intensity of 48.9 ± 0.3 % is ascribed to pick-off annihilation of ortho-positronium (o-Ps) annihilation. To understand the 2 γ annihilation processes of o-Ps in the liquid, we examined theeffects of dissolved gases (nitrogen, oxygen, helium and argon) and mixing ratio of isoparaffin and pseudocumene
which were the main components of the liquid scintillator. The lifetime of o-Ps was drastically shortened in thepresence of oxygen, but not for other gases. The reaction rate constant for quenching of o-Ps by oxygen was
obtained from the O2 concentration dependence of o-Ps lifetime component. The pick-off annihilation of o-Ps
with the liquid scintillator is explained based on the bubble model. We discuss a possible microscopic picture of
the surroundings of Ps in the liquid scintillator.
e+ + e− → 2γ.

1. Introduction
Recently an epoch making discovery has been made inelementary particle physics. Namely evidence for neutrino
oscillation was observed by a large water Cherenkov detector
called SuperKamiokande.1 This observation is the first clue toa theory beyond the standard model of elementary particles,
giving excitement to physicists. There are three kinds ofneutrinos; an electron-type (νe), a muon-type (νµ) and a tautype (ντ). What they observed was the oscillation of νµ.
Another large neutrino detector, called KamLAND(Kamioka Liquid scintillator AntiNeutrino Detector), is underconstruction next to SuperKamiokande.2 A main purpose of
KamLAND experiments is to look for oscillation of electrontype neutrino by detecting electron antineutrinos (νe : antiparticle of νe) generated in nuclear reactors located around 170
km away. This experiment is fully sensitive to a set of oscillation parameters, so called MSW Large Angle Solution (forexample, see Reference 3, further references therein), which
gives an answer to the puzzle of solar neutrino deficit, and has
a good chance to observe the oscillation of electron-type
neutrinos. To compensate for the very small reaction crosssections of neutrinos, the KamLAND detector makes use of
1,000 tons of a liquid scintillator (a mixture of paraffin oil,pseudocumene and DPO (2,5-diphenyloxazole)) as the active
target. Theνe reacts with a proton in the liquid scintillator to
produce a positron and a neutron,νe + p → e+ + n.

(1)

A typical energy of the positron is a few MeV and the positronannihilates with a surrounding electron within a few ns,
producing two 511 keV γ rays,*Corresponding author. E-mail: kino@mail.cc.tohoku.ac.jp. FAX:
+88-22-217-6597.

(2)

The neutron is thermalized quickly, and then absorbed by aproton after 170 µs of lifetime, producing a 2.2 MeV γ ray,n + p → d + γ.

(3)The νe is identified by observing a coincident event of both thepositron-related signals (eq 1, 2) and the deuteron signal (eq3). It is important to know the time structure of positron annihilation, because the coincidence measurement is sensitive tothe positron annihilation lifetime (PAL) in a detector.
Moreover, this information can be used to distinguish positron
signals from other instantaneous background signals, such as βrays from natural radioactive substances contained in the liquid
scintillator.
Some of the positrons injected and stopped in bulk liquidannihilate with the surrounding electrons directly, while otherpositrons form positronium (Ps) which is a neutral bound stateof a positron and an electron. Positronium is the lightest of thehydrogen-like atoms. Positronium has two substates
depending on the total spin angular momentum S. The spin
singlet state (S=0) is called para-positronium (p-Ps) whichannihilates emitting two mono energetic 511 keV γ rays withthe lifetime of 0.125 ns. The spin triplet state (S=1) is called
ortho-positronium (o-Ps) which annihilates emitting three γ
rays with the lifetime of 140 ns in vacuum. However, incondensed matters the lifetime of o-Ps is reduced to several ns,
due to interactions with surrounding electrons emitting two
mono energetic 511 keV γ rays. The processes involved are a"pick-off", a "chemical reaction" and a "spin conversion". The
intensity and the lifetime of Ps strongly depend on the physicaland chemical conditions of the bulk liquid. Over the past few
decades, a number of studies have been made on the positronannihilation in nonpolar organic solutions (for example, see
Reference 4, further references therein). Generally, a lifetime© 2000 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 12/28/2000

Kino

64 J. Nucl. Radiochem. Sci., Vol. 1, No. 2, 2000
of positron in nonpolar organic liquids comprises two shortcomponents and one or more long components. Approximately,
the two short lifetimes lie in the range of 0.1−0.5 ns, and thelong lifetime is a few ns. The intensity of the long lifetime
component ranges from 5 to 50 %. Structures of the lifetime
spectrum depend on liquid species, and are changed by dissolution of oxygen.5−10 Quenching of o-Ps by oxygen was firstfound in liquid argon and nitrogen by Paul. 5 Kerr et al. 6
reported an angular correlation between the two annihilation γ
rays. Their experimental data showed that the quenching was
associated with the pick-off process. Systematic lifetime
measurements for various organic liquids were carried out by
Lee and Celitans.8 They claimed that the chemical reaction
between o-Ps and O2 (or NO) is a diffusion-controlled process.
In this paper, we examine the time structure of positronannihilation in the liquid scintillator to be used for theνe detection. We also investigate dependence of the PAL spectra on
gaseous species such as oxygen, nitrogen, helium and argondissolved in it, and discuss a o-Ps formation process in theliquid scintillator.
2. Experimental
The PAL spectra were obtained by a conventional fast-fastcoincidence system with plastic scintillators, having a time
resolution of 0.3 ns at FWHM. A 22Na positron source (0.6
MBq) was sandwiched between two sheets of 7.5 µm polyimide (Kapton) film where 15 % of positrons annihilated witha single lifetime component (τ = 0.38 ns). The total counts ofeach measurement was about 107. The lifetime measurements
were performed at room temperature (23 °C) in pseudocumene(PC: COSMO) from Matsuyama Peteroleum Co., isoparaffin(IP: PARAOL250) from Showa Shell Sekiyu and mixtures ofPC and IP solutions. In addition, the lifetime was measured
for a liquid scintillator (LS), to be used for theνe detection,
composed of 80 % of IP, 20 % of PC and 2 g L −1 of 2,5diphenyloxazole (DPO) from Dojindo Laboratories. The
samples were not degassed as in References 4−10. Because
the IP used here is a mixture of various fractions having
different boiling points, it was difficult to degas the sample
without causing a change in the initial composition. The
positron source was dipped in the scintillation liquid (15 mL)
in a glass vial. The liquid was saturated with gases (oxygen,nitrogen, helium, argon or a mixture of nitrogen and oxygen)by bubbling under the atmospheric pressure. The glass vial
was tightly capped and sealed in a vinyl bag filled with thesame gas, and then subjected to the lifetime measurement.
An appropriate mixing ratio of nitrogen and oxygen was
attained by using a gas mixer (GB-2B, KOFLOC. Co.), and theconcentrations of nitrogen and oxygen in the liquid were determined by gas chromatography. The pure gas concentrations in
the liquid calculated by applying the Henry's law using the
published gas solubilities11 are listed in Table 1.
Doppler broadening spectra were taken with a pure germanium solid state detector equipped with a pulse hight analyser
in the energy region around 511 keV during the life timemeasurements. An FWHM value for γ ray of 514 keV from85
Sr was determined as 0.755 keV.

TABLE 1: Gas Concentration (1021 molecules L-1) in Organic
Liquids Used

3. Results and Discussion
The accumulated PAL data were analyzed using a program
PATFIT12 with three components of the lifetime. The χ2 perdegree of freedom of each analysis was about 1.0. The lifetimes of the components were about 0.2, 0.5 and 3 ns, respectively. The first two components represent mixing of lifetimesof the p-Ps and free positron annihilation in the bulk liquid.
The third component with a long exponential-tail separated
from the other components represents 2γ-annihilation caused
by interactions between o-Ps and bulk liquid.
Figure 1 shows PAL spectra observed for the LS saturated
with N 2 and O 2 . The lifetime of o-Ps appearing in the tailregion of the spectra was drastically shortened in the presenceof oxygen. In Table 2, the lifetimes (τi ) and intensity (Ii ) after
correcting for the components corresponding to the positrons
annihilating in the source material are listed for the N2 and O2
saturated samples. In the case of N2 saturation, the values inTable 2 give a time structure of positron annihilation corresponding to theνe-injected LS for the KamLAND project. The
o-Ps intensity I3 did not change by dissolution of O2 and N2,
indicating that neitrher O2 nor N2 would affect the Ps formation process in the LS.
The measured lifetimes and intensities of the o-Ps component are summarized in Table 3. All but oxygen gas dissolution in the liquid scintillators examined here hardly affected
the o-Ps lifetime τ 3.
An effect of O2 concentration on the o-Ps annihilation rate
(λ3 = τ3−1) is shown in Figure 2 for the concentration from 10−3
to 10 −2 M. The λ 3 linearly increases with increasing O 2
concentration, indicating the presence of chemical reaction ofo-Ps with O2 molecule in the annihilation process. Therefore
the annihilation rate λ3 should be expressed as
λ3 = λ3γ + λliquid + κ [O2],(4)

Figure 1. PAL spectra for the liquid scintillator (LS); the black dots
for N2 saturation and the gray dots for O 2 saturation (1 channel =0.0253 ns).

TABLE 2: Lifetime and Intensity of the ith Component in
PAL Spectra Measured for the Liquid Scintillator (LS)
i

N2

O2

He

Ar

N2 saturated τi /ns

IP

3.5

5.5

0.59

0.54

Ii /%

PC

2.8

4.1

0.53

6.0

O2 saturated τi /ns

LS

3.4

5.2

0.58

1.6

Ii /%

1

2

3

0.19 ± 0.05

0.48 ± 0.05

3.41 ± 0.02

30 ± 221 ± 248.9 ± 0.3

0.21 ± 0.04

0.49 ± 0.03

1.83 ± 0.01

21 ± 230 ± 348.9 ± 0.4

Positron Annihilation in Liquid Scintillator

J. Nucl. Radiochem. Sci., Vol. 1, No. 2, 2000 65

TABLE 3: Lifetime τ3 and Intensity I3 of o-Ps in Isoparaffin (IP), Pseudocumene (PC) and Liquid Scintillator (LS)τ3 / ns
He
Ar
N2
O2

τ3 / %

IP

PC

LS

IP

PC

LS

3.25 ± 0.01
3.32 ± 0.03
3.50 ± 0.03
1.88 ± 0.01

2.98 ± 0.01
3.01 ± 0.03
3.03 ± 0.02
1.78 ± 0.01

3.20 ± 0.02
3.42 ± 0.03
3.41 ± 0.02
1.83 ± 0.01

40.2 ± 0.2
40.7 ± 0.4
39.6 ± 0.2
40.7 ± 0.2

45.1 ± 0.4
45.8 ± 0.6
46.1 ± 0.3
44.2 ± 0.2

48.5 ± 0.3
49.5 ± 0.7
48.9 ± 0.3
49.1 ± 0.5

where λ3γ is the rate of 3γ-annihilation of o-Ps in vacuum, λliquid
is the rate of pick-off annihilation of o-Ps with electrons in thesurrounding species, and the third term is the rate of 2γ-annihilation of o-Ps through a chemical reaction with dissolved
oxygen. Here, κ is the reaction rate constant and [O2] is the O2
concentration. The straight lines in Figure 2 obtained by theχ2-fit with eq 4 give the rate constants κ as 29.2 ± 0.3 M−1ns−1
for LS, 32 ± 4 M−1ns−1 for PC and 26.5 ± 0.6 M−1ns−1 for IP.
These values are consistent with those of Reference 8 (κ = 10
∼ 100 M−1ns−1) and Reference 7 (κ = 20 ∼ 50 M−1ns−1). For the
pick-off annihilation induced by one of the electrons in molecules, λliquid is given by
λliquid = πr02cnZeff,

λliquid = πr02cnZeff P(x),(6)

where x is a variable depending on the state of the Ps bubble.
We assume that Ps is in a three dimensional square-well potential. The zero-point energy ε (kr) of Ps in this potential iscalculated by means of a quantum mechanical procedure,

ε (kr) = U sin2(kr),(7)

where U and r are the depth and the radius of the Ps bubble,
respectively. The value of k is the wave number of Ps givenby the boundary condition of the wave function at the bubble
surface. The total energy E(r) of the Ps bubble is(5)

E(r) = ε (kr) + 4 πr2σ +2where r0 is the classical radius of electron (r0=α aBohr=2.8 fm),c the speed of light, n the number density of molecules and Zeff
the effective number of annihilation electrons per molecules.
It is difficult to determine the value Zeff directly. We assume
that Zeff is represented by the number of valence electrons of amolecule. Because a positron, having positive charge, feels
repulsive force from a cation inside the valence orbital, theprobability of finding a positron in the inner shell is expected
to be small. To calculate λ 3 , we used Z eff =92 for IP and
Z e f f =48 for PC. Ambiguity of the choice of Z e f f will be
discussed later. The values of λ3 calculated with eq 5 wereseveral times larger than observed ones. We recall the bubble
model 13 to explain the overestimation. The bubble model
assumes the existence of a space where o-Ps is free from pickoff annihilation. A repulsive electron exchange interaction
between Ps and the surrounding molecules traps Ps in the freespace called a positronium bubble. Because of a strong
quantum effect of Ps having the light mass (2me), a part of the
wave function of Ps can spread outside the bubble, where thepick-off annihilation occurs. Taking account of this model, we
modify the λ liquid of eq 5 multiplying a probability P(x) of
finding Ps outside the bubble,

4π 3
r p.
3

(8)

The second term represents the surface energy associated withthe surface tension σ of the bulk liquid and the third term
represents the volume energy at pressure p. We neglect thethird term, the value of which is estimated to be 2 orders ofmagnitude smaller than the other terms. The Ps bubble stably
exists at the stationary point of E(r), namely,
d
E(r)
= 0,
dr
r=a

(9)

where a is the most probable radius. Using the Ps bubble wave
function Ψk (r), the probability P(x) is given by,∞

P(x) = ∫a | Ψk (r) |2 r2dr =sin2 x,1−xcot x

(10)

with
x = ka.

(11)

Here, x is the only one dimensionless variable in the bubble
model, and describes all of the physical quantities (a, E(a),ε(x), U and µ). Because the probability P(x) is in the range of
0−1, the variable x is defined inπ ≤ x ≤ π.
2

(12)Using the observed values of λ3, x is determined from eqs. 4, 6
and 10.
The calculated values of a, E(a), ε (x), U and µ are listed inTable 4. The values of a, ε (x) and U are given as,
1

a=

(

4
h2
x3
,
x−tanx16π meσ)ε (x) = h πσ x(x−tanx),
me

(13)

(14)

and
U = h πσ x(x−tanx)
.
me
sin2x
Figure 2. Oxygen concentration dependence of λ3. Circle, square andtriangle stand for PC, LS and IP, respectively. The solid lines show arelation expressed in eq 4.

(15)

A penetration length µ is estimated by the density of o-Ps
outside the potential (bubble),Kino

66 J. Nucl. Radiochem. Sci., Vol. 1, No. 2, 2000( )|Ψk (r ≥ a)| 2 ∝ exp − r ,µstrong quenching of the luminescence of DPO by oxygen.
According to eq 13, the radius of the Ps bubble is inversely
proportional to the fourth root of the surface tension of thebulk liquid, because the probabilities P(x) are almost constantfor both alkane and aromatic compounds.
The formation of o-PsO 2 (an analog of HO 2 ) compound
would play an important role in rapid quenching of o-Ps lifetime in bulk liquids.5 The direct spin conversion process
o-Ps+O2 → p-Ps+O2* should be impossible, because this reaction needs at least 0.977 eV (O 2 ( 3 Σ g− ) → O 2 ( 1 ∆ g )) which ismuch higher than thermal energy. Since the thermalization
rate of o-Ps is significantly higher than the quenching rate ofo-Ps by oxygen, the epithermal effect is negligible. A resonant
state of o-PsO2 is formed during the collision,(16)

namely,hµ=− 12 16π meσ

(

2

1
4

tanx .
) x(x−tanx)
4(17)

The number of carbon atoms in an IP molecule is assumed as
15 on an average. The physical quantities listed in Table 4
hardly change against the number of carbon atoms because of
the cancellation in the term of nZ eff . The bubble model
contains ambiguity of the choice of Zeff, and we examined Zeffdependence of the physical quantities. The physical quantities
summarized in Table 4 were calculated with Z eff as (a) the
number of valence electrons of the molecule, (b) the number ofall electrons of the molecule and (c) a half of the valence electrons. Case (b) gives the upper limit of Zeff and case (c) is forcomparison. The radius a, energies ε (x) and E(a) of the Ps
bubble are approximately independent of the choice of Zeff,
because the values of a, ε (x) and E(a) change abruptly at
x=π/2 where P(x)=1 and Z eff has the minimum value, andgradualy change elsewhere. On the other hand, the potential
depth U and the penetration length µ strongly depend on the
choice of Zeff.
A positronium can be regarded as a rigid particle in the
bubble, because kinetic energy ε (x) is much smaller than thefirst excited energy of Ps (5.1 eV). Excitation of thesurrounding molecules in the collision with Ps is negligible,
because the Ps is light and its momentum transfer is small. A
radius of the Ps bubble is about four times larger than that ofPs, and close to a size of the surrounding molecules. The
potential of the Ps bubble may be affected by a shape and aconfiguration of molecules. For further investigation of a Ps
bubble the surface tension σ is modified by taking account of
microscopic information on molecules. The penetration depth
is smaller than the size of the surrounding molecule.
Positronium in the Ps bubble can contact only a few molecules
and a surface effect of the potential well is not negligible.
To examine the effects of dissolved gas on the Ps lifetime,
our experimental results were compared with literature
values.14 In Table 5, the values of τ3 are listed together withthe surface tension σ and the density ρ of a variety of organic
liquids. The probability P(x) of finding Ps outside the bubble
is calculated with the relation,

λ3 = λ3γ + πr02cnZeff P(x).

o-Ps+O2 → [o-PsO2]*.

(19)

There are two 2γ-annihilation processes via the o-PsO2 state.
One is the spin conversion process. Because of the strong
spin-spin interaction between the o-Ps and the O2, the o-Ps
would change its spin state changing the orbital angularmomentum of the resonant state.
TABLE 5: o-Ps lifetime τ3 in IP and PC in Comparison withthat in Alkane and Aromatic Compounds 14 Obtained for
Degassed Samples
τ3 /ns σ/dyn cm−1 ρ /g cm−3

(18)

From the literature values the probabilities P(x) are given as
0.150 ± 0.009 for alkane and 0.161 ± 0.004 for aromaticcompounds. The probabilities of both N2-dissolved IP and PC
show the same tendencies as the degassed samples. Therefore,
the use of samples saturated with N2 instead of the degassed
samples is a good approximation. Note that the LS is saturated
with N2 in the practical use for theνe detection to avoid theP(x)Alkanen-Pentane
4.25
n-Hexane
3.92
n-Heptane
3.81
n-Octane
3.49
n-Dodecane
3.43
n-Tetradecane
3.35
Isooctane
4.05
2,2-Dimethylbutane 4.46
average

16.05
18.4
20.14
21.62
25.35
26.56
18.77
16.31

0.62620.66030.68370.69850.74870.76280.69190.6485

0.146
0.151
0.151
0.162
0.155
0.157
0.141
0.135
0.150 ± 0.009

IP(Thiswork)

3.50

23.10

0.787

0.150

Aromatic
BenzeneTolueneEthylbenzene
o-Xylene
m-Xylenep-Xylene
Mesithylene
average

3.15
3.24
3.02
3.08
3.2
3.21
3.21

28.9
28.52
29.29
30.31
29.02
28.54
28

0.87650.86690.867
0.88010.86420.86104
0.8652

0.164
0.158
0.168
0.162
0.159
0.159
0.156
0.161 ± 0.004

PC(Thiswork)

3.03

29.71

0.87580.164

TABLE 4: Physical Quantities of Ps Bubble Calculated with Zeff Adopting (a) the Number of Valence Electrons in the Molecule, (b)the Number of all of Electrons in the Molecule and (c) the Number of half of Valence Electrons in Isoparaffin (IP) and
Pseudocumene (PC)(a) IP

Zeff

x

P(x)

a/nm

E(a)/eVε (x)/eV

U/eV

µ /nm

92

2.35

0.150

0.45

0.89

0.52

1.04

0.096

PC

48

2.32

0.164

0.42

1.00

0.59

1.11

0.096

(b) IP

122

2.43

0.113

0.46

0.91

0.53

1.22

0.083

PC

66

2.41

0.120

0.43

1.03

0.59

1.34

0.080

(c) IP

46

2.14

0.361

0.41

0.82

0.52

0.74

0.149

PC

24

2.10

0.330

0.38

0.93

0.60

0.80

0.151

Positron Annihilation in Liquid Scintillator[o-PsO2]* → [p-PsO2]*' → p-Ps+O2,

J. Nucl. Radiochem. Sci., Vol. 1, No. 2, 2000 67(20)

where [p-PsO2]*' is another resonant state having different
quantum number from [p-PsO2]*. The other is annihilation
with orbital electron in oxygen atoms. Although the resonant
state is a short-lived state, [o-PsO2]* is stabilized in collision
with the surrounding molecule M,[o-PsO2]* + M → [o-PsO2] + M*.

(21)

We have measured Doppler broadening of the 511 keV annihilation γ rays with a pure germanium solid state detector having
a resolution of 0.755 keV (FWHM at 514 keV from 85Sr). The
spin conversion process gives a sharp peak profile, because thep-Ps described in eq 20 is in thermal energy. On the other
hand the pick-off annihilation with orbital electrons gives a
broad peak profile, because orbital electrons have a higher
momentum (∼keV/c). The observed γ ray energy spectra had
the same FWHM (1.25 keV) and FWTM (2.29 keV) for all of
the samples examined here. These results suggest that thequenching of o-Ps by oxygen in the LS may be ascribed to thespin conversion process via o-PsO2 compound, and are consistent with the angular correlation reported in Reference 6.
Figure 3 shows the annihilation rate λ3 and the intensity I3 ina mixture of IP and PC saturated with N2 as a function of the
PC concentration. The value of λ3 has linear dependence on
the PC concentration having a slope of (4.8 ± 0.3) × 10−4 ns−1%−1.
The value of I3 steeply increases to a peak around 20 % of PC
concentration, and gradually decreases with increasing PC
concentration. The Ps intensity depends on the probability offinding excess electrons. This may be explained in terms ofanti-recombination effect (see Reference 15 and the references
cited therein). This effect involves shallow electron traps thatare normally provided by aromatic compounds like PC. In theterminal positron spur the positron competes with the parent
ions (M+) in capturing electrons as,e+ + e− → Ps,(22)

M+ + e− → M*.

(23)

When aromatic compounds like PC are added, the electrons
are scavenged by aromatic compounds. The electron mobility
is suppressed, and hence the recombination of electrons withthe positive ions is delayed in time.
e− + PC → PC−.

(24)

Meanwhile the positron can pick up the shallowly-trappedelectron.
e+ + PC− → Ps + PC.

(25)

In this way PC interrupts recombination process of (23) andeffectively enhances the Ps formation. This effect is called
anti-recombination. It is known that many aromaticcompounds that can provide shallow traps of electrons show
the anti-recombination effect.15 The increase of the Ps intensity is saturated at PC concentration of about 20 %, and gradually decreases at higher concentrations. It is not easy to
explain this gradual decrease in a straightforward way since
many factors, like the number of excess electrons, the spur
size, the electron and positron mobilities and so on, maychange at the wide range of composition of IP and PC.
In conclusion, the measured time structure of positron annihilation in the liquid scintillator for electron antineutrino detection are described as follows. The lifetimes (intensities) of two
fast compornents are 0.19 ± 0.05 ns (30 ± 2 %) and 0.48 ± 0.05
ns (21 ± 2 %) corresponding to the mixture of p-Ps annihilation and free positron annihilation. The lifetime (intensity) of
the delayed component is 3.41 ± 0.02 ns (48.9 ± 0.3 %) foro-Ps annihilation. The lifetime of the third component is close
to the transit time spread (3.6 ns at FWHM) of photomultiplier
which is to be used for KamLAND projects. The measured
reaction rate constant for quenching of o-Ps by oxygen in theliquid scintillator was 29.2 ± 0.3 M−1ns−1. The pick-off annihilation of o-Ps with liquid scintillator is explained based on the
bubble model. The radius and the energies estimated for thePs bubble are approximately independent of the choice of theeffective number of annihilation electrons per molecule Zeff.
Acknowledgments. We thank Professor K. Nagase andDoctor W. Zheng for determination of the gas concentration in
the liquid samples using gas chromatography. We also thankProfessor M. Kikuchi for the use of a gas mixer and an oxygen
analyzer. YK wishes to acknowledge Inoue Foundation for
Science for their generous financial support.
References(1) Y. Fukuda, et al. (Super-Kamiokande Collaboration), Phys.
Rev. Lett. 81, 1562 (1998).
(2) http://www.awa.tohoku.ac.jp/KamLAND/index.html.
This web site contains detailed information and present
status about KamLAND project.

Figure 3. (a) PC concentration dependence of λ3 in a mixture of IP and PC. (b) PC concentration dependence of I3 in a mixture of IP and PC. The
circle stands for experimental values and the lines are a guide for eyes.

68 J. Nucl. Radiochem. Sci., Vol. 1, No. 2, 2000
(3) J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, Phys.
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(6) D. P. Kerr, A. M. Cooper, and B. G. Hogg, Can. J. Phys.
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